18ME743 Theory of Plasticity syllabus for ME

Brief review of fundamentals of elasticity:

Concept of stress, stress invariants, principal Stresses, octahedral normal and shear stresses, spherical and deviatoric stress, stress transformation; concept of strain, engineering and natural strains, octahedral strain, deviator and spherical strain tensors, strain rate and strain rate tensor, cubical dilation, generalized Hooke’s law, numerical problems.

Plastic Deformation of Metals:

Crystalline structure in metals, mechanism of plastic deformation, factors affecting plastic deformation, strain hardening, recovery, re crystallization and grain growth, flow figures or Luder’s cubes.

Yield Criteria:

Introduction, yield or plasticity conditions, Von Mises and Tresca criterion, geometrical representation, yield surface, yield locus (two-dimensional stress space), experimental evidence for yield

Stress Strain Relations:

Idealised stress-strain diagrams for different material models, empirical equations, Levy-Von Mises equation, Prandtl -Reuss and Saint Venant theory, experimental verification of Saint Venant’s theory of plastic flow. Concept of plastic potential, maximum work hypothesis, mechanical work for deforming a plastic substance.

Bending of Beams:

Stages of plastic yielding, analysis of stresses, linear and nonlinear stress strain curve, problems.

Torsion of Bars:

Introduction, plastic torsion of a circular bar, elastic perfectly plastic material, elastic work hardening of material, problems.

Slip Line Field Theory:

Introduction, basic equations for incompressible two-dimensional flows, continuity equations, stresses in conditions of plain strain, convention for slip lines, geometry of slip line field, properties of the slip lines, construction of slip line nets.

Course Outcomes:

At the end of the course the student will be able to:

CO1: Understand stress, strain, deformations, relation between stress and strain and plastic deformation in solids.

CO2: Understand plastic stress-strain relations and associated flow rules.

CO3: Perform stress analysis in beams and bars including Material nonlinearity.

CO4: Analyze the yielding of a material according to different yield theory for a given state of stress.

CO5: Interpret the importance of plastic deformation of metals in engineering problems.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbook/s

1 Theory of Plasticity Chakraborty Elsevier 3rd Edition 2 Theory of Plasticity and Metal forming Process Sadhu Singh Khanna Publishers, Delhi

Reference Books

1 Engineering Plasticity-Theory and Application to Metal Forming Process R.A.C. Slater McMillan Press Ltd.

2 Basic Engineering Plasticity DWA Rees Elsevier 1st Edition

3 Engineering Plasticity W. Johnson and P. B. Mellor Van NoStrand Co. Ltd 2000

4 Advanced Mechanics of solids L. S. Srinath Tata Mc. Graw Hill 2009