Loading and Unloading Processes in Elastic-Plastic Contact of a Rough Surface With a Flat

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Contact Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Normal Contact ◽  
Elastic Plastic ◽  
Force Components ◽  
Plastic Parts

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the Chang, Etsion and Bogy (CEB) model of contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Each force component comprises elastic and elastic-plastic parts. Statistical summation of normal force components leads to the derivation of the normal contact force for the elastic-plastic contact akin to the CEB model. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction.

An Extension of CEB Elastic-Plastic Contact Model

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Contact Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Normal Contact ◽  
Elastic Plastic ◽  
Force Components ◽  
Plastic Parts

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is by developing the equations governing the shoulder-shoulder contact of asperities based on the Chang, Etsion and Bogy (CEB) model of contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Each force component comprises elastic and elastic-plastic parts. Statistical summation of normal force components leads to the derivation of the normal contact force for the elastic-plastic contact akin to the CEB model. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction.

Closed-Form Equations for Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Elastic Plastic ◽  
Functional Forms

Approximate closed-form equations governing the shoulder-shoulder contact of asperities are derived based on a generalization by Chang, Etsion, and Bogy. The work entails the consideration of asperity shoulder-shoulder contact in which the volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact gives rise to a slanted contact force comprising tangential and normal components. Each force component comprises elastic and plastic terms, which upon statistical summation yields the force component for the elastic and plastic forces for the contact of two rough surfaces. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction. Two sets of equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within 9%. The second set is enhanced equations derived from the first set of approximate equations that achieve an accuracy of within 0.2%.

Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces: Approximate Closed-Form Equations

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Elastic Plastic ◽  
Form Closure

Approximate closed-form (closure) equations governing the shoulder-shoulder contact of asperities are derived based on a generalization of Chang, Etsion and Bogy (CEB). The work entails the consideration of asperity shoulder-shoulder contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact gives rise to a slanted contact force comprising tangential and normal components. Each force component comprises elastic and elastic-plastic terms, which upon statistical summation yields the force component for the elastic and elastic-plastic force for the contact of two rough surfaces. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction. Two sets of closure equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within nine percent (9%). The second set of closure equations are closed form equations of more complicated form but with accuracy to within 0.2 percent (0.2%).

Viscoelastic Contact of Rough Surfaces in Relative Normal and Sliding Motion

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Contact Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Asperity Contact ◽  
Sliding Motion ◽  
Force Velocity ◽  
Force Components ◽  
Viscoelastic Contact ◽  
Approximate Equations

Mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. The development of the contact model is based on the asperity shoulder-shoulder contact leading to slanted asperity contact force. Thus an asperity force contains both normal and tangential components. Three dimensional consideration of asperity contact force yields directionally dependence of both the normal and tangential force components. A previously reported statistical approach is employed in which the dependence of the asperity normal and tangential contact force components on relative tangential velocity of two asperities are cast as corrective factors in the mathematical description of normal and tangential force components. The two corrective coefficients are the force directionality corrective coefficient and the force-velocity directionality corrective coefficient. Approximate equations are found for each of the normal and half-plane tangential force components that achieve accuracy within five (5) percent error.

scholarly journals A Finite Element-Based Elastic-Plastic Model for the Contact of Rough Surfaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Contact Area ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Element Model ◽  
Tangential Component ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Force Components

Three-dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity constitutive relations from a finite element model of the elastic-plastic interaction proposed by Kogut and Etsion (2002), in which asperity scale constitutive relations are derived using piecewise approximate functions. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. Shoulder-shoulder asperity contact yields a slanted contact force consisting of two components, one in the normal direction and a half-plane tangential component. Statistical summation of the asperity level contact force components and asperity level contact area results in the total contact force and total contact area formulae between two rough surfaces. Approximate equations are developed in closed form for contact force components and contact area.

Friction Due to Elastic-Plastic Contact of Rough Surfaces

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Half Plane ◽  
Normal Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Tangential Component ◽  
Force Term ◽  
Three Dimensional Model ◽  
Tangential Plane ◽  
Elastic Plastic

A three dimensional model based on CEB elastic-plastic contact leads to the derivation of two force components due to the shoulder-shoulder interaction of the asperities. A normal force component is resulted that upon summation of all possible interactions, in a statistical sense, obtains the normal force between the two surfaces. A second component of asperity force would be along the tangential plane (mean plane). When there is not net applied tangential force the tangential component of force on an asperity due to all its interactions would vanish. Upon impending motion, however, the tangential force can no longer cancel since the existence of a net tangential applied load would disrupt the symmetry of loading in the tangential direction. A three dimensional elastic-plastic model then furnishes a half-plane tangential elastic-plastic force term that would exist when relative movement of one surface on another occurs along an arbitrary axis in the tangential plane. This paper addresses an account of friction due to the elastic-plastic interaction of two surfaces by recognizing that the tangential half-plane elasto-plastic force term is the resisting force when two surfaces in elastic-plastic contact are made to slide.

Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces Based on FEA-Based Constitutive Asperity Contact Relations and Including Asperity Shoulder Contact

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Contact Force ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Cumulative Effect ◽  
Element Model ◽  
Tangential Component ◽  
Normal Direction ◽  
Asperity Contact ◽  
Elastic Plastic

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction proposed by Kogut and Etsion [12]. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.

Approximate Macroscale Constitutive Relations Using a Finite Element Based Constitutive Equations for Microscale Contact

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Cumulative Effect ◽  
Element Model ◽  
Tangential Component ◽  
Total Force ◽  
Asperity Contact ◽  
Elastic Plastic

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Multiscale modeling of the elastic-plastic rough surface contact is presented in which asperity-level FE-based constitutive relations are statistically summed to obtain total force in the normal and tangential direction. The equations derived are in the form of integral functions and provide expectation of contact force components between two rough surfaces. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.

Tangential Force Model for the Combined Finite-Discrete Element Method

2019 ◽  
Vol 17 (09) ◽  
pp. 1950068
Author(s):  
Xunnan Liu ◽  
Lanhao Zhao ◽  
Jia Mao ◽  
Tongchun Li
Keyword(s):  
Discrete Element Method ◽  
Contact Interaction ◽  
Contact Force ◽  
Tangential Force ◽  
Numerical Test ◽  
Discrete Element ◽  
Force Model ◽  
Normal Contact ◽  
Tangential Contact ◽  
Element Method

In the past, contact model in the combined finite-discrete element method (FDEM) does not include the influence of the tangential contact interaction, and the deficient model associated with the contact force can seriously degrade the computing accuracy. In order to overcome this defect, an improved FDEM is developed in this work. The potential contact mechanism is implemented to calculate the normal contact force; meanwhile, the force-displacement law by coupling the classical Mohr–Coulomb type frictional algorithm and the rotation transformation algorithm is applied for the accurate computation of the tangential contact force. Consequently, a holonomic system of the calculation algorithm for the contact interaction is proposed, accounting for the influence of the tangential contact force. The performance of the approach is validated with well-known benchmarks including a frictional numerical test, the dynamic response of the block under the seismic excitation, a sliding/toppling test of a joint rock slope, a numerical simulation for joints structure affecting a sliding rock mass and the 2008 Donghekou Landslide trigged by the Wenchuan Earthquake. The results are compared against the experimental data and analytical solutions. Excellent agreements between the computational result and existing measurements show that the proposed approach has an outstanding ability to describe the complex mechanical properties among the separate entities.

An Analytical Solution for Three-Dimensional Elliptical Elastic-Plastic Rolling Contact

2014 ◽  
Vol 658 ◽  
pp. 207-212
Author(s):  
Gabriel Popescu
Keyword(s):  
Residual Stresses ◽  
Yield Criterion ◽  
Tangential Force ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Plastic Behavior ◽  
Elastic Plastic

An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

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