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 experimentally. 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 evaluated 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 associated 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 extension 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/polyetheretherketone (PEEK) composite. At the first loading increment, the delamination 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 extension 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 delamination 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 displacement 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 fiberbridging 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 fracture test of a ductile matrix composite. P(NL), P(vis.), and P(max.) denote loads at onset of nonlinearity, 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