Prediction for multi-index constrained forming limit in shear bending process of Ti-alloy thin-walled tube under differential temperature fields

Predictions for multi-index constrained forming limits and forming limits of Ti-alloy thin-walled tubes have become key problems urgently in need of solutions in order to improve forming potential in their shear bending processes under differential temperature fields. To address this, a method for predicting this type of forming limits was presented by coupling a thermal-mechanical-coupled finite element model for simulating these bending processes, with an energy model for the tubes’ shear-enforced plastic wrinkling predictions and utilizing the response surface designs. Reliable multi-index response surface models corresponding to the wrinkling, the thinning, and the flattening were developed for these TA2 Ti-alloy tubes’ shear bending processes, and their multi-index constrained forming limits were predicted. This found that forming limits, i.e., the maximum moving die displacements depend on the over-thinning or over-flattening for the present conditions. The smaller the values of the outer corner radius, the smaller both the feasible region ranges of the bending die cavity radius and/or the mandrel diameter and these forming limits. When the value of the outer corner radius is a half of the mandrel diameter and the values of the inner corner radius are from 4 to 6 mm; their feasible region ranges are the maximum. The effects of the feasible region of the bending die cavity radius on these forming limits are larger than the mandrel diameter. The moving die displacements located in the vertexes of their feasible regions are the maximum.