Plastic zones for ductile layer sandwiched between two different substrates

Abstract

This study is an extension of previously developed models of plasticity occurring in the vicinity of ​​a longitudinal crack in a thin elastic-plastic layer sandwiched between two identical, ideally elastic substrates: Varias–Suo–Shih [1], Rogowski-Molski [2], and Rogowski [3]. The solution presented in the current study describes the plastic zone size problem in a thin constrained layer bonded to two different substrates. A well-known two-term K-T Williams [4] stress solution for interfacial cracks is used to obtain the plastic zone size. A new equation with coefficients dependent on the layer and substrate material properties was obtained, allowing for the calculation of the plastic zone size in the thin ductile layer based on the values of the complex stress intensity factor K and T-stresses. The proposed model is tested for several arbitrarily selected interfacial crack geometries, load conditions, bonding layers, and substrate material properties. Because of the complicated oscillatory description of the local stress field, the final solution of the mathematical equation is obtained numerically, ignoring a small zone of intense stress oscillations near the crack tip. Good agreement is obtained between the results from the proposed model and the FEM results in terms of quantity and quality. A novel approach may be utilized in the future as a method for estimating the parameter of fracture criterion for bonded joints.