structura materialelor_metalurgie fizica

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Van der Waals Bond

The van der Waal bonds occur to some extent in all materials but are particularly important in

plastics and polymers. These materials are made up of a long string molecules consisting of

carbon atoms covalently bonded with other atoms, such as hydrogen, nitrogen, oxygen, fluorine.

The covalent bonds within the molecules are very strong and rupture only under extremeconditions. The bonds between the molecules that allow sliding and rupture to occur are called

van der Waal forces.

When ionic and covalent bonds are present,there is some imbalance in the electrical

charge of the molecule. Take water as an

example. Research has determined thehydrogen atoms are bonded to the oxygen

atoms at an angle of 104.5°. This angle

produces a positive polarity at the hydrogen-

rich end of the molecule and a negative polarity at the other end. A result of this

charge imbalance is that water molecules are

attracted to each other. This is the force thatholds the molecules together in a drop of

water.

This same concept can be carried on to plastics, except that as molecules become

larger, the van der Waal forces between

molecules also increases. For example, in polyethylene the molecules are composed of hydrogen

and carbon atoms in the same ratio as ethylene gas. But there are more of each type of atom inthe polyethylene molecules and as the number of atoms in a molecule increases, the matter

passes from a gas to a liquid and finally to a solid.

Polymers are often classified as being either a thermoplastic or a thermosetting material.

Thermoplastic materials can be easily remelted for forming or recycling and thermosettingmaterial cannot be easily remelted. In thermoplastic materials consist of long chainlike

molecules. Heat can be used to break the van der Waal forces between the molecules and change

the form of the material from a solid to a liquid. By contrast, thermosetting materials have athree-dimensional network of covalent bonds. These bonds cannot be easily broken by heating

and, therefore, can not be remelted and formed as easily as thermoplastics.

Solid State Structure

In the previous pages, some of the mechanisms that bond together the multitude of individual

atoms or molecules of a solid material were discussed. These forces may be primary chemical bonds, as in metals and ionic solids, or they may be secondary van der Waals’ forces of solids,

such as in ice, paraffin wax and most polymers. In solids, the way the atoms or molecules

arrange themselves contributes to the appearance and the properties of the materials.



Atoms can be gathered together as an aggregate through a number of different processes,

including condensation, pressurization, chemical reaction, electrodeposition, and melting. The

process usually determines, at least initially, whether the collection of atoms will take to form of a gas, liquid or solid. The state usually changes as its temperature or pressure is changed.

Melting is the process most often used to form an aggregate of atoms. When the temperature of a

melt is lowered to a certain point, the liquid will form either a crystalline solid or and amorphoussolid.

Amorphous Solids

A solid substance with its atoms held apart at equilibrium spacing, but with no long-range

periodicity in atom location in its structure is an amorphous solid. Examples of amorphous solidsare glass and some types of plastic. They are sometimes described as supercooled liquids

because their molecules are arranged in a random manner some what as in the liquid state. For

example, glass is commonly made from silicon dioxide or quartz sand, which has a crystallinestructure. When the sand is melted and the liquid is cooled rapidly enough to avoid

crystallization, an amorphous solid called a glass is formed. Amorphous solids do not show a

sharp phase change from solid to liquid at a definite melting point, but rather soften graduallywhen they are heated. The physical properties of amorphous solids are identical in all directions

along any axis so they are said to have isotropic properties, which will be discussed in more

detail later

.

Crystalline Solids

More than 90% of naturally occurring and artificially prepared solids are crystalline. Minerals,

sand, clay, limestone, metals, carbon (diamond and graphite), salts ( NaCl, KCl etc.), all have

crystalline structures. A crystal is a regular, repeating arrangement of atoms or molecules. Themajority of solids, including all metals, adopt a crystalline arrangement because the amount of

stabilization achieved by anchoring interactions between neighboring particles is at its greatest



when the particles adopt regular (rather than random) arrangements. In the crystalline

arrangement, the particles pack efficiently together to minimize the total intermolecular energy.

The regular repeating pattern that the atoms arrange in is called the crystalline lattice. Thescanning tunneling microscope (STM) makes it possible to image the electron cloud associated

individual atoms at the surface of a material. Below is an STM image of a platinum surfaceshowing the regular alignment of atoms.

Courtesy: IBM Research, Almaden Research Center.

Crystal Structure

Crystal structures may be conveniently specified by describing the arrangement within the solid

of a small representative group of atoms or molecules, called the ‘unit cell.’ By multiplyingidentical unit cells in three directions, the location of all the particles in the crystal is determined.

In nature, 14 different types of crystal structures or lattices are found. The simplest crystalline

unit cell to picture is the cubic, where the atoms are lined up in a square, 3D grid. The unit cell issimply a box with an atom at each corner. Simple cubic crystals are relatively rare, mostly

because they tend to easily distort. However, many crystals form body-centered-cubic (bcc) or

face-centered-cubic (fcc) structures, which are cubic with either an extra atom centered in thecube or centered in each face of the cube. Most metals form bcc, fcc or Hexagonal Close Packed

(hpc) structures; however, the structure can change depending on temperature. These three

structures will be discussed in more detail on the following page.



Crystalline structure is important because it contributes to the properties of a material. For

example, it is easier for planes of atoms to slide by each other if those planes are closely packed.

Therefore, lattice structures with closely packed planes allow more plastic deformation thanthose that are not closely packed. Additionally, cubic lattice structures allow slippage to occur

more easily than non-cubic lattices. This is because their symmetry provides closely packed

planes in several directions. A face-centered cubic crystal structure will exhibit more ductility(deform more readily under load before breaking) than a body-centered cubic structure. The bcc

lattice, although cubic, is not closely packed and forms strong metals. Alpha-iron and tungsten

have the bcc form. The fcc lattice is both cubic and closely packed and forms more ductilematerials. Gamma-iron, silver, gold, and lead have fcc structures. Finally, HCP lattices are

closely packed, but not cubic. HCP metals like cobalt and zinc are not as ductile as the fcc

metals.

Primary Metallic Crystalline Structures(BCC, FCC, HCP)

As pointed out on the previous page, there are 14 different types of crystalunit cell structures or lattices are found in nature. However most metals and

many other solids have unit cell structures described as body center cubic

(bcc), face centered cubic (fcc) or Hexagonal Close Packed (hcp). Sincethese structures are most common, they will be discussed in more detail.

Body-Centered Cubic (BCC) Structure

The body-centered cubic unit cell has atoms at each of the eight corners of a cube (like the cubic

unit cell) plus one atom in the center of the cube (left image below). Each of the corner atoms isthe corner of another cube so the corner atoms are shared among eight unit cells. It is said to

have a coordination number of 8. The bcc unit cell consists of a net total of two atoms; one in the

center and eight eighths from corners atoms as shown in the middle image below (middle image below). The image below highlights a unit cell in a larger section of the lattice.

The bcc arrangement does not allow the atoms to pack together as closely as the fcc or hcp

arrangements. The bcc structure is often the high temperature form of metals that are close-



packed at lower temperatures. The volume of atoms in a cell per the total volume of a cell is

called the packing factor. The bcc unit cell has a packing factor of 0.68.

Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium, alpha-iron and tungsten. Metals which have a bcc structure are usually harder

and less malleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the bcc structure. It should

be noted that there are other important mechanisms for hardening materials, such as introducingimpurities or defects which make slipping more difficult. These hardening mechanisms will be

discussed latter.

Face Centered Cubic (FCC) Structure

The face centered cubic structure has atoms located at each of the corners and the centers of all

the cubic faces (left image below). Each of the corner atoms is the corner of another cube so the

corner atoms are shared among eight unit cells. Additionally, each of its six face centered atoms

is shared with an adjacent atom. Since 12 of its atoms are shared, it is said to have a coordination

number of 12. The fcc unit cell consists of a net total of four atoms; eight eighths from cornersatoms and six halves of the face atoms as shown in the middle image above. The image below

highlights a unit cell in a larger section of the lattice.

In the fcc structure (and the hcp structure) the atoms can pack closer together than they can in the

bcc structure. The atoms from one layer nest themselves in the empty space between the atoms

of the adjacent layer. To picture packing arrangement, imagine a box filled with a layer of ballsthat are aligned in columns and rows. When a few additional balls are tossed in the box, they will

not balance directly on top of the balls in the first layer but instead will come to rest in the pocketcreated between four balls of the bottom layer. As more balls are added they will pack together

to fill up all the pockets. The packing factor (the volume of atoms in a cell per the total volumeof a cell) is 0.74 for fcc crystals. Some of the metals that have the fcc structure include

aluminum, copper, gold, iridium, lead, nickel, platinum and silver.

Hexagonal Close Packed (HPC) Structure

Another common close packed structure is the hexagonal close pack. The hexagonal structure of



alternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms

from one layer nest themselves in the empty space between the atoms of the adjacent layer just

like in the fcc structure. However, instead of being a cubic structure, the pattern is hexagonal.(See image below.) The difference between the HPC and FCC structure is discussed later in this

section.

The hcp structure has three layers of atoms. In each the top and bottom layer, there are six atoms

that arrange themselves in the shape of a hexagon and a seventh atom that sits in the middle of

the hexagon. The middle layer has three atoms nestle in the triangular "grooves" of the top and bottom plane. Note that there are six of these "grooves" surrounding each atom in the hexagonal

plane, but only three of them can be filled by atoms.

As shown in the middle image above, there are six atoms in the hcp unit cell. Each of the 12

atoms in the corners of the top and bottom layers contribute 1/6 atom to the unit cell, the twoatoms in the center of the hexagon of both the top and bottom layers each contribute ½ atom and

each of the three atom in the middle layer contribute 1 atom. The image on the right above

attempts to show several hcp unit cells in a larger lattice.

The coordination number of the atoms in this structure is 12. There are six nearest neighbors inthe same close packed layer, three in the layer above and three in the layer below. The packing

factor is 0.74, which is the same as the fcc unit cell. The hcp structure is very common for

elemental metals and some examples include beryllium, cadmium, magnesium, titanium, zincand zirconium.

Similarities and Difference Between theFCC and HCP Structure

The face centered cubic and hexagonal close packed structures both have a packing factor of

0.74, consist of closely packed planes of atoms, and have a coordination number of 12. Thedifference between the fcc and hcp is the stacking sequence. The hcp layers cycle among the two

equivalent shifted positions whereas the fcc layers cycle between three positions. As can be seen

in the image, the hcp structure contains only two types of planes with an alternating ABAB



arrangement. Notice how the atoms of the third plane are in exactly the same position as the

atoms in the first plane. However, the fcc structure contains three types of planes with a

ABCABC arrangement. Notice how the atoms in rows A and C are no longer aligned.Remember that cubic lattice structures allow slippage to occur more easily than non-cubic

lattices, so hcp metals are not as ductile as the fcc metals.

The table below shows the stable room temperature crystal structures for several elemental

metals.

Metal Crystal Structure Atomic Radius (nm)Aluminum FCC 0.1431

Cadmium HCP 0.1490

Chromium BCC 0.1249

Cobalt HCP 0.1253

Copper FCC 0.1278

Gold FCC 0.1442

Iron (Alpha) BCC 0.1241

Lead FCC 0.1750

Magnesium HCP 0.1599Molybdenum BCC 0.1363

Nickel FCC 0.1246

Platinum FCC 0.1387

Silver FCC 0.1445

Tantalum BCC 0.1430



Titanium (Alpha) HCP 0.1445

Tungsten BCC 0.1371

Zinc HCP 0.1332

A nanometer (nm) equals 10

-9

meter or 10 Angstrom units.

Solidification

The crystallization of a large amount of material from a single point of nucleation results in a

single crystal. In engineering materials, single crystals are produced only under carefully

controlled conditions. The expense of producing single crystal materials is only justified for special applications, such as turbine engine blades, solar cells, and piezoelectric materials.

Normally when a material begins to solidify, multiple crystals begin to grow in the liquid and a

polycrystalline (more than one crystal) solid forms.

The moment a crystal begins to grow is know as nucleation and the point where it occurs is thenucleation point. At the solidification temperature, atoms of a liquid, such as melted metal, begin

to bond together at the nucleation points and start to form crystals. The final sizes of the

individual crystals depend on the number of nucleation points. The crystals increase in size bythe progressive addition of atoms and grow until they impinge upon adjacent growing crystal.

a) Nucleation of crystals, b) crystal growth, c) irregular grains form as crystals grow together,d) grain boundaries as seen in a microscope.



In engineering materials, a crystal is usually referred to as a grain. A grain is merely a crystal

without smooth faces because its growth was impeded by contact with another grain or a

boundary surface. The interface formed between grains is called a grain boundary. The atoms between the grains (at the grain boundaries) have no crystalline structure and are said to be

disordered.

Grains are sometimes large enough to be visible under an ordinary light microscope or even to

the unaided eye. The spangles that are seen on newly galvanized metals are grains. Rapid coolinggenerally results in more nucleation points and smaller grains (a fine grain structure). Slow

cooling generally results in larger grains which will have lower strength, hardness and ductility.

Dendrites

In metals, the crystals that form in the liquid during

freezing generally follow a pattern consisting of a main

branch with many appendages. A crystal with this

morphology slightly resembles a pine tree and is called a

dendrite, which means branching. The formation of dendrites occurs because crystals grow in defined planes

due to the crystal lattice they create. The figure to the rightshows how a cubic crystal can grow in a melt in three

dimensions, which correspond to the six faces of the cube.

For clarity of illustration, the adding of unit cells withcontinued solidification from the six faces is shown simply

as lines. Secondary dendrite arms branch off the primary

arm, and tertiary arms off the secondary arms and etcetera.

During freezing of a polycrystalline material, many

dendritic crystals form and grow until they eventually become large enough to impinge upon each other.

Eventually, the interdendriticspaces between thedendrite arms crystallize to yield a more regular

crystal. The original dendritic pattern may not be apparent

when examining the microstructure of a material.

However, dendrites can often be seen in solidificationvoids that sometimes occur in castings or welds, as shown

to the right..

Shrinkage

Most materials contract or shrink duringsolidification and cooling. Shrinkage is the result of:

• Contraction of the liquid as it cools prior to its

solidification

• Contraction during phase change from a liquid to solid

• Contraction of the solid as it continues to cool to ambient temperature.



Shrinkage can sometimes cause cracking to occur in component as it solidifies. Since the coolest

area of a volume of liquid is where it contacts a mold or die, solidification usually begins first at

this surface. As the crystals grow inward, the material continues to shrink. If the solid surface istoo rigid and will not deform to accommodate the internal shrinkage, the stresses can become

high enough to exceed the tensile strength of the material and cause a crack to form. Shrinkage

cavitation sometimes occurs because as a material solidifies inward, shrinkage occurred to suchan extent that there is not enough atoms present to fill the available space and a void is left.

Anisotropy and Isotropy

In a single crystal, the physical and mechanical properties often differ with orientation. It can be

seen from looking at our models of crystalline structure that atoms should be able to slip over

one another or distort in relation to one another easier in some directions than others. When the properties of a material vary with different crystallographic orientations, the material is said to be

anisotropic.

Alternately, when the properties of a material are the same in all directions, the material is said to be isotropic. For many polycrystalline materials the grain orientations are random before anyworking (deformation) of the material is done. Therefore, even if the individual grains are

anisotropic, the property differences tend to average out and, overall, the material is isotropic.

When a material is formed, the grains are usually distorted and elongated in one or moredirections which makes the material anisotropic. Material forming will be discussed later but

let’s continue discussing crystalline structure at the atomic level.

Crystal Defects

A perfect crystal, with every atom of the same type in the correct position, does not exist. All

crystals have some defects. Defects contribute to the mechanical properties of metals. In fact,using the term “defect” is sort of a misnomer since these features are commonly intentionally

used to manipulate the mechanical properties of a material. Adding alloying elements to a metal

is one way of introducing a crystal defect. Nevertheless, the term “defect” will be used, just keepin mind that crystalline defects are not always bad. There are basic classes of crystal defects:

• point defects, which are places where an atom is missing or irregularly placed in the

lattice structure. Point defects include lattice vacancies, self-interstitial atoms,

substitution impurity atoms, and interstitial impurity atoms

• linear defects, which are groups of atoms in irregular positions. Linear defects are

commonly called dislocations.

• planar defects, which are interfaces between homogeneous regions of the material. Planar

defects include grain boundaries, stacking faults and external surfaces.

It is important to note at this point that plastic deformation in a material occurs due to the

movement of dislocations (linear defects). Millions of dislocations result for plastic forming

operations such as rolling and extruding. It is also important to note that any defect in the regular lattice structure disrupts the motion of dislocation, which makes slip or plastic deformation more



difficult. These defects not only include the point and planer defects mentioned above, and also

other dislocations. Dislocation movement produces additional dislocations, and when

dislocations run into each other it often impedes movement of the dislocations. This drives up theforce needed to move the dislocation or, in other words, strengthens the material. Each of the

crystal defects will be discussed in more detail in the following pages.

Point Defects

Point defects are where an atom is missing or is in an

irregular place in the lattice structure. Point defectsinclude self interstitial atoms, interstitial impurity

atoms, substitutional atoms and vacancies. A self

interstitial atom is an extra atom that has crowded itsway into an interstitial void in the crystal structure.

Self interstitial atoms occur only in low

concentrations in metals because they distort and

highly stress the tightly packed lattice structure.

A substitutional impurity atom is an atom of a

different type than the bulk atoms, which has

replaced one of the bulk atoms in the lattice.Substitutional impurity atoms are usually close in

size (within approximately 15%) to the bulk atom.

An example of substitutional impurity atoms is thezinc atoms in brass. In brass, zinc atoms with a radius

of 0.133 nm have replaced some of the copper atoms,

which have a radius of 0.128 nm.

Interstitial impurity atoms are much smaller than the

atoms in the bulk matrix. Interstitial impurity atoms fit into the open space between the bulk

atoms of the lattice structure. An example of interstitial impurity atoms is the carbon atoms thatare added to iron to make steel. Carbon atoms, with a radius of 0.071 nm, fit nicely in the open

spaces between the larger (0.124 nm) iron atoms.

Vacancies are empty spaces where an atom should be, but is missing. They are common,

especially at high temperatures when atoms are frequently and randomly change their positionsleaving behind empty lattice sites. In most cases diffusion (mass transport by atomic motion) can

only occur because of vacancies.

Linear Defects - Dislocations

Dislocations are another type of defect in crystals. Dislocations are areas were the atoms are out

of position in the crystal structure. Dislocations are generated and move when a stress is applied.The motion of dislocations allows slip – plastic deformation to occur.



Before the discovery of the dislocation by Taylor, Orowan and Polyani in 1934, no one could

figure out how the plastic deformation properties of a metal could be greatly changed by solely

by forming (without changing the chemical composition). This became even bigger mysterywhen in the early 1900’s scientists estimated that metals undergo plastic deformation at forces

much smaller than the theoretical strength of the forces that are holding the metal atoms together.

Many metallurgists remained skeptical of the dislocation theory until the development of thetransmission electron microscope in the late 1950’s. The TEM allowed experimental evidence to

be collected that showed that the strength and ductility of metals are controlled by dislocations.

There are two basic types of dislocations, the edge dislocation and the screw dislocation.

Actually, edge and screw dislocations are just extreme forms of the possible dislocation

structures that can occur. Most dislocations are probably a hybrid of the edge and screw forms

but this discussion will be limited to these two types.

Edge Dislocations

The edge defect can be easily visualized as an extra half-plane of atoms in a lattice. The

dislocation is called a line defect because the locus of defective points produced in the lattice bythe dislocation lie along a line. This line runs along the top of the extra half-plane. The inter-

atomic bonds are significantly distorted only in the immediate vicinity of the dislocation line.

Understanding the movement of a dislocation is key to understanding why dislocations allow

deformation to occur at much lower stress than in a perfect crystal. Dislocation motion is

analogous to movement of a caterpillar. The caterpillar would have to exert a large force to moveits entire body at once. Instead it moves the rear portion of its body forward a small amount and



creates a hump. The hump then moves forward and eventual moves all of the body forward by a

small amount.

As shown in the set of images above, the dislocation moves similarly moves a small amount at a

time. The dislocation in the top half of the crystal is slipping one plane at a time as it moves tothe right from its position in image (a) to its position in image (b) and finally image (c). In the

process of slipping one plane at a time the dislocation propagates across the crystal. Themovement of the dislocation across the plane eventually causes the top half of the crystal to

move with respect to the bottom half. However, only a small fraction of the bonds are broken at

any given time. Movement in this manner requires a much smaller force than breaking all the bonds across the middle plane simultaneously.

Screw Dislocations

There is a second basic type of dislocation,

called screw dislocation. The screw dislocation is

slightly more difficult to visualize. The motionof a screw dislocation is also a result of shear

stress, but the defect line movement is perpendicular to direction of the stress and the

atom displacement, rather than parallel. To

visualize a screw dislocation, imagine a block of metal with a shear stress applied across one end

so that the metal begins to rip. This is shown in

the upper right image. The lower right image

shows the plane of atoms just above the rip. Theatoms represented by the blue circles have not

yet moved from their original position. Theatoms represented by the red circles have movedto their new position in the lattice and have

reestablished metallic bonds. The atoms

represented by the green circles are in the process of moving. It can be seen that only a

portion of the bonds are broke at any given time.

As was the case with the edge dislocation,



movement in this manner requires a much smaller force than breaking all the bonds across the

middle plane simultaneously.

If the shear force is increased, the atoms will continue to slip to the right. A row of the greenatoms will find there way back into a proper spot in the lattice (and become red) and a row of the

blue atoms will slip out of position (and become green). In this way, the screw dislocation willmove upward in the image, which is perpendicular to direction of the stress. Recall that the edge

dislocation moves parallel to the direction of stress. As shown in the image below, the net plasticdeformation of both edge and screw dislocations is the same, however.

The dislocations move along the densest planes of atoms in a material, because the stress needed

to move the dislocation increases with the spacing between the planes. FCC and BCC metals

have many dense planes, so dislocations move relatively easy and these materials have highductility. Metals are strengthened by making it more difficult for dislocations to move. This may

involve the introduction of obstacles, such as interstitial atoms or grain boundaries, to “pin” the

dislocations. Also, as a material plastically deforms, more dislocations are produced and theywill get into each others way and impede movement. This is why strain or work hardening

occurs.

In ionically bonded materials, the ion must move past an area with a repulsive charge in order toget to the next location of the same charge. Therefore, slip is difficult and the materials are brittle. Likewise, the low density packing of covalent materials makes them generally more

brittle than metals.

Planar Defects



Stacking Faults and Twin Boundaries

A disruption of the long-range stacking sequence can produce two other common types of crystal

defects: 1) a stacking fault and 2) a twin region. A change in the stacking sequence over a fewatomic spacings produces a stacking fault whereas a change over many atomic spacings produces

a twin region.

A stacking fault is a one or two layer interruption in the stacking sequence of atom planes.

Stacking faults occur in a number of crystal structures, but it is easiest to see how they occur in

close packed structures. For example, it is know from a previous discussion that face centeredcubic (fcc) structures differ from hexagonal close packed (hcp) structures only in their stacking

order. For hcp and fcc structures, the first two layers arrange themselves identically, and are said

to have an AB arrangement. If the third layer is placed so that its atoms are directly above those

of the first (A) layer, the stacking will be ABA. This is the hcp structure, and it continuesABABABAB. However it is possible for the third layer atoms to arrange themselves so that they

are in line with the first layer to produce an ABC arrangement which is that of the fcc structure.

So, if the hcp structure is going along as ABABAB and suddenly switches to ABABABCABAB,

there is a stacking fault present.

Alternately, in the fcc arrangement the pattern is ABCABCABC. A stacking fault in an fcc

structure would appear as one of the C planes missing. In other words the pattern would become

ABCABCAB_ABCABC.

If a stacking fault does not corrects itself immediately but continues over some number of atomic

spacings, it will produce a second stacking fault that is the twin of the first one. For example if

the stacking pattern is ABABABAB but switches to ABCABCABC for a period of time before

switching back to ABABABAB, a pair of twin stacking faults is produced. The red region in thestacking sequence that goes ABCABCACBACBABCABC is the twin plane and the twin

boundaries are the A planes on each end of the highlighted region.

Grain Boundaries in Polycrystals

Another type of planer defect is the grain boundary. Up to this point, the discussion has focused

on defects of single crystals. However, solids generally consist of a number of crystallites or

grains. Grains can range in size from nanometers to millimeters across and their orientations are

usually rotated with respect to neighboring grains. Where one grain stops and another begins isknow as a grain boundary. Grain boundaries limit the lengths and motions of dislocations.

Therefore, having smaller grains (more grain boundary surface area) strengthens a material. The

size of the grains can be controlled by the cooling rate when the material cast or heat treated.Generally, rapid cooling produces smaller grains whereas slow cooling result in larger grains.

For more information, refer to the discussion on solidification.

Bulk Defects

Bulk defects occur on a much bigger scale than the rest of the

crystal defects discussed in this section. However, for the sakeof completeness and since they do affect the movement of

dislocations, a few of the more common bulk defects will be



mentioned. Voids are regions where there are a large number of atoms missing from the lattice.

The image to the right is a void in a piece of metal The image was acquired using a Scanning

Electron Microscope (SEM). Voids can occur for a number of reasons. When voids occur due toair bubbles becoming trapped when a material solidifies, it is commonly called porosity. When a

void occurs due to the shrinkage of a material as it solidifies, it is called cavitation.

Another type of bulk defect occurs when impurity atoms cluster together to form small regions

of a different phase. The term ‘phase’ refers to that region of space occupied by a physicallyhomogeneous material. These regions are often called precipitates. Phases and precipitates will

be discussed in more detail latter.

Elastic/Plastic Deformation

When a sufficient load is applied to a metal or other structural material, it will cause the material

to change shape. This change in shape is called deformation. A temporary shape change that isself-reversing after the force is removed, so that the object returns to its original shape, is called

elastic deformation. In other words, elastic deformation is a change in shape of a material at lowstress that is recoverable after the stress is removed. This type of deformation involves stretchingof the bonds, but the atoms do not slip past each other.

When the stress is sufficient to permanently

deform the metal, it is called plastic

deformation. As discussed in the section oncrystal defects, plastic deformation

involves the breaking of a limited number

of atomic bonds by the movement of dislocations. Recall that the force needed to

break the bonds of all the atoms in a crystal plane all at once is very great. However, themovement of dislocations allows atoms in

crystal planes to slip past one another at a

much lower stress levels. Since the energy

required to move is lowest along thedensest planes of atoms, dislocations have a

preferred direction of travel within a grain

of the material. This results in slip thatoccurs along parallel planes within the

grain. These parallel slip planes group

together to form slip bands, which can beseen with an optical microscope. A slip

band appears as a single line under the

microscope, but it is in fact made up of closely spaced parallel slip planes as shown

in the image.

Fatigue Crack Initiation



While on the subject of dislocations, it is appropriate to briefly

discuss fatigue. Fatigue is one of the primary reasons for the

failure of structural components. The life of a fatigue crack hastwo parts, initiation and propagation. Dislocations play a major

role in the fatigue crack initiation phase. It has been observed

in laboratory testing that after a large number of loading cyclesdislocations pile up and form structures called persistent slip

bands (PSB). An example of a PSB is shown in the micrograph

image to the right.

PSBs are areas that riseabove (extrusion) or fall below (intrusion) the surface of

the component due to movement of material along slip

planes. This leaves tiny steps in the surface that serve asstress risers where fatigue cracks can initiate. A crack at the

edge of a PSB is shown in the image below taken with a

scanning electron microscope (SEM).



Diffusion

Diffusion is the migration of atoms from a region of high concentration to

a region of low concentration. In a homogeneous material, atoms are

routinely moving around but the movement is random (i.e. there is always

an equal number of atoms moving in all directions). In an inhomogeneousmaterial, all the atoms are moving near randomly, but there is a migration

of atoms to areas where their concentrations are lower. In other words,there is a net diffusion.

Atom diffusion can occur by the motion of host or substitutional atoms to

vacancies (vacancy diffusion), or interstitial impurities atoms to different

interstitial positions (interstitial diffusion). In order to move, an atommust overcome the bond energy due to nearby atoms. This is more easily

achieved at high temperatures when the atoms are vibrating strongly.

Carburizing, which will be discussed later, is an example of diffusion is

used.

Property Modification

Many structural metals undergo some special treatment to modify their properties so that they

will perform better for their intended use. This treatment can include mechanical working, such

as rolling or forging, alloying and/or thermal treatments. Consider aluminum as an example.Commercially pure aluminum (1100) has a tensile strength of around 13,000 psi, which limits its

usefulness in structural applications. However, by cold-working aluminum, its strength can be

approximately doubled. Also, strength increases are obtained by adding alloying metals such asmanganese, silicon, copper, magnesium and zinc. Further, many aluminum alloys are

strengthened by heat treatment. Some heat-treatable aluminum alloys obtain tensile strengths thatcan exceed 100,000 psi.

Strengthening/Hardening Mechanisms

As discussed in the previous section, the ability of a crystalline material to plastically deformlargely depends on the ability for dislocation to move within a material. Therefore, impeding the

movement of dislocations will result in the strengthening of the material. There are a number of

ways to impede dislocation movement, which include:

• controlling the grain size (reducing continuity of atomic planes)

• strain hardening (creating and tangling dislocations)

• alloying (introducing point defects and more grains to pin dislocation)

Control of Grain Size

The size of the grains within a material also has an effect

on the strength of the material. The boundary between

grains acts as a barrier to dislocation movement and the



resulting slip because adjacent grains have different orientations. Since the atom alignment is

different and slip planes are discontinuous between grains. The smaller the grains, the shorter the

distance atoms can move along a particular slip plane. Therefore, smaller grains improve thestrength of a material. The size and number of grains within a material is controlled by the rate of

solidification from the liquid phase.

Strain Hardening

Strain hardening (also called work-hardening or cold-working) is the process of making a metalharder and stronger through plastic deformation. When a metal is plastically deformed,

dislocations move and additional dislocations are generated. The more dislocations within a

material, the more they will interact and become pinned or tangled. This will result in a decreasein the mobility of the dislocations and a strengthening of the material. This type of strengthening

is commonly called cold-working. It is called cold-working because the plastic deformation must

occurs at a temperature low enough that atoms cannot rearrange themselves. When a metal isworked at higher temperatures (hot-working) the dislocations can rearrange and little

strengthening is achieved.

Strain hardening can be easily demonstrated with piece of wire or a paper clip. Bend a straight

section back and forth several times. Notice that it is more difficult to bend the metal at the same place. In the strain hardened area dislocations have formed and become tangled, increasing the

strength of the material. Continued bending will eventually cause the wire to break at the bend

due to fatigue cracking. (After a large number of bending cycles, dislocations form structurescalled Persistent Slip Bands (PSB). PSBs are basically tiny areas where the dislocations have

piled up and moved the material surface out leave steps in the surface that act as stress risers or

crack initiation points.)

It should be understood, however, that increasing the

strength by cold-working will also result in a reduction inductility. The graph to the right shows the yield strengthand the percent elongation as a function of percent cold-

work for a few example materials. Notice that for each

material, a small amount of cold-working results in asignificant reduction in ductility.

Effects of Elevated Temperature on Strain Hardened

Materials

When strain hardened materials are exposed to elevatedtemperatures, the strengthening that resulted from the plastic deformation can be lost. This can

be a bad thing if the strengthening is needed to support a load. However, strengthening due to

strain hardening is not always desirable, especially if the material is being heavily formed sinceductility will be lowered.

Heat treatment can be used to remove the effects of strain hardening. Three things can occur

during heat treatment:



1. Recovery

2. Recrystallization

3. Grain growth

Recovery

When a stain hardened material is held at

an elevated temperature an increase inatomic diffusion occurs that relieves

some of the internal strain energy.

Remember that atoms are not fixed in position but can move around when they

have enough energy to break their bonds.

Diffusion increases rapidly with risingtemperature and this allows atoms in

severely strained regions to move to

unstrained positions. In other words,atoms are freer to move around and

recover a normal position in the lattice

structure. This is known as the recovery

phase and it results in an adjustment of strain on a microscopic scale. Internal residual stressesare lowered due to a reduction in the dislocation density and a movement of dislocation to lower-

energy positions. The tangles of dislocations condense into sharp two-dimensional boundaries

and the dislocation density within these areas decrease. These areas are called subgrains. There isno appreciable reduction in the strength and hardness of the material but corrosion resistance

often improves.

Recrystallization

At a higher temperature, new, strain-free grains nucleate and grow inside the old distorted grainsand at the grain boundaries. These new grains grow to replace the deformed grains produced by

the strain hardening. With recrystallization, the mechanical properties return to their originalweaker and more ductile states. Recrystallization depends on the temperature, the amount of time

at this temperature and also the amount of strain hardening that the material experienced. The

more strain hardening, the lower the temperature will be at which recrystallization occurs. Also,a minimum amount (typically 2-20%) of cold work is necessary for any amount of

recrystallization to occur. The size the new grains is also partially dependant on the amount of

strain hardening. The greater the stain hardening, the more nuclei for the new grains, and theresulting grain size will be smaller (at least initially).

Grain GrowthIf a specimen is left at the high temperature beyond the time needed for complete

recrystallization, the grains begin to grow in size. This occurs because diffusion occurs across the

grain boundaries and larger grains have less grain boundary surface area per unit of volume.

Therefore, the larger grains lose fewer atoms and grow at the expense of the smaller grains.Larger grains will reduce the strength and toughness of the material.



Alloying

Only a few elements are widely used commercially in their pure form. Generally, other elements

are present to produce greater strength, to improve corrosion resistance, or simply as impurities

left over from the refining process. The addition of other elements into a metal is called alloying

and the resulting metal is called an alloy. Even if the added elements are nonmetals, alloys maystill have metallic properties.

Copper alloys were produced very early in our history. Bronze, an alloy of copper and tin, was

the first alloy known. It was easy to produce by simply adding tin to molten copper. Tools andweapons made of this alloy were stronger than pure copper ones. The typical alloying elements

in some common metals are presented in the table below.

Alloy Composition

Brass Copper, Zinc

Bronze Copper, Zinc, TinPewter Tin, Copper, Bismuth, Antimony

Cast Iron Iron, Carbon, Manganese, Silicon

Steel Iron, Carbon (plus small amounts of other elements)

Stainless Steel Iron, Chromium, Nickel

The properties of alloys can be manipulated by varying composition. For example steel formed

from iron and carbon can vary substantially in hardness depending on the amount of carbon

added and the way in which it was processed.

When a second element is added, two basically different structural changes are possible:

1. Solid solution strengthening occurs when the atoms of the new element form a solidsolution with the original element, but there is still only one phase. Recall that the term

‘phase’ refers to that region of space occupied by a physically homogeneous material.

2. The atoms of the new elements form a new second phase. The entire microstructure maychange to this new phase or two phases may be present.

Solid Solution Strengthening

Solid solution strengthening involves the addition of other metallic elements that will dissolve in

the parent lattice and cause distortions because of the difference in atom size between the parent

metal and the solute metal. Recall from the section on crystal point defects that it is possible tohave substitutional impurity atoms, and interstitial impurity atoms. A substitutional impurity

atom is an atom of a different type than the bulk atoms, which has replaced one of the bulk atomsin the lattice. Substitutional impurity atoms are usually close in size (within approximately 15%)

to the bulk atom. Interstitial impurity atoms are much smaller than the atoms in the bulk matrix.

Interstitial impurity atoms fit into the open space between the bulk atoms of the lattice structure.



Since the impurity atoms are smaller or larger than the surrounding atoms they introduce tensile

or compressive lattice strains. They disrupt the regular arrangement of ions and make it more

difficult for the layers to slide over each other. This makes the alloy stronger and less ductilethan the pure metal. For example, an alloy of 30% nickel raises the cast tensile strength of copper

from 25,000 PSI to 55,000 PSI.

Multiphase Metals

Still another method of strengthening the metal is adding elements that have no or partialsolubility in the parent metal. This will result in the appearance of a second phase distributed

throughout the crystal or between crystals. These secondary phases can raise or reduce the

strength of an alloy. For example, the addition of tin, zinc, or aluminum to copper will result inan alloy with increased strength, but alloying with lead or bismuth with result in a lower strength

alloy. The properties of a polyphase (two of more phase) material depend on the nature, amount,

size, shape, distribution, and orientation of the phases. Greek letters are commonly used todistinguish the different solid phases in a given alloy.

Phases can be seen on a microscopic scale with an optical microscope after the surface has been properly polished and etched. Below is a micrograph take at 125x of lead-tin alloy composed of

two phases. The light colored regions are a tin-rich phase and the dark colored regions are a lead-

rich phase.

Alloying (continued)

Phase Diagrams

As previously stated, the phase diagram is simply a map showing the structure of phases present

as the temperature and overall composition of the alloy are varied. It is a very useful tool for

understanding and controlling the structures of polyphase materials. A binary phase diagram

shows the phases formed in differing mixtures of two elements over a range of temperatures.When an alloy exhibits more than two phases, a different type of phase diagram must be used,



such as a ternary diagram for three phase alloys. This discussion will focus on the binary phase

diagram.

On the binary phase diagram, compositions runfrom 100% Element A on the left, through all

possible mixtures, to 100% Element B on theright. The composition of an alloy is given in the

form A - x%B. For example, Cu - 20%Al is 80%copper and 20% aluminum. Weight percentages

are often used to specify the proportions of the

alloying elements, but atomic percent aresometimes used. Weight percentages will be used

throughout this text.

Alloys generally do not have a single melting

point, but instead melt (or alternately solidify)

over a range of temperatures. At each end of the phase diagram only one of the elements is

present (100% A or 100% B) so a specificmelting point does exists. Additionally, there

is sometimes a mixture of the constituent

elements which produces melting at a singletemperature like a pure element. This is called

the eutectic point.

At compositions other than at the pure A, pure B

and the eutectic points, when the alloy is cooled

from a high temperature it will begin to solidify ata certain temperature but will remain in a mushy

(liquid plus solid) condition over a range of temperatures. If experiments are conducted over a

range of compositions to determine the

temperature at which the alloys start to solidify,

this data can be potted on the phase diagram to produce a curve. This “start of solidification

curve” will join the three single solidification

points and is called the liquidus line.

Up to a few percent of composition, it is possiblefor one element to remain dissolve in another

while both are in the solid state. This is called

solid solubility and the solubility limit normallychanges with temperature. The extent of the solid

solubility region can be plotted onto the phase

diagram. In this example, the alpha phase is theregion of solid solution where some of B atoms



have dissolved in a matrix of A atoms. The beta phase is the region where a small percentage of

A atoms have dissolved in a matrix of B atoms. It is important to note that some elements have

zero solid solubility in other elements. An example is aluminum/silicon alloys, where aluminumhas zero solid solubility in silicon.

If an alloy's composition does not place it withinthe alpha or beta solid solution regions, the alloy

will become fully solid at the eutectic

temperature. The eutectic line on the phase

diagram indicates where this transformation will

occur over the range of compositions. At alloycompositions and temperatures between the

liquidus temperature and the eutectic temperature,

a mushy mix of either alpha or beta phase willexist as solid masses within a liquid mixture of A

and B. These are the alpha plus liquid and the beta

plus liquid areas on the phase diagram. The region below the eutectic line, and outside the solidsolution region, will be a solid mixture of alpha and beta.

lloying (continued)

Tie and Lever Rules

Simply by looking at a phase diagram it is possible to tell what phase or phases an alloy will

have at a given temperature. But, it is also possible to get quantitative information from thediagram. Consider the alloy at the temperature shown on the phase diagram. It is easy to see that

at this temperature, it is a mixture of alpha and

liquid phases. Using a tie line it is also possible to

determine the composition of the phases at thistemperature. A tie line is an isothermal (constant

temperature) line drawn through the alloy's

position on the phase diagram when it is in a two phase field. The points where the ends of the tie

line intersect the two adjacent solubility curves

indicate the compositions of the two phases thatexist in equilibrium at this temperature. In this

example, the tie line shows that the alpha phase is

5.2%B and the liquid phase is 34.5%B at this temperature. It is important to keep in mind that

the tie rule addresses the determination of the compositions of the constituent phases within the

sample and it does not address the overall chemical composition of the sample, which remainsunchanged.

It is also possible to determine how much of each phase exists at the given temperature using thelever rule. It is important to know the amounts of each phase present because the properties of

the alloy depend on the amount of each phase present. The lever rule uses the tie line and the

basic scientific principle of the conservation of mass to determine the ratio of the two phases

present. The tie-line gives the chemical compositions of each of the two phases, and the



combined amounts of these two compositions must add up to the alloy's overall composition

(Co), which is known. In other words, Co must be composed of the appropriate amount of α at

composition Cα and of liquid at Cliq. So basically, the proportions of the phases present are given by the relative lengths of the two sections of the tie line.

The fraction of alpha phase present is the given by the ratio of the Co to Cliq portion of the tie lineand the total length of the tie line (C liq to Cα). Mathematically the relationships can be written as

f α << (Cliq – Co)/(Cliq - Cα). The fraction of liquid phase present is given by the ratio of the C o toCα portion of the tie line and the total length of the tie line (Cliq to Cα). Mathematically this

relationships can be written as f liq << (Co - Cα)/(Cliq - Cα). Of course, the two values must total to

equal one.

Note that the right side of the tie line gives the proportion of the phase on the left (α phase in this

example) and left side of the tie line gives the proportion of the phase to the right (liquid phase in

this example). It is easy to keep this relationship straight by simply considering what the ratio

would be near one of the tie line intersect points. For example, if Co were near the liquidus line

the ratio of the liquid section of the line to the total length of the line will be nearly one.

Alloying (continued)

Composition, Microstructure, and the Phase Diagram

Let’s finish this discussion on phase diagrams by briefly looking at three different compositions

of elements A and B, and how their microstructures will differ because of their positions on the phase diagram. First a eutectic alloy, which is an alloy with composition right at the eutectic

point, will be considered. Then compositions on both sides of the eutectic point will be

discussed. An alloy with a composition that lies to the left of the eutectic point on the phasediagram is called a hypoeutectic alloy, and an alloy with a composition that lies to the right of

the eutectic point is called hypereutectic alloy. At this point, only the condition of slow cooling,which will allow the alloy to solidify into it equilibrium condition, will be considered. Themicrostructure can be controlled by manipulating the speed of cooling the alloy, but this will be

covered in the section on heat treatments.

Eutectic Alloys

First, consider the eutectic alloy of elements Aand B as it is cooled from a temperature at

location 1 to location 4 on the phase diagram. At

location 1, the alloy is at a high enoughtemperature to make the mixture fully liquid. The

circles below show a representation of the alloy'smicrostructure at each of the locations numbered

on the phase diagram.

At location 1, there is nothing of interest as the

alloy is completely liquid. As the alloy is slow

cooled, it remains liquid until it reaches the eutectic temperature (location 2) where it starts to

solidify at any favorable nucleation sites. From the microstructure image 2, it can be see that as



the alloy solidifies it forms into alternate layers of alpha and beta phase. This layered

microstructure is known as lamellar microstructure and the layers are often only of the order of 1

micron across. The reason that a eutectic alloy forms in this way has to do with the diffusiontimes required to form the solid.

The grains grow by adding alpha to alpha and beta to beta until they encounter another grain(location 3). Further nucleation sites will also continue to form within the liquid parts of the

mixture. This solidification happens very rapidly as any given volume of liquid in the melt

reaches the eutectic temperature. Remember that a eutectic composition solidifies at a singletemperature like a pure element and not over a temperature range.

As the now sold alloy cools to location 4, the composition of the layers of alpha and beta

continue to change as it cools. Atoms of A and B will diffuse between the two phases to produce

the equilibrium compositions of alpha and beta phase at a given temperature. By drawing tielines at various temperatures the eutectic point on the phase diagram, it can be seen that the

solubility of A in the beta phase and B in the alpha phase decreases as the temperature decreases.

Since this phase composition change is due to diffusion, which is a relatively a slow process), itis important that eutectic alloys be allowed to cool slowly to produce the correct microstructure.

Hypoeutectic Alloys

Next, consider an alloy of A and B that has an

overall composition that places it to the left of theeutectic point. When an alloy falls to the left of

the eutectic point it is called a hypoeutectic alloy.

At location 1, the alloy is at a temperature that ishigh enough to put it in a fully liquid phase.

When the alloy is cooled, it remains in the liquid

state until it reaches the temperature where it

crosses the liquidus line (location 2). At thistemperature, the alpha phase starts to solidify at

any favorable nucleation sites. The alpha solidifies as dendrites which grow to become grains of

alpha. The first solid phase to form is called the primary phase so, in this case, primary alpha isformed.



As the alloy continues to cool (location 3) the existing nucleation sites will grow as dendrites andfurther nucleation sites will form within the liquid part of the mixture. The melt will have that

mushy consistency of chunks in liquid while it is in the “alpha + liquid” region of the phase

diagram. Since the alpha phase is mostly element A (with a small amount of B atoms in solidsolution), the remaining liquid becomes slightly richer in B as the liquid cools, which is indicated

by the liquidus line. The composition of the solid alpha phase also becomes slightly richer in B

atoms as the solid solution line shows.

This primary alpha phase growth and the accompanying phase composition shifts continue untilenough A atoms have been removed so that the remaining liquid is of eutectic composition. This

composition is achieved at the point where the temperature crosses the eutectic line (location 4).

At this point the primary alpha phase stops forming. The remaining liquid starts to solidify intothe lamellar (alternating layers of alpha and beta phases) structure of a eutectic composition. The

eutectic structure will grow; adding alpha to the layers of alpha and beta to the layers of beta in

the eutectic regions, and new solidification sites will continue to form. Remember that

solidification occurs rapidly and without the need for a further decrease in temperature once theliquid reaches the eutectic line. At this point, the entire alloy has solidified into a mixture

comprised of grains of alpha and grains of eutectic mixture (alpha and beta). The microstructure

from this point at the eutectic line down to ambient temperature will look something like thatshown in micro 5.

Diffusion occurs as the alloy cools since the amount of element B in the alpha phase changes

with temperature. This occurs exactly like it did for the eutectic alloy. Diffusion must also occur

in the grains of pure alpha, as the composition of alpha phase also changes with temperature.

Hypereutectic

Finally, consider an alloy of A and B that has an

overall composition that places it to the right of

the eutectic point. When an alloy falls to the rightof the eutectic point it is called a hypereutectic

alloy. This alloy will solidify like the hypoeutectic

alloy did except it will pass through the “beta +liquid” region of the phase diagram rather than the

“alpha + liquid” region. This will result in a

microstructure comprised of grains of beta andgrains of eutectic mixture (alpha and beta) rather

than grains of alpha and grains of eutectic mixture

(alpha and beta) as the hypoeutectic alloy had.



At location 1, the alloy is at a temperature that is high enough to put it in a fully liquid phase.

When the alloy is cooled, it remains in the liquid state until it reaches the temperature where it

crosses the liquidus line (location 2). At this temperature, the beta phase starts to solidify at anyfavorable nucleation sites. The beta solidifies as dendrites which grow to become grains of beta.

The first solid phase to form is called the primary phase so, in this case, primary beta is formed.

As the alloy continues to cool (location 3) the existing nucleation sites will grow as dendrites and

further nucleation sites will form within the liquid part of the mixture. Since the beta phase is

mostly element B (with a small amount of A atoms in solid solution), the remaining liquid becomes richer in A as the liquid cools, which is indicated by the liquidus line. The composition

of the solid beta phase also becomes slightly richer in A atoms as the solid solution line shows.

This primary beta phase growth and the accompanying phase composition shifts continue until

enough B atoms have been removed so that the remaining liquid is of eutectic composition. Thiscomposition is achieved at the point where the temperature crosses the eutectic line (location 4).

At this point the primary beta phase stops forming. The remaining liquid starts to solidify into

the lamellar (alternating layers of alpha and beta phases) structure of a eutectic composition. Theeutectic structure will grow; adding alpha to the layers of alpha and beta to the layers of beta in

the eutectic regions, and new solidification sites will continue to form. At this point, the entire

alloy quickly solidifies into a mixture of beta grains and eutectic mixture (alpha and beta) grains.

The microstructure from this point at the eutectic line down to ambient temperature will look something like that shown in micro 5.

Diffusion occurs as the alloy cools since the amount of element B in the alpha phase changes

with temperature. This occurs exactly like it did for the eutectic alloy. Diffusion must also occur in the grains of pure alpha, as the composition of alpha phase also changes with temperature.

Thermal Treatments (Heat-Treating)

In the previous pages on the subjects of alloying and the binary phase diagram, the

microstructures of alloys that were allowed to solidify by slow cooling were considered. Itshould also be known, however, that it is possible to modify the microstructure of an alloy bysubjecting it to various thermal treatments. Heat-treating is a term used to describe all of the

controlled heating and cooling operations performed on a material in the solid state for the

purpose of altering its microstructure and/or properties. The focus of this discussion will be on

metals but is should be noted that heat-treatment is also used on ceramics and composites tomodify their properties.



The major objectives of the different kinds of thermal treatments are:

1. Soften the material for improved workability.

2. Increase the strength or hardness of the material.

3. Increase the toughness or resistance to fracture of the material.

4. Stabilize mechanical or physical properties against changes that might occur duringexposure to service environments.

5. Insure part dimensional stability.

6. Relieve undesirable residual stresses induced during part fabrication.

Different metals respond to treatment at different temperatures. Each metal has a specific

chemical composition, so changes in physical and structural properties take place at different,critical temperatures. Even small percentages of elements in the metal composition, such as

carbon, will greatly determine the temperature, time, method and rate of cooling that needs to be

used in the heat treating process. Depending on the thermal treatment used, the atomic structureand/or microstructure of a material may change due to movement of dislocations, an increase or

decrease in solubility of atoms, an increase in grain size, the formation of new grains of the same

or different phase, a change in the crystal structure, and others mechanisms.

Since there are so many ways in which metals are heat treated, it is not practical to discuss them

all. But, as an example, let’s look at how heat treatment is used to strengthen a copper aluminum

alloy.

Precipitation Hardening

In designing alloys for strength, an approach often taken is to develop an alloy with a structure

that consists of particles (which impede dislocation movement) dispersed in a ductile matrix.Such a dispersion can be obtained by choosing an alloy that is a single phase at elevated

temperature but on cooling will precipitate another phase in the matrix. A thermal process is then

developed to produce the desired distribution of precipitate in the matrix. When the alloy is

strengthened by this thermal treatment, it is called precipitation strengthening or hardening.

Precipitation hardening consists of three main steps: solution treatment, quenching, and aging.

Solution treatment involves heating the alloy to a temperature that allows the alloying atoms

(called the solute) to dissolve into the solution. This results in a homogeneous solid solution of

one phase. Quenching rapidly cools the solution and freezes the atoms in solution. In moretechnical terms, the quenching cools the material so fast that the atoms of the alloying elements

do not have time to diffuse out of the solution. In the as-quenched condition, the solute is

supersaturated meaning that the lattice is overly stressed by the alloying atoms. Aging is the process where the solute particles diffuse out of solution and into clusters that distort and

strengthen the material.

The precipitation hardening process for a copper-aluminum alloy is shown graphically in the

image below. On the right is phase diagram, which is a very useful tool for understanding and



controlling polyphase structures. The phase diagram is simply a map showing the structure of

phases present as the temperature and overall composition of the alloy are varied. The images on

the right in the image show the resulting microstructure at each step in the process.

Common Heat Treating Processes

A few of the more common terms used in heat treating are introduced below. It should be notedthat not all of the term are applicable to all alloys.

Age Hardening is a relatively low-temperature heat treatment process that strengthens a material

by causing the precipitation of components or phases of alloy from a super-saturated solid

solution condition.

Annealing is a softening process in which metals are heated and then allowed to cool slowly.

The purpose of annealing is to soften the material for improve machinability, formability, and

sometimes to control magnetic properties.

Normallizing is much like annealing, but the cooling process is much faster. This results inincreased strength but less ductility in the metal. Its purpose is to refine grain structure, produce

more uniform mechanical properties, and sometimes to relieve internal and surface stresses.

Precipitation Heat Treatment is the three step process of solution treating, quenching, and age

hardening to increase the strength or hardness of an alloy.

Solution Heat Treatment involves heating the material to a temperature that puts all the

elements in solid solution and then cooling very rapidly to freeze the atoms in place.

Stress Relieving is a low temperature heat treat process that is used to reduce the level of

residual stresses in a material.

Tempering involves gently heating a hardened metal and allowing it to cool slowly will producea metal that is still hard but also less brittle. This process is known as tempering.



Quenching is the rapid cooling of a hot material. The medium used to quench the material can

vary from forced air, oil, water and others. Many steels are hardened by heating and quenching.

Quenching results in a metal that is very hard but also brittle.

More information on heat treatment can be found in the material (ie aluminum, steel, titanium,

etc.) sections

Ceramic Structures

As discussed in the introduction, ceramics and related materials cover a wide range of objects.

Ceramics are a little more complex than metallic structures, which is why metals were coveredfirst. A ceramic has traditionally been defined as “an inorganic, nonmetallic solid that is prepared

from powdered materials and is fabricated into products through the application of heat. Most

ceramics are made up of two or more elements. This is called a compound. For example, alumina

(Al2O3) is a compound made up of aluminum atoms and oxygen atoms.

The two most common chemical bonds for ceramic materials are covalent and ionic. The bonding of atoms together is much stronger in covalent and ionic bonding than in metallic. This

is why ceramics generally have the following properties: high hardness, high compressivestrength, and chemical inertness. This strong bonding also accounts for the less attractive

properties of ceramics, such as low ductility and low tensile strength. The absence of free

electrons is responsible for making most ceramics poor conductors of electricity and heat.

However, it should be noted that the crystal structures of ceramics are many and varied and thisresults in a very wide range of properties. For example, while ceramics are perceived as

electrical and thermal insulators, ceramic oxide (initially based on Y-Ba-Cu-O) is the basis for

high temperature superconductivity. Diamond and silicon carbide have a higher thermal

conductivity than aluminum or copper. Control of the microstructure can overcome inherentstiffness to allow the production of ceramic springs, and ceramic composites which have been

produced with a fracture toughness about half that of steel. Also, the atomic structures are often

of low symmetry that gives some ceramics interesting electromechanical properties like piezoelectricity, which is used in sensors and transducers.

The structure of most ceramics varies from relatively simple to very complex. The

microstructure can be entirely glassy (glasses only); entirely crystalline; or a combination of

crystalline and glassy. In the latter case, the glassy phase usually surrounds small crystals, bonding them together. The main compositional classes of engineering ceramics are the oxides,

nitrides and carbides.

Ceramic Structures (continued)

Ceramic Glass

Ceramics with an entirely glassy structure have certain properties that are quite different fromthose of metals. Recall that when metal in the liquid state is cooled, a crystalline solid

precipitates when the melting freezing point is reached. However, with a glassy material, as the

liquid is cooled it becomes more and more viscous. There is no sharp melting or freezing point.



It goes from liquid to a soft plastic solid and finally becomes hard and brittle. Because of this

unique property, it can be blown into shapes, in addition to being cast, rolled, drawn and

otherwise processed like a metal.

Glassy behavior is related to the atomic structure of the material. If pure silica (SiO2) is fused

together, a glass called vitreous silica is formed on cooling. The basic unit structure of this glassis the silica tetrahedron, which is composed of a single silicon atom surrounded by four

equidistant oxygen atoms. The silicon atoms occupy the openings (interstitials) between theoxygen atoms and share four valence electrons with the oxygen atoms through covalent bonding.

The silica atom has four valence electrons and each of the oxygen atoms has two valence

electrons so the silica tetrahedron has four extra valence electrons to share with adjacenttetrahedral. The silicate structures can link together by sharing the atoms in two corners of the

SiO2 tetrahedrons, forming chain or ring structures. A network of silica tetrahedral chains form,

and at high temperatures these chains easily slide past each other. As the melt cools, thermalvibrational energy decreases and the chains can not move as easily so the structure becomes

more rigid. Silica is the most important constituent of glass, but other oxides are added to change

certain physical characteristics or to lower the melting point.

Ceramic Crystalline or Partially Crystalline Material

Most ceramics usually contain both metallic and nonmetallic elements with ionic or covalent

bonds. Therefore, the structure the metallic atoms, the structure of the nonmetallic atoms, and the

balance of charges produced by the valence electrons must be considered. As with metals, theunit cell is used in describing the atomic structure of ceramics. The cubic and the hexagonal cells

are most common. Additionally, the difference in radii between the metallic and nonmetallic ions

plays an important role in the arrangement of the unit cell.

In metals, the regular arrangement of atoms into densely packed planes led to the occurrence of

slip under stress, which gives metal their characteristic ductility. In ceramics, brittle fracturerather than slip is common because both the arrangement of the atoms and the type of bonding is

different. The fracture or cleavage planes of ceramics are the result of planes of regularlyarranged atoms.

The building criteria for the crystal structure are:

• maintain neutrality

• charge balance dictates chemical formula

• achieve closest packing

A few of the different types of ceramic materials outside of the glass family are described below.

Silicate Ceramics

As mentioned previously, the silica structure is the basic

structure for many ceramics, as well as glass. It has aninternal arrangement consisting of pyramid (tetrahedral or

four-sided) units. Four large oxygen (0) atoms surround each

smaller silicon (Si) atom. When silica tetrahedrons share



three corner atoms, they produce layered silicates (talc, kaolinite clay, mica). Clay is the basic

raw material for many building products such as brick and tile. When silica tetrahedrons share

four comer atoms, they produce framework silicates (quartz, tridymite). Quartz is formed whenthe tetrahedra in this material are arranged in a regular, orderly fashion. If silica in the molten

state is cooled very slowly it crystallizes at the freezing point. But if molten silica is cooled more

rapidly, the resulting solid is a disorderly arrangement which is glass.

Cement

Cement (Portland cement) is one of the main ingredients of concrete. There are a number of

different grades of cement but a typical Portland cement will contain 19 to 25% SiO2 , 5 to 9%

Al2O3, 60 to 64% CaO and 2 to 4% FeO. Cements are prepared by grinding the clays andlimestone in proper proportion, firing in a kiln, and regrinding. When water is added, the

minerals either decompose or combine with water, and a new phase grows throughout the mass.

The reaction is solution, recrystallization, and precipitation of a silicate structure. It is usuallyimportant to control the amount of water to prevent an excess that would not be part of the

structure and would weaken it. The heat of hydration (heat of reaction in the adsorption of water)

in setting of the cement can be large and can cause damage in large structures.

Nitride Ceramics

Nitrides combine the superior hardness of ceramics with high

thermal and mechanical stability, making them suitable for

applications as cutting tools, wear-resistant parts andstructural components at high temperatures. TiN has a cubic

structure which is perhaps the simplest and best known of

structure types. Cations and anions both lie at the nodes of

separate fcc lattices. The structure is unchanged if the Ti and N atoms (lattices) are interchanged.

Ferroelectric Ceramics

Depending on the crystalstructure, in some crystal lattices, the centers of the positive

and negative charges do not coincide even without the

application of external electric field. In this case, it is said

that there exists spontaneous polarization in thecrystal. When the polarization of the dielectric can be

altered by an electric field, it is called ferroelectric. A

typical ceramic ferroelectric is barium titanate,BaTiO3. Ferroelectric materials, especially polycrystalline

ceramics, are very promising for varieties of

application fields such as piezoelectric/electrostrictivetransducers, and electrooptic.

Phase Diagram

The phase diagram is important in understanding the formation and control of the microstructure

of the microstructure of polyphase ceramics, just as it is with polyphase metallic materials. Also,



nonequilibrium structures are even more prevalent in ceramics because the more complex crystal

structures are more difficult to nucleate and to grow from the melt.

Imperfections in Ceramics

Imperfections in ceramic crystals include point

defects and impurities like in metals. However,in ceramics defect formation is strongly affected

by the condition of charge neutrality because thecreation of areas of unbalanced charges requires

an expenditure of a large amount of energy. In

ionic crystals, charge neutrality often results indefects that come as pairs of ions with opposite

charge or several nearby point defects in which

the sum of all charges is zero. Charge neutraldefects include the Frenkel and Schottky

defects. A Frenkel-defect occurs when a host

atom moves into a nearby interstitial position tocreate a vacancy-interstitial pair of cations. A

Schottky-defect is a pair of nearby cation and anion vacancies. Schottky defect occurs when a

host atom leaves its position and moves to the surface creating a vacancy-vacancy pair.

Sometimes, the composition may alter slightly to arrive at a more balanced atomic charge. Solidssuch as SiO2, which have a well-defined chemical formula, are called stoichiometric compounds.

When the composition of a solid deviates from the standard chemical formula, the resulting solid

is said to be nonstoichiometric. Nonstoichiometry and the existence of point defects in a solid are

often closely related. Anion vacancies are the source of the nonstoichiometry in SiO2-x,

Introduction of impurity atoms in the lattice is likely in conditions where the charge ismaintained. This is the case of electronegative impurities that substitute a lattice anion or

electropositive substitutional impurities. This is more likely for similar ionic radii since thisminimizes the energy required for lattice distortion. Defects will appear if the charge of the

impurities is not balanced.

Physical and Chemical Properties

Physical properties are those that can be observed without changing the identity of the substance.

The general properties of matter such as color, density, hardness, are examples of physical properties. Properties that describe how a substance changes into a completely different

substance are called chemical properties. Flammability and corrosion/oxidation resistance areexamples of chemical properties.

The difference between a physical and chemical property is straightforward until the phase of thematerial is considered. When a material changes from a solid to a liquid to a vapor it seems like

them become a difference substance. However, when a material melts, solidifies, vaporizes,

condenses or sublimes, only the state of the substance changes. Consider ice, liquid water, and



water vapor, they are all simply H2O. Phase is a physical property of matter and matter can exist

in four phases – solid, liquid, gas and plasma.

Some of the more important physical and chemical properties from an engineering materialstandpoint will be discussed in the following sections.

• Phase Transformation Temperatures

• Density

• Specific Gravity

• Thermal Conductivity

• Linear Coefficient of Thermal Expansion

• Electrical Conductivity and Resistivity

• Magnetic Permeability

• Corrosion Resistance

• Phase Transformation Temperatures

• When temperature rises and pressure is

held constant, a typical substance changes

from solid to liquid and then to vapor.

Transitions from solid to liquid, fromliquid to vapor, from vapor to solid and

visa versa are called phase transformations

or transitions. Since some substances haveseveral crystal forms, technically there can

also be solid to another solid form phase

transformation.

• Phase transitions from solid to liquid, and

from liquid to vapor absorb heat. The

phase transition temperature where a solid

changes to a liquid is called the melting point . The temperature at which the vapor

pressure of a liquid equals 1 atm (101.3 kPa) is called the boiling point . Some materials,

such as many polymers, do not go simply from a solid to a liquid with increasing

temperature. Instead, at some temperature below the melting point, they start to lose their crystalline structure but the molecules remain linked in chains, which results in a soft and

pliable material. The temperature at which a solid, glassy material begins to soften andflow is called the glass transition temperature.

• Mechanical Properties

• The mechanical properties of a material are those properties that involve a reaction to an

applied load. The mechanical properties of metals determine the range of usefulness of a



material and establish the service life that can be expected. Mechanical properties are

also used to help classify and identify material. The most common properties considered

are strength, ductility, hardness, impact resistance, and fracture toughness.

• Most structural materials are anisotropic, which means that their material properties vary

with orientation. The variation in properties can be due to directionality in the

microstructure (texture) from forming or cold working operation, the controlledalignment of fiber reinforcement and a variety of other causes. Mechanical properties are

generally specific to product form such as sheet, plate, extrusion, casting, forging, and

etc. Additionally, it is common to see mechanical property listed by the directional grainstructure of the material. In products such as sheet and plate, the rolling direction is called

the longitudinal direction, the width of the product is called the transverse direction, and

the thickness is called the short transverse direction. The grain orientations in standardwrought forms of metallic products are shown the image.



•

Th

e mechanical properties of a material are not constants and often change as a function of

temperature, rate of loading, and other conditions. For example, temperatures below

room temperature generally cause an increase in strength properties of metallic alloys;while ductility, fracture toughness, and elongation usually decrease. Temperatures above

room temperature usually cause a decrease in the strength properties of metallic alloys.Ductility may increase or decrease with increasing temperature depending on the samevariables

• It should also be noted that there is often significant variability in the values obtained

when measuring mechanical properties. Seemingly identical test specimen from the samelot of material will often produce considerable different results. Therefore, multiple tests

are commonly conducted to determine mechanical properties and values reported can be



an average value or calculated statistical minimum value. Also, a range of values are

sometimes reported in order to show variability.

• Loading

• The application of a force to an object is known as loading. Materials can be subjected to

many different loading scenarios and a material’s performance is dependant on the

loading conditions. There are five fundamental loading conditions; tension, compression,

bending, shear, and torsion. Tension is the type of loading in which the two sections of material on either side of a plane tend to be pulled apart or elongated. Compression is the

reverse of tensile loading and involves pressing the material together. Loading by

bending involves applying a load in a manner that causes a material to curve and resultsin compressing the material on one side and stretching it on the other. Shear involves

applying a load parallel to a plane which caused the material on one side of the plane to

want to slide across the material on the other side of the plane. Torsion is the applicationof a force that causes twisting in a material.

•

• If a material is subjected to a constant force, it is called static loading. If the loading of

the material is not constant but instead fluctuates, it is called dynamic or cyclic loading.

The way a material is loaded greatly affects its mechanical properties and largely

determines how, or if, a component will fail; and whether it will show warning signs before failure actually occurs.



Stress and Strain

Stress

The term stress (s) is used to express the loading in terms of force applied to a certain cross-

sectional area of an object. From the perspective of loading, stress is the applied force or system

of forces that tends to deform a body. From the perspective of what is happening within amaterial, stress is the internal distribution of forces within a body that balance and react to the

loads applied to it. The stress distribution may or may not be uniform, depending on the nature of

the loading condition. For example, a bar loaded in pure tension will essentially have a uniformtensile stress distribution. However, a bar loaded in bending will have a stress distribution that

changes with distance perpendicular to the normal axis.

Simplifying assumptions are often used to represent stress as a vector quantity for many

engineering calculations and for material property determination. The word "vector " typicallyrefers to a quantity that has a "magnitude" and a "direction". For example, the stress in an axially

loaded bar is simply equal to the applied force divided by the bar's cross-sectional area.

Some common measurements of stress are:

Psi = lbs/in2 (pounds per square inch)ksi or kpsi = kilopounds/in2 (one thousand or 103 pounds per square inch)

Pa = N/m 2 (Pascals or Newtons per square meter)

kPa = Kilopascals (one thousand or 103 Newtons per square meter)GPa = Gigapascals (one million or 106 Newtons per square meter)

*Any metric prefix can be added in front of psi or Pa to indicate the multiplication factor

It must be noted that the stresses in most

2-D or 3-D solids are actually morecomplex and need be defined more

methodically. The internal force acting

on a small area of a plane can be resolvedinto three components: one normal to the

plane and two parallel to the plane. The

normal force component divided by thearea gives the normal stress (s), and

parallel force components divided by thearea give the shear stress (t). These

stresses are average stresses as the area is



finite, but when the area is allowed to approach zero, the stresses become stresses at a point.

Since stresses are defined in relation to the plane that passes through the point under

consideration, and the number of such planes is infinite, there appear an infinite set of stresses ata point. Fortunately, it can be proven that the stresses on any plane can be computed from the

stresses on three orthogonal planes passing through the point. As each plane has three stresses,

the stress tensor has nine stress components, which completely describe the state of stress at a point.

Strain

Strain is the response of a system to an applied stress. When a material is loaded with a force, it

produces a stress, which then causes a material to deform. Engineering strain is defined as theamount of deformation in the direction of the applied force divided by the initial length of the

material. This results in a unitless number, although it is often left in the unsimplified form, such

as inches per inch or meters per meter. For example, the strain in a bar that is being stretched intension is the amount of elongation or change in length divided by its original length. As in the

case of stress, the strain distribution may or may not be uniform in a complex structural element,

depending on the nature of the loading condition.

If the stress is small, the material may only strain a small amount and the material will return toits original size after the stress is released. This is called elastic deformation, because like elastic

it returns to its unstressed state. Elastic deformation only occurs in a material when stresses are

lower than a critical stress called the yield strength. If a material is loaded beyond it elastic limit,the material will remain in a deformed condition after the load is removed. This is called plastic

deformation.

Engineering and True Stress and Strain

The discussion above focused on engineering stress and strain, which use the fixed, undeformedcross-sectional area in the calculations. True stress and strain measures account for changes in

cross-sectional area by using the instantaneous values for the area. The engineering stress-straincurve does not give a true indication of the deformation characteristics of a metal because it is

based entirely on the original dimensions of the specimen, and these dimensions changecontinuously during the testing used to generate the data.

Engineering stress and strain data is commonly used because it is easier to generate the data and

the tensile properties are adequate for engineering calculations. When considering the stress-strain curves in the next section, however, it should be understood that metals and other materials



continues to strain-harden until they fracture and the stress required to produce further

deformation also increase.

Stress Concentration

When an axial load is applied to a piece of material

with a uniform cross-section, the norm al stress will be uniformly distributed over the cross-section.

However, if a hole is drilled in the material, thestress distribution will no longer be uniform. Since

the material that has been removed from the hole is

no longer available to carry any load, the load must be redistributed over the remaining material. It is

not redistributed evenly over the entire remaining

cross-sectional area but instead will be redistributedin an uneven pattern that is highest at the edges of

the hole as shown in the image. This phenomenon

is known as stress concentration.

Tensile Properties

Tensile properties indicate how the material will react to forces being applied in tension. Atensile test is a fundamental mechanical test where a carefully prepared specimen is loaded in a

very controlled manner while measuring the applied load and the elongation of the specimenover some distance. Tensile tests are used to determine the modulus of elasticity, elastic limit,

elongation, proportional limit, reduction in area, tensile strength, yield point, yield strength and

other tensile properties.

The main product of a tensile test is a load versus elongation curve which is then converted into astress versus strain curve. Since both the engineering stress and the engineering strain are

obtained by dividing the load and elongation by constant values (specimen geometry

information), the load-elongation curve will have the same shape as the engineering stress-strain

curve. The stress-strain curve relates the applied stress to the resulting strain and each materialhas its own unique stress-strain curve. A typical engineering stress-strain curve is shown below.

If the true stress, based on the actual cross-sectional area of the specimen, is used, it is found thatthe stress-strain curve increases continuously up to fracture.



Linear-Elastic Region and Elastic Constants

As can be seen in the figure, the stress and strain initially increase with a linear relationship. This

is the linear-elastic portion of the curve and it indicates that no plastic deformation has occurred.In this region of the curve, when the stress is reduced, the material will return to its original

shape. In this linear region, the line obeys the relationship defined as Hooke's Law where theratio of stress to strain is a constant.

The slope of the line in this region where stress is proportional to strain and is called themodulus of elasticity or Young's modulus. The modulus of elasticity (E) defines the properties

of a material as it undergoes stress, deforms, and then returns to its original shape after the stress

is removed. It is a measure of the stiffness of a given material. To compute the modulus of elastic , simply divide the stress by the strain in the material. Since strain is unitless, the modulus

will have the same units as the stress, such as kpi or MPa. The modulus of elasticity applies

specifically to the situation of a component being stretched with a tensile force. This modulus isof interest when it is necessary to compute how much a rod or wire stretches under a tensile load.

There are several different kinds of moduli depending on the way the material is being stretched,

bent, or otherwise distorted. When a component is subjected to pure shear, for instance, a

cylindrical bar under torsion, the shear modulus describes the linear-elastic stress-strainrelationship.

Axial strain is always accompanied by lateral strains of opposite sign in the two directions

mutually perpendicular to the axial strain. Strains that result from an increase in length are



designated as positive (+) and those that result in a decrease in length are designated as negative

(-). Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain

for a uniaxial stress state.

Poisson's ratio is sometimes also defined as the ratio of the absolute values of lateral and axialstrain. This ratio, like strain, is unitless since both strains are unitless. For stresses within the

elastic range, this ratio is approximately constant. For a perfectly isotropic elastic material,

Poisson's Ratio is 0.25, but for most materials the value lies in the range of 0.28 to 0.33.Generally for steels, Poisson’s ratio will have a value of approximately 0.3. This means that if

there is one inch per inch of deformation in the direction that stress is applied, there will be 0.3

inches per inch of deformation perpendicular to the direction that force is applied.

Only two of the elastic constants are independent so if two constants are known, the third can becalculated using the following formula:

E = 2 (1 + n) G.

Where: E = modulus of elasticity (Young's modulus)

n = Poisson's ratio

G = modulus of rigidity (shear modulus).

A couple of additional elastic constants that may be encountered include the bulk modulus (K),

and Lame's constants (m and l). The bulk modulus is used describe the situation where a pieceof material is subjected to a pressure increase on all sides. The relationship between the change

in pressure and the resulting strain produced is the bulk modulus. Lame's constants are derived

from modulus of elasticity and Poisson's ratio.

Yield Point

In ductile materials, at some point, the stress-strain curve deviates from the straight-line

relationship and Law no longer applies as the strain increases faster than the stress. From this

point on in the tensile test, some permanent deformation occurs in the specimen and the materialis said to react plastically to any further increase in load or stress. The material will not return to

its original, unstressed condition when the load is removed. In brittle materials, little or no plastic

deformation occurs and the material fractures near the end of the linear-elastic portion of thecurve.

With most materials there is a gradual transition from elastic to plastic behavior, and the exact

point at which plastic deformation begins to occur is hard to determine. Therefore, various

criteria for the initiation of yielding are used depending on the sensitivity of the strainmeasurements and the intended use of the data. (See Table) For most engineering design and

specification applications, the yield strength is used. The yield strength is defined as the stress



required to produce a small, amount of plastic deformation. The offset yield strength is the stress

corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of

the curve offset by a specified strain (in the US the offset is typically 0.2% for metals and 2% for plastics).

To determine the yield strength using this offset, the point isfound on the strain axis (x-axis) of 0.002, and then a line parallel

to the stress-strain line is drawn. This line will intersect the stress-strain line slightly after it begins to curve, and that intersection is

defined as the yield strength with a 0.2% offset. A good way of

looking at offset yield strength is that after a specimen has beenloaded to its 0.2 percent offset yield strength and then unloaded it

will be 0.2 percent longer than before the test. Even though the

yield strength is meant to represent the exact point at which the material becomes permanentlydeformed, 0.2% elongation is considered to be a tolerable amount of sacrifice for the ease it

creates in defining the yield strength.

Some materials such as gray cast iron or soft copper exhibit essentially no linear-elastic

behavior. For these materials the usual practice is to define the yield strength as the stressrequired to produce some total amount of strain.

• True elastic limit is a very low value and is related to the motion of a few hundred

dislocations. Micro strain measurements are required to detect strain on order of 2 x 10 -6

in/in.

• Proportional limit is the highest stress at which stress is directly proportional to strain. It

is obtained by observing the deviation from the straight-line portion of the stress-strain

curve.

• Elastic limit is the greatest stress the material can withstand without any measurable

permanent strain remaining on the complete release of load. It is determined using a

tedious incremental loading-unloading test procedure. With the sensitivity of strainmeasurements usually employed in engineering studies (10 -4in/in), the elastic limit is

greater than the proportional limit. With increasing sensitivity of strain measurement, the

value of the elastic limit decreases until it eventually equals the true elastic limitdetermined from micro strain measurements.

• Yield strength is the stress required to produce a small-specified amount of plastic

deformation. The yield strength obtained by an offset method is commonly used for engineering purposes because it avoids the practical difficulties of measuring the elastic

limit or proportional limit.

Ultimate Tensile Strength

The ultimate tensile strength (UTS) or, more simply, the tensile strength, is the maximumengineering stress level reached in a tension test. The strength of a material is its ability to

withstand external forces without breaking. In brittle materials, the UTS will at the end of the

linear-elastic portion of the stress-strain curve or close to the elastic limit. In ductile materials,

In Great Britain, the yieldstrength is often referred to

as the proof stress. The

offset value is either 0.1%or 0.5%



the UTS will be well outside of the elastic portion into the plastic portion of the stress-strain

curve.

On the stress-strain curve above, the UTS is the highest point where the line is momentarily flat.Since the UTS is based on the engineering stress, it is often not the same as the breaking

strength. In ductile materials strain hardening occurs and the stress will continue to increase untilfracture occurs, but the engineering stress-strain curve may show a decline in the stress level

before fracture occurs. This is the result of engineering stress being based on the original cross-section area and not accounting for the necking that commonly occurs in the test specimen. The

UTS may not be completely representative of the highest level of stress that a material can

support, but the value is not typically used in the design of components anyway. For ductilemetals the current design practice is to use the yield strength for sizing static components.

However, since the UTS is easy to determine and quite reproducible, it is useful for the purposes

of specifying a material and for quality control purposes. On the other hand, for brittle materialsthe design of a component may be based on the tensile strength of the material.

Measures of Ductility (Elongation and Reduction of Area)The ductility of a material is a measure of the extent to which a material will deform before

fracture. The amount of ductility is an important factor when considering forming operationssuch as rolling and extrusion. It also provides an indication of how visible overload damage to a

component might become before the component fractures. Ductility is also used a quality control

measure to assess the level of impurities and proper processing of a material.

The conventional measures of ductility are theengineering strain at fracture (usually called the

elongation ) and the reduction of area at

fracture. Both of these properties are obtained

by fitting the specimen back together after fracture and measuring the change in length and

cross-sectional area. Elongation is the change inaxial length divided by the original length of the

specimen or portion of the specimen. It is

expressed as a percentage. Because an

appreciable fraction of the plastic deformationwill be concentrated in the necked region of the

tensile specimen, the value of elongation will

depend on the gage length over which themeasurement is taken. The smaller the gage length the greater the large localized strain in the

necked region will factor into the calculation. Therefore, when reporting values of elongation ,

the gage length should be given.

One way to avoid the complication from necking is to base the elongation measurement on theuniform strain out to the point at which necking begins. This works well at times but some

engineering stress-strain curve are often quite flat in the vicinity of maximum loading and it is

difficult to precisely establish the strain when necking starts to occur.



Reduction of area is the change in cross-sectional area divided by the original cross-sectional

area. This change is measured in the necked down region of the specimen. Like elongation, it is

usually expressed as a percentage.

As previously discussed, tension is just one of the way that a material can be loaded. Other ways

of loading a material include compression, bending, shear and torsion, and there are a number of standard tests that have been established to characterize how a material performs under these

other loading conditions. A very cursory introduction to some of these other material propertieswill be provided on the next page.

Compressive, Bearing, & Shear Properties

Compressive Properties

In theory, the compression test is simply the opposite of the tension test

with respect to the direction of loading. In compression testing the sampleis squeezed while the load and the displacement are recorded.

Compression tests result in mechanical properties that include thecompressive yield stress, compressive ultimate stress, and compressivemodulus of elasticity.

Compressive yield stress is measured in a manner identical to that done for

tensile yield strength. When testing metals, it is defined as the stress

corresponding to 0.002 in./in. plastic strain. For plastics, the compressiveyield stress is measured at the point of permanent yield on the stress-strain

curve. Moduli are generally greater in compression for most of the

commonly used structural materials.

Ultimate compressive strength is the stress required to rupture a specimen.This value is much harder to determine for a compression test than it is for a tensile test since

many material do not exhibit rapid fracture in compression. Materials such as most plastics that

do not rupture can have their results reported as the compressive strength at a specificdeformation such as 1%, 5%, or 10% of the sample's original height.

For some materials, such as concrete, the compressive strength is the most important material

property that engineers use when designing and building a structure. Compressive strength is

also commonly used to determine whether a concrete mixture meets the requirements of the jobspecifications.

Bearing Properties Bearing properties are used when designing mechanically fastened joints. The purpose of a

bearing test is to determine the the deformation of a hole as a function of the applied bearingstress. The test specimen is basically a piece of sheet or plate with a carefully prepared hole

some standard distance from the edge. Edge-to-hole diameter ratios of 1.5 and 2.0 are common.

A hardened pin is inserted through the hole and an axial load applied to the specimen and the pin. The bearing stress is computed by dividing the load applied to the pin, which bears against

the edge of the hole, by the bearing area (the product of the pin diameter and the sheet or plate



thickness). Bearing yield and ultimate stresses are obtained from bearing tests. BYS is computed

from a bearing stress deformation curve by drawing a line parallel to the initial slope at an offset

of 0.02 times the pin diameter. BUS is the maximum stress withstood by a bearing specimen.

Shear Properties

A shearing stress acts parallel to the stress plane, whereas a tensile or compressive stress actsnormal to the stress plane. Shear properties are primarily used in the design of mechanically

fastened components, webs, and torsion members, and other components subject to parallel,opposing loads. Shear properties are dependant on the type of shear test and their is a variety of

different standard shear tests that can be performed including the single-shear test, double-shear

test, blanking-shear test, torsion-shear test and others. The shear modulus of elasticity isconsidered a basic shear property. Other properties, such as the proportional limit stress and

shear ultimate stress, cannot be treated as basic shear properties because of “form factor” effects.

Creep and Stress Rupture Properties

Creep PropertiesCreep is a time-dependent deformation of amaterial while under an applied load that is

below its yield strength. It is most often occurs

at elevated temperature, but some materialscreep at room temperature. Creep terminates in

rupture if steps are not taken to bring to a halt.

Creep data for general design use are usually

obtained under conditions of constant uniaxialloading and constant temperature. Results of

tests are usually plotted as strain versus time upto rupture. As indicated in the image, creepoften takes place in three stages. In the initial

stage, strain occurs at a relatively rapid rate but the rate gradually decreases until it becomes

approximately constant during the second stage. This constant creep rate is called the minimum

creep rate or steady-state creep rate since it is the slowest creep rate during the test. In the thirdstage, the strain rate increases until failure occurs.

Creep in service is usually affected by changing conditions of loading and temperature and the

number of possible stress-temperature-time combinations is infinite. While most materials aresubject to creep, the creep mechanisms is often different between metals, plastics, rubber,

concrete.

Stress Rupture Properties

Stress rupture testing is similar to creep testing except that the stresses are higher than those usedin a creep testing. Stress rupture tests are used to determine the time necessary to produce failure

so stress rupture testing is always done until failure. Data is plotted log-log as in the chart

above. A straight line or best fit curve is usually obtained at each temperature of interest. This



information can then be used to extrapolate time to failure for longer times. A typical set of stress

rupture curves is shown below.

Toughness

The ability of a metal to deform plastically and to absorb energy in the process before fracture is

termed toughness. The emphasis of this definition should be placed on the ability to absorb

energy before fracture. Recall that ductility is a measure of how much something deforms plastically before fracture, but just because a material is ductile does not make it tough. The key

to toughness is a good combination of strength and ductility. A material with high strength and

high ductility will have more toughness than a material with low strength and high ductility.

Therefore, one way to measure toughness is by calculating the area under the stress strain curvefrom a tensile test. This value is simply called “material toughness” and it has units of energy per

volume. Material toughness equates to a slow absorption of energy by the material.



There are several variables that have a profound influence on the toughness of a material. These

variables are:

• Strain rate (rate of loading)

• Temperature

• Notch effect

A metal may possess satisfactory toughness under static loads but may fail under dynamic loads

or impact. As a rule ductility and, therefore, toughness decrease as the rate of loading increases.

Temperature is the second variable to have a major influence on its toughness. As temperature islowered, the ductility and toughness also decrease. The third variable is termed notch effect, has

to due with the distribution of stress. A material might display good toughness when the applied

stress is uniaxial; but when a multiaxial stress state is produced due to the presence of a notch,the material might not withstand the simultaneous elastic and plastic deformation in the various

directions.

There are several standard types of toughness test that generate data for specific loading

conditions and/or component design approaches. Three of the toughness properties that will bediscussed in more detail are 1) impact toughness, 2) notch toughness and 3) fracture toughness



Impact Toughness

The impact toughness (AKA Impact strength) of a material can be determined with a Charpy or

Izod test. These tests are named after their inventors and were developed in the early 1900’s

before fracture mechanics theory was available. Impact properties are not directly used in

fracture mechanics calculations, but the economical impact tests continue to be used as a qualitycontrol method to assess notch sensitivity and for comparing the relative toughness of

engineering materials.

The two tests use different specimens andmethods of holding the specimens, but both tests

make use of a pendulum-testing machine. For

both tests, the specimen is broken by a singleoverload event due to the impact of the pendulum.

A stop pointer is used to record how far the

pendulum swings back up after fracturing the

specimen. The impact toughness of a metal isdetermined by measuring the energy absorbed in

the fracture of the specimen. This is simply

obtained by noting the height at which the pendulum is released and the height to which the

pendulum swings after it has struck the specimen .

The height of the pendulum times the weight of the pendulum produces the potential energy and

the difference in potential energy of the pendulum

at the start and the end of the test is equal to the absorbed energy.

Since toughness is greatly affected by temperature, aCharpy or Izod test is often repeated numerous times with

each specimen tested at a different temperature. This

produces a graph of impact toughness for the material as afunction of temperature. An impact toughness versus

temperature graph for a steel is shown in the image. It can

be seen that at low temperatures the material is more brittle and impact toughness is low. At high temperatures

the material is more ductile and impact toughness is

higher. The transition temperature is the boundary

between brittle and ductile behavior and this temperature

is often an extremely important consideration in theselection of a material.

Notch-Toughness

Notch toughness is the ability that a material possesses to absorb energy in the presence of aflaw. As mentioned previously, in the presence of a flaw, such as a notch or crack, a material will

likely exhibit a lower level of toughness. When a flaw is present in a material, loading induces a



triaxial tension stress state adjacent to the flaw. The material develops plastic strains as the yield

stress is exceeded in the region near the crack tip. However, the amount of plastic deformation is

restricted by the surrounding material, which remains elastic. When a material is prevented fromdeforming plastically, it fails in a brittle manner.

Notch-toughness is measured with a variety of specimens such as the Charpy V-notch impactspecimen or the dynamic tear test specimen. As with regular impact testing the tests are often

repeated numerous times with specimens tested at a different temperature. With these specimensand by varying the loading speed and the temperature, it is possible to generate curves such as

those shown in the graph. Typically only static and impact testing is conducted but it should be

recognized that many components in service see intermediate loading rates in the range of thedashed red line.

Fracture Toughness

Fracture toughness is an indication of the amount of stress required to propagate a preexisting

flaw. It is a very important material property since the occurrence of flaws is not completely

avoidable in the processing, fabrication, or service of a material/component. Flaws may appear

as cracks, voids, metallurgical inclusions, weld defects, design discontinuities, or somecombination thereof. Since engineers can never be totally sure that a material is flaw free, it is

common practice to assume that a flaw of some chosen size will be present in some number of

components and use the linear elastic fracture mechanics (LEFM) approach to design criticalcomponents. This approach uses the flaw size and features, component geometry, loading

conditions and the material property called fracture toughness to evaluate the ability of a

component containing a flaw to resist fracture.



A parameter called the stress-intensity factor (K) is used to determine

the fracture toughness of most materials. A Roman numeral subscript

indicates the mode of fracture and the three modes of fracture areillustrated in the image to the right. Mode I fracture is the condition in

which the crack plane is normal to the direction of largest tensile

loading. This is the most commonly encountered mode and, therefore,for the remainder of the material we will consider K I

The stress intensity factor is a function of loading, crack size, and

structural geometry. The stress intensity factor may be represented by

the following equation:

Wher

e:

K

I is the fracture toughness in

s is the applied stress in MPa or psia is the crack length in meters or inches

Bis a crack length and component geometry factor that is

different for each specimen and is dimensionless.

Role of Material Thickness

Specimens having standard proportions

but different absolute size producedifferent values for K I. This results

because the stress states adjacent to the

flaw changes with the specimen

thickness (B) until the thickness exceedssome critical dimension. Once the

thickness exceeds the critical

dimension, the value of K I becomesrelatively constant and this value, K IC ,

is a true material property which is

called the plane-strain fracturetoughness. The relationship between

stress intensity, K I, and fracture

toughness, K IC, is similar to therelationship between stress and tensile

stress. The stress intensity, K I, represents the level of “stress” at the tip of the crack and thefracture toughness, K IC, is the highest value of stress intensity that a material under very specific(plane-strain) conditions that a material can withstand without fracture. As the stress intensity

factor reaches the K IC value, unstable fracture occurs. As with a material’s other mechanical

properties, K IC is commonly reported in reference books and other sources.



Plane-Strain and Plane-Stress

When a material with a crack is loaded in tension, the materials

develop plastic strains as the yield stress is exceeded in the regionnear the crack tip. Material within the crack tip stress field,

situated close to a free surface, can deform laterally (in the z-

direction of the image) because there can be no stresses normal tothe free surface. The state of stress tends to biaxial and the

material fractures in a characteristic ductile manner, with a 45o

shear lip being formed at each free surface. This condition iscalled “plane-stress" and it occurs in relatively thin bodies where

the stress through the thickness cannot vary appreciably due to the

thin section.

However, material away from the free surfaces of a relativelythick component is not free to deform laterally as it is

constrained by the surrounding material. The stress state

under these conditions tends to triaxial and there is zero strain perpendicular to both the stress axis and the direction of

crack propagation when a material is loaded in tension. This

condition is called “plane-strain” and is found in thick plates.

Under plane-strain conditions, materials behave essentiallyelastic until the fracture stress is reached and then rapid

fracture occurs. Since little or no plastic deformation is noted,

this mode fracture is termed brittle fracture.

Plane-Strain Fracture Toughness Testing

When performing a fracture

toughness test, the mostcommon test specimenconfigurations are the single

edge notch bend (SENB or

three-point bend), and thecompact tension (CT)

specimens. From the above

discussion, it is clear that anaccurate determination of the

plane-strain fracture toughness

requires a specimen whose thickness exceeds some critical

thickness (B). Testing has shown that plane-strain conditionsgenerally prevail when:

Where: B is the minimum thickness that produces a condition where plastic strain

Plane Strain - a condition of a

body in which the displacements

of all points in the body are

parallel to a given plane, and the

values of theses displacements do

not depend on the distance perpendicular to the plane

Plane Stress – a condition of a

body in which the state of stress issuch that two of the principal

stresses are always parallel to a

given plane and are constant in the

normal direction.



energy at the crack tip in minimal

K IC is the fracture toughness of the material

sy is the yield stress of material

When a material of unknown fracture toughness is tested, a specimen of full material section

thickness is tested or the specimen is sized based on a prediction of the fracture toughness. If thefracture toughness value resulting from the test does not satisfy the requirement of the aboveequation, the test must be repeated using a thicker specimen. In addition to this thickness

calculation, test specifications have several other requirements that must be met (such as the size

of the shear lips) before a test can be said to have resulted in a K IC value.

When a test fails to meet the thickness and other test requirement that are in place to insure plane-strain condition, the fracture toughness values produced is given the designation K C.

Sometimes it is not possible to produce a specimen that meets the thickness requirement. For

example when a relatively thin plate product with high toughness is being tested, it might not be

possible to produce a thicker specimen with plain-strain conditions at the crack tip.

Plane-Stress and Transitional-Stress States

For cases where the plastic energy at the crack tip is not negligible, other fracture mechanics

parameters, such as the J integral or R-curve, can be used to characterize a material. Thetoughness data produced by these other tests will be dependant on the thickness of the product

tested and will not be a true material property. However, plane-strain conditions do not exist in

all structural configurations and using K IC values in the design of relatively thin areas may result

in excess conservatism and a weight or cost penalty. In cases where the actual stress state is plane-stress or, more generally, some intermediate- or transitional-stress state, it is more

appropriate to use J integral or R-curve data, which account for slow, stable fracture (ductile

tearing) rather than rapid (brittle) fracture.

Uses of Plane-Strain Fracture Toughness

K IC values are used to determine the critical crack length when a given stress is applied to a

component.

Where: sc is the critical applied stress that will cause failure

K IC is the plane-strain fracture toughness

Y is a constant related to the sample's geometry

ais the crack length for edge cracks

or one half crack length for internal crack

K IC values are used also used to calculate the critical stress value when a crack of a given length

is found in a component.



Where: ais the crack length for edge cracks

or one half crack length for internal crack

s is the stress applied to the material

K IC is the plane-strain fracture toughness

Y is a constant related to the sample's geometry

Orientation

The fracture toughness of a material commonly varies with grain direction. Therefore, it is

customary to specify specimen and crack orientations by an ordered pair of grain direction

symbols. The first letter designates the grain direction normal to the crack plane. The secondletter designates the grain direction parallel to the fracture plane. For flat sections of various

products, e.g., plate, extrusions, forgings, etc., in which the three grain directions are designated

(L) longitudinal, (T) transverse, and (S) short transverse, the six principal fracture path directionsare: L-T, L-S, T-L, T-S, S-L and S-T.

Fatigue Properties

Fatigue cracking is one of the primary damage mechanisms of structural components. Fatigue

cracking results from cyclic stresses that are below the ultimate tensile stress, or even the yield

stress of the material. The name “fatigue” is based on the concept that a material becomes “tired”and fails at a stress level below the nominal strength of the material. The facts that the original

bulk design strengths are not exceeded and the only warning sign of an impending fracture is an

often hard to see crack, makes fatigue damage especially dangerous.

The fatigue life of a component can be expressed as the number of loading cycles required toinitiate a fatigue crack and to propagate the crack to critical size. Therefore, it can be said that



fatigue failure occurs in three stages – crack initiation; slow, stable crack growth; and rapid

fracture.

As discussed previously, dislocations play a major role in the fatiguecrack initiation phase. In the first stage, dislocations accumulate near

surface stress concentrations and form structures called persistentslip bands (PSB) after a large number of loading cycles. PSBs are

areas that rise above (extrusion) or fall below (intrusion) the surfaceof the component due to movement of material along slip planes.

This leaves tiny steps in the surface that serve as stress risers where

tiny cracks can initiate. These tiny crack (called microcracks)nucleate along planes of high shear stress which is often 45o to the

loading direction.

In the second stage of fatigue, some of the tiny microcracks join

together and begin to propagate through the material in a direction that is perpendicular to the

maximum tensile stress. Eventually, the growth of one or a few crack of the larger cracks willdominate over the rest of the cracks. With continued cyclic loading, the growth of the dominate

crack or cracks will continue until the remaining uncracked section of the component can nolonger support the load. At this point, the fracture toughness is exceeded and the remaining

cross-section of the material experiences rapid fracture. This rapid overload fracture is the third

stage of fatigue failure.

Factors Affecting Fatigue Life

In order for fatigue cracks to initiate, three basic factors are necessary. First, the loading pattern

must contain minimum and maximum peak values with large enough variation or fluctuation.

The peak values may be in tension or compression and may change over time but the reverse

loading cycle must be sufficiently great for fatigue crack initiation. Secondly, the peak stresslevels must be of sufficiently high value. If the peak stresses are too low, no crack initiation will

occur. Thirdly, the material must experience a sufficiently large number of cycles of the appliedstress. The number of cycles required to initiate and grow a crack is largely dependant on the

first to factors.

In addition to these three basic factors, there are a host of other variables, such as stress

concentration, corrosion, temperature, overload, metallurgical structure, and residual stresseswhich can affect the propensity for fatigue. Since fatigue cracks generally initiate at a surface,

the surface condition of the component being loaded will have an effect on its fatigue life.

Surface roughness is important because it is directly related to the level and number of stress

concentrations on the surface. The higher the stress concentration the more likely a crack is tonucleate. Smooth surfaces increase the time to nucleation. Notches, scratches, and other stress

risers decrease fatigue life. Surface residual stress will also have a significant effect on fatigue

life. Compressive residual stresses from machining, cold working, heat treating will oppose atensile load and thus lower the amplitude of cyclic loading



The figure shows several types of loading that could initiate a fatigue crack. The upper left figure

shows sinusoidal loading going from a tensile stress to a compressive stress. For this type of

stress cycle the maximum and minimum stresses are equal. Tensile stress is considered positive,and compressive stress is negative. The figure in the upper right shows sinusoidal loading with

the minimum and maximum stresses both in the tensile realm. Cyclic compression loading canalso cause fatigue. The lower figure shows variable-amplitude loading, which might be

experienced by a bridge or airplane wing or any other component that experiences changingloading patterns. In variable-amplitude loading, only those cycles exceeding some peak threshold

will contribute to fatigue cracking.

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