Determination of the Gurson–Tvergaard damage model parameters for simulating small punch tests

The objective of the final small punch test (SPT) is to determine the fracture properties of materials, such as fracture toughness, when not enough material is available for the conduct of conventional fracture tests. The damage model developed by Gurson, and subsequently modified by Tvergaard and Needleman (GTN), allows for the numerical simulation of the elastic-plastic behaviour until fracture. This model is based on several constitutive material parameters that must be calibrated if the model is to be properly applied. In this paper, we develop a consistent methodology for the identification of the GTN damage parameters based on the adjustment of the load-displacement curve obtained in the SPTs. The methodology presented is applicable to simulating other different SPTs with different thicknesses and test temperatures. Also, the three-dimensional modelling developed will be useful in the future for analysing the possible anisotropy exhibited by some materials. The next step in the simulation will be to determine its validity in other stress fields with different triaxiality ratios, like the one present in CT specimens, the ultimate goal being to allow for the estimation of the material fracture toughness.