• 固体力学 •

### 黏弹性接触界面端附近的奇异应力场

1. 湖南大学汽车车身先进设计与制造国家重点实验室,长沙 410082
• 收稿日期:2018-08-09 接受日期:2018-10-22 出版日期:2019-03-18 发布日期:2019-03-27
• 作者简介:2) 彭凡,教授,主要研究方向：疲劳与断裂. E-mail: fanpeng@hnu.edu.cn|3) 戴宏亮,教授,主要研究方向：多场耦合力学. E-mail: hldai@hnu.edu.cn
• 基金资助:
深海载人装备国家重点实验室开放基金资助项目(702SKL201705)

### SINGULAR STRESS FIELD IN VISCOELASTIC CONTACT INTERFACE ENDS

Fan Peng,Shuangshuang Xie,Hongliang Dai

1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
• Received:2018-08-09 Accepted:2018-10-22 Online:2019-03-18 Published:2019-03-27

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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