On the first-matrix-cracking stress in unidirectional fiber-reinforced brittle materials
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A simple model which is able to account for the distribution of matrix crack spacings as a function of applied stress in unidirectional fiber-reinforced brittle materials has been used to generate stress-strain curves for such materials up to the maximum stress level at which transverse matrix cracking can occur when a tensile stress is applied parallel to the length of the fibers. The results give an insight into how to tackle the experimental problem of determining accurately the level of first-matrix-cracking stress in such materials.
I. INTRODUCTION For many unidirectional fiber-reinforced brittle matrices, such as ceramics and cements, the strain to failure of the matrix is less than that of the fiber, and so when a stress is applied parallel to the length of the fibers, the matrix usually fails before a statistically significant fraction of the fibers. If the volume fraction of the fibers is sufficiently high, the fibers can withstand the entire external load in a section of the composite where the matrix has failed, forming a through-thickness transverse crack perpendicular to the direction of applied stress. Thus, instead of the composite breaking up catastrophically after the formation of the first matrix crack, it will remain intact and the matrix will continue to crack and form regular multiple matrix cracks perpendicular to the length of the fibers.1 It is generally recognized that these multiple matrix cracks provide free passages for the environment into the composite, as a consequence of which both the matrix-fiber interface and the fibers themselves can be degraded substantially under attack from a suitably aggressive environment. Therefore, the magnitude of the stress at which transverse matrix cracking first occurs is a vital parameter in designing a brittle matrix composite. Since the work of Aveston et al.,1 it has usually been assumed in experimental studies on the mechanical properties of unidirectional fiber-reinforced brittle matrices that the matrix cracking stress is the stress at which the stress-strain curve deflects away from the initial linear stress-strain relationship.2"4 However, Kim and Pagano5 demonstrated recently that such a deflection from the initial linear relationship does not occur in the stressstrain curves that they determined from their specimens of fiber-reinforced glass ceramics, even though matrix cracks were clearly detected by acoustic emission and optical microscope observations in the linear region of their stress-strain curves. They observed only a clear J. Mater. Res., Vol. 8, No. 2, Feb 1993
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plateau in the stress-strain curve after the stress had been increased far beyond the first-matrix-cracking stress. Kim and Pagano5 suggested that this plateau in the stress-strain curve arises from damage accumulation from a number of small cracks in the matrix and/or at the matrix-fiber interface, the latter of which would allow slip to occur between the fibers and the matrix. In our computer simulation of the proc
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