COMPLAS 2023

A Data-Based Derivation of Internal Correction Stress for the Coarse-Graining in Dislocation-Based Plasticity

  • Lee, Sing-Huei (Karlsruhe Institute of Technology)
  • Schulz, Katrin (Karlsruhe Institute of Technology)

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The plasticity properties of metal, such as strength and ductility, are governed by the movement and the interaction of dislocations. Therefore, for small scale simulations, incorporating the knowledge regarding dislocation dynamics becomes more important due to the existence of size effect and micro level heterogeneity. Among the pioneer works, a key component capturing the microscopic characteristics is the back stress conjugated with the defect energy potential. The defect energy potential is often assumed to be of a quadratic form and derived based on thermodynamic consistency. The resulting back stress will be of the second order gradient of plastic strain, and shows good capability for simulating material behaviour at smaller scales. However, until now, the exact formulation of the defect energy potential and the back stress term as well as the connection to the dislocation characteristics stay unclear. In this presentation, we thus introduce a framework for the derivation of the back stress term based on the statistical analysis of data from discrete dislocation dynamic simulations. By investigating the dislocation structure formation within the coarse-graining benchmark systems under various combinations of numerical and microstructure conditions, e.g. element size, initial dislocation density, and the gradient of geometrically necessary dislocations, the heterogeneous dislocation structures formation within an element is identified. The resulting structure can be further predicted by the collected data base statistically or by a machine learning approach. We derive the near field correction stress within a coarse-grained system according to the uneven stress field induced by the heterogeneous dislocation structure formation. The derivation is assumed to be a mechanism-based explanation applicable to the back stress within gradient plasticity theory.