Presentation on theme: "Mechanical Properties of Metals"— Presentation transcript:
1 Mechanical Properties of Metals Chapter 6 OutlineMechanical Properties of MetalsHow do metals respond to external loads?Stress and StrainTensionCompressionShearTorsionElastic deformationPlastic DeformationYield StrengthTensile StrengthDuctilityToughnessHardnessNot tested: true stress-true stain relationships, resilience, details of the different types of hardness tests, variability of material properties
2 How materials deform as a function of applied load IntroductionHow materials deform as a function of applied load Testing methods and language for mechanical properties of materials.Stress, (MPa)Strain, (mm / mm)
3 Types of Loading Tensile Compressive Shear Torsion Torsional forces (T) produce a rotational motion about the longitudinal axis of one end of the member relative to the otherShearTorsion
4 (For Tension and Compression) Stress(For Tension and Compression)To compare specimens , the load is calculated per unit area.Stress: = F / AoF: is loadA0: cross-sectional areaA0 perpendicular to F before application of the load.
5 Strain (For Tension and Compression) Strain: = l / lo ( 100 %)l: change in lengthlo: original length.Stress / strain = /
6 Shear and Torsion Shear stress: = F / Ao F is applied parallel to upper and lower faces each having area A0.Shear strain: = tan ( 100 %) is strain angleShearTorsion
7 Torsion Torsion: like shear. Load: applied torque, T Strain: angle of twist, .TorsionShear
8 Stress-Strain Behavior (Tension)Elastic PlasticElastic deformationReversible:( For small strains)Stress removed material returns to original sizePlastic deformationIrreversible:Stress removed material does not return to original dimensions.StressStrain
9 Higher E higher “stiffness” Elastic deformationGives Hooke's law for Tensile Stress = E E = Young's modulus or modulus of elasticity (same units as , N/m2 or Pa)UnloadSlope = modulus ofelasticity EStressLoadStrainHigher E higher “stiffness”
10 Nonlinear elastic behavior In some materials (many polymers, concrete...), elastic deformation is not linear, but it is still reversible./ = tangent modulus at 2Definitions of E/ = secant modulus between origin and 1
11 Elastic Deformation: Atomic scale Chapter 2: Potentials and ForceAttractive is positive hereHigh modulusStronglybondedForce, FSeparation, rLow modulusWeaklybondedE ~ (dF/dr) at roF= (sign) dV/dr E~ curvature of potentialat equilibrium, r0
12 (time dependence of elastic deformation) Anelasticity(time dependence of elastic deformation)Have assumed elastic deformation is time independent(applied stress produces instantaneous strain)Elastic deformation takes time; can continue even after load release.This behavior is known as anelasticity.Small effect in metals; can be significant for polymers (visco-elastic).
13 Poisson’s ratio Loaded Unloaded Tension shrink laterally Compression bulge.Ratio of lateral to axial strain calledPoisson's ratio .
14 Poisson’s ratio dimensionless. Sign: lateral strain opposite to longitudinal strainTheoretical value:for isotropic material: 0.25Maximum value: 0.50,Typical value:
15 = G , Shear Modulus Unloaded Loaded Shear stress to shear strain: ZoyUnloadedLoadedShear stress to shear strain:= G , = tan = y / zoG is Shear Modulus (Units: N/m2)
16 Elastic Modulus Poisson’s Ratio and Shear Modulus For isotropic material:E = 2G(1+) G ~ 0.4ESingle crystals are usually elastically anisotropicElastic behavior varies with crystallographic direction.
17 Plastic deformation (Tension) Plastic deformation: stress not proportional to straindeformation is not reversibledeformation occurs by breaking and re-arrangement of atomic bonds (crystalline materials by motion of defects)
18 Tensile properties: Yielding Elastic PlasticyYield point: PWhere strain deviates from being proportional to stress(the proportional limit)PStressStrainYield strength: y Permanent strain= 0.0020.002A measure of resistance to plastic deformation
19 Tensile properties: Yielding StressStrainFor a low-carbon steel, the stress vs. strain curve includes both an upper and lower yield point.The yield strength is defined in this case as the average stress at the lower yield point.
20 Tensile Strength Tensile strength = max. stress (~ 100 - 1000 MPa) If stress maintained specimen will breakFracture StrengthStress, “Necking”Tensile strength =max. stress(~ MPa)Strain, Yield stress, y , usually more important than tensile strength. Once yield stress has been passed, structure has deformed beyond acceptable limits.
21 Tensile properties: Ductility Ductility Deformation at Fracture Strain offset method to define the yield strengthDuctility Deformation at Fracturepercent elongationorpercent reduction in area
22 Mechanical Properties of Metals Yield strength and tensile strength vary with thermal and mechanical treatment, impurity levels, etc.Variability related to behavior of dislocations (Elastic moduli are relatively insensitive)Yield and tensile strengths and modulus of elasticity: Decrease with increasing temperature.Ductility increases with temperature.
23 ToughnessToughness: ability to absorb energy up to fracture (Area under the strain-stress curve up to fracture)Units: the energy per unit volume, e.g. J/m3Can be measured by an impact test (Chapter 8).
24 True Stress and Strain True Stress True Strain T = F/Ai T = ln(li/lo) = F/Ao = (li-lo/lo)True StrainTrue stress: load divided by actual area in the necked-down region, continues to rise to the point of fracture, in contrast to the engineering stress.
25 Elastic Recovery During Plastic Deformation Deformed plastically, stress released, material has permanent strain.If stress is reapplied, material again responds elastically at the beginning up to a new yield point that is higher than the original yield point.Elastic strain before reaching the yield point is called elastic strain recovery.
26 Hardness (I)Hardness measure of material’s resistance to localized plastic deformation(e.g. dent or scratch)Moh’s scale ability of a material to scratch another material: from 1 (softest = talc) to 10 (hardest = diamond).Variety of hardness tests(Rockwell, Brinell, Vickers, etc.). Small indenter (sphere, cone, or pyramid) forced into surface of material under controlled magnitude and rate of loading.Depth or size of indentation is measured.Tests are approximate, but popular because they are easy and non-destructive (except for the small dent).
27 Hardness proportional to tensile strength Hardness (II)Tensile strength (MPa)Tensile strength (103 psi)Brinell hardness numberTensile strength and hardness degree of resistance to plastic deformation.Hardness proportional to tensile strengthProportionality constant depends on material.
28 What are the limits of “safe” deformation? StressFor practical engineering design, the yield strength is usually the important parameterReliability is a big area… take into account economical, legal and other factors…StrainDesign stress:d = N’c : c = maximum anticipated stress,N’ the “design factor” > 1.Make sure d < y, safe or working stress:w = y/N where N is “factor of safety” > 1.
29 Summary Make sure you understand language and concepts: Anelasticity DuctilityElastic deformationElastic recoveryEngineering strainEngineering stressHardnessModulus of elasticityPlastic deformationPoisson’s ratioProportional limitShearTensile strengthToughnessYieldingYield strength
30 Reading for next class: Chapter 7: Dislocations and Strengthening MechanismsDislocations and Plastic DeformationMotion of dislocations in response to stressSlip SystemsPlastic deformation insingle crystalspolycrystalline materialsStrengthening mechanismsGrain Size ReductionSolid Solution StrengtheningStrain HardeningRecovery, Recrystallization, and Grain GrowthOptional reading (Part that is not covered / not tested):7.7 Deformation by twinningIn our discussion of slip systems, §7.4, we will not get into direction and plane nomenclature