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.

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

Recent work in metal additive manufacturing (AM) suggests that mechanical properties may vary with feature size; however, these studies do not provide a statistically robust description of this phenomenon, nor do they provide a clear causal mechanism. Because of the huge design freedom afforded by 3D printing, AM parts typically contain a range of feature sizes, with particular interest in smaller features, so the size effect must be well understood in order to make informed design decisions. This work investigates the effect of feature size on the stochastic mechanical performance of laser powder bed fusion tensile specimens. A high-throughput tensile testing method was used to characterize the effect of specimen size on strength, elastic modulus and elongation in a statistically meaningful way. The effective yield strength, ultimate tensile strength and modulus decreased strongly with decreasing specimen size: all three properties were reduced by nearly a factor of two as feature dimensions were scaled down from 6.25 mm to 0.4 mm. Hardness and microstructural observations indicate that this size dependence was not due to an intrinsic change in material properties, but instead the effects of surface roughness on the geometry of the specimens. Finite element analysis using explicit representations of surface topography shows the critical role surface features play in creating stress concentrations that trigger deformation and subsequent fracture. The experimental and finite element results provide the tools needed to make corrections in the design process to more accurately predict the performance of AM components.

Size-dependent stochastic tensile properties in additively manufactured 316L stainless steel

Lagrangian formulations, in which material models are established upon a mapping from a deformed domain back to an undeformed reference configuration, have traditionally been employed in most previous developments of the peridynamic theory. In this paper, a semi-Lagrangian constitutive framework for peridynamics is proposed, in which peridynamic material point interactions depend only on their current properties (e.g. position and stress values) in the deformed configuration. A nonlocal version of the velocity gradient is proposed to determine the Cauchy stress rate, using local constitutive theories, as an intermediate quantity in computing peridynamic bond forces. It is shown that a pure state-based peridynamic approach would involve material instabilities. A bond-associated formulation is presented to benefit from both bond-based and state-based views, resulting in an enhanced stability. A bond-associated, correspondence damage modeling is introduced to incorporate classical failure criteria in a convenient way. The proposed framework opens up new pathways in modeling extreme events, where excessive material deformation and damage make the Lagrangian formulation unsuitable. Capabilities of the new theory is showcased in a handful of illustrative scenarios.

A semi-Lagrangian constitutive correspondence framework for peridynamics

Metal additive manufacturing (AM) presents advantages such as increased complexity for a lower part cost and part consolidation compared to traditional manufacturing. The multiscale, multiphase AM processes have been shown to produce parts with non-homogeneous microstructures, leading to variability in the mechanical properties based on complex process–structure–property (p-s-p) relationships. However, the wide range of processing parameters in additive machines presents a challenge in solely experimentally understanding these relationships and calls for the use of digital twins that allow to survey a larger set of parameters using physics-driven methods. Even though physics-driven methods advance the understanding of the p-s-p relationships, they still face challenges of high computing cost and the need for calibration of input parameters. Therefore, data-driven methods have emerged as a new paradigm in the exploration of the p-s-p relationships in metal AM. Data-driven methods are capable of predicting complex phenomena without the need for traditional calibration but also present drawbacks of lack of interpretability and complicated validation. This review article presents a collection of physics- and data-driven methods and examples of their application for understanding the linkages in the p-s-p relationships (in any of the links) in widely used metal AM techniques. The review also contains a discussion of the advantages and disadvantages of the use of each type of model, as well as a vision for the future role of both physics-driven and data-driven models in metal AM.

https://iopscience.iop.org/article/10.1088/2515-7639/abca7b/pdf

Modeling process–structure–property relationships in metal additive manufacturing: a review on physics-driven versus data-driven approaches

Abstract Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. 

/pdf/a-comparative-review-of-peridynamics-and-phase-field-models-2mea193n.pdf

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

The Sandia Fracture Challenges provide a forum for the mechanics community to assess its ability to predict ductile fracture through a blind, round-robin format where mechanicians are challenged to predict the deformation and failure of an arbitrary geometry given experimental calibration data. The Third Challenge (SFC3) required participants to predict fracture in an additively manufactured (AM) 316L stainless steel bar containing through holes and internal cavities that could not have been conventionally machined. The volunteer participants were provided extensive data including tension and notched tensions tests of 316L specimens built on the same build-plate as the Challenge geometry, micro-CT scans of the Challenge specimens and geometric measurements of the feature based on the scans, electron backscatter diffraction (EBSD) information on grain texture, and post-test fractography of the calibration specimens. Surprisingly, the global behavior of the SFC3 geometry specimens had modest variability despite being made of AM metal, with all of the SFC3 geometry specimens failing under the same failure mode. This is attributed to the large stress concentrations from the holes overwhelming the stochastic local influence of the AM voids and surface roughness. The teams were asked to predict a number of quantities of interest in the response based on global and local measures that were compared to experimental data, based partly on Digital Image Correlation (DIC) measurements of surface displacements and strains, including predictions of variability in the resulting fracture response, as the basis for assessment of the predictive capabilities of the modeling and simulation strategies. Twenty-one teams submitted predictions obtained from a variety of methods: the finite element method (FEM) or the mesh-free, peridynamic method; solvers with explicit time integration, implicit time integration, or quasi-statics; fracture methods including element deletion, peridynamics with bond damage, XFEM, damage (stiffness degradation), and adaptive remeshing. These predictions utilized many different material models: plasticity models including J2 plasticity or Hill yield with isotropic hardening, mixed Swift-Voce hardening, kinematic hardening, or custom hardening curves; fracture criteria including GTN model, Hosford-Coulomb, triaxiality-dependent strain, critical fracture energy, damage-based model, critical void volume fraction, and Johnson-Cook model; and damage evolution models including damage accumulation and evolution, crack band model, fracture energy, displacement value threshold, incremental stress triaxiality, Cocks-Ashby void growth, and void nucleation, growth, and coalescence. Teams used various combinations of calibration data from tensile specimens, the notched tensile specimens, and literature data. A detailed comparison of results based of these different methods is presented in this paper to suggest a set of best practices for modeling ductile fracture in situations like the SFC3 AM-material problem. All blind predictions identified the nominal crack path and initiation location correctly. The SFC3 participants generally fared better in their global predictions of deformation and failure than the participants in the previous Challenges, suggesting the relative maturity of the models used and adoption of best practices from previous Challenges. This paper provides detailed analyses of the results, including discussion of the utility of the provided data, challenges of the experimental-numerical comparison, defects in the AM material, and human factors.

/pdf/the-third-sandia-fracture-challenge-predictions-of-ductile-2b7qy97bnz.pdf

Christopher I. Hammetter

Papers

The third Sandia fracture challenge: predictions of ductile fracture in additively manufactured metal

Spacecraft Pyroshock Attenuation in Three Parts