On Friction of Ploughing by Rigid Asperities in the Presence of Straining—Upper Bound Method

1990 ◽  
Vol 112 (2) ◽  
pp. 324-329 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Finite Element ◽  
Friction Factor ◽  
Upper Bound ◽  
Plastic Material ◽  
High Accuracy ◽  
The Other ◽  
Periodic Array ◽  
Combined Loading ◽  
Upper Bound Method ◽  
Perfectly Plastic

Upper bound applications traditionally assume that a rigid/perfectly-plastic material moves by rigid blocks, creating discontinuities of velocity at the interfaces between the blocks. In the present version, the elements (blocks) are plastically deformable and there are no velocity discontinuities between adjacent sides. Since this modification incorporates major features of finite element representation employing arbitrary cells, it allows the use of many parameters for minimization, thus achieving high accuracy. On the other hand, it retains the advantage of upper bound techniques in that the incremental procedure for loading is not necessary, and the results for steady processes are obtained directly. Some energy statements for combined loading are derived and a technique for calculating the ploughing force is presented. Examples for a single fully embedded rigid pyramid and a periodic array of asperities ploughing through the rigid/perfectly plastic material in the presence of subsurface straining are given. The friction factor decreased as the rate of subsurface straining increased, as the pyramid angle of the asperities increased, and as the distance between asperities increased.

A Generalization of the Upper Bound Method With Particular Reference to the Problem of a Ploughing Indenter

1989 ◽  
Vol 56 (1) ◽  
pp. 10-14 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Finite Element ◽  
Upper Bound ◽  
Plastic Material ◽  
Approximate Solutions ◽  
Upper Bound Method ◽  
Numerical Examples ◽  
Perfectly Plastic

An algorithm based on a combination of the upper bound method and finite element repesentation has been developed. The algorithm is applied to the problem of a rigid indenter ploughing through a rigid/perfectly-plastic material. Numerical examples are given and the results are compared with previous approximate solutions. Limitations of the upper bound method are discussed.

Extension of the Upper Bound Method to Include Estimation of Stresses

1991 ◽  
Vol 58 (2) ◽  
pp. 493-498 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Plastic Deformation ◽  
Stress Field ◽  
Upper Bound ◽  
Plastic Material ◽  
Approximate Solutions ◽  
Incompressible Material ◽  
Bulk Deformation ◽  
Upper Bound Method ◽  
Convenient Tool ◽  
Perfectly Plastic

The upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. Since the rate of work for an incompressible material depends only on the deviator portion of the stress, the hydrostatic portion does not enter the formulation and the stress field is not determined. Here we show that this limitation can be overcome by adding a relatively simple postprocessing procedure. We then apply this technique to examples of rigid asperities penetrating a plastic material undergoing subsurface bulk deformation and compare our results with previous approximate solutions.

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.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

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.

A Finite Element Based Study on the Elastic-Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Shankar ◽  
M. M. Mayuram
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Plastic Material ◽  
Plastic Region ◽  
Real Contact Area ◽  
Real Contact ◽  
Perfectly Plastic ◽  
The Difference ◽  
Elastic Perfectly Plastic ◽  
Green Model

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios (ω∕ωc) for the evolution of the elastic core and the plastic region within the asperity for different Y∕E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y∕E ratio of the material.

scholarly journals Stress Concentration Factor of Expanded Aluminum Tubes Using Finite Element Modeling

2013 ◽  
Vol 10 (1) ◽  
pp. 88
Author(s):  
L Mhamdi ◽  
AC Seibi ◽  
A Karrech ◽  
S El-Borgi ◽  
I Barsoum
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Plastic Material ◽  
Structural Response ◽  
Perfectly Plastic ◽  
Empirical Relations ◽  
Aluminum Tubes ◽  
Semi Empirical

 This paper discusses the development of semi-empirical relations for the maximum stress concentration factor (SCF) around circular holes embedded in aluminum tubes under various expansion ratios and mandrel angles. Finite element models were developed to study the expansion of a typical aluminum tube with embedded holes of various sizes. An elastic perfectly-plastic material behaviour was used to describe the structural response of the tubes under expansion. Various hole-diameter-to-tubewall- thickness ratios, tube expansion ratios, and mandrel angles were considered to determine the stress state around the hole at zero and 90 degree locations from which the maximum SCF was determined. Semi-empirical relations for the maximum SCF using the Lagrange interpolation formulation were developed. The developed relations were found to predict the SCFs accurately. 

Elastic, Plastic Stresses in Free Plate With Periodically Varying Surface Temperature

1958 ◽  
Vol 25 (4) ◽  
pp. 603-606
Author(s):  
Halil Yüksel
Keyword(s):  
Steady State ◽  
Surface Temperature ◽  
Constant Temperature ◽  
Thermal Stresses ◽  
Plastic Material ◽  
The Other ◽  
Perfectly Plastic ◽  
Temperature Oscillations ◽  
Steady State Temperature ◽  
Elastic Perfectly Plastic

Abstract The paper is concerned with a free plate that consists of an elastic, perfectly plastic material and is subjected to a harmonically varying temperature at one face, while the other face is kept at a constant temperature and the edge is perfectly insulated. The thermal stresses associated with the steady-state temperature oscillations are analyzed, and the development of plastic regions is discussed.

Limit Design of a Full Reinforcement for a Circular Cutout in a Uniform Slab

1952 ◽  
Vol 19 (3) ◽  
pp. 397-401
Author(s):  
H. J. Weiss ◽  
W. Prager ◽  
P. G. Hodge
Keyword(s):  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Curved Beam ◽  
Shearing Stress ◽  
Concentric Ring ◽  
Perfectly Plastic ◽  
Circular Cutout

Abstract A thin square slab with a central circular cutout reinforced by a concentric ring is subjected to uniform tensions Tx and Ty on the exterior edges. It is desired to determine the dimensions of the reinforcement if the slab is not to collapse under any load which could be supported by a similar slab without any cutout or reinforcement. It is assumed that the slab and reinforcement are made of a perfectly plastic material which satisfies the Tresca yield criterion of maximum shearing stress, and that the dimensions of the reinforcement are such that it may reasonably be approximated by a curved beam. Under these assumptions, an upper bound on the necessary thickness of the reinforcement for any given radius is obtained. Certain practical limitations of the theory are discussed.

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