Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part II: Subsurface Results

1995 ◽  
Vol 62 (1) ◽  
pp. 29-42 ◽  
Author(s):  
E. R. Kral ◽  
K. Komvopoulos ◽  
D. B. Bogy
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Half Space ◽  
Peak Load ◽  
Interfacial Shear ◽  
Rigid Sphere ◽  
Shear Stresses ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic

Finite element solutions are presented for the subsurface stress and deformation fields in a layered elastic-plastic half-space subjected to repeated frictionless indentation by a rigid sphere. A perfectly adhering layer is modeled using two different thicknesses and elastic modulus and yield stress two and four times greater than those of the substrate. The significance of strain hardening during plastic deformation is investigated by assuming elastic-perfectly plastic and isotropically strain-hardening constitutive laws for both the layer and substrate materials. At least three load-unload cycles are applied to a peak load of 300 times the load necessary to initiate yielding in a homogeneous half-space with substrate properties. The effects of the layer thickness and material properties of the layer and substrate on the loaded and residual stresses are interpreted, and the consequences for subsurface crack initiation are discussed. The maximum principal and interfacial shear stresses are given as a function of a nondimensional strain parameter. The effect of subsequent load cycles on the loaded, residual, and maximum tensile and interfacial shear stresses and the protection provided by the harder and stiffer layer are analyzed. Reyielding during unloading and the possibility of elastic shakedown are discussed, and the accumulation of plastic strain in the yielding regions is tracked through subsequent load cycles.

Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere

1993 ◽  
Vol 60 (4) ◽  
pp. 829-841 ◽  
Author(s):  
E. R. Kral ◽  
K. Komvopoulos ◽  
D. B. Bogy
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Half Space ◽  
Contact Pressure ◽  
Peak Load ◽  
Rigid Sphere ◽  
Load Range ◽  
Elastic Plastic ◽  
Residual Displacements

The elastic-plastic contact problem of a rigid sphere indenting a homogeneous halfspace is analyzed with the finite element method. Emphasis is placed on the load range between elastic and fully plastic deformation, which has not yet been fully investigated. The rigid sphere is modeled by contact elements, thus eliminating the need to assume a particular pressure profile. Different elastic properties, with both elastic-perfectly plastic and isotropic strain hardening behaviors, are considered. Up to four complete frictionless load-unload cycles are applied to a peak load of 300 times the load necessary for the initiation of yielding. Results for the contact pressure, surf ace and subsurface stresses, initiation and growth of the plastic zone, and yielding of the half-space during unloading are presented. The effect of residual displacements on the contact pressure during subsequent load cycles is examined. The influence of strain hardening on the loading and residual stresses is analyzed and the consequences for crack initiation are discussed in light of these results. The accumulation of plastic strain in the yielding regions is tracked through the subsequent load cycles as the material approaches a steady-state elastic cycle, and the significance of the loading and residual stresses on the deformation characteristics is interpreted in the context of finite element results.

Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part I: Surface Results

1995 ◽  
Vol 62 (1) ◽  
pp. 20-28 ◽  
Author(s):  
E. R. Kral ◽  
K. Komvopoulos ◽  
D. B. Bogy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Peak Load ◽  
Rigid Sphere ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Surface Stresses ◽  
Residual Displacements

A comprehensive elastic-plastic finite element analysis is presented for the axisym-metric problem of a frictionless rigid sphere indenting a half-space with a harder and stiffer layer. The indenter is modeled by contact elements, thereby avoiding a priori assumptions for the pressure profile. Two layer thicknesses are examined, with layer elastic modulus and yield stress both two and four times greater than those of the substrate. Perfectly plastic and isotropic strain-hardening behavior of the layer and substrate media are investigated. At least three complete load-unload cycles are applied to a peak load of 300 times the load necessary to initiate yielding in a half-space of the substrate material. The effect of hardening properties on the loaded and residual stresses is presented and the consequences for crack initiation at the surface are discussed. Results for the contact pressure and surface stresses and deformations are presented, and the influence of residual displacements and load cycles on the contact pressure and the loaded and residual surface stresses is investigated.

Dynamic Finite Element Analysis of an Elastic-Plastic Half-Space Indented by a Rigid Sphere

2010 ◽  
Author(s):  
A. Lee ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Equivalent Plastic Strain ◽  
Dynamic Contact ◽  
Rigid Sphere ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Wide Range ◽  
Deformation Velocity ◽  
Elastic Plastic Materials

Dynamic indentation of an elastic-plastic half-space by a rigid sphere was studied with the finite element method. A parametric analysis was performed to examine the effects of indentation velocity and yield strength of the half-space material on dynamic contact deformation. Velocity effects are discussed in the context of simulation results of global and local contact parameters, such as mean contact pressure, contact area, and equivalent plastic strain. The evolution of deformation as the material response transitions from elastic to fully-plastic deformation during dynamic contact is interpreted in light of numerical results. This study elucidates the effect of dynamic contact loading on the deformation behavior of elastic-plastic materials for a wide range of length scales where a continuum mechanics description holds.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

A Finite Element Analysis of the Effect of Hardening Rules on the Indentation Test

1998 ◽  
Vol 120 (2) ◽  
pp. 143-148 ◽  
Author(s):  
N. Huber ◽  
Ch. Tsakmakis
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Indentation Test ◽  
Rigid Sphere ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Hardening Rules

Using the Finite Element Method, an analysis is given of the indentation of an elasticplastic half-space by a rigid sphere. In particular, attention is focused on the effect of hardening rules on the material response. The materials considered are supposed to exhibit isotropic and kinematic hardening. Moreover, it is shown that the possibility of similar behavior due to effects of friction can be ruled out.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 1: Analysis of Single Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 67-74 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Rolling Contact ◽  
Stress And Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Contact Width ◽  
Elastic Perfectly Plastic

This paper describes a two-dimensional (plane strain) elastic-plastic finite element model of rolling contact that embodies the elastic-perfectly plastic, cycle and amplitude-independent material of the Merwin and Johnson theory, but is rigorous with respect to equilibrium and continuity requirements. The rolling contact is simulated by translating a semielliptical pressure distribution. Both Hertzian and modified Hertzian pressure distributions are used to estimate the effect of plasticity on contact width and the continuity of the indentor-indentation interface. The model is tested for its ability to reproduce various features of the elastic-plastic indentation problem and the stress and strain states of single rolling contacts. This paper compares the results derived from the finite element analysis of a single, frictionless rolling contact at p0/k = 5 with those obtained from the Merwin and Johnson analysis. The finite element calculations validate basic assumptions made by Merwin and Johnson and are consistent with the development of “forward” flow. However, the comparison also reveals significant differences in the distribution of residual stress and strain components after a single contact cycle.

A theoretical model for the contact of elastoplastic bodies

2001 ◽  
Vol 216 (4) ◽  
pp. 421-431 ◽  
Author(s):  
L-Y Li ◽  
C-Y Wu ◽  
C Thornton
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Contact Problems ◽  
Rigid Sphere ◽  
Element Analysis ◽  
Normal Contact ◽  
Perfectly Plastic ◽  
Static Contact ◽  
Elastic Perfectly Plastic ◽  
Force Displacement

The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. Formulae describing the force-displacement relationship for static contact problems and the coefficient of restitution for dynamic impact problems are derived. The present model can be considered as a modification of Johnson's model by using a more detailed pressure distribution function which is based on finite element analysis (PEA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, finite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coefficients. Good agreements between the model predictions and the FEA results are found.

Indentation Analysis of Elastic-Plastic Homogeneous and Layered Media: Criteria for Determining the Real Material Hardness

2003 ◽  
Vol 125 (4) ◽  
pp. 685-691 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Constitutive Models ◽  
Layered Media ◽  
Rigid Sphere ◽  
The Real ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Real Material ◽  
Material Hardness

A hardness analysis based on finite element simulation results and contact constitutive models is presented for both homogeneous and layered elastic-plastic media. The analysis provides criteria for obtaining the real material hardness from indentation experiments performed with spherical indenters. Emphasis is given on the estimation of the hardness of thin surface layers. The critical (maximum) interference distance that yields an insignificant effect of the substrate deformation on the estimation of the layer hardness is determined from the variation of the equivalent hardness of the layered medium with the interference distance (indentation depth). A relation between hardness, yield strength, and elastic modulus, derived from finite element simulations of a homogeneous half-space indented by a rigid sphere, is used in conjunction with a previously developed contact constitutive model for layered media to determine the minimum interference distance needed to produce sufficient plasticity in order to ensure accurate measurement of the material hardness. An analytical approach for estimating the layer hardness from indentations performed on layered media is presented and its applicability is demonstrated in light of finite element indentation results for an elastic-perfectly plastic layered medium with a hard surface layer.

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