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.

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.

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.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2005 ◽  
Vol 127 (2) ◽  
pp. 325-330 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2004 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

Impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β ≤ 1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β ≤ 1, and increases gradually for β > 1. Based on finite element results for the subsurface stress, strain, and velocity fields, and simple theoretical model that yields approximated closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β ≤ 1), and its validity was confirmed by favor comparisons with finite element results.

scholarly journals Relationship Between Rockwell C Hardness and Inelastic Material Constants

2002 ◽  
Vol 124 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Akihiko Hirano ◽  
Masao Sakane ◽  
Naomi Hamada
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Strain Hardening ◽  
Yield Stress ◽  
Plastic Material ◽  
Stress And Strain ◽  
Material Constants ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Hardening Coefficient

This paper describes the relationship between Rockwell C hardness and elastic-plastic material constants by using finite element analyses. Finite element Rockwell C hardness analyses were carried out to study the effects of friction coefficient and elastic-plastic material constants on the hardness. The friction coefficient and Young’s modulus had no influence on the hardness but the inelastic materials constants, yield stress, and strain hardening coefficient and exponent, had a significant influence on the hardness. A new equation for predicting the hardness was proposed as a function of yield stress and strain hardening coefficient and exponent. The equation evaluated the hardness within a ±5% difference for all the finite element and experimental results. The critical thickness of specimen and critical distance from specimen edge in the hardness testing was also discussed in connection with JIS and ISO standards.

Finite Element Analysis of the Thermal Residual Stresses of Diamond Cutting Tools in the Sintering Process

2008 ◽  
Vol 587-588 ◽  
pp. 695-699 ◽  
Author(s):  
Luís G. Reis ◽  
Pedro M. Amaral ◽  
Bin Li ◽  
Carlos A. Anjinho ◽  
Luís Guerra Rosa ◽  
...  
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Diamond Tool ◽  
Diamond Particle ◽  
Elastic Behaviour ◽  
Tensile Behaviour ◽  
Sintering Process ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Thermal Residual Stresses

The main objective of the present work is to present and discuss the effects of the residual stresses generated in the matrix. Both, elastic and elastic-plastic models using explicit finite element code Abaqus were developed to investigate the thermal residual stresses generated around a diamond particle embedded in a metal matrix (a binder) during the sintering process for obtaining a diamond tool. The first part of the work consists in examining the thermal residual stress field generated by using three sintering temperatures from which the bodies are cooled from (T1=800°C, T2=700°C and T3=600°C) and two diamond shapes modelled with 2D axisymmetric elements, one from a circle the other from an octagon, respectively. In this case only one type of binder showing typical elastic behaviour is considered. The second part of this work consists in comparing the finite element solutions using binders with different tensile behaviour (elastic vs. elastic-plastic behaviour). This last study has used a particle shape generated from the octagon, since this shape allows, in a great number of real situations, the simulation of a particle with a larger number of facets, in line with what it is observed when looking at a conventional diamond tool.

Elastic-Plastic Finite Element Analysis of Indented Layered Media

1989 ◽  
Vol 111 (3) ◽  
pp. 430-439 ◽  
Author(s):  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Plastic Zone ◽  
Contact Pressure ◽  
Critical Parameters ◽  
The Finite Element Method ◽  
Contact Pressure Distribution ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Substrate Properties ◽  
Layered Half Space

The elastic-plastic contact problem of a layered half-space indented by a rigid surface is solved with the finite element method. The case of a layer stiffer and harder than the substrate is analyzed and solutions for the contact pressure, subsurface stresses and strains, and location, shape, and growth of the plastic zone are presented for various layer thicknesses and indentation depths. Finite element results for a halfspace having the substrate properties are also given for comparison purposes. Differences between the elastic and elastic-plastic solutions are discussed and the significance of critical parameters such as the layer thickness, mechanical properties of layer and substrate materials, indentation depth, and interfacial friction on the threshold of plasticity, contact pressure distribution, and growth of the plastic zone are examined. Additionally, the mechanisms of layer decohesion and subsurface crack initiation are interpreted in light of the results obtained in this study.

Tube-to-Tubesheet Joints: Maximum Tensile Stress and Contact Pressure Due to Thermal Loading and Temperature Cycling

2002 ◽  
Author(s):  
Mahdi A. Allam ◽  
Andre Bazergui ◽  
Luc Marchand ◽  
Michel Derenne
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Finite Element Model ◽  
Contact Pressure ◽  
Thermal Loading ◽  
Element Model ◽  
Maximum Tensile Stress ◽  
Temperature Cycling ◽  
Operating Conditions ◽  
Service Reliability

Service reliability and durability of tubular heat exchangers and steam generators are much dependent on the proper response of the tube-to-tubesheet joints to the operating conditions. In this paper a 2-D axisymmetric finite element model is proposed and compared to a 3-D finite element solution for the purpose of predicting the temperature effect on the residual contact pressure and maximum tensile residual stresses of such joints. A parametric study using the finite element results shows that, although thermal loading and temperature cycling have a negligible effect on the maximum tensile residual stresses, the room-temperature initial residual contact pressure may be completely relieved following the initiation of plastic deformation in either the tube or the tubesheet during thermal loading. A comparison between the results of the proposed finite element model and those obtained from the literature shows good agreement. A simplified analytical approach, which may be used for the design of tube-to-tubesheet joints, is also proposed to predict the joint behavior at the operating conditions.

Combined Effects of Tube Projection, Initial Tube-Tubesheet Clearance, and Tube Material Strain Hardening on Rolled Joint Strength

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
N. Merah ◽  
A. Al-Aboodi ◽  
A. N. Shuaib ◽  
Y. Al-Nassar ◽  
S. S. Al-Anizi
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Contact Pressure ◽  
Joint Strength ◽  
Element Model ◽  
Design Parameters ◽  
Radial Clearance ◽  
Tube Material ◽  
Element Analysis ◽  
Interfacial Pressure

The tube-to-tubesheet joint strength is measured in terms of interfacial pressure between the tube’s outer surface and tubesheet bore. The strength of a rolled joint is influenced by several design parameters, including the type of tube and tubesheet materials, initial tube projection, and the initial radial clearance between the tube and tubesheet, among other factors. This paper uses finite element analysis (FEA) to evaluate the effect of several parameters on the strength of rolled joints having large overtolerances, a situation that applies to used equipment. An axisymmetric finite element model based on the sleeve diameter and rigid tube expanding roller concepts was used to analyze the effects of tube projection, initial tube-tubesheet clearance, and tube material strain-hardening property on the deformation behavior of the rolled tube and on the strength of the tube-tubesheet joint. The FEA results show that for zero tube projection (flush) the initial clearance effect is dependent on the strain-hardening capability of the tube material. For low strain-hardening tube material the interfacial pressure remains constant well above the Tubular Exchanger Manufacturer’s Association maximum overtolerance. A drastic reduction in joint strength is observed at high values of radial clearances. The cut-off clearance (clearance at which the interfacial pressure starts to drop) is found to vary linearly with the tube material hardening level, and the contact stress increases slightly for moderate strain-hardening tube materials but shows lower cut-off clearance levels. Furthermore, with flush tubes the maximum contact pressure occurs close to the secondary face (at the end of rolling) while for joints with initial tube projection the contact pressure shows two maxima occurring near the primary and the secondary faces. This is attributed to the presence of two elbows in tube deformation near the primary and secondary faces. The average interfacial pressure increased with increasing projection length for all clearances. Tube material strain hardening enhances the interfacial pressure in a similar fashion for all initial tube projection lengths considered in the analysis.

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