A nonlinear ductile damage growth law

One of the commonly used approaches for the prediction of ductile fracture is the continuum damage mechanics model, in which the void density is represented by a continuum variable called damage. For the prediction of fracture, an evolution law for the void growth, called the damage growth law, is needed. As per the continuum thermodynamics framework, the damage growth law is obtained from some proposed expression for the damage potential. The damage growth laws reported in the literature, based on some proposed expressions for the damage potential, have played a useful role in predicting fracture initiation in some engineering materials. However, some of them do not agree with the experimental trends of damage growth in other engineering materials. In almost all the laws, while expressing the material constants in terms of the measurable quantities in tension test, the triaxiality is assumed constant which does not happen after the necking. In the present work, an expression for the damage potential is proposed that leads to a nonlinear ductile damage growth law for steel. The material constants of the damage growth law are determined from the experimental measurement of void growth as well as triaxiality at various plastic strain levels in tension test conducted at IIT Kanpur. Thus, it avoids making any assumption about the triaxiality. It is shown that this law is consistent with the trends of damage growth of some other experimental results reported in the literature.