Explicit Analytic Solutions for the Subsurface Stress Field in Single Plane Contacts of Elastically Similar Truncated Cylinders or Wedges

IF 12.2 1区 工程技术 Q1 MECHANICS Applied Mechanics Reviews Pub Date : 2022-11-29 DOI:10.3390/applmech3040077
E. Willert
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引用次数: 1

Abstract

As has been pointed out recently, a possible solution strategy to the wear–fatigue dilemma in fretting, operating on the level of contact mechanics and profile geometries, can be the introduction of “soft” sharp edges to the contact profiles, for example, by truncating an originally smooth profile. In that regard, analysis of possible mechanical failure of a structure, due to the contact interaction, requires the knowledge of the full subsurface stress state resulting from the contact loading. In the present manuscript, a closed-form exact solution for the subsurface stress state is given for the frictional contact of elastically similar truncated cylinders or wedges, within the framework of the half-plane approximation and a local-global Amontons–Coulomb friction law. Moreover, a fast and robust semi-analytical method, based on the appropriate superposition of solutions for parabolic contact, is proposed for the determination of the subsurface stress fields in frictional plane contacts with more complex profile geometries, and compared with the exact solution. Based on the analytical solution, periodic tangential loading of a truncated cylinder is considered in detail, and important scalar characteristics of the stress state, like the von-Mises equivalent stress, maximum shear stress, and the largest principal stress, are determined. Positive (i.e., tensile) principal stresses only exist in the vicinity of the contact edge, away from the pressure singularity at the edge of the profile, and away from the maxima of the von-Mises equivalent stress, or the maximum shear stress. Therefore, the fretting contact should not be prone to fatigue crack initiation.
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弹性相似截形圆柱或楔形单平面接触下应力场的显式解析解
正如最近所指出的那样,在接触力学和轮廓几何水平上操作的微动磨损疲劳困境的可能解决策略可以是在接触轮廓中引入“软”锐边,例如,通过截断原本光滑的轮廓。在这方面,分析由于接触相互作用导致的结构可能的机械故障,需要了解由接触载荷引起的整个地下应力状态。本文在半平面近似和局部-全局Amontons-Coulomb摩擦定律的框架下,给出了弹性相似截形圆柱或楔形摩擦接触的亚表面应力状态的封闭精确解。此外,基于抛物面接触解的适当叠加,提出了一种快速、鲁棒的半解析方法,用于确定具有更复杂几何形状的摩擦面接触的地下应力场,并与精确解进行了比较。在解析解的基础上,详细考虑了截断圆柱的周期性切向加载,确定了应力状态的重要标量特征,如von-Mises等效应力、最大剪应力和最大主应力。正主应力(即拉伸主应力)只存在于接触边缘附近,远离轮廓边缘的压力奇点,远离冯-米塞斯等效应力的最大值或最大剪切应力。因此,微动接触不应容易产生疲劳裂纹。
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来源期刊
CiteScore
28.20
自引率
0.70%
发文量
13
审稿时长
>12 weeks
期刊介绍: Applied Mechanics Reviews (AMR) is an international review journal that serves as a premier venue for dissemination of material across all subdisciplines of applied mechanics and engineering science, including fluid and solid mechanics, heat transfer, dynamics and vibration, and applications.AMR provides an archival repository for state-of-the-art and retrospective survey articles and reviews of research areas and curricular developments. The journal invites commentary on research and education policy in different countries. The journal also invites original tutorial and educational material in applied mechanics targeting non-specialist audiences, including undergraduate and K-12 students.
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