PowerPoint Presentation

1Mechanical Properties of Metals

How do metals respond to external loads?

Stress and Strain Tension Compression Shear Torsion Elastic deformation

Plastic Deformation Yield Strength Tensile Strength Ductility Toughness HardnessChapter 6 OutlineNot tested: true stress-true stain relationships, resilience, details of the different types of hardness tests, variability of material propertiesIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering12How materials deform as a function of applied load Testing methods and language for mechanical properties of materials. Introduction

Stress, (MPa)Strain, (mm / mm)Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering23Types of Loading

TensileCompressive

ShearTorsionIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering3Torsional forces (T) produce a rotational motion about the longitudinal axis of one end of the member relative to the other4Stress(For Tension and Compression)To compare specimens , the load is calculated per unit area.

Stress: = F / Ao F: is loadA0: cross-sectional area

A0 perpendicular to F before application of the load.Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering45Strain(For Tension and Compression)

Strain: = l / lo ( 100 %)l: change in length lo: original length.

Stress / strain = /

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering6Shear and TorsionShear stress: = F / Ao F is applied parallel to upper andlower faces each having area A0.Shear strain: = tan ( 100 %) is strain angle

ShearTorsionIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering67TorsionTorsion: like shear.

Load: applied torque, T Strain: angle of twist, .

ShearTorsionIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering8Stress-Strain Behavior(Tension)

Elastic PlasticStressStrainElastic deformationReversible:( For small strains)Stress removed material returns to original size

Plastic deformationIrreversible: Stress removed material does not return to original dimensions.Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering89Elastic deformationE = Young's modulus or modulus of elasticity (same units as , N/m2 or Pa) Gives Hooke's law for Tensile Stress

StressStrainLoadSlope = modulus ofelasticity EUnload = E Higher E higher stiffnessIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering910Nonlinear elastic behaviorIn some materials (many polymers, concrete...), elastic deformation is not linear, but it is still reversible.

Definitions of E/ = tangent modulus at 2/ = secant modulus between origin and 1

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1011Elastic Deformation: Atomic scale Chapter 2: Potentials and Force

High modulusLow modulusE ~ (dF/dr) at roF= (sign) dV/dr E~ curvature of potentialat equilibrium, r0Separation, rWeaklybondedStronglybondedForce, FAttractive is positive hereIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1112Anelasticity(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).Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1213Poissons ratioTension shrink laterally Compression bulge.

Ratio of lateral to axial strain called Poisson's ratio .

UnloadedLoadedIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1314Poissons ratio

dimensionless.

Sign: lateral strain opposite to longitudinal strain

Theoretical value: for isotropic material: 0.25

Maximum value: 0.50, Typical value: 0.24 - 0.30Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering15Shear Modulus

Zoy

UnloadedLoadedShear stress to shear strain: = G , = tan = y / zoG is Shear Modulus (Units: N/m2)Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1516Elastic ModulusPoissons RatioandShear ModulusFor isotropic material:E = 2G(1+) G ~ 0.4E

Single crystals are usually elastically anisotropic

Elastic behavior varies with crystallographic direction.

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering17Plastic 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)

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1718Tensile properties: Yielding

Elastic PlasticStressStrainYield strength: y Permanent strain= 0.002 Yield point: PWhere strain deviates from being proportional to stress(the proportional limit)A measure of resistance to plastic deformationPy0.002Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1819Tensile 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. Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering1920Tensile Strength

Tensile strength = max. stress (~ 100 - 1000 MPa)If stress maintained specimen will breakFracture StrengthNeckingStress, Strain, Yield stress, y , usually more important than tensile strength. Once yield stress has been passed, structure has deformed beyond acceptable limits.Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2021Tensile properties: Ductilitypercent elongationor percent reduction in areaDuctility Deformation at Fracture

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering21Strain offset method to define the yield strength22Mechanical 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. Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2223Toughness

Toughness: 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/m3 Can be measured by an impact test (Chapter 8).Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2324True Stress and Strain

True 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. = F/Ao = (li-lo/lo)T = F/Ai T = ln(li/lo)True StrainTrue StressIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2425Elastic Recovery During Plastic DeformationDeformed 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.

y

y

Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2526Hardness (I)Hardness measure of materials resistance to localized plastic deformation (e.g. dent or scratch)

Mohs 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). Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2627Hardness (II)Tensile strength and hardness degree of resistance to plastic deformation.Hardness proportional to tensile strengthProportionality constant depends on material.

Tensile strength (MPa)Tensile strength (103 psi) Brinell hardness numberIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2728What are the limits of safe deformation?Design stress: d = Nc : 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.

For practical engineering design, the yield strength is usually the important parameterStrainStressIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering28Reliability is a big area take into account economical, legal and other factors29SummaryAnelasticity Ductility Elastic deformation Elastic recovery Engineering strain Engineering stress Hardness Modulus of elasticity Plastic deformation Poissons ratio Proportional limit Shear Tensile strength Toughness Yielding Yield strengthMake sure you understand language and concepts:Introduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering2930Reading for next class:Chapter 7: Dislocations and Strengthening Mechanisms

Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip Systems Plastic deformation in single crystals polycrystalline materials

Strengthening mechanisms Grain Size Reduction Solid Solution Strengthening Strain Hardening

Recovery, Recrystallization, and Grain Growth

Optional 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 nomenclatureIntroduction To Materials Science, Chapter 6, Mechanical Properties of MetalsUniversity of Virginia, Dept. of Materials Science and Engineering30