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Evaluation of the accuracy of the four-point bend end-notched flexure test for mode II delamination toughness determination
Composites Science and Technology 60 (2000) 2137±2146
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Evaluation of the accuracy of the four-point bend end-notched ¯exure test for mode II delamination toughness determination Clara Schuecker 1, Barry D. Davidson * Department of Mechanical, Aerospace and Manufacturing Engineering, Syracuse University, Syracuse, NY 13244, USA Received 22 November 1999; received in revised form 9 March 2000; accepted 11 May 2000
Abstract Results are presented from an experimental study to investigate the accuracy of the four-point bend end-notched ¯exure (4ENF) test for the determination of mode II delamination toughness. In previous studies, 4ENF tests have yielded higher delamination toughnesses than the more commonly used three-point bend end-notched ¯exure (ENF) test. In a recent ®nite-element study, it was found that the higher toughnesses found by the 4ENF test cannot fully be attributed to frictional eects. This current study was performed in order to examine if the dierence between ENF and 4ENF results is due to current methods used to determine crack length and compliance during a 4ENF test. It was found that if these two parameters are measured accurately then the 4ENF test yields toughnesses similar to those obtained from ENF testing. # 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The three-point bend end-notched ¯exure (ENF) test is perhaps the most commonly used test for determining the mode II delamination toughness, GIIc, of laminated composites [1±3]. The drawback of the ENF is that crack growth is unstable and therefore only one data point per specimen can be obtained. Recently, a modi®ed version of the test, an end-notched ¯exure specimen subjected to four-point bending has been proposed [4]. Unlike the ENF, in the four-point bend end-notched ¯exure (4ENF) test, crack growth is stable under displacement control. Hence it is possible to obtain several data points from each specimen during the test and a complete resistance (R) curve can be generated from the data of just one test. Although one would expect to obtain the same value of GIIc from either the 4ENF or ENF tests, this has so far not been observed to be the case. In recent experimental studies [4±6], it has been observed that the 4ENF test produced toughnesses 8± 20% higher than those obtained from the ENF test. It has also been reported that the dierence between the * Corresponding author. Tel.: +1-315-443-4201; fax: +1-315-4439099. E-mail address: [email protected] (B.D. Davidson). 1 Visiting Research Scholar, Vienna University of Technology, Institute for Mechanical Engineering, Karlsplatz 13, A ± 1040 Vienna, Austria.
4ENF and ENF increases with increasing ratio of inner span versus outer span [5,6]. In a recent ®nite-element study, the question of whether the dierences in delamination toughness obtained by the ENF and 4ENF tests could be attributed to friction between the crack faces was investigated [7]. In this work, it was shown that the eect of friction on GIIc is slightly higher in the 4ENF than ENF con®guration, and that the eect of friction increases with span ratio. However, if data reduction is by compliance calibration, it was found that friction will increase the apparent value of GIIc by 5% or less in the 4ENF test, and by 2% or less in the ENF test. Thus, it was concluded that frictional eects were not large enough to fully account for the observed dierence in delamination toughness. As a result, it was postulated that the error might be due to inexact measuring techniques for determining crack length and compliance during the 4ENF test. In light of the above, the goal of the present work was to study the eects on GIIc of the various measurement techniques that could be used for assessing crack length and compliance during a 4ENF test. Initially, 4ENF tests were performed to determine GIIc directly from pre-implanted Te¯on inserts. The crack length and compliance data from these initiation tests were obtained in a variety of ways. These data were reduced to obtain several dierent measures of GIIc, and these results were compared to toughnesses found from ENF
0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00113-5
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tests of specimens from the same batch of material. Subsequently, 4ENF tests to determine GIIc from a propagating crack were conducted. The data from these propagation tests were also reduced by a variety of methods and the various propagation toughnesses were compared. 2. Test geometry and previous experimental procedures A schematic of the 4ENF test is presented in Fig. 1. The load is introduced via bearings onto a loading platen to which the loading pins are attached. This allows the loading platen to rotate freely about an axis perpendicular to the specimen's length and ensures that both loading pins transmit the same amount of force onto the specimen. The support pins are designed to be able to rotate about an axis parallel to the specimen's length in order to prevent uneven loading across the width of the specimen. The inner span is centered between the outer support rollers. The most accurate method to determine toughness from 4ENF test data is by the compliance calibration technique. That is, it has been shown that beam-theory and ®nite element based data reduction techniques can produce errors in toughness (Gc) as obtained from mode II bending tests [2,3]. These errors arise primarily due to the fact that it is dicult to accurately determine the ¯exural rigidity of each test specimen. Compliance calibration (CC) is a direct data reduction method that only assumes linear elastic behaviour and self-similar crack advance. As such, any errors due to uncertainties in the geometric or material properties of each test specimen are avoided. The fundamental equation used for the CC technique is [8]
Gc
P2c @C 2B @a
1
In the above, Pc is the critical load, C is the compliance, a is the crack length, B is the specimen's width, and @C/@a is the slope of the compliance vs. crack length curve at the crack length at which growth occurs. In order to employ this equation, all of these quantities must be determined before, during or after the test. In all previous studies on the 4ENF test [4±6], essentially the same testing procedure was followed. This consisted simply of loading the specimen until crack advance occurred and, as the crack advanced, periodically noting the crack length from visual measurements on both sides of the specimen. The test was continued until the crack front approached to within approximately 10 mm of the second loading pin. During the test, load and de¯ection values were continuously recorded, where de¯ection was taken to be the machine's actuator displacement. Subsequent to the test, the specimen's C vs. a curve was generated, de®ning compliance as the ratio of maximum de¯ection, max, over maximum load, Pmax, for each crack length ai Ci imax =Pimax ). Here, crack length was de®ned to be the mean of the values visually measured on the left and right sides of the specimen during the test. According to beam theory and ®nite element results [4,7], there is a linear relationship between compliance and crack length. Therefore, a linear curve ®t was used to relate compliance to crack length, and its slope yielded the specimen's toughness following Eq. (1). For propagation, the critical load can be taken as the average of all Pmax values to get an average toughness for the specimen. Alternatively, if an R-curve is desired, GIIc can be calculated from Pmax of each crack increment. Note that
Fig. 1. Schematic of the 4ENF ®xture.
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@C/@a stays constant with a because of the linear curve ®t. With this testing procedure there are three possible sources of error. First, to get the exact de¯ections for CC, the de¯ection underneath each loading pin may need to be independently measured and averaged [4,7] instead of using the test machine's actuator displacement. Otherwise, the ®xture's compliance is included in the compliance calculation of the test specimen. Although actuator displacement works well for the ENF test, it is likely that there is more ``play'' in the 4ENF ®xture because of it's greater complexity. Therefore, it is probable that errors due to this eect are larger in the 4ENF test. The second possible source of error is the measurement of crack length during the test. It is very hard to visually discern the precise location of the crack tip in shear tests, and errors in crack length will clearly aect the calculated compliance. Also the crack front will not necessarily continue to be straight as the crack advances, which will aect the validity of the derivative @C/@a. Lastly, it is unclear whether calculating compliance from only one data point (i.e. the maximum values of load and de¯ection) is suciently accurate, as opposed to using a curve-®t of the data of the loadingcurve. These issues are addressed in the following section. 3. Experimental investigation Fig. 2 shows a photograph of the 4ENF test ®xture that was used for this study. Note that the loading platen on top is free to rotate about the axis perpendicular to the specimen's length to provide equal forces at the loading pins, while the support pins rotate about the
Fig. 2. Photograph of the 4ENF ®xture.
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longitudinal axis to ensure even loading across the specimen's width. All those rotation points as well as the loading pins and the support pins are equipped with bearing arrangements to keep friction in those parts to a minimum and enable the ®xture to align itself during load-up. Extended on the left hand side a constraint can be seen, which is always placed at the uncracked end of the specimen to keep the specimen from sliding during the test. There were two geometries that were tested in the 4ENF con®guration. Referring to Fig. 1, geometry ``A'' had an inner span length of d=50.8 mm and an outer span of 2L=127 mm (span ratio d/2L=0.4), and the dimensions of geometry ``B'' were d=76.2 mm and 2L=152.4 mm (d/2L=0.5). All specimens tested were cut from the same plate of 24 ply unidirectional Hexcel IM7/8552 carbon ®ber/epoxy and had an approximate width of B=25.4 mm. A 12.7 mm thick te¯on insert was implanted in the plate during the production process to produce a mid-plane delamination. In order to investigate the three issues mentioned in the previous section, a rather lengthy test procedure was employed. First, prior to testing, the specimen's initial crack length was measured by an ultrasonic nondestructive inspection system (c-scan) using a 25 MHz transducer and a 100 MHz transient waveform digitizer. The specimen was then placed in a modi®ed test ®xture to that shown in Fig. 2. The modi®cations to the ®xture consisted of two linear variable displacement transducers (LVDTs) that made contact with the specimen beneath each loading pin. Next, the specimens were compliance calibrated at 4±5 dierent crack lengths. That is, the specimen was loaded up to one-half of the estimated critical load at several crack lengths and compliance at each crack length was calculated from the slope of the load vs. de¯ection data. This yields a C vs. a curve that can be used to calculate @C/@a, which is needed to compute Gc [cf. Eq. (1)]. The dierent crack lengths were simulated by simply shifting the specimen in the ®xture. This is the same procedure used for ENF tests and was followed in order to be able to conclusively compare initiation results from both test methods. The ®rst fracture test performed was to determine the initiation toughness, de®ned here to be that required for crack advance directly from the Te¯on insert. For this initiation test the specimen was loaded, in displacement control, until crack advance occurred. At that point, the specimen was partially unloaded and a visual measurement of crack length taken. The specimen was then fully unloaded. During the loading/unloading process, the load, actuator displacement, and displacements from the two LVDTs were continuously recorded. Following this procedure, the specimen was removed from the ®xture and its crack length was measured using the c-scan system. All initiation tests were performed at a crack length of a=53.3 mm. This length was chosen because it leaves
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enough space between the loading pin and the crack tip to rule out any unwanted eects from the compressive stresses of the loading pin. When testing from the insert the crack typically ``jumped'' about 12 mm. This occurred due to the fact that the toughness as measured from the insert was higher than that required to propagate the delamination from a mode II starter crack. This dierence in mode II toughness between precracked and nonprecracked specimens is similar to that found in other graphite/epoxies [2, 4±6, 9] and is discussed further in a subsequent section. Because of this crack jump, those specimens tested in geometry ``A'' were shifted when reinserted into the ®xture such that the crack length was again 53.3 mm. This was necessary in order to have enough room for at least 6 crack propagations (each of approximately 2.5 mm). For geometry ``B'' it was not required to shift the specimen because of its larger inner span. Following the above, propagation tests were conducted in a similar fashion. The only dierence in these tests was that crack propagation was always stable and there were never any signi®cant crack jumps. As will be shown subsequently, this stable growth occurred because the mode II toughness was found to be relatively unaected by increasing amounts of crack advance, but stable growth will also be observed in specimens that show a resistance curve [4±6]. After each increment of growth, the specimen was unloaded completely, the visually observed crack length was noted and a c-scan was performed. The specimen was then returned to the ®xture and the process repeated. Markings on the specimen, as well as the left-side restraint visible in Fig. 2, ensured that the specimen was replaced in the ®xture in the same position after each c-scan. Following the test, the specimen's de¯ection, , was determined two ways: (1) from the testing machine's actuator displacement, and (2) from the average of the two LVDT readings, i.e. [4]
wL wR 2
2
where wL and wR represent the de¯ection of the specimen underneath the left and right loading pin, respectively. The specimen's crack length could also be determined two ways: (1) from the visual measurements, or (2) from the c-scan results. Finally, compliance could be de®ned as the ratio of maximum values of displacement and load (max /Pmax), or as the slope of the load vs. de¯ection curve. This leads to eight possible permutations to generate the C vs. a curve from the collected data. All of these are expected to be linear relationships. Thus, as in previous studies [4±6], a linear curve ®t of the form C C0 C1 a
3
was used to calculate compliance as a function of crack length for each permutation. Substituting Eq. (3) into Eq. (1) yields: G4ENF IIc
P2c C1 2B
4
In the above, we have made use of the previous result [4,7] that the 4ENF is a pure mode II test. Hence, the data from the 4ENF tests may be reduced to produce eight dierent values of GIIc. Of these, the combination of the crack length measured by the c-scan, and the compliance as determined from the slope of the loading curve as recorded by the two LVDTs, was considered to provide the most accurate result. In order to compare toughness results, a series of ENF tests were also conducted. In these tests, crack advance occurred directly from the preimplanted Te¯on insert. The ®xture used for the ENF tests is shown in Ref. 3. It is similar to that shown in Figs. 1 and 2, except that the upper part contains only one loading pin at its centre. The compliance versus crack length curve for each specimen was determined prior to fracture testing by loading the specimen to approximately 50% of the predicted critical load at ®ve dierent crack lengths. The specimen's de¯ection was measured by actuator displacement only, and compliance at each crack length was calculated from the slope of the appropriate load versus center-point de¯ection curve. The compliance versus crack length results were then ®t with a third order polynomial of the form[3,9]: C C0 C1 a C2 a2 C3 a3
5
Substituting Eq. (5) into Eq. (1) yields the mode II toughness as obtained by the ENF test as: GENF IIc
P2c ÿ C1 2C2 a 3C3 a2 2B
6
The ENF tests used for comparison were conducted on specimens from the same batch of material that was used for the 4ENF tests. Only initiation tests were performed with a span length of 2L=127 mm and a crack length of a=31.8 mm. 4. Results 4.1. Initiation As described in the previous section, the same procedure was used for ENF and 4ENF tests in order to compare initiation toughnesses from both test methods. That is, the compliance versus crack length relation of each specimen was determined, by appropriately shifting
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the specimen, prior to the fracture test. Compliance was determined as the slope of the load vs. de¯ection curve at each crack length. For determining toughness, the peak value of load that occurred during the test was taken as the critical load. Fig. 3 shows a summary of these results. For each of the two 4ENF geometries there are two results: the ®lled bars labelled ``4ENF LVDT'' represent the mean values obtained using data recorded by the two LVDTs, while the white bars denoted ``4ENF AD'' show the mean values obtained from actuator displacement. The error bars show the 1 normal standard deviations of a sample of 5±7 specimens. First, looking at only the 4ENF results, it is seen that the actuator displacement gives higher values of GIIc than the LVDTs for both geometries, i.e. for geometry ``A'' a dierence of 3.4% is observed between the LVDT and actuator mean values, and for geometry ``B'' the dierence is 7.0%. Comparing 4ENF to ENF results shows that those from 4ENF are 2.0±12.7% higher. The closest 4ENF results to the ENF values are from geometry ``B'' (d/2L=0.5) using the LVDT data. The mean toughness data from these tests is only 1.96% higher than that obtained from the ENF tests. It is interesting to note that the scatter in toughness data is signi®cantly less for all 4ENF tests than it is for the ENF. Considering the large scatter in the ENF, the results from this ®gure indicate that if both tests are run in the same fashion, then both give the same result, regardless of which geometry is used or which method is used to determine de¯ection. It is also interesting to note that test geometry ``B'' with the larger span ratio yields slightly lower values of toughness than geometry ``A''. This is in contrast to the results of experiments presented in Ref. 6, where tests from a span
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ratio of 0.5 gave 9% higher results than those from a span ratio of 0.4. Considering the results of Ref. 7, which showed that frictional eects are slightly larger in geometry ``B'' than in ``A,'' these results indicate that the dierent frictional eects in the two geometries are negligible in comparison to the scatter of the data. This agrees with the conclusion of Ref. 7. In all previous studies using the 4ENF test, compliance calibration was not performed prior to testing. Rather, as previously described, the slope of the compliance vs. crack length (@C/@a) curve was obtained from data taken during the test. Since those specimens tested in geometry ``A'' were shifted after testing from the insert, the C vs. a curve from those propagation tests does not re¯ect that which occurred due to delamination growth during the initiation tests. Consequently, it was only possible to investigate the applicability of the procedure used in previous studies for geometry ``B''. The outcome is shown in Fig. 4. The labelling used in Fig. 4 is as follows: LVDT AD
Ð data recorded from LVDT output Ð data recorded from actuator displacement load curve Ð compliance calculated from the loading curve up to approx. 12 Pc max Ð compliance calculated from maximum values of load and de¯ection prior Ð data obtained prior to testing by compliance calibration scan Ð crack length measured by c-scan vis. Ð crack length measured from visual observation
Fig. 3. Initiation toughnesses from ENF and 4ENF, Geometries ``A'' and ``B''.
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So, for example, the ®rst column marked ``LVDT load curve Ð prior'' is the same as seen in Fig. 3 as ``4ENF LVDT'' for geometry ``B'', and is considered to be the most accurate of the 4ENF results. Note that this column has the least scatter of all data reduction techniques. Column number 4, ``AD load curve Ð prior'', also appears in Fig. 3, and is the toughness obtained with compliance calibration using actuator displacement. Here the error compared to the ®rst column, where the LVDTs were used, is over 7% which is the highest error of all methods shown here. Examining the
®nal column of Fig. 4, ``AD max Ð vis.'', which represents the procedure used in all previous 4ENF studies, it is observed that this method yields virtually the same result as column number one. This indicates that in our con®guration, all the possible errors (play in the ®xture, determination of C and imprecise measurement of a) apparently cancel each other out. However, we point out that the same operator in our study did both the visual crack length measurements and operated the cscan. Thus, there was likely a great deal of ``learning'' that occurred, because each time a crack length was
Fig. 4. Initiation toughnesses from 4ENF Geometry ``B'' with various measuring and data reduction techniques.
Fig. 5. Load-de¯ection plot of 4ENF test of Geometry ``B''.
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measured visually, there was immediate feedback on the accuracy of the measurement from the subsequent cscan result. It is very possible that, as a result of this learning, the visual crack length measurements made in this study were signi®cantly more accurate than those that would be made in the absence of the c-scan feedback loop. Finally, we point out that for all c-scan images in this and other portions of the study, crack fronts were relatively straight across the specimen's width. 4.2. Propagation Before presenting results from the propagation tests, it is necessary to explain how the critical load, Pc, was determined. Fig. 5 shows a typical load-de¯ection plot from a complete test; this speci®c test was conducted in geometry ``B''. For all our specimens, the initiation toughness was higher than the propagation toughness. Thus, there was always some unstable growth during the initial crack increment during which time there was a drop in the load. Afterwards, crack growth was always stable and the load at which the crack advanced remained nearly constant. If desired, a complete Rcurve could be generated from this test data, where the maximum load of each crack increment would be used to calculate GIIc following Eq. (1). However, since the critical load stayed almost the same for each propagation, there would be little variation in GIIc with a. Consequently, a mean critical load from all crack propagations was determined and was used to calculate an average GIIc for each specimen. This method is equivalent to plotting the results for GIIc vs. a and then reporting propagation toughness to be the mean value
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from all points excluding that for initiation directly from the Te¯on insert. This would seem to be a more expedient method for reducing the data for those specimens where the fracture load remains constant (and which therefore show no appreciable toughening with crack advance). Considering Eq. (1), this means that, for each specimen, the toughness is directly proportional to the slope of the compliance vs. crack length curve. Therefore, the error between the dierent ways of determining GIIc depends only on @C/@a. Fig. 6 presents a typical graph of compliance vs. crack length. Here, six sets of data points are displayed. The labelling is the same as for Fig. 4. Each set of data points has been ®t with a straight line. The most apparent observation is that all compliance curves using actuator displacement are higher than those using the LVDTs. What is important, however, is not the compliance curve itself but its derivative @C/@a. There is only a moderate eect on slope from the dierent methods used. Of the six curves, the two where compliance was determined from the loading curves and a visual crack length measurement have a slightly lower slope than the other four. Note that, for the two curves where crack length was measured by c-scan, more data points appear to fall on the best-®t line than for the curves where crack length was measured visually. This is likely a result of the more accurate crack length assessments by the former method. Figs. 7 and 8 present propagation toughnesses for geometries ``A'' and ``B'', respectively, as obtained by the various methods of data reduction. The labelling convention in these ®gures is the same as used in Figs. 4 and 6. The ®rst column, where the compliance was obtained from the slope of the load versus LVDT data,
Fig. 6. Typical C vs. a curves from a 4ENF test of Geometry ``B''.
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and the crack length was measured by c-scan, is considered to provide the most accurate results. The maximum dierence between the mean value of toughness as provided by this method of data reduction and any of the others considered is 4.9% in Fig. 7 and 1.2% in Fig. 8. The method of the last column, which is the method used in previous studies, yields a mean toughness that is only 1.2% dierent from the method of column 1 in Fig. 7, and only 0.5% dierent in Fig. 8. Thus, similar to the results for initiation, in our propagation studies, all of the errors that may have occurred when the maximum load versus actuator displacement is used for compliance, and crack length is measured visually, apparently cancelled each other out in the determination of ERR. Considering the results shown in Figs. 3, 7 and 8, initiation and propagation toughnesses as found through 4ENF testing can be compared. To make this comparison, consider toughness values as obtained from the compliance of the load versus LVDT displacement results with crack length measured by c-scan. Comparing the ®rst shaded column of Fig. 7 to the shaded column in Fig. 3 corresponding to Geometry A, it is found that this geometry (d/2L=0.4) produces a propagation toughness that is an average of 30% lower than the initiation toughness. For Geometry B, comparing the ®rst shaded column of Fig. 8 to the appropriate shaded column of Fig. 3, it is observed that the propagation toughnesses for this geometry (d/2L=0.5) is 21% lower than the initiation toughness. Similar to that found in previous studies [2,4±6,9], these results indicate that there can be a rather large arti®cial increase in GIIc when testing directly from the insert.
This supports the necessity to perform tests for delamination toughness on precracked specimens. Considering the results of Ref. 10, it is preferable that precracking be performed in mode II, which is easily accomplished using the 4ENF test. 4.3. Discussion The results of Fig. 3 indicate that the toughness values as obtained by the 4ENF correlate well with those by ENF, regardless of data reduction method. Also, for both initiation and propagation, Figs. 4, 7 and 8 show that all data reduction methods that were evaluated produced GIIc values that vary by 7% or less from the method considered to be the most accurate. However, the results from this study cannot automatically be applied to other testing rigs and testing labs for two primary reasons. First, the results one obtains for compliance are certainly a function of the test ®xture, test machine, and possibly data acquisition system that is used. Secondly, the same operator in our tests performed both visual crack length assessments and c-scan measurements. Thus, there was likely signi®cant learning that occurred during this process, and it is not clear that an operator who does not have access to c-scan corroboration will make visual crack length assessments to the same accuracy as was obtained in this study. With the above restrictions in mind, we turn our attention to the results from this study that can be generally applied. Examining Figs. 3, 7 and 8, if the crack length is measured in the same manner, then there is no consistent trend between the dierence in GIIc as obtained by the dierent methods of measuring compliance. This
Fig. 7. Propagation toughnesses from 4ENF tests of Geometry ``A''.
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Fig. 8. Propagation toughnesses from 4ENF tests of Geometry ``B''.
should generally be the case, i.e. no real dierence in results, providing that there is minimal amount of free play in the ®xture, the testing machine and ®xture are sti as compared to the specimen, and the specimen does not display signi®cant nonlinearities prior to crack advance. However, the ``allowable'' amounts of nonlinearity from the various sources is hard to quantify, and it would likely be best to avoid this source of error by always obtaining compliance from the slope of the load versus de¯ection plot. This means that a test with a propagating crack would need to be run in a loadunload-load manner, similar to that done herein. While that will slightly increase testing times, it will undoubtedly improve the accuracy of the compliance data. Furthermore, it will allow ample time for crack lengths to be measured on both sides of the specimen, thereby improving the accuracy of the crack length data as well. Regarding the means of measuring crack length, it would seem that the best way of assessing accuracy, short of repeating the type of study that was done herein, would be to perform compliance calibration before testing 4ENF specimens in the same manner as is done for the ENF test. A comparison of GIIc found from the ``prior'' compliance calibration to that obtained from crack length measurements taken during the test would provide immediate feedback about the accuracy of the visual crack length measurements. If poor correlation were obtained, then it would be best to increase the number of crack length measurements taken during a test. We have found that some visual crack length estimates are long and some are short, and the greater the sampling, the greater the probability that the mean curve will converge to the true result.
5. Conclusions A series of 4ENF tests were conducted and de¯ection, compliance and crack length were measured by dierent techniques. These dierent measures were then used in a compliance calibration method of obtaining GIIc and the results compared. Also, for delamination growth directly from the Te¯on insert, values of GIIc as obtained by the 4ENF and the various measurement techniques were compared to those from ENF tests. The results of the various comparisons were used to draw some general conclusions about the most accurate means of reducing data from a 4ENF test and to assess whether ENF and 4ENF tests produce the same toughness values. The results of this study indicate that, if compliance and crack length are measured accurately, then 4ENF and ENF tests will produce essentially the same values for toughness. It is possible that errors in measuring these parameters contributed to the dierences reported in earlier studies. To reduce possible errors in future studies, it is recommended that compliance in the 4ENF test be obtained from the slope of the load versus de¯ection plot. This means that tests are conducted in a load-unload-reload manner, similar to that done herein. The unloading is performed after each noticeable increment of crack advance, and the new crack length is measured with the specimen subjected to a low load leg (50% of Pc) and the crack arrested. In addition, it has been pointed out that a simple means of assessing the accuracy of the crack length measurements taken during a 4ENF test is to perform compliance calibration before testing the 4ENF specimens in the same manner as is done for the ENF test. A comparison of GIIc found
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from the ``prior'' compliance calibration to that obtained from crack length measurements taken during the test will provide immediate feedback about the accuracy of the visual crack length measurements. If poor correlation is obtained, then improved accuracy may be obtained by increasing the number of crack length measurements taken during a test.
References [1] Carlsson LA, Gillespie Jr JW, Pipes RB. On the analysis and design of the end notched ¯exure (ENF) specimen for mode II testing. Journal of Composite Materials 1986;20:594±604. [2] O'Brien TK, Murri GB, Salpekar SA. Interlaminar shear fracture toughness and fatigue thresholds for composite materials. In: Lagace PA, editior. Composite materials: fatigue and fracture, second volume, ASTM STP 1012, American Society for Testing and Materials, 1989, pp. 222±50. [3] Davidson BD, Altonen CS, Polaha JJ. Eect of stacking sequence on delamination toughness and delamination growth behavior in composite end-notched ¯exure specimens. In: Deo RB, Sa CR, editors. Composite Materials: Testing and Design (Twelfth Volume), ASTM STP 1274, American Society for Testing and Materials, 1996, pp. 393±413.
[4] Martin RH, Davidson BD. Mode II fracture toughness evaluation using a four point bend end notched ¯exure test. Plastics, Rubber and Composites 1999;28(8):401±6. [5] Chin RJM. Fracture testing of composite materials. BEng Project Report, Faculty of Engineering, University of Hertfordshire, May 1998. [6] Martin RH, Elms T, Bowron S. Characterization of mode II delamination using the 4ENF. Proceedings of the 4th European Conference on Composite Materials: Testing and Standardization, Institute of Materials, London, 1998. p. 161±70. [7] Schuecker C, Davidson BD. Eect of friction on the perceived mode II delamination toughness from three- and four-point bend end-notched ¯exure tests. In: Grant PE, Rousseau CQ, editors. Composite Structures: Theory and Practice, ASTM STP 1383, American Society for Testing and Materials, 2000, pp. 334± 344. [8] Broek D. Elementary engineering fracture mechanics, 4th Edition, Kluwer Academic Publishers, Inc., 1986. [9] Polaha JJ, Davidson BD, Hudson RC, Pieracci A. Eects of mode ratio, ply orientation and precracking on the delamination toughness of a laminated composite. Journal of Reinforced Plastics and Composites 1996;15(2):141±73. [10] Davidson BD, Koudela KL. In¯uences of the mode mix of precracking on the delamination toughness of laminated composites. Journal of Reinforced Plastics and Composites 1999; 18(15):1408±14.
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Evaluation of the accuracy of the four-point bend end-notched ¯exure test for mode II delamination toughness determination Clara Schuecker 1, Barry D. Davidson * Department of Mechanical, Aerospace and Manufacturing Engineering, Syracuse University, Syracuse, NY 13244, USA Received 22 November 1999; received in revised form 9 March 2000; accepted 11 May 2000
Abstract Results are presented from an experimental study to investigate the accuracy of the four-point bend end-notched ¯exure (4ENF) test for the determination of mode II delamination toughness. In previous studies, 4ENF tests have yielded higher delamination toughnesses than the more commonly used three-point bend end-notched ¯exure (ENF) test. In a recent ®nite-element study, it was found that the higher toughnesses found by the 4ENF test cannot fully be attributed to frictional eects. This current study was performed in order to examine if the dierence between ENF and 4ENF results is due to current methods used to determine crack length and compliance during a 4ENF test. It was found that if these two parameters are measured accurately then the 4ENF test yields toughnesses similar to those obtained from ENF testing. # 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The three-point bend end-notched ¯exure (ENF) test is perhaps the most commonly used test for determining the mode II delamination toughness, GIIc, of laminated composites [1±3]. The drawback of the ENF is that crack growth is unstable and therefore only one data point per specimen can be obtained. Recently, a modi®ed version of the test, an end-notched ¯exure specimen subjected to four-point bending has been proposed [4]. Unlike the ENF, in the four-point bend end-notched ¯exure (4ENF) test, crack growth is stable under displacement control. Hence it is possible to obtain several data points from each specimen during the test and a complete resistance (R) curve can be generated from the data of just one test. Although one would expect to obtain the same value of GIIc from either the 4ENF or ENF tests, this has so far not been observed to be the case. In recent experimental studies [4±6], it has been observed that the 4ENF test produced toughnesses 8± 20% higher than those obtained from the ENF test. It has also been reported that the dierence between the * Corresponding author. Tel.: +1-315-443-4201; fax: +1-315-4439099. E-mail address: [email protected] (B.D. Davidson). 1 Visiting Research Scholar, Vienna University of Technology, Institute for Mechanical Engineering, Karlsplatz 13, A ± 1040 Vienna, Austria.
4ENF and ENF increases with increasing ratio of inner span versus outer span [5,6]. In a recent ®nite-element study, the question of whether the dierences in delamination toughness obtained by the ENF and 4ENF tests could be attributed to friction between the crack faces was investigated [7]. In this work, it was shown that the eect of friction on GIIc is slightly higher in the 4ENF than ENF con®guration, and that the eect of friction increases with span ratio. However, if data reduction is by compliance calibration, it was found that friction will increase the apparent value of GIIc by 5% or less in the 4ENF test, and by 2% or less in the ENF test. Thus, it was concluded that frictional eects were not large enough to fully account for the observed dierence in delamination toughness. As a result, it was postulated that the error might be due to inexact measuring techniques for determining crack length and compliance during the 4ENF test. In light of the above, the goal of the present work was to study the eects on GIIc of the various measurement techniques that could be used for assessing crack length and compliance during a 4ENF test. Initially, 4ENF tests were performed to determine GIIc directly from pre-implanted Te¯on inserts. The crack length and compliance data from these initiation tests were obtained in a variety of ways. These data were reduced to obtain several dierent measures of GIIc, and these results were compared to toughnesses found from ENF
0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00113-5
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tests of specimens from the same batch of material. Subsequently, 4ENF tests to determine GIIc from a propagating crack were conducted. The data from these propagation tests were also reduced by a variety of methods and the various propagation toughnesses were compared. 2. Test geometry and previous experimental procedures A schematic of the 4ENF test is presented in Fig. 1. The load is introduced via bearings onto a loading platen to which the loading pins are attached. This allows the loading platen to rotate freely about an axis perpendicular to the specimen's length and ensures that both loading pins transmit the same amount of force onto the specimen. The support pins are designed to be able to rotate about an axis parallel to the specimen's length in order to prevent uneven loading across the width of the specimen. The inner span is centered between the outer support rollers. The most accurate method to determine toughness from 4ENF test data is by the compliance calibration technique. That is, it has been shown that beam-theory and ®nite element based data reduction techniques can produce errors in toughness (Gc) as obtained from mode II bending tests [2,3]. These errors arise primarily due to the fact that it is dicult to accurately determine the ¯exural rigidity of each test specimen. Compliance calibration (CC) is a direct data reduction method that only assumes linear elastic behaviour and self-similar crack advance. As such, any errors due to uncertainties in the geometric or material properties of each test specimen are avoided. The fundamental equation used for the CC technique is [8]
Gc
P2c @C 2B @a
1
In the above, Pc is the critical load, C is the compliance, a is the crack length, B is the specimen's width, and @C/@a is the slope of the compliance vs. crack length curve at the crack length at which growth occurs. In order to employ this equation, all of these quantities must be determined before, during or after the test. In all previous studies on the 4ENF test [4±6], essentially the same testing procedure was followed. This consisted simply of loading the specimen until crack advance occurred and, as the crack advanced, periodically noting the crack length from visual measurements on both sides of the specimen. The test was continued until the crack front approached to within approximately 10 mm of the second loading pin. During the test, load and de¯ection values were continuously recorded, where de¯ection was taken to be the machine's actuator displacement. Subsequent to the test, the specimen's C vs. a curve was generated, de®ning compliance as the ratio of maximum de¯ection, max, over maximum load, Pmax, for each crack length ai Ci imax =Pimax ). Here, crack length was de®ned to be the mean of the values visually measured on the left and right sides of the specimen during the test. According to beam theory and ®nite element results [4,7], there is a linear relationship between compliance and crack length. Therefore, a linear curve ®t was used to relate compliance to crack length, and its slope yielded the specimen's toughness following Eq. (1). For propagation, the critical load can be taken as the average of all Pmax values to get an average toughness for the specimen. Alternatively, if an R-curve is desired, GIIc can be calculated from Pmax of each crack increment. Note that
Fig. 1. Schematic of the 4ENF ®xture.
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@C/@a stays constant with a because of the linear curve ®t. With this testing procedure there are three possible sources of error. First, to get the exact de¯ections for CC, the de¯ection underneath each loading pin may need to be independently measured and averaged [4,7] instead of using the test machine's actuator displacement. Otherwise, the ®xture's compliance is included in the compliance calculation of the test specimen. Although actuator displacement works well for the ENF test, it is likely that there is more ``play'' in the 4ENF ®xture because of it's greater complexity. Therefore, it is probable that errors due to this eect are larger in the 4ENF test. The second possible source of error is the measurement of crack length during the test. It is very hard to visually discern the precise location of the crack tip in shear tests, and errors in crack length will clearly aect the calculated compliance. Also the crack front will not necessarily continue to be straight as the crack advances, which will aect the validity of the derivative @C/@a. Lastly, it is unclear whether calculating compliance from only one data point (i.e. the maximum values of load and de¯ection) is suciently accurate, as opposed to using a curve-®t of the data of the loadingcurve. These issues are addressed in the following section. 3. Experimental investigation Fig. 2 shows a photograph of the 4ENF test ®xture that was used for this study. Note that the loading platen on top is free to rotate about the axis perpendicular to the specimen's length to provide equal forces at the loading pins, while the support pins rotate about the
Fig. 2. Photograph of the 4ENF ®xture.
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longitudinal axis to ensure even loading across the specimen's width. All those rotation points as well as the loading pins and the support pins are equipped with bearing arrangements to keep friction in those parts to a minimum and enable the ®xture to align itself during load-up. Extended on the left hand side a constraint can be seen, which is always placed at the uncracked end of the specimen to keep the specimen from sliding during the test. There were two geometries that were tested in the 4ENF con®guration. Referring to Fig. 1, geometry ``A'' had an inner span length of d=50.8 mm and an outer span of 2L=127 mm (span ratio d/2L=0.4), and the dimensions of geometry ``B'' were d=76.2 mm and 2L=152.4 mm (d/2L=0.5). All specimens tested were cut from the same plate of 24 ply unidirectional Hexcel IM7/8552 carbon ®ber/epoxy and had an approximate width of B=25.4 mm. A 12.7 mm thick te¯on insert was implanted in the plate during the production process to produce a mid-plane delamination. In order to investigate the three issues mentioned in the previous section, a rather lengthy test procedure was employed. First, prior to testing, the specimen's initial crack length was measured by an ultrasonic nondestructive inspection system (c-scan) using a 25 MHz transducer and a 100 MHz transient waveform digitizer. The specimen was then placed in a modi®ed test ®xture to that shown in Fig. 2. The modi®cations to the ®xture consisted of two linear variable displacement transducers (LVDTs) that made contact with the specimen beneath each loading pin. Next, the specimens were compliance calibrated at 4±5 dierent crack lengths. That is, the specimen was loaded up to one-half of the estimated critical load at several crack lengths and compliance at each crack length was calculated from the slope of the load vs. de¯ection data. This yields a C vs. a curve that can be used to calculate @C/@a, which is needed to compute Gc [cf. Eq. (1)]. The dierent crack lengths were simulated by simply shifting the specimen in the ®xture. This is the same procedure used for ENF tests and was followed in order to be able to conclusively compare initiation results from both test methods. The ®rst fracture test performed was to determine the initiation toughness, de®ned here to be that required for crack advance directly from the Te¯on insert. For this initiation test the specimen was loaded, in displacement control, until crack advance occurred. At that point, the specimen was partially unloaded and a visual measurement of crack length taken. The specimen was then fully unloaded. During the loading/unloading process, the load, actuator displacement, and displacements from the two LVDTs were continuously recorded. Following this procedure, the specimen was removed from the ®xture and its crack length was measured using the c-scan system. All initiation tests were performed at a crack length of a=53.3 mm. This length was chosen because it leaves
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enough space between the loading pin and the crack tip to rule out any unwanted eects from the compressive stresses of the loading pin. When testing from the insert the crack typically ``jumped'' about 12 mm. This occurred due to the fact that the toughness as measured from the insert was higher than that required to propagate the delamination from a mode II starter crack. This dierence in mode II toughness between precracked and nonprecracked specimens is similar to that found in other graphite/epoxies [2, 4±6, 9] and is discussed further in a subsequent section. Because of this crack jump, those specimens tested in geometry ``A'' were shifted when reinserted into the ®xture such that the crack length was again 53.3 mm. This was necessary in order to have enough room for at least 6 crack propagations (each of approximately 2.5 mm). For geometry ``B'' it was not required to shift the specimen because of its larger inner span. Following the above, propagation tests were conducted in a similar fashion. The only dierence in these tests was that crack propagation was always stable and there were never any signi®cant crack jumps. As will be shown subsequently, this stable growth occurred because the mode II toughness was found to be relatively unaected by increasing amounts of crack advance, but stable growth will also be observed in specimens that show a resistance curve [4±6]. After each increment of growth, the specimen was unloaded completely, the visually observed crack length was noted and a c-scan was performed. The specimen was then returned to the ®xture and the process repeated. Markings on the specimen, as well as the left-side restraint visible in Fig. 2, ensured that the specimen was replaced in the ®xture in the same position after each c-scan. Following the test, the specimen's de¯ection, , was determined two ways: (1) from the testing machine's actuator displacement, and (2) from the average of the two LVDT readings, i.e. [4]
wL wR 2
2
where wL and wR represent the de¯ection of the specimen underneath the left and right loading pin, respectively. The specimen's crack length could also be determined two ways: (1) from the visual measurements, or (2) from the c-scan results. Finally, compliance could be de®ned as the ratio of maximum values of displacement and load (max /Pmax), or as the slope of the load vs. de¯ection curve. This leads to eight possible permutations to generate the C vs. a curve from the collected data. All of these are expected to be linear relationships. Thus, as in previous studies [4±6], a linear curve ®t of the form C C0 C1 a
3
was used to calculate compliance as a function of crack length for each permutation. Substituting Eq. (3) into Eq. (1) yields: G4ENF IIc
P2c C1 2B
4
In the above, we have made use of the previous result [4,7] that the 4ENF is a pure mode II test. Hence, the data from the 4ENF tests may be reduced to produce eight dierent values of GIIc. Of these, the combination of the crack length measured by the c-scan, and the compliance as determined from the slope of the loading curve as recorded by the two LVDTs, was considered to provide the most accurate result. In order to compare toughness results, a series of ENF tests were also conducted. In these tests, crack advance occurred directly from the preimplanted Te¯on insert. The ®xture used for the ENF tests is shown in Ref. 3. It is similar to that shown in Figs. 1 and 2, except that the upper part contains only one loading pin at its centre. The compliance versus crack length curve for each specimen was determined prior to fracture testing by loading the specimen to approximately 50% of the predicted critical load at ®ve dierent crack lengths. The specimen's de¯ection was measured by actuator displacement only, and compliance at each crack length was calculated from the slope of the appropriate load versus center-point de¯ection curve. The compliance versus crack length results were then ®t with a third order polynomial of the form[3,9]: C C0 C1 a C2 a2 C3 a3
5
Substituting Eq. (5) into Eq. (1) yields the mode II toughness as obtained by the ENF test as: GENF IIc
P2c ÿ C1 2C2 a 3C3 a2 2B
6
The ENF tests used for comparison were conducted on specimens from the same batch of material that was used for the 4ENF tests. Only initiation tests were performed with a span length of 2L=127 mm and a crack length of a=31.8 mm. 4. Results 4.1. Initiation As described in the previous section, the same procedure was used for ENF and 4ENF tests in order to compare initiation toughnesses from both test methods. That is, the compliance versus crack length relation of each specimen was determined, by appropriately shifting
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the specimen, prior to the fracture test. Compliance was determined as the slope of the load vs. de¯ection curve at each crack length. For determining toughness, the peak value of load that occurred during the test was taken as the critical load. Fig. 3 shows a summary of these results. For each of the two 4ENF geometries there are two results: the ®lled bars labelled ``4ENF LVDT'' represent the mean values obtained using data recorded by the two LVDTs, while the white bars denoted ``4ENF AD'' show the mean values obtained from actuator displacement. The error bars show the 1 normal standard deviations of a sample of 5±7 specimens. First, looking at only the 4ENF results, it is seen that the actuator displacement gives higher values of GIIc than the LVDTs for both geometries, i.e. for geometry ``A'' a dierence of 3.4% is observed between the LVDT and actuator mean values, and for geometry ``B'' the dierence is 7.0%. Comparing 4ENF to ENF results shows that those from 4ENF are 2.0±12.7% higher. The closest 4ENF results to the ENF values are from geometry ``B'' (d/2L=0.5) using the LVDT data. The mean toughness data from these tests is only 1.96% higher than that obtained from the ENF tests. It is interesting to note that the scatter in toughness data is signi®cantly less for all 4ENF tests than it is for the ENF. Considering the large scatter in the ENF, the results from this ®gure indicate that if both tests are run in the same fashion, then both give the same result, regardless of which geometry is used or which method is used to determine de¯ection. It is also interesting to note that test geometry ``B'' with the larger span ratio yields slightly lower values of toughness than geometry ``A''. This is in contrast to the results of experiments presented in Ref. 6, where tests from a span
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ratio of 0.5 gave 9% higher results than those from a span ratio of 0.4. Considering the results of Ref. 7, which showed that frictional eects are slightly larger in geometry ``B'' than in ``A,'' these results indicate that the dierent frictional eects in the two geometries are negligible in comparison to the scatter of the data. This agrees with the conclusion of Ref. 7. In all previous studies using the 4ENF test, compliance calibration was not performed prior to testing. Rather, as previously described, the slope of the compliance vs. crack length (@C/@a) curve was obtained from data taken during the test. Since those specimens tested in geometry ``A'' were shifted after testing from the insert, the C vs. a curve from those propagation tests does not re¯ect that which occurred due to delamination growth during the initiation tests. Consequently, it was only possible to investigate the applicability of the procedure used in previous studies for geometry ``B''. The outcome is shown in Fig. 4. The labelling used in Fig. 4 is as follows: LVDT AD
Ð data recorded from LVDT output Ð data recorded from actuator displacement load curve Ð compliance calculated from the loading curve up to approx. 12 Pc max Ð compliance calculated from maximum values of load and de¯ection prior Ð data obtained prior to testing by compliance calibration scan Ð crack length measured by c-scan vis. Ð crack length measured from visual observation
Fig. 3. Initiation toughnesses from ENF and 4ENF, Geometries ``A'' and ``B''.
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So, for example, the ®rst column marked ``LVDT load curve Ð prior'' is the same as seen in Fig. 3 as ``4ENF LVDT'' for geometry ``B'', and is considered to be the most accurate of the 4ENF results. Note that this column has the least scatter of all data reduction techniques. Column number 4, ``AD load curve Ð prior'', also appears in Fig. 3, and is the toughness obtained with compliance calibration using actuator displacement. Here the error compared to the ®rst column, where the LVDTs were used, is over 7% which is the highest error of all methods shown here. Examining the
®nal column of Fig. 4, ``AD max Ð vis.'', which represents the procedure used in all previous 4ENF studies, it is observed that this method yields virtually the same result as column number one. This indicates that in our con®guration, all the possible errors (play in the ®xture, determination of C and imprecise measurement of a) apparently cancel each other out. However, we point out that the same operator in our study did both the visual crack length measurements and operated the cscan. Thus, there was likely a great deal of ``learning'' that occurred, because each time a crack length was
Fig. 4. Initiation toughnesses from 4ENF Geometry ``B'' with various measuring and data reduction techniques.
Fig. 5. Load-de¯ection plot of 4ENF test of Geometry ``B''.
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measured visually, there was immediate feedback on the accuracy of the measurement from the subsequent cscan result. It is very possible that, as a result of this learning, the visual crack length measurements made in this study were signi®cantly more accurate than those that would be made in the absence of the c-scan feedback loop. Finally, we point out that for all c-scan images in this and other portions of the study, crack fronts were relatively straight across the specimen's width. 4.2. Propagation Before presenting results from the propagation tests, it is necessary to explain how the critical load, Pc, was determined. Fig. 5 shows a typical load-de¯ection plot from a complete test; this speci®c test was conducted in geometry ``B''. For all our specimens, the initiation toughness was higher than the propagation toughness. Thus, there was always some unstable growth during the initial crack increment during which time there was a drop in the load. Afterwards, crack growth was always stable and the load at which the crack advanced remained nearly constant. If desired, a complete Rcurve could be generated from this test data, where the maximum load of each crack increment would be used to calculate GIIc following Eq. (1). However, since the critical load stayed almost the same for each propagation, there would be little variation in GIIc with a. Consequently, a mean critical load from all crack propagations was determined and was used to calculate an average GIIc for each specimen. This method is equivalent to plotting the results for GIIc vs. a and then reporting propagation toughness to be the mean value
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from all points excluding that for initiation directly from the Te¯on insert. This would seem to be a more expedient method for reducing the data for those specimens where the fracture load remains constant (and which therefore show no appreciable toughening with crack advance). Considering Eq. (1), this means that, for each specimen, the toughness is directly proportional to the slope of the compliance vs. crack length curve. Therefore, the error between the dierent ways of determining GIIc depends only on @C/@a. Fig. 6 presents a typical graph of compliance vs. crack length. Here, six sets of data points are displayed. The labelling is the same as for Fig. 4. Each set of data points has been ®t with a straight line. The most apparent observation is that all compliance curves using actuator displacement are higher than those using the LVDTs. What is important, however, is not the compliance curve itself but its derivative @C/@a. There is only a moderate eect on slope from the dierent methods used. Of the six curves, the two where compliance was determined from the loading curves and a visual crack length measurement have a slightly lower slope than the other four. Note that, for the two curves where crack length was measured by c-scan, more data points appear to fall on the best-®t line than for the curves where crack length was measured visually. This is likely a result of the more accurate crack length assessments by the former method. Figs. 7 and 8 present propagation toughnesses for geometries ``A'' and ``B'', respectively, as obtained by the various methods of data reduction. The labelling convention in these ®gures is the same as used in Figs. 4 and 6. The ®rst column, where the compliance was obtained from the slope of the load versus LVDT data,
Fig. 6. Typical C vs. a curves from a 4ENF test of Geometry ``B''.
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and the crack length was measured by c-scan, is considered to provide the most accurate results. The maximum dierence between the mean value of toughness as provided by this method of data reduction and any of the others considered is 4.9% in Fig. 7 and 1.2% in Fig. 8. The method of the last column, which is the method used in previous studies, yields a mean toughness that is only 1.2% dierent from the method of column 1 in Fig. 7, and only 0.5% dierent in Fig. 8. Thus, similar to the results for initiation, in our propagation studies, all of the errors that may have occurred when the maximum load versus actuator displacement is used for compliance, and crack length is measured visually, apparently cancelled each other out in the determination of ERR. Considering the results shown in Figs. 3, 7 and 8, initiation and propagation toughnesses as found through 4ENF testing can be compared. To make this comparison, consider toughness values as obtained from the compliance of the load versus LVDT displacement results with crack length measured by c-scan. Comparing the ®rst shaded column of Fig. 7 to the shaded column in Fig. 3 corresponding to Geometry A, it is found that this geometry (d/2L=0.4) produces a propagation toughness that is an average of 30% lower than the initiation toughness. For Geometry B, comparing the ®rst shaded column of Fig. 8 to the appropriate shaded column of Fig. 3, it is observed that the propagation toughnesses for this geometry (d/2L=0.5) is 21% lower than the initiation toughness. Similar to that found in previous studies [2,4±6,9], these results indicate that there can be a rather large arti®cial increase in GIIc when testing directly from the insert.
This supports the necessity to perform tests for delamination toughness on precracked specimens. Considering the results of Ref. 10, it is preferable that precracking be performed in mode II, which is easily accomplished using the 4ENF test. 4.3. Discussion The results of Fig. 3 indicate that the toughness values as obtained by the 4ENF correlate well with those by ENF, regardless of data reduction method. Also, for both initiation and propagation, Figs. 4, 7 and 8 show that all data reduction methods that were evaluated produced GIIc values that vary by 7% or less from the method considered to be the most accurate. However, the results from this study cannot automatically be applied to other testing rigs and testing labs for two primary reasons. First, the results one obtains for compliance are certainly a function of the test ®xture, test machine, and possibly data acquisition system that is used. Secondly, the same operator in our tests performed both visual crack length assessments and c-scan measurements. Thus, there was likely signi®cant learning that occurred during this process, and it is not clear that an operator who does not have access to c-scan corroboration will make visual crack length assessments to the same accuracy as was obtained in this study. With the above restrictions in mind, we turn our attention to the results from this study that can be generally applied. Examining Figs. 3, 7 and 8, if the crack length is measured in the same manner, then there is no consistent trend between the dierence in GIIc as obtained by the dierent methods of measuring compliance. This
Fig. 7. Propagation toughnesses from 4ENF tests of Geometry ``A''.
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Fig. 8. Propagation toughnesses from 4ENF tests of Geometry ``B''.
should generally be the case, i.e. no real dierence in results, providing that there is minimal amount of free play in the ®xture, the testing machine and ®xture are sti as compared to the specimen, and the specimen does not display signi®cant nonlinearities prior to crack advance. However, the ``allowable'' amounts of nonlinearity from the various sources is hard to quantify, and it would likely be best to avoid this source of error by always obtaining compliance from the slope of the load versus de¯ection plot. This means that a test with a propagating crack would need to be run in a loadunload-load manner, similar to that done herein. While that will slightly increase testing times, it will undoubtedly improve the accuracy of the compliance data. Furthermore, it will allow ample time for crack lengths to be measured on both sides of the specimen, thereby improving the accuracy of the crack length data as well. Regarding the means of measuring crack length, it would seem that the best way of assessing accuracy, short of repeating the type of study that was done herein, would be to perform compliance calibration before testing 4ENF specimens in the same manner as is done for the ENF test. A comparison of GIIc found from the ``prior'' compliance calibration to that obtained from crack length measurements taken during the test would provide immediate feedback about the accuracy of the visual crack length measurements. If poor correlation were obtained, then it would be best to increase the number of crack length measurements taken during a test. We have found that some visual crack length estimates are long and some are short, and the greater the sampling, the greater the probability that the mean curve will converge to the true result.
5. Conclusions A series of 4ENF tests were conducted and de¯ection, compliance and crack length were measured by dierent techniques. These dierent measures were then used in a compliance calibration method of obtaining GIIc and the results compared. Also, for delamination growth directly from the Te¯on insert, values of GIIc as obtained by the 4ENF and the various measurement techniques were compared to those from ENF tests. The results of the various comparisons were used to draw some general conclusions about the most accurate means of reducing data from a 4ENF test and to assess whether ENF and 4ENF tests produce the same toughness values. The results of this study indicate that, if compliance and crack length are measured accurately, then 4ENF and ENF tests will produce essentially the same values for toughness. It is possible that errors in measuring these parameters contributed to the dierences reported in earlier studies. To reduce possible errors in future studies, it is recommended that compliance in the 4ENF test be obtained from the slope of the load versus de¯ection plot. This means that tests are conducted in a load-unload-reload manner, similar to that done herein. The unloading is performed after each noticeable increment of crack advance, and the new crack length is measured with the specimen subjected to a low load leg (50% of Pc) and the crack arrested. In addition, it has been pointed out that a simple means of assessing the accuracy of the crack length measurements taken during a 4ENF test is to perform compliance calibration before testing the 4ENF specimens in the same manner as is done for the ENF test. A comparison of GIIc found
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from the ``prior'' compliance calibration to that obtained from crack length measurements taken during the test will provide immediate feedback about the accuracy of the visual crack length measurements. If poor correlation is obtained, then improved accuracy may be obtained by increasing the number of crack length measurements taken during a test.
References [1] Carlsson LA, Gillespie Jr JW, Pipes RB. On the analysis and design of the end notched ¯exure (ENF) specimen for mode II testing. Journal of Composite Materials 1986;20:594±604. [2] O'Brien TK, Murri GB, Salpekar SA. Interlaminar shear fracture toughness and fatigue thresholds for composite materials. In: Lagace PA, editior. Composite materials: fatigue and fracture, second volume, ASTM STP 1012, American Society for Testing and Materials, 1989, pp. 222±50. [3] Davidson BD, Altonen CS, Polaha JJ. Eect of stacking sequence on delamination toughness and delamination growth behavior in composite end-notched ¯exure specimens. In: Deo RB, Sa CR, editors. Composite Materials: Testing and Design (Twelfth Volume), ASTM STP 1274, American Society for Testing and Materials, 1996, pp. 393±413.
[4] Martin RH, Davidson BD. Mode II fracture toughness evaluation using a four point bend end notched ¯exure test. Plastics, Rubber and Composites 1999;28(8):401±6. [5] Chin RJM. Fracture testing of composite materials. BEng Project Report, Faculty of Engineering, University of Hertfordshire, May 1998. [6] Martin RH, Elms T, Bowron S. Characterization of mode II delamination using the 4ENF. Proceedings of the 4th European Conference on Composite Materials: Testing and Standardization, Institute of Materials, London, 1998. p. 161±70. [7] Schuecker C, Davidson BD. Eect of friction on the perceived mode II delamination toughness from three- and four-point bend end-notched ¯exure tests. In: Grant PE, Rousseau CQ, editors. Composite Structures: Theory and Practice, ASTM STP 1383, American Society for Testing and Materials, 2000, pp. 334± 344. [8] Broek D. Elementary engineering fracture mechanics, 4th Edition, Kluwer Academic Publishers, Inc., 1986. [9] Polaha JJ, Davidson BD, Hudson RC, Pieracci A. Eects of mode ratio, ply orientation and precracking on the delamination toughness of a laminated composite. Journal of Reinforced Plastics and Composites 1996;15(2):141±73. [10] Davidson BD, Koudela KL. In¯uences of the mode mix of precracking on the delamination toughness of laminated composites. Journal of Reinforced Plastics and Composites 1999; 18(15):1408±14.