钛合金微观位错与整体结构件加工变形的数学模型研究

Study on Mathematical Model between Dislocations of Titanium Alloy and Machining Deformation of Monolithic Component

以钛合金梁整体结构件为研究对象,根据位错动力学理论建立了整体结构件加工变形的运动位错分布模型;通过位错滑移系统模型建立了整体结构件最大塑性变形量与微观位错的理论数学关系。通过对该数学关系模型的分析表明:钛合金梁整体结构件的最大塑性变形量发生在梁中间附近,且最大变形位置由基面滑移和柱面滑移与工件端面之间的夹角确定;最大塑性变形量与已加工表面下不同深度处的应力场、加工变形过程中位错的增殖强度以及工件的长度成正比,与工件的厚度成反比,且仅从宏观尺寸上来看,工件的长度越长,厚度越小,工件的变形量越大。

This paper puts titanium alloy monolithic component as the research object. According to dislocation dynamics, distribution model of moving dislocations in the process of machining deformation in titanium alloy monolithic component was established. According to dislocation slip systems, the mathematical model between dislocations and the maximum deformation of monolithic component was established. It is shown that the maximum deformation of titanium alloy monolithic component occurs near the middle of the beam, and its place depends on the angle between the basal slip, cylindrical slip and the end face. The maximum deformation is directly proportional to the stress field at different depths beneath the surface layer, proliferation strength of dislocation and the length of the work piece, and inversely proportional to the thickness of the work piece, and only from the macroscopic point of view, the longer and the thinner the work piece is, the greater the amount of deformation is produced.