R.J. Kerans, T.A. Parthasarathy /Composites. ParT 4 30(1999)521-524 assumed and still perform the necessary function of crack sequence [19]. Since the microscopic details of fracture deflection. This result suggests that the window of proper- are difficult to probe experimentally, the exact sequence ties that can be possessed by an oxide alternative coating, of events in real fibrous composites has remained a matter for example, is larger than previously thought. This is an of speculation. Nevertheless, it is a matter of some impor important result because the very low fracture energies tance in understanding the design and analysis of coating previously thought necessary will likely be difficult to systems. In one case, the interfacial fracture will be deter- obtain with oxides or other alternative materials mined by the radial tensile strength, while in the other case. The value of 28 J/m" obtained for the fracture energy of it will be determined by the interfacial shear strengths pyrocarbon is in good agreement with literature mode I Understanding the process is also important in interpreting values [12, 13]. Nevertheless, it is a good deal higher than test data. Fiber push/pullout tests, for example, may the 0-3 J/m typically inferred from composites demon- measure a somewhat different property than the one that strating tough behavior, and often thought of as a necessary determines debonding during composite failure condition [5]. This also raises a question regarding the suit The difference in fracture behavior observed in the two ability of the usual use of crack deflection criteria suggested composites discussed in the first section seems to provide by Cook and Gordon[ 14] and the more rigorous analyses of convincing evidence for debonding by the tensile mode in at He and coworkers [15, 16 least one system. The differences in behavior of the treated- fiber composite system as compared to a more convention 3. The nature of crack deflection and suitable criteria untreated-fiber composite, have been attributed to the differ ent interfacial cracking behavior [6,7]. Specifically, the 3.1. Deflection in the coating interfacial crack in untreated-fiber composites has been reported to be confined to the C/SiO2 interface near the l Go Porous consideration of the details of crack deflection fiber surface, or the C layers very near to the interface [7, mplex. The implied hope has been that the problems 201. Such composites are measured to have interfacial frac can be adequately addressed with simplified treatments. As implied by the preceding section, this has sometimes led to has been inferred to strengthen the interface region to a level which is above the strength of the pyrocarbon coating itself, misleading application of crack deflection criteria. For thereby shifting the fracture to the pyrocarbon: the next- example, the He and Hutchinson [15] criterion was derived for deflection in a true interface between two materials and the relevant figure of merit for the competition between The C coatings in both composites are taken to be the crack deflection at the interface and crack propagation Same except perhaps very near the coating/fiber interface. In into the second material was the ratio of interfacial the case of an untreated-fiber composite failing in tension (presumed to be principally mode If) fracture energy to the weak coating/fiber interface region fails, while the coat- issue is crack deflection within a coating, the analogous before the crack enters the coating, due to the stress field in figure of merit will be the ratio of the coating (presumed front of the crack. Had the crack run through the coating, it principally mode ID) fracture energy for a debonding crack would have deflected in the coating. The proof of this state- to coating axial mode I fracture energy [11]. In principle, the ment is provided by the treated-fiber materials, in which the suitability of a material that is intended to promote crack cracks deflect in the coating before reaching the fiber/coat- interface. Provided that the debonding in the weak-inter deflection by cleaving can be evaluated independently of the face(untreated fiber)composites is truly at or very near the a debonding crack within a coating can be expected to devi- coating/fiber interface, this seems to provide a definitive ate towards the coating/fiber interface and, in many cases, to arrive there [1l(see section below). The question nterface composite addressed by He and Hutchinson is then raised, but at a different point in the failure process 3.3. Of-axis shear cracking 3. 2. Tensile crack Recent theoretical and experimental work by Pagano and coworkers [18, 22] has presented strong evidence of a differ- Crack deflection is usually assumed to be literally that; ent mode of crack deflection. The experimental work was the matrix crack tip propagates into the interfacial region performed on highly uniform composites comprising SiC then turns parallel to the fiber surface. However, it has been monofilaments coated first with C, then with TiB2, in glass suggested that the interfacial crack that develops in a matrices. Post-failure analysis revealed that the debonding composite under tension may initiate as a mode I crack in occurred predominately by propagation of a crack in the C the tensile(normal to the fiber surface)stress field ahead of very near the C/Sic interface. However, triangular-section the crack tip [17, 18, and observations on model laminate rings, mountains of C remained on the fiber at the location materials have confirmed the existence of such a failure of matrix cracks, implying double deflection of impingingassumed and still perform the necessary function of crack deflection. This result suggests that the window of proper￾ties that can be possessed by an oxide alternative coating, for example, is larger than previously thought. This is an important result because the very low fracture energies previously thought necessary will likely be difficult to obtain with oxides or other alternative materials. The value of 28 J/m2 obtained for the fracture energy of pyrocarbon is in good agreement with literature mode I values [12,13]. Nevertheless, it is a good deal higher than the 0–3 J/m2 typically inferred from composites demon￾strating tough behavior, and often thought of as a necessary condition [5]. This also raises a question regarding the suit￾ability of the usual use of crack deflection criteria suggested by Cook and Gordon [14] and the more rigorous analyses of He and coworkers [15,16]. 3. The nature of crack deflection and suitable criteria 3.1. Deflection in the coating Rigorous consideration of the details of crack deflection is complex. The implied hope has been that the problems can be adequately addressed with simplified treatments. As implied by the preceding section, this has sometimes led to misleading application of crack deflection criteria. For example, the He and Hutchinson [15] criterion was derived for deflection in a true interface between two materials, and the relevant figure of merit for the competition between crack deflection at the interface and crack propagation into the second material was the ratio of interfacial (presumed to be principally mode II) fracture energy to material 2 (mode I) fracture energy. However, if the relevant issue is crack deflection within a coating, the analogous figure of merit will be the ratio of the coating (presumed principally mode II) fracture energy for a debonding crack, to coating axial mode I fracture energy [11]. In principle, the suitability of a material that is intended to promote crack deflection by cleaving can be evaluated independently of the fiber fracture properties. Nevertheless, it is also argued that a debonding crack within a coating can be expected to devi￾ate towards the coating/fiber interface and, in many cases, to arrive there [11] (see section below). The question addressed by He and Hutchinson is then raised, but at a different point in the failure process. 3.2. Tensile crack Crack deflection is usually assumed to be literally that; the matrix crack tip propagates into the interfacial region then turns parallel to the fiber surface. However, it has been suggested that the interfacial crack that develops in a composite under tension may initiate as a mode I crack in the tensile (normal to the fiber surface) stress field ahead of the crack tip [17,18], and observations on model laminate materials have confirmed the existence of such a failure sequence [19]. Since the microscopic details of fracture are difficult to probe experimentally, the exact sequence of events in real fibrous composites has remained a matter of speculation. Nevertheless, it is a matter of some impor￾tance in understanding the design and analysis of coating systems. In one case, the interfacial fracture will be deter￾mined by the radial tensile strength, while in the other case, it will be determined by the interfacial shear strengths. Understanding the process is also important in interpreting test data. Fiber push/pullout tests, for example, may measure a somewhat different property than the one that determines debonding during composite failure. The difference in fracture behavior observed in the two composites discussed in the first section seems to provide convincing evidence for debonding by the tensile mode in at least one system. The differences in behavior of the treated- fiber composite system as compared to a more conventional untreated-fiber composite, have been attributed to the differ￾ent interfacial cracking behavior [6,7]. Specifically, the interfacial crack in untreated-fiber composites has been reported to be confined to the C/SiO2 interface near the fiber surface, or the C layers very near to the interface [7, 20]. Such composites are measured to have interfacial frac￾ture energies of no more than a few J/m2 . The fiber treatment has been inferred to strengthen the interface region to a level which is above the strength of the pyrocarbon coating itself, thereby shifting the fracture to the pyrocarbon: the next￾weakest link [7,21]. The C coatings in both composites are taken to be the same except perhaps very near the coating/fiber interface. In the case of an untreated-fiber composite failing in tension, the weak coating/fiber interface region fails, while the coat￾ing itself does not. This implies that the interface must fail before the crack enters the coating, due to the stress field in front of the crack. Had the crack run through the coating, it would have deflected in the coating. The proof of this state￾ment is provided by the treated-fiber materials, in which the cracks deflect in the coating before reaching the fiber/coat￾ing interface. Provided that the debonding in the weak-inter￾face (untreated fiber) composites is truly at or very near the coating/fiber interface, this seems to provide a definitive sequence of events for the deflection process in weak￾interface composites. 3.3. Off-axis shear cracking Recent theoretical and experimental work by Pagano and coworkers [18,22] has presented strong evidence of a differ￾ent mode of crack deflection. The experimental work was performed on highly uniform composites comprising SiC monofilaments coated first with C, then with TiB2, in glass matrices. Post-failure analysis revealed that the debonding occurred predominately by propagation of a crack in the C very near the C/SiC interface. However, triangular-section rings, ‘mountains’ of C remained on the fiber at the location of matrix cracks, implying double deflection of impinging 522 R.J. Kerans, T.A. Parthasarathy / Composites: Part A 30 (1999) 521–524