3-D Dynamic Problems for Cracked Layered Materials with Contact Interaction of Crack Faces

材料科学的成就，如新型高科技材料，如微纳米复合材料，使设计的复合材料结构的强度和刚度显著提高成为可能。另一方面，由于不可预测的断裂成本总是非常高，因此对安全要求的水平也随之提高。除了经济价值外，还必须记住，在极端情况下，材料或结构断裂可能危及人类健康。众所周知，所有现有的复合材料都含有各种组件间和组件内部缺陷（裂纹，分层等）。这些缺陷出现在实际材料的制造或使用过程中（疲劳、冲击后果等）。该问题的另一个重要方面是由于初始静载荷下的微屈曲导致的非零开口裂纹的出现。裂缝和分层的存在大大降低了复合材料结构的强度和寿命，同时也显著增加了开发成本。不幸的是，微缺陷不能完全避免。由于裂纹尖端处的应力奇点，裂纹充当了局部应力集中点的作用，在意外的小载荷作用下可能导致突然断裂。因此，有必要确保复合结构的残余强度在所需的使用寿命内不会低于可接受的水平。当材料发生动态变形时，现有裂纹的相反面相互作用，显著改变裂纹尖端附近的应力和应变场。两个裂纹表面之间的接触相互作用的性质非常复杂。然而，由于感兴趣的区域隐藏在固体中，直接观察和测量接触特性是非常困难的。在材料变形作用下，初始接触区域会随时间发生变化。接触区域的形状事先是未知的，必须作为解决方案的一部分来确定。接触行为对两个接触面的材料特性和外部载荷的类型非常敏感，这一事实进一步加剧了问题的复杂性。这种依赖关系使得接触裂纹问题高度非线性。因此，在以往的研究中忽略了裂纹面的相互作用，因此，由于难以找到合适的解，忽略了真实的应力-应变分布。初步计算表明，即使是最简单的均匀固体中的便士形裂纹，裂纹面的接触相互作用也会在定量和定性上改变解，显著影响裂纹尖端附近的应力-应变状态，并影响应力强度因子的分布。然而，该行业需要解决涉及三维固体中相互作用裂缝系统的更复杂问题。本项目将重点解决谐波载荷下三维层状材料（复合材料、岩石等）中具有相互作用表面的构件间和构件内裂纹系统的弹性动力学问题。将研究层的性质、裂纹的位置、外载荷的频率、大小和方向的影响。开发一个用户友好的软件包来解决这个问题也是该项目的主要目标之一。该项目是基于机械工程和应用/数值数学专业知识的跨学科工作。

The achievements of material science such as the new high-tech materials, like micro- and nano-composites, make it possible to significantly increase the strength and stiffness of designed composite structures. On the other hand, the level of safety requirements increases consequently because the cost of unpredictable fracture is always enormously high. Apart from the economic value it is necessary to remember that in the extreme cases the material or structural fracture can put human health at risk. It is common knowledge that all existing composite materials contain various inter- and intra-component defects (cracks, delaminations, etc). Such defects appear in real-life materials during the fabrication or in-service (fatigue, consequences of an impact, etc). Another important aspect of the problem is the appearance of cracks with a non-zero opening attributed to the micro-buckling under initial static loading. The presence of cracks and delaminations considerably decreases the strength and the lifetime of composite structures as well as significantly increases the cost of exploitation. Unfortunately, the micro-defects cannot be fully avoided. A crack acts as a local stress concentrator because of the stress singularities at the crack tips, which can lead to a sudden fracture under unexpectedly small loading. Therefore it is necessary to ensure the residual strength of the composite structure will not fall below an acceptable level over the required service life. The opposite faces of existing cracks interact with each other when material undergoes dynamic deformation, altering significantly the stress and strain fields near the crack tips. The nature of the contact interaction between two crack surfaces is very complex. However, the direct observation and measurement of the contact characteristics is very difficult since the area of interest is hidden in the solid. Under deformation of the material, the initial contact region will change in time. The shape of the contact region is unknown beforehand and must be determined as a part of the solution. The complexity of the problem is further compounded by the fact that the contact behaviour is very sensitive to the material properties of two contacting surfaces and the type of the external loading. Such dependences make the contact crack problem highly non-linear.As the consequence, in the previous studies the interaction of crack faces was neglected and, therefore, the real stress-strain distribution was ignored due to the difficulties of finding appropriate solutions. The preliminary calculations have shown, that even in the simplest case of a penny-shaped crack in a homogeneous solid, the contact interaction of crack faces changes the solution both quantitatively and qualitatively, significantly influencing the stress-strain state in the vicinity of the crack tips, and affecting the distribution of the stress intensity factors. However the industry requires solutions of even more complex problems involving a system of interacting cracks in three-dimensional solids. This project will be focused on solving the elastodynamics problem for a system of inter- and intra-component cracks with interacting surfaces in three-dimensional layered materials (composites, rocks, etc) under harmonic loading. The effect of the properties of the layers, location of the cracks, frequency, magnitude and direction of the external loading will be investigated. Developing of a user-friendly software package for solving the problem is also one of the main goals of the project.The project is an interdisciplinary work based on the expertise in mechanical engineering and in applied/numerical mathematics.