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Mechanical PropertiesThe adaptability of a material to a particular use is determined by its mechanical properties.Properties are affected by
Bonding typeCrystal StructureImperfectionsProcessing
Learning Objectives
Define engineering stress and engineering strain.State Hooke’s law, and note the conditions under which it is valid.Given an engineering stress–strain diagram, determine (a) the modulus of elasticity, (b) the yield strength (0.002 strain offset), and (c) the tensile strength, and (d) estimate the percent elongation.Name the two most common hardness-testing techniques; note two differences between them.Define the differences between ductile and brittle materials.State the principles of impact, creep and fatigue testing.State the principles of the ductile-brittle transition temperature.
Types of Mechanical TestingSlow application of stress
Allows dislocations to move to equilibrium positionsTensile testing
Rapid application of stressAbility of a material to absorb energy as it fails. Does not allow dislocations to move to equilibrium positions.Impact testing
Fracture ToughnessHow does a material respond to cracks and flaws
FatigueWhat happens when loads are cycled?
High Temperature LoadsCreep
Some DefinitionsTensile stress:Where F: force, normal to the cross-sectional area,
A0: original cross-sectional area0AF
=σ
Shear StressFs: force, parallel to the cross-
sectional area A0: the cross-sectional areaunit of stress:
0AFs=τ
2mN
areaForce
=1Pa = 1 Nm-2;
1MPa = 106Pa; 1GPa=109Pa
Engineering StrainNominal tensile strain (Axial strain)
00
0
ll
lll ∆
=−
=ε
For small strain:
θγ tan=
θγ ≅
Engineering Shear Strain
Poisson’s ratio
z
zz l
l
0
∆=ε
x
xx l
l
0
∆−=ε
z
x
straintensilestrainlateral
εε
−=−=
p
pp
p
V-∆VVV∆
=∆
Nominal lateral strain (transverse strain)
Poisson’s ratio: ν
Dilatation (Volume strain)Under pressure: the volume will change
σ
ε
E
Elastic Behavior of Materials(Hooke’s Law)
When strains are small, most of materials are linear elastic.
Young’s modulus
Tensile: σ = Ε ε
Shear: τ = G γ
Hydrostatic: – p = κ ∆
Shear modulus
Bulk modulus
Modulus of Elasticity - Metals
Modulus of Elasticity - Ceramics
Modulus of Elasticity - Polymers
0.01-0.1Rubbers
1-5Polyesters
2-4Nylon
3-3.4Polystyrene (PS)
0.2-0.7Polyethylene (PE)
Elastic Modulus (GPa)Polymers
Physical Basis of Young’s Modulus
dxdUF =Review: Inter-atomic forces (attractive and repulsive forces)
002
2
0 xxxx dxdF
dxUdS == ==
Define: stiffness
Assume the strain is small,
)(
)(
000
00
rrNSAF
rrSF
−==
−≈
σ
Where N: number of bonds/unit area, N=1/r02
σ σ
Unit area
εεσ ErS
rrr
rS
==−
=0
0
0
0
0
0 )(
Young’s modulus0
0 )(rrr −
=εQo
o
rSE ==
εσ
Stiffness & Young’s Modulus for different bonds
2-40.5-1Van der Waals
8-122-3Hydrogen
60-30015-75Metallic
200-100050-180Covalent (i.e: C-C)
32-968-24Ionic(i.e: NaCl)
E(GPa)S0(Nm-1)Bonding type
Material E (GPa)Metals: 60 ~ 400Ceramics: 10 ~ 1000Polymers: 0.001 ~ 10
Tensile Testing• The sample is pulled slowly• The sample deforms and then fails• The load and the deformation are measured
Standard tensile specimenThe load and deformation are easily transform into engineering stress (σ) and engineering strain (ε)
A curve stress-strain is obtained 0AF
=σ00
0
ll
lll ∆
=−
=ε
Parameters Obtained From Stress Strain CurveStrength Parameters
Modulus of ElasticityYield StrengthUltimate Tensile StrengthFracture StrengthFracture Energy
Ductility ParametersPercent ElongationPercent Reduction of AreaStrain Hardening Parameter
Modulus of ElasticityIt is a measure of material stiffness and relates
stress to strain in the linear elastic range.
12
12
ε−εσ−σ
=δεδσ
=E
Yielding and Yield Strength
Proportionality Limit (P): Departure from linearity of the stress-strain curveYielding Point – Elastic Limit: the turning point which separate the elastic and plastic regions –onset of plastic deformationYield strength: the stress at the yielding point.Offset yielding (proof stress): if it is difficult to determine the yielding point, then draw a parallel line starting from the 0.2% strain, the cross point between the parallel line and the σ−ε curve
Prior to TS, the stress in the specimen is uniformly distributed.After TS, necking occurs with localization of the deformation to the necking area, which will rapidly go to failure.
Tensile Strength (TS)
The stress increases after yielding until a maximum is reached. It is also known as the Ultimate Tensile Strength (UTS), or Maximum Uniform Strength.
Fracture Strength
o
ff AP
=σ
σf
Elastic RecoveryAfter a load is released from a
stress-strain test, some of the total deformation is recovered as elastic deformation.
During unloading, the curve traces a nearly identical straight line path from the unloading point parallel to the initial elastic portion of the curve
The recovered strain is calculated as the strain at unloading minus the strain after the load is totally released.
ResilienceResilience is the capacity of a material to absorb energy when it is deformed
elastically and then, upon unloading, to have this energy recovered.
∫=y dUr
εεσ
0Modulus of resilience UrIf it is in a linear elastic region,
EEU yyyyyr 22
121 2σσσεσ =
==
Ductility
100*)(%0
0
lll f −=EL
100*)(%0
0
AAA f−=AR
Ductility is a measure of the degree of plastic deformation at fracture
expressed as percent elongation
also expressed as percent area reduction
lO and AO are the original gauge length and original cross-section area respectively
lf and Af are length and area at fracture
Percentage elongation and percentage area reduction are UNITLESS
A smaller gauge length will produce a larger overall %elongation due to the contribution from necking. Therefore %elongation should be reported with original gauge length.
%Reduction is not affected by sample size, thus it is a better measure of ductility