The Application of Limit Analysis to Punch-Indentation Problems

1953 ◽  
Vol 20 (4) ◽  
pp. 453-460
Author(s):  
R. T. Shield ◽  
D. C. Drucker
Keyword(s):  
Limit Analysis ◽  
Plane Surface ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Flat Punch ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

Three-Dimensional Analysis of Ice Sheet Indentation: Limit Analysis Solutions

1989 ◽  
Vol 111 (1) ◽  
pp. 63-69 ◽  
Author(s):  
D. G. Karr ◽  
J. C. Watson ◽  
M. HooFatt
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Upper Bound Theorem ◽  
Infinite Layer ◽  
Perfectly Plastic ◽  
Aspect Ratios

A method is presented for determining the collapse pressures of an ice sheet subjected to a uniformly distributed edge load by applying the upper-bound theorem of limit analysis. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. A quadratic anisotropic yield criterion is used to calculate the indentation pressures. The ice sheet consists of columnar ice and is assumed isotropic in the plane of the ice sheet. Upper-bound solutions are found by optimizing a three-dimensional discontinuous velocity field representing an assumed collapse pattern of the ice sheet. Solutions are based on various ratios of indentor width to ice thickness, thereby providing an envelope of indentation pressures over a range of aspect ratios, from conditions of plane strain to plane stress. Solutions are then compared with corresponding two and three-dimensional lower-bound analyses.

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 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.

Plastic Limit Loads for Through-Wall Cracked Pipes Using Finite Element Limit Analysis

2006 ◽  
Vol 321-323 ◽  
pp. 724-728
Author(s):  
Nam Su Huh ◽  
Yoon Suk Chang ◽  
Young Jin Kim
Keyword(s):  
Finite Element ◽  
Limit Analysis ◽  
Structural Integrity ◽  
Three Dimensional ◽  
Limit Load ◽  
Plastic Behavior ◽  
Plastic Limit ◽  
Integrity Assessment ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper provides plastic limit load solutions for axial and circumferential through-wall cracked pipes based on detailed three-dimensional (3-D) finite element (FE) limit analysis using elastic-perfectly plastic behavior. As a loading condition, both single and combined loadings are considered. Being based on detailed 3-D FE limit analysis, the present solutions are believed to be valuable information for structural integrity assessment of cracked pipes.

Limit Analysis of Ice Sheet Indentation

1983 ◽  
Vol 105 (3) ◽  
pp. 352-355 ◽  
Author(s):  
D. G. Karr ◽  
S. C. Das
Keyword(s):  
Limit Analysis ◽  
Plastic Material ◽  
Yield Criterion ◽  
Ice Sheet ◽  
Yield Function ◽  
Infinite Layer ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Yield Functions ◽  
Stress Ratios

The methods of plastic limit analysis are used to determine the indentation pressures of a flat rectangular punch on an ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Lower bounds are computed by application of the lower bound limit theorem. The suitability of basic yield functions are assessed based on their ability to predict failure at demonstrated ice failure stress ratios. The particular yield functions that are employed include the generalized Mohr-Coulomb (or Drucker-Prager) criterion, a modified Drucker-Prager criterion, as well as a parabolic yield criterion used previously in literature on this topic. A study of the effects on indentation pressure of varying ice strength parameters is presented. Limit analysis solutions are obtained for plane stress conditions, and thus the applicability of a particular yield function can be evaluated for a range of ice strengths for indentation problems involving high aspect ratios.

On Plastic Collapse of Media With Random Yield Strength

2001 ◽  
Vol 68 (5) ◽  
pp. 715-724 ◽  
Author(s):  
A. P.-D. Ku ◽  
R. P. Nordgren
Keyword(s):  
Yield Strength ◽  
Plane Problem ◽  
Gaussian Random Field ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Plastic Collapse ◽  
Variable Yield ◽  
Perfectly Plastic ◽  
Fixed Load ◽  
Elastic Perfectly Plastic

This paper concerns the plastic collapse of an elastic/perfectly plastic medium with randomly variable yield strength under a fixed load. The yield strength is represented by a Gaussian random field of known statistical properties. Using the theorems of limit analysis and the methods of reliability theory, algorithms are developed for the computation of upper and lower bounds on the probability of plastic collapse. By varying the magnitude of the fixed load, bounds on the probability distribution function for the collapse load can be computed. Results are given for uniform pressure applied to a rectangular region of the surface of an elastic/plastic half-space. For the corresponding plane problem, results for the classical Hill and Prandtl failure mechanisms are compared. Three-dimensional results are found to differ significantly from those of the plane problem. Comparison is made with results of a previous approximate method for three-dimensional problems.

Methods for the simulation of the pressure, stress, and temperature distribution in the contact of fractal generated rough surfaces

2016 ◽  
Vol 231 (4) ◽  
pp. 489-502 ◽  
Author(s):  
Balázs Magyar ◽  
Bernd Sauer
Keyword(s):  
Surface Roughness ◽  
Temperature Distribution ◽  
Plastic Material ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Sliding Contact ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Pressure Stress

In this paper, the influence of surface roughness on the local tribological load with a dry sliding contact is studied. First, three artificial rough surfaces with similar structure but different asperity heights are generated and projected on a smooth ball. After that, a contact pattern is determined between a rough ball and a smooth surface taking into account the elastic only as well as the linear elastic-perfectly plastic material description. On the basis of the calculated contact pressure distribution, the subsurface stresses and a three-dimensional temperature distribution in the sliding contact are calculated. The solutions show that a low surface roughness not necessarily results in low local tribological load of the surface.

Numerical Study of Defect Free Elbows Subjected to In-Plane Bending Moment

2011 ◽  
Vol 189-193 ◽  
pp. 1494-1497
Author(s):  
Wang Chen ◽  
Yin Pei Wang ◽  
Pei Ning Li ◽  
Chen Jin ◽  
Xiao Ming Sun
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Three Dimensional ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Piping System ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Bending Radius ◽  
Elastic Perfectly Plastic

Elbow is a type of components widely used in a piping system, and so it is very important to know the plastic carrying capacity of elbow. In this study, the elastic-plastic behavior of elbows with various ratios of t/rm and relative bending radius R/rm were investigated in detail by using of three-dimensional (3D) non-linear finite element (FE) analyses, assuming elastic-perfectly-plastic material behaviour and taking geometric nonlinearity into account. The analyses indicated that elbow exhibited different behavior obviously at the elastic-plastic states subjected to In-Plane opening bending moment and closing bending moment. The closed form equations of elbow involving effect of tangent pipes were established.

Lower Bound Net-Section Limit Loads for Circumferential Part-Through Surface Cracked Pipes Under Combined Pressure and Bending

2007 ◽  
Author(s):  
Chang-Kyun Oh ◽  
Yun-Jae Kim ◽  
Jong-Sung Kim ◽  
Te-Eun Jin
Keyword(s):  
Hoop Stress ◽  
Plastic Material ◽  
Three Dimensional ◽  
Limit Load ◽  
Surface Cracks ◽  
Stress Distributions ◽  
Plastic Limit ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

This paper provides plastic limit loads of pipes with constant-depth, circumferential part-through surface cracks under combined pressure and bending. A key issue is to postulate discontinuous hoop stress distributions in the net-section. Validity of the proposed limit load solutions are checked against the results from three-dimensional (3-D) finite element (FE) limit analyses using elastic-perfectly plastic material behaviour.

scholarly journals On The Mechanics of Indentation Induced Lateral Cracking

2004 ◽  
Vol 841 ◽  
Author(s):  
Xi Chen
Keyword(s):  
Mechanical Properties ◽  
Axisymmetric Problem ◽  
Plastic Material ◽  
Three Dimensional ◽  
Indentation Load ◽  
Mode I ◽  
Vickers Indentation ◽  
Annular Crack ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

ABSTRACTThe mechanics governing the lateral cracks that form when a hard object plastically penetrates a ceramic is presented. The roles of indentation load, penetration depth and work of indentation are all highlighted, as are the influences of the mechanical properties of the substrate. The three dimensional axisymmetric problem for an annular crack driven by a rigid spherical or conical indenter pushed into a semi-infinite half-space of elastic-perfectly plastic material is solved using numerical methods. The region of highest tensile stress is identified corresponding to the location where a crack is most likely to nucleate. This location coincides with the depth below the surface where the crack will expand parallel to the surface under mode I conditions. The solutions have been validated by comparison with measurements of the cracks that form upon Vickers indentation. The basic formula for the crack radius has been used to predict trends in cracking upon static penetration.

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