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

How materials deform as a function of applied load  Introduction How materials deform as a function of applied load  Testing methods and language for mechanical properties of materials. Stress,  (MPa) Strain,  (mm / mm)

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 other Shear Torsion

(For Tension and Compression) 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 F before application of the load.

Strain (For Tension and Compression) Strain:  = l / lo ( 100 %) l: change in length lo: original length. Stress / strain = / 

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

Torsion Torsion: like shear. Load: applied torque, T Strain: angle of twist, . Torsion Shear

Stress-Strain Behavior (Tension) Elastic Plastic Elastic deformation Reversible: ( For small strains) Stress removed  material returns to original size Plastic deformation Irreversible: Stress removed  material does not return to original dimensions. Stress Strain

Higher E  higher “stiffness” 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) Unload Slope = modulus of elasticity E Stress Load Strain Higher E  higher “stiffness”

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

Elastic Deformation: Atomic scale Chapter 2: Potentials and Force Attractive is positive here High modulus Strongly bonded Force, F Separation, r Low modulus Weakly bonded E ~ (dF/dr) at ro F= (sign) dV/dr  E~ curvature of potential at equilibrium, r0

(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).

Poisson’s ratio Loaded Unloaded Tension  shrink laterally Compression  bulge. Ratio of lateral to axial strain called Poisson's ratio .

Poisson’s ratio dimensionless. Sign: lateral strain opposite to longitudinal strain Theoretical value: for isotropic material: 0.25 Maximum value: 0.50, Typical value: 0.24 - 0.30

= G , Shear Modulus Unloaded Loaded Shear stress to shear strain: Zo y  Unloaded Loaded Shear stress to shear strain: = G ,  = tan = y / zo G is Shear Modulus (Units: N/m2)

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.

Plastic deformation (Tension) Plastic deformation: stress not proportional to strain deformation is not reversible deformation occurs by breaking and re-arrangement of atomic bonds (crystalline materials by motion of defects)

Tensile properties: Yielding Elastic Plastic y Yield point: P Where strain deviates from being proportional to stress (the proportional limit) P Stress Strain Yield strength: y Permanent strain= 0.002 0.002 A measure of resistance to plastic deformation

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.

Tensile Strength Tensile strength = max. stress (~ 100 - 1000 MPa) If stress maintained specimen will break Fracture Strength Stress,  “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.

Tensile properties: Ductility Ductility  Deformation at Fracture Strain offset method to define the yield strength Ductility  Deformation at Fracture percent elongation or percent reduction in area

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.

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).

True Stress and Strain True Stress True Strain 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.

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.

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).

Hardness proportional to tensile strength Hardness (II) Tensile strength (MPa) Tensile strength (103 psi) Brinell hardness number Tensile strength and hardness  degree of resistance to plastic deformation. Hardness proportional to tensile strength Proportionality constant depends on material.

What are the limits of “safe” deformation? Stress For practical engineering design, the yield strength is usually the important parameter Reliability is a big area… take into account economical, legal and other factors… 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.

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

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