Ductile fracture prediction in axisymmetric upsetting using continuum damage mechanics

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. These micro-cracks grow in the presence of tensile stresses leading to a fracture. A ductile fracture criterion based on the microscopic phenomena of void nucleation, growth and coalescence is used to predict the micro-crack initiation in axisymmetric upsetting. The above criterion is explored along with the results of an axisymmetric large deformation elasto-plastic finite element code developed during the present work using updated Lagrangian formulation. A new incremental objective stress measure and the logarithmic strain measure are employed. The Newton–Raphson iterative technique is used to solve the non-linear incremental equations. In the present work, material is assumed as elasto-plastic, yielding according to von-Mises criterion and hardening according to a power law relationship. Interfacial friction is modeled using Coulomb friction law. A comprehensive parametric study is carried out to study the effect of two process parameters, namely friction and height-to-diameter ratio on the deformation level at which micro-crack initiate at three distinct locations of the deformation geometry namely, die–work interface, center of the workpiece and meridian surface. The micro-cracks first initiate along the die–work interface region nearer to the free surface, then at the center of the deformation zone and subsequently at the meridian surface. The possibility of formation of central cavity increases with height-to-diameter ratio. With increase in friction micro-cracks initiate at smaller deformation levels. Study of stress distributions reveals that the fracture at the meridian surface occurs at smaller deformation level when height-to-diameter ratio is equal to 1 rather than values other than unity.