Rate of strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 0=240 MPa [og] SiC/CAS ll 200 Hz, RT 15K 1静028 0210310′ 0510° Number of cycles, N Fig 8. Residual co ngth as a function of the number of cycled to 10 cycles and tested in monotonic tension thereafter cycles. The residual strength is fully retained at approximately 500 MPa until 10 cycles, but decreases to 240 MPa within a short number of cycle suggest that T was lower for the precycled specimens than for the virgin material IV. A Possible High Cycle Fatigue Damage Mechanism (1 Summary of Observed Behavior (4) Model Prediction of Residual Strength There are several characteristic features of the high-frequency Existing models for composite strength predict that a decrease fatigue process in T should result in a decrease in the residual strength. These (1)The temperature of the specimen increases during the models are valid only if global load sharing(GLS)takes place; this initial stages of fatigue. Next, it levels off and, for long-duration requirement is fulfilled for specimens where fiber pull-out occurs atigue at moderate stress levels. decreases. If failure is avoided across the entire fracture surface and the fiber pull-out length the shape of the temperature rise curve is often bell shaped. If varies from one fiber to the next. These assumptions are fulfilled failure occurs, a sharp rise in temperature occurs within the for the virgin specimens and the specimens cycled to 10 cycles localized zone immediately prior to fracture(typically of the order GLS models predict that the residual strength after N cycles, of several seconds ). o (N), is related to the initial composite strength, ou,as (2) The density of matrix rapidly during the itial stages of fatigue. For o(N)/(N)\/m+l) density quickly stabilizes and for the duration of (1) the fatigue life. The development of matrix cracks is assumed to be influenced by stress corrosion crackingand decrease in T due to where T is the initial value of T, M is the value attained after M interfacial wea cycles, and m is the Weibull modulus describing the strength ( The hysteresis modulus decreases rapidly during the initial tages of fatigue, reaches an approximate plateau, and, if failure is ariation of the fibers(in Eq (1)the fiber strength is assumed to avoided, may show a gradual increase. The initial modulus remain unchanged during cycling). Equation(1)predicts that if T decreases during cycling(aN)<T), then the residual strength of decrease is attributed to the formation of matrix cracks and a posite decreases as well. U =20MPa,N=105) decrease in T, the later modulus recovery is likely to be caused by 6 MPa, m=3(value taken from Curtin), ou= 508 MPa (Table an increase in T. The increase in T may be caused by various D), Eq (1) predicts o (N=10 )=376 MPa. This prediction mechanisms, such as accumulation of debris along the interface ol significantly lower than the experimental results(491 MPa, Tabl a chemical reaction, increasing the interfacial sliding resistance or bondin II). This inconsistency indicates that a decrease in the interfacial shear stress, acting alone, may not have the effect predicted by the formation of a central zone where the fiber pull-out lengths are GLS models, and that the models do not adequately describe the negligible. Surrounding this zone, which consumes roughly half of the fracture surface, is a zone of extensive fiber pull-out. Speci- mens that were prefatigued at the same stress level, followed by (5) Residnal Strength as a Function of cycles monotonic loading to failure, exhibited extensive fiber pull-out From the measured strength values a graph that shows the throughout the entire fracture surface. Virgin specimens tested residual strength of the composite as a function of the number of cles can be constructed. The four specimens that were cycled to pull-out across the entire fracture surface. failure are also included in this graph, since the residual strength of these specimens must have been equal to omax(i.e, 240 MPa) (2) Interpretation of Fracture Surface and Failure Mode when they failed. The results are presented in Fig. 8. As already Since the fracture surface of the prefatigued specimens exhib- mentioned the residual strength of the specimens cycled for 10 ited extensive fiber pull-out, the central core(in specimens cycled les was almost the same as that measured for th to failure) must have formed very rapidly just prior to specimen specimens. From Fig 8, we conclude that the loss of composite fracture( between 10 cycles and the occurrence of fatigue failure) strength does not occur gradually over the fatigue life, rather, for To understand the development of the core region, we must this unidirectional composite, the loss of residual strength of th identify a mechanism that can form a region with no fiber pull-out composite occurs within the last 20% of the specimen lifetime within a short number of cycles. Apparently the final stage It should be noted that although the present results are obtained (localization) is not cycle count dependent but damage and at specific test conditions, similar results have been found under temperature rise dependent different conditions. Therefore, the trends of the results are likely The lack of fiber pull-out in the core region indicates that the to be of a general nature usual composite behavior (interfacial slip) has been hindered,suggest that t was lower for the precycled specimens than for the virgin material. (4) Model Prediction of Residual Strength Existing models for composite strength predict that a decrease in t should result in a decrease in the residual strength.8,19 These models are valid only if global load sharing (GLS) takes place; this requirement is fulfilled for specimens where fiber pull-out occurs across the entire fracture surface and the fiber pull-out length varies from one fiber to the next. These assumptions are fulfilled for the virgin specimens and the specimens cycled to 105 cycles. GLS models predict that the residual strength after N cycles, su(N), is related to the initial composite strength, su 0 , as19 su~N! su 0 5 S t~N! t0 D 1/~m11! (1) where t0 is the initial value of t, t(N) is the value attained after N cycles, and m is the Weibull modulus describing the strength variation of the fibers (in Eq. (1) the fiber strength is assumed to remain unchanged during cycling). Equation (1) predicts that if t decreases during cycling (t(N) , t0 ), then the residual strength of the composite decreases as well. Using t 5 20 MPa, t(N5105 ) 5 6 MPa, m 5 3 (value taken from Curtin8 ), su 0 5 508 MPa (Table I), Eq. (1) predicts su(N5105 ) 5 376 MPa. This prediction is significantly lower than the experimental results (491 MPa, Table II). This inconsistency indicates that a decrease in the interfacial shear stress, acting alone, may not have the effect predicted by the GLS models, and that the models do not adequately describe the high cycle fatigue failure of CMCs. (5) Residual Strength as a Function of Cycles From the measured strength values a graph that shows the residual strength of the composite as a function of the number of cycles can be constructed. The four specimens that were cycled to failure are also included in this graph, since the residual strength of these specimens must have been equal to smax (i.e., 240 MPa) when they failed. The results are presented in Fig. 8. As already mentioned the residual strength of the specimens cycled for 105 cycles was almost the same as that measured for the virgin specimens. From Fig. 8, we conclude that the loss of composite strength does not occur gradually over the fatigue life; rather, for this unidirectional composite, the loss of residual strength of the composite occurs within the last 20% of the specimen lifetime. It should be noted that although the present results are obtained at specific test conditions, similar results have been found under different conditions.36 Therefore, the trends of the results are likely to be of a general nature. IV. A Possible High Cycle Fatigue Damage Mechanism (1) Summary of Observed Behavior There are several characteristic features of the high-frequency fatigue process: (1) The temperature of the specimen increases during the initial stages of fatigue. Next, it levels off and, for long-duration fatigue at moderate stress levels, decreases. If failure is avoided, the shape of the temperature rise curve is often bell shaped. If failure occurs, a sharp rise in temperature occurs within the localized zone immediately prior to fracture (typically of the order of several seconds). (2) The density of matrix cracks increases rapidly during the initial stages of fatigue. For a fixed maximum stress, this crack density quickly stabilizes and remains constant for the duration of the fatigue life. The development of matrix cracks is assumed to be influenced by stress corrosion cracking37 and decrease in t due to interfacial wear.17 (3) The hysteresis modulus decreases rapidly during the initial stages of fatigue, reaches an approximate plateau, and, if failure is avoided, may show a gradual increase. The initial modulus decrease is attributed to the formation of matrix cracks and a decrease in t; the later modulus recovery is likely to be caused by an increase in t. The increase in t may be caused by various mechanisms, such as accumulation of debris along the interface or a chemical reaction, increasing the interfacial sliding resistance or bonding. (4) A unique feature of high cycle fatigue failure is the formation of a central zone where the fiber pull-out lengths are negligible. Surrounding this zone, which consumes roughly half of the fracture surface, is a zone of extensive fiber pull-out. Speci￾mens that were prefatigued at the same stress level, followed by monotonic loading to failure, exhibited extensive fiber pull-out throughout the entire fracture surface. Virgin specimens tested under monotonic tension also exhibited nearly uniform fiber pull-out across the entire fracture surface. (2) Interpretation of Fracture Surface and Failure Mode Since the fracture surface of the prefatigued specimens exhib￾ited extensive fiber pull-out, the central core (in specimens cycled to failure) must have formed very rapidly just prior to specimen fracture (between 105 cycles and the occurrence of fatigue failure). To understand the development of the core region, we must identify a mechanism that can form a region with no fiber pull-out within a short number of cycles. Apparently the final stage (localization) is not cycle count dependent but damage and temperature rise dependent. The lack of fiber pull-out in the core region indicates that the usual composite behavior (interfacial slip) has been hindered, Fig. 7. SEM micrographs of a typical fracture surface of a specimen cycled to 105 cycles and tested in monotonic tension thereafter. Fig. 8. Residual composite strength as a function of the number of load cycles. The residual strength is fully retained at approximately 500 MPa until 105 cycles, but decreases to 240 MPa within a short number of cycles thereafter. June 2000 Rate of Strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 1473