확률론적 파괴역학 및 Size Effect Law에 적용을 위한 다중 균열 구조물에서의 에너지 해방률의 고차 미분값 계산
Computation of the Higher Order Derivatives of Energy Release Rates in a Multiply Cracked Structure for Probabilistic Fracture Mechanics and Size Effect Law
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초록
본 논문에서는 다중 균열 구조물에서의 균열 진전에 따른 에너지 해방율 및 고차 미분값을 구할 수 있는 가상균열 진전법을 제시한다. 이 방법은 다중 균열 체계의 에너지 해방율과 고차 미분값이 단 한번의 해석으로 수행될 수 있는 장점이 있다. 예제에서 얻어진 해의 최대 오차는 에너지 해방율 0.2%, 일차 미분값 2～3%, 이차 미분값 5～10%이다. 이 방법으로 구한 에너지 해방률의 미분값들은 파괴 확률을 구하거나, size effect law에 적용될 수 있다.
Abstract
In this paper, we further generalize the work of Lin and Abel to the case of the first and the second order derivatives of energy release rates for two-dimensional, multiply cracked systems. The direct integral expressions are presented for the energy release rates and their first and second order derivatives. The salient feature of this numerical method is that the energy release rates and their first and second order derivatives can be computed in a single analysis. It is demonstrated through a set of examples that the proposed method gives expectedly decreasing, but acceptably accurate results for the energy release rates and their first and second order derivatives. The computed errors were approximately 0.5% for the energy release rates, 3～5% for their first order derivatives and 10～20% for their second order derivatives for the mesh densities used in the examples. Potential applications of the present method include a universal size effect model and a probabilistic fracture analysis of cracked structures.
참고문헌 (16)
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