Analysis of frictional contacts with heat generation considering temperature dependent properties

Highlights

• The problem of thermoelastic contact is investigated.

• Frictional heat causes the change of material thermoelastic properties.

• Iterative code is developed and implemented by using finite element analysis.

• Comparative study is made for the contact stress and temperature distributions.

Abstract

The problem of thermoelastic contact for the homogenous isotropic half-plane with a sliding rigid flat punch problem is investigated. As the rigid flat punch is assumed to slide over the surface of the material, heat is generated due to the friction between the punch and a surface. This heat causes the change of material thermoelastic properties and this change is taken into account in this work by using temperature dependent material properties. In order to obtain the steady state solution, frictional heat in the contact surface must be in equilibrium. Hence, an iterative code is developed and implemented to solve this problem by using finite element analysis. The steady state results for the contact of homogenous isotropic half-plane with a rigid flat punch are obtained. Moreover, comparative study is made for the contact stress and temperature distributions.

Introduction

Contacts with different solid bodies play a significant role in especially the maintenance of mechanical and structural assemblages. Therefore, contact mechanics is one of the main interesting topics for researchers to improve reliability and durability of contacts. In order to achieve enhanced reliability and durability of such contacting bodies, especially near and at the surfaces, the utilization of the coated system has become a common practice in a broad range of modern technological applications [1]. Therefore, coating materials become important for protecting the underlying material against planar wear, heat and corrosion damages. The solutions of contact problems for different loading conditions on the elastic half space were proposed [2]. Frictional contact problems with heat generation were investigated by Matysiak and Yevtushenko [3] and stationary, quasistationary and non-stationary cases of contacts were also examined. Some thermoelastic contact problems with frictional heat generation were investigated analytically and one of the bodies was assumed insulated. Besides, analytical results were obtained for axisymmetrical, sphere/plane and cylinder/plane contacts [4]. Dundurs and Comninou [5] analyzed the external contact of two bodies by using Green׳s functions and it was stated that the frictional heat on the contact can cause separation. Barber and Moran [6] also used Green׳s functions to solve the unsteady thermoelastic contact problems, heat source was defined analytically on the contact zone and the analytic expressions on the contact zone was discretized to solve the problem numerically. Contact problem of sliding rigid insulated punch and a metallic substrate was investigated in the work conducted by Hills and Barber [7] and heat generation due to the Coulomb type friction was taken into account. The effects of thermal deformations on contact stresses were represented and significant results were obtained. In their work, stress and temperature distributions were also represented. Kulchytsky-Zhyhailo and Yevtushenko [8] developed an approximate method for an analysis of the contact temperature and pressure due to frictional load in an elastic layered medium. In their work, thermal and mechanical contact of bodies were assumed perfect and the axisymmetric thermoelastic contact problem for the layered half space with frictional heating was investigated. Fourier integral transform technique was utilized. Chao and Gao [9] analyzed rigid stamp indentation for a thermoelastic half-plane and a rigid punch of various shapes and contact problem was solved explicitly by the method of analytical continuation. The effects of applied loadings, the profile of the punch and material properties on the contact stress under the punch face were obtained. Giannokopulos and Pallot [10] obtained analytical solutions for the two dimensional contact of rigid cylinders on graded elastic substrates. When it is not possible to derive analytical closed form solutions for contact problems, usually the problem is reduced to a singular integral equation (SIE) which is solved numerically. Dag and Erdogan [11] represented such an SIE based technique to examine the behavior of a surface crack located in an FGM half-plane which is loaded through a frictional flat stamp. Guler [12] and Guler and Erdogan [13] investigated the contact between graded coatings and different types of rigid stamp profiles and the influences of material inhomogeneity, coefficient of friction and various other parametres on contact stresses were represented and analytical benchmark results were obtained. Guler [14] also obtained closed-form solution of the two dimensional sliding frictional contact problem for an orthotropic medium and it reveals that the orthotropic material parameters and the coefficient of friction have a great effect on contact stresses. Frictional sliding contact problem between a rigid circular conducting stamp and a magneto-electro-elastic half-plane was solved by Elloumi et al. [15]. Hou et al. [16] proposed a method based on Green function for the orthotropic coating-substrate system under a normal line force and numerical results were represented to show the accuracy and efficiency of this method in studies on the interface effect, interface debonding, coating tensile failure and the relationship between the orthotropic elastic moduli with the stress distributions. The influence of the wear partition factor on wear evolution modeling of sliding surfaces was studied by Mattei and Puccio [17]. They introduced the concept of wear partition factor to take into account different wear behaviors of the rubbing elements and described procedures and results of the numerical simulations of a two-dimensional wear evolution problem, defined by a cylinder sliding over a plate. Dag et al. [18] analyze the contact problem between a laterally graded medium and a rigid flat and triangular punch profiles both by analytically and by using a finite element method. Liu et al. [19] investigated the elastic dynamic stabilities about a homogenous elastic half-plane sliding against an FGM coated half-plane. The effects of the coating gradient index, friction coefficient and sliding speed on the dynamic stability were discussed. In the work conducted by Slavic et al. [20] roughness-induced vibrations on a slider were investigated and simple Poisson impact and Coulomb friction laws on multiple concurrent contacts between geometrically random rough surfaces and their effect on slider׳s roughness induced vibrations were investigated and a good agreement was satisfied between the results of studied models and the experiments. Ke and Wang [21], [22] developed SIE based solution techniques for two dimensional sliding frictional contact problems of FGMs and for contact problems of FGMs with partial slip [23], [24]. Ke et al. [25] studied two dimensional thermoelastic contact problem of FGMs involving frictional heating and even take into account convective effects due to sliding.

In all the studies mentioned in the foregoing paragraph, solutions are obtained by using temperature independent material thermoelastic properties. However, in frictional contacts, generated heat in the contact region may be significant and since this heat flows through the contacting material, it may cause changing the material thermoelastic properties. The main objective of the present study is to analyze the contact stresses and temperatures by using temperature dependent material properties. Moreover, comparative study is done between the results of temperature independent and dependent properties in order to reveal the differences between these two results when frictional heat reaches considerable amounts on contact surface. By taking into account of temperature dependency of material properties, it is also aimed to find more realistic results. Since it is very hard to get closed form analytical solutions, the finite element method is used and a solution algorithm is developed and implemented.