Damage tolerant ceramic matrix composites 1049 J/m. Alternatively, the critical value of G is called and strain states at any point in the material. For the fracture toughness. Sometimes in the literature continuum mechanics to be applicable for materials the term toughness is used loosely when fracture experiencing distributed damage, the test volume ghness is meant. This may cause confusion In (gage length of extensometer or strain gauge)must our paper toughness is defined by(1)and fracture be much larger than any microstructural dimen- sions(e.g. matrix crack spacing), such that the The work of fracture is defined by the total measured volume behaviour is scale-independent, energy absorped (during a quasi-static fracture and the definitions apply. Moreover, the test process) by the specimen per unit fracture area, volume must have uniform stress and strain fields i.e. the area under the load-displacement curve In bending tests the normal stress distribution is per cross-sectional area(see e.g. ref. 22), non-uniform (going from tension on one side to compression on the other ), and so is the damage P(△) sketched in Fig. 2. The true (3) A stress-strain curve cannot be determined since the stress and strain distributions across the specimen where A is the cross-sectional area of the specimen, depth are not known (when damage takes place, P is the load and 4 is the elongation. ywor has the the distribution of normal stress is not linear, but SI unit J/m2 depends on the type of damage mechanism and From the definitions it follows that the quanti- degree of damage ). Furthermore, at the peak load, ties mentioned are suited for characterizing differ localized fibre failure takes place at the tensile ent phenomena. U relates the energy uptake(prior surfacc, multiple matrix cracking takes place to localization) to the volume, and is the proper the central region of the specimen, and the com- measure of the fracture initiation energy. G is pression side may still be undamaged. From the a measure related to characterizing phenomena bending load-displacement curve it is not possible appearing with growth of a single crack. Work of to distinguish between the efects of distributed mech- fracture relates the total energy absorped(fracture anisms (matrix cracking, fibre/matrix debond energy) to the full crack area ng and interfacial sliding) and localized(fibre breakage and pull out ). Furthermore, a shear 2.2 Distributed versus localized energy absorption stress field is present in bending tests. Thus, the of uniaxial fibre composites damage evolution and failure may be due to shear When unidirectional fibre composites are loaded or compressive stress components, rather than in the fibre direction a range of distributed damage tension mechanisms occur before final failure. The frac It is unfortunate that bending tests have been so ture occurs as a localized phenomenon, since fibre widely used for characterizing ceramic composites fracture and pull out only take place at a single since this has led to incorrect conclusions concern matrix crack, namely where the specimen sepa- ing the matcrial bchaviour. For instance, it has rates into two pieces. Throughout this paper sometimes been suggested that the tail (the down- distinction will be made between distributed energy going part)of the load-displacement curve(mea- uptake and energy absorped during localization. surable in displacement controlled experiments Distributed energy uptake should be measured by only) represents the energy dissipation due to fibre a quantity that reflects that the energy uptake is by distributed phenomena, such as the area under the stress-strain curve, U. The energy dissipation during localization also involves distributed and localized mechanisms. It is of importance to mea- sure and calculate these contributions separately, at tension surface since they do not scale in the same manner with specimen geometry, as will be elaborated later 2.3 Choice of test method-bending or pure tension Having recognised the importance of distingu ⊥战A ing between distributed and localized mechanisms we now proceed with a discussion of test methods for measurements of the toughness. Materials having fig. 2. A schematic illustration of various damage mech distributed damage are characterized by non- nisms operating simultaneously during a bending experiment linear constitutive laws. Per definition a consti- The damage evolution is not uniform throughout the depth tutive law is the relationship between the stress of the specimenDamage tolerant ceramic matrix composites 1049 J/m2. Alternatively, the critical value of G is called the fracture toughness. Sometimes in the literature the term toughness is used loosely when fracture toughness is meant. This may cause confusion. In our paper toughness is defined by (1) and fracture toughness by (2). The work of fracture is defined by the total energy absorped (during a quasi-static fracture process) by the specimen per unit fracture area, i.e. the area under the load-displacement curve, per cross-sectional area (see e.g. ref. 22), A s ““f’(A) dA YWOF = __ o-4 ’ (3) where A is the cross-sectional area of the specimen, P is the load and A is the elongation. ywor has the SI unit J/m2. From the definitions it follows that the quanti￾ties mentioned are suited for characterizing differ￾ent phenomena. 6’ relates the energy uptake (prior to localization) to the volume, and is the proper measure of the fracture initiation energy. G is a measure related to characterizing phenomena appearing with growth of a single crack. Work of fracture relates the total energy absorped (fracture energy) to the full crack area. 2.2 Distributed versus 1oc:alized energy absorption of uniaxial fibre composites When unidirectional fibre composites are loaded in the fibre direction a range of distributed damage mechanisms occur before final failure. The frac￾ture occurs as a localized phenomenon, since fibre fracture and pull out only take place at a single matrix crack, namely where the specimen sepa￾rates into two pieces. Throughout this paper distinction will be made between distributed energy uptake and energy absorped during localization. Distributed energy uptake should be measured by a quantity that reflects .that the energy uptake is by distributed phenomena, such as the area under the stress-strain curve, i!J. The energy dissipation during localization also involves distributed and localized mechanisms. It is of importance to mea￾sure and calculate these contributions separately, since they do not scale in the same manner with specimen geometry, as will be elaborated later. 2.3 Choice of test method - bending or pure tension Having recognised the importance of distinguish￾ing between distributed and localized mechanisms, we now proceed with a discussion of test methods for measurements of the toughness. Materials having distributed damage are characterized by non￾linear constitutive laws. Per definition a consti￾tutive law is the relationship between the stress and strain states at any point in the material. For continuum mechanics to be applicable for materials experiencing distributed damage, the test volume (gage length of extensometer or strain gauge) must be much larger than any microstructural dimen￾sions (e.g. matrix crack spacing), such that the measured volume behaviour is scale-independent, and the definitions apply. Moreover, the test volume must have uniform stress and strain fields. In bending tests the normal stress distribution is non-uniform (going from tension on one side to compression on the other), and so is the damage evolution, as sketched in Fig. 2. The true stress-strain curve cannot be determined, since the stress and strain distributions across the specimen depth are not known (when damage takes place, the distribution of normal stress is not linear, but depends on the type of damage mechanism and degree of damage). Furthermore, at the peak load, localized fibre failure takes place at the tensile surface, multiple matrix cracking takes place in the central region of the specimen, and the com￾pression side may still be undamaged. From the bending load-displacement curve it is not possible to distinguish between the eflects of distributed mech￾anisms (matrix cracking, fibre/matrix debond￾ing and interfacial sliding) and localized (fibre breakage and pull out). Furthermore, a shear stress field is present in bending tests. Thus, the damage evolution and failure may be due to shear or compressive stress components, rather than tension.23 It is unfortunate that bending tests have been so widely used for characterizing ceramic composites, since this has led to incorrect conclusions concern￾ing the material behaviour. For instance, it has sometimes been suggested that the tail (the down￾going part) of the loadclisplacement curve (mea￾surable in displacement controlled experiments only) represents the energy dissipation due to fibre Onset of localized fibre failure at tension surface Onset of 4--- matrix cracking \I at tension surface A Locus of fibre breakage ‘, and pull out moves Fig. 2. A schematic illustration of various damage mecha￾nisms operating simultaneously during a bending experiment. The damage evolution is not uniform throughout the depth of tile specimen