Finite element analysis of cyclic indentation of an elastic-perfectly plastic half-space by a rigid sphere

2003 ◽  
Vol 217 (5) ◽  
pp. 505-514 ◽  
Author(s):  
S L Yan ◽  
L Y Li
Keyword(s):  
Finite Element ◽  
Pressure Distribution ◽  
Half Space ◽  
Contact Force ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Perfectly Plastic ◽  
Contact Behaviour ◽  
Cyclic Indentation ◽  
Elastic Perfectly Plastic

This paper presents a numerical study on the cyclic indentation of an elastic-perfectly plastic half-space by a rigid sphere. The study is performed using non-linear finite element methods. Results of contact pressure distribution, relationships between contact force, displacement and contact radius during loading, unloading and reloading are presented. The results show that the deformation during unloading from a contact beyond the elastic limit is perfectly elastic. However, the pressure distribution returns to the Hertzian elliptical distribution only when the maximum pressure at the contact centre is below 1.6αy. The reloading curve is found to be exactly the same as the unloading curve and the pressure distributions in reloading and unloading are the same for the same contact force. The influence of the plastic permanent deformation and residual stresses on the contact behaviour during reloading is discussed.

scholarly journals Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Hamid Ghaednia ◽  
Matthew R. W. Brake ◽  
Michael Berryhill ◽  
Robert L. Jackson
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Material Model ◽  
Real Contact Area ◽  
Contact Radius ◽  
Elastic Contact ◽  
Elastic Deformations ◽  
Real Contact ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

For elastic contact, an exact analytical solution for the stresses and strains within two contacting bodies has been known since the 1880s. Despite this, there is no similar solution for elastic–plastic contact due to the integral nature of plastic deformations, and the few models that do exist develop approximate solutions for the elastic–perfectly plastic material model. In this work, the full transition from elastic–perfectly plastic to elastic materials in contact is studied using a bilinear material model in a finite element environment for a frictionless dry flattening contact. Even though the contact is considered flattening, elastic deformations are allowed to happen on the flat. The real contact radius is found to converge to the elastic contact limit at a tangent modulus of elasticity around 20%. For the contact force, the results show a different trend in which there is a continual variation in forces across the entire range of material models studied. A new formulation has been developed based on the finite element results to predict the deformations, real contact area, and contact force. A second approach has been introduced to calculate the contact force based on the approximation of the Hertzian solution for the elastic deformations on the flat. The proposed formulation is verified for five different materials sets.

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 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.

Spherical Indentation of an Elastic–Perfectly Plastic Half-Space: Deformation Map and Evolution of Plasticity

2009 ◽  
Author(s):  
Z. Song ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Material Properties ◽  
Deformation Behavior ◽  
Spherical Indentation ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Wide Range ◽  
Elastic Perfectly Plastic

A finite element analysis of the indentation of an elastic-perfectly plastic half-space by a rigid sphere was performed for a wide range of material properties. The post-yield deformation behavior was found to consist of four deformation regimes, namely linear elastic-plastic, non-linear elastic-plastic, transient fully-plastic, and steady-state fully-plastic deformation. The boundaries of these deformation regimes were determined numerically in terms of elastic-plastic material properties. The deformation behavior in different regimes was examined in the context of finite element results showing the evolution of subsurface plasticity for different material properties.

The finite element analysis of a strain hardening layered medium under normal loading by (a) a rigid and (b) a deformable indenter

1998 ◽  
Vol 33 (6) ◽  
pp. 401-410 ◽  
Author(s):  
K C Tang ◽  
A Faulkner ◽  
S Sen ◽  
R D Arnell
Keyword(s):  
Finite Element ◽  
Tensile Stress ◽  
Strain Hardening ◽  
Plastic Substrate ◽  
Plastic Layer ◽  
Rigid Sphere ◽  
Normal Loading ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Contact Pressures

The finite element method (FEM) is used to investigate the normal indentation problem of a deformable indenter in contact with a strain hardening substrate coated with an elastic—perfectly plastic layer. In order to assess the influence of the deformable indenter, the solution is compared with results of a rigid sphere indenting the same system. The comparison shows that, when the indenter is assumed to be rigid, the contact pressures are significantly higher than those for the deformable indenter during elastic deformation. When plasticity is more pronounced, the peak pressures at just inside the contact edge are also higher for the rigid indenter. Similarly, the results assuming a rigid indenter give a lower value of maximum radial tensile stress along the coating surface when compared with those using a deformable indenter, which is responsible for the cracking of the film. In order to examine the effects of strain hardening, the above solutions are compared with a system having an elastic—perfectly plastic substrate. Comparison between the two sets of results shows that the strain hardening medium develops a smaller contact area and higher central and peak contact pressures inside the contact edge during plastic deformation. It also shows that the use of a strain hardening substrate alleviates the maximum radial tensile stress just outside the contact edge.

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.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Input Parameter ◽  
Time Integration ◽  
Strain Increment ◽  
Total Strain ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Time Stepping ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

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