Analytical mechanics modeling of residual stress in laser powder bed considering flow hardening and softening

Residual stress builds up during the fabrication of components via laser powder bed fusion (L-PBF) process which causes parts to fail due to the crack initiation and growth, low fatigue life, and fall outside of the specified dimensions. During the thermal loading, the grain size affected by strain hardening and flow softening is altered at the subsurface through dynamic recrystallization (DRx) and subsequent recovery. The yield strength of the alloys is largely determined by the size of nucleated grains, and it has a substantial influence on flow stress and residual stress build-up. In this work, a physics-based analytical model is proposed to predict the residual stress affected by the strain hardening, flow softening, and microstructural evolution during L-PBF process with IN718 as a material system for exploration. The temperature field is predicted using a transient moving point heat source approach. Due to the non-uniform heating, materials experience high thermal stress which may exceed the yield strength of the material. The thermal stress is obtained from Green’s functions of stresses due to the point body load. A material constitutive flow stress model known as Johnson-Cook is used to determine the yield surface. This flow stress model is modified to incorporate the effects of flow softening and grain size. The dynamic recrystallization and grain refinement models are used to calculate the grain size using recrystallized volume fraction from nucleation and growth rates. As a result of the cyclic heating and cooling and the fact that the material is yielded, the residual stress build-up is precited using incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with the equilibrium and compatibility conditions. Results from the analytical residual stress model showed good agreement with X-ray diffraction measurements used to determine the residual stresses in the IN718 specimens built via L-PBF.