Data Reduction Techniques

As discussed in Section 2.2, a number of different methods that have been used to calculate GIIIc for mode III toughness tests. Due to its complex fixture and load application, data

reduction in the original STB (Davidson and Sediles, 2011) was determined via a FE based method with a critical load determined by experiments. However, it is possible that a compliance calibration based method may be possible herein. Thus, both FE based and compliance

calibration based methods were investigated for STB and SST data reduction as part of these initial studies.

4.6.1. Compliance Calibration

4.6.1.1. Compliance Calibration Technique

The compliance calibration (CC) technique was explored as a potential data reduction technique due to the minimal assumptions required, in comparison to other techniques, to

calculate GIIIc. Due to the tabs on SST and STB specimens which preclude shifting the specimen

in the fixture to obtain multiple delamination lengths, a multi-specimen compliance calibration similar to the method of Szekrényes (2009) discussed in Section 2.2.4.3 is considered.

4.6.1.2. Compliance Calibration of Tabbed Specimens

Due to its simplicity, the SST test was used for the initial evaluation of the potential accuracy of a multi-specimen compliance calibration data reduction method. Only NE specimens were considered in order to ensure similarity from specimen to specimen. In view of the above, both 24-ply and 32-ply IM7/977-3 test specimens with 150 mm long Teflon inserts were

fabricated to determine the viability of the CC approach. Specimens with end tabs were prepared with delamination lengths of 91.5 – 106.5 mm in 5 mm increments. Compliance tests were performed to various percentages of the predicted critical load. Although different specimen responses were clearly obtained at the different delamination lengths (for each given specimen thickness), there was never a long, highly linear region within the load versus displacement plots where compliance could uniquely and unambiguously be defined. The reasons for this behavior are discussed subsequently. That is, all load versus displacement responses were similar to, or

more severe than, Figure 4.7, as significant nonlinearities were present in the tests. This behavior precluded the possibility of using CC with these test geometries.

4.6.1.3. Untabbed Specimen Assessments

Although the above work showed that compliance calibration was not viable with tabbed specimens, exploratory SST tests on untabbed specimens were conducted to examine whether a more linear load versus displacement plot might be obtained, and therefore a compliance

calibration method of data reduction might be viable. Because of the specific geometry of the test fixture, it was found that untabbed specimens could only be tested if tab blanks were used as spacers between the specimen and load blocks. Rather than modify the fixture, a decision was made to initially consider this approach and, if promising, subsequently modify the fixture as necessary. Thus, a limited number of 18 ply T800S/3900-2B and 26 ply IM7/977-3 specimens without load tabs were tested for this purpose. In comparison to tabbed specimens, the

undelaminated regions of all of these specimens showed a significant amount of rotation about the x-axis (cf. Figure 4.1) during loading. Further, as there is less contact area for load

introduction, variations in the load pin length had a strong influence on the load versus

displacement results and on the observed rotations. It was difficult or impossible to get the load pin to have full contact over the edge of one delamination leg while not contacting the surface of the other leg, and there were slight variations in contact from specimen to specimen. It was therefore concluded that the above problems were significant and that the accuracy and repeatability required to make a multi-specimen compliance calibration viable could not be achieved with untabbed specimens, regardless of whether or not fixture modifications were performed to eliminate the load tab blanks. For these reasons, untabbed specimens were not

pursued further in this study, and the compliance calibration was no longer considered as a possible data reduction technique.

4.6.2. FE Based Method

As CC was found to be non-viable for the desired test and specimen geometries, focus shifted to a FE based method of data reduction. Here, the VCCT (Rybicki and Kanninen, 1977; Krueger, 2004) is used to calculate ERRs along the delamination front, as in Figure 4.6. These ERRs are used in conjunction with the critical load for delamination advance to determine the toughness.

4.6.2.1. GIIIc Basis for Baseline Configurations

The experimental results discussed in Section 4.5.3 indicate that the critical load in tests of both STB ED and SST ED specimens corresponds to delamination advance across the full width of the specimen. Thus, if this critical load (Pc) were used in a FE analysis of that particular

specimen, the critical ERR (Gc) may be obtained. Due to full-width advance, Gc should be based

on Gavg, i.e., one should evaluate Gc as Gavg at P = Pc. Alternatively, as the test is essentially pure

mode III, the approach of Davidson and Sediles (2011) may be adopted, where one ignores the small mode II component and defines GIIIc as GIII-avg at P = Pc. This latter approach is adopted

herein. Note that this approach also ignores the peak ERRs that occur at the delamination’s edges (cf. Figure 4.6b). However, considering the peak ERRs that occur near the EDs, i.e., near y/B = 1/16 and y/B = 15/16, the regions where the magnitude of the peak exceeds the center value is confined to the single element at each of these edge locations. Thus, the most refined model considered (92 elements across the width) indicates that the peak is confined to a region that is

on the order of 0.5-1% of the specimen’s width. This is not dramatically different from the small mode III component that occurs at the edges of mode II end-notched flexure specimens

(Davidson et al., 1995), and experience has shown that this has no observable effect on toughness.

In contrast to the above, the experimental results indicate that, in NE specimens, GIIIc

must be based on the ERR in the center of the specimen, which represents the peak value in these geometries, GIII-pk. This agrees with the conclusions from the baseline FE analysis. Thus, in the

case of NE geometries, GIIIc = GIII-pk at P=Pc.

4.6.2.2. Determinations of GIIIc of Baseline Configurations

To facilitate data reduction, the equation for average mode III ERR for an STB specimen with a=32 mm is introduced (Davidson and Sediles, 2011):

𝐺_{𝐼𝐼𝐼−𝑎𝑣𝑔}𝑆𝑇𝐵 ₌ 𝑃2 𝐵2_ℎ𝐺

12(1−2𝛽)(0.66 + 1.15√

𝐺12

𝐸11) (4.1)

In Equation (4.1), B is the specimen width, β is the normalized edge delamination length, E11 and

G12 are experimentally determined material properties, and P is the applied load. For

convenience, Equation (4.1) is used as a scaling factor to express all key FE results for the different baseline configurations, and therefore to have a simple expression for data reduction. Correction factors were used to scale the FE results from the four baseline configurations to Equation (4.1) such that

𝐺_{𝐼𝐼𝐼−𝑎𝑣𝑔} = 𝐶_𝑓𝑎𝐺_{𝐼𝐼𝐼−𝑎𝑣𝑔}𝑆𝑇𝐵 _𝐺

where Cfa is a correction factor for the average ERR and Cfp is a correction factor for the peak

ERR. Values of Cfa and Cfp are extracted from a comparison of Equation (4.2) to the FE results

and are presented in Table 4.2 for the baseline geometries. The first row presents the test configuration, the second is the basis on which GIIIc is to be determined, and the final two rows

provide the appropriate correction factor. Note that Cfa and Cfp do not depend on the material

used.

In the tests that follow, all data reduction was performed using Equation (4.1), Equation (4.2) and the appropriate correction factor from Table 4.2. Note that Equation (4.1) and Equation (4.2) simply provide a convenient expression to obtain GIIIc from the measured Pc in the test.

Fundamentally, data reduction is being performed via FE analysis.