Compositions of unidirectional short boron fibers and titanium, magnesium, and aluminum matrices are considered. The Rosen and Kelly parameters (the ineffective and critical lengths) characterizing the interaction of short fibers and the matrix are studied. These parameters as functions of material characteristics of components of the composites are established on rectangular (with a 2D reinforcement) or rectangular parallelepiped samples (with a 3D one) containing an inclusion in the form of a single short fiber. It is shown that the Rosen parameter is determined only by material characteristics of fibers and matrices, but the critical fiber length (Kelly parameter), in addition, also depends on the strain state of composition. In order to assess the interaction of a short reinforcing fiber with the matrix, a new parameter — the effective length — is introduced. This is the part of the short fiber whose stresses make up 100φ % (0.95 < φ < 1) of the stiffness of the same sample with a continuous fiber. A method for constructing the representative volumes of metal matrices statistically uniformly reinforced by unidirectional short boron fibers is proposed. It is shown that the ratio of the characteristic size of the representative volume of composite to the fiber length can reach two or more units. The elastic characteristics of unidirectionally reinforced short-fiber composites in relation to the fiber length are studied. On the basis of a numerical analysis of this dependence, the concept of the equivalent length of a short fiber is formulated. This length provides the stiffness of a short-fiber-reinforced sample equal to 100 φ % (0.95 < φ < 1) of that in the case of a continuous reinforcing fiber. Results of the studies are illustrated by graphs and tables.

中文翻译：

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单向短硼纤维和金属基体的成分特性

考虑了单向短硼纤维和钛、镁和铝基体的组合物。研究了表征短纤维和基体相互作用的 Rosen 和 Kelly 参数（无效长度和临界长度）。这些作为复合材料组件材料特性函数的参数是在矩形（具有 2D 增强材料）或长方体样品（具有 3D 增强材料）上建立的，其中包含单根短纤维形式的夹杂物。结果表明，Rosen 参数仅由纤维和基体的材料特性决定，但临界纤维长度（Kelly 参数）还取决于成分的应变状态。为了评估短增强纤维与基体的相互作用，引入了一个新参数——有效长度。这是短纤维的一部分，其应力占具有连续纤维的同一样品刚度的 100 φ % (0.95 < φ < 1)。提出了一种用于构造由单向短硼纤维在统计上均匀增强的金属基体的代表性体积的方法。结果表明，复合材料代表体积的特征尺寸与纤维长度的比值可以达到两个或两个以上单位。研究了与纤维长度相关的单向增强短纤维复合材料的弹性特性。在对这种相关性进行数值分析的基础上，提出了短纤维等效长度的概念。该长度提供了等于 100 φ % (0.95 < φ < 1) 在连续增强纤维的情况下。研究结果以图表形式说明。