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Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

Predictions for the 2012 Sandia Fracture Challenge were generated using a transient-dynamic finite element code with a Multilinear Elastic Plastic Failure (MLEPF) model developed at Sandia (Wellman 2012). This model is a conventional, rate-independent, vonMises plasticity model for metals with user prescribed hardening as a function of equivalent plastic strain. In addition to conventional plasticity, this model has an empirical criterion for crack initiation and growth. Failure initiates when the tearing parameter, \(t_{p}\), given by the following equation reaches a critical level

A combined elastoplasticity and decohesion model is used with the Material Pont Method (MPM) for the Sandia Fracture Challenge 2012 problem. Before the critical strength is reached, von Mises plasticity with a linear hardening rule models the inelastic material behavior. Based on the previous work (Chen 1996; Chen et al. 2005), the computational efficiency of decohesion modeling is improved by prescribing the critical normal and tangential decohesion strengths directly, without performing discontinuous bifurcation analysis in each time step, to predict the post-peak response with a single-processor personal computer. The MPM (Chen et al. 2002; Sulsky et al. 1994) is employed to simulate the three-dimensional evolution of failure from microcracking to macrocracking without the need for remeshing.

We have used the XSHELL toolkit developed in-house to predict the fracture pattern and its associated load-deflection curve for the 2012 Sandia Fracture Challenge problem. Given the limitation of the plane stress approximation in the XSHELL modeling approach, a plane strain core approach has been developed to capture the thickness constraint induced stress triaxility and its effect on the ductile fracture in the vicinity of the crack tip. A rational mixture of plane strain and plane stress plasticity model was implemented via a calibration at the coupon level to evaluate the geometry dependent constraint. A mesh independent kinematic description of crack initiation and propagation is accomplished through an elementwise crack insertion with cohesive injection once its accumulative plastic strain reaches a critical value.

To explore the applicability of XSHELL prediction of a 3D structure, a nonlinear stress strain behavior is calibrated first from the experimental force displacement curve of the simple tension coupon tested by Sandia National Lab using XSHELL. As shown in Fig. 41a, material softening behavior cannot be captured fully due to the incapability of XSHELL in characterization of the necking behavior. The load and crack opening displacement (P-COD) curve for the compact specimen with \(a/W\) of 13.82 was used next to determine the geometry dependent plane strain core parameters. The plane strain composition parameter \(\alpha \) and its steady state failure strain (\(\varepsilon _{p})\) were determined together from the best matching of XSHELL prediction with the P-COD curve of the compact specimen as shown in Fig. 41b. The determined \(\alpha \) and the steady state failure strain \(\varepsilon _{p}\) are 0.04 and 0.25, respectively. The plane strain core band width used in the calibration model is set to be twice of the plate thickness. The deviation shown in Fig. 41b is attributed to the blunt notch representation of a sharp crack in the XSHELL simulation model.

The model has three parameters of \(\hbox {c}_1,\hbox {c}_2\), and \(\hbox {c}_3\) to be determined from tests, thus requiring at least three experiments for calibration. In the special case where \(\hbox {c}_1 =0\) and \(\hbox {c}_3 =1\), the model reduces to the maximum shear stress criterion. To fully exploit the accuracy and predictive power of the MMC model, dense experimental programs covering a wide range of stress states are recommended, such as the ones shown in Beese et al. (2010) and Luo and Wierzbicki (2010). In addition, MIT team makes use of the inverse calibration (or so-called hybrid experimental-numerical) procedure that requires FE simulation of each test. This procedure is explained in detail in Dunand and Mohr (2010) and Luo et al. (2012). Sandia provided us with the result of the uniaxial tension and toughness tests. FE simulation of the toughness test with the pre-existing sharp crack introduces a very strong mesh dependency. Therefore, toughness tests were not used by MIT team for the model calibration. Two approaches were taken in this research. We first considered the maximum shear stress model with only one parameter to be found from the test. The stress state inside of the neck of the dog-bone specimen is not proportional (see Fig. 47). Hence, an incremental damage rule is needed in conjunction with the Eq. (32). It is assumed that fracture initiates when the function in Eq. (33) reaches unity. 2b1af7f3a8