Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 150, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2020.104222
Keywords
Strain gradient elasticity; Phase field; Dislocation
Funding
- Deutsche Forschungsgemeinschaft (DFG), Germany [SFB 799]
- European Research Council through the ERC Grant [759419]
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In this study, a framework based on first strain gradient elasticity is introduced to regularize the dislocation core, with two different strain energy densities compared. The results show that strain energy quadratic in the gradient of the full deformation tensor can regularize both stresses and driving forces for the order parameter.
In classical elasticity theory the stress-field of a dislocation is characterized by a 1/..-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces for the order parameter, resulting in non-physical (and discretization-dependent) predictions for the interaction between dislocations and phase-, twin- or grain-boundaries. We introduce a framework based on first strain gradient elasticity to regularize the dislocation core. It is shown that the use of strain energy density that is quadratic in the gradient of elastic deformation results in non-singular stresses but may result in singular driving forces, whereas a strain energy, which is quadratic in the gradient of the full deformation tensor, regularizes both stresses and driving forces for the order parameter and is therefore a suitable choice. The applicability of the framework is demonstrated using a comprehensive example.
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