Analysis of edge crack behaviour influenced by non‐symmetrical contact tractions and bulk tension

Abstract

A B S T R A C T This paper analyses a crack growth behaviour, which is initiated from the contact edge between a square punch with rounded edges and a half plane. Investigated are the influences of the contact profile, magnitude of the bulk tension and, crack obliquity, in particular, misalignment between the punch and half plane on the variation of the stress intensity factors K I and K II during the crack growth. The misalignment is simulated by a tilting of the punch. A partial slip regime is considered for the contact shear force to accommodate a general fretting fatigue condition. It was found that a crack closure occurs if only the contact forces are applied. The crack grows longer before it is closed if the punch is tilted (clockwise, in this paper) such that it initiates at the opposite site with respect to the direction of tilting. The closure phenomenon disappears when the bulk tension is added and exceeds a certain magnitude, which significantly depends on not only the contact profile but also the degree and direction of tilting. Provided are the lowest values of the bulk tensile stress due to a fatigue load necessary to extend the crack without a closure for each condition of the contact profile and misalignment. This may be used as a design guideline to restrain the contact-induced failure.Keywords contact-induced failure; contact profile; crack closure; misalignment. N O M E N C L A T U R Ea = crack length A = combined elastic properties of contacting bodies b, b ref = a half contact length and a reference half contact length (at l/b = 0.1), respectively b i (i = x, y, x′, y′) = Burgers vector B(u), B i ( j) (i = x, y, x′, y′; j = s, s′) = dislocation density functions f = coefficient of friction G = shear modulus = crack driving force h(x), g(x) = normal and tangential displacements on the contact surface due to contact tractions, respectively k(v,u), k J i y′; s′ ð Þ (i = x′ or y′; J = N or T ) = kernels l, R, W = flat region, corner radius and width of a punch with rounded corners (see Figure 1) in order n = number of integration points along the crack line N = number of subdivisions of the contact region p(x), q(x) = contact normal and shear tractions, respectively p m , p ref m = averaged contact normal traction and its reference (at l/b = 0.1) P, Q = contact normal and shear forces, respectively s = location of a pseudo edge dislocation on the crack measured from the contact surface

A fracture mechanics based model for the analysis of seal effectiveness

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Effects of a tilted flat-ended punch on the receding contact between a graded and a homogeneous layer

“…The indentation of a homogeneous half-plane due to a tilted shallow wedge in the contexts of classical [31] and couple-stress elasticity [32] has been examined. Sackfield et al [33], Kim [34], and Andresen et al [35] analyzed the asymmetrical contact responses of a semi-infinite substrate under the indentation of tilted flat-ended punch with round edges.…”