PSI - Issue 71

Ayub Khan et al. / Procedia Structural Integrity 71 (2025) 461–468 463 In the CP model, the evolves with slip on systems, which can be uniquely defined once the crystal structure is known. In this work, we have differentiated the flow rule between the bulk of a grain and at the grain boundary region. A diffused representation is assumed at the grain boundary region where the plastic velocity gradient is homogenised following a mixture rule such that =∑ =1 ∑ =1 ̇ ̃ (5) where is the number of grains that share the GB region in which the material point lies, and is the number of slip systems at the material point. These material point weights are evaluated from element weights (explained later in section 2.4). At a particular point, the sum of weights due to all nearby grains ∑ =1 =1 (Fig.1}). In Eq. 5, ̃ = ⊗ the Schmid tensor and depends on the slip plane normal ( ) and direction ( ). Fig. 1. The variation of weights due to ℎ grain in a bicrystal. While this study focuses on FCC and BCC polycrystals, the framework can be extended to other material systems, such as HCP structures and complex concentrated alloys (CCAs) with appropriate modifications. HCP materials, which exhibit non-basal slip systems, twinning, and pronounced anisotropy, would benefit from the diffused interface approach to capture the gradual transition between parent and twin states, as well as the unique stress and strain distributions near grain boundaries. This approach would also enable a more realistic representation of twinning behavior and dislocation-twin interactions. In CCAs, the diffused interface model could be applied to study grain boundary segregation, phase stability, and the effects of compositional heterogeneity on dislocation behavior, including how local variations in composition influence dislocation motion and the activation of different slip systems. 1.2. Evolution of plastic shear A phenomenological relation for the evolution of plastic shear is used (Asaro and Needleman (1985); Kalidindi et al. (1992)) such that ̇ = 0 ̇ | | 1 ( ) (6) where is the resolved shear stress on a slip system . The evolution of slip system resistance is given by (Anahid et al. (2011)) ̇ =∑ ℎ | ̇ |+ 0 ( ̂ 2 2 ) 2( − 0 ) ∑ | ̇ | (7) where 0 and ̂ are dimensionless material constants, is the magnitude of Burgers vector, is the shear modulus, 0 is the initial slip system resistance. The slip system hardening rate ℎ = ℎ 0 (8) To incorporate the effect of GNDs, the slip plane lattice incompatibility parameter is calculated from = ( : ) 1 2 (9) where is the slip plane normal and Nye’s dislocation tensor is evaluated using the plastic deformation gradient as = ( ) (10)