Modelling Crack Closure for an Interface Crack Under Harmonic Loading

Abstract

The paper is devoted to a linear crack located between two dissimilar elastic half-spaces under normally incident harmonic tension-compression loading. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The dynamic stress intensity factors (the opening and the transverse shear modes) are computed as functions of the loading frequency taking the contact interaction of the opposite crack faces into account. The results are compared with those obtained neglecting the crack closure.

Contact Problems for Interface Cracks Under Harmonic Shear Loading

“…In both half-spaces the equation of motion and the generalized Hooke's law lead to the linear Lamé equations of elastodynamics for the displacement field with the standard initial and boundary conditions for displacements and stresses (namely, no initial deformations; given initial load at the crack faces, (1) and (2) ; continuity conditions at the bonding interface, * = (1) ∩ (2) ; and the Sommerfeld radiation-type condition at the infinity). Furthermore, the components of the displacement could be represented in terms of the boundary displacements and tractions using the Somigliana dynamic identity with the appropriate fundamental solutions ( ) ( , , − ) and ( ) ( , , − ) [1,7,12,16,17,20]:…”

“…The contact constraints (2)-(4) ensure that there is no interpenetration of the opposite crack faces, the normal component of the contact force is unilateral; and the opposite crack faces remain immovable with respect to each other in tangential direction while they are held by the friction force before the slipping occurs [16,17,20,24].…”

“…It shall be specifically noted that the opposite faces of the existing cracks almost always interact with each other under deformation, significantly changing the solution near the crack [13][14][15][16][17][18][19][20][21][22][23]. The nature of the dynamic contact interaction between opposite crack faces is very complex.…”

Elastodynamic problem for a layered composite with penny‐shaped crack under harmonic torsion

“…Its generalization on the dynamic problems mostly relates the bimaterial cracked solids. Time‐harmonic loading of a penny‐shaped crack lying on the interface between dissimilar elastic half‐spaces with accounting the crack surfaces closure was considered by Guz et al ., Menshykova et al ., Mikucka and Menshykov . The propagation of time‐harmonic elastic waves through an array of periodically distributed interfacial penny‐shaped and elliptic cracks was investigated by Golub and Doroshenko .…”

2D Elastodynamics of Interface Microcracks: The Effect of Cracks Interaction

“…The complexity of the study of the contact interaction lies in the fact that the area of interest is hidden in the solid and the direct observation and measurement of the contact characteristics is impossible. Also should be taken into account the fact that the contact behaviour is very sensitive to the material properties of two contacting surface, frequency, magnitude and direction of the external loading [24,25,[36][37][38][39][40][41][42]. Thus considering the crack closure effect will be the natural next stage of this research [43].…”