4848 LIU et al.: LAMINATED COMPOSITE an isolated ply caused by the thermal mismatch stress on reaches 140 MPa for unidirectional between the fiber and the matrix [4]. CAS/SiC 18, 101, which corresponds to om The first part (ply residual stress)arises because of 187.4 MPa from equation( 8). When the maximum the anisotropy in the coefficients of thermal expansion stress criterion is applied, based on the matrix crack (CTE). In CAS/SiC, the Cte transverse to the fiber initiation stress of the unidirectional composite, the direction(ar =4.5X10-6K-)is larger than in the predicted applied stress for matrix crack initiation in fiber direction(a,=4.3X10-6K- )[20]. Clearly, if the 0/900 cross-ply laminate is 56 MPa [equation aL=ar, there will be no thermal residual stress (7). This is in good agreement with the lowest stress resulting from differently oriented plies. Using lami- level where surface cracks were visually detected nation theory [2] for a symmetric laminate(the case [ Fig. 3(a). Mechanical testing shows that the stress- in our study), the residual stress from this source is strain curve starts to deviate from linear behavior at uniform within each layer, but changes discontinu- 50 MPa, and the corresponding AE recording also Following lamination theory and assuming that about the same stress level(Fig. 2). Other work lEB ously across the ply bor indicates that the onset of matrix cracking occurs each layer is homogeneous [2], the lamination also shown that the matrix cracking stress o ranges residual stress in each ply is calculated to be biaxial from 40 to 60 MPa [3]. Some of this discrepancy can with a magnitude of about 13 MPa. The 90 plies are be attributed to sample differences. Additionally, it under tension in the loading (i.e, global 1-)direction has also been noted that in unidirectional CMCs, while the 0 plies are in compression in the l-direc- matrix cracking initiation depends on the local fiber tion, Fig. 1. Because the residual stresses in the 0 distribution; matrix cracking can be initiated in the and 90 plies are of identical magnitude but opposite matrix-rich region at a lower stress level than where in sign, the net residual force on the laminate is zero. the fibers are more densely and uniformly distributed To this stress state we a Id the effects due to the [23 Also, free edge effects(although considered to CTE mismatch between the fiber and the matrix. be small in this case)on surface crack initiation in a Since the matrix has a higher Cte than the fiber, the 0/90 laminate [24] were not investigated in above matrix is under axial and circumferential(hoop)ten- simplified analysis. Regardless, the overall agreement sion, and the fiber/matrix interface(radial direction) between theory and experimental observation is good is under compression. Using an elastic composite cyl- Finally, we note that the residual stress analysis inder model [21, 22], the calculated residual matrix above showed that the maximum matrix tensile stress axial stress Oa=81 MPa and the radial interfacial occurred in the loading direction, within the 90 pl stress OR=-57 MPa, assuming 0.35 fiber volume The observation that matrix cracks initiated preferen- fraction. These values are in reasonable agreement tially near the boundaries of 90 plys must be either with previously reported values(axial 89 MPa and a consequence of a locally higher matrix fraction at radial -65 MPa)[8]. The hoop stress, oBe, in the the ply interface or variations in stress at the 0%/900 matrix calculated from the composite cylinder model ply boundary [25]. Further studies are needed to is tensile with a maximum at the fiber/matrix bound- improve the incorporation of matrix crack initiation ary of -120 MPa. For the laminate system investi- in models of laminate mechanics gated here, the contribution from the laminae residual tress is much less than the residual stress resulting from CtE mismatch between the fiber and the matrix 6. CONCLUSIONS When an external stress o, is applied, the stress The elastic stiffness degradation of a 0%/90cross- is distributed among the layers. Using lamination ply laminate has been evaluated by a combination of theory, the stress distributions on 0 and 90 layers a laser-ultrasonic characterization, acoustic emission are approximately 1.0350, and 0.965o11-Thus, the and surface replicas. The LU technique allowed a maximum total stress along the loading direction, detailed characterization of the anisotropic damage including contributions from applied load, lamination through ultrasonic velocity measurements in various residual stress and hoop residual stress, on the 90 propagation directions during loading and unloading ply prior to matrix crack initiation is f the composite. Damage along the three principal directions was characterized by the elastic constants Gm=0.965G1+dB+o (7) CIl, C2 and C33. The largest stiffness reduction was observed in Cll, the loading-direction modulus. This has been linked to transverse matrix cracking initiat For unidirectional CAS/SiC, the total stress carried in 90 plies with an initiation stress of about 50 by the matrix is MPa. Smaller reductions for C2? and C33 in the trans- verse plane are attributed to interface damage in th +oR=0.760+oR.(8)0 plies that initiated at about 75 MPa, Matrix cracks died stress levels than in unidirec- tional CAS/SiC composites. This observation is Surface matrix cracks are detected when the applied rationalized by residual stress analy4848 LIU et al.: LAMINATED COMPOSITE an isolated ply caused by the thermal mismatch between the fiber and the matrix [4]. The first part (ply residual stress) arises because of the anisotropy in the coefficients of thermal expansion (CTE). In CAS/SiC, the CTE transverse to the fiber direction (aT 5 4.531026 K21 ) is larger than in the fiber direction (aL 5 4.331026 K21 ) [20]. Clearly, if aL 5 aT, there will be no thermal residual stress resulting from differently oriented plies. Using lami￾nation theory [2] for a symmetric laminate (the case in our study), the residual stress from this source is uniform within each layer, but changes discontinu￾ously across the ply boundary. Following lamination theory and assuming that each layer is homogeneous [2], the lamination residual stress in each ply is calculated to be biaxial with a magnitude of about 13 MPa. The 90° plies are under tension in the loading (i.e., global 1-) direction while the 0° plies are in compression in the 1-direc￾tion, Fig. 1. Because the residual stresses in the 0° and 90° plies are of identical magnitude but opposite in sign, the net residual force on the laminate is zero. To this stress state we add the effects due to the CTE mismatch between the fiber and the matrix. Since the matrix has a higher CTE than the fiber, the matrix is under axial and circumferential (hoop) ten￾sion, and the fiber/matrix interface (radial direction) is under compression. Using an elastic composite cyl￾inder model [21, 22], the calculated residual matrix axial stress sR aa 5 81 MPa and the radial interfacial stress sR rr 5 257 MPa, assuming 0.35 fiber volume fraction. These values are in reasonable agreement with previously reported values (axial 89 MPa and radial 265 MPa) [8]. The hoop stress, sR θθ, in the matrix calculated from the composite cylinder model is tensile with a maximum at the fiber/matrix bound￾ary of |120 MPa. For the laminate system investi￾gated here, the contribution from the laminae residual stress is much less than the residual stress resulting from CTE mismatch between the fiber and the matrix. When an external stress s11 is applied, the stress is distributed among the layers. Using lamination theory, the stress distributions on 0° and 90° layers are approximately 1.035s11 and 0.965s11. Thus, the maximum total stress along the loading direction, including contributions from applied load, lamination residual stress and hoop residual stress, on the 90° ply prior to matrix crack initiation is sm 5 0.965s11 1 sR θθ 1 sR 90. (7) For unidirectional CAS/SiC, the total stress carried by the matrix is sm 5 Em Ec s11 1 sR aa 5 0.76s11 1 sR aa. (8) Surface matrix cracks are detected when the applied stress s11 reaches 140 MPa for unidirectional CAS/SiC [8, 10], which corresponds to sm 5 187.4 MPa from equation (8). When the maximum stress criterion is applied, based on the matrix crack initiation stress of the unidirectional composite, the predicted applied stress for matrix crack initiation in the 0°/90° cross-ply laminate is 56 MPa [equation (7)]. This is in good agreement with the lowest stress level where surface cracks were visually detected [Fig. 3(a)]. Mechanical testing shows that the stress– strain curve starts to deviate from linear behavior at |50 MPa, and the corresponding AE recording also indicates that the onset of matrix cracking occurs at about the same stress level (Fig. 2). Other work has also shown that the matrix cracking stress s11 ranges from 40 to 60 MPa [3]. Some of this discrepancy can be attributed to sample differences. Additionally, it has also been noted that in unidirectional CMCs, matrix cracking initiation depends on the local fiber distribution; matrix cracking can be initiated in the matrix-rich region at a lower stress level than where the fibers are more densely and uniformly distributed [23]. Also, free edge effects (although considered to be small in this case) on surface crack initiation in a 0°/90° laminate [24] were not investigated in above simplified analysis. Regardless, the overall agreement between theory and experimental observation is good. Finally, we note that the residual stress analysis above showed that the maximum matrix tensile stress occurred in the loading direction, within the 90° ply. The observation that matrix cracks initiated preferen￾tially near the boundaries of 90° plys must be either a consequence of a locally higher matrix fraction at the ply interface or variations in stress at the 0°/90° ply boundary [25]. Further studies are needed to improve the incorporation of matrix crack initiation in models of laminate mechanics. 6. CONCLUSIONS The elastic stiffness degradation of a 0°/90° cross￾ply laminate has been evaluated by a combination of a laser-ultrasonic characterization, acoustic emission and surface replicas. The LU technique allowed a detailed characterization of the anisotropic damage through ultrasonic velocity measurements in various propagation directions during loading and unloading of the composite. Damage along the three principal directions was characterized by the elastic constants C11, C22 and C33. The largest stiffness reduction was observed in C11, the loading-direction modulus. This has been linked to transverse matrix cracking initiat￾ing in 90° plies with an initiation stress of about 50 MPa. Smaller reductions for C22 and C33 in the trans￾verse plane are attributed to interface damage in the 0° plies that initiated at about 75 MPa. Matrix cracks in this cross-ply composite are found to initiate at much lower applied stress levels than in unidirec￾tional CAS/SiC composites. This observation is rationalized by residual stress analysis