R.J. Kerans, T.A. Parthasarathy /Composites: Part A 30(1999)521-52 matrix cracks in the C layer, followed by propagation of short-period crack regime would correspond to initial crack each crack obliquely to the fiber surface, followed by deflec- deflection in the coating an od crack would tion along(or near) the surface. The radial stresses in the correspond to the coating/fiber interfacial crack oatings were calculated using the Axisymmetric Damage Model to be compressive, which would tend to inhibit axial shear or radial tension modes. The maximum stresses in the 4 Interfacial roughness field of an impinging matrix crack that could lead to crack ing were found to be shear stresses along planes consistent The potential of significant effects due to surface rough- with the oblique paths forming the mountainous' ring less was first discussed in the context of increased radial Evidence was also found that fiber failure occurs predomi- stresses due to the geometric misfit [24]. Contradictions in nately in the stress concentration at the tip of the debonding measured and calculated sliding friction led to the sugges- tion of roughness effects, and experimental confirmation of them by the push back seating drop'of Jero and coworkers 34. crack within a coating [25, 26]. A simple geometric misfit model has provided further evidence that the effects can be important [27] Further consideration of the failure process for a crack Briefly, a fiber pulling out of a matrix under axial loading running within a coating implies additional complexity is subjected to radial stresses which differ along its length regarding both deflection criteria and roughness, and The interfacial normal stress in the un-slipped region provides interesting speculation on the degree to which (Region I)ahead of the crack tip is determined by the resi- oxide coatings can be expected to provide protection against dual stresses, and to a minor degree, by differences in Pois- oxidation of the fiber [11]. Consider the tensile failure sons ratios and the applied axial stress. Well behind the process of a composite in which cracks deflect in the coat- crack tip(Region If), the displacement between fiber and ing. A matrix crack impinges on a coated fiber and is matrix is sufficient to effect the full geometric misfit, and the deflected in the coating. The consequent debonding crack normal stress is the sum of the residual stresses and the propagates some distance in the coating away from the stresses resulting from the full effect of the misfit. The matrix crack plane. With subsequent loading, the matrix roughness induced stresses may be larger than the thermal crack bypasses the fiber and the debonding crack propagates stresses. The intermediate region(Region If) extends with somewhat further, within the coating. At that point, the increasing misfit from the crack tip to the beginning of crack is bridged by a fiber still coated by the remaining Region Ill. This region both complicates analysis and intact portion of the coating. It is this remaining coating gives rise to a number of interesting effects. A full solution which could provide some protection. However, unless the of the problem for one simple form of roughness [27] has coating is extremely strain tolerant, it must fail in tension shown that the friction can actually be highest in Region Il with subsequent loading, introducing another mode I crack. and that the effects can be very much larger than the region That crack may deflect into another mode ll crack running Ill misfit alone. Fiber pushout load-deflection curves fo parallel to the fiber axis, but the process must repeat until the composites where the Region Il effects are large, such as coating is completely cracked and there is a debonding those of the first section, demonstrate unusual features such crack running in the fiber/coating interface. The only possi- as upward curvature and discontinuous derivatives. Comp bility for retaining the coating is if it is as strain tolerant (to site behavior may not be well described by conventional axial tensile strains) as the fiber (in the neighborhood of models 1%), i.e. far more strain tolerant than would be expected from equivalent bulk materials. Although thin coatings can be expected to exhibit increasing strain-to-failure with 5 Summary decreasing thickness(see, for example, [23]), such high alues may be problematical for approaches such as porous The coatings that have enabled the development of oxides. This scenario implies two consequences: (1)even conventional composites have fortuitously possessed a though crack deflection occurred in the coating, post failure suite of properties well suited to the task. New oxide coat analysis may show cracks in the coating/fiber interface, and ings will require active design of the coatings, and of the (2)any oxidation protection provided by the coating may be entire composite system, to accomplish the same mechani- limited by the tensile strain-to-failure of the coating. The cal goals. This, in turn, will require a more thorough under- first of these requires that the conclusions based on the standing of crack deflection and sliding processes than arguments of the preceding section be based on sound heretofore necessary. The entire process, from conception, evidence regarding the location of the initial crack deflec- through design, processing, and evaluation, to ultimate tion because all debonding cracks will tend to eventually run performance of composites with new oxidation-resistant in or near the interface. This scenario is also consistent with interface control systems will be greatly facilitated by, if the analysis based on two successive modes of cracking not dependent upon, understanding the details that govern behavior used in the preceding section, wherein the initial crack deflection, debonding and slidingmatrix cracks in the C layer, followed by propagation of each crack obliquely to the fiber surface, followed by deflec￾tion along (or near) the surface. The radial stresses in the coatings were calculated using the Axisymmetric Damage Model to be compressive, which would tend to inhibit axial shear or radial tension modes. The maximum stresses in the field of an impinging matrix crack that could lead to crack￾ing were found to be shear stresses along planes consistent with the oblique paths forming the ‘mountainous’ rings. Evidence was also found that fiber failure occurs predomi￾nately in the stress concentration at the tip of the debonding crack. 3.4. Crack path within a coating Further consideration of the failure process for a crack running within a coating implies additional complexity regarding both deflection criteria and roughness, and provides interesting speculation on the degree to which oxide coatings can be expected to provide protection against oxidation of the fiber [11]. Consider the tensile failure process of a composite in which cracks deflect in the coat￾ing. A matrix crack impinges on a coated fiber and is deflected in the coating. The consequent debonding crack propagates some distance in the coating away from the matrix crack plane. With subsequent loading, the matrix crack bypasses the fiber and the debonding crack propagates somewhat further, within the coating. At that point, the crack is bridged by a fiber still coated by the remaining intact portion of the coating. It is this remaining coating which could provide some protection. However, unless the coating is extremely strain tolerant, it must fail in tension with subsequent loading, introducing another mode I crack. That crack may deflect into another mode II crack running parallel to the fiber axis, but the process must repeat until the coating is completely cracked and there is a debonding crack running in the fiber/coating interface. The only possi￾bility for retaining the coating is if it is as strain tolerant (to axial tensile strains) as the fiber (in the neighborhood of 1%), i.e. far more strain tolerant than would be expected from equivalent bulk materials. Although thin coatings can be expected to exhibit increasing strain-to-failure with decreasing thickness (see, for example, [23]), such high values may be problematical for approaches such as porous oxides. This scenario implies two consequences: (1) even though crack deflection occurred in the coating, post failure analysis may show cracks in the coating/fiber interface, and (2) any oxidation protection provided by the coating may be limited by the tensile strain-to-failure of the coating. The first of these requires that the conclusions based on the arguments of the preceding section be based on sound evidence regarding the location of the initial crack deflec￾tion because all debonding cracks will tend to eventually run in or near the interface. This scenario is also consistent with the analysis based on two successive modes of cracking behavior used in the preceding section, wherein the initial short-period crack regime would correspond to initial crack deflection in the coating and the long-period crack would correspond to the coating/fiber interfacial crack. 4. Interfacial roughness The potential of significant effects due to surface rough￾ness was first discussed in the context of increased radial stresses due to the geometric misfit [24]. Contradictions in measured and calculated sliding friction led to the sugges￾tion of roughness effects, and experimental confirmation of them by the ‘push back seating drop’ of Jero and coworkers [25,26]. A simple geometric misfit model has provided further evidence that the effects can be important [27]. Briefly, a fiber pulling out of a matrix under axial loading is subjected to radial stresses which differ along its length. The interfacial normal stress in the un-slipped region (Region I) ahead of the crack tip is determined by the resi￾dual stresses, and to a minor degree, by differences in Pois￾son’s ratios and the applied axial stress. Well behind the crack tip (Region III), the displacement between fiber and matrix is sufficient to effect the full geometric misfit, and the normal stress is the sum of the residual stresses and the stresses resulting from the full effect of the misfit. The roughness induced stresses may be larger than the thermal stresses. The intermediate region (Region II) extends with increasing misfit from the crack tip to the beginning of Region III. This region both complicates analysis and gives rise to a number of interesting effects. A full solution of the problem for one simple form of roughness [27] has shown that the friction can actually be highest in Region II and that the effects can be very much larger than the Region III misfit alone. Fiber pushout load–deflection curves for composites where the Region II effects are large, such as those of the first section, demonstrate unusual features such as upward curvature and discontinuous derivatives. Compo￾site behavior may not be well described by conventional models. 5. Summary The coatings that have enabled the development of conventional composites have fortuitously possessed a suite of properties well suited to the task. New oxide coat￾ings will require active design of the coatings, and of the entire composite system, to accomplish the same mechani￾cal goals. This, in turn, will require a more thorough under￾standing of crack deflection and sliding processes than heretofore necessary. The entire process, from conception, through design, processing, and evaluation, to ultimate performance of composites with new oxidation-resistant interface control systems will be greatly facilitated by, if not dependent upon, understanding the details that govern crack deflection, debonding and sliding. R.J. Kerans, T.A. Parthasarathy / Composites: Part A 30 (1999) 521–524 523