《纺织复合材料》课程参考文献（Experimental Characterization of Advanced Composite Materials, Third Edition）14 Characterization of Delamination Failure

14 Characterization of Delamination Failure The interlaminar mode of fracture(delamination)has aroused considerable attention since the early 1970s [1].With the introduction of laminated composites into structures subjected to service loads,it has become appar- ent that the delamination failure mode has the potential for being the major life-limiting failure process.These delaminations are typically induced in composite laminates during service.However,delaminations may also be introduced during processing of the lay-up,for example as a result of contamination of the prepreg,leading to locally poor ply adhesion,or they may form locally in regions of high void content.Delamination may also be introduced during post-fabrication handling of the structure. It is recognized that a delamination represents a crack-like discontinuity between the plies and that it may propagate during application of mechan- ical or thermal loads,or both.It thus seems appropriate to approach the delamination using fracture mechanics (Section 2.7),which indeed has evolved as a fruitful approach for material selection and assessment of struc- tural integrity.Fracture mechanics of delaminations is commonly based on the strain energy release rate,and fracture toughness is expressed as the work of fracture.Consequently,many new fracture tests have been devised for measuring the static interlaminar fracture toughness,as well as the crack propagation rate during cyclic loading.Most such tests and standard test procedures are limited to unidirectional [Ol laminates in which a delamina- tion propagates between the plies along the fiber direction.In laminates with multidirectional plies,the crack may have a tendency to branch through the neighboring plies,invalidating the coplanar assumption in fracture analysis [2-4].Composites with tough resin films(called interleaves)between the plies may experience peculiar delamination resistance behavior depending on crack path selection,i.e.,if the crack propagates cohesively in the tough interlayer or adhesively at the film-composite interface [5].In woven fabric composites,a delamination crack will interact with matrix regions and inter- lacing yarns during its propagation,and as a result,will experience varying growth resistance [6].Composites with through-thickness reinforcement may experience large extended regions where the reinforcements bridge the crack(bridging zones),which invalidates data reduction schemes based on linear elastic fracture mechanics [7].Although fiber bridging is common in unidirectional (all 0 plies)composites,characterization of the delamination ©2003 by CRC Press LLC

14 Characterization of Delamination Failure The interlaminar mode of fracture (delamination) has aroused considerable attention since the early 1970s [1]. With the introduction of laminated composites into structures subjected to service loads, it has become appar￾ent that the delamination failure mode has the potential for being the major life-limiting failure process. These delaminations are typically induced in composite laminates during service. However, delaminations may also be introduced during processing of the lay-up, for example as a result of contamination of the prepreg, leading to locally poor ply adhesion, or they may form locally in regions of high void content. Delamination may also be introduced during post-fabrication handling of the structure. It is recognized that a delamination represents a crack-like discontinuity between the plies and that it may propagate during application of mechan￾ical or thermal loads, or both. It thus seems appropriate to approach the delamination using fracture mechanics (Section 2.7), which indeed has evolved as a fruitful approach for material selection and assessment of struc￾tural integrity. Fracture mechanics of delaminations is commonly based on the strain energy release rate, and fracture toughness is expressed as the work of fracture. Consequently, many new fracture tests have been devised for measuring the static interlaminar fracture toughness, as well as the crack propagation rate during cyclic loading. Most such tests and standard test procedures are limited to unidirectional [0]n laminates in which a delamina￾tion propagates between the plies along the fiber direction. In laminates with multidirectional plies, the crack may have a tendency to branch through the neighboring plies, invalidating the coplanar assumption in fracture analysis [2–4]. Composites with tough resin films (called interleaves) between the plies may experience peculiar delamination resistance behavior depending on crack path selection, i.e., if the crack propagates cohesively in the tough interlayer or adhesively at the film–composite interface [5]. In woven fabric composites, a delamination crack will interact with matrix regions and inter￾lacing yarns during its propagation, and as a result, will experience varying growth resistance [6]. Composites with through-thickness reinforcement may experience large extended regions where the reinforcements bridge the crack (bridging zones), which invalidates data reduction schemes based on linear elastic fracture mechanics [7]. Although fiber bridging is common in unidirectional (all 0° plies) composites, characterization of the delamination TX001_ch14_Frame Page 185 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

resistance of such composites tends to be associated with fewer complications. Consequently,we will here limit attention to unidirectional composites. Fracture mechanics analysis,preparation of test specimens,testing,and data reduction will be described for some contemporary interlaminar frac- ture test specimens,namely,the double-cantilever beam (DCB)specimen (Mode I),end-notched flexure (ENF)specimen (Mode II),four-point bend end-notched flexure(4ENF)specimen(Mode Il),the mixed-mode bending (MMB)specimen,and the edge crack torsion (ECT)specimen (Mode III). The various fracture modes are defined in Figure 2.9. FIGURE 14.1 DCB specimen geometry. 14.1 Double-Cantilever Beam (DCB)Test The DCB specimen for Mode I fracture testing and the test principle is shown in Figure 14.1.This specimen is a standard test method,ASTM D 5528[8]. The purpose of the test is to determine the opening mode interlaminar fracture toughness,Gic,of continuous fiber composite materials with a poly- mer matrix.First developed in a tapered form by Bascom,et al.[9],the straight-sided geometry proposed by Wilkins et al.[10],shown in Figure 14.1,has become standard.Although data reduction does not rely on the classical beam theory approach used by Wilkins,et al.[10],the simplicity of this theory makes it easy to examine some features of the DCB specimen. If we assume that classical beam theory is valid,the load-point compliance, C=8/P,of the DCB specimen becomes C= 2a3 (14.1) 3E,I where P is the load applied,6 is the crack opening,a is the crack length,and EI is the flexural rigidity of each beam of the specimen,with E being the Young's modulus of the composite in the fiber direction and I the moment ©2003 by CRC Press LLC

resistance of such composites tends to be associated with fewer complications. Consequently, we will here limit attention to unidirectional composites. Fracture mechanics analysis, preparation of test specimens, testing, and data reduction will be described for some contemporary interlaminar frac￾ture test specimens, namely, the double-cantilever beam (DCB) specimen (Mode I), end-notched flexure (ENF) specimen (Mode II), four-point bend end-notched flexure (4ENF) specimen (Mode II), the mixed-mode bending (MMB) specimen, and the edge crack torsion (ECT) specimen (Mode III). The various fracture modes are defined in Figure 2.9. 14.1 Double-Cantilever Beam (DCB) Test The DCB specimen for Mode I fracture testing and the test principle is shown in Figure 14.1. This specimen is a standard test method, ASTM D 5528 [8]. The purpose of the test is to determine the opening mode interlaminar fracture toughness, GIC, of continuous fiber composite materials with a poly￾mer matrix. First developed in a tapered form by Bascom, et al. [9], the straight-sided geometry proposed by Wilkins et al. [10], shown in Figure 14.1, has become standard. Although data reduction does not rely on the classical beam theory approach used by Wilkins, et al. [10], the simplicity of this theory makes it easy to examine some features of the DCB specimen. If we assume that classical beam theory is valid, the load-point compliance, C = δ/P, of the DCB specimen becomes (14.1) where P is the load applied, δ is the crack opening, a is the crack length, and E1I is the flexural rigidity of each beam of the specimen, with E1 being the Young’s modulus of the composite in the fiber direction and I the moment FIGURE 14.1 DCB specimen geometry. C a E I = 2 3 3 1 TX001_ch14_Frame Page 186 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

of inertia(Figure 14.1).The strain energy release rate,G=G,is obtained from Equation (2.59) G= P2 dC (14.2) 2w da in which w is the specimen width.Equations (14.1)and (14.2)give G=Pa2 (14.3) wEI If Gic is a true material constant,stable crack growth requires(see Section 2.7), dG/da s0 (14.4) For the DCB specimen under fixed-load conditions,dG/da is obtained from Equation (14.3)as dG 2P2a (14.5) da wE,I This quantity is always positive and thus the crack growth is unstable under load-controlled testing conditions. For fixed-grip conditions,dG/da may be obtained by substitution of P=8/C in Equation(14.2)and differentiation dG_-462a (14.6) da c'wE I This quantity is always negative,and thus the crack growth is stable. Experimentally,most testing is performed under fixed-grip conditions (displacement control),which should render stable crack growth. 14.1.1 DCB Specimen Preparation and Test Procedure The DBC specimen should be at least 125 mm long and between 20 and 25 mm wide.The number of plies,dimensions,and preparation of the panel are outlined in Appendix B.An even number of plies should be employed to achieve a thickness (h in Figure 14.1)between 3 and 5 mm.Variations in thickness should be less than 0.1 mm.Tough composites may require thicker specimens to avoid large displacements and nonlinear response.Figures 14.2 and 14.3 show the DCB specimen with hinge loading tabs prepared and ©2003 by CRC Press LLC

of inertia (Figure 14.1). The strain energy release rate, G = GI, is obtained from Equation (2.59) (14.2) in which w is the specimen width. Equations (14.1) and (14.2) give (14.3) If GIC is a true material constant, stable crack growth requires (see Section 2.7), dG/da ≤ 0 (14.4) For the DCB specimen under fixed-load conditions, dG/da is obtained from Equation (14.3) as (14.5) This quantity is always positive and thus the crack growth is unstable under load-controlled testing conditions. For fixed-grip conditions, dG/da may be obtained by substitution of P = δ/C in Equation (14.2) and differentiation (14.6) This quantity is always negative, and thus the crack growth is stable. Experimentally, most testing is performed under fixed-grip conditions (displacement control), which should render stable crack growth. 14.1.1 DCB Specimen Preparation and Test Procedure The DBC specimen should be at least 125 mm long and between 20 and 25 mm wide. The number of plies, dimensions, and preparation of the panel are outlined in Appendix B. An even number of plies should be employed to achieve a thickness (h in Figure 14.1) between 3 and 5 mm. Variations in thickness should be less than 0.1 mm. Tough composites may require thicker specimens to avoid large displacements and nonlinear response. Figures 14.2 and 14.3 show the DCB specimen with hinge loading tabs prepared and G P w dC da = 2 2 G P a wE I = 2 2 1 dG da P a wE I = 2 2 1 dG da a c wE I = −4 2 2 1 δ TX001_ch14_Frame Page 187 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

-Film Insert Piano hinge FIGURE 14.2 FIGURE 14.3 DCB test setup. Hinge loading tab arrangement for the DCB specimen. bonded as described in Chapter 4.The precrack is defined by inserting a thin film (<13 um)at the midplane of the panel(see Appendix B).Crack length,a,is defined as the distance from the line of load application to the crack tip,Figure 14.3.The length of the film insert should be adjusted to obtain a precrack length,ao,of approximately 50 mm(see Appendix B). Measure thickness and width of the specimen close to each end and at the center and calculate averages.Paint the specimen edges with a thin,white, brittle coating such as typewriter correction fluid.To aid in recording of crack length,mark the first 5 mm from the insert with thin vertical lines every 1 mm.Mark the remaining 20 mm every 5 mm. The specimen should be mounted in the grips of a properly calibrated test machine with a sufficiently sensitive load cell.A traveling optical microscope with approximately 10x magnification and a cross hair can be positioned on one side of the specimen to enable monitoring of the delamination crack tip and its extension during the fracture test within +0.5 mm.Locate the cross hair at the delamination front without applying load to the specimen to obtain a record of the precrack length,a(Figure 14.3).Set the crosshead rate at 0.5 mm/min,and plot load vs.crosshead displacement for real-time visual inspection of the load-displacement response.Displacement of the loaded ends(8 in Figure 14.1)can be taken as the crosshead travel,provided the machine and load cell are stiff enough not to deform more than 2%of the total opening displacement. Observe the delamination front as the specimen is being loaded.When the delamination begins to grow from the end of the insert,mark this incident as ao on the chart recording as indicated in Figure 14.4.Continue to observe the front of the growing crack,and mark the chart accordingly. ©2003 by CRC Press LLC

bonded as described in Chapter 4. The precrack is defined by inserting a thin film (<13 µm) at the midplane of the panel (see Appendix B). Crack length, a, is defined as the distance from the line of load application to the crack tip, Figure 14.3. The length of the film insert should be adjusted to obtain a precrack length, a0 , of approximately 50 mm (see Appendix B). Measure thickness and width of the specimen close to each end and at the center and calculate averages. Paint the specimen edges with a thin, white, brittle coating such as typewriter correction fluid. To aid in recording of crack length, mark the first 5 mm from the insert with thin vertical lines every 1 mm. Mark the remaining 20 mm every 5 mm. The specimen should be mounted in the grips of a properly calibrated test machine with a sufficiently sensitive load cell. A traveling optical microscope with approximately 10× magnification and a cross hair can be positioned on one side of the specimen to enable monitoring of the delamination crack tip and its extension during the fracture test within ±0.5 mm. Locate the cross hair at the delamination front without applying load to the specimen to obtain a record of the precrack length, ao (Figure 14.3). Set the crosshead rate at 0.5 mm/min, and plot load vs. crosshead displacement for real-time visual inspection of the load-displacement response. Displacement of the loaded ends (δ in Figure 14.1) can be taken as the crosshead travel, provided the machine and load cell are stiff enough not to deform more than 2% of the total opening displacement. Observe the delamination front as the specimen is being loaded. When the delamination begins to grow from the end of the insert, mark this incident as ao on the chart recording as indicated in Figure 14.4. Continue to observe the front of the growing crack, and mark the chart accordingly. FIGURE 14.2 DCB test setup. FIGURE 14.3 Hinge loading tab arrangement for the DCB specimen. TX001_ch14_Frame Page 188 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

00 increasing 8 crack length 910 Load,P Displacement,δ FIGURE 14.4 Schematic load-displacement record during crack growth for a DCB test. For the first 5 mm of crack growth,each 1 mm increment should be marked. After 5 mm of crack extension,the crosshead rate may be increased.Mark every 5 mm of crack length on the graph.Observe the opposite edge to monitor deviations from uniform crack extension across the beam width. The difference in crack length between the two edges should be less than 2 mm for a valid test.When the delamination has extended about 25 mm, the specimen may be unloaded while the unloading load-displacement response (see Figure 14.4)is recorded.A common occurrence in testing unidirectional DCB specimens is fiber bridging,which refers to debonded fibers bridging the fracture surfaces,as illustrated in Figure 14.5.The fiber bridging elevates the fracture resistance as a result of the closure tractions that develop in the fibers that bridge the crack faces behind the crack tip, and the energy consumed as the bridged fibers debond from the matrix [11]. It is common to display the fracture toughness measured at various crack lengths as a resistance curve(R-curve).As discussed by Suo et al.[11],such R-curves do not represent true material behavior because they depend on specimen thickness.Fiber bridging is less likely to occur in multidirectional laminates used in composite structures because less opportunity exists for fiber wash,i.e.,intermingling of wavy fibers between adjacent plies.Fiber bridging is thus likely to lead to nonconservative estimates of the actual delamination toughness.It is argued that the most meaningful,and also conservative,estimate of fracture toughness is the initiation toughness, Gic(init.),associated with the initial crack propagation from the Teflon insert [8],because this value is not influenced by fiber bridging.Further discussion will follow. 14.1.2 DCB Data Reduction Several data reduction methods for evaluating the Mode I fracture tough- ness,Gic,have been proposed [12].A simple,yet accurate method is the 2003 by CRC Press LLC

For the first 5 mm of crack growth, each 1 mm increment should be marked. After 5 mm of crack extension, the crosshead rate may be increased. Mark every 5 mm of crack length on the graph. Observe the opposite edge to monitor deviations from uniform crack extension across the beam width. The difference in crack length between the two edges should be less than 2 mm for a valid test. When the delamination has extended about 25 mm, the specimen may be unloaded while the unloading load-displacement response (see Figure 14.4) is recorded. A common occurrence in testing unidirectional DCB specimens is fiber bridging, which refers to debonded fibers bridging the fracture surfaces, as illustrated in Figure 14.5. The fiber bridging elevates the fracture resistance as a result of the closure tractions that develop in the fibers that bridge the crack faces behind the crack tip, and the energy consumed as the bridged fibers debond from the matrix [11]. It is common to display the fracture toughness measured at various crack lengths as a resistance curve (R-curve). As discussed by Suo et al. [11], such R-curves do not represent true material behavior because they depend on specimen thickness. Fiber bridging is less likely to occur in multidirectional laminates used in composite structures because less opportunity exists for fiber wash, i.e., intermingling of wavy fibers between adjacent plies. Fiber bridging is thus likely to lead to nonconservative estimates of the actual delamination toughness. It is argued that the most meaningful, and also conservative, estimate of fracture toughness is the initiation toughness, GIC(init.), associated with the initial crack propagation from the Teflon insert [8], because this value is not influenced by fiber bridging. Further discussion will follow. 14.1.2 DCB Data Reduction Several data reduction methods for evaluating the Mode I fracture tough￾ness, GIC, have been proposed [12]. A simple, yet accurate method is the FIGURE 14.4 Schematic load-displacement record during crack growth for a DCB test. TX001_ch14_Frame Page 189 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

empirical compliance method suggested originally by Berry [13],where the beam compliance,C=8/P,is expressed as a power function of crack length, C=a (14.7) H where a is the crack length,and n and H are parameters determined exper- imentally.If classical beam theory and the assumption of fixed ends are valid, n=3 and H=3E I/2.In reality,the legs of the DCB specimen are elastically built into the uncracked portion of the specimen rather than being rigidly fixed.This will cause deviations from classical beam theory. To establish the actual values of the empirical parameters in Equation (14.7),measured load and displacement data at each crack length are eval- uated from the load-displacement graph(Figure 14.4),and the stiffness,i.e., the inverse of the compliance(1/C=P/8),is plotted vs.crack length(a) in a double-logarithmic graph as shown in Figure 14.6.By fitting a straight line to the data,it is possible to establish the exponent,n,in Equation(14.7). Substitution of Equation (14.7)into (14.2)yields at fracture nPδe (14.8) 2wa in which P.and 8.are the critical load and displacement associated with each crack length,a. Three toughness values corresponding to crack growth from the insert may be defined.Gic(NL)refers to the critical load and displacement associ- ated with the deviation from linear response(Figure 14.4).The second defi- nition,Gic(vis.),refers to the visual observance of crack growth measured with the traveling microscope.The third definition,Gic(5%),uses the load PoPd)5o1 Bridged fibers log a FIGURE 14.5 FIGURE 14.6 Fiber bridging in DCB testing. Log-log plot of DCB specimen stiffness vs. crack length. ©2003 by CRC Press LLC

empirical compliance method suggested originally by Berry [13], where the beam compliance, C = δ/P, is expressed as a power function of crack length, (14.7) where a is the crack length, and n and H are parameters determined exper￾imentally. If classical beam theory and the assumption of fixed ends are valid, n = 3 and H = 3E1I/2. In reality, the legs of the DCB specimen are elastically built into the uncracked portion of the specimen rather than being rigidly fixed. This will cause deviations from classical beam theory. To establish the actual values of the empirical parameters in Equation (14.7), measured load and displacement data at each crack length are eval￾uated from the load-displacement graph (Figure 14.4), and the stiffness, i.e., the inverse of the compliance (1/C = Pc/δc), is plotted vs. crack length (a) in a double-logarithmic graph as shown in Figure 14.6. By fitting a straight line to the data, it is possible to establish the exponent, n, in Equation (14.7). Substitution of Equation (14.7) into (14.2) yields at fracture (14.8) in which Pc and δc are the critical load and displacement associated with each crack length, a. Three toughness values corresponding to crack growth from the insert may be defined. GIC(NL) refers to the critical load and displacement associ￾ated with the deviation from linear response (Figure 14.4). The second defi- nition, GIC(vis.), refers to the visual observance of crack growth measured with the traveling microscope. The third definition, GIC(5%), uses the load FIGURE 14.5 Fiber bridging in DCB testing. FIGURE 14.6 Log–log plot of DCB specimen stiffness vs. crack length. C a H n = G nP wa IC c c = δ 2 TX001_ch14_Frame Page 190 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

2.5 Carbon/PEEK 13μm Kopton insert 2.0 Gic [prop.) Gic 5%a ● m2 1.5 邓8 1.0 0.5 30 45 60 75 90 Crack Length,mm FIGURE 14.7 R-curve describing mode I interlaminar fracture resistance of carbon-PEEK with a 13 um insert. and displacement at a 5%increase in compliance.Gic(NL)is typically the most conservative estimate of the fracture toughness and is recommended as a measure of Mode I delamination toughness.For subsequent crack growth,Gic is calculated from Equation(14.8)using the recorded loads and crack lengths (Figure 14.4). A crack growth resistance curve (R-curve)displaying Gic vs.crack exten- sion can be constructed from the fracture toughness,Gic,and crack length, a,data.Figure 14.7 shows an example of an R-curve for a carbon/polyether- etherketone(PEEK)composite.At the first loading increment,the delamina- tion grows from the tip of the thin film insert starter crack without any influence from fiber bridging.The corresponding three initiation fracture toughness values,Gic(NL),Gic(vis.),and Gic(5%),are indicated in Figure 14.7. As the crack grows,the crack surfaces become more and more separated and bridged fibers may fracture or become pulled out from the matrix,which causes the apparent fracture toughness to increase.With further crack exten- sion a steady-state toughness,Gic(prop.),is usually reached,corresponding to an equilibrium number of bridged fibers per unit crack area.As mentioned earlier,the initial value associated with propagation of the crack from the film insert constitutes a well-defined measure of fracture toughness because it is unaffected by the fiber bridging that occurs with crack extension [11,12]. 14.2 End-Notched Flexure(ENF)Test The ENF specimen(Figure 14.8)was introduced as a pure Mode II delamina- tion specimen for testing of composites by Russell and Street [14].The purpose of the ENF specimen is to determine the critical strain energy release rate in pure Mode II loading of unidirectional composites [14,15].The ENF specimen ©2003 by CRC Press LLC

and displacement at a 5% increase in compliance. GIC(NL) is typically the most conservative estimate of the fracture toughness and is recommended as a measure of Mode I delamination toughness. For subsequent crack growth, GIC is calculated from Equation (14.8) using the recorded loads and crack lengths (Figure 14.4). A crack growth resistance curve (R-curve) displaying GIC vs. crack exten￾sion can be constructed from the fracture toughness, GIC , and crack length, a, data. Figure 14.7 shows an example of an R-curve for a carbon/polyether￾etherketone (PEEK) composite. At the first loading increment, the delamina￾tion grows from the tip of the thin film insert starter crack without any influence from fiber bridging. The corresponding three initiation fracture toughness values, GIC(NL), GIC(vis.), and GIC(5%), are indicated in Figure 14.7. As the crack grows, the crack surfaces become more and more separated and bridged fibers may fracture or become pulled out from the matrix, which causes the apparent fracture toughness to increase. With further crack exten￾sion a steady-state toughness, GIC(prop.), is usually reached, corresponding to an equilibrium number of bridged fibers per unit crack area. As mentioned earlier, the initial value associated with propagation of the crack from the film insert constitutes a well-defined measure of fracture toughness because it is unaffected by the fiber bridging that occurs with crack extension [11,12]. 14.2 End-Notched Flexure (ENF) Test The ENF specimen (Figure 14.8) was introduced as a pure Mode II delamina￾tion specimen for testing of composites by Russell and Street [14]. The purpose of the ENF specimen is to determine the critical strain energy release rate in pure Mode II loading of unidirectional composites [14,15]. The ENF specimen FIGURE 14.7 R-curve describing mode I interlaminar fracture resistance of carbon–PEEK with a 13 µm insert. TX001_ch14_Frame Page 191 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

P/2 (B) P/2 FIGURE 14.8 ENF specimen. produces shear loading at the crack tip without introducing excessive friction between the crack surfaces [16,17].The ENF specimen is standardized in Europe [18]and Japan [19],and has been studied extensively in the U.S.by the ASTM D-30 Committee as a candidate for ASTM standardization.As will be discussed,however,the ENF specimen is inherently unstable under dis- placement control,which has slowed acceptance of this specimen as a standard fracture test. Assuming that classical beam theory is valid,an expression for the strain energy release rate,G,can be derived [14,15]: 9P2Ca2 G= (14.9) 2w(2L3+3a3) where P is the applied load,C is the compliance,a is the crack length,w is the specimen width,and L is the span between the central loading cylinders and the outer support cylinders(Figure 14.8).The specimen compliance as given by beam theory [14,15]is c= L+3a3 (14.10) 8E wh3 where E is the flexural modulus,and h is one half the total thickness of the beam,i.e.,the thickness of each sub-beam of the delaminated region. The stability of crack growth may be judged from the sign of dG/da.For fixed-load conditions,Equations (14.9)and (14.10)give dG 9ap2 da 8Ew2h3 (14.11) This quantity is positive,hence the crack growth is unstable. For fixed-grip conditions,Equations(14.9)and(14.10)give dG 982a 9a3 da 8E,w2hC2 2L3+3a3 (14.12) 2003 by CRC Press LLC

produces shear loading at the crack tip without introducing excessive friction between the crack surfaces [16,17]. The ENF specimen is standardized in Europe [18] and Japan [19], and has been studied extensively in the U.S. by the ASTM D-30 Committee as a candidate for ASTM standardization. As will be discussed, however, the ENF specimen is inherently unstable under dis￾placement control, which has slowed acceptance of this specimen as a standard fracture test. Assuming that classical beam theory is valid, an expression for the strain energy release rate, G, can be derived [14,15]: (14.9) where P is the applied load, C is the compliance, a is the crack length, w is the specimen width, and L is the span between the central loading cylinders and the outer support cylinders (Figure 14.8). The specimen compliance as given by beam theory [14,15] is (14.10) where E1 is the flexural modulus, and h is one half the total thickness of the beam, i.e., the thickness of each sub-beam of the delaminated region. The stability of crack growth may be judged from the sign of dG/da. For fixed-load conditions, Equations (14.9) and (14.10) give (14.11) This quantity is positive, hence the crack growth is unstable. For fixed-grip conditions, Equations (14.9) and (14.10) give (14.12) FIGURE 14.8 ENF specimen. G P Ca wL a = + 9 22 3 2 2 3 3 ( ) C L a E wh = 2 3 + 8 3 3 1 3 dG da aP Ew h = 9 8 2 2 3 dG da a EwhC a L a = − +       9 8 1 9 2 3 2 1 23 2 3 3 3 δ TX001_ch14_Frame Page 192 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

Stable crack growth requires dG/da to be less than or equal to zero.This gives a≥L//3≈0.7L (14.13) Consequently,for the commonly used a =L/2,the crack growth is unstable also under fixed-grip conditions.This has the consequence that only one measurement of the fracture toughness is obtained for each specimen. 14.2.1 ENF Specimen Preparation and Test Procedure The ENF specimen is typically 120 mm long and 20 to 25 mm wide.Specimen thicknesses for unidirectional carbon-and glass-fiber composites are typically 3 and 5 mm(60%fiber volume fraction),respectively.The specimen is loaded in a three-point bend fixture (Figure 14.9)with a distance between the supports,2L,of 100 mm.The loading and support cylinders should be about 5 mm in diameter.The crack length-to-half span ratio,a/L,should be 0.5 at propagation of the crack.Panels should be prepared with a nonadhesive Teflon or Kapton film of thickness less than 13 um placed at the midplane to define a starter crack.Further details of specimen preparation are presented in Appendix B.After specimens have been cut from the panel,the width and thickness at the center and 1 cm from each end should be measured for all specimens.The thickness variations should not exceed 0.1 mm.Prior to testing,a brittle white coating should be applied to the specimen edges as described in Section 14.1.1. The issue of whether precraking of the ENF specimen should be performed has long been discussed.Precracking in Mode I is likely to create the fiber- bridging discussed in Section 14.1,and is not recommended [20].A shear precrack may be achieved by loading the specimen in the stable crack length regime,a >0.7L,according to Equation (14.13),until a short extension of the crack occurs.Unfortunately,however,it is difficult to detect the exact position and shape of the shear precrack after completion of the fracture test,and it is also difficult to obtain a straight and uniform crack front.For reasons of simplicity and consistency with the DCB procedure (Section 14.1),crack propagation from specimens with thin insert films,but without additional extension of the precrack,is advocated. The ENF specimen is placed in a standard three-point bend fixture [21], so that a crack length,a,of 25 mm is achieved(Figures 14.9 and 14.10).To facilitate appropriate positioning of the crack tip,a low-magnification(10x) traveling microscope is useful.Mark the support location on the specimen edge for subsequent measurement of crack length.Measure the center beam deflection (load-point displacement),6,with a linear variable differential transformer(LVDT),or from the crosshead displacement corrected for the machine compliance.Use a crosshead rate in the range of 0.5 to 1 mm/min, and monitor the load-displacement response.Record both loading and 2003 by CRC Press LLC

Stable crack growth requires dG/da to be less than or equal to zero. This gives (14.13) Consequently, for the commonly used a = L/2, the crack growth is unstable also under fixed-grip conditions. This has the consequence that only one measurement of the fracture toughness is obtained for each specimen. 14.2.1 ENF Specimen Preparation and Test Procedure The ENF specimen is typically 120 mm long and 20 to 25 mm wide. Specimen thicknesses for unidirectional carbon- and glass-fiber composites are typically 3 and 5 mm (60% fiber volume fraction), respectively. The specimen is loaded in a three-point bend fixture (Figure 14.9) with a distance between the supports, 2L, of 100 mm. The loading and support cylinders should be about 5 mm in diameter. The crack length-to-half span ratio, a/L, should be 0.5 at propagation of the crack. Panels should be prepared with a nonadhesive Teflon or Kapton film of thickness less than 13 µm placed at the midplane to define a starter crack. Further details of specimen preparation are presented in Appendix B. After specimens have been cut from the panel, the width and thickness at the center and 1 cm from each end should be measured for all specimens. The thickness variations should not exceed 0.1 mm. Prior to testing, a brittle white coating should be applied to the specimen edges as described in Section 14.1.1. The issue of whether precraking of the ENF specimen should be performed has long been discussed. Precracking in Mode I is likely to create the fiber￾bridging discussed in Section 14.1, and is not recommended [20]. A shear precrack may be achieved by loading the specimen in the stable crack length regime, a >0.7L, according to Equation (14.13), until a short extension of the crack occurs. Unfortunately, however, it is difficult to detect the exact position and shape of the shear precrack after completion of the fracture test, and it is also difficult to obtain a straight and uniform crack front. For reasons of simplicity and consistency with the DCB procedure (Section 14.1), crack propagation from specimens with thin insert films, but without additional extension of the precrack, is advocated. The ENF specimen is placed in a standard three-point bend fixture [21], so that a crack length, a, of 25 mm is achieved (Figures 14.9 and 14.10). To facilitate appropriate positioning of the crack tip, a low-magnification (10×) traveling microscope is useful. Mark the support location on the specimen edge for subsequent measurement of crack length. Measure the center beam deflection (load-point displacement), δ, with a linear variable differential transformer (LVDT), or from the crosshead displacement corrected for the machine compliance. Use a crosshead rate in the range of 0.5 to 1 mm/min, and monitor the load-displacement response. Record both loading and a L/ 0.7L ≥ ≈ 3 3 TX001_ch14_Frame Page 193 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC

P/2 FIGURE 14.9 FIGURE 14.10 ENF specimen geometry parameters. ENF test setup. unloading paths.Observe the crack tip during loading(a traveling microscope is recommended)to detect any slow,stable crack propagation prior to fast fracture.Slow crack propagation preceding fast fracture is commonly observed in ductile matrix composites and leads to a nonlinear load-displacement curve (Figure 14.11 [22]).Indicate this event on the load-deflection curve.An example of a load-deflection curve for a brittle carbon/epoxy composite is shown in Figure 14.12.For this composite,fast fracture occurred without noticeable stable crack extension,and the response curve is essentially linear up to fracture. 14.2.2 ENF Data Reduction Evaluation of the Mode II fracture toughness,Guc,requires a record of the load-displacement response,e.g.,Figures 14.11 and 14.12.Toughness values Guc(NL),Guc(vis.),and Guc(max.),referring to the loads at the onset of nonlinearity,visual stable crack extension,and maximum load,respectively, Max 800 VIS 600 Z ENF 400 L=50.8mm 200 a=27.9mm [0124 0 1.0 2.03.0 4.0 Displacement,8 Displacement,mm FIGURE 14.11 FIGURE 14.12 Schematic load-displacement curve for ENF frac- Load-deflection curve for a carbon/epoxy ture test of a ductile matrix composite.P(NL), (AS4/3501-6)ENF specimen.L=50.8 mm, P(vis.),and P(max.)denote loads at onset of non- w =25.4 mm,and a =27.9 mm. linearity,onset of visible stable crack growth,and onset of fast fracture,respectively. ©2003 by CRC Press LLC

unloading paths. Observe the crack tip during loading (a traveling microscope is recommended) to detect any slow, stable crack propagation prior to fast fracture. Slow crack propagation preceding fast fracture is commonly observed in ductile matrix composites and leads to a nonlinear load-displacement curve (Figure 14.11 [22]). Indicate this event on the load-deflection curve.An example of a load-deflection curve for a brittle carbon/epoxy composite is shown in Figure 14.12. For this composite, fast fracture occurred without noticeable stable crack extension, and the response curve is essentially linear up to fracture. 14.2.2 ENF Data Reduction Evaluation of the Mode II fracture toughness, GIIC , requires a record of the load-displacement response, e.g., Figures 14.11 and 14.12. Toughness values GIIC(NL), GIIC(vis.), and GIIC(max.), referring to the loads at the onset of nonlinearity, visual stable crack extension, and maximum load, respectively, FIGURE 14.9 ENF specimen geometry parameters. FIGURE 14.10 ENF test setup. FIGURE 14.11 Schematic load-displacement curve for ENF frac￾ture test of a ductile matrix composite. P(NL), P(vis.), and P(max.) denote loads at onset of non￾linearity, onset of visible stable crack growth, and onset of fast fracture, respectively. FIGURE 14.12 Load-deflection curve for a carbon/epoxy (AS4/3501-6) ENF specimen. L = 50.8 mm, w = 25.4 mm, and a = 27.9 mm. TX001_ch14_Frame Page 194 Saturday, September 21, 2002 5:09 AM © 2003 by CRC Press LLC