September 1998 Assessment of the Interfacial Properties of CMCs Using Strain Partition under load 2411 600 250 Crack Free Zone 200 50 200 Fig. 10. Characteristic lengths of the transverse microcracking of a 2D SiC-SiC composite Using the elastic strains calculated from Eq.(21), the pre- tion, or failure, occurs. The model describes what can be called dicted linear variation of the inelastic strains that appear in Fig. a mixed bonding-that is to say, an initially strong bonding 8, the parameters identified from the micrographs in Fig.9 that promotes elasticity, becomes weak with increasing stress, (given in Table ID), together with the variations of the compli and then allows fiber-matrix sliding when delamination oc- ances that appear as plain lines in Fig. 5, it is possible to predict curs. Furthermore, the increase of T at both scales can be re- the characteristic lengths, intercrack distances(Eq.(3), and ated to the saturation of the sliding. The relative fiber-matrix debond lengths(Eq.(22) of the microcracking(Fig. 10), as sliding does not become more difficult because of a clamping well as the interfacial sliding stress at both scales of the com stress or debris that lock the sliding; more probably, the diffi- posite(Fig. 11). The average lengths of the elementary cell culty is caused by the decrease in the number of sliding sites, given in Table II take into account the waviness of the because of saturation. bundle remark must be made regarding the interbundle scale. considering a linear variation for the inelastic strains V. Conclusion stead of the values directly identified from the experiment ( Fig. 8)is equivalent to compensate the delay that results from The fundamental strain mecl of ceram the mode acking. In Fig. 10, as the intercrack distance posites(CMCs)are matrix mi king, which induces a loss diminishes, the sliding length increases; it increases up to one of stiffness. and fiber-matrix ing which leads to inter- half the intercrack distance and then stabilizes because of satu- facial frictional sliding. Thu ial sliding stress is a k ation. No further transverse cracking appears, and either the arameter in the global behavior. Accurate knowledge of the cracking begins at another scale or the sample breaks. In regard strain mechanisms is necessary to correctly identify the value to T(Fig. 11), the average value at the interbundle scale is of the interfacial sliding stress. Ultrasonic characterization different from the value at the fiber scale. This variation can be through the complete determination of the stiffness tensor explained by the difference that exists in the radii, as well as in along the entire test can detect all the damage mechanisms of the debond lengths. The lower value at the bundle scale is-200 CMCs: the transverse matrix microcracking. as well as the 1Pa, whereas it is -100 MPa at the fiber scale. This range is resence of longitudinal cracks at the fiber/matrix interface consistent with previous results found elsewhere. 34 The higher is of great help in the aniso- value of T at the bundle scale explains the progressive slidin tropic damage and it also allows one to conduct the strain whereas, at the fiber scale, the sliding occurs simultaneously to partition under load. Because the strain partition under loa the increment of stress. It is noteworthy that, whatever the separates the various mechanisms responsible for the nonlinear scale. the evaluation is not constant. It decreases to a minimum behavior of cmcs. it then seems clear that those two elemen- value and then increases to an even-higher value when satura- tary mechanisms occur at both scales of the material: at the tra bundle 300 H200 Stress(MPa) Fig. 11. Interfacial sliding stress of a 2D SiC-SiC composite.Using the elastic strains calculated from Eq. (21), the pre￾dicted linear variation of the inelastic strains that appear in Fig. 8, the parameters identified from the micrographs in Fig. 9 (given in Table II), together with the variations of the compli￾ances that appear as plain lines in Fig. 5, it is possible to predict the characteristic lengths, intercrack distances (Eq. (3)), and debond lengths (Eq. (22)) of the microcracking (Fig. 10), as well as the interfacial sliding stress at both scales of the com￾posite (Fig. 11). The average lengths of the elementary cell given in Table II take into account the waviness of the bundle.36 A remark must be made regarding the interbundle scale: considering a linear variation for the inelastic strains instead of the values directly identified from the experiment (Fig. 8) is equivalent to compensate the delay that results from the Mode II cracking. In Fig. 10, as the intercrack distance diminishes, the sliding length increases; it increases up to one￾half the intercrack distance and then stabilizes, because of satu￾ration. No further transverse cracking appears, and either the cracking begins at another scale or the sample breaks. In regard to t (Fig. 11), the average value at the interbundle scale is different from the value at the fiber scale. This variation can be explained by the difference that exists in the radii, as well as in the debond lengths. The lower value at the bundle scale is ∼200 MPa, whereas it is ∼100 MPa at the fiber scale. This range is consistent with previous results found elsewhere.34 The higher value of t at the bundle scale explains the progressive sliding, whereas, at the fiber scale, the sliding occurs simultaneously to the increment of stress. It is noteworthy that, whatever the scale, the evaluation is not constant. It decreases to a minimum value and then increases to an even-higher value when satura￾tion, or failure, occurs. The model describes what can be called a mixed bonding—that is to say, an initially strong bonding that promotes elasticity, becomes weak with increasing stress, and then allows fiber–matrix sliding when delamination oc￾curs. Furthermore, the increase of t at both scales can be re￾lated to the saturation of the sliding. The relative fiber–matrix sliding does not become more difficult because of a clamping stress or debris that lock the sliding; more probably, the diffi￾culty is caused by the decrease in the number of sliding sites, because of saturation. V. Conclusion The fundamental strain mechanisms of ceramic-matrix com￾posites (CMCs) are matrix microcracking, which induces a loss of stiffness, and fiber–matrix debonding, which leads to inter￾facial frictional sliding. Thus, interfacial sliding stress is a key parameter in the global behavior. Accurate knowledge of the strain mechanisms is necessary to correctly identify the value of the interfacial sliding stress. Ultrasonic characterization through the complete determination of the stiffness tensor along the entire test can detect all the damage mechanisms of CMCs: the transverse matrix microcracking, as well as the presence of longitudinal cracks at the fiber/matrix interface. Thus, this technique is of great help in measuring the aniso￾tropic damage, and it also allows one to conduct the strain partition under load. Because the strain partition under load separates the various mechanisms responsible for the nonlinear behavior of CMCs, it then seems clear that those two elemen￾tary mechanisms occur at both scales of the material: at the Fig. 10. Characteristic lengths of the transverse microcracking of a 2D SiC–SiC composite. Fig. 11. Interfacial sliding stress of a 2D SiC–SiC composite. September 1998 Assessment of the Interfacial Properties of CMCs Using Strain Partition under Load 2411