July 2007 Thermal Cycling Damage in Ceramic Matrix Composites Under a Constant Stress 2139 (3) AE Characterization of Damage Initiation and Evolution the first cycle, although the driving force will decrease due to During Thermal Cycle reduction in material stiffness E after cracking, it is impossibly Acoustic emission. i.e. transient elastic waves generated within a below the matrix cracking stress ome immediately and the re- material due to sudden irreversible structural change. has been sidual thermal stress between fibers and matrix is impossibly bserved and recorded during thermal cycling of the C/SiC com- relaxed completely. As a result, the matrix continues to crack posite. Figure 8 presents AE activities, s en strain. and tem- with repetitive thermal cycles until the decreasing driving force ure measured during the fourth cycle as a typical example becomes smaller than omc, where the crack density reaches As can be seen, the specimen strain reveals an absolute depen discussed in Section Ill (2). It is coml dence on temperature. Namely, the strain increases upon heat that the modulus of the composites de ch cycle. It is gene cycles due to continuous matrix cracking. 374ases with thermal that AE signals are produced -by collective microstructural dam- Besides, in a single cycle, the resultant driving stress oM act ing on the matrix changes with temperature(see Fig 9): reach- testing emit fewer acoustic emissions at the stage of heat he lower ing, but as the cooling stage approaches the emission rate in temperature limit, creases rapidly. This indicates that a large damage accompanied by multiplication of microcracking in composite materials mainly AT1>0 occurs once cooled. When a C/Sic is heated in a certain cycle, the increasing temperature renders the wide crack opening displace 50 MP ment in the matrix more homogeneously by its thermal expan sion, and then above the crack closure temperature(. e, 900C), and. declining to the minimum value odr on heating to the tensile stress acting on the fibers emerges but does not pro- upper temperature limit, duce extensive fiber fracture. A reasonable interpretation is that the high strength of the fibers, the softness of the Pyc interphase (Fig. 1(b), and the lower top temperature (only 1200C)are F=0<0.=q8Bm 0. oAC= 50MPa fracture. Thus, detectable AE hardly appears before the top cycle temperature is reached. When the C/SiC specimen is cooled This driving stress just reveals an opposite tendency with ob- down from the upper cycle temperature, the compressive stress- served thermal strain: the higher the temperature the larger the es diminish rapidly and tensile stresses in the matrix build up. aE thermal strain and the smaller the resultant driving stress oM should take place due to relaxation of the tensile stresses in the matrix by the deformation mechanism of matrix cracking, and and vice versa. Thus. a ic stress between gdr and odr is eated in the matrix over the same period as the temperature should persist down to the lower cycle temperature. During cooling, thermally induced stresses in the matrix may Generally, the appearance of significant AE at a certain reload comprise, - apart from the residual thermal stresses as men- ing level below the previous maximum-applied stress level is tioned previously in Eq (2). thermal shock-induced stress due to referred to as the felicity effect. The ratio of stress at the onset temperature gradient between the exterior and interior of the of emission to the previous peak stress, known as the Felicit sample. Thus, the driving force behind the cracking of the ratio, is an indication of the severity and extent of damage matrix can be a sum of the thermally induced stresses ar As shown in Fig 9, AE responses exhibit the apparent Felicit he applied stress, as effect as AE in each cycle is detected at stresses below the pre- vious peak stress. Assuming that emissions within the n+I cycle (4) will occur as long as the driving force exceeds the matrix crack ing stress ome, the Felicity ratio, RF, may be simply expressed as The subscript M denotes the matrix. om refers to the applied R constant stress. oM is the thermal shock-induced stress at the surface of the material, and can be classically written as' Evidently AEα△Ti activity occurred because the resultant driving stress was much igher than the stress required to propagate the cracks mce ndicating a quite low Felicity ratio associated with the appear- where modulus E, CtE a, and poissons ratio v are either matrix ance of significant damage. Subsequently, the Felicity ratio in- or volume-averaged properties. The parameter"A"is termed creased as the driving stress od decreased after cracking and the"stress reduction factor. ATk is the temperature difference the damage of each cycle gradually diminished. Fi ween the interior(Tin)and exterior(Tex) temperature of the for the applied stress, the driving stress of the matrix cracking material during thermal shock (i.e, ATk= Tin-Tex). Thus, disappeared basically because the thermally induced stress multiple matrix cracking perpendicular to the fibers occurs when was released completely with the saturation both in the crack the resultant driving stress obr along the fiber direction be- density and in the damage when Gpr comes higher than the stress required to cause matrix fracture damage-saturated composite did not exhibit any response to (referred to as matrix strength omu, which is usually low for ce- the destructive energy of thermal cycling because macro-cracks ramics and approximately equal to ome). According to Eqs. (2), of the matrix and the weakened interphase had enough spac approximately obtained on cooling from the matrix cracking Felicity ratio approached one. The notion that thermae, the 4)and(5), a tensile driving stress of at least 286 MPa can be to tolerate micro-thermal expansion. As a consequen temperature to 700c by simply substituting the material damage decreased with cycles will be further confirmed by the parameter OM in Eq. 2 using the composite modulus E. There- accumulated AE energy as later shown in Fig. 10 fore, in the first cycle, the driving force of matrix cracking may igure 9 also depicts the relationship of the thermal strain, be high enough to initiate and develop the matrix cracks. After the AE activities, and the accumulated aE energy with cycles. Hs=14285GPa×48-(-0.1×10-6/C×(900 It is interesting that the stepwise increasing AE energy is stress 6x14285GPa x 3 enhanced only at the cooling stage of each cycle, and all these Abov e the 6 micra lothe data ratd ue bo frthe selected physical parameters(i.e, thermal strain, AE hits, and 210 s as well as their excitation source of temperature. It is also(3) AE Characterization of Damage Initiation and Evolution During Thermal Cycles Acoustic emission, i.e., transient elastic waves generated within a material due to sudden irreversible structural change, has been observed and recorded during thermal cycling of the C/SiC com￾posite. Figure 8 presents AE activities, specimen strain, and tem￾perature measured during the fourth cycle as a typical example. As can be seen, the specimen strain reveals an absolute depen￾dence on temperature. Namely, the strain increases upon heating and decreases with cooling at each cycle. It is generally accepted that AE signals are produced by collective microstructural dam￾age generation and motion.42–45 The thermally cycled specimens during testing emit fewer acoustic emissions at the stage of heat￾ing, but as the cooling stage approaches the emission rate in￾creases rapidly. This indicates that a large damage accompanied by multiplication of microcracking in composite materials mainly occurs once cooled. When a C/SiC is heated in a certain cycle, the increasing temperature renders the wide crack opening displace￾ment in the matrix more homogeneously by its thermal expan￾sion, and then above the crack closure temperature (i.e., 9001C), tensile stress acting on the fibers emerges but does not pro￾duce extensive fiber fracture. A reasonable interpretation is that the high strength of the fibers, the softness of the PyC interphase (Fig. 1(b)), and the lower top temperature (only 12001C) are advantageous in preventing the fibers from undergoing a large fracture. Thus, detectable AE hardly appears before the top cycle temperature is reached. When the C/SiC specimen is cooled down from the upper cycle temperature, the compressive stress￾es diminish rapidly and tensile stresses in the matrix build up. AE should take place due to relaxation of the tensile stresses in the matrix by the deformation mechanism of matrix cracking, and should persist down to the lower cycle temperature. During cooling, thermally induced stresses in the matrix may comprise,52 apart from the residual thermal stresses as men￾tioned previously in Eq. (2), thermal shock-induced stress due to a temperature gradient between the exterior and interior of the sample. Thus, the driving force behind the cracking of the matrix can be a sum of the thermally induced stresses and the applied stress, as sDR M ¼ sRES M þ sTS M þ sAC M (4) The subscript M denotes the matrix. sAC M refers to the applied constant stress. sTS M is the thermal shock-induced stress at the surface of the material, and can be classically written as55 sTS M ¼ AEaDTk 1 n (5) where modulus E, CTE a, and Poisson’s ratio n are either matrix or volume-averaged properties. The parameter ‘‘A’’ is termed the ‘‘stress reduction factor.’’ DTk is the temperature difference between the interior (Tin) and exterior (Tex) temperature of the material during thermal shock (i.e., DTk ¼ Tin Tex). Thus, multiple matrix cracking perpendicular to the fibers occurs when the resultant driving stress sDR M along the fiber direction be￾comes higher than the stress required to cause matrix fracture (referred to as matrix strength smu, which is usually low for ce￾ramics and approximately equal to smc). According to Eqs. (2), (4) and (5), a tensile driving stress of at least 286 MPa can be approximatily obtainedy on cooling from the matrix cracking temperature to 7001C by simply substituting the material parameter YM in Eq. 2 using the composite modulus E. There￾fore, in the first cycle, the driving force of matrix cracking may be high enough to initiate and develop the matrix cracks. After the first cycle, although the driving force will decrease due to reduction in material stiffness E after cracking, it is impossibly below the matrix cracking stress smc immediately and the re￾sidual thermal stress between fibers and matrix is impossibly relaxed completely. As a result, the matrix continues to crack with repetitive thermal cycles until the decreasing driving force becomes smaller than smc, where the crack density reaches sat￾uration as discussed in Section III (2). It is commonly accepted that the modulus of the composites decreases with thermal cycles due to continuous matrix cracking.37,49–50 Besides, in a single cycle, the resultant driving stress sDR M act￾ing on the matrix changes with temperature (see Fig. 9): reach￾ing the maximum value sDR max on cooling to the lower temperature limit, sRES M ¼ sRES max To¼700C DTF > 0 > 0;sTS M ¼ sTS max Tex¼700C DTk > 0 > 0;sAC M ¼ 50 MPa (6) and, declining to the minimum value sDR min on heating to the upper temperature limit, sRES M ¼ sRES min To¼1200C DTF < 0 < 0;sTS M ¼ sTS min Tex¼1200C DTk < 0 < 0;sAC M ¼ 50 MPa (7) This driving stress just reveals an opposite tendency with ob￾served thermal strain: the higher the temperature, the larger the thermal strain and the smaller the resultant driving stress sDR M , and vice versa. Thus, a cyclic stress between sDR min and sDR max is repeated in the matrix over the same period as the temperature and its amplitude gradually decreases with the continued cycle. Generally, the appearance of significant AE at a certain reload￾ing level below the previous maximum-applied stress level is referred to as the Felicity effect. The ratio of stress at the onset of emission to the previous peak stress, known as the Felicity ratio, is an indication of the severity and extent of damage. As shown in Fig. 9, AE responses exhibit the apparent Felicity effect as AE in each cycle is detected at stresses below the pre￾vious peak stress. Assuming that emissions within the n11 cycle will occur as long as the driving force exceeds the matrix crack￾ing stress smc, the Felicity ratio, RF, may be simply expressed as RF ¼ smcðn þ 1Þ sDR maxðnÞ (8) Evidently, during the initial several cycles, major acoustic activity occurred because the resultant driving stress was much higher than the stress required to propagate the cracks smc, indicating a quite low Felicity ratio associated with the appear￾ance of significant damage. Subsequently, the Felicity ratio in￾creased as the driving stress sDR M decreased after cracking and the damage of each cycle gradually diminished. Finally, except for the applied stress, the driving stress of the matrix cracking disappeared basically because the thermally induced stress was released completely with the saturation both in the crack density and in the damage when sDR M ¼ smc. At that time, the damage-saturated composite did not exhibit any response to the destructive energy of thermal cycling because macro-cracks of the matrix and the weakened interphase had enough space to tolerate micro-thermal expansion.56 As a consequence, the Felicity ratio approached one. The notion that thermal cycling damage decreased with cycles will be further confirmed by the accumulated AE energy as later shown in Fig. 10. Figure 9 also depicts the relationship of the thermal strain, the AE activities, and the accumulated AE energy with cycles. It is interesting that the stepwise increasing AE energy is enhanced only at the cooling stage of each cycle, and all these selected physical parameters (i.e., thermal strain, AE hits, and AE energy) follow a strict periodicity over the same period of 210 s as well as their excitation source of temperature. It is also y Residual thermal stress sRES M ¼ 142:85 GPa ½4:8 ð0:1Þ 106= C ð900 700ÞC ¼ 140 MPa; Thermal shock-induced stress sTS M ¼ 0:6 142:85 GPa 3:6 106=C ð900 700Þ  C=ð1 0:36Þ ¼ 96MPa. All the data used can be found in Mei and colleagues46,52–54. Above the matrix crack closure temperature, due to further expansion the residual thermal stress in the matrix transforms into compression, leading to decrease in the driving stress. July 2007 Thermal Cycling Damage in Ceramic Matrix Composites Under a Constant Stress 2139