Analysis of damage localization for ductile metal in process of shear band propagation

Distribution of localized damage in shear band can' t be predicted theoretically based on classical elastoplastic theory. The average damage variable in shear band was considered to be a non-local variable. Based on non-local theory, an analytical expression for the localized damage in strain-softening region of shear band in the process of shear band propagation was presented using boundary condition and symmetry of local damage variable, etc. The results show that dynamic shear softening modulus, dynamic shear strength and shear elastic modulus influence the distribution of the localized damage in shear band. Internal length of ductile metal only governs the thickness of shear band. In the strain-softening region of shear band, the local damage variable along shear band's tangential and normal directions is non-linear and highly non-uniform. The non-uniformities in the normal and tangential directions of shear band stem from the interactions and interplaying among microstructures and the non-uniform distribution of shear stress, respectively. At the tail of the strain-softening region, the maximum value of local damage variable reaches 1. This means that material at this position fractures completely. At the tip of shear band and upper as well as lower boundaries, no damage occurs. Local damage variable increases as dynamic shear softening modulus decreases or shear elastic modulus increases, leading to difficulty in identification or detection of damage for less ductile metal material at higher strain rates.