A cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.
Background: Using a thin-walled tube torsion test to characterize a material’s shear response is a well-known technique; however, the thin walled specimen tends to buckle before reaching large shear deformation and failure. An alternative technique is the surface stress method (Nadai 1950; Wu et al. J Test Eval 20:396–402, 1992), which derives a shear stress-strain curve from the torque-angular displacement relationship of a solid cylindrical bar. The solid bar torsion test uniquely stabilizes the deformation which allows us to control and explore very large shear deformation up to failure. However, this method has rarely been considered in the literature, possibly due to the complexity of the analysis and experimental issues such as twist measurement and specimen uniformity. Objective: In this investigation, we develop a method to measure the large angular displacement in the solid bar torsion experiments to study the large shear deformation of two common engineering materials, Al6061-T6 and SS304L, which have distinctive hardening behaviors. Methods: Modern stereo-DIC methods were applied to make deformation measurements. The large angular displacement of the specimen posed challenges for the DIC analysis. An analysis method using multiple reference configurations and transformation of deformation gradient is developed to make the large shear deformation measurement successful. Results: We successfully applied the solid bar torsion experiment and the new analysis method to measure the large shear deformation of Al6061-T6 and SS304L till specimen failure. The engineering shear strains at failure are on the order of 2–3 for Al6061-T6 and 3–4 for SS304L. Shear stress-strain curves of Al6061-T6 and SS304L are also obtained. Conclusions: Solid bar torsion experiments coupled with 3D-DIC technique and the new analysis method of deformation gradient transformation enable measurement of very large shear deformation up to specimen failure.
The method of thin-wall tube torsion to characterize metal’s shear response is well-known. Unfortunately, the thin wall tube specimen tends to buckle before reaching large shear deformation and failure. An alternative technique, which has rarely been considered, is Nadai’s surface stress method (Nadai, Theory of Flow and Fracture of Solids. McGraw-Hill, New York, 1950). It derives shear stress-strain curve from the torque-twist relationship of a solid bar. Although the analysis is more complex due to nonlinear shear stress distribution along the radius, the deformation is stable through large shear deformation to failure. Solid bar torsion experiments were conducted to study large shear deformation of Al6061-T6. Two experiments were described in this study. Since few tests were available in the literature, these experiments were to explore the large deformation behaviors of an engineering alloy and the application of modern measurement techniques, such as 3D DIC method, under torsion. Results show during twisting, the surface shear strain distribution was uniform initially and then localized on a narrow band; eventually, the specimen was cracked and failed within the band. Depending on the specimen size, the twist could be greater than 360°. Details are discussed.
This project has developed models of variability of performance to enable robust design and certification. Material variability originating from microstructure has significant effects on component behavior and creates uncertainty in material response. The outcomes of this project are uncertainty quantification (UQ) enabled analysis of material variability effects on performance and methods to evaluate the consequences of microstructural variability on material response in general. Material variability originating from heterogeneous microstructural features, such as grain and pore morphologies, has significant effects on component behavior and creates uncertainty around performance. Current engineering material models typically do not incorporate microstructural variability explicitly, rather functional forms are chosen based on intuition and parameters are selected to reflect mean behavior. Conversely, mesoscale models that capture the microstructural physics, and inherent variability, are impractical to utilize at the engineering scale. Therefore, current efforts ignore physical characteristics of systems that may be the predominant factors for quantifying system reliability. To address this gap we have developed explicit connections between models of microstructural variability and component/system performance. Our focus on variability of mechanical response due to grain and pore distributions enabled us to fully probe these influences on performance and develop a methodology to propagate input variability to output performance. This project is at the forefront of data-science and material modeling. We adapted and innovated from progressive techniques in machine learning and uncertainty quantification to develop a new, physically-based methodology to address the core issues of the Engineering Materials Reliability (EMR) research challenge in modeling constitutive response of materials with significant inherent variability and length-scales.
The advent of fabrication techniques such as additive manufacturing has focused attention on the considerable variability of material response due to defects and other microstructural aspects. This variability motivates the development of an enhanced design methodology that incorporates inherent material variability to provide robust predictions of performance. In this work, we develop plasticity models capable of representing the distribution of mechanical responses observed in experiments using traditional plasticity models of the mean response and recently developed uncertainty quantification (UQ) techniques. To account for material response variability through variations in physical parameters, we adapt a recent Bayesian embedded modeling error calibration technique. We use Bayesian model selection to determine the most plausible of a variety of plasticity models and the optimal embedding of parameter variability. To expedite model selection, we develop an adaptive importance-sampling-based numerical integration scheme to compute the Bayesian model evidence. We demonstrate that the new framework provides predictive realizations that are superior to more traditional ones, and how these UQ techniques can be used in model selection and assessing the quality of calibrated physical parameters.
The third Sandia Fracture Challenge highlighted the geometric and material uncertainties introduced by modern additive manufacturing techniques. Tasked with the challenge of predicting failure of a complex additively-manufactured geometry made of 316L stainless steel, we combined a rigorous material calibration scheme with a number of statistical assessments of problem uncertainties. Specifically, we used optimization techniques to calibrate a rate-dependent and anisotropic Hill plasticity model to represent material deformation coupled with a damage model driven by void growth and nucleation. Through targeted simulation studies we assessed the influence of internal voids and surface flaws on the specimens of interest in the challenge which guided our material modeling choices. Employing the Kolmogorov–Smirnov test statistic, we developed a representative suite of simulations to account for the geometric variability of test specimens and the variability introduced by material parameter uncertainty. This approach allowed the team to successfully predict the failure mode of the experimental test population as well as the global response with a high degree of accuracy.
We use machine learning (ML) to infer stress and plastic flow rules using data from representative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response functions. The ML process does not choose appropriate inputs or outputs, rather it is trained on selected inputs and output. Likewise, its discrimination of features is crucially connected to the chosen input-output map. Hence, we draw upon classical constitutive modeling to select inputs and enforce well-accepted symmetries and other properties. In the context of the results of numerous simulations, we discuss the design, stability and accuracy of constitutive NNs trained on typical experimental data. With these developments, we enable rapid model building in real-time with experiments, and guide data collection and feature discovery.
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves conver- gence behavior. Finally, a novel approach for modeling ductile failure has been developed, moti- vated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software im- plementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.
A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses.
The objective of the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Very Long Term Storage (VLTS) Project is to develop a simple, benchmark model that describes the performance of Zry4 d-hydrides in cladding, under conditions of long-term storage of used fuel. This model will be used to further explore the requirements of hydride modeling for used fuel storage and transport. It is expected that this model will be further developed as its weaknesses are understood, and as a basis of comparison as the Used Fuel Disposition (UFD) Campaign explores more comprehensive, multiscale approaches. Cladding hydride processes, a thermal model, a hydride model API, and the initial implementation of the J2Fiber hydride model is documented in this report.
Fracture or tearing of ductile metals is a pervasive engineering concern, yet accurate prediction of the critical conditions of fracture remains elusive. Sandia National Laboratories has been developing and implementing several new modeling methodologies to address problems in fracture, including both new physical models and new numerical schemes. The present study provides a double-blind quantitative assessment of several computational capabilities including tearing parameters embedded in a conventional finite element code, localization elements, extended finite elements (XFEM), and peridynamics. For this assessment, each of four teams reported blind predictions for three challenge problems spanning crack initiation and crack propagation. After predictions had been reported, the predictions were compared to experimentally observed behavior. The metal alloys for these three problems were aluminum alloy 2024-T3 and precipitation hardened stainless steel PH13-8Mo H950. The predictive accuracies of the various methods are demonstrated, and the potential sources of error are discussed.
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Sandia currently lacks a high fidelity method for predicting loads on and subsequent structural response of earth penetrating weapons. This project seeks to test, debug, improve and validate methodologies for modeling earth penetration. Results of this project will allow us to optimize and certify designs for the B61-11, Robust Nuclear Earth Penetrator (RNEP), PEN-X and future nuclear and conventional penetrator systems. Since this is an ASC Advanced Deployment project the primary goal of the work is to test, debug, verify and validate new Sierra (and Nevada) tools. Also, since this project is part of the V&V program within ASC, uncertainty quantification (UQ), optimization using DAKOTA [1] and sensitivity analysis are an integral part of the work. This project evaluates, verifies and validates new constitutive models, penetration methodologies and Sierra/Nevada codes. In FY05 the project focused mostly on PRESTO [2] using the Spherical Cavity Expansion (SCE) [3,4] and PRESTO Lagrangian analysis with a preformed hole (Pen-X) methodologies. Modeling penetration tests using PRESTO with a pilot hole was also attempted to evaluate constitutive models. Future years work would include the Alegra/SHISM [5] and AlegrdEP (Earth Penetration) methodologies when they are ready for validation testing. Constitutive models such as Soil-and-Foam, the Sandia Geomodel [6], and the K&C Concrete model [7] were also tested and evaluated. This report is submitted to satisfy annual documentation requirements for the ASC Advanced Deployment program. This report summarizes FY05 work performed in the Penetration Mechanical Response (ASC-APPS) and Penetration Mechanics (ASC-V&V) projects. A single report is written to document the two projects because of the significant amount of technical overlap.