Exploration of Shear-Dominated Geometries for Material Characterization and Model Calibration; Part 2: Calibration.
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This memo summarizes the simulation of ductile failure propagation work conducted under the ASC project “V&V of Ductile Failure” conducted during FY 23. Physically, the failure propagation consists of crack propagation in the material. In the numerical setting—specifically in a finite element model—propagation can be accomplished through element death when critical conditions occur locally at an element that is then deleted from the simulation. The validation of the finite element models is evaluated by direct comparison between the experimental and simulation results regarding the rate of crack growth and its influence on the load-deflection response of the specimens tested. This work considers two geometries that display stable crack propagation under displacement-controlled conditions. The first geometry consists of hat specimens loaded in compression with nominally identical geometries but made with three different materials: Steel A286, Al 7075-T651 and 304L stainless steel. The three materials represent a range of ductility values that affect the response and crack propagation within the specimen. The crack induced propagates under an essentially mode-II type of deformation. The second geometry consists of a pre-cracked 304L stainless steel compact tension test specimen loaded so as to induce a mode-I deformation at the crack.
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The Sandia Mechanics Challenge (SMC) provides the solid-mechanics community a forum for assessing its ability to predict mechanical behavior in structures and materials through a blind, round-robin format. Computationalists are asked to predict the behavior of an unfamiliar geometry given experimental calibration data, their predictions are compared to experimental measurements of the SMC scenario, and then the participants assess and compare their approaches, documenting their findings. The SMC broadens the scope of Sandia-hosted benchmarking problems that previously focused on ductile failure through the Sandia Fracture Challenges, enabling an enduring, community-wide self-assessment of predictive capabilities for a variety of mechanics topics. The SMC is part of the Structural Reliability Partnership, which offers other benchmarking challenges hosted by several participating institutions.
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The objective of this project is to validate low-fidelity models of 304L to 304L stainless steel partial-penetration laser welds for thin sheets. Low-fidelity means that the weld is represented by coarsely meshed element blocks. Here, the hexahedral element size is approx imately half the weld penetration depth. The material behavior of the block is represented by a J2 plasticity model with a Voce hardening function. The source of the data used in this work is an extensive experimental study conducted by Sharlotte Kramer (1528) and published in 2015. Figure 1 shows a cross-section of the weld of interest. The nominal thickness of the sheets is 0.063 in. while the target penetration depth of the weld is in the range of 0.028 to 0.032 in., extending about half the sheet thickness. Uniaxial tension tests provided data for calibration of base material and weld models. Results of two validation geometries were also provided. The principal validation geometry is shown in Fig. 2. It consists of a plate specimen with in-plane dimensions 6 in × 2.875 in loaded in tension. A circular plug with a 1.5 in. diameter was cut from the center of the plate and then welded in place. The details of the welding schedule are given. An important assumption is that the welds in the calibration and validation specimens have similar geometric and material properties as those in the validation tests. The task was to first calibrate models for the base material and the welds and then simulate the validation tests until the point of weld first failure.
The motivation for this work came from the simulation of components subjected to impact. In these problems, repeated loading can be generated by vibrational motion between internal parts of the component or by the occurrence of multiple impacts. Graphs of tensile equivalent plastic strain $(\overline{\varepsilon}_T^\rho)$ versus time from such cases had the character shown in Fig. 1. The equivalent plastic strain grew by alternating periods of accumulation and hold. The periods of hold indicate times when $d\overline{\varepsilon}_T^\rho$ did not accumulate. This can be due to the material unloading into the elastic range, or actually plastically reverse loading with hydrostatic stress σ h < 0 as was demonstrated for an impact simulation. Similar observations were made from the simulation of a 2-degree-of-freedom mass-elastic-plastic-spring system subjected to impact.
The following details calibration of a material model for Al7075-T6511. This aluminum alloy is commonly used across a host of engineering applications. Owing to its widespread prevalence, there is great benefit in improving simulation predictions for this alloy. In the present effort, a calibration is performed of its elastic-plastic response accounting for both rate and temperature dependence. The calibration is informed by a series of tests that include specimens of different geometries tested at different rates and temperatures. All specimens are derived from the same barstock, 3.5 inches in diameter. The fitted model itself uses an anisotropic, Hill yield surface coupled with a Johnson-Cook hardening model. Failure predictions are had by means of a modified Wilkins failure criterion. Following calibration of the material model, a validation exercise is performed against platepuncture experiments. These experiments include multiple probe shapes, probe diameters, and plate thicknesses. The puncture experiments are replicated in simulation with mesh studies performed to assess uncertainty. Key quantities of interest, notably the absorbed energy up to failure, are compared between simulation and experiment providing a means to assess the suitability of the calibration in puncture simulations.
This work aimed to apply Sandia’s expertise in metallurgy and modeling to enable the use of hybrid laser arc welding for building nuclear reactor containment structures, via a collaboration with Holtec International. Experimental observations were coupled with finite element analysis to resolve microstructure development, mechanical properties, distortion, and residual stress in welds relevant to the production of the Holtec SMR-160. High residual stresses were observed in welds that were not subjected to preheat. Meanwhile, the microstructure of the welds generally exhibited a narrow heat affected zone relative to conventional arc welds. FEA appeared to be effective in simulating the thermal/mechanical conditions that occur during hybrid laser arc welding of simplified and instrumented test welds. Subsequently, FEA was used to perform sensitivity analyses for various weld geometries that would be prohibitively costly to assess with physical experiments. Insights from the study were used to inform Holtec’s welding process, and successful production welds were performed in 2025.
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This paper documents the blind and post-blind analysis predictions for the 2023 Sandia Mechanics Challenge (SMC), which involved predicting the behavior of a threaded fastener joint structure subjected to shock loading. Utilizing repeat sets of fastener calibration data from various experimental configurations including tension, double shear, and joint tension, we developed a library of calibrated models which were propagated through the application model using the Discrete-Direct (DD) uncertainty quantification (UQ) approach. Although the initial blind predictions did not incorporate spare-sample processing to quantify fastener failure probabilities, the analyses yielded reasonable conclusions aligned with experimental results. In the post-blind analysis phase, we focused on enhancing the fidelity of the aluminum constitutive model and innovating the DD approach to obtain probabilistic predictions for fastener failure, particularly when quantities of interest (QoIs) approach their bounds. The improved aluminum model captures the behavior of the cantilever under shock loading more accurately, predicting both partial and complete cracks, although it tends to underpredict failure propagation. The enhanced DD approach facilitates probabilistic predictions that reflect the interdependent failure mechanisms of the fasteners and the cantilever, revealing that while certain fasteners are more likely to fail, the failure does not necessarily follow a progressive pattern. Overall, the post-blind analyses significantly improved the predictive capabilities of the model, providing valuable insights into the SMC application and establishing a robust foundation for informed engineering decisions. The methodology demonstrates a cost-effective and extensible approach suitable for a wide range of applications, highlighting the importance of uncertainty quantification to provide context for engineering decision making.
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