Abstract
Two-dimensional discrete dislocation plasticity (2D-DDP) has shown to be a powerful tool for studying micro-plasticity problems such as size effects in single crystals, fracture of bimaterial interfaces, delamination of thin films, fatigue crack growth etc. The power of 2D-DDP lies in the application of edge dislocation dipoles as the vehicle for plastic slip: the loss of accuracy in the description of dislocation structures is counter-balanced by its simplicity and the possibility to reach larger plastic strains. The constitutive rules for dislocation evolution in 2D-DDP used so far are tuned to FCC crystals and need to be modified to be used for BCC materials. One of the key challenges in extending the method to BCC materials is that, contrary to FCC, the mobilities of edge and screw dislocations in BCC crystals differ vastly from each other, so that the screw mobility will be rate limiting the plastic slip. Thus, a method is required to map the edge and screw mobilities of dislocation loops into an effective mobility to be used in 2D. To do so, we here propose a 3D-to-2D procedure that is based on the notion of conservation of in-plane plastic strain rate. The consequence of this approach is that the effective 2D mobility for FCC crystals is not simply equal to the uniform mobility of a dislocation loop, as has been assumed by all 2D models to date, but also on the size of edge dipoles. In order to assess the consequences of this departure from the current literature, we considered a few key problems involving plasticity size effects and crack growth, and compared the predictions assuming constant mobility versus the proposed effective mobility. After observing that, overall, the predictions do not deviate substantially, we proceed with application of the 3D-to-2D procedure to compute the effective 2D mobility for BCC materials based on their edge and screw mobilities. The validation of the approach is done by comparison of the predicted rate sensitivity of polycrystalline iron with the experimental rate sensitivity at room temperature, which are found to be in fairly good agreement.
Highlights
Dislocations are the fundamental carriers of plastic flow in ductile crystals
Since in this study there are more, and larger, grains, we do not need as many sources as used by Shishvan and Van der Giessen [14]: a density of ρnuc = 20 μm− 2 ensures that the log-normal distribution of strengths is represented accurately. This value can be used for all strain rates since Agnihotri and Van der Giessen [49] have shown that the rate sensitivity of an face-centered cubic (FCC) polycrystal is independent of the source density
To validate the effective-mobility approach, 2D-discrete dislocation plasticity (DDP) simulations were employed to compare the prediction of the rate sensitivity of the yield stress at high strain rates in polycrystalline iron with experiments
Summary
Dislocations are the fundamental carriers of plastic flow in ductile crystals. The discreteness of dislocations plays an important role at the micron/sub-micron scale where several features of deformation are directly affected by the motion and interaction of individual disloca tions. The use of two-dimensional plane strain DDP models (2D-DDP) has been popular during the past two decades, especially after the inception of a versatile superposition method for solving complex boundary value problems by Van der Giessen and Needleman [6]. Even though it cannot capture detailed aspects of 3D dislocation microstructures, 2D-DDP has shown to be a powerful tool in understanding many aspects of dislocation physics. While the studies cited above assumed isotropic elasticity, Shishvan and Van der Giessen [38] took the cubic symmetries of single crystals into account
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