G.N. Morscher / Composites Science and Technology 64(2004)1311-1319 composites tested in this study, it is evident that the strain curve [14] for a range of 2D woven architectures strain where matrix cracking occurs can vary consider- number of plies, and composite thickness. For example ably (Fig. 5(a))dependent on architecture(type of the stress-dependent matrix crack distribution for the reave, number of plies, etc. ) interfacial shear stress, and higher epi composites(>7. 1 epcm) was fit with a simple starting elastic modulus. Also, there are no minicom- linear relationship for ominimatrix above 95 MPa(Fig 8) posite ligaments independent of the rest of the structure, i.e., all load-bearing minicomposites are bonded P=0.1034 strongly through a dense matrix to the 90 tows, the where Pe is the stress-dependent matrix crack density .This primary flaw source. Also, matrix do essentially propa- data was then used to model the o/& curve over the ap gate through-the-thickness or link-up with one another propriate stress range for two specimens(012 and 068) as will be described below. Curtin et al. [21] have pro- with similar interfacial shear stress, t, of 70 MPa(Fig 8) posed a matrix cracking model based on the distribution from the approach taken in [12] based on [21,22] of flaws in the matrix, the distribution of matrix cracks E=G/E+aS(d)P/Er(a+Gth); for P-1> 28,(3) action of neighboring matrix cracks that ultimately leads where the sliding length to matrix crack saturation when the fiber sliding lengths 8=ar(o+oth)/2t extend the length of the uncracked matrix segments. An attempt was made to model the matrix crack distribu r is the fiber radius. and tion according to the Weibull model put forward by (1-f)Em/fec Curtin et al. [21]; however, it was not very robust for the ariety of composites studied here The stress-dependent matrix cracking behavior at It is evident from the analysis in this study that the room temperature can be used to model the time-de- ress-dependence for matrix cracking of 2D woven pendent elevated temperature life expectancy at stress Sylramic/BN/MI SiC composites with same number of [6]. The stress-strain curve of these composites upon fibers per tow was dependent on the stress in the ma- initial loading varies only slightly 200°C[2 trix outside of the load-bearing minicomposite, i.e, the ittle difference is observed in load-unload beh minimatrix stress, the source of flaws for matrix crack 815C, including oth, until higher stresses are reached formation in the"minimatrix'"being the 90 tows. This (>275 MPa) after considerable exposure time(30 min can be well characterized by a simple rule-of-mixtures in air at temperature during the unload-reload test relationship(Eq. (1)up to about half the saturation Therefore, it can be assumed that the matrix cracking of crack density, 5 cracks/mm. For higher fiber volume these materials upon initial loading behaves essentially fraction composites, this relates to stresses in excess of as at room temperature and the stress-depen- 250 MPa, much higher than their expected use condi- dent matrix-crack distribution can be used as the initial tions for long-time combustor applications [2]. Only a crack density at elevated temperatures upon loading few properties of the composite were required to for Evidence for this has been demonstrated for a mulate this relationship: the undamaged elastic modu- number of the panels tested in this study where speci- lus, Ec, the residual stress in the matrix, Oth, and the mens have been subjected to stress-rupture testing at properties of the load-bearing minicomposite, Eminimatrix 815C. After rupture, through-thickness cracks remain ind ominimatrix. The former two properties were found open due to the formation of solid oxidation products from a simple load-unload tensile test at room tem in the matrix crack and there is no need to etch the perature and the later two properties were estimated polished sections. The measured crack densities after from the composite processing data. If one fabricated rupture are commensurate with what would have been component out of this material, all they would require expected from the ae data and known final crack would be to fabricate a few" witness "panels of varying density measured after room temperature testing to architecture to determine the needed composite prop- failure(Fig 9). For specimens from the 007 and 044 erties and verify this stress-dependent matrix cracking composite panels, the matrix crack densities after from acoustic techniques and Possible to determine Ec stress-rupture at an intermediate stress were nearly testing witness panels would give one insight as to the AE data. For specimens from the 017 composite panel, interfacial debonding and sliding properties which the matrix crack densities after stress-rupture at an could be estimated from the stress-strain curve and intermediate stress were slightly lower by approxi stress-dependent matrix crack distribution and would mately 33% of what was to be expected from the room be necessary for modeling the stress-strain behavior temperature ae data which represents the largest de- viation from estimated crack density observed. It The understanding of the stress-dependent matrix should be noted that for the Sylramic/BN/MI system, it acking behavior can now be used to model the stress- has been shown that relatively little global AE activitycomposites tested in this study, it is evident that the strain where matrix cracking occurs can vary consider￾ably (Fig. 5(a)) dependent on architecture (type of weave, number of plies, etc.), interfacial shear stress, and starting elastic modulus. Also, there are no minicom￾posite ligaments independent of the rest of the structure, i.e., all load-bearing minicomposites are bonded strongly through a dense matrix to the 90
tows, the primary flaw source. Also, matrix do essentially propa￾gate through-the-thickness or link-up with one another as will be described below. Curtin et al. [21] have pro￾posed a matrix cracking model based on the distribution of flaws in the matrix, the distribution of matrix cracks that emanate from some of those flaws, and the inter￾action of neighboring matrix cracks that ultimately leads to matrix crack saturation when the fiber sliding lengths extend the length of the uncracked matrix segments. An attempt was made to model the matrix crack distribu￾tion according to the Weibull model put forward by Curtin et al. [21]; however, it was not very robust for the variety of composites studied here. It is evident from the analysis in this study that the stress-dependence for matrix cracking of 2D woven Sylramic/BN/MI SiC composites with same number of fibers per tow was dependent on the stress in the ma￾trix outside of the load-bearing minicomposite, i.e, the minimatrix stress, the source of flaws for matrix crack formation in the ‘‘minimatrix’’ being the 90
tows. This can be well characterized by a simple rule-of-mixtures relationship (Eq. (1)) up to about half the saturation crack density,
5 cracks/mm. For higher fiber volume fraction composites, this relates to stresses in excess of 250 MPa, much higher than their expected use condi￾tions for long-time combustor applications [2]. Only a few properties of the composite were required to for￾mulate this relationship: the undamaged elastic modu￾lus, Ec, the residual stress in the matrix, rth, and the properties of the load-bearing minicomposite, Eminimatrix and rminimatrix. The former two properties were found from a simple load–unload tensile test at room tem￾perature and the later two properties were estimated from the composite processing data. If one fabricated a component out of this material, all they would require would be to fabricate a few ‘‘witness’’ panels of varying architecture to determine the needed composite prop￾erties and verify this stress-dependent matrix cracking relationship. It would also be possible to determine Ec from acoustic techniques and estimate rth. However, testing witness panels would give one insight as to the interfacial debonding and sliding properties which could be estimated from the stress–strain curve and stress-dependent matrix crack distribution and would be necessary for modeling the stress–strain behavior [14]. The understanding of the stress-dependent matrix cracking behavior can now be used to model the stress– strain curve [14] for a range of 2D woven architectures, number of plies, and composite thickness. For example, the stress-dependent matrix crack distribution for the higher epi composites (>7.1 epcm) was fit with a simple linear relationship for rminimatrix above 95 MPa (Fig. 8): qc ¼ 0:1034rminimatrix 9:8074; ð2Þ where qc is the stress-dependent matrix crack density. This data was then used to model the r=e curve over the ap￾propriate stress range for two specimens (012 and 068) with similar interfacial shear stress, s, of
70 MPa (Fig. 8) from the approach taken in [12] based on [21,22]: e ¼ r=Ec þ adðrÞqc=Efðr þ rthÞ; for q1 c > 2d; ð3Þ where the sliding length d ¼ arðr þ rthÞ=2s ð4Þ r is the fiber radius, and a ¼ ð1 f ÞEm=fEc: ð5Þ The stress-dependent matrix cracking behavior at room temperature can be used to model the time-de￾pendent elevated temperature life expectancy at stress [6]. The stress–strain curve of these composites upon initial loading varies only slightly up to 1200
C [2]. Little difference is observed in load–unload behavior at 815
C, including rth, until higher stresses are reached (>275 MPa) after considerable exposure time (
30 min) in air at temperature during the unload–reload test. Therefore, it can be assumed that the matrix cracking of these materials upon initial loading behaves essentially the same as at room temperature and the stress-depen￾dent matrix-crack distribution can be used as the initial crack density at elevated temperatures upon loading. Evidence for this has been demonstrated for a number of the panels tested in this study where speci￾mens have been subjected to stress-rupture testing at 815
C. After rupture, through-thickness cracks remain open due to the formation of solid oxidation products in the matrix crack and there is no need to etch the polished sections. The measured crack densities after rupture are commensurate with what would have been expected from the AE data and known final crack density measured after room temperature testing to failure (Fig. 9). For specimens from the 007 and 044 composite panels, the matrix crack densities after stress-rupture at an intermediate stress were nearly ex￾actly what was expected from the room temperature AE data. For specimens from the 017 composite panel, the matrix crack densities after stress-rupture at an intermediate stress were slightly lower by approxi￾mately 33% of what was to be expected from the room temperature AE data which represents the largest de￾viation from estimated crack density observed. It should be noted that for the Sylramic/BN/MI system, it has been shown that relatively little global AE activity G.N. Morscher / Composites Science and Technology 64 (2004) 1311–1319 1317