Bending is a conventional manufacturing process of sheet forming. This process induces reasonable residual stress through the thickness. Prediction of this residual stress profile is more difficult in bilayer sheet bending due to different material properties and thickness of layers. In this article, the residual stress distribution will be derived analytically for a bilayer sheet. The induced stress profile due to loading and released stress after unloading has been derived by integration along with the thickness. Also, the neutral axis movement due to non-uniform plastic deformation has been involved in the solution. The stress distribution has been derived analytically for elastic–perfect plastic, elastic–linear plastic and elastic–power law hardening material behavior. The results obtained from the proposed equation are compared by a finite element analysis. The finite element analysis contains bending a bilayer sheet to a specified curvature radius by a three-roll bending process. Comparing the results of the analytical solution and finite element analysis shows good agreement. The location of the neutral axis and the maximum of residual stresses in the thickness have been predicted very well with the proposed equation.

中文翻译：

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一种封闭形式的解析解决方案，用于解决由于双层板弯曲而产生的残余应力

弯曲是片材成形的常规制造过程。此过程会在整个厚度范围内引起合理的残余应力。由于不同的材料特性和层的厚度，在双层板弯曲中，这种残余应力分布的预测更加困难。在本文中，将通过分析得出双层薄板的残余应力分布。归因于加载的应力分布和卸载后释放的应力已通过积分以及厚度推导得出。而且，由于不均匀塑性变形而引起的中性轴运动也涉及到解决方案中。通过分析可以得出弹性完美塑性，弹性线性塑性和弹性幂律硬化材料行为的应力分布。通过有限元分析比较了从提出的方程中获得的结果。有限元分析包括通过三辊弯曲工艺将双层板弯曲到指定的曲率半径。将解析解和有限元分析的结果进行比较显示出很好的一致性。用所提出的方程很好地预测了中性轴的位置和厚度中的残余应力的最大值。