Question

02) a) For isotropic material and a complex stress state explain yield criteria 16] and yield curve.

Answer 1

pie yield criteria edit] um Principal Stress Theory - by WJ.M Rankine (1850). Yeld occurs when the largest principal stress exceeds the uniaxial tersile yield sirength. Although this criterion or a quick andeasy comparison with experimen al data it is rarely suitble for design purposes. This theory gives gaod predictions for britte materials m Principal strain Theory-by St.renant. Yed occurs when the maximum pnn pal strain reaches the strain coresponding :o the yield point dunng a simple tensile test, n the principal stresses ths is determined by the equation m Shear Stress Theary- Also known as the Tresca yield criterion, ater the French scientist Henri Tresca. This assumes thatyield occus when the shear stress Texceeds r yield strengh T rain Energy Theory This theory assumes that the storec energy associated with elastic deformation at the point of yield is independentof the specfic stress tensor. Thus curs when the strain enegy per unit volume is greater than the strain energy at the elastic limit in simpletension. Far a 3-dimersional stress state this is given by. m Distortion Energy Theory (von Mises yield criterion) This theory proposes that the total strain enegy can be separated into two components: tte volumetrc tati) strain energy and the shape (distortion or shear) strain energy. It s proposec that yield occurs when the distorton component exceecs that at the yield poin for a simpe est This theory is also known as the von Mises yield criterion n a direrent theoretical underpinning this expression is also referred to as oetahedral shear stress theory liration sGeded

4 -Isotropic plasticity, homogeneous Isotropic plasticity, localised --Anisotropic plasticity, homogeneous -Anisotropic plasticity, localised x Plasticity Bifurcation Shear band analyses Stress-strain curve for isotropic and cross-anisotropic plasticity with horizontal isotropic planes.

Tess STin Relations Plastic Range ung LOCALISEL TLONGATION Ae GAUGE LENGTH PERMANENT ELONGATION KecowEr Fig- 1 A-Original cross section of the specimen. LOriginal gauge length A-instantaneous cnoss section of the specimen L.-intantancous length of specimen after extension