Estimation of Welding-Induced Plastic Zone Size and Residual Stress Levels: Linear Heat Input Approximation

Welding is a highly nonlinear temperature distribution process, where the presence of high-temperature gradients leads to the development of significantly high residual stress levels, up to and/or beyond the material yield strength magnitude and localized plastic deformation. To achieve the desired dimensional accuracy, determination of plastic zone size, shape, and location is critically important in reducing or controlling final distortions, decreasing the residual stress according to length scale, and defining the optimum sequence of the welding process. The plastic zone caused by welding has been found to be directly proportional to linear heat input, defined in (J/mm). The use of actual linear heat input in the estimation of welding-induced residual stress in finite element models often results in an overestimation of heat transferred to the fusion zone of the metal. This manuscript highlights the importance of estimating plastic zone, developed during thermal processes like welding, and its role in mitigating final distortion by using a 3-bar model for the determination of final residual stresses. In the second part, previously developed analytical linear heat input solution for 2D residual stress models is discussed and further demonstrated using examples from open literature. Lastly, a sequentially uncoupled thermal and thermo-mechanical finite element analysis (FEA) is performed, using a generalized plane strain element, and concluded by validation of the numerically developed plastic zone size with analytically developed solutions.