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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Chapter 6 Outline Mechanical 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 Hardness Not tested: true stress-true stain relationships, resilience, details of the different types of hardness tests, variability of material properties University of Virginia, Dept. of Materials Science and Engineering 1 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Introduction Stress, (MPa) How materials deform as a function of applied load Testing methods and language for mechanical properties of materials. Strain, (mm / mm) University of Virginia, Dept. of Materials Science and Engineering 2 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Types of Loading Tensile Compressive Shear Torsion University of Virginia, Dept. of Materials Science and Engineering 3 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Stress (For Tension and Compression) To compare specimens , the load is calculated per unit area. Stress: = F / Ao F: is load A0: cross-sectional area A0 perpendicular to application of the load. F before University of Virginia, Dept. of Materials Science and Engineering 4 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Strain (For Tension and Compression) Strain: = l / lo ( 100 %) l: change in length lo: original length. Stress / strain = / University of Virginia, Dept. of Materials Science and Engineering 5 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals 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 angle Shear Torsion University of Virginia, Dept. of Materials Science and Engineering 6 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Torsion Torsion: like shear. Load: applied torque, T Strain: angle of twist, . Torsion Shear University of Virginia, Dept. of Materials Science and Engineering 7 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Stress-Strain Behavior (Tension) Elastic Plastic Elastic deformation Reversible: Stress ( For small strains) Stress removed material returns original size to Plastic deformation Irreversible: Strain Stress removed material does not return to original dimensions. University of Virginia, Dept. of Materials Science and Engineering 8 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Elastic deformation Gives Hooke's law for Tensile Stress = E E = Young's modulus or modulus of elasticity (same units as , N/m2 or Pa) Stress Unload Slope = modulus of elasticity E Load Strain Higher E higher “stiffness” University of Virginia, Dept. of Materials Science and Engineering 9 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Nonlinear elastic behavior In some materials (many polymers, concrete...), elastic deformation is not linear, but it is still reversible. / = tangent modulus at 2 Definitions of E / = secant modulus between origin and 1 University of Virginia, Dept. of Materials Science and Engineering 10 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Elastic Deformation: Atomic scale Chapter 2: Potentials and Force Force, F High modulus Strongly bonded Attractive is positive here Separation, r Low modulus Weakly bonded E ~ (dF/dr) at ro F= (sign) dV/dr E~ curvature of potential at equilibrium, r0 University of Virginia, Dept. of Materials Science and Engineering 11 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals 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). University of Virginia, Dept. of Materials Science and Engineering 12 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Poisson’s ratio Unloaded Loaded Tension shrink laterally Compression bulge. Ratio of lateral to axial strain called Poisson's ratio . University of Virginia, Dept. of Materials Science and Engineering 13 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Poisson’s ratio y x z z dimensionless. Sign: lateral strain opposite to longitudinal strain Theoretical value: for isotropic material: 0.25 Maximum value: 0.50, Typical value: 0.24 - 0.30 University of Virginia, Dept. of Materials Science and Engineering 14 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Shear Modulus y Zo Unloaded Loaded Shear stress to shear strain: = G , = tan = y / zo G is Shear Modulus (Units: N/m2) University of Virginia, Dept. of Materials Science and Engineering 15 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Elastic Modulus Poisson’s Ratio and Shear Modulus For isotropic material: E = 2G(1+) G ~ 0.4E Single crystals are usually elastically anisotropic Elastic behavior varies with crystallographic direction. University of Virginia, Dept. of Materials Science and Engineering 16 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Plastic deformation (Tension) Plastic deformation: • stress not proportional to strain • deformation is not reversible • deformation occurs by breaking and rearrangement of atomic bonds (crystalline materials by motion of defects) University of Virginia, Dept. of Materials Science and Engineering 17 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Tensile properties: Yielding Elastic Plastic Stress y P Yield point: P Where strain deviates from being proportional to stress (the proportional limit) Strain Yield strength: y 0.002 Permanent strain= 0.002 A measure of resistance to plastic deformation University of Virginia, Dept. of Materials Science and Engineering 18 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Tensile properties: Yielding Stress Strain For 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. University of Virginia, Dept. of Materials Science and Engineering 19 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Tensile Strength If stress maintained specimen will break Stress, Fracture Strength “Necking” Tensile strength = max. stress (~ 100 - 1000 MPa) Strain, Yield stress, y , usually more important than tensile strength. Once yield stress has been passed, structure has deformed beyond acceptable limits. University of Virginia, Dept. of Materials Science and Engineering 20 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Tensile properties: Ductility Ductility Deformation at Fracture percent elongation or percent reduction in area lf l0 100 %EL l0 A0 Af 100 %RA A0 University of Virginia, Dept. of Materials Science and Engineering 21 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals 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. University of Virginia, Dept. of Materials Science and Engineering 22 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Toughness 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). University of Virginia, Dept. of Materials Science and Engineering 23 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals True Stress and Strain True Stress T = F/Ai T = ln(li/lo) = F/Ao = (li-lo/lo) True 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. University of Virginia, Dept. of Materials Science and Engineering 24 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Elastic Recovery During Plastic Deformation y y 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. University of Virginia, Dept. of Materials Science and Engineering 25 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals 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). University of Virginia, Dept. of Materials Science and Engineering 26 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Tensile strength (103 psi) Tensile strength (MPa) Hardness (II) Brinell hardness number Tensile strength and hardness degree of resistance to plastic deformation. Hardness proportional to tensile strength Proportionality constant depends on material. University of Virginia, Dept. of Materials Science and Engineering 27 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Stress What are the limits of “safe” deformation? For practical engineering design, the yield strength is usually the important parameter Strain Design 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. University of Virginia, Dept. of Materials Science and Engineering 28 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Summary Make sure you understand language and concepts: Anelasticity Ductility Elastic deformation Elastic recovery Engineering strain Engineering stress Hardness Modulus of elasticity Plastic deformation Poisson’s ratio Proportional limit Shear Tensile strength Toughness Yielding Yield strength University of Virginia, Dept. of Materials Science and Engineering 29 Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals Reading 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 twinning In our discussion of slip systems, §7.4, we will not get into direction and plane nomenclature University of Virginia, Dept. of Materials Science and Engineering 30