This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

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Meeting the Contact-Mechanics Challenge

In this paper, a phase-field model for ductile fracture previously proposed in the kinematically linear regime is extended to the three-dimensional finite strain setting, and its predictions are qualitatively and quantitatively compared with several experimental results, both from ad-hoc tests carried out by the authors and from the available literature. The proposed model is based on the physical assumption that fracture occurs when a scalar measure of the accumulated plastic strain reaches a critical value, and such assumption is introduced through the dependency of the phase-field degradation function on this scalar measure. The proposed model is able to capture the experimentally observed sequence of elasto-plastic deformation, necking and fracture phenomena in flat specimens; the occurrence of cup-and-cone fracture patterns in axisymmetric specimens; the role played by notches and by their size on the measured displacement at fracture; and the sequence of distinct cracking events observed in more complex specimens.

A phase-field model for ductile fracture at finite strains and its experimental verification

A simple, nonstandardized material test specimen, which fails along one of two different likely crack paths, is considered herein. The result of deviations in geometry on the order of tenths of a millimeter, this ambiguity in crack path motivates the consideration of as-manufactured component geometry in the design, assessment, and certification of structural systems. Herein, finite element models of as-manufactured specimens are generated and subsequently analyzed to resolve the crack-path ambiguity. The consequence and benefit of such a “personalized” methodology is the prediction of a crack path for each specimen based on its as-manufactured geometry, rather than a distribution of possible specimen geometries or nominal geometry. The consideration of as-manufactured characteristics is central to the Digital Twin concept. Therefore, this work is also intended to motivate its development.

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On the Effects of Modeling As-Manufactured Geometry: Toward Digital Twin

The mechanisms of ductile rupture

Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in $$\sim $$
 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

The second Sandia Fracture Challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading

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.

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L. Quinkert

Papers

The Sandia Fracture Challenge: blind round robin predictions of ductile tearing

The Sandia Fracture Challenge: blind round robin predictions of ductile tearing