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To evaluate the mechanical strength of fiber-reinforced composites, it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. A square array of rectangular inclusions under longitudinal tension is considered in this paper. The body-force method is applied to a unit cell region. Then, the problem is formulated as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. The unknown functions are expressed as piecewisesmooth functions using power series and two types of fundamental densities which express singular stresses. Generalized stress intensity factors at the corners of inclusions are systematically calculated with varying the shape and spacing of a square array of square and rectangular inclusions. IntroductionTo evaluate the mechanical strength of fiber-reinforced composites, it is necessary to consider singular stresses at the corners of fibers because they cause crack initiation, propagation, and final failure. To obtain the magnitude of the singular stress, a single rectangular inclusion was analyzed as a 2D model in [1], [2], and a single cylindrical inclusion was solved as a 3D model in [3]; then, both results were compared. To discuss interaction effects of fibers, two rectangular inclusions situated generally in the (x,y)-plane of matrix were treated in [4]. Also, several combinations of rectangular inclusions situated in the transverse directions were considered in [5], [6].Since actual composites have large numbers of fibers, total interactions of fibers distributed in every direction should be evaluated. In this paper, a rectangular array of square and rectangular inclusions, Fig. 1, will be treated as a two-dimensional model of many fibers. Their interaction will be clarified by varying the location, shape, spacing, and the elastic ratios of inclusions.In this analysis, the body-force method, [7], will be applied to a unit cell region of an array of fibers. Then, the singular integral equations will be solved numerically. Generalized stress intensity factors (GSIFs), which control the stresses around the fiber's ends, will be discussed using this model. The discussion will be used for considering the mechanical strength of fiberreinforced composites. Singular stress at the corner of a fiber endConsider an inclusion corner under in-plane deformation as shown in Fig. 2. The singular stress field is controlled by GSIFs K I;k 1 and K II;k 2 as shown in the following equation, [8]:

In this work stress concentration factors Kt for a flat bar with fillets are considered on the basis of exact solutions now available for special cases and accurate numerical results. Then, a convenient Ktformula useful for any dimensions of the fillet is proposed. The conclusions can be summarized as follows. 1. For the limiting cases of deep (d) and shallow (s) fillets, the body force method is used to calculate the Ktvalues. Then, the formulas are obtained as Ktd and Kts. 2. On the one hand, upon comparison of Kt and Ktd, it is found that Kt is nearly equal to Ktd if the fillet is deep or blunt. 3. On the other hand, if the fillet is sharp or shallow, Kt is controlled mainly by Kts and the fillet depth. 4. The fillet shape is classified into several groups according to the fillet radius and fillet depth. Then, the least-squares method is applied for calculation of Kt/Ktd and Kt/Kts. 5. Finally, convenient formulas are proposed that are useful for any dimensions of fillet in a flat bar. The formulas give SCFs with less than about 1 % error in most cases for any dimensions of fillet under tension and bending.

Engineering plastics provide superior performance to ordinary plastics for wide range of the use. For polymer materials, dynamic stress and strain rate may be major factors to be considered when the strength is evaluated. Recently, high‐speed tensile test is being recognized as a standard testing method to confirm the strength under dynamic loads. In this study, therefore, high‐speed tensile test is analysed by the finite element method; then, the maximum dynamic stress and strain rate are discussed with varying the tensile speed and maximum forced displacement. The maximum strain rate increases with increasing the tensile speed u/t, but the strain rate concentration factor italicKtitalicεtrue˙italict=trueε˙italicyAitalict/trueε˙italicynomitalict is found to be constant independent of tensile speed, which is defined as the maximum strain rate italicεtrue˙italicyA,max appearing at the notch root over the average nominal strain rate at the minimum section trueε˙italicynomitalict. It is found that the strain rate at the notch root depends on the dynamic stress rate at the notch root and independent of the notch root radius ρ. It is found that the difference between the static and dynamic maximum stress concentration (σyA,max − σyA,st) at the notch root is proportional to the tensile speed when u/t = 5000 mm/s. Strain rate concentration factors are also discussed with varying the notch depth and specimen length. Based on the elastic strain rate concentration factor, the master curve is obtained useful for understanding the impact fracture of polycarbonate for the wide range of temperature and impact speed.

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