Abstract
This work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.
Highlights
Dislocations are one of the most influential defect types in crystalline materials
The model is based on the eigenstrain theory of dislocations, and the concept of spreading the Burgers vector around the slip plane from the non-singular continuum theory of dislocations is adopted to calculate the distribution of eigenstrain
The derivation of the Eshelby stress tensor through the gradient of the potential energy of dislocated elastic bodies is revisited based on the non-singular continuum theory of dislocations
Summary
Dislocations are one of the most influential defect types in crystalline materials. For instance, plasticity and hardening in crystalline materials are caused by the collective movement of dislocations, making the influence of dislocations essential for the mechanical properties [1,2]. The model has been successfully used to analyze the driving forces on point defects, material interfaces and cracks This numerical concept on the basis of the configurational force theory allows studies on defects in problems involving complex external loads and boundary conditions [16] or for the coupled electro-elastic problems [17,18]. We first formulate explicitly the eigenstrain on the basis of the spreading function of the Burgers vector, and contrast the resultant numerical elastic fields of dislocations with those analytical results of Cai et al [22] and the classical singular solutions. To demonstrate the flexibility of the model and its application potential for complex situations, a cluster of edge dislocations is simulated We obtained both the critical passing stress and the driving force on each individual dislocation, which are otherwise difficult to calculate
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