An Experimental and Computational Framework Incorporating Uncertainty for Modeling Ductile Failure of Metals

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Policy makers and technical decision makers increasingly rely on results of large-scale computations. Climate change policy, for instance, may be guided by predictions of rise in global temperatures obtained using computational fluid dynamics procedures. Such predictions invariably include uncertainty. This is tantamount to putting error bars on computational results. In contrast, in solid mechanics computations, large-scale automobile crash simulations are carried out, the results post-processed, and metrics to assess passenger safety of the design computed -- but the associated uncertainties are ignored.Uncertainty stems from the metal's response during failure, the models used to describe the failure behaviour; and uncertainty on account of the algorithms used for discretization of space and time. In the modeling of ductile failure of metals, my research programme will investigate mitigation and quantification of uncertainty stemming these three sources, and the probabilistic (Bayesian) tools used to quantify the uncertainty. Personal experience with material testing of conventional engineering alloys has shown that components and structures display more scatter in deformation and failure response than the specimens used for material property evaluation. Accordingly, I propose to develop a novel specimen geometry, in which strategically located cut-outs leads to a sequence of failures when the specimen is loaded under tension. In the specimen, because of the cut outs, multiple failure paths are observed and fewer tests for model calibration are required. Such specimens may be used to characterize the uncertainty in deformation and failure behaviour at the structural-level with a limited number of tests.The second source of uncertainty is the constitutive description of the deformation and failure. Full-field displacement measurements of the developed specimens will be used to estimate the uncertainty in the deformation and failure parameters. A third source of uncertainty is the computational modeling of failure. I propose to develop a novel element, for use in the explicit dynamic computations that uses the floating node method of Chen et al. The implementation will be in a general purpose finite element software such as Abaqus. The brute-force computation of uncertainty and associated statistical parameters requires a large number of computations especially in the context of dynamic loading. I propose to investigate techniques such as response surface (also called surrogate model analysis) to quantify the uncertainty and Bayesian methods for model calibration. All of the above developments constitute a framework for application in sectors such as dynamic fracture of pressurized oil pipelines, response of armor and layered armor systems, and failure of multi-material welds.