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.
Limited fatigue data exists for small-volume welded austenitic stainless steel components typically employed in hydrogen infrastructure due to the difficulty of testing these components with conventional specimen designs. To assess the fatigue performance of orbital tube welds of austenitic stainless steels, a hole-drilled tubular specimen was designed to produce a stress concentration in the center of the orbital weld. Fatigue life testing was performed on welded and non-welded 316L stainless steel hole-drilled tubular specimens, and the effects of hydrogen were evaluated by testing specimens with no added hydrogen and with internal hydrogen introduced through gaseous precharging. When accounting for the differences in flow stress caused by microstructural variations and the presence of internal hydrogen, the total fatigue life and fatigue crack initiation life of the welded and non-welded tubes were comparable and were reduced by internal hydrogen. In addition, the fatigue life results produced with the hole drilled tubular specimens were consistent with fatigue life data from circumferentially notched stainless steel specimens that have a similar elastic stress concentration factor. To better understand the mechanics of this specimen geometry, mechanics modeling was performed to compare the stress and strain distributions that develop at the stress concentration in the hole-drilled tubular and circumferentially notched specimens during fatigue cycling.
Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. This work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.
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.
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multi- scale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plas- ticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. Beyond cases studies in concurrent multiscale, we explore progress in crystal plastic- ity through modular designs, solution methodologies, model verification, and extensions to Sierra/SM and manycore applications. Advances in conformal microstructures having both hexahedral and tetrahedral workflows in Sculpt and Cubit are highlighted. A structure-property case study in two-phase metallic composites applies the Materials Knowledge System to local metrics for void evolution. Discussion includes lessons learned, future work, and a summary of funded efforts and proposed work. Finally, an appendix illustrates the need for two-way coupling through a single degree of freedom.
Circumferentially notched specimens of several austenitic stainless steel alloys subjected to positive load ratio, load-controlled fatigue have been cycled to failure in high pressure hydrogen gas. The number of cycles to failure for a given applied stress amplitude varies among the alloys tested indicating that control of fatigue life in hydrogen environments may be attained through informed alloy selection. The number of cycles to initiate a crack does not vary significantly among the alloys tested, however the total life to failure varied by over an order of magnitude. This difference in life is attributed to variations of the stress and strain fields ahead of the blunt notch. These fields are influenced by the strength and strain hardening characteristics of each alloy and they dictate the driving force for fatigue crack growth while the crack is small.