A modified cohesive zone model for a high‐speed expanding crack

Abstract

A B S T R A C T The present work studies a self-similar high-speed expanding crack of mode-I in a ductile material with a modified cohesive zone model. Compared with existing Dugdale models for moving crack, the new features of the present model are that the normal stress parallel to crack faces is included in the yielding condition in the cohesive zone and traction force in the cohesive zone can be non-uniform. For a ductile material defined by von Mises criterion without hardening, the present model confirms that the normal stress parallel to crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. In addition, strain hardening effect is examined based on a non-uniform traction distribution in the cohesive zone.C 1 , C 2 = longitudinal and transverse elastic wave speeds C R = Rayleigh wave speed f = traction distribution function F xx , ……G xt = eight analytic functions G = energy release rate G I = elastostatic energy release rate M, M 1 , M 2 = speed-dependent functions q 1 = a constant measuring traction distribution r = polar coordinate R = Rayleigh wave function S y = normal traction on cohesive zone t = time coordinates T = remote mode-I tensile loading u x , u y = components of displacement vector V a , V c = crack tip velocity and cohesive zone tip velocityx, y = rectangular coordinates Y = yielding stress of material α 1 , α 2 = the quantities (1 À V a 2 /C 1 2 ) 1/2 and (1 À V a 2 /C 2 2 ) 1/2 δ = crack tip opening displacement ζ , ζ d , ζ s = complex variables κ = dimensionless material parameter defined by Poisson's ratio μ = elastic shear modulus ν = Poisson's ratio ξ, η 1 , η 2 = rectangular coordinates in the transformed planes ρ = mass density σ xx , σ xy , σ yy = components of stress tensor φ, ψ = two wave functions Correspondence: C. Q. Ru.

Experimental study on cracking process and fracture properties of granite under mode I loading by acoustic emission and digital image correlation

“…Related theoretical studies have shown that a relatively large FPZ may partially extend beyond the K‐dominant region and lead to significant stress redistribution, with noticeable effects on fracture toughness and fracture angle 10–12 . In general, the cohesive zone model is widely used to characterize the nonlinear fracture characteristics of quasi‐brittle materials 13–17 . In the cohesive zone model, the microcrack in the FPZ is idealized as a cohesive crack and the real crack is regarded as a cohesionless crack.…”

“…[10][11][12] In general, the cohesive zone model is widely used to characterize the nonlinear fracture characteristics of quasi-brittle materials. [13][14][15][16][17] In the cohesive zone model, the microcrack in the FPZ is idealized as a cohesive crack and the real crack is regarded as a cohesionless crack. When the crack tip opening displacement (CTOD) is small, the stress-induced cohesive cracks form the FPZ.…”