September 1998 Assessment of the Interfacial Properties of CMCs Using Strain Partition under load 2409 250 elastic ￡fsE 6. Under-load strain partition of a 2D SiC-SiC composite to interpret wave propagation. 3I Under tensile stress, this com- matrix cracking. This damage mechanism starts at a stress of posite exhibits a nonlinear behavior related to the matrix mi--80 MPa and saturates at a stress of-120 MPa. Then, the cocracking, because the matrix has a lower failure than variation of S33 becomes smaller, which indicates that another the fibers. The specimen, which has a flat dogbone shape, a mechanism is occurring. This mechanism is the matrix micro- thickness of 3 mm, and a density of 2.7 g/cm, was submitted cracking that spreads inside the bundles. The same comments to tensile stress in direction 3, parallel to the direction of one of can be made on the variation of S22, although there is less the bundles. The stress-strain curve of the sample is shown in global variation. This variation, which is due to the fiber- Fig. 4 latrix debonding, occurs with a 10 MPa delay, compared The loading was applied over eighteen steps of stress until the transverse cracking the sample failed. These steps were necessary for the ultrasonic When unloading/reloading cycles are performed, the sliding evaluation. During the test, the total strain, a, was measured that occurs at the fiber/matrix interface is subordinate to the with an extensometer specially configured to work under im- direction of the load. As the stress decreases during unloading, mersion. The total strain to failure reached 0.8%. The behavior sliding opposite to that created by an increase in stress car occur. The transverse cracks that have been created during the ycles performed are hysteresis loops that exhibit many monotonic loading are then prone to close. Thus, the inelastic changes in slope, relevant to the interfacial debonding exte strain varies during the cycles. Therefore, identifying the in- and emphasize the presence of sliding with friction that need elastic strains as the residual strains at zero stress leads to ar a threshold of stress to occur. Even after unloading, the residual underestimate of their contribution to the total strain. To sepa train remains far from negligible. It is noteworthy that, until rate and accurately identify the effects of the initiation and 150 MPa, the stress-strain curve of the 2D SiC-SiC composite growth of matrix microcracks under tensile loading, as well as that th the he effec acks w clic load steps, which are performed at constant stress is necessary to perform a strain partition under load The accuracy and the reliability of the complete determina- Complete determination of the stiffness tensor, together with tion of the stiffness tensor, together with its variation during the its variation during the test, allows one to assess the elastic test, allow, by inverting this tensor, one to obtain the tensor of portion of the material behavior. The elastic strain is obtained elastic compliances and its own variation. Table I shows the initial elastic compliances with their confidence intervals. They tensile axis is then simply S33, depicted in Fig. 5, multiplied by have been recovered from the experimental measurements of the applied stress the stiffness of the material Figure 5 shows the compliances that were most affected by (21) the transverse and longitudinal crack patterns, with their con- fidence intervals. As observed in the stress-strain curve. the Because the extensometer gives access to the total strain, we compliance variations exhibit three domains. Until a stress of 0 MPa(which is the damage threshold of this composite)is elastic attained, the various compliances remain unchanged. After this int, matrix microcracking begins. The compliance variation The results of the strain partition are plotted in Fig. 6. Simi- along the tensile axis is very large; the value of S33 increases by lar to the compliance variations, this plot exhibits three zones more than 300%, which is representative of a large interbundle Until the damage threshold, the behavior is linear elastic. Then, Inter- Bundle Crack Density Intra-Bundle Crack Density -t- Stress(MPa) Fig. 7. Constitutive laws of the 2D SiC-SiC composite, depicting the crack-density variations interbundle scale an intrabundle scaleto interpret wave propagation.31 Under tensile stress, this com￾posite exhibits a nonlinear behavior related to the matrix mi￾crocracking, because the matrix has a lower failure strain than the fibers. The specimen, which has a flat dogbone shape, a thickness of 3 mm, and a density of 2.7 g/cm3 , was submitted to tensile stress in direction 3, parallel to the direction of one of the bundles. The stress–strain curve of the sample is shown in Fig. 4. The loading was applied over eighteen steps of stress until the sample failed. These steps were necessary for the ultrasonic evaluation. During the test, the total strain, «, was measured with an extensometer specially configured to work under im￾mersion. The total strain to failure reached 0.8%. The behavior remained elastic until a load of ∼80 MPa was attained. The two cycles performed are hysteresis loops that exhibit many changes in slope, relevant to the interfacial debonding extent, and emphasize the presence of sliding with friction that needs a threshold of stress to occur. Even after unloading, the residual strain remains far from negligible. It is noteworthy that, until 150 MPa, the stress–strain curve of the 2D SiC–SiC composite shows that the strain increases during the ultrasonic evaluation steps, which are performed at constant stress. The accuracy and the reliability of the complete determina￾tion of the stiffness tensor, together with its variation during the test, allow, by inverting this tensor, one to obtain the tensor of elastic compliances and its own variation. Table I shows the initial elastic compliances with their confidence intervals. They have been recovered from the experimental measurements of the stiffness of the material. Figure 5 shows the compliances that were most affected by the transverse and longitudinal crack patterns, with their con￾fidence intervals. As observed in the stress–strain curve, the compliance variations exhibit three domains. Until a stress of 80 MPa (which is the damage threshold of this composite) is attained, the various compliances remain unchanged. After this point, matrix microcracking begins. The compliance variation along the tensile axis is very large; the value of S33 increases by more than 300%, which is representative of a large interbundle matrix cracking. This damage mechanism starts at a stress of ∼80 MPa and saturates at a stress of ∼120 MPa. Then, the variation of S33 becomes smaller, which indicates that another mechanism is occurring. This mechanism is the matrix micro￾cracking that spreads inside the bundles. The same comments can be made on the variation of S22, although there is less global variation. This variation, which is due to the fiber– matrix debonding, occurs with a 10 MPa delay, compared to the transverse cracking. When unloading/reloading cycles are performed, the sliding that occurs at the fiber/matrix interface is subordinate to the direction of the load. As the stress decreases during unloading, sliding opposite to that created by an increase in stress can occur. The transverse cracks that have been created during the monotonic loading are then prone to close. Thus, the inelastic strain varies during the cycles. Therefore, identifying the in￾elastic strains as the residual strains at zero stress leads to an underestimate of their contribution to the total strain. To sepa￾rate and accurately identify the effects of the initiation and growth of matrix microcracks under tensile loading, as well as the effect of these cracks when cyclic loading is performed, it is necessary to perform a strain partition under load. Complete determination of the stiffness tensor, together with its variation during the test, allows one to assess the elastic portion of the material behavior. The elastic strain is obtained from the generalized Hooke’s law. The elastic strain along the tensile axis is then simply S33, depicted in Fig. 5, multiplied by the applied stress: «elastic = S33s (21) Because the extensometer gives access to the total strain, we have «inelastic = «total − «elastic (22) The results of the strain partition are plotted in Fig. 6. Simi￾lar to the compliance variations, this plot exhibits three zones. Until the damage threshold, the behavior is linear elastic. Then, Fig. 6. Under-load strain partition of a 2D SiC–SiC composite. Fig. 7. Constitutive laws of the 2D SiC–SiC composite, depicting the crack-density variations on an interbundle scale and an intrabundle scale. September 1998 Assessment of the Interfacial Properties of CMCs Using Strain Partition under Load 2409