We analyze the impact of matrix anisotropy on crack interactions and on the effective moduli is analysed (9-D formulation). Crack orientations, as well as matrix anisotropy are assumed to be arbitrary (the orthotropic matrix with interacting cracks aligned with the othotropy axes was considered earlier by Mauge and Kachanov [1]). Here, we highlight some physically important effects and refer to the forth coming paper of Mauge and Kachanov [2].
- M e t h o d of Analysis. The method of [3] is used here. The problem of a linear elastic solid with uniform stress ~ at infinity containing N interacting cracks (with unit normals _n i) is replaced by the equivalent problem: crack faces are loaded by tractions t = -n * . ~ and stresses vanish at infinity. The latter problem is reduced to N sub-problems containing only one crack each but loaded by unknown tractions: ith crack is loaded by ~i(~) = ~ ..~ ~k/ktki(~) where At ki is the traction induced by the (isolated) kth crack along the ith crack site in a continuous material.
According to the key simplifying assumption of the method of [3], traction Atki(~) is taken as generated by the kth crack loaded by a uniform avera9 e traction (t*). Thus, whereas the traction ti(~) on any given ith crack is non-uniform, the impact on t i of the traction non-uniformity t k -(t k) on the kth crack is neglected. If (t k) were known, the interaction problem would be solved, since the kth crack-generated stress field is a product of (t ~) times the "standard" field ~r ~ (generated by the kth crack loaded by uniform traction of unit intensity). (t k) are found by interrelating them through 2N linear algebraic equations involving transmission factors A ki (characterizing the average traction along the ith crack site induced by o'k). Since the standard fields in 2-D matrices of arbitrary anisotropy can be derived in elementary functions (Mauge and Kachanov [2]), the procedure is straightforward. Test problems [4,5] show that the method remains accurate at spacings between cracks substantially smaller than the crack sizes [2].
Anisotropy of the matrix is reflected in the A-factors (and, therefore, (ti)) being functions not only of the crack geometry array, but, also, of the matrix moduli. For example, transmission of stresses and, therefore, crack interactions are enhanced (weakened) along the "stiffer" ("softer") direction of the matrix.
- I m p a c t of M a t r i x A n i s o t r o p y on Stress I n t e n s i t y Factors (SIFs). Several crack arrangements (Figs. 1-3 show some of them) have been analyzed.
(a) Interactions are stronger (weaker), as compared to the case of the isotropic matrix, for the cracks normal to the "stiffer" ("softer") direction of the matrix.
(b) The above described effect is strongly asymmetric: the enhancement is much more pronounced than the weakening.