Iinvariance in terms of the deviatoric stresses, representative stress - Engineering and natural strains, cubical dilation, finite strains co-efficients, Octahedral strain, strain rate and the strain rate tensor.
Yield criteria for ductile metal - Yield criteria for an anisotropic material. Stress – Strain Relations – Plastic stress-strain relations, Prandtl Roeuss Saint Venant, Levy – Von Mises, Yield locus, symmetry convexity, normality rule.
Application to problems, simple forms of indentation problems using upper bounds. Problems of metal forming.
Crystal Plasticity, the crystalline state, crystallographic indices, the preferential planes and directions, critical shear stress, theory of simultaneous slip, slip bands, the plastic bending in crystals, dislocations and crystal growth, polycrystals and grain boundaries,
Plane plastic strain and the theory of the slip line filed, two dimensional problems of steady and non steady motion, plastic anisotropy.
REFERENCES
1) Narayanasamy R, “Theory of Engineering Plasticity”, Ahuja Publications, 2000.
2) Johnson and Mellor, “Plasticity for Mechanical Engineers”, Ban Nostrand, 1973.
3) R.Hill , “The Mathematic theory of Plasticity”, Oxford Publication, 1982.
