Strong-anisotropy-induced instability and discussion on kink band under complex loads

Compressive instability, such as the occurrence of kink bands, is common in composite materials and other highly anisotropic layered materials, limiting their use. Most previous research has focused on the microstructure and heterogeneity in studying the compressive instability of composites. In this paper, to highlight and quantify the influence of anisotropy, we investigate the deformation instability of effective homogeneous solids with strong anisotropy. Firstly, we re-write the local instability criterion from an energy perspective and verify its applicability. Even when the heterogeneity of the composites is eliminated, the derived criterion can reasonably predict the kink band instability and can be reduced to the well-known Rosen’s estimate. The strong stiffness anisotropy plays a dominant role in kink band instability. For unidirectional fiber-reinforced composites, increasing the modulus of the hard phase contributes little to an increase in the compressive strength because, as the anisotropy increases, the critical strain decreases and becomes approximately inversely proportional to the anisotropy degree. The kink band instability is also investigated under complex loads. We find that lateral tension increases the critical kink band load, while lateral compression or shear decreases the critical kink band load. To estimate the instability, we develop a series of instability phase diagrams that can be used as a guideline for predicting the compressive instability of composite materials. We have found that reducing the anisotropy of the material is the main way to increase the critical load of kink band instability, which is important for material design and engineering applications.