Surface-treated bodies are considered under the assumption that the plastic strain distribution is uniform along the surface and changes only with depth. The elastic problem of the surface-treated plate is solved. The obtained solution is used to derive the explicit exact reconstruction formulas for distributions of main tangential components of the plastic strain tensor. It has been proved that the deflection of the surface-treated strip does not depend on the width of the strip. These results are intended for use in destructive testing methods and for numerical prediction of strength. The following initial data were used: (a) the dependence of the deflection on the thickness of the removed material layer obtained by the Davidenkov method, (b) the dependence of the tangential residual stress components on the depth, and (c) the dependence of the surface tangential stress components or elastic strain tangential components on the thickness of the removed material layer obtained by the X-ray diffraction method. The obtained formulas were analyzed and approved for all types of initial data, wherefore two experiments were conducted. A way to incorporate the plastic strain distribution into a model of a machine part of complex geometry to take into account the residual stress field in fatigue, wear, cracking, the and corrosion strength predictions is presented.

中文翻译：

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表面处理板塑性应变分布的精确重构公式及其应用

在假定塑性应变分布沿表面均匀且仅随深度变化的假设下考虑表面处理过的物体。解决了表面处理板的弹性问题。获得的解用于推导出塑性应变张量的主要切向分量分布的显式精确重建公式。已经证明，经过表面处理的带材的偏转与带材的宽度无关。这些结果旨在用于破坏性测试方法和强度的数值预测。使用以下初始数据：(a) 挠度对通过 Davidenkov 方法获得的去除材料层厚度的依赖性，(b) 切向残余应力分量对深度的依赖性，(c) 表面切向应力分量或弹性应变切向分量对通过X射线衍射法得到的去除材料层厚度的依赖性。对所有类型的初始数据对获得的公式进行了分析和批准，因此进行了两次实验。提出了一种将塑性应变分布合并到复杂几何形状的机器零件模型中的方法，以考虑疲劳、磨损、开裂、腐蚀强度预测中的残余应力场。