Stress and Strain
- Normal stress: sigma = F/A (force per unit area, Pa or psi)
- Normal strain: epsilon = delta_L / L0 (change in length over original length)
- Shear stress: tau = V/A (shear force per unit area)
- Shear strain: gamma = delta_x / L (angular deformation)
- Hooke's law: sigma = E * epsilon (E = Young's modulus)
- Shear: tau = G * gamma (G = shear modulus)
- Poisson's ratio: nu = -(lateral strain) / (axial strain)
- Relationship: G = E / [2*(1+nu)]
Mechanical Properties
- Yield strength: stress at onset of permanent deformation (0.2% offset method)
- Ultimate tensile strength (UTS): maximum stress on engineering stress-strain curve
- Ductility: percent elongation = (Lf - L0)/L0 * 100
- Resilience: energy absorbed up to yield (area under elastic region)
- Toughness: total energy absorbed to fracture (total area under curve)
- Hardness: resistance to indentation (Brinell, Rockwell, Vickers scales)
Crystal Structures
- BCC (body-centered cubic): 2 atoms/cell, coordination number 8 (Fe, W, Cr)
- FCC (face-centered cubic): 4 atoms/cell, coordination number 12 (Al, Cu, Au, Ni)
- HCP (hexagonal close-packed): 6 atoms/cell, coordination number 12 (Zn, Mg, Ti)
- APF (atomic packing factor): BCC = 0.68, FCC = 0.74, HCP = 0.74
- Lattice parameter to atomic radius: BCC: a = 4r/sqrt(3); FCC: a = 2r*sqrt(2)
Phase Diagrams
- Iron-carbon diagram: key for steel and cast iron
- Eutectic: liquid transforms to two solid phases simultaneously
- Eutectoid: one solid transforms to two different solids (austenite to pearlite at 727 C, 0.76% C)
- Lever rule: weight fraction = (opposite arm) / (total tie line length)
- Phase: alpha-ferrite (BCC, <0.022% C), austenite/gamma (FCC, up to 2.14% C), cementite (Fe3C, 6.67% C)
Failure Theories
- Maximum normal stress theory (Rankine): failure when sigma_max >= S_ut or sigma_min <= -S_uc
- Maximum shear stress theory (Tresca): failure when tau_max >= S_y/2
- Von Mises (distortion energy): failure when sigma_vm >= S_y
- sigma_vm = sqrt(sigma1^2 - sigma1*sigma2 + sigma2^2) for biaxial stress
- Fatigue: S-N curve, endurance limit (ferrous metals ~0.5*S_ut)
- Creep: time-dependent deformation at elevated temperatures
Thermal Properties
- Thermal expansion: delta_L = alpha * L0 * delta_T
- Thermal conductivity: q = -k * dT/dx (Fourier's law)
- Thermal stress: sigma = E * alpha * delta_T (when constrained)
- Specific heat: Q = m * c * delta_T