S. Baste/ Composites Science and Technology 61(2001)2285-2297 2293 wedging of the cracks by grain bridging [301. To main damage mode and induces a fully anisotropic describe this later fact, another aspect ratio 8 that takes degradation. In particular, the coupling stiffnesses C34, the residual opening into account is introduced [15]. C24, C14 and C56, which are naturally about zero at 0 Finally, the variations of inelastic strains during the MPa, become non-negligible at 40 MPa. After 60 MPa whole test can be described by [15] they decrease and recover their initial value of about zero. It coincides with the increase of inelastic strain e=B(F(8-8)+8) (21) The fibrous reinforcement stops and deviates the The inelastic strains are thus a function of the transverse matrix microcracking in mode Il Sliding occurs in the crack density and of the aspect ratio of the cracks whether fibre-matrix interphase and leads to other cracking modes they are completely open or not(Fig. 25) consisting in slit cracks whose orientations coincide with The predictions of the three dimensional changes in elasticity and of the inelastic strains under cyclic loading are shown to compare favourably with experimental data. While the crack density describes the inelastic strains and the drop in elastic modulus, the opening closure variable modulates these effects when cyclic ading is applied [ 15]- 6. Effective elastic stiffnesses of an anisotropic medium permeated by tilted cracks In composite materials, failure mechanisms favour the Fig. 26. The 300 off-axis solicitation sample, cut out according to generation of microcracks oriented normally to the tensile 300 angle from fibre axes, and loading in this direction. stress [1]. An off-axis tensile loading creates microcracks whose orientation does not coincide with the fibre axes [31, 32] and induces a fully anisotropic elastic degrad tion. To emphasise the induced anisotropy and the loss of elastic symmetry caused by ofi-principal solicitations, the measurement of the changes of all the stiffness tensor components has been done [33] for a 2D C-C-SiC composite material, subjected to a tensile solicitation at 30 from one of the fibre directions(Fig. 26). The load induced changes of the thirteen stiffnesses. associated 8x, with a monoclinic symmetry, have been recovered from ultrasonic velocity data [33] Damage-induced changes of the thirteen stiffnesses (Cii identified in the geometric coordinate system of the sample are plotted in Fig. 27 as a function of the applied b行 tensile stress [33]. The loss of stiffness along the tensile axis x3 is very important and occurs from the first stress levels. The variation of the experimental stiffnesses C33 Ca and Css leads us to consider that the matrix micro- cracking oriented normally to the tensile loading is the 灿出江 Applied Stress (MPay experinental vahcs with thcir 90 s confidence interval prediction af the stiffness changes Inelastic Strain (%) Fig. 25. Variation of the inelastic strains during cyclic loading of a 2D Fig. 27. Variation of the stiffness tensor as a function of a tensile C-SiC stress applied within directionwedging of the cracks by grain bridging [30]. To describe this later fact, another aspect ratio d’ that takes the residual opening into account is introduced [15]. Finally, the variations of inelastic strains during the whole test can be described by [15]: "in ¼ ðFð 0 Þ þ 0 Þ ð21Þ The inelastic strains are thus a function of the transverse crack density and of the aspect ratio of the cracks whether they are completely open or not (Fig. 25). The predictions of the three dimensional changes in elasticity and of the inelastic strains under cyclic loading are shown to compare favourably with experimental data. While the crack density describes the inelastic strains and the drop in elastic modulus, the opening closure variable modulates these effects when cyclic loading is applied [15]. 6. Effective elastic stiffnesses of an anisotropic medium permeated by tilted cracks In composite materials, failure mechanisms favour the generation of microcracks oriented normally to the tensile stress [1]. An off-axis tensile loading creates microcracks whose orientation does not coincide with the fibre axes [31,32] and induces a fully anisotropic elastic degrada￾tion. To emphasise the induced anisotropy and the loss of elastic symmetry caused by off-principal solicitations, the measurement of the changes of all the stiffness tensor components has been done [33] for a 2D C–C–SiC composite material, subjected to a tensile solicitation at 30
from one of the fibre directions (Fig. 26). The load￾induced changes of the thirteen stiffnesses, associated with a monoclinic symmetry, have been recovered from ultrasonic velocity data [33]. Damage-induced changes of the thirteen stiffnesses (Cij) identified in the geometric coordinate system of the sample are plotted in Fig. 27 as a function of the applied tensile stress [33]. The loss of stiffness along the tensile axis x3 is very important and occurs from the first stress levels. The variation of the experimental stiffnesses C33, C44 and C55 leads us to consider that the matrix micro￾cracking oriented normally to the tensile loading is the main damage mode and induces a fully anisotropic degradation. In particular, the coupling stiffnesses C34, C24, C14 and C56, which are naturally about zero at 0 MPa, become non-negligible at 40 MPa. After 60 MPa, they decrease and recover their initial value of about zero. It coincides with the increase of inelastic strain (Fig. 29). The fibrous reinforcement stops and deviates the matrix microcracking in mode II. Sliding occurs in the fibre-matrix interphase and leads to other cracking modes consisting in slit cracks whose orientations coincide with Fig. 26. The 30
off-axis solicitation sample, cut out according to a 30
angle from fibre axes, and loading in this direction. Fig. 25. Variation of the inelastic strains during cyclic loading of a 2D C–SiC. Fig. 27. Variation of the stiffness tensor as a function of a tensile stress applied within direction 3. S. Baste / Composites Science and Technology 61 (2001) 2285–2297 2293