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.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Layered Media Under Thermomechanical Surface Loading

2002 ◽  
Vol 125 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Numerical Solutions ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Thin Layers ◽  
Surface Loading ◽  
Elastic Plastic ◽  
Thermomechanical Surface

The simultaneous effects of mechanical and thermal surface loadings on the deformation of layered media were analyzed with the finite element method. A three-dimensional model of an elastic sphere sliding over an elastic-plastic layered medium was developed and validated by comparing finite element results with analytical and numerical solutions for the stresses and temperature distribution at the surface of an elastic homogeneous half-space. The evolution of deformation in the layered medium due to thermomechanical surface loading is interpreted in light of the dependence of temperature, von Mises equivalent stress, first principal stress, and equivalent plastic strain on the layer thickness, Peclet number, and sliding distance. The propensity for plastic flow and microcracking in the layered medium is discussed in terms of the thickness and thermal properties of the layer, sliding speed, medium compliance, and normal load. It is shown that frictional shear traction and thermal loading promote stress intensification and plasticity, especially in the case of relatively thin layers exhibiting low thermal conductivity.

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.

Effect of Residual Stress in Surface Layer on Contact Deformation of Elastic-Plastic Layered Media

2003 ◽  
Vol 125 (4) ◽  
pp. 692-699 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Surface Layer ◽  
Coefficient Of Friction ◽  
Layered Medium ◽  
Equivalent Stress ◽  
Equivalent Plastic Strain ◽  
Layered Media ◽  
Contact Loading ◽  
Elastic Plastic

The effect of residual stress in the surface layer on the deformation of elastic-plastic layered media due to indentation and sliding contact loading and unloading was analyzed with the finite element method. A three-dimensional finite element model of a rigid sphere interacting with a deformable layered medium was developed, and its accuracy was evaluated by contrasting finite element results with analytical solutions for the surface stresses of an elastic homogeneous half-space subjected to normal and friction surface traction. Deformation of the layered medium is interpreted in terms of the dependence of the von Mises equivalent stress, first principal stress, and equivalent plastic strain on the magnitudes of residual stress and coefficient of friction. The effect of residual stress on the propensity for yielding and cracking in the layered medium is discussed in the context of results for the maximum Mises and tensile stresses and the evolution of plasticity in the subsurface. It is shown that the optimum residual stress in the surface layer depends on the type of contact loading (indentation or sliding), coefficient of friction, and dominant deformation mode in the layer (i.e., plastic deformation or cracking).

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.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham Π theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Dynamic Indentation of an Elastic-Plastic Multi-Layered Medium by a Rigid Cylinder

2004 ◽  
Vol 126 (1) ◽  
pp. 18-27 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Layered Medium ◽  
Equivalent Stress ◽  
Contact Analysis ◽  
Radius Of Curvature ◽  
Dynamic Indentation ◽  
Rigid Cylinder ◽  
Elastic Plastic ◽  
Static Contact

A plane-strain analysis of dynamic indentation of an elastic-plastic multi-layered medium by a rigid cylinder was performed using the finite element method. Conversely to plane-strain static contact analysis, the solutions of a dynamic contact analysis within a subsurface domain adjacent to the contact region are independent of mesh size, provided the mesh dimensions are sufficiently large such that the propagating waves reflected from the artificial boundaries do not reach the domain of interest during the analysis. Simulation results for the normal force, contact pressure distribution, subsurface stresses, and evolution of plasticity in the multi-layered medium are presented in terms of the speed and radius of the rigid indenter. The likelihood of mechanical failure due to excessive plastic deformation and cracking is interpreted in terms of finite element results for the von Mises equivalent stress, first principal stress, and equivalent plastic strain obtained for different values of the indenter speed and radius of curvature.

Adhesive Contact of Elastic-Plastic Layered Media: Effective Tabor Parameter and Mode of Surface Separation

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Z. Song ◽  
K. Komvopoulos
Keyword(s):  
Layer Thickness ◽  
Material Properties ◽  
Layered Medium ◽  
Adhesive Contact ◽  
Rigid Sphere ◽  
Maximum Surface ◽  
Elastic Plastic ◽  
Surface Separation ◽  
Plasticity Parameter ◽  
Tabor Parameter

Adhesive contact of a rigid sphere with a layered medium consisting of a stiff elastic layer perfectly bonded to an elastic-plastic substrate is examined in the context of finite element simulations. Surface adhesion is modeled by nonlinear spring elements obeying a force-displacement relation governed by the Lennard–Jones potential. Adhesive contact is interpreted in terms of the layer thickness, effective Tabor parameter (a function of the layer thickness and Tabor parameters corresponding to layer and substrate material properties), maximum surface separation, layer-to-substrate elastic modulus ratio, and plasticity parameter (a characteristic adhesive stress expressed as the ratio of the work of adhesion to the surface equilibrium distance, divided by the yield strength of the substrate). It is shown that surface separation (detachment) during unloading is not encountered at the instant of maximum adhesion (pull-off) force, but as the layered medium is stretched by the rigid sphere, when abrupt surface separation (jump-out) occurs under a smaller force (surface separation force). Ductile- and brittle-like modes of surface detachment, characterized by the formation of a neck between the rigid sphere and the layered medium and a residual impression on the unloaded layered medium, respectively, are interpreted for a wide range of plasticity parameter and maximum surface separation. Numerical results illustrate the effects of layer thickness, bulk and surface material properties, and maximum surface separation (interaction distance) on the pull-off and surface separation forces, jump-in and jump-out contact instabilities, and evolution of substrate plasticity during loading and unloading. Simulations of cyclic adhesive contact demonstrate that incremental plasticity (ratcheting) in the substrate is the most likely steady-state deformation mechanism under repetitive adhesive contact conditions.

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.

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