Fretting damage modeling of liner-bearing interaction by combined finite element – discrete element method

Abstract

This paper presents a methodology to study the fretting damage behavior by combined finite element-discrete element method based on FFD method and cut boundary displacement method. A discrete element modeling technique is developed. An inter-element contact constitutive model and its microscopic parameters are determined and calibrated to reproduce continuous and discontinuous behaviors of material in DEM. A crack visualization technique is developed to display cracks according to their failure mode and time dependency. The effect of fretting condition on crack initiation and propagation as well as fretting damage is studied. The mechanism of fretting wear is investigated.

Introduction

In general, fretting is defined as a small displacement oscillatory motion between two solids in contact. The fretting wear and fretting fatigue may become relevant failure mechanism when two or more solids in contact experience small reciprocating motion. Experimental and analytical investigations have shown that fretting process is a complex combination of science, relating to Tribology, Contact Mechanics, Fatigue; it is affected by 50 different variables [1]. In aeronautic and astronautic industries, fretting damage has been one of the most detrimental damage and it may cause catastrophic consequences.

Fretting damage has been reported and investigated for over 50 years. Scientists and engineers have occupied themselves to develop analytical solution, experimental measurement and numerical algorithm to study fretting problems. Cattaneo [2] and Mindlin [3] proposed independently the first analytical solutions to solve fretting problem; Goryacheva [4] developed an analytical model for fretting wear based on Archard wear equation; Kasarekar modeled the fretting contact between randomly generated three-dimensional rough contacts solving elasticity equations by Fast Fourier Transform [5].

Also, the fretting process has been experimentally evaluated via full scale test or coupon scale test using specially designed test rigs. However, main problems remained in experimental method include: (1) there has been no standard or generally accepted test rig for fretting experiment up to now. As a result, the experimental results obtained from different test rigs cannot be consistent with one another; (2) previous studies found that the evolution of fretting damage behavior was difficult to accurately measure in practice, such as the process of crack initiation and propagation inside specimen and dynamical behavior of third body particles between contact and target surfaces during fretting; also, it was impossible to control each of the different parameters involved without modifying the others.

More recently, with rapid development of multi-core CPU technique, it is possible to study fretting problem by means of numerical algorithm, such as finite element method (FEM), boundary element method (BEM), molecular dynamics (MD), discrete element method (DEM), and so on.

The FEM, based on continuum mechanics, has already been widely used to solve fretting problem. Earlier fretting models built upon earlier finite element models were used to study sliding wear [6], [7] and reciprocating sliding [8]; McColl [9] originally studied fretting wear using a commercial FEM software; Fouvry [10] and Paulin [11] developed finite element models to study fretting wear. In general, the processes of fretting analysis based on FEM can be more or less summarized as follows: (1) modeling contact and target solids to allow them to rub against each other along a given sliding distance under specified loading and boundary condition; (2) using an Archard-type law, the volume of matter that should be removed from material is calculated and the geometry feature is modified according to the loss volume for the next time step. The FEM-based method is able to solve non-linear contact problem with reasonable accuracy and computational efficiency, however, it is lack of capability or qualification to reproduce the discontinuous behavior of material during fretting process. For a FEM-based fretting simulation, the calculated results are strongly dependent on the parameters obtained from the corresponding experiment, such as the initially prescribed crack path and the wear coefficient of materials; the third body particles (debris) are not permitted to be retained in contact zone during fretting calculation. As a result, the FEM is not an ideal tool to solve fretting problem with high fidelity. It is necessary to develop an adequate algorithm to evaluate the discontinuous behaviors during fretting process.

The DEM, originally proposed by Cundall [12], [13] for geotechnical applications, has been an ideal tool to simulate discontinuous, heterogeneous, anisotropic medium behavior. More recently, scientists have successfully used the DEM to study material's fracture, damage, wear behaviors and contact mechanics between rough surfaces [14], [15], [16], [17], [18], [19], [20]. It has been proved that the DEM has a practical potential to simulate the evolution of crack initiation and propagation as well as the behavior of third body particles with high fidelity. However, the DEM is a time consuming algorithm in nature. Therefore, it is merely adopted to simulate assembly systems constructed by a relatively small amount of elements.

Considering the strengths and weaknesses of the FEM and the DEM for solving fretting problem, scientists have developed FE-DE coupled algorithm to solve fretting problem [21]. This algorithm is gaining popularity for problems involving contact modeling.

The aim of our current work is to develop a fundamental method to numerically analyze the fretting problem taking into account the discontinuous behavior of material and the balance between computational efficiency and accuracy. This paper is composed of five sections. In Section 2, a series of non-linear contact analyses are carried out by FEM. The risk position is predicted based on FFD method and FEM simulated results. In Section 3, a discrete element modeling technique is proposed and the microscopic parameters required by DEM are determined and calibrated. In Section 4, a series of DEM simulations are performed. The mechanisms of fretting wear and fatigue are investigated. A crack visualization technique is proposed to display cracks according to their failure mode and/or time dependency. The effect of fretting condition on crack initiation and propagation as well as fretting damage is studied. Section 5 concludes the paper.