Predicts crack propagation in brittle materials when released potential energy exceeds surface energy. Critical for glass, ceramics, and concrete failure analysis.
σ = √[(2 × γₛ × E) / (π × a)]
Breaking strength for brittle fracture
Quantifies stress field near crack tip using stress intensity factor K. Essential for bridge ties, aircraft structures, and pressure vessel integrity assessment.
K₁ = σ × √(π × a)
F_max = (K_IC / √(π × a)) × Area
Mode I opening stress intensity
Predicts fatigue crack growth rate under cyclic loading. Fundamental for aircraft maintenance schedules, rotating machinery, and component lifespan estimation.
da/dN = A × (ΔK)^m
ΔK = Δσ × √(π × a)
Crack growth per loading cycle
Predicts yielding in ductile materials based on distortion energy. Widely used in ASME pressure vessel codes and finite element analysis (FEA).
σ_vm = √[0.5 × ((σ₁-σ₂)² + (σ₂-σ₃)² + (σ₃-σ₁)²)]
Equivalent stress for multiaxial loading
Maximum shear stress theory for ductile failure. More conservative than Von Mises, preferred for safety-critical shaft, bolt, and pin designs.
τ_max = (σ₁ - σ₃) / 2 = σ_y / 2
Maximum shear stress failure criterion
Analyzes stress in thin-walled pressure vessels (t/r < 0.1). Essential for pipeline, storage tank, boiler, and compressed gas cylinder design per ASME BPVC.
σ_hoop = (P × d) / (2 × t)
σ_long = (P × d) / (4 × t)
Thin-walled cylinder stresses