The Relation Between Similarity Fields and Invariant Path Integrals in Nonlinear Fracture Mechanics

非线性断裂力学中相似场与不变路径积分的关系

• 批准号: 0600408
• 负责人: Gustavo Gioia
• 金额: --
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-05-15 至 2010-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600408&HistoricalAwards=false
• 关键词: Relation; Between; Similarity; Fields; Invariant

The Relation Between Similarity Fields and Invariant Path Integrals in Nonlinear Fracture MechanicsGustavo Gioia, University of Illinois at Urbana-Champaign Computational simulations indicate that the plastic-zone fields of growing cracks depend on the stress intensity factor K and the t-stress T through a single similarity variable, implying that we can ascertain the type of fracture (brittle or ductile) associated with any combination of K and T by performing experiments over a range of values of a single variable. Yet the origin of similiarity fields remains unknown. Here we will trace these similarity fields to the existence of invariant path integrals. We will relate the similarity variable to the crack-tip energy flux, viscosity, cohesion, and triaxiality. For several failure criteria, we will construct diagrams identifying the ductile, transitional, and brittle regions in K-T space. We will also study separable crack-tip similarity fields and establish their connection with critical phenomena. Last, we will study the case of stationary cracks, where the fields are not similarity ields but there exists an invariant path integral.

Gustavo Gioia，University of Illinois at Urbana-Champaign计算模拟表明，扩展裂纹的塑性区场通过单一相似变量依赖于应力强度因子K和t应力T，这意味着我们可以通过在单个变量的值范围内进行实验来确定与K和T的任何组合相关的断裂类型（脆性或韧性）。然而，相似场的起源仍然未知。在这里，我们将跟踪这些相似领域的存在不变的路径积分。我们将把相似变量与裂纹尖端能通量、粘性、内聚力和三轴度联系起来。 对于几种破坏准则，我们将在K-T空间中构建识别韧性、过渡和脆性区域的图。我们还将研究可分离的裂纹尖端相似场，并建立它们与临界现象的联系。最后，我们将研究静止裂纹的情形，其中场不是相似场，但存在一个不变的路径积分。