A stochastic approach to damage evolution in die-cast zinc alloys

拟议的研究项目的目标是开发一种方法，用于预测材料损伤和机械载荷对典型工业部件预期寿命的影响。示例性地，我们考虑由ZAMAK制成的窗五金件，ZAMAK是一种锌合金，其通常是压铸的并且广泛用于承载部件。新的设计，如大型玻璃幕墙和隐藏的枢纽建筑，在第一个资助期内，我们专注于ZAMAK合金的微观结构，并研究了波动和确定性机械应力导致的缺陷演变。在建议的第二个资助期内，我们仔细检查了模具的结构响应-在材料中的分布缺陷和不确定的载荷条件的影响下，尽管ZAMAK组件广泛使用，但关于ZAMAK组件的长期性能的可靠数据很少。极高的机械性能在部件的使用寿命中会逐渐降低。这促使我们研究ZAMAK由于材料中的分布缺陷和不确定的载荷条件而导致的机械强度损失。特别是在某些情况下滥用的窗口组件和由此产生的高应力下不确定的输入将在本项目中考虑。为了实现这一目标，我们将 采用基于多保真度抽样的方法。合并具有不同保真度水平的模型的一般思想是基于替代低保真度模型的定义。大多数抽样都是用这些便宜的近似模型完成的。为了解释低保真度和真实的高保真解之间的差异，对训练样本采用贝叶斯回归。 然后，可以使用相关性来获得高保真模型内的故障概率。总结我们的声明，不确定的材料属性，环境影响，生产过程中的扰动与不确定的载荷条件相结合，导致模具的极限载荷和预期寿命发生很大变化，作为本研究的结果，将预测ZAMAK的机械强度和承载能力的衰减。预测在这里是指考虑了关于问题的不完整和不确定的信息，并且提供了平均值的概率分布或误差条作为模拟结果。

The goal of the proposed research project is to develop a method for predicting the influence of material damage and mechanical load on the life expectation of a typical industrial component. Exemplarily we consider window hardware made of ZAMAK, a zinc alloy which is typically die-cast and widely used for load-bearing parts. New designs, like large glass facades and hidden pivot architecture, require these parts to be small but safe over a long period of time.In the first funding period we focused on the microstructure of the ZAMAK alloy and studied the evolution of defects as a result of fluctuations and deterministic mechanical stresses.In the advised second funding period we scrutinize the structural response of the die-cast component under effects of distributed defects in the material and of uncertain loading conditions. Despite of the widespread use there are only few reliable data available regarding the long term behavior of ZAMAK components. The very high mechanical properties diminish in the course of the component's life. This motivates us to study the loss of mechanical strength in ZAMAK as a result of distributed defects in the material and of uncertain loading conditions. Especially the misuse of the window components in certain situations and the resulting high stresses under uncertain inputs will be considered in this project. To achieve this we will employ a multi-fidelity sampling-based approach.The general idea of incorporating models with different levels of fidelity is based on the definition of surrogate low-fidelity models. Most of the sampling is then done with these cheap, approximate models. To account for the discrepancy between the low-fidelity and the real, high-fidelity solution, a Bayesian regression is employed on a training sample. Then it is possible to use the correlation to gain a probability of the failure within the high-fidelity model.Summarizing we state that uncertain material properties, environmental effects, perturbations in the production process combined with uncertain loading conditions results in a large variations of limit loads and life-expectation of die-cast ZAMAK components.As the result of this research the decay of ZAMAK's mechanical strength andload carrying capacity will be predicted. Prediction is meant here in the sense that incomplete and uncertain information about the problem is accounted for and that probability distributions or error bars on mean values are provided as simulation results.