Abstract
An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was analyzed, and the crack extension should occur in the format of self-similarity. When the fiber strength is over its maximum tensile stress, the fiber breaks. By means of complex variable functions, the problem considered can be easily translated into Reimann-Hilbert mixed boundary value problem. Utilizing the built dynamic model of bridging fiber pull-out in unidirectional composite materials, analytical solutions of the displacements, stresses and stress intensity factors under the action of increasing loads Pt5/x5, Px5/t4 are obtained, respectively. After those analytical solutions were used by superposition theorem, the solutions to arbitrary complex problems were acquired.
Highlights
It is well known that the matrix cracking as well as fracture process of the bridging fibers is one of the significant mechanisms of the cracking expansion in fiberreinforced composite materials, such as unidirectional fiberreinforced brittle matrix composites [1,2], and threedimensional fiber-reinforced composites with an orthogonal fiber structure [3]
Composite materials are often referred to as orthotropic aniostropic body in virtue of the direction of their fibers, while bridging fibers play an important role in their strength, queries on bridging fiber pull-out are one of the most complex advancing tasks in mechanics of composite materials
The problem of an internal central crack with bridging fiber pull-out of composite materials is analyzed under the dynamic conditions by means of Reimann-Hilbert mixed boundary value, and that analytical solutions for unidirectionally reinforced composite materials with bridging fibers parallel to the free surface are presented
Summary
It is well known that the matrix cracking as well as fracture process of the bridging fibers is one of the significant mechanisms of the cracking expansion in fiberreinforced composite materials, such as unidirectional fiberreinforced brittle matrix composites [1,2], and threedimensional fiber-reinforced composites with an orthogonal fiber structure [3]. Literature [4] proposed an approach for the assessment of the distribution of the traction force for a crack with bridging fibers in an infinite, orthotropic elastic plane under a uniform remove tension stress. Most researchers, such as Woo, Lee and Tsai [5,6,7] etc, almost investigated static problems of composite materials; they obtained only numerical solutions. If the fiber failure is governed by maximum tensile stress, which appears at the crack plane, the fiber breaks and the crack expansion should occur in the modality of self-similarity [13,14]. Self-similar functions are resolved analytically by means of KeldyshSedov’s method
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