| Summary: | The current available damage models do not accurately predict effective plastic strain to failure in low triaxiality stress states. A damage model was developed for low triaxiality that is appropriate to hot rolling of steel. This work focuses on nucleation and growth of damage as well as the effect of the strain and stress path. The latter is especially important for the rolling of bar and other complex cross-section products. A study of damage mechanisms and methods to model them has been undertaken. It is pointed out that the many models are only useful under certain conditions but can be used when the expected damage mechanisms are active. Several test types were evaluated to assess their ability to simulate stress state in rolling. A program has been written to evaluate the stress state for plane and axisymmetric tests, which allows one to choose the most appropriate test-piece geometry. A test has been designed and implemented. Thermal and mechanical data was gathered, which has been used to relate the stress triaxiality to damage growth and identify appropriate damage growth models. The size and spacing distributions of inclusions in free cutting steels have been measured. The different distributions have an effect on the ductility of the different steels. This effect has been found to change at different strain rates and temperatures. By better accounting for the effect of inclusions on damage growth under a range of test conditions, the damage model can be significantly improved. Free cutting steels that contained different additions of heavy metals were tested. The ductility and damage mechanisms were compared in each of the steels. The effect of the precipitation of the different heavy metals at the inclusion to matrix boundary was highlighted. The same damage mechanisms were observed in each steel but the ability to accommodate damage varied between the steels. Ex-situ synchrotron x-ray micro-tomography was used to better measure and quantify the distribution of inclusions and damage evolution in a free cutting steel. Localised damage coalescence away from the centre of the uniaxial tensile test-piece was attributed to the effect of inclusion clustering. This research was used to develop a realistic damage model, which can predict damage growth and coalescence for a range of forming parameters and different stress-state conditions related to hot rolling applications. The micro-mechanics based model includes the effects of inclusion distribution on damage. The model is calibrated using twenty six temperature based material constants.
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