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Energy-based equivalence between damage and fracture in concrete under fatigue

机译：疲劳下混凝土损伤与断裂之间的基于能量的当量

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摘要

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.
机译：由于微裂纹的形成和合并，混凝土构件的损坏以分散的方式发生，这可以通过局部损坏方法轻松描述。在随后的加载周期中，此微裂纹的分布区域转变为大裂纹，从而在构件中引入了不连续的不连续性。在此阶段，可以使用断裂力学的概念来描述结构构件的行为。在这项工作中，开发了一种通过能量等效概念关联断裂和损伤力学并预测疲劳载荷下混凝土损伤情况的方法。目的是平稳地从断裂力学理论过渡到损伤力学理论，反之亦然，以表征损伤。本文开发的分析方法已在文献中以一些已有数据为例进行了说明。已经使用可用的指标（例如强度降低和刚度降低系数）来表征由于逐渐开裂或损伤分布增加而导致的强度和刚度降低。通过数值示例可以看出，使用断裂和损伤力学理论得出的强度和刚度下降指数相互吻合。因此，得出的结论是，通过能量方法，可以将离散裂纹建模为等效损坏区域，其中两者均对应于相同的能量损失。最后，表明通过知道临界损伤区的尺寸，可以获得临界断裂性能，例如断裂能。

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