K.K. Chawla/Journal of the European Ceramic Sociery 28(2008)447-453 Fiber pullout Debonding where a is the elastic mismatch parameter and is defined as E2-E, where Er where e is the elastic modulus and v is the poissons ratio for each material of interest For debonding and sliding to occur, the interfacial energy, Ti must not exceed an upper bound relative Main crack direction to the fracture energy of the second material, T2. Unfortunately, reliable Ti and T2 are usually not readily available for many systems, making this criterion difficult or impossible to use when exploring new material systems. 3. Importance of interfacial characteristics for debonding Fig. 1. A schematic of different failure mechanisms that may when a crack moves through a matrix containing unidirectional fibers. a rough fiber/matrix interface results in strong mechanical keying, which can prevent interfacial debonding and fiber pull out. A smooth interface. on the other hand. results in weak 2.1. Strength-based criterion keying, which is conducive to fiber pullout. Fig. 2 shows a schematic of a periodic roughness at the fiber/matrix inter- Debonding of the fiber/matrix interface appears to be a pre- face. Many investigators have found that interfacial roughness requisite for phenomena such as crack deflection, crack bridging has a pronounced effect on the interfacial sliding stress. The by fibers, and fiber pullout. Cook and Gordon first proposed radial strain at the fiber/matrix interface consists of two parts crack deflection or the formation of a secondary crack at a weak one is due to the thermal mismatch between the fiber and interface.For the case of a fiber/matrix system having identi- matrix, which can be either tensile or compressive, and the cal elastic constants (i. e, identical materials), Cook and Gordon, other one comes from the roughness induced clamping, which estimated the strength of the interface necessary to cause a diver- is always in compression or zero. The important point to note sion of the crack from its original direction. For any given crack, here is that even when the coefficients of thermal expansion either a triaxial state of stress (plane strain)or a biaxial stress of the coating, fiber, and matrix are such that a radial ten- plane stress) is present at the crack tip The applied principal sile stress exists at the fiber/coating interface, fiber pullout stress component, Cy, has a very high value at the crack tip, may not occur because of a strong mechanical bonding due which decreases sharply with distance from the crack tip as it to a roughness induced clamping at the fiber/matrix. Thus, in must be because the surface of a crack is a free surface. ox, the CMCs having an extremely rough interface, the pullout would stress component normal to the fiber/matrix interface, is 0 at the not be expected, and they would likely fail like monolithic crack tip. o then rises quickly to a maximum a short distance materials away from the tip and then quickly decreases with distance in The two sources that contribute to the radial stress component a fashion similar to that seen with ay. If the fiber/matrix tensile acting normal to the fiber/matrix interface are interface strength is less than the 1 maximum value of r fracture should occur at the interface ahead of the approaching crack tip. (i) thermal mismatch induced radial compressive stress: Cook and Gordon estimated that if the interface had strength of (ii) mechanical gripping induced by the fibersurface roughness about 1/5 or less than that of the main stress component, y, it will debond in front of the crack tip. Again, it should be noted In ceramic matrix composites, interfacial roughness induced that they studied a system with identical component interface stresses, especially the radial stress, will affect the interface debonding, the sliding friction of debonded fibers, as 2.2. Energy-based criterion shown in Fig. l, and the fiber pullout length. Fiber pullout is one of the important energy dissipating fracture processes in fiber reinforced ceramic or glass matrix composites. An absence An energy-based criterion has been proposed for interna- of strong chemical bond and a purely mechanical bond at the ial debonding by He and Hutchinson. If Ti is the interfacial fiber/matrix interface is highly desirable for the fiber pullout (debond)energy and r2 is the fracture energy of the second to occur. Even when the coefficients of thermal expansion of material or fiber in Mode I then interfacial debonding and slid- the coating, fiber, and matrix are such that a radial tensile stress ing will occur rather than brittle cracking through the fiber, when exists at the fiber/coating interface after cooling from anelevated the following inequality is satisfied: processing temperature, fiber pullout may not occur because of a strong mechanical bonding due to a roughness induced n≤()2fora=0 (1) clamping at the fiber/matrix interface. The radial stress result ing from the surface roughness of the fiber during fiber pullout,448 K.K. Chawla / Journal of the European Ceramic Society 28 (2008) 447–453 Fig. 1. A schematic of different failure mechanisms that may come into play when a crack moves through a matrix containing unidirectional fibers. 2.1. Strength-based criterion Debonding of the fiber/matrix interface appears to be a pre￾requisite for phenomena such as crack deflection, crack bridging by fibers, and fiber pullout. Cook and Gordon first proposed crack deflection or the formation of a secondary crack at a weak interface.4 For the case of a fiber/matrix system having identi￾cal elastic constants (i.e., identical materials), Cook and Gordon, estimated the strength of the interface necessary to cause a diver￾sion of the crack from its original direction. For any given crack, either a triaxial state of stress (plane strain) or a biaxial stress (plane stress) is present at the crack tip. The applied principal stress component, σy, has a very high value at the crack tip, which decreases sharply with distance from the crack tip as it must be because the surface of a crack is a free surface. σx, the stress component normal to the fiber/matrix interface, is 0 at the crack tip. σx then rises quickly to a maximum a short distance away from the tip and then quickly decreases with distance in a fashion similar to that seen with σy. If the fiber/matrix tensile interface strength is less than the maximum value of σx, fracture should occur at the interface ahead of the approaching crack tip. Cook and Gordon estimated that if the interface had strength of about 1/5 or less than that of the main stress component, σy, it will debond in front of the crack tip. Again, it should be noted that they studied a system with identical components. 2.2. Energy-based criterion An energy-based criterion has been proposed for interfa￾cial debonding by He and Hutchinson.5 If Γ i is the interfacial (debond) energy and Γ 2 is the fracture energy of the second material or fiber in Mode I, then interfacial debonding and slid￾ing will occur rather than brittle cracking through the fiber, when the following inequality is satisfied: Γi ≤ 1 4 Γ2 for α = 0 (1) where α is the elastic mismatch parameter and is defined as: α = E 2 − E 1 E 2 − E 1 , where E = E (1 − υ2) (2) where E is the elastic modulus and υ is the Poisson’s ratio for each material of interest. For debonding and sliding to occur, the interfacial energy, Γ i must not exceed an upper bound relative to the fracture energy of the second material, Γ 2. Unfortunately, reliable Γ i and Γ 2 are usually not readily available for many systems, making this criterion difficult or impossible to use when exploring new material systems. 3. Importance of interfacial characteristics for debonding A rough fiber/matrix interface results in strong mechanical keying, which can prevent interfacial debonding and fiber pull￾out. A smooth interface, on the other hand, results in weak keying, which is conducive to fiber pullout. Fig. 2 shows a schematic of a periodic roughness at the fiber/matrix inter￾face. Many investigators have found that interfacial roughness has a pronounced effect on the interfacial sliding stress. The radial strain at the fiber/matrix interface consists of two parts: one is due to the thermal mismatch between the fiber and matrix, which can be either tensile or compressive, and the other one comes from the roughness induced clamping, which is always in compression or zero. The important point to note here is that even when the coefficients of thermal expansion of the coating, fiber, and matrix are such that a radial ten￾sile stress exists at the fiber/coating interface, fiber pullout may not occur because of a strong mechanical bonding due to a roughness induced clamping at the fiber/matrix. Thus, in CMCs having an extremely rough interface, the pullout would not be expected, and they would likely fail like monolithic materials. The two sources that contribute to the radial stress component acting normal to the fiber/matrix interface are: (i) thermal mismatch induced radial compressive stress; (ii) mechanical gripping induced by the fiber surface roughness. In ceramic matrix composites, interfacial roughness induced interface stresses, especially the radial stress, will affect the interface debonding, the sliding friction of debonded fibers, as shown in Fig. 1, and the fiber pullout length. Fiber pullout is one of the important energy dissipating fracture processes in fiber reinforced ceramic or glass matrix composites. An absence of strong chemical bond and a purely mechanical bond at the fiber/matrix interface is highly desirable for the fiber pullout to occur. Even when the coefficients of thermal expansion of the coating, fiber, and matrix are such that a radial tensile stress exists at the fiber/coating interface after cooling from an elevated processing temperature, fiber pullout may not occur because of a strong mechanical bonding due to a roughness induced clamping at the fiber/matrix interface. The radial stress result￾ing from the surface roughness of the fiber during fiber pullout,