Numerical Simulation of Delayed Fracture by Surface Reaction in Material Structures of Small Feature Sizes

9988788Prevost许多先进的设备，如微处理器和微机电系统（MEMS），是小特征尺寸的材料结构。 由于这些设备是所有主要工程系统的一部分，因此预测其寿命的能力对国防和商业行业都非常重要。 这些特征的微小性对科学计算提出了广泛的挑战。 一个普遍存在的问题是在小尺寸的开裂，由残余应力和环境分子的联合作用驱动。 这种破裂经常在装置制造之后很久才发生。 还没有开发出预测这种装置中延迟开裂的方法。 在为大型工程部件建立的寿命预测方法的背景下，主要困难是容易理解的。 对于再入航天器上的陶瓷砖这样的大型构件，寿命预测依赖于裂纹扩展模型。 它假设裂纹预先存在于瓷砖中，并且在应力和环境分子的共同作用下生长。 预测寿命需要两个实验数据：初始裂纹尺寸和裂纹扩展规律（即，作为应力强度因子的函数的裂纹速度）。 然而，对于微型器件来说，两者都很难获得。 制造过程被控制到特征尺寸，使得初始裂纹的含义是模糊的，并且在任何情况下，其尺寸将永远不会在常规基础上通过实验测量。 此外，允许的裂纹速度是如此之小（例如0.1微米每年），没有实验方法存在，以获得裂纹扩展规律。该提案建议通过数值模拟来解决这些问题。本项目将开发微型器件的寿命预测方法。 该方法依赖于裂纹成核模型。 器件最初没有尖锐的裂纹，但应力集中部位（如拐角）无处不在。 固体成分，如二氧化硅，通过表面上的化学反应向环境中损失质量。 反应的速率取决于局部应力。 由于应力场是不均匀的，反应在拐角根部比其他地方进行得更快，逐渐将根部变成尖锐的裂纹。 这种模式是在20世纪60年代设想的，近年来重新引起了人们的兴趣。 使用该模型的一个主要困难是计算。 现有的工作一直局限于理想化的几何形状和材料。 本文将发展一种有限元方法来模拟复杂结构中的裂纹形核过程，该方法结合了Z。索这项工作将集中在设备的寿命主要用于裂纹成核而不是随后的裂纹生长的情况下。使用2D模型的初步工作显示出相当大的希望，这项工作将进一步扩展，并解决非常困难的3D问题。组建了一个跨学科的研究团队，整合了多物理过程，多处理器有限元实施和网格适应大形状变化和强化应力场的专业知识。 数值工作将与A.G.教授正在进行的实验工作相结合。埃文斯和一个由美国国家科学基金会资助的实验研究工作的补充W。索博耶霍都在普林斯顿大学。这些将提供用于验证我们的计算模型的测试用例。***

9988788Prevost Many advanced devices, such as microprocessors and Micro-Electro-Mechanical-Systems (MEMS), are material structures of small feature sizes. Because these devices are part of all major engineering systems, an ability to predict their lifetime is of great importance to both the defense and the commercial industry. The smallness of the features poses a broad challenge to scientific computation. One pervasive problem is cracking in the small dimension, driven by the combined action of residual stresses and environmental molecules. Such cracking often occurs long after the devices have been made. No method has been developed to predict the delayed cracking in such devices. The main difficulties are readily understood in the context of the lifetime prediction method established for large engineering components. For a large component such as a ceramic tile on a reentry space vehicle, the lifetime prediction relies on the crack growth model. It assumes that cracks pre-exist in the ceramic tile, and grow under the combined action of stresses and environmental molecules. To predict the lifetime requires two experimental data: the initial crack size, and the crack growth law (i.e., the crack velocity as a function of the stress intensity factor). However, both are difficult to obtain for micro devices. Fabrication processes are controlled down to the feature sizes, so that the meaning of an initial crack is ambiguous, and in any case its size will never be measured experimentally on a routine basis. Moreover, the allowable crack velocity is so small (say 0.1 micron per year) that no experimental method exists to obtain the crack growth law. This proposal proposes to address these problems via numerical simulations. This program will develop a lifetime prediction method for micro devices. The method relies on a crack nucleation model. A device initially has no sharp cracks, although stress concentration sites, such as corners, are pervasive. A solid constituent, such as silicon dioxide, loses mass to its environment by chemical reaction on the surface. The rate of the reaction depends on the local stress. Because the stress field is nonuniform, the reaction proceeds faster at a corner root than elsewhere, gradually changing the root into a sharp crack. This model was envisioned in the 1960s, and has regenerated interest in recent years. A main difficulty in using the model has been computational. Existing work has been restricted to idealized geometries and materials. The proposed work will develop a finite element method to simulate the crack nucleation process in complex structures incorporating interface models formulated by Prof. Z. Suo. The work will focus on situations where a device spends its lifetime mainly on crack nucleation rather than subsequent crack growth. Preliminary work using 2D models shows considerable promise, and this work will be further extended and address the very difficult 3D problems. An interdisciplinary research team is assembled, integrating expertise in multiphysical processes, multiprocessor finite element implementation, and mesh adaptation for large shape change and intensifying stress field. The numerical effort will be coupled with ongoing experimental works by Professor A.G. Evans and a complementary NSF-funded experimental research effort by Professor W. Soboyejo both at Princeton University. These will provide test cases that will be used to validate our computational models. ***