Influence of non-steady state loading on two-dimensional wheel-rail pure rolling contact stresses and deformation
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摘要: 为了揭示轮轨波状表面与非稳态载荷的内在联系, 利用有限元法, 建立了二维弹塑性轮轨纯滚动接触计算模型, 分析法向接触载荷波动值对钢轨残余应力、应变和变形的影响。模型中材料本构采用考虑棘轮效应的Jiang-Sehitoglu模型, 非稳态仅考虑法向接触载荷的简谐变化, 用弹塑性无限半空间表面上重复移动赫兹法向压力分布模拟反复纯滚动接触过程。发现非稳态法向接触载荷作用下产生同样波长的波状接触表面; 随滚动次数的增加, 残余应力增大, 但很快趋于稳定, 而残余应变也增大, 但增大速率衰减; 载荷波动值越大, 波谷和波峰处的纵向残余应力越大, 波谷处的轴向残余应力、残余剪应变和表面纵向位移越大, 而波峰处的轴向残余应力、残余剪应变和表面纵向位移越小, 波深越大。Abstract: In order to study the relation between wheel-rail corrugation surface and non-steady state loading, a two-dimensional elastic-plastic model of repeated frictionless wheel-rail rolling contact was established, the effects of the fluctuating amplitude coefficient of normal contact pressure on the residual stresses, strains and displacements of rail were analyzed.An advanced cyclic plasticity model developed by Jiang and Sehitoglu was used, material ratchetting effect was considered, non-steady state rolling contact was only considered as the harmonic variation of normal contact pressure, repeated rolling contact was simulated by the multiple translations of varying semielliptical Hertzian pressure distribution across elastic-plastic semi-infinite half space.Analysis result shows that non-steady state normal contact pressure results in a wavy rail surface profile with the same wavelength as the pressure; as rolling time increases, rail residual stress increases, but tends to stabilize, rail residual strain also increases, but ratchetting rate decays; when preassure fluctuating amplitude coefficient increases, rail residual stress in rolling direction below the trough and crest of wavy deformation increase respectively, rail residual stress in axial direction, rail residual shear strain and surface displacement in longitudinal direction below the trough increase respectively, but rail residual stress in axial direction, rail residual shear strain and rail surface displacement in longitudinal direction below the crest decrease respectively, the wave depth increases.
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图 9 C0对残余应力和残余剪应变的影响
Figure 9. Influences of C0 onresidual stresses and residual shear strains
表 1 塑性模型
Table 1. Plasticity model
屈服准则 f= (S-α) · (S-α) -2k2=0 S为偏应力张量; α为背应力张量; k为剪切屈服强度 流动准则 n为屈服面的法线方向; h为塑性模量; εp为塑性应变张量; 〈〉为Macauley括号, 即〈x〉=0.5 (x+x) 硬化准则 α= αi为第i个背应力张量分量; M为背应力张量分量总数; dp为等效塑性应变增量; ci、ri、χi为材料常数 
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表 2 材料常数
Table 2. Material constants
E=210 GPa, υ=0.3, k=100 MPa, M=5 c1=1632.3, c2=493.0, c3=149.0, c4=45.0, c5=13.6 r1=120.5 MPa, r2=76.3 MPa, r3=89.6 MPa, r4=100.4 MPa, r5=152.5 MPa χ1 =χ2 =χ3 =χ4=χ5=5
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