A multi-scale framework for predicting residual deformation of laser directed energy deposition considering the kinematic hardening behavior of materials

The accumulation of plastic strain resulting from repeated thermal cycling can lead to residual deformation that seriously impacts the forming quality of functionally gradient materials (FGMs) during laser directional energy deposition (L-DED) processing. The accumulated plastic strain in L-DED depends mainly on the high-temperature constitutive behavior of the material. Therefore, the construction of a model that accurately reproduces the plastic strain evolution resulting from thermal cycling is essential to predict the residual deformation of FGMs with greater accuracy. Many existing studies ignore the impact of the plastic strain evolution under thermal cycling. Therefore, this study proposes a multi-scale framework: firstly, a meso-scale thermal-mechanical coupling model considering the nonlinear kinematic hardening criterion (Chaboche constitutive model), which can simulate the plastic strain evolution behavior under thermal cycling of cladding and obtain the magnitude of accumulated plastic strain, and then apply it to the part-scale model by the inherent strain method to achieve the prediction of residual deformation. Finally, the proposed multi-scale framework is validated by single-material thin-walled parts and two distributions of FGMs thin-walled parts. The results indicate that the prediction accuracy of the residual deformation of single-material and FGMs thin-walled parts is improved. This is because the framework not only considers the plastic strain evolution under thermal cycling, but also avoids overestimation of the accumulated plastic strain due to the presence of the dynamic recovery item in the constitutive model. The multi-scale framework, which considers the nonlinear kinematic hardening criterion, predicts residual deformation with higher agreement to experiment than the conventional bilinear isotropic hardening criterion (Biso constitutive model). This framework proposed in this paper can be utilized to predict the residual deformation caused by multiple thermal cycling of L-DED process.