THE EFFECT OF DAMAGE AT AN ENSEMBLE OF MICROSTRUCTURE POINTS ON THE MARGIN OF SAFETY IN STRUCTURALLY HETEROGENEOUS MATERIALS

Diagnostics, Resource and Mechanics of materials and structures Pub Date : 2019-10-25 DOI:10.17804/2410-9908.2019.5.060-072

S. Volkov

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引用次数: 1

Abstract

Fracture concentration regions are considered in a microstructure under loading. A mathematical model of a micro-heterogeneous medium with random properties of elements is used for the calculations. The initial data in the problem includes the characteristics of the distributions of random elastic moduli and ultimate strengths in the microstructure elements. The microstructure strength condition is a difference between stresses and ultimate strengths for a multitude of points of a given configuration. The probability of stress simultaneously exceeding the ultimate strength in a given set of elements determines the probability of fracture in this ensemble of points and relative damage at the micro level. A multidimensional normal distribution is used to calculate damage. The structure of the correlation matrix of distribution takes into account the kind of the damage concentration region. The relationship between critical microstructure damage and the margin of safety is determined. Examples of calculating the probability of fracture in two, three, and four microstructure elements are given.

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结构非均质材料中微观结构点集合处损伤对安全裕度的影响

在载荷作用下，微观结构中考虑断裂集中区。采用具有元素随机性质的微非均质介质的数学模型进行计算。该问题的初始数据包括随机弹性模量和极限强度在微观结构单元中的分布特征。微观结构强度条件是给定结构中多个点的应力和极限强度之间的差值。在给定的一组单元中，应力同时超过极限强度的概率决定了这组点的断裂概率和微观上的相对损伤。损伤计算采用多维正态分布。相关分布矩阵的结构考虑了损伤集中区的类型。确定了临界组织损伤与安全裕度的关系。给出了计算二、三、四微观单元断裂概率的实例。

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Diagnostics, Resource and Mechanics of materials and structures

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