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

提出的研究项目的目标是开发一种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的方法。举例来说，我们考虑用Zamak制成的窗户五金，Zamak是一种锌合金，通常是压铸而成，广泛用于承重部件。新的设计，如大型玻璃幕墙和隐式枢轴结构，要求这些部件小但长期安全。在第一个资金期，我们重点研究Zamak合金的微观结构，研究由于波动和确定性机械应力造成的缺陷的演变。在建议的第二个资金期，我们仔细检查压铸部件在材料中分布缺陷和不确定加载条件影响下的结构响应。尽管Zamak被广泛使用，但有关Zamak组件的长期行为的可靠数据很少。非常高的机械性能在部件的使用过程中会减弱。这促使我们研究Zamak的机械强度损失，这是由于材料中的分布缺陷和不确定的加载条件造成的。特别是在某些情况下窗部件的误用以及在不确定输入下产生的高应力将在本项目中被考虑。为了实现这一点，我们将采用基于多保真抽样的方法。合并具有不同保真程度的模型的总体思路是基于代理低保真模型的定义。然后，大部分抽样都是用这些廉价的近似模型进行的。为了解释低保真和真实高保真解决方案之间的差异，对训练样本进行了贝叶斯回归。综上所述，材料性能的不确定性、环境的影响、生产过程中的扰动以及不确定的加载条件会导致压铸Zamak部件的极限载荷和寿命预期发生很大的变化，作为本研究的结果，Zamak的机械强度和承载能力的衰减将被预测。预测在这里的意思是，关于问题的不完全和不确定的信息被考虑在内，并且关于平均值的概率分布或误差条被提供作为模拟结果。

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.