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MAT-00 · laboratory

Materials

Hooke, Hall–Petch, Arrhenius, Paris law and the lever rule.

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34 governing sheets

MAT-01
Hooke's law
σ = E ε in the linear elastic regime.
Elasticity
MAT-02
Hall–Petch grain-size strengthening
σy = σ0 + ky / √d.
Strengthening
MAT-03
Arrhenius rate
k = A exp(−Ea /(R T)) for thermally activated processes.
Kinetics
MAT-04
Paris crack-growth law
da/dN = C (ΔK)^m in the mid-ΔK regime.
Fracture
MAT-05
Lever rule
Wα = (Cβ − C0)/(Cβ − Cα) for a two-phase alloy.
Phase diagrams
MAT-06
True stress from engineering
σt = σe (1+εe) at constant volume.
Plasticity
MAT-07
Griffith brittle-fracture stress
σf = √(2 E γ /(π a)) for a through crack.
Fracture
MAT-08
Mohr–Coulomb failure
τ = c + σ tan φ on the failure plane.
Failure
MAT-21
Hall–Petch grain-size strengthening
σy = σ0 + ky / √d. Yield rises as grains shrink.
Strengthening
MAT-22
Paris crack-growth law
da/dN = C (ΔK)^m in the mid-ΔK regime.
Fracture
MAT-23
Lever rule
Wα = (Cβ − C0)/(Cβ − Cα) for a two-phase alloy.
Phase diagrams
MAT-24
True stress from engineering
σt = σe (1+εe), εt = ln(1+εe) at constant volume.
Plasticity
MAT-25
Considère necking strain
For Hollomon σ = K ε^n, necking starts at εt = n. Load maximum dP = 0.
Plasticity
MAT-26
Norton power-law creep
ε̇ = A σ^n. Secondary (steady) creep rate.
Creep
MAT-27
Fracture toughness KIc
KIc = Y σ √(π a). Critical stress-intensity in mode I.
Fracture
MAT-28
Taylor dislocation forest
τ = α G b √ρ. Forest hardening from dislocation density.
Strengthening
MAT-29
Bragg diffraction
n λ = 2 d sinθ. Constructive interference from crystal planes.
Crystallography
MAT-30
Fick first-law flux
J = −D (c2−c1)/Δx. Steady diffusion down a concentration gradient.
Diffusion
MAT-31
Linear thermal expansion
ΔL = α L ΔT. Length change from a temperature step.
Elasticity
MAT-32
Poisson ratio
ν = −εlat / εlong. Lateral contraction over axial stretch.
Elasticity
MAT-33
Bulk modulus K=E/3(1−2ν)
K = E / [3(1−2ν)]. Volumetric stiffness of an isotropic solid.
Elasticity
MAT-34
Shear modulus G=E/2(1+ν)
G = E / [2(1+ν)]. The isotropic relation between E, G and ν.
Elasticity
MAT-35
Endurance-limit estimate
Se ≈ 0.5 Sut · ka kb kc. Marin factors on a rotating-beam limit.
Fatigue
MAT-36
Hollomon hardening
σ = K ε^n. Power-law true stress–strain in the plastic range.
Plasticity
MAT-37
Larson–Miller parameter
P = T (C + log10 tr) / 1000. Time–temperature collapse of rupture data.
Creep
MAT-38
Orowan looping stress
τ = G b / λ. Bypass of impenetrable particles by dislocation loops.
Strengthening
MAT-39
True strain
Logarithmic strain.
Governing
MAT-40
Considère necking
Necking when n equals true strain for Hollomon.
Governing
MAT-41
Norton creep
Steady-state power-law creep.
Governing
MAT-42
Griffith crack
Brittle fracture of a through-crack.
Governing
MAT-43
Hall–Petch
Grain-size strengthening.
Governing
MAT-44
Rule of mixtures
Isostrain composite modulus.
Governing
MAT-09
Hooke's law
σ = E ε in the linear elastic range.
Mechanics of materials
MAT-10
Arrhenius rate
k = A exp(−Ea / RT). Thermal activation over a barrier Ea.
Mechanics of materials