week 4 mechanical properties and tests
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Week 4 MECHANICAL PROPERTIES AND TESTS. Materials Science. Stress. Stress is a measure of the intensity of the internal forces acting within a deformable body. Mathematically, it is a measure of the average force per unit area of a surface within a the body on which internal forces act - PowerPoint PPT PresentationTRANSCRIPT
MATERIALS SCIENCE
Week 4MECHANICAL
PROPERTIES AND TESTS
Stress
Stress is a measure of the intensity of the internal forces acting within a deformable body.
Mathematically, it is a measure of the average force per unit area of a surface within a the body on which internal forces act
The SI unit for stress is Pascal (symbol Pa), which is equivalent to one Newton (force) per square meter (unit area).
Three types of stresses -> Tensile; Compressive; Shear
Mechanism of Stress (Tensile)
Strain
Strain is deformation of a physical body under the action of applied forces
It is the geometrical measure of deformation representing the relative displacement between particles in the material body
Strain is a dimensionless quantityStrain accounts for elongation, shortening, or
volume changes, or angular distortionNormal stress causes normal strain (tensile or
compressive)Shear strain is defined as the change in angle
between two originally orthogonal material lines
Types of Strains
tensile load producesan elongation andpositive linearstrain.
compressive loadproduces contractionand a negative linearstrain.
torsionaldeformation
TENSILE TEST AND STRESS-STRAIN RELATIONSHIP
Tensile Test
Used for determining UTS, yield strength, %age elongation, and Young’s Modulus of Elasticity
The ends of a test piece are fixed into grips. The specimen is elongated by the moving crosshead; load cell and extensometer measure, respectively, the magnitude of the applied load and the elongation
Stress-Strain Relationship
Important Terms (Stress-Strain Rel.)
Elastic Limit -> Maximum amount of stress up to which the deformation is absolutely temporary
Proportionality Limit -> Maximum stress up to which the relationship between stress & strain is linear.
Hooke’s Law -> Within elastic limit, the strain produced in a body is directly proportional to the stress applied.
σ = E ε
Important Terms (Stress-Strain Rel.)
Young’s Modulus of elasticity -> the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds
Elasticity -> the tendency of a body to return to its original shape after it has been stretched or compressed
Yield Point -> the stress at which a material begins to deform plastically
Important Terms (Stress-Strain Rel.)
Plasticity -> the deformation of a material undergoing non-reversible changes of shape in response to applied forces
Ultimate Strength -> It is the maxima of the stress-strain curve. It is the point at which necking will start.
Necking -> A mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material
Important Terms (Stress-Strain Rel.)
Fracture Point -> The stress calculated immediately before the fracture.
Ductility -> The amount of strain a material can endure before failure.
Ductility is measured by percentage elongation or area reduction
Important Terms (Stress-Strain Rel.)
A knowledge of ductility is important for two reasons:
1.It indicates to a designer the degree to which a structure will deform plastically before fracture.
2.It specifies the degree of allowable deformation during fabrication
Engineering stress– strain behavior for Iron at three temperatures
Resilience
Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered
Modulus of Resilience (Ur) is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.
Resilience
Assuming a linear elastic region
For SI units, this is joules per cubic meter (J/m3, equivalent to Pa)
Thus, resilient materials are those having high yield strengths and low moduli of elasticity; such alloys would be used in spring applications
Shear and Torsional Tests
Shear Stress:
The shear strain γ is defined as the tangent of the strain angle θTorsion is a variation of pure shear, wherein a structural member is twisted in the manner of the figureTorsional stress -> The shear stress on a transverse cross section resulting from a twisting actionTorsional forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end
ANELASTICITY
In most engineering materials, there also exists a time-dependent elastic strain component.
This time-dependent elastic behavior is known as anelasticity
For metals the anelastic component is normally small and is often neglected
For some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior
EXAMPLE PROBLEM 6.1
A piece of copper originally 305mm (12 in.) long is pulled in tension with a stress of 276MPa (40,000psi). If the deformation is entirely elastic, what will be the resultant elongation?
Magnitude of E for copper from Table 6.1 is 110GPa
Poisson’s Ratio
Poisson’s ratio is defined as the ratio of the lateral and axial strains
Theoretically, Poisson’s ratio for isotropic materials should be 1/4; furthermore, the maximum value for ν is 0.50
For isotropic materials, shear and elastic moduli are related
EXAMPLE PROBLEM 6.2
A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10mm. Determine the magnitude of the load required to produce a 0.0025mm change in diameter if the deformation is entirely elastic.
For the strain in the x direction:
EXAMPLE PROBLEM 6.2
True Stress and Strain
The decline in the stress necessary to continue deformation past the point M, indicates that the metal is becoming weaker.
Material is increasing in strength.True stress σT is defined as the
load F divided by the instantaneous cross-sectional area Ai over which deformation is occurring
True strain ЄT is defined as:
True Stress and Strain
If no volume change occurs during deformation—that is, if Aili = A0l0
Then true and engineering stress and strain are related according to
The equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, cross-sectional area, and gauge length measurements
Assignment
(a) Completely describe “Compression Test”. (b) How is it different from Tensile test? (c) What are the effects of Friction and Workpiece’s height-to-diameter ratio on the test? (d) Derive relationship between true stress/strain and engineering stress/strain for compression test (also show by stress-strain curve)
Only hand-written assignments
EXAMPLE PROBLEM 6.4
A cylindrical specimen of steel having an original diameter of 12.8mm is tensile tested to fracture and found to have an engineering fracture strength σf of 460MPa. If its cross-sectional diameter at fracture is 10.7mm, determine:
(a) The ductility in terms of percent reduction in area(b) The true stress at fractureDuctility is computed as
EXAMPLE PROBLEM 6.4
True stress is defined by Equationwhere the area is taken as the fracture area Af
However, the load at fracture must first be computed from the fracture strength as
And the true stress is calculated as
Elastic Recovery after Plastic Deformation
Upon release of the load during the course of a stress–strain test, some fraction of the total deformation is recovered as elastic strain
During the unloading cycle, the curve traces a near straight-line path from the point of unloading (point D), and its slope is virtually parallel to the initial elastic portion of the curve
The magnitude of this elastic strain, which is regained during unloading, corresponds to the strain recovery
Hardness
Hardness is the property of material by virtue of which it resists against surface indentation and scratches.
Macroscopic hardness is generally characterized by strong intermolecular bonds
Hardness is dependent upon strength and ductility
Common examples of hard matter are diamond, ceramics, concrete, certain metals, and superhard materials (PcBN, PcD, etc)
Hardness Tests (BRINELL HARDNESS TEST)
Used for testing metals and nonmetals of low to medium hardness
The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece
A hardened steel (or cemented carbide) ball of 10mm diameter is pressed into the surface of a specimen using load of 500, 1500, or 3000 kg.
BRINELL HARDNESS TEST
where:P = applied force (kgf) D = diameter of indenter
(mm) d = diameter of indentation
(mm)The resulting BHN has
units of kg/mm2, but the units are usually omitted in expressing the numbers
Rockwell Hardness Test
Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a preload
A cone shaped indenter or small diameter ball (D = 1.6 or 3.2mm) is pressed into a specimen using a minor load of 10kg
Then, a major load of 150kg is appliedThe additional penetration distance d is
converted to a Rockwell hardness reading by the testing machine.
Rockwell Hardness Test
Vickers Hardness Test
Uses a pyramid shaped indenter made of diamond.It is based on the principle that impressions made
by this indenter are geometrically similar regardless of load.
The basic principle, as with all common measures of hardness, is to observe the questioned material's ability to resist plastic deformation from a standard source.
Accordingly, loads of various sizes are applied, depending on the hardness of the material to be measured
Vickers Hardness Test
Where:F = applied load (kg)D = Diagonal of the impression
made the indenter (mm)The hardness number is
determined by the load over the surface area of the indentation and not the area normal to the force
Knoop Hardness Test
It is a microhardness test - a test for mechanical hardness used particularly for very brittle materials or thin sheets
A pyramidal diamond point is pressed into the polished surface of the test material with a known force, for a specified dwell time, and the resulting indentation is measured using a microscope
Length-to-width ratio of the pyramid is 7:1
Knoop Hardness Test (contd…)
The indenter shape facilitates reading the impressions at lighter loads
HK = Knoop hardness value; F = load (kg); D = long diagonal of the impression (mm)
Hardness of Metals and Ceramics
Hardness of Polymers
TOUGHNESS
It is a property of material by virtue of which it resists against impact loads.
Toughness is the resistance to fracture of a material when stressed
Mathematically, it is defined as the amount of energy per volume that a material can absorb before rupturing
Toughness can be determined by measuring the area (i.e., by taking the integral) underneath the stress-strain curve
Toughness (contd…)
Toughness =
Whereε is strainεf is the strain upon failureσ is stressThe Area covered under
stress strain curve is called toughness
Toughness (contd…)
Toughness is measured in units of joules per cubic meter (J/m3) in the SI system
Toughness and Strength -> A material may be strong and tough if it ruptures under high forces, exhibiting high strains
Brittle materials may be strong but with limited strain values, so that they are not tough
Generally, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupture
Effect of Temperature on Properties
Generally speaking, materials are lower in strength and higher in ductility, at elevated temperatures
Hot Hardness
A property used to characterize strength and hardness at elevated temperatures is Hot Hardness
It is the ability of a material to retain its hardness at elevated temperatures
Numerical Problems
Problems 6.3 to 6.9; 6.14 to 6.23; 6.25 to 6.33; 6.46 to 6.48