Mathematical Modeling of Damage in Unidirectional Composites
Solutions are developed for the two-dimensional region containing unidirectional fibers embedded in an elastic matrix with an initial flaw in the form of a transverse notch, a rectangular cut-out, and a circular hole. Subsequent damage due to the presence of the flaw is generated by remote stresses acting parallel to the fibers. This work is an extension of the paper by Goree and Gross  in which the flaw was taken in the form of a notch (crack) and the subsequent damage, due to loading, consisted of longitudinal matrix yielding and splitting at the end of the notch. The present study accounts for longitudinal matrix damage as in  and, in addition, includes transverse matrix and fiber damage in the vicinity of the flaw for the above three initial shapes. The fibers are taken as linearly elastic, the matrix material as elasticperfectly plastic and the classical shear-lag stress displacement assumptions are used. An ultimate stress failure criterion is used for both the fibers and the matrix; simple tension for the fibers and shear failure for the matrix. For ductile matrix composites (boron/aluminum) the present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Interestingly, the extent of the transverse damage region at failure is shown to be approximately constant, independent of the initial flaw shape or length. Very little difference is found between the results for the three types of initial damage, i.e. the notch, rectangular cut-out and circular hole. In all cases, the presence of additional damage changes the nature of the stress distribution in the unbroken fibers. For the original Hedgepeth problem of a notched laminate the stresses decay as the square root of the distance from the notch tip. Inclusion of longitudinal or transverse damage significantly reduces the maximum stress concentration in the unbroken fibers and gives a much more uniform stress state. It is shown that this behavior cannot be accounted for by introducing an effective notch length or crack tip damage zone with a square root behavior. © 1983.
L. R. Dharani et al., "Mathematical Modeling of Damage in Unidirectional Composites," Engineering Fracture Mechanics, Elsevier, Jan 1983.
The definitive version is available at https://doi.org/10.1016/0013-7944(83)90115-7
Mechanical and Aerospace Engineering
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