A fiber-bundle model for the continuum deformation of brittle material

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• 作者：K. Z. Nanjo
• 关键词：Fracture ; Brittle deformation ; Rheology ; Fiber ; bundle ; Yield stress ; Viscoelasticity
• 刊名：International Journal of Fracture
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：204
• 期：2
• 页码：225-237
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Characterization and Evaluation of Materials; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-2673
• 卷排序：204

文摘

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.