Applications of the Gurson’s model in sheet metal forming

Recent advances in the modelling of metals encompass modelling of metals structural inhomogeneity, damage, porosity, twinning/untwining and non-local and second order effects. This presentation is focused on modelling the void growth in ductile fractures. The growth and coalescence of microscopic voids are the main mechanisms in ductile fracture of bulk metallic parts. In sheet metals, ductile fracture is preceded by necking during which existing voids do not have significant growth. However, necking is highly sensitive to plastic flow direction which in turn is sensitive to the presence of voids. Also, under biaxial strain loading, the final fracture in the necking region is still controlled by void growth; hence an accurate fracture prediction is crucial for crash simulations. Finally, in super-plastic sheet forming, void growth and coalescence may precede or accompany necking. Therefore, there is as increasing interest in modelling of voids in the sheet metals. As an application, we show how the predictions of some forming limit curves (FLCs) can be affected by accurate simulation of voids growth.

Shakedown Fatigue Limits for Materials With Minute Porosity

The intention of this study is to predict the fatigue-safe long life behavior of elastoplastic porous materials subjected to zero-tension fluctuating load. It is assumed that the materials contain a dilute amount of voids (less than 5%) and obey Gurson’s model of plastic yielding. The question to be answered is what would be the highest allowable stress amplitude that a porous material can endure (the “endurance limit”) when undergoing an infinite number of loading/unloading cycles. To reach the answer we employ the two shakedown theorems: (a) Melan’s static shakedown theorem (“elastic shakedown”) for establishing the lower bound to fatigue limit and (b) Koiter’s kinematic shakedown theorem (“plastic shakedown”) for establishing its upper bound. The two bounds are formulated rigorously but solved with some numerical assistance, mainly due to the nonlinear pressure dependency of the material behavior and the complex description of the plastic flow near stress-free voids. Both bounds (“dual bounds”) are adjusted to capture Gurson-like porous materials with noninteractive voids. General residual stresses (either real or virtual) are presented in the analysis. They are assumed to be time-independent as generated, say, by permanent temperature gradient between void surfaces and remote material boundaries. Such a situation is common, for instance, in ordinary porous sleeves (used in space industry and alike). A few experiments agree satisfactorily with the shakedown bounding concept.

Transferability of the Gurson Damage Model Parameters with Charpy and Tensile Tests with Different Constrain Level

Little work has been published concerning the transferability of Gurson’s ductile damage model parameters in specimens tested at different strain rates and in the rolling direction of a Grade A ship plate steel. In order to investigate the transferability of the damage model parameters of Gurson’s model, tensile specimens with different constraint level and impact Charpy specimens were simulated to investigate the effect of the strain rate on the damage model parameters of Gurson model. The simulations were performed with the finite element program ABAQUS Explicit [1]. ABAQUS Explicit is ideally suited for the solution of complex nonlinear dynamic and quasi–static problems [2], especially those involving impact and other highly discontinuous events. ABAQUS Explicit supports not only stress–displacement analyses but also fully coupled transient dynamic temperature, displacement, acoustic and coupled acoustic–structural analyses. This makes the program very suitable for modelling fracture initiation and propagation. In ABAQUS Explicit, the element deletion technique is provided, so the damaged or dead elements are removed from the analysis once the failure criterion is locally reached. This simulates crack growth through the microstructure. It was found that the variation of the strain rate affects slightly the value of the damage model parameters of Gurson model.