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FINITE ELEMENT STUDY OF ELASTIC PLASTIC CONTACT

PERFORMANCE OF RIGID SPHERE AGAINST A DEFORMABLE

FLAT - EFFECT OF STRAIN HARDNESS

V. C. Sathish Gandhi1 Dr. R. Marappan2

1. Assistant Professor, Department of Mechanical Engineering, Anna University of

Technology Tirunelveli, Tirunelveli, Tamilnadu-627007, India.

E-mail: vcsgandhi@gmail.com

2. Director (Academic), K.R.S College of Engineering, Tiruchencode. Namakkal ,

Tamilnadu 637 215, India.

Abstract The present study considers an elastic-plastic contact analysis of a rigid spherewith a deformable flat (RS model) using finite element method. The effect of tangent

modulus on the contact behaviour of a non-adhesive frictionless elastic-plastic contact is

analysed using commercial finite element software ANSYS. To study this effect we have

taken different materials in terms of the ratio of Youngs modulus to yield strength. The

result clearly shows that for different tangent modulus values of the same material expresses

the different stress values. If this modulus increases the stress reached the maximum value at

a limit and again decreases. The hardness value of material also increases. The increasing in

tangent modulus value the stress in the material (E/Y < 1000) increases up to 0.5E. After that

stress decreases with the increase in the tangent modulus. If stress in the material (E/Y >

1000) increases up to 0.3E, the stress decreases with the increase in the tangent modulus.

Here it is observed that the higher stress is developed in the material E/Y < 1000 of hardness

H = 1 and H = 0.43 for the material having E/Y > 1000. It is established that the tangent

modulus increases the hardness of the material. The material behaviour is dependent on the

tangent modulus. So far many of the researchers considered the tangent modulus E T = 0.00E.

That has to be modified.

The indentation pressure under elastic, elastic-plastic and fully plastic conditions may

be correlated on a non-dimensional form of pm/Y as a function of (E* tan /Y) where is the

angle of the indenter at the edge of the contact. With a spherical indenter we put tan sin

= a/R which varies during indentation process. Where a is width of the contact area (d/2),

projected surface diameter isd and R is the radius of the ball (D/2). The plastic strains are,

of course, not uniform. But whatever their quantitative value, the strain will be a function of

d/D. We then made a very bold assumption, namely that there is a representative strain () in

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the specimen which is a power function of d/D. But the tangent modulus is increased; the d/D

ratio is decreased. It is presented that as the tangent modulus increases, the straining action

effect of the material decreases. For loading condition as the straining action reduces, the

strain hardening effect increases in the material. With increase in these parameters the

resistance to deformation of a material is increased and the material becomes capable of

carrying higher amount of load in smaller contact area.

The Visual Basic codes are generated to develop a design calculator for calculating

the various contact parameters. It is very useful for Design Engineers to select the suitable

material based on the material properties for designing a component under loading contact

condition.

Key-words: Tangent modulus, Youngs modulus, Yield strength,E/Y ratio,Elastic-plastic,

Spherical indenter, Strain hardening, Visual Basic codes and Design

calculator.

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