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Three-Dimensional Modeling of Elasto-Plastic Sinusoidal Contact under Time Dependent Deformation Including Both Stress Relaxation and Creep Analysis




Rostami, Amir

Type of Degree



Mechanical Engineering


Computational modeling of contact between rough surfaces has attracted a great deal of attention due to the developing technological needs of industry. Most of the early models of rough surface contacts assumed a cylindrical or spherical/ellipsoidal shape for the asperities on the surfaces. Due to high memory space and computational time requirements, researchers use simplified geometries to model the asperities or peaks on rough surfaces. Recent works tried to use a sinusoidal shape for asperities to improve the previous models. The sinusoidal geometry gives a better prediction of asperity interaction, especially for heavily loaded contacts. The effect of adjacent asperities is considered in sinusoidal contacts by using a symmetric boundary condition. Also, most of the multiscale contact models for rough surfaces use the Fourier series or Weierstrass profile to transform a rough surface to combination of sine and cosine functions. Therefore, it seems more reasonable to use a sinusoidal shape for asperities. In the current work, the transient effect of creep and stress relaxation in contact between sinusoidal surfaces is studied using FE simulations. A three-dimensional sinusoidal asperity is created, and is modeled in contact with a rigid flat surface. The material of the sinusoidal surface is modeled as elasto-plastic, bi-linear isotropic hardening solid. The Garofalo formula is used in the current work to model the transient behavior of creep and stress relaxation. Two load steps are used in commercial software ANSYS (version 13.0) to model the effect of creep and stress relaxation. The first load step is static deformation or the stress build-up stage that is used to pressurize the asperity by the rigid flat surface. The second load step is the transient process during which creep and stress relaxation occur. To verify the model, the results for the purely elastic and elasto-plastic cases (without the creep and stress relaxation effects) are compared to the previous works in the literature. Transient results under both constant displacement (stress relaxation) and constant force (creep) boundary conditions are presented and discussed. A parametric study is done to analyze the effect of the different material and geometrical properties and also the Garofalo constants on the transient results. In the end, empirical equations are developed for both contact area and contact pressure based on the FEM results. The empirical equations are dependent on the surface separation, aspect ratio, and the Garofalo formula constants. In the contact area and contact pressure results for stress relaxation, a critical interference or surface separation was found that the contact area and contact pressure showed different behaviors above and below this value. The aspect ratio rate, , is introduced as a parameter that is independent from the height of the asperity during the stress relaxation process. This rate can be used in a multiscale contact model for rough surfaces to predict the real contact area as a function of time.