Characterization of the tip field of a discrete dislocation pileup for the development of physically based micromechanics

Wavelet decomposed dual-time scale crystal plasticity FE model for analyzing cyclic deformation induced crack nucleation in polycrystals

“…The method developed here requires a suitable basis for decomposing the displacement (and hence the strain/deformation gradient) fields over time as in equation (10). The basis function chosen should satisfy the following conditions:…”

“…Various dislocation level fatigue failure models, e.g. [10,[28][29][30][31], have discussed the equivalence in the dependences of crack evolution ahead of dislocation pile-ups and at crack tips. This equivalence in the functional forms has been utilized in [26] to develop a grain-level crack nucleation criterion.…”

“…at the boundary of a soft grain adjacent to a hard grain, have been shown to be equivalent to cracks, e.g. in [10], in the way they cause stress concentration and crack nucleation at their tip. The dislocation pile-up length in the crack nucleation model is hence assumed to scale with the pre-crack length in the corresponding crack tip initiation models [32].…”

“…A single integration step of equation ( 11) can be used to jump over many cycles ( N ), resulting in significant computational savings and is discussed in section 3.2. The method developed here requires a suitable basis for decomposing the displacement (and hence the strain/deformation gradient) fields over time as in equation (10). The basis function chosen should satisfy the following conditions:…”

“…Microstructural features such as grain size, grain neighborhood distributions and grain orientations are accounted for in a statistically equivalent sense in the model in [7][8][9]. (ii) Physics-based crack nucleation criterion that accounts for the effects of inhomogeneities in the microstructure: the proposed crack nucleation model developed in this work is motivated by similarities in the functional forms of the stress fields and crack evolution criteria ahead of a crack tip and dislocation pile-up, respectively [10]. The criterion incorporates an effective mixed mode stress acting on a slip plane, defined as a combination of normal and shear stresses to account for mode mixity.…”