1056 B. F. Sorensen, R. Talreja i(Vm -vR)-(V-vf 2 Ta t dx= St EC Ts a er 3 1-f a' Em Er where e is Ec=fE+(1-ner The strain energy of the fibres per unit volume of the composite is (in similar fashion to eqn(18)on A) B) noting that the applied stress is zero and the sign in front of Ts is changed since the slip direction is reversed) 52 Φ*= (30) 6 4 e and that of the matriⅸisφn=φn. From eqn (26)it follows that the energy dissipation by dis- tributed mechanisms increases with an increasing specimen length, while the pull out energy dissipa- D) tion does not. An important consequence of this is Fig. 7(A) An impact loading at a component made of a that the distributed energy dissipation can b damage tolerant ceramic matrix composite. B)All the kinetic raised as much as one desires simply by increasing energy is absorbed by distributed energy uptake. (C)The L. Therefore the concept of work of fracture, kinetic energy is absorbed by distributed and localized energy ywoF(eqn 3), is not applicable for this class of mechanisms. (D) The kinetic energy is higher than what can materials be absorbed by distributed and localized mechanisms, so the 5.3 Energy absorption and fracture stability of components because the two parts of the composite are only Now consider an impact loading of a component in kept together by frictional stresses acting at the service( Fig. 7A). This situation is different from a broken fibres.(2) If the impact energy is higher displacement controlled tensile test. In this case it than the total fracture initiation energy and higher is the actual amount of kinetic energy transferred than the total energy absorped (eqn 26)(Fig. 7D), to the specimen in the form of deformation energy then the component will fracture unstably, since it that determines how the fracture behaviour will cannot absorb the kinetic energy of the object. be Consider an object hitting the composite com Imagine that the component was a turbine ponent such that the direction of the moving blade in a jet-engine( this is a typical considered object is in the fibre direction, and that during the application for ceramic matrix composites). In impact the object causes uniform tension in the such an application it is very important whether composite. Will the composite break, and in case or not the component fractures, since a fractured it does. in which manner? blade may lead to total failure of the engine(this The first possibility is that the kinetic energy could be fatal for the aircraft). Now, if a turbine lower than the total available distributed energy blade was hit by a bird uptake, U L A(Fig. 7B). Then the composite will specific amount of kinetic energy, what would absorb the energy without fracture(it will be dam- happen to the componcnt? IfU L A was sufficient aged, but it will not break). Alternatively, when to absorb the energy, then the component woul the kinetic energy is higher than U L A, the com- be damaged, but it would retain its strength. Thus, posite will fracture; the fibres will break, and the the aircraft would be able to land safely and the composite will lose strength. In this scenario, how- damaged component could be replaced. If the ever, two possibilities exist: (1)If the kinetic pact energy was so high that the component energy is higher than the total fracture initiation fractured, the pull out energy might stop the nergy but lower than the total energy dissipation object, but now the component strength has eqn 26), the component will be damaged and decreased. The inertia forces of the rotating com artly fractured(Fig. 7C); with fibres broken and ponent could be sufficiently high that the blade partly pulled out. The composite will lose strength, could fracture completely, and the engine would1056 B. F. Swensen, R. Talreja W,T =$f I(v,-v*,)-(vf-vT)12naTsdx= 0 s U” 2 f s’E,+ ---_---- (28) 2a Ef 3 l-fa2E,Er’ where EC is EC =fE, + (1 -f) E,. (29) The strain energy of the fibres per unit volume of the composite is (in similar fashion to eqn (18) on noting that the applied stress is zero and the sign in front of TV is changed since the slip direction is reversed) a*= f s2 7: f 6 a2 Ef (30) and that of the matrix is @,* = Qmul. From eqn (26) it follows that the energy dissipation by dis￾tributed mechanisms increases with an increasing specimen length, while the pull out energy dissipa￾tion does not. An important consequence of this is that the distributed energy dissipation can be raised as much as one desires simply by increasing L. Therefore, the concept of work of fracture, 3/war (eqn 3) is not applicable for this ChSS of materials. 5.3 Energy absorption and fracture stability of components Now consider an impact loading of a component in service (Fig. 7A). This situation is different from a displacement controlled tensile test. In this case it is the actual amount of kinetic energy transferred to the specimen in the form of deformation energy that determines how the fracture behaviour will be. Consider an object hitting the composite com￾ponent such that the direction of the moving object is in the fibre direction, and that during the impact the object causes uniform tension in the composite. Will the composite break, and in case it does, in which manner? The first possibility is that the kinetic energy is lower than the total available distributed energy uptake, U L A (Fig. 7B). Then the composite will absorb the energy without fracture (it will be dam￾aged, but it will not break). Alternatively, when the kinetic energy is higher than U L A, the com￾posite will fracture; the fibres will break, and the composite will lose strength. In this scenario, how￾ever, two possibilities exist: (1) If the kinetic energy is higher than the total fracture initiation energy but lower than the total energy dissipation (eqn 26), the component will be damaged and partly fractured (Fig. 7C); with fibres broken and partly pulled out. The composite will lose strength, B) Fig. 7. (A) An impact loading at a component made of a damage tolerant ceramic matrix composite. (B) All the kinetic energy is absorbed by distributed energy uptake. (C) The kinetic energy is absorbed by distributed and localized energy mechanisms. (D) The kinetic energy is higher than what can be absorbed by distributed and localized mechanisms, so the component fractures. because the two parts of the composite are only kept together by frictional stresses acting at the broken fibres. (2) If the impact energy is higher than the total fracture.initiation energy and higher than the total energy absorped (eqn 26) (Fig. 7D), then the component will fracture unstably, since it cannot absorb the kinetic energy of the object. Imagine that the component was a turbine blade in a jet-engine (this is a typical considered application for ceramic matrix composites). In such an application it is very important whether or not the component fractures, since a fractured blade may lead to total failure of the engine (this could be fatal for the aircraft). Now, if a turbine blade was hit by a bird or a stone having a specific amount of kinetic energy, what would happen to the component? If U L A was sufficient to absorb the energy, then the component would be damaged, but it would retain its strength. Thus, the aircraft would be able to land safely and the damaged component could be replaced. If the impact energy was so high that the component fractured, the pull out energy might stop the object, but now the component strength has decreased. The inertia forces of the rotating com￾ponent could be sufficiently high that the blade could fracture completely, and the engine would