cven214- lecture 3 mechanical properties of materials -dr. wael alnahhal

7/25/2019 CVEN214- Lecture 3 Mechanical Properties of Materials -Dr. Wael Alnahhal

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COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL & ARCHITECTURAL ENGINEERING

CVEN 214: STRENGTH OF MATERIALS

WAEL I. ALNAHHAL, Ph. D., P. Eng

Spring, 2015

Chapter 3: MECHANICAL PROPERTIES OF MATERIAL


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The Tension and Compression Test

The strength of a material depends on its ability to

sustain a load without excessive deformation or failure.

Material strength is determined under the tension or

compression experiments.

Some machine are designed to read the load and strain

for a given a specimen.

Tension or compression experimentscan be used to

determine nominal stress-normal strain relationships

for engineering materials such as metals, ceramics,

polymers and composites materials such as reinforcedconcrete


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The Tension and Compression Test

Tension/Compression Testing Machines

Test Specimen


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The StressStrain Diagram

StressStrain Diagram

Nominal or engineering stress is obtained by

dividing the applied load P by the specimens original

cross-sectional area.

Nominal or engineering strain is obtained by

dividing the change in the specimens gauge length

by the specimens original gauge length.

0A

P=

0

0 0

L L

L L

= =


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The StressStrain Diagram Elastic Behaviour

Stress is directly proportional to the strain.

Material is said to be linearly elastic. Elasticityis the ability of a material to return to its previous shape

after stress is released

Yielding

Increase in stress aboveelastic limit will cause material to

deform permanently.

Plasticity or plastic deformation is

the opposite of elastic deformation andis accepted as unrecoverable strain

Most engineering design is done within the elastic range


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The StressStrain Diagram

Strain Hardening.

After yielding a further load will

reaches an ultimate stress or strength .

The ultimate strength is the maximum stress that a material can withstand

before material breaks or weakens

NeckingAt ultimate stress, cross-sectional

area begins to decrease in a

localized region of the specimen.

Specimen breaks at thefracture stress.


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Necking


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Ductile Materials

Material that can be subjected tolarge strains before it ruptures is

called a ductile material

Exhibit high plasticity

e.g plastic, copper

Brittle Materials

Materials that exhibit low strain,

little or no yielding before failureare referred to as brittle materials

Brittle material do not or exhibit

low plasticity

e.g ceramics, wood.

StressStrain Behavior of Ductile and Brittle Materials


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Stress-Strain Diagram for Steel


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Stress-strain diagram for a typical structural

steel in tension (not to scale)

Nominal stress and strain (in the

calculations we use the initial cross-sectional area A)

True stress (in the calculations we use thecross-sectional area A when failure occurs)

True strain if we use a strain gauge

Stress-strain diagrams contain importantinformation about mechanical propertiesand behaviour

Stress () strain () diagrams


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Stress () strain () diagrams-Mild Steel


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Compressive Strength of

Concrete

12

Compressive strength is determined by testinga 6x12 in(150x300 mm) cylinder at an age of28 days

The specified compressive strength of concreteis denoted by the symbol

'

cf

For most applications, the range of concretestrength is 3,000 to 4,000 psi (21 to 28MPa)


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Compression Test Setup for f"c


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Concrete Stress Strain

14


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15

The relationship between stress and strain isroughly linear at stress levels equal toabout one-third to one-half the ultimatestrength.Beyond thisrange the

relationshipis non-linear


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16

Regardless of compressive strength, allconcretesreach

theirmaximumstrengthat a strainof about0.002


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17

Concrete does not have a well-define yieldpoint.


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18

Ultimate strain achieved is on the order of0.003 to 0.004. Lower strength concreteachieveshigherultimatestrains than

does higherstrengthconcrete


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Plasticity

Plasticityis the characteristic of a material which undergoes inelastic strains beyond thestrain at the elastic limit

When large deformations occur in a ductile material loaded in the plastic region, thematerial is undergoingplastic flow


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Reloading of a material

If the material is in the elastic range, it can beloaded, unloaded and loaded again without

significantly changing the behaviourWhen loaded in the plastic range, the internalstructure of the material is altered and theproperties change

If the material is reloaded (fig 1-19), CB is a linearly

elastic region with the same slope as the slope of thetangent to the original loading curve at origin O

By stretching steel or aluminium into the plasticrange, the properties of the material are changed


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1.Modulus of Elasticity: Hookes Law The stress-strain diagrams for most engineering

materials exhibits a linear relationship between stress

and strain within the elastic region

Most engineering design is based on the elastic range


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Hookes Lawdefines the linear relationshipbetween stress and strain within the elastic

region.

Ecan be used only if a material has linearelastic behaviour.

E

=

= stress

E= modulus of elasticity or Youngs modulus (N/m2)

= strain

Modulus of Elasticity: Hookes Law:


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Offset method

When the yield point is not obvious,like in the previous case, and undergoeslarge strains, an arbitrary yield stresscan be determined by the offset method

The intersection of the offset line and

the stress-strain curve (point A) definesthe yield stress


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2. Modulus of Resilience: Strain Energy

When material is deformed by external loading, it will store energyinternally throughout its volume.

Energy is related to the strains called strain energy.

Modulus of Resilience

When stress reaches the proportional limit, the strain-energy density

is the modulus of resilience, ur.

2

21 1,

2 2

pl

r pl plu Nm

E

= =


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3. Modulus of Toughness: Strain Energy

Toughnessis also defined as the resistance tofracture of a material when stressed

Modulus of toughness, ut, represents the entire

area under the stressstrain diagram.

It indicates the strain-energy density of the material

just before it fractures.


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StressStrain Behavior of Ductile and Brittle Materials


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EXAMPLE 3.1


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EXAMPLE 3.1

(CONTINUED)


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4. Poissons Ratio

Poissons ratio, v, states that in the elastic range, theratio of its two strains is a constantsince the

deformations are proportional.

Negative sign since longitudinal elongation (positive

strain) causes lateral contraction (negative strain), and

vice versa.

lateral

longidudinal

v

= Poissons ratio is dimensionless.

Typical values are 1/3 or 1/4.


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Limitations

Poissons ratio is constant in the linearly elasticrange

Material must be homogeneous (samecomposition at every point)

Materials having the same properties in all

directions are called isotropic

If the properties differ in various directions thematerials called anisotropic


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SHEAR STRESS-STRAIN DIAGRAM

Strength parameter G Shear modulus of elasticity or themodules of rigidity

G is related to the modulus of elasticity E and Poissons ratiov.

G=

( )vE

G+

=

12


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EXAMPLE 3.4


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EXAMPLE 3.4

(CONTINUED)


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EXAMPLE 3.5


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EXAMPLE 3.5

(CONTINUED)


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EXAMPLE 3.6


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EXAMPLE 3.6

(CONTINUED)


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*Failure of Materials Due to Creep and Fatigue

Creep When material support a load for long period of time,

it will deform until a sudden fracture occurs.

This time-dependent permanent deformation is

known as creep.

Both stress and/or temperature play a significant role

in the rate of creep.

Creep strength will decrease

for higher temperatures or

higher applied stresses.


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*Failure of Materials Due to Creep and Fatigue

Fatigue When metal subjected to repeated cycles of stress

or strain, it will ultimately leads to fracture.

This behaviour is called fatigue.

Endurance or fatigue limitis a limit which no failure

can be detected after applying a load for a specified

number of cycles.

This limit can be

determined in S-N diagram.

cven214- lecture 3 mechanical properties of materials -dr. wael alnahhal

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