A Photoelastic Technique for Characterising Fatigue Crack Closure and the Effective Stress Intensity Factor

Nomenclature A k , a k Fourier series coefficients, d mean difference between theoretical and experimental stress values, i square root of –1, m mapping function shape descriptor, r, θ polar coordinates in the mapping plane, s standard deviation in the difference between stress values, t distance from the crack tip, x, y Cartesian coordinates in the physical plane, z complex coordinate in the physical plane, B rigid body translation of the mapping plane, C rigid body rotation of the mapping plane, K I , K II mode I and II stress intensity factors, K max maximum value of stress intensity factor, P pressure loading on the crack, R mapping function length descriptor, T shear loading on the crack, α principal stress direction at infinity, κ material constant, ν Poisson's ratio, σ 1,α maximum principal stress at infinity, σ 2,α minimum principal stress at infinity, τ rθ shear stress, ω mapping function, ζ complex coordinate in the mapping plane, Γ rigid body movement of the mapping plane, Φ, Ψ complex stress functions.