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 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linear- elastic Non-Linear- elastic d Elastic means reversible!
Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds p lanes stretch still & planes sheared shear d plastic d elastic + plastic F F linear linear elastic elastic d d plastic Plastic means permanent!
Forces and Responses • Tensile – applied loads “pull” the sample
F • Hooke's Law: s s = Ee E F e simple Linear- tension test elastic Linear Elastic Properties • Modulus of Elasticity, E: (also known as Young's modulus)
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 t G g • Special relation for isotropic materials: E = G 2(1+n) • Elastic Shear modulus, G: t = Gg
eL e e n - L n = - e Poisson's ratio, n • Poisson's ratio, n: metals: n ~ 0.33ceramics: n~ 0.25polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: dimensionless
TS F = fracture or ultimate strength Neck – acts as stress concentrator y stress engineering Typical response of a metal strain engineering strain (Ultimate) Tensile Strength, TS • Maximum stress on engineering stress-strain curve. 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 small toughness (ceramics) E ngineering tensile large toughness (metals) s stress, very small toughness Adapted from Fig. 6.13, Callister 7e. (unreinforced polymers) e Engineering tensile strain, • 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 Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy
Toughness • Impact (toughness) – applied loads “hit” the sample • Impact (charpy, dart)
1 @ s e U r y y 2 Resilience, Ur • Ability of a material to store energy • Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to 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.
s s large hardening y 1 s y small hardening 0 e hardening exponent: ( ) n n = 0.15 (some steels) s = e K T T to n = 0.5 (some coppers) “true” strain: ln(L/Lo) “true” stress (F/A) Hardening • An increase in sy due to plastic deformation. • Curve fit to the stress-strain response:
Stress-Strain Diagram ultimate tensile strength 3 necking Strain Hardening Slope=E 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)
apply known force measure size e.g., of indent after 10 mm sphere removing load Smaller indents d D mean larger hardness. most brasses easy to machine cutting nitrided plastics Al alloys steels file hard tools steels diamond increasing hardness Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. Adapted from Fig. 7.18.
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 where n is the number of data points
Property Variability and Design/Safety Factors Average and standard deviation c07f32
Design or Safety Factors d 1045 plain carbon steel: L o s = 310 MPa y 5 TS = 565 MPa F = 220,000N • 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. 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.