Mechanical Properties • Stress and strain: What are they and why are they used instead of load and deformation? • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? • Hardness: What is hardness of a material and how do we measure it?

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

Elastic Deformation d F F d 1. Initial 2. Small load 3. Unload bonds stretch return to initial F d Linear- elastic Non-Linear- Elastic means reversible!

Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload p lanes still sheared F d elastic + plastic bonds stretch & planes shear plastic F d linear elastic plastic Plastic means permanent!

Tensile – applied loads “pull” the sample Forces and Responses Tensile – applied loads “pull” the sample

Linear Elastic Properties • Modulus of Elasticity, E: (also known as Young's modulus) F simple tension test • Hooke's Law: s = E e s Linear- elastic E e

Tensile Forces Gripping Zone Gripping Zone Failure Zone ¾ inch ½ inch 8 ½ inches

Forces and Responses Compression: applied loads “squeeze” the sample

Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 6.7, Callister 7e.

Other Elastic Properties • Elastic Shear modulus, G: t G g t = G g • Special relation for isotropic materials: 2(1 + n) E G =

Poisson's ratio, n e n = - eL e - n • Poisson's ratio, n: Units: metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 eL e - n Units: E: [GPa] or [psi] n: dimensionless

Plastic Deformation

(Ultimate) Tensile Strength, TS • Maximum stress on engineering stress-strain curve. y strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain Adapted from Fig. 6.11, Callister 7e.

Ductility Measures how much the material can be stretched before fracture High ductility: platinum, steel, copper Good ductility: aluminum Low ductility (brittle): chalk, glass, graphite

Ductility (%EL and %RA) • Plastic tensile strain at failure: Adapted from Fig. 6.13, Callister 7e.

Toughness • The ability to absorb energy up to fracture = the total area under the strain-stress curve up to fracture Units: the energy per unit volume, e.g. J/m3 very small toughness (unreinforced polymers) Engineering tensile strain, e E ngineering tensile stress, s small toughness (ceramics) large toughness (metals) Adapted from Fig. 6.13, Callister 7e. Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

Toughness Impact (toughness) – applied loads “hit” the sample Impact (charpy, dart)

Resilience, Ur 2 1 U e s @ Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @ Adapted from Fig. 6.15, Callister 7e.

True Stress & Strain True stress True Strain Adapted from Fig. 6.16, Callister 7e.

Elastic Solid Stress-strain What happens when force is removed? Recovery

Elastic Strain Recovery Adapted from Fig. 6.17, Callister 7e.

( ) Hardening s e • An increase in sy due to plastic deformation. large hardening small hardening y 1 • Curve fit to the stress-strain response: s T = K e ( ) n “true” stress (F/A) “true” strain: ln(L/Lo) hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)

Stress-Strain Diagram ultimate tensile strength 3 necking Slope=E Strain Hardening yield strength Fracture 5 2 Elastic region slope =Young’s (elastic) modulus yield strength Plastic region ultimate tensile strength strain hardening fracture Plastic Region Stress (F/A) Elastic Region 4 1 Strain ( ) (DL/Lo)

Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. e.g., 10 mm sphere apply known force measure size of indent after removing load d D Smaller indents mean larger hardness. increasing hardness most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided diamond Adapted from Fig. 7.18.

Hardness Testers

Hardness: Measurement Rockwell No major sample damage Each scale runs to 130 but only useful in range 20-100. Minor load 10 kg Major load 60 (A), 100 (B) & 150 (C) kg A = diamond, B = 1/16 in. ball, C = diamond HB = Brinell Hardness TS (MPa) = 3.45 x HB TS (psi) = 500 x HB

Conversion of Hardness Scales c07f30 Also see: ASTM E140 - 07 Volume 03.01 Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness

Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation All samples have same value Because of large variability must have safety margin in engineering specifications where n is the number of data points

c07f32 Property Variability and Design/Safety Factors Average and standard deviation c07f32

Design or Safety Factors • Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is between 1.2 and 4 • Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 1045 plain carbon steel: s y = 310 MPa TS = 565 MPa F = 220,000N d L o 5 d = 0.067 m = 6.7 cm

Summary • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure.