分布位错法研究钢轨表面边缘直裂纹的力学行为

目的钢轨表面损伤机理较为复杂,因此进行相应的理论研究来探究其力学原理,为实际的工程应用提供理论依据。方法利用叠加原理将主问题分解成两个子问题,通过函数拟合得到轮轨接触力,基于弹性力学集中力的Flamant解求解子问题1,基于分布位错技术求解子问题2。进一步建立了两类关于位错密度的积分方程,利用Gauss-Chebyshev数值求积法解决位错密度的奇异积分方程,得到了相关的力学参量。结果得到了列车在含边缘直裂纹钢轨上运行时的最危险位置,以及张开部分裂纹长度和不同类型裂纹的尖端应力强度因子等。分析了不同轮重大小、列车运行状态(稳态滚动和全滑动)等因素对裂尖应力强度因子及张开裂纹长度的影响,还分析了列车运行中裂纹面的滑移等。结论列车稳态滚动于含初始边缘长裂纹的钢轨表面时,以剪切破坏为主,列车所处最危险位置是裂纹位于接触斑边缘附近;全滑动运行时,裂纹面上的应力大小和方向均会发生改变,导致裂纹面状态(张开或闭合)随之改变,裂纹较短时,钢轨表面容易发生沿深度方向的张开型扩展。

Mechanical Behavior of Straight Crack on the Edge of Rail Surface by Distributed Dislocation Method

The work aims to explore the mechanical principle of rail surface through corresponding theoretical research in view of the complex damage mechanisms of rail surface,so as to provide theoretical basis for practical applications.The problem was divided into two sub-problems based on the superposition principle.The wheel-rail contact force was obtained by function fitting.The first sub-problem was solved by Flamant’s solution of the concentrated force in the elastic mechanics and the second sub-problem was solved by the distributed dislocation technique.Further,two types of the singular integral equations about dislocation density were established.The numerical solution of the equations was presented by means of Gauss-Chebyshev quadrature method and the relevant mechanical parameters were obtained.The most dangerous position of the train running on the rail with edge crack,and the crack length of the open part and the stress intensity factor at crack tips(SIF)were obtained.The effects of different wheel weight,and the running state of the train(steady-state rolling or full sliding)on SIF were analyzed.The problem of the crack surface slip during the operation of the train was also analyzed.When the train is rolling steadily on the rail surface with long initial edge crack,the shear failure is the dominant,and the most dangerous position of the load is that the crack is located near the edge of the contact spot.When the train is running in the extreme state of full sliding,the magnitude and direction of stress on the crack surface will change,which will cause the crack surface state(opening or closed)to change as well.When the crack is shorter,the surface of rail is prone to open failure along the direction of depth.