An interpretable machine learning method, physics-informed genetic programming-based symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to developing constitutive models. The proposed strategy for combining a thermodynamic analysis with P-GPSR is demonstrated by generating a yield function for an idealized material with voids, i.e., the Gurson yield function. First, a thermodynamic-based analysis is used to derive model requirements that are exploited in a custom P-GPSR implementation as fitness criteria or are strongly enforced in the solution. The P-GPSR implementation improved accuracy, generalizability, and training time compared to the same GPSR code without physics-informed fitness criteria. The yield function generated through the P-GPSR framework is in the form of a composite function that describes a class of materials and is characteristically more interpretable than GPSR-derived equations. The physical significance of the input functions learned by P-GPSR within the composite function is acquired from the thermodynamic analysis. Fundamental explanations of why the implemented P-GPSR capabilities improve results over a conventional GPSR algorithm are provided.
Accurate prediction of ductile failure is critical to Sandia’s NW mission, but the models are computationally heavy. The costs of including high-fidelity physics and mechanics that are germane to the failure mechanisms are often too burdensome for analysts either because of the person-hours it requires to input them or because of the additional computational time, or both. In an effort to deliver analysts a tool for representing these phenomena with minimal impact to their existing workflow, our project sought to develop modern data-driven methods that would add microstructural information to business-as-usual calculations and expedite failure predictions. The goal is a tool that receives as input a structural model with stress and strain fields, as well as a machine-learned model, and output predictions of structural response in time, including failure. As such, our project spent substantial time performing high-fidelity, three-dimensional experiments to elucidate materials mechanisms of void nucleation and evolution. We developed crystal-plasticity finite-element models from the experimental observations to enrich the findings with fields not readily measured. We developed engineering length-scale simulations of replicated test specimens to understand how the engineering fields evolve in the presence of fine-scale defects. Finally, we developed deep learning convolutional neural networks, and graph-based neural networks to encode the findings of the experiments and simulations and make forward predictions in time for structural performance. This project demonstrated the power of data-driven methods for model development, which have the potential to vastly increase both the accuracy and speed of failure predictions. These benefits and the methods necessary to develop them are highlighted in this report. However, many challenges remain to implementing these in real applications, and these are discussed along with potential methods for overcoming them.
The damage mechanisms that lead to failure in engineering alloys have been studied extensively, but converting this knowledge into constitutive models that are suitable for engineering-scale analysis remains a challenge. Evolution laws for continuum damage have been developed in the past and have proven effective but suffer from many non-physical assumptions that inhibit the overall accuracy of the model. Further, the assumptions inherent in these existing models prevent them from being applicable to a broad class of materials. At the same time, computational models of fine-scale damage mechanisms continue to advance making it tractable to generate large training data sets through computer simulation. Data-driven machine learning approaches can leverage these data sets to avoid making limiting assumptions, and instead produce models directly from the results of microstructural simulations and/or experiments. Many of these machine learning approaches are rapid and accurate, but they offer little to no insight into the underlying relationships among state variables being discovered. Conversely, genetic programming symbolic regression (GPSR) is a machine learning method that produces analytic expressions relating the state variables, allowing maximal insight and interpretability. To that end, we propose using GPSR as a data-driven method of obtaining microstructurally informed continuum damage models. Data is generated using microstructural simulations of damage evolution, parameterized over microstructural statistics (i.e., pore shape) and nominally applied deformations. Analytic expressions for damage evolution are obtained from the data using GPSR, and these expressions are then utilized within a continuum constitutive model. Overall, this approach is a promising method of automatically obtaining analytic relations describing constitutive phenomena in a material.
Type 2 high-pressure hydrogen vessels for storage at hydrogen refueling stations are designed assuming a predefined operational pressure cycle and targeted autofrettage conditions. However, the resulting finite life depends significantly on variables associated with the autofrettage process and the pressure cycles actually realized during service, which many times are not to the full range of the design. Clear guidance for cycle counting is lacking, therefore industry often defaults to counting every repressurization as a full range pressure cycle, which is an overly conservative approach. In-service pressure cycles used to predict the growth of cracks in operational pressure vessels results in significantly longer life, since most in-service pressure cycles are only a fraction of the full design pressure range. Fatigue crack growth rates can vary widely for a given pressure range depending on the details of the residual strains imparted during the autofrettage process because of their influence on crack driving forces. Small changes in variables associated with the autofrettage process, e.g., the target autofrettage overburden pressure, can result in large changes in the residual stress profile leading to possibly degraded fatigue life. In this paper, computational simulation was used for sensitivity studies to evaluate the effect of both operating conditions and autofrettage conditions on fatigue life for Type 2 highpressure hydrogen vessels. The analysis in this paper explores these sensitivities, and the results are used to provide guidance on cycle counting. In particular, we identify the pressure cycle ranges that can be ignored over the life of the vessel as having negligible effect on fatigue life. This study also examines the sensitivity of design life to the autofrettage process and the impact on life if the targeted residual strain is not achieved during manufacturing.
High pressure hydrogen storage vessels are frequently retired upon reaching their designed number of pressure cycles, even in cases where the in-use pressure cycles are significantly less severe than the design pressure cycle. One method for extending the life of hydrogen vessels is recertification through non-destructive evaluation (NDE); however, NDE techniques are frequently evaluated with machined defects in test samples rather than fatigue cracks which occur during pressure cycling and may be more difficult to detect. In this paper, 50 mm wide ring sections (called C-rings, since they represent slightly more than half the circumference) were extracted from pressure vessels and mechanically cycled to establish fatigue cracks. Sub-millimeter starter notches were machined, via plunge electrical discharge machining (EDM), to control the location of crack initiation. Crack growth was monitored via direct current potential difference (DCPD) and backface strain gauges, both of which were shown to be good indicators for crack propagation. The C-ring geometry and fatigue crack growth were modeled to demonstrate the ability to monitor/control the crack length and area, which can be used to develop calibration samples of varying crack depth for NDE techniques. Additionally, this sample is intended to evaluate the influence of residual stresses on the sensitivity of NDE techniques, such as the design stresses in autofrettaged vessels.
High pressure Type 2 hoop-wrapped, thick-walled vessels are commonly used at hydrogen refueling stations. Vessels installed at stations circa 2010 are now reaching their design cycle limit and are being retired, which is the motivation for exploring life extension opportunities. The number of design cycles is based on a fatigue life calculation using a fracture mechanics assessment according to ASME Section VIII, Division 3, which assumes each cycle is the full pressure range identified in the User's Design Specification for a given pressure vessel design; however, assessment of service data reveals that the actual pressure cycles are more conservative than the design specification. A case study was performed in which in-service pressure cycles were used to re-calculate the design cycles. It was found that less than 1% of the allowable crack extension was consumed when crack growth was assessed using in-service design pressures compared to the original design fatigue life from 2010. Additionally, design cycles were assessed on the 2010 era vessels based on design curves from the recently approved ASME Code Case 2938, which were based on fatigue crack growth rate relationships over a broader range of K. Using the Code Case 2938 design curves yielded nearly 2.7 times greater design cycles compared to the 2010 vessel original design basis. The benefits of using inservice pressure cycles to assess the design life and the implications of using the design curves in Code Case 2938 are discussed in detail in this paper.
In this study, a multiscale electron microscopy-based approach is applied to understanding how different aspects of the microstructure in a notched AA6061-T6, including grain boundaries, triple junctions, and intermetallic particles, promote localized dislocation accumulation as a function of applied tensile strain and depth from the sample surface. Experimental measurements and crystal plasticity simulations of dislocation distributions as a function of distance from specified microstructural features both showed preferential dislocation accumulation near intermetallic particles relative to grain boundaries and triple junctions. High resolution electron backscatter diffraction and site-specific transmission electron microscopy characterization showed that high levels of dislocation accumulation near intermetallic particles led to the development of an ultrafine sub-grain microstructure, indicative of a much higher level of local plasticity than predicted from the coarser measurements and simulations. In addition, high resolution measurements in front of a crack tip suggested a compounding influence of intermetallic particles and grain boundaries in dictating crack propagation pathways.
We describe an approach to predict failure in a complex, additively-manufactured stainless steel part as defined by the third Sandia Fracture Challenge. A viscoplastic internal state variable constitutive model was calibrated to fit experimental tension curves in order to capture plasticity, necking, and damage evolution leading to failure. Defects such as gas porosity and lack of fusion voids were represented by overlaying a synthetic porosity distribution onto the finite element mesh and computing the elementwise ratio between pore volume and element volume to initialize the damage internal state variables. These void volume fraction values were then used in a damage formulation accounting for growth of these existing voids, while new voids were allowed to nucleate based on a nucleation rule. Blind predictions of failure are compared to experimental results. The comparisons indicate that crack initiation and propagation were correctly predicted, and that an initial porosity field superimposed as higher initial damage may provide a path forward for capturing material strength uncertainty. The latter conclusion was supported by predicted crack face tortuosity beyond the usual mesh sensitivity and variability in predicted strain to failure; however, it bears further inquiry and a more conclusive result is pending compressive testing of challenge-built coupons to de-convolute materials behavior from the geometric influence of significant porosity.