Experimental identification of a damage evolution law for steel

The physical background of damage evolution in metals consists of initiation, growth and coalescence of voids. To include such a mechanical behaviour in a macroscopic sense, the concept of Continuum Damage Mechanics has been developed. An essential part of a continuum damage formulation is the damage evolution law, which is used to calculate the amount of damage during the deformation process. The damage evolves from 0 (no damage) to 1 (fully damaged material) as a function of the nonlocal equivalent plastic strain. To identify a damage evolution law from experiments, the amount of damage that has developed during deformation as well as the corresponding nonlocal equivalent plastic strain has been determined. Micro-indentation appears to provide a way to determine the spatial distribution of damage, based on the decrease of hardness of the material during damage evolution. Tensile experiments are performed to produce damaged specimens in which the damage varies continuously from 0 (undeformed material) to 1 (fracture surface in the necking zone). Micro indentation experiments are performed on these specimens, namely a micro Berkovich hardness test and a micro Vickers hardness test, to obtain the spatial distribution of the hardness variation. The results of the micro Vickers hardness test did not show a variation in the hardness distribution. The decrease of the hardness and the Young’s modulus for the damaged material probably led to the same remaining indentation width after indentation as for the undamaged material. The micro Berkovich hardness experiments on the other hand did show a variation of the hardness over the domain of the specimen. For that reason, this technique has been used to determine the spatial distribution of the hardness of the specimen. The spatial distribution of the nonlocal equivalent plastic strain is obtained by means of digital image correlation (DIC) software. During the tensile experiments, several images are recorded of the deforming tensile specimen. Afterwards these images are processed with the DIC software and the resulting local equivalent plastic strain is obtained. An analysis showed that for a physically motivated lengthscale of the material, the nonlocal and local equivalent plastic strain are almost similar. Therefore, the damage evolution law is written in terms of the local equivalent plastic strain instead of the nonlocal equivalent plastic strain. Once the hardness distribution and the local equivalent plastic strain are determined, the damage evolution law has been determined according to the modified power law and an exponential damage evolution law, which described the measured damage evolution accurately. Unfortunately, these damage evolution laws do not incorporate triaxiality ( σ h σeq ). Because damage also evolved during the indentation experiments, the obtained damage evolution law does not correspond to the tensile experiment only. The amount of damage that evolves by means of the indentation experiments has not been investigated. Furthermore, experiments showed a variation of the Young’s modulus over the domain of the specimen as well, which suggest that this material parameter also decreases during damage evolution. During the indentation experiments, a rapid decrease of the Young’s modulus as function of the indentation depth was measured. The reason for this behaviour has not been investigated.