Eric Bayerschen

Equivalent Plastic Strain Gradient Plasticity with Grain Boundary Hardening and Comparison to Discrete Dislocation Dynamics

The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33–46. (doi:10.1016/j.ijplas.2013.07.001)), incorporating an equivalent plastic strain γeq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientation-dependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model.

Power-law defect energy in a single-crystal gradient plasticity framework: a computational study

A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the finite element discretization of the theory. Three exemplary choices of the defect energy exponent are compared in finite element simulations of elastic-plastic tricrystals under tensile loading. The influence of the power-law exponent is discussed related to the distribution of gradients and in regard to size effects. In addition, an analytical solution is presented for the single slip case supporting the numerical results. The influence of the power-law exponent is contrasted to the influence of the normalization constant.

Modeling contrary size effects of tensile- and torsion-loaded oligocrystalline gold microwires

When Chen et al. (Acta Mater 87:78–85, 2015) investigated the deformation behavior of oligocrystalline gold microwires with varying diameters in both uniaxial tension and torsion, contrary size effects were observed for the different load cases. In accompanying microstructural studies it was found that the microwires of different thicknesses reveal distinctive differences in grain size and texture, respectively. As a consequence, a significant influence of these microstructural variations on the determined size effects was assumed. However, within the frame of their work, a direct confirmation could only be presented for the effect of the grain size. In the present work, the size-dependent mechanical response of the microwires is modeled with a gradient plasticity theory. By finite element simulations of simplified grain aggregates, the influence of the texture on the size effects is investigated under both loading conditions. It is shown that the experimentally observed contrary size effects can only be reproduced when taking into account the individual textures of the microwires of different thicknesses within the modeling.