Dynamic fracture of metals may be brittle or ductile depending on factors such as material properties, loading rate and specimen geometry. At high strain rates, a thermo plastic instability known as shear banding may occur, which typically precedes fracture.

No abstract

Shear bands are material instabilities associated with highly localized intense plastic deformation zones which can form in materials undergoing high strain rates. Determining the onset of shear band localization is a difficult task and past work reported in the literature attempt to detect this instability by computing the eigenvalues of the acoustic tensor or by studying the linear stability of the perturbed governing equations. However, both methods have their limitations and are not suited for general rate dependent materials in multidimensions.In this work we propose a novel approach to determine the onset of shear band localization and alleviate the limitations of the above mentioned methods.Owing to the implicit mixed finite elements discretization employed in this work, we propose to cast the instability analysis as a generalized eigenvalue problem by employing a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases where no special simplifying assumptions ought to be made.To verify the accuracy of the proposed eigenvalue analysis, we first extend an analytical criterion by applying linear perturbation techniques to the continuous PDE model, considering an elastoplastic material with thermal diffusion and a nonlinear Taylor-Quinney coefficient. While this extension is novel on its own, it requires strenuous derivations and is not easily extended to general multidimension applications. Hence, herein it is only used for verification purposes in 1D.Numerical results on one-dimensional problems show that the eigenvalue analysis exactly recovers the instability point predicted by the analytical criterion with non-linear Taylor-Quinney coefficient. In addition, the proposed generalized eigenvalue analysis is applied on two-dimensional problems where propagation of the instability can be easily determined.

No abstract

Well known experiments of projectile impacts on pre-notched plates have demonstrated a transition from brittle to ductile failure with increasing strain rate. At low rates cracks form at the notch tip and propagate at roughly 70 degrees counter clockwise from the loading direction. At high rates shear bands form and propagate in a downward curving path. This occurs because of the formation of shear bands, which occurs more readily at the higher velocities, prevents the development of the large principal strains needed to initiate a crack. In this paper, we present a coupled model that is capable of capturing the failure transition. The finite deformation model consists of a thermoviscoplastic material with strain and strain rate hardening, thermal softening and diffusive regularization. Fracture is modeled with the phase field method, for which a novel modification is presented to account for degradation of the material due to inelastic working. The numerical model including the discretization and linearization and monolithic scheme is presented and discussed in details. Numerical simulations of the notched plate impact problem studied by (Zhou et al., 1996b) are presented up to the point of shear band or fracture initiation, demonstrating the transition from brittle fracture under minor yielding to ductile failure by shear banding.