Publications

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The purpose of this document is to provide evidence for assessing the adequacy of parameterized material models for a collection of materials used in a finite element analyses setting. “Adequacy” is relative to the intended use of the material in particular analyses. The intended application of the material models covered within this document is for system level abnormal mechanical solid mechanics analyses. Generally, material model parameterizations should be valid from temperatures of approximately -50 to 70° C, across a range of strain rates, and (depending on details of the parts involved) large deformations. Each material covered in this document is presented in its own chapter with a common format across materials. Model assumptions, limitations, existing validation results, readiness for use with uncertainty quantification, general usage guidance, and failure considerations are all provided along with specific parameterization inputs suitable for the finite element analysis code Sierra/Solid Mechanics.

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In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. We verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. We then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.

The Virtual Fields Method (VFM) is an inverse technique used for parameter estimation and calibration of constitutive models. Many assumptions and approximations—such as plane stress, incompressible plasticity, and spatial and temporal derivative calculations—are required to use VFM with full-field deformation data, for example, from Digital Image Correlation (DIC). This work presents a comprehensive discussion of the effects of these assumptions and approximations on parameters identified by VFM for a viscoplastic material model for 304L stainless steel. We generated synthetic data from a Finite-Element Analysis (FEA) in order to have a reference solution with a known material model and known model parameters, and we investigated four cases in which successively more assumptions and approximations were included in the data. We found that VFM is tolerant to small deviations from the plane stress condition in a small region of the sample, and that the incompressible plasticity assumption can be used to estimate thickness changes with little error. A local polynomial fit to the displacement data was successfully employed to compute the spatial displacement gradients. The choice of temporal derivative approximation (i.e., backwards difference versus central difference) was found to have a significant influence on the computed rate of deformation and on the VFM results for the rate-dependent model used in this work. Finally, the noise introduced into the displacement data from a stereo-DIC simulator was found to have negligible influence on the VFM results. Evaluating the effects of assumptions and approximations using synthetic data is a critical first step for verifying and validating VFM for specific applications. The results of this work provide the foundation for confidently using VFM for experimental data.

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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.

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Traditionally, material identification is performed using global load and displacement data from simple boundary-value problems such as uni-axial tensile and simple shear tests. More recently, however, inverse techniques such as the Virtual Fields Method (VFM) that capitalize on heterogeneous, full-field deformation data have gained popularity. In this work, we have written a VFM code in a finite-deformation framework for calibration of a viscoplastic (i.e. strain-rate dependent) material model for 304L stainless steel. Using simulated experimental data generated via finite-element analysis (FEA), we verified our VFM code and compared the identified parameters with the reference parameters input into the FEA. The identified material model parameters had surprisingly large error compared to the reference parameters, which was traced to parameter covariance and the existence of many essentially equivalent parameter sets. This parameter non-uniqueness and its implications for FEA predictions is discussed in detail. Finally, we present two strategies to reduce parameter covariance – reduced parametrization of the material model and increased richness of the calibration data – which allow for the recovery of a unique solution.

Modeling material and component behavior using finite element analysis (FEA) is critical for modern engineering. One key to a credible model is having an accurate material model, with calibrated model parameters, which describes the constitutive relationship between the deformation and the resulting stress in the material. As such, identifying material model parameters is critical to accurate and predictive FEA. Traditional calibration approaches use only global data (e.g. extensometers and resultant force) and simplified geometries to find the parameters. However, the utilization of rapidly maturing full-field characterization tech- niques (e.g. Digital Image Correlation (DIC)) with inverse techniques (e.g. the Virtual Feilds Method (VFM)) provide a new, novel and improved method for parameter identification. This LDRD tested that idea: in particular, whether more parameters could be identified per test when using full-field data. The research described in this report successfully proves this hypothesis by comparing the VFM results with traditional calibration methods. Important products of the research include: verified VFM codes for identifying model parameters, a new look at parameter covariance in material model parameter estimation, new validation tech- niques to better utilize full-field measurements, and an exploration of optimized specimen design for improved data richness.

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Partial penetration laser welds join metal surfaces without additional filler material, providing hermetic seals for a variety of components. The crack-like geometry of a partial penetration weld is a local stress riser that may lead to failure of the component in the weld. Computational modeling of laser welds has shown that the model should include damage evolution to predict the large deformation and failure. We have performed interrupted tensile experiments both to characterize the damage evolution and failure in laser welds and to aid computational modeling of these welds. Several EDM-notched and laser-welded 304L stainless steel tensile coupons were pulled in tension, each one to a different load level, and then sectioned and imaged to show the evolution of damage in the laser weld and in the EDM-notched parent 304L material (having a similar geometry to the partial penetration laser-welded material). SEM imaging of these specimens revealed considerable cracking at the root of the laser welds and some visible micro-cracking in the root of the EDM notch even before peak load was achieved in these specimens. The images also showed deformation-induced damage in the root of the notch and laser weld prior to the appearance of the main crack, though the laser-welded specimens tended to have more extensive damage than the notched material. These experiments show that the local geometry alone is not the cause of the damage, but also microstructure of the laser weld, which requires additional investigation.

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The second Sandia Fracture Challenge illustrates that predicting the ductile fracture of Ti-6Al-4V subjected to moderate and elevated rates of loading requires thermomechanical coupling, elasto-thermo-poro-viscoplastic constitutive models with the physics of anisotropy and regularized numerical methods for crack initiation and propagation. We detail our initial approach with an emphasis on iterative calibration and systematically increasing complexity to accommodate anisotropy in the context of an isotropic material model. Blind predictions illustrate strengths and weaknesses of our initial approach. We then revisit our findings to illustrate the importance of including anisotropy in the failure process. Mesh-independent solutions of continuum damage models having both isotropic and anisotropic yields surfaces are obtained through nonlocality and localization elements.

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 (Formula presented.) 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.

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Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack-like features with a high degree of variability in the geometry and material properties of the welded structure. Furthermore, accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. We found that traditional modeling approaches could not be efficiently employed. Consequently, a method is presented for constructing a surrogate model, based on stochastic reduced-order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking – and thus peak load – plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results.

Team Sandia California (Team H) used the Sandia code SIERRA Solid Mechanics: Implicit (SIERRA SM) to model the SFC2 challenge problem. SIERRA SM is a Lagrangian, three-dimensional, implicit code for the analysis of solids and structures. It contains a versatile library of continuum and structural elements, and an extensive library of material models. For all SFC2 related simulations, our team used Q1P0, 8 node hexahedral elements with element side lengths on the order 0.175 mm in failure regions. To model crack initiation and failure, element death removed elements from the simulation according to a continuum damage model. SIERRA SM’s implicit dynamics, implemented with an HHT time integration scheme for numerical damping [1], was used to model the unstable failure modes of the models. We chose SIERRA SM’s isotropic Elasto Viscoplastic material model for our simulations because it contains most of the physics required to accurately model the SFC2 challenge problem such as the flexibility to include temperature and rate dependence for a material.

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