cfa mater..Vol.44.No.10.pp.3903922.199 Pergamon Copynght ['1996 Acta Metallurgie PIIS1359645496)00087 GROWTH OF INTERFACE DEFECTS AND ITS EFFECT ON CRACK DEFLECTION AND TOUGHENING CRITERIA W. LEE, S J. HOWARD and w.J. CLEGG Department of Materials Science, University of Cambridge. Pembroke Street Cambridge CB 3QZ England (Receied 29 June 1995: in revised form 31 January1996 Abstract-The role of interface defects in crack deflection at planar interfaces direct observation of interface and crack growth in laminates of poly( methyl ate)and a finite element analysis. It was observed that crack deflection occurred by the growth ce defects ahead of the growing primary crack. It was also observed that the growth of these def sure toughening through crack deflection, but that a further condition, that any interface efects must not kink out of the interface, must be also satisfied. A finite element an observed deflection mechanism suggests that initial crack deflection is possible when fracture energy is less than 64% of that of the bulk material, which is consistent with experimental lowever he analysis also predicts that this is somewhat dependent on layer thicknesses and gl ing states for relatively longer interface defects. Copyright C 1996 Acta Metallurgica ine 1 INTRODUCTION bulk material acting normal to the direction of crack extension. In this case it was predicted that the It is well known that the presence of weak interfaces interface must have a strength less than about 0.35 ransverse to a crack growing in a brittle material that of the matrix where there was no elast causes the crack to be deflected with a consequent mismatch to ensure crack deflection increase in the resistance to crack growth [1]. In Kendall 7] suggested that, as there was no driving certain cases the onset of deflection may also be force for the opening of an interface ahead of the required if other energy absorbing mechanisms, such as fibre pull-out are to operate[2, 3]. The conditions n crack, crack deflection could only occur by the for a crack to be deflected at an interface were first primary through-thickness crack changing its path once it had reached the interface Crack deflection investigated by Cook and Gordon [4]. They found was assumed to occur when the force required to that the stress component opening an elliptical shape crack.aw, has a very high value at the crack tip grow the interfacial crack was less than that required to grow the crack across the interface. An energy and decreases with distance from the crack tip based analysis predicted that crack deflection would whilst the stress component acting perpendicular to then occur if the fracture energy of the interface is less the interface. Or is zero at the crack tip but rises to than about 10-20% of the bulk the exact value a maximum at one crack tip radius from the crack tip depending on the relative thickness of the two layers and then decreases The ratio of the peak value of ox which was supported by model experiments.More to o, is 1/5 and from this it was inferred that an recently the problem has been analysed extensively by interface with a theoretical tensile strength of less He and Hutchinson (8)and Martinez and Gupta[9] than 1/5 that of the matrix will debond ahead of the for the case where a primary crack terminates at an interface between two semi-infinite planes. Crack However when a crack with a sharp tip is deflection was assumed to occur when ,< Rand considered. both a and the plane of the crack .>R:i.e.when have the same value and decrease monotonically with distance from the crack tip at the same rate [5]. For his case, Gupta et al. [6 proposed that the deflection R (2) criterion would then b where sa is the strain energy release rate of the (I)deflected crack, s, is that of the penetrating crack, R, is the fracture energy of the interface and Rm is that where o is the interface strength, omf is the strength of the bulk material beneath the interface, since then of the bulk material, ax(0") is the stress acting the condition for propagation in the interface will be ormal to the interface and o (90 )is the stress in the met at a lower applied load than that for penetration
~ Pergamon PIi S 1359-6454(96)00068-7 Acta mater. Vol. 44. No. 10. pp. 3905-3922. 1996 Copyright ( 1996 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454'96 $15.00 + 0.00 GROWTH OF INTERFACE DEFECTS AND ITS EFFECT ON CRACK DEFLECTION AND TOUGHENING CRITERIA W. LEE, S. J. HOWARD and W. J. CLEGG Department of Materials Science, University of Cambridge, Pembroke Street. Cambridge CB2 3QZ, England (Received 29 June 1995; in revised form 31 Januao' 1996) Abstract--The role of interface defects in crack deflection at planar interfaces has been studied by the direct observation of interface and crack growth in laminates of poly(methyl methacrylate) and a finite element analysis. It was observed that crack deflection occurred by the growth of interface defects ahead of the growing primary crack. It was also observed that the growth of these defects is not sufficient to ensure toughening through crack deflection, but that a further condition, that any growing interface defects must not kink out of the interface, must be also satisfied. A finite element analysis based on the observed deflection mechanism suggests that initial crack deflection is possible when the interfacial fracture energy is less than 64% of that of the bulk material, which is consistent with experimental values. However, the analysis also predicts that this is somewhat dependent on layer thicknesses and global loading states for relatively longer interface defects. Copyright © 1996 Acta Metallurgica In('. l. INTRODUCTION It is well known that the presence of weak interfaces transverse to a crack growing in a brittle material causes the crack to be deflected with a consequent increase in the resistance to crack growth [1]. In certain cases the onset of deflection may also be required if other energy absorbing mechanisms, such as fibre pull-out, are to operate [2, 3]. The conditions for a crack to be deflected at an interface were first investigated by Cook and Gordon [4]. They found that the stress component opening an elliptical shape crack, a,,, has a very high value at the crack tip and decreases with distance from the crack tip, whilst the stress component acting perpendicular to the interface, a ..... is zero at the crack tip but rises to a maximum at one crack tip radius from the crack tip and then decreases. The ratio of the peak value of a.,.~ to a, is 1/5 and from this it was inferred that an interface with a theoretical tensile strength of less than 1/5 that of the matrix will debond ahead of the main crack allowing crack deflection to occur. However when a crack with a sharp tip is considered, both tr~ and o,, in the plane of the crack have the same value and decrease monotonically with distance from the crack tip at the same rate [5]. For this case, Gupta et al. [6] proposed that the deflection criterion would then be a~ a~x(O °) < -- (1) O'mf a..(90 °) where cr~r is the interface strength, a,.r is the strength of the bulk material, ax..(O °) is the stress acting normal to the interface and a..(90 °) is the stress in the bulk material acting normal to the direction of crack extension. In this case it was predicted that the interface must have a strength less than about 0.35 that of the matrix where there was no elastic mismatch to ensure crack deflection. Kendall [7] suggested that, as there was no driving force for the opening of an interface ahead of the main crack, crack deflection could only occur by the primary through-thickness crack changing its path once it had reached the interface. Crack deflection was assumed to occur when the force required to grow the interfacial crack was less than that required to grow the crack across the interface. An energy based analysis predicted that crack deflection would then occur if the fracture energy of the interface is less than about 10-20% of the bulk, the exact value depending on the relative thickness of the two layers, which was supported by model experiments. More recently the problem has been analysed extensively by He and Hutchinson [8] and Martinez and Gupta [9] for the case where a primary crack terminates at an interface between two semi-infinite planes. Crack deflection was assumed to occur when ff, < R~ and c~ > R~: i.e. when Ri Cffd < (2) Rm ffp where f#a is the strain energy release rate of the deflected crack, (~ is that of the penetrating crack, R~ is the fracture energy of the interface and Rm is that of the bulk material beneath the interface, since then the condition for propagation in the interface will be met at a lower applied load than that for penetration 3905
Lee et al. CRACK DEFLECTION AND TOUGHENING across the interface. thus the critical condition is met 2. EXPERIMENTAL when u p=R/R. This approach gave a critical S,/s, ratio of 0.26 for a doubly defected crack [9] Specimens containing planar interfaces with a and 0.25 for a singly deflected crack [8]when there is range of diferent properties were prepared by no elastic modulus mismatch across the interface. pressing together sheets of poly(methyl methacry This result is in good agreement with early late), PMMA, at temperatures above the glass late nmental work [7] and has been confirmed by transition temperature. Sheets, approx, 150 mm later experimentation [10]. Gupta et al. [6] and square and 5 mm thick, were washed in soap an Martinez and Gupta [9 considered the effect of water and then briefly rinsed in acetone and then elastic orthotropy and He et al. [11] extended He water again before drying with purified compressed and Hutchinsons original analysis by considering air. The sheets were then pressed together in a the effect of residual stress. These analyses showed pre- heated press at temperatures between 110 and that critical crack deflection criterion can be 140C at a pressure of 1. 5 MPa for 30 min before changed due to elastic orthotropy and to the cooling down to room temperature under pressure presence of residual stresses. Numerical method gave The pressed blocks, with a final thickness of 8 mm, almost identical solutions to the analytical solutions were then cut into test specimens approx. 150 mm long and 20 mm wide. The cut edges were then Most of the theories essentially consider whether polished to allow observation of the crack as it he driving force for the crack to grow along the approached the interface. Starter notches, 1.75 mm interface will exceed the fracture energy of the deep and 0. 34 mm wide, were cut into the specimens interface, before the driving force for the primary using a diamond impregnated wire. crack exceeds the fracture energy of the matrix. Some preliminary tests were carried out in tension The conditions under which deflection will occur and in four point bending, but growth of the crack are therefore those in which the primary crack is from the notch occurred so rapidly that it was stationary and terminated at the interface. Such an difficult to observe the crack as it was deflected at the analysis will predict in which direction the crack will interface. Only when the notches were cut close to the grow as the applied force on the material is increased interface, approx. 500 um above the interface, was it from zero. However, this is not always the situation observed that the interface debonded before the main in most real systems, where the applied force is such crack grew from the notch. However, it was not clear that the primary crack is moving, often in an unstable whether the same(debonding of the interface before manner. Therefore, it is not clear that the the formation of a T-shaped crack)would occur if the consideration of the path of such a stationary crack crack had a sharp tip. Therefore it was necessary to at an interface provides a general criterion for crack observe what would happen when a sharp crack deflection grows toward the interface. Many of the loading In addition all the work described above considers geometries designed for slow crack growth require only homogeneous interfaces with low fracture special apparatus or complex specimen geometry and is not unusual for structural solids, analysis (19-22]. Instead a wedge loading method including ceramics, to contain defects especially shown in Fig. I was used. A wedge 0.5 mm thick, was at interphase boundaries [3, 13-17]. Considering driven to the root of the notch with the base of the this structural effect, recently Mammoli et al. [18] specimen completely supported. This caused a very und that the presence of defects in the interface small crack to be initiated at the notch-tip. the load can increase the critical R /Re ratio for crack normal to the interface was then slowly removed deflection allowing the specimen to bend and the crack to grow Despite this work it is still not clear how a crack By controlling the rate of this unloading, crack is defected at the interface and how other factors growth rates as low as 10 um s- could be obtained influence the crack deflection criteria. The first aim of crack and the interface to be observed easily Whi such as global loading states and layer thicknesses allowing the interaction between a growing prima this paper is therefore to observe how growing cracks this enabled slow crack growth to be observed, it was are deflected at interfaces and the structure of the not possible to measure the load applied by the interface. Subsequently, a finite element analysis, wedge. Instead this was estimated using finite based on the experimental observations of the crack element analysis, where the displacement of the notch deflection process and of the interface structure, faces was taken to be the difference between the is carried out to establish the properties that thickness of the wedge and the width of the notch, interfaces must have if deflection is to occur as a which is 80 um in this case. Figure A2 in the consequence of the interaction between a primary Appendix shows how the wedging load is predicted crack and an interface defect of various lengths. to vary with displacement for different interfacia Finally, the effects of the global stress state and the crack lengths geometry of the specimen on the criterion for crack Experiments on specimens of the same dimensions deflection and on the subsequent toughening containing no interface were carried out and showed behaviour are discussed that under the conditions used here, the crack would
3906 LEE et al.: CRACK DEFLECTION AND TOUGHENING across the interface. Thus the critical condition is met when fq~/f#p = R,/Rm. This approach gave a critical f#~/f#p ratio of 0.26 for a doubly deflected crack [9] and 0.25 for a singly deflected crack [8] when there is no elastic modulus mismatch across the interface. This result is in good agreement with early experimental work [7] and has been confirmed by later experimentation [10]. Gupta et al. [6] and Martinez and Gupta [9] considered the effect of elastic orthotropy and He et al. [11] extended He and Hutchinson's original analysis by considering the effect of residual stress. These analyses showed that critical crack deflection criterion can be changed due to elastic orthotropy and to the presence of residual stresses. Numerical method gave almost identical solutions to the analytical solutions [121. Most of the theories essentially consider whether the driving force for the crack to grow along the interface will exceed the fracture energy of the interface, before the driving force for the primary crack exceeds the fracture energy of the matrix. The conditions under which deflection will occur are therefore those in which the primary crack is stationary and terminated at the interface. Such an analysis will predict in which direction the crack will grow as the applied force on the material is increased from zero. However, this is not always the situation in most real systems, where the applied force is such that the primary crack is moving, often in an unstable manner. Therefore, it is not clear that the consideration of the path of such a stationary crack at an interface provides a general criterion for crack deflection. In addition all the work described above considers only homogeneous interfaces with low fracture energy. It is not unusual for structural solids, including ceramics, to contain defects especially at interphase boundaries [3, 13-17]. Considering this structural effect, recently Mammoli et al. [18] found that the presence of defects in the interface can increase the critical RJRm ratio for crack deflection. Despite this work it is still not clear how a crack is deflected at the interface and how other factors such as global loading states and layer thicknesses influence the crack deflection criteria. The first aim of this paper is therefore to observe how growing cracks are deflected at interfaces and the structure of the interface. Subsequently, a finite element analysis, based on the experimental observations of the crack deflection process and of the interface structure, is carried out to establish the properties that interfaces must have if deflection is to occur as a consequence of the interaction between a primary crack and an interface defect of various lengths. Finally, the effects of the global stress state and the geometry of the specimen on the criterion for crack deflection and on the subsequent toughening behaviour are discussed. 2. EXPERIMENTAL Specimens containing planar interfaces with a range of different properties were prepared by pressing together sheets of poly(methyl methacrylate), PMMA, at temperatures above the glass transition temperature. Sheets, approx. 150mm square and 5 mm thick, were washed in soap and water and then briefly rinsed in acetone and then water again before drying with purified compressed air. The sheets were then pressed together in a pre-heated press at temperatures between 110 and 140°C at a pressure of 1.5 MPa for 30 min before cooling down to room temperature under pressure. The pressed blocks, with a final thickness of 8 mm, were then cut into test specimens approx. 150 mm long and 20 mm wide. The cut edges were then polished to allow observation of the crack as it approached the interface. Starter notches, 1.75 mm deep and 0.34 mm wide, were cut into the specimens using a diamond impregnated wire. Som e preliminary tests were carried out in tension and in four point bending, but growth of the crack from the notch occurred so rapidly that it was difficult to observe the crack as it was deflected at the interface. Only when the notches were cut close to the interface, approx. 500/tm above the interface, was it observed that the interface debonded before the main crack grew from the notch. However, it was not clear whether the same (debonding of the interface before the formation of a T-shaped crack) would occur if the crack had a sharp tip. Therefore it was necessary to observe what would happen when a sharp crack grows toward the interface. Many of the loading geometries designed for slow crack growth require special apparatus or complex specimen geometry and analysis [19-22]. Instead a wedge loading method shown in Fig. 1 was used. A wedge, 0.5 mm thick, was driven to the root of the notch with the base of the specimen completely supported. This caused a very small crack to be initiated at the notch-tip. The load normal to the interface was then slowly removed, allowing the specimen to bend and the crack to grow. By controlling the rate of this unloading, crack growth rates as low as 10/am s -~ could be obtained, allowing the interaction between a growing primary crack and the interface to be observed easily. Whilst this enabled slow crack growth to be observed, it was not possible to measure the load applied by the wedge. Instead, this was estimated using finite element analysis, where the displacement of the notch faces was taken to be the difference between the thickness of the wedge and the width of the notch, which is 80#m in this case. Figure A2 in the Appendix shows how the wedging load is predicted to vary with displacement for different interfacial crack lengths. Experiments on specimens of the same dimensions containing no interface were carried out and showed that, under the conditions used here, the crack would
LEE et al. CRACK DEFLECTION AND TOUGHENING Interface at the notch root Knife Wedge Rigid si Rigid Supt Unloading by the Remova of the Rigid Support an Further crack Growth Fig. I. Schematic illustration of the wedge loading used to obtain slow crack growth grow across about 70% of the full thickness of the tures. In this case, no further growth of the primary mpie. Thus, there was sufficient driving force to crack was observed suggesting that the growth of the ensure that a crack would grow across any interface interface debond crack had absorbed strain energy i present in the mid-plane of a specimen. The preference to the primary crack terfacial fracture energies of the specimens, where In the specimens pressed at intermediate tempera- rack deflection occurred on wedge loading, were tures shorter interface debond cracks were observed ubsequently measured using the four point bend The primary crack then grew and eventually it was delamination test (23). In those specimens where the arrested by the short interface debond crack to form primary crack stopped before it reached the interface a T-shaped crack. In this case the defected crack debond crack, further loading was applied to typically kinked into the matrix when further loading completely break the cracked layer and to make was applied in bending as shown in Fig 3.Whilst the tarter notches for the four point bend delamination length of the interface debond crack became shorter test. The fracture energy of bulk PMMA was as the interface became tougher, half debond lengths measured as 372 J m: using notched specimens shorter than about 500 um were not observed tested in three-point bending [24]. The Young's The interface fracture energies of the specimens modulus was measured as 3.0 GPa using an tested in wedge loading were subsequently measured unnotched specimen in four point bending. The using the four point bend delamination test. By interfacial structure of the PMMA laminates was also relating the interface fracture energy measured in a observed using scanning electron microscopy four point bend test to the debon during wedge loading, the trend shown in Fig. 4 was 3. OBSERVATIONS OF CRACK DEFLECTION obtained. The interfacial fracture energies of the specimens having a half interface debond length less When wedge loading was applied to the specimens, than about 750 um could not be measured using the crack deflection was not always observed. In such four point bend test since the interface debond crack cases. the primary through-thickness crack grew kinked into the matrix after propagating a very short across the interfaces, which were pressed at 140 C In distance. The implications of this are discussed in pecimens pressed at lower temperatures, the growth Section 5. Figure 4 suggests that the initial deflection of the primary crack towards the interface caused the of the primary crack at the interface is still possible interface to delaminate ahead of the growing crack, when the fracture energy of the interface is as high as as shown in Fig. 2. The distance between the tip of about 60% of that of the matrix the growing crack and the interface was somewhat Scanning electron microscopy (SEM)of variable but was generally of the order of 50 interface showed that it was not completely un Once initiated the interfacial crack grew extremely but contained some unbonded regions with total rapidly in the specimens pressed at lower tempera- lengths varying between 0. 1 and 100 um. Figure 5
® Interface LEE et al.: F CRACK DEFLECTION AND TOUGHENING F Knife Wedge Notch )ot 3907 PMMA model composite Rigid Support Rigid Support Unloading by the Removal of the Rigid Support and Further Crack Growth Fig. 1. Schematic illustration of the wedge loading used to obtain slow crack growth. grow across about 70% of the full thickness of the sample. Thus, there was sufficient driving force to ensure that a crack would grow across any interface present in the mid-plane of a specimen. The interfacial fracture energies of the specimens, where crack deflection occurred on wedge loading, were subsequently measured using the four point bend delamination test [23]. In those specimens where the primary crack stopped before it reached the interface debond crack, further loading was applied to completely break the cracked layer and to make starter notches for the four point bend delamination test. The fracture energy of bulk PMMA was measured as 372Jm-: using notched specimens tested in three-point bending [24]. The Young's modulus was measured as 3.0GPa using an unnotched specimen in four point bending. The interfacial structure of the PMMA laminates was also observed using scanning electron microscopy. 3. OBSERVATIONS OF CRACK DEFLECTION When wedge loading was applied to the specimens, crack deflection was not always observed. In such cases, the primary through-thickness crack grew across the interfaces, which were pressed at 140°C. In specimens pressed at lower temperatures, the growth of the primary crack towards the interface caused the interface to delaminate ahead of the growing crack, as shown in Fig. 2. The distance between the tip of the growing crack and the interface was somewhat variable but was generally of the order of 50#m. Once initiated the interfacial crack grew extremely rapidly in the specimens pressed at lower temperatures. In this case, no further growth of the primary crack was observed suggesting that the growth of the interface debond crack had absorbed strain energy in preference to the primary crack. In the specimens pressed at intermediate temperatures, shorter interface debond cracks were observed. The primary crack then grew and eventually it was arrested by the short interface debond crack to form a T-shaped crack. In this case the deflected crack typically kinked into the matrix when further loading was applied in bending as shown in Fig. 3. Whilst the length of the interface debond crack became shorter as the interface became tougher, half debond lengths shorter than about 500 #m were not observed. The interface fracture energies of the specimens tested in wedge loading were subsequently measured using the four point bend delamination test. By relating the interface fracture energy measured in a four point bend test to the debond length measured during wedge loading, the trend shown in Fig. 4 was obtained. The interfacial fracture energies of the specimens having a half interface debond length less than about 750/tm could not be measured using the four point bend test since the interface debond crack kinked into the matrix after propagating a very short distance. The implications of this are discussed in Section 5. Figure 4 suggests that the initial deflection of the primary crack at the interface is still possible when the fracture energy of the interface is as high as about 60% of that of the matrix. Scanning electron microscopy (SEM) of the interface showed that it was not completely uniform but contained some unbonded regions with total lengths varying between 0.1 and 100#m. Figure 5
LEE er al.: CRACK DEFLECTION AND TOUGHENING Fig. 2. Photograph showing crack deflection which occurred by the debonding of the interface ahead of the growing primary crack shows a typical interface structure in the PMma the matrix fracture energy. The suggested mechanism laminates used in this work. by which crack deflection occurs is also supported by The experimental observations are supported by the recent experimental observation of a Zro: Al O the earlier observations of Phillipps et al. [25] laminate system[26] and SiC/ C laminate system [10] crack deflection in Sic C laminates occurred where the interface defects grew before the primary the interface fracture energy was measured at 56% of crack reached the interface Fig 3. Photograph showing the formation of a T-shaped crack and the subsequent kinking of the crack t of the interface at the initial stage of crack deflection
3908 LEE et al.: CRACK DEFLECTION AND TOUGHENING Fig. 2. Photograph showing crack deflection which occurred by the debonding of the interface ahead of the growing primary crack. shows a typical interface structure in the PMMA laminates used in this work. The experimental observations are supported by the earlier observations of Phillipps et al. [25] where crack deflection in SiC/C laminates occurred when the interface fracture energy was measured at 56% of the matrix fracture energy. The suggested mechanism by which crack deflection occurs is also supported by the recent experimental observation of a ZrO:/AbO~ laminate system [26] and SiC/C laminate system [10] where the interface defects grew before the primary crack reached the interface. Fig. 3. Photograph showing the formation of a T-shaped crack and the subsequent kinking of the crack out of the interface at the initial stage of crack deflection
LEE el al. CRACK DEFLECTION AND TOUGHENING by whether the observed interfacial defect can grow rather than whether a primary crack can change its path upon reaching a weak defect-free interface. To The shortest half- debond investigate this point further. consider the beam length observed (500 um shown in Fig. 6, which is loaded by a combination of axial forces and bending moments. Note that the axial force P, and bending moment M, acting in beam I are not zero as there is a small bridging ligament between the primary crack and the interface and that only half the whole geometry is considered due to symmetry. Using beam theory it can be shown that the driving force for the growth of the interfacia crack is [27] Half Debond Length(mm) °5++盒 Fig. 4. The relation between the half-debond length of the interface and the fracture energy of the interface(measured separately from the same specimen). Note that half-debond where b is the width of beam. E is Youngs dicates that crack deflection is not possible when the modulus, A is the cross-sectional area of the beam fracture energy of the interface is higher than about 60% of and I is the second moment of area of the beam the matrix for this loading arrangement and which is bh:12 specimen geometry. In the specific case considered in the experime hown in Fig. 6(b). from force and moment equilibrium conditions, the force and moment GROWTH OF AN INTERFACE DEFECT AHEAD OF components for equation (3)are THE PRIMARY CRACK PI=P.-Pn 4.1. The origin of the driring force for the growth of the interfacial defects ) The observed crack deflection process suggests that there is a physical mechanism which produces a driving force for interfacial crack growth before the M=Pmn-2)+几 rimary crack reaches the interface. It is suggested that, when defects exist in the interface. the condition 十 for the occurrence of crack deflection is determined E=5. 1 Fn K y Fig. 5. SEM photograph showing a typical interface structure including the defects
E 0.8 0.6 LEE et al.: CRACK DEFLECTION AND TOUGHENING The shortest half-debond length observed (500 gm) 0.2 0 , , J ~ , ~ I , ~ : T , ~ , I J , ~ I 0 2 4 6 8 10 Half Debond Length (mm) Fig. 4. The relation between the half-debond length of the interface and the fracture energy of the interface (measured separately from the same specimen). Note that half-debond lengths shorter than 500 pm were not observed, which indicates that crack deflection is not possible when the fracture energy of the interface is higher than about 60% of that of the matrix for this loading arrangement and specimen geometry. 3909 4. GROWTH OF AN INTERFACE DEFECT AHEAD OF THE PRIMARY CRACK 4.1. The origin of the driving .force for the growth of the interfacial defects The observed crack deflection process suggests that there is a physical mechanism which produces a driving force for interfacial crack growth before the primary crack reaches the interface. It is suggested that, when defects exist in the interface, the condition for the occurrence of crack deflection is determined by whether the observed interfacial defect can grow, rather than whether a primary crack can change its path upon reaching a weak defect-free interface. To investigate this point further, consider the beam shown in Fig. 6, which is loaded by a combination of axial forces and bending moments. Note that the axial force P~ and bending moment M~ acting in beam 1 are not zero as there is a small bridging ligament between the primary crack and the interface and that only half the whole geometry is considered due to symmetry. Using beam theory, it can be shown that the driving force for the growth of the interfacial defect or crack is [27] 1[ P~ M~ + P~ M~ P~ M~ 1 (qi= ~IA~ + E,L ~-A,.+ E,.I ,_ E3A~ (3) where b is the width of the beam, E is Young's modulus, A is the cross-sectional area of the beam and I is the second moment of area of the beam, which is bh~;12. In the specific case considered in the experiment shown in Fig. 6(b), from force and moment equilibrium conditions, the force and moment components for equation (3) are PI = P~- Pb (4) P-" = (P,, - Pb) (5) f'h = " M,. (7) Fig. 5. SEM photograph showing a typical interface structure including the defects