Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals

The fracture toughness of ductile materials depends upon the ability of the material to resist the growth of microscale voids near a crack tip. Mechanics analyses of the elastic–plastic deformation state around such voids typically assume the surrounding material to be isotropic. However, the voids exist predominantly within a single grain of a polycrystalline material, so it is necessary to account for the anisotropic nature of the surrounding material. In the present work, anisotropic slip line theory is employed to derive the stress and deformation state around a cylindrical void in a single crystal oriented so that plane strain conditions are admitted from three effective in-plane slip systems. The deformation state takes the form of angular sectors around the circumference of the void. Only one of the three effective slip systems is active within each sector. Each slip sector is further subdivided into smaller sectors inside of which it is possible to derive the stress state. Thus the theory predicts a highly heterogeneous stress and deformation state. In addition, it is shown that the in-plane pressure necessary to activate plastic deformation around a cylindrical void in an anisotropic material is significantly higher than that necessary for an isotropic material. Experiments and single crystal plasticity finite element simulations of cylindrical voids in single crystals, both of which exhibit a close correspondence to the analytical theory, are discussed in a companion paper.