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

政策制定者和技术决策者越来越依赖大规模计算的结果。例如，气候变化政策可以利用计算流体动力学程序获得的全球气温上升预测为指导。这样的预测总是包含不确定性。这相当于在计算结果上加上误差条。相比之下，在实体力学计算中，进行大规模的汽车碰撞模拟，对结果进行后处理，并计算出评估设计乘客安全的指标，但忽略了相关的不确定性。不确定性源于金属在失效时的响应，用于描述失效行为的模型；不确定性是由于空间和时间离散化算法造成的。在金属韧性破坏的建模中，我的研究计划将调查这三种来源的不确定性的缓解和量化，以及用于量化不确定性的概率（贝叶斯）工具。传统工程合金材料试验的个人经验表明，与用于材料性能评估的试样相比，构件和结构在变形和破坏响应方面表现出更大的分散。因此，我建议开发一种新的试样几何形状，在这种几何形状中，当试样在张力下加载时，有策略地定位切口会导致一系列失效。在试样中，由于切割，观察到多个破坏路径，较少的模型校准试验。这种试样可以用有限数量的试验来表征结构水平上变形和破坏行为的不确定性。不确定性的第二个来源是变形和破坏的本构描述。开发试件的全场位移测量将用于估计变形和破坏参数的不确定性。不确定性的第三个来源是故障的计算建模。我建议开发一种新的元素，用于使用Chen等人的浮动节点方法的显式动态计算。实现将在Abaqus等通用有限元软件中进行。不确定性及相关统计参数的蛮力计算需要大量的计算量，特别是在动态加载的情况下。我建议研究响应面（也称为代理模型分析）等技术来量化不确定性和贝叶斯方法来校准模型。所有这些发展都构成了一个应用框架，例如在压力输油管道的动态断裂、装甲和分层装甲系统的响应以及多材料焊缝失效等领域。

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.