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 引用本文: 彭凡, 谢双双, 戴宏亮. 黏弹性接触界面端附近的奇异应力场[J]. 力学学报, 2019, 51(2): 494-502.
Fan Peng, Shuangshuang Xie, Hongliang Dai. SINGULAR STRESS FIELD IN VISCOELASTIC CONTACT INTERFACE ENDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 494-502.
 Citation: Fan Peng, Shuangshuang Xie, Hongliang Dai. SINGULAR STRESS FIELD IN VISCOELASTIC CONTACT INTERFACE ENDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 494-502.

## SINGULAR STRESS FIELD IN VISCOELASTIC CONTACT INTERFACE ENDS

• 摘要: 研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.

Abstract: The paper concerns the problem of singular stress filed in viscoelastic contact interface ends under creep loading. The local boundary conditions taking into account the contact friction are linearized by the assumptions of tiny relative slip and invariant slip direction between interfaces. The solution of stress field at the interface end in the Laplace transform domain is obtained based on the correspondence principle, and the convolution integral expressions of the singular stress field in the time domain is developed. The numerical inversion of convolution integral kernel is made by considering two types of combinations of contact materials. One is that the durable modulus has a difference in magnitude, and the other is that the durable modulus is nearly the same. The results of inversion show that kernel functions can be approximated by analytical expressions obtained by the quasi-elastic method with a good accuracy. On this basis, simplified formulas of the viscoelastic singular stress field are developed by using the integral mean value theorem and introducing the correction coefficient of each stress component. The value range of expressions for correction coefficient is investigated in combination with the examination the numerical inversion results of the kernel functions, following conclusions are drawn as follows. If the durable modulus of the two-phase contact material differs greatly, the quasi-elastic solution can be used to describe the singular stress fields near the interface end; in general, there is no uniform singular value and no uniform stress intensity factor for stress fields; when the solution of viscoelastic stress is approximated by formulas similar to the quasi-elastic solution, the error limit can be estimated. In the last part of the paper, the viscoelastic stress analysis of viscoelastic plate at support ends is performed by means of finite element simulation as plane strain problem. The example includes two types of contact interface ends, one is constructed by the viscoelastic plate and an elastic metal support, the other is formed by a viscoelastic plate and viscoelastic cushion layers. The theoretical conclusions obtained in the front part of the paper are validated by the simulation results.

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