Three-dimensional crack surface evolution in mode III delamination toughness tests

Engineering Fracture Mechanics xxx (2015) xxx–xxx

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Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech

Three-dimensional crack surface evolution in mode III delamination toughness tests Allison L. Horner a, Michael W. Czabaj b, Barry D. Davidson a,⇑, James G. Ratcliffe c a

Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, NY 13244, USA Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA c National Institute of Aerospace, Durability, Damage Tolerance, and Reliability Branch, NASA Langley Research Center, Hampton, VA 23681, USA b

a r t i c l e

i n f o

Article history: Received 31 October 2014 Received in revised form 24 June 2015 Accepted 8 July 2015 Available online xxxx Keywords: Composites Fractography Fracture mechanics Toughness testing Crack growth

a b s t r a c t The three-dimensional evolution of a delamination and multiple coupled transverse cracks is studied in laminated tape composites using different mode III tests and specimens. All combinations produce 45° transverse cracks that initiate at the delamination front prior to delamination advance. For unidirectional laminates, the transverse crack length is governed by thickness, whereas for multidirectional laminates the transverse crack length is controlled by the ply angle and stacking sequence. These and other details of laminate architecture are shown to dictate the crack surface evolution, and provide distinguishing characteristics between the different laminates tested as well as in comparison to homogenous materials. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The determination of the mode III delamination toughness, GIIIc, of laminated polymeric matrix composite materials has proven to be a problematic issue. Although a number of proposed test methods have been shown to produce global mode III loading conditions, corresponding measurements of the apparent value of GIIIc have been found to exhibit a dependence on test geometry. This has been demonstrated through a dependence of apparent GIIIc on the length of the delamination [1–9] and, for the edge crack torsion (ECT) test, on the length of the overhang [7]. To understand the mechanisms contributing to the above, it is useful to consider the behavior of homogenous materials under anti-plane shear loading. Here, rather than a planar ‘‘mode III extension’’ as has been previously assumed to occur in the various mode III delamination toughness tests, crack growth initiates through the development of an array, or echelon, of parahelical cracks that are distributed along the original crack front [10–13]. These cracks are oriented at a 45° angle to the original crack plane, such that they are perpendicular to the direction of maximum tensile stress associated with the original mode III near-tip stress field. Macroscopic advance of the original planar crack consists of the extension and ultimately coalescence of these parahelical cracks. This discontinuous surface evolution occurs in essentially the same manner in rock formations subjected to anti-plane shear loading, where it is typically referred to as echelon cracking [e.g., 12–15]. This behavior is also similar – and closely related to – that which has been observed in mixed mode I–III fracture of homogenous materials, where it is commonly described as a combination of crack front rotation and segmentation [14–20]. ⇑ Corresponding author at: Department of Mechanical and Aerospace Engineering, 263 Link Hall, Syracuse University, Syracuse, NY 13244, USA. Tel.: +1 315 443 4201. E-mail addresses: [email protected] (A.L. Horner), [email protected] (M.W. Czabaj), [email protected] (B.D. Davidson), [email protected] (J.G. Ratcliffe). http://dx.doi.org/10.1016/j.engfracmech.2015.07.013 0013-7944/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013

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Nomenclature a b B CT D16, D26 ECT GIIIc h l L MSCB P Pmax Pnl SST w

delamination length width of the ECT specimen width of the SST specimen computed tomography bending-twisting coupling stiffnesses edge crack torsion mode III delamination toughness SST specimen half thickness distance between load points along an ECT specimen’s length length of the ECT specimen modified split cantilever beam applied load maximum applied load load at onset of nonlinearity in load-displacement plot split-shear torsion distance between load points along an ECT specimen’s width

Studies using laminated composite materials and a variety of different anti-plane shear test methods have found results analogous to those described above. Here, transverse cracks have been found to initiate in the matrix material above and below the original delamination plane. Evidence of this type of behavior was first observed in modified split cantilever beam (MSCB) specimens via post-test fractographic examinations of the delamination plane [21]. These cracks were referred to as ‘‘shear crevices’’ and were stated to be normal to the plane of maximum tension. Similar cracks were observed independently in ECT specimens by Ratcliffe [1] and Li et al. [2], and both studies concluded that a true mode III toughness was not being measured. Recent works using the split-shear torsion (SST) [9] and ECT [22] tests also identified this behavior, and have further shown that the transverse matrix cracks initiate prior to the advance of the planar delamination, thereby invalidating the associated data reduction procedures used to extract an apparent mode III toughness. Refs. [9,22] therefore concluded that the mechanisms originally observed in homogenous and geologic materials explain, or contribute to, the observed dependence on test and specimen geometry of the apparent mode III toughness of laminated polymeric composites. These conclusions are expected to apply when the specimen’s stacking sequence is such that the plies bounding the delaminated interface have their fibers aligned with the intended direction of mode III growth, and therefore do not constrain the formation of transverse cracks. For these cases, an intrinsic coupling of transverse matrix cracking with planar delamination growth will occur in typical mode III test specimens [9,22]. While the initiation behaviors observed previously in SST and ECT specimens were quite similar, clear differences were observed in the details associated with macroscopic delamination advance [9,22]. In order to predict delamination growth for a variety of loading conditions and interfaces, it is important that the mechanics of both initiation and propagation are understood. To this end, the goals of this study were to determine (1) the fracture surface evolution in SST and ECT tests, i.e., the manner in which the coupled system of a delamination and multiple transverse cracks develops and advances, (2) the way in which this evolution is influenced by specimen geometry and laminate architecture, (3) the relation to similar observations in homogeneous materials, and (4) the application to mode III delamination toughness testing and delamination growth prediction. To achieve the above, a series of ECT and SST specimens were manufactured and tested. Ultrasonic inspection, X-ray computed tomography (CT) and optical microscopy were utilized to view the evolution of cracking both before and after the onset of planar delamination growth. In what follows, the three-dimensional fracture surfaces from the two test types are compared to each other and to analogous results from homogeneous materials, and the effects of specimen geometry and architecture on fracture surface evolution are assessed. The results are then used to draw inferences on the application of conventional toughness test and delamination prediction methodologies to laminated composites. 2. Methodolody 2.1. Test and specimen geometries Fig. 1a presents a schematic representation of the SST test [9,23]. The specimen is unidirectional with all plies oriented in the x-direction. It contains a preimplanted insert at its midplane that spans the specimen’s width, B, and which creates a starter delamination of length a. As shown in the figure, load is introduced to the specimen through loading tabs and blocks. The upper load block (so-named as it attaches to the upper portion of the load frame) is fully constrained, and the lower load block is constrained such that only vertical (y-direction) translation may occur. Thus, both shear and torsional loadings are transmitted to the specimen. This is conceptually similar to the loading configuration utilized for the MSCB test, which was Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013

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Fig. 1. Test methods used. (a) SST and (b) ECT.

developed from the observation that the original split cantilever beam test [24] did not produce a state of pure anti-plane shear; rather, it produced significant mode II components along the outer portions of the delamination front [25]. The addition of the torsional load reduced these mode II components significantly and was shown to produce pure mode III conditions along the majority of the delamination front [25]. A similar distribution of energy release rate is observed in the SST specimen [8,9,23]. In the MSCB test, the shear load and torque are applied via a pin loading arrangement along the cracked edges of the laminate [5,6,21]. The configuration of the SST test is perhaps somewhat simpler and allows thinner specimens to be used. The ECT specimen geometry, developed by Lee [26], is presented in Fig. 1b. The rectangular ECT specimen contains a preimplanted insert at its midplane that spans its full length, L, and which creates a starter delamination of length a. Hemispherically tipped pins are used to apply equal and opposite couples to each end of the specimen, which produces mode III dominated stresses along the delamination front [1,2]. The coordinate system and ply orientation conventions used in Fig. 1b agree with those that are conventionally used for the ECT test [1–4,7,22,26]. The delamination is bounded by 90° plies and delamination growth is parallel to the 90° fiber direction. In view of the ply orientation conventions used in Fig. 1, note that delamination advance occurs parallel to the local fiber direction in both the ECT and SST specimens, i.e., the direction of growth in relation to the delamination’s bounding plies is identical in the two test geometries.

2.2. Specimen fabrication Unidirectional IM7/8552 pre-preg tape was used to make all specimens for this study. Both 24- and 48-ply SST specimens were fabricated with nominal thicknesses of 2h = 3.0 mm and 6.0 mm, respectively. All SST specimens were nominally sized to have widths, B, of 25.4 mm and delamination lengths, a, of 32 mm. The 24-ply specimen geometries were chosen based on the results in Refs. [8,9,23]. The 48-ply specimen geometries used the same values of a and B in order that any variation in fracture surface evolution between the 24- and 48-ply specimens would be due solely to their different thicknesses. All SST test specimens were fabricated at the Syracuse University Composite Materials Laboratory using an autoclave and the manufacturer’s recommended cure cycle [27]. The fabrication procedure generally followed that described in Ref. [8]. Here, two rectangular, 13 lm thick Teflon sheets were placed at the midplane of a 305 mm  305 mm plate during manufacture. The sheets were oriented orthogonally to the fiber direction. One sheet was located at each end of the laminate to create the desired insert lengths. Plates were debulked every 8 plies. One plate of each thickness was fabricated in this manner, after which they were cut parallel to the fiber direction (perpendicular to the Teflon inserts) into ten 25.4 mm wide strips. Each of these strips contained a Teflon insert at each end, thereby producing 20 specimens. The procedure for tabbing specimens was carried out in accordance with Ref. [8]. All ECT specimens were obtained from a single plate that was fabricated at NASA Langley Research Center using a hot press [22]. This plate was cut into specimens with nominal lengths, L, of 89 mm and widths, b, of 38 mm. The stacking sequence utilized for the ECT specimens was modified from the original design [26] to eliminate bending–twisting coupling (D16 and D26) in the cracked and uncracked portions of the specimen. The stacking sequence used was [(90/45/( 45)2/90/(45)2/ 45)s ||]s, where the ‘‘||’’ symbol designates the location of the Teflon insert, and the ply orientations are as defined in Fig. 1b. Specimens were cut with normalized insert lengths, a/b, ranging from 0.10 to 0.35, and had an average thickness of 3.85 mm. After fabrication, both SST and ECT specimens were ultrasonically inspected to obtain a pre-test image of the delamination front. All specimens were ultrasonically inspected a second time after testing. Comparisons of the pre- and post-test images were performed to determine whether or not the crack front advanced and, in those instances where growth did occur, to ascertain the shape of the new delamination front. Subsequent to testing, both non-destructive X-ray CT and destructive optical microscopy assessments were conducted. Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013

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2.3. Tests and fixtures A photograph of the SST test fixture containing a tabbed specimen is presented in Fig. 2a. The specimen is sandwiched in-between two load block/grip assemblies. These are integral units, each of which contains two bolt holes and a backing plate that presses against the outer surface of the load tab. The upper assembly connects to the load cell and remains stationary during testing. The lower assembly is mounted to a platen that connects to a servohydraulic actuator and is displaced downwards during the test. As shown in the figure, this lower load block/grip assembly is bolted to the platen through slots. This allows it to slide during specimen installation and thereby to accommodate specimens of different thicknesses. The procedures to install specimens into the grips were developed to maximize reproducibility and are detailed in Ref. [8]. All SST tests were performed under displacement control at a loading rate of 0.4 mm/min, which was chosen to ensure a slow, stable fracture surface evolution, as well as to allow direct correlation to the results from earlier works [8,9,23]. All ECT tests were performed in a servohydraulic load frame with the stationary load cell connection on the bottom and the actuator connection on top. The test fixture is pictured in Fig. 2b. The diameter of the hemispherical-tipped loading and support pins is 6.4 mm. The distances between the pins in the length and the width directions, respectively, are l = 76.2 mm and w = 31.8 mm. The upper set of load pins are fixed to a plate which is bolted to the actuator. The lower pins are fixed to a plate that is connected directly to the load cell. The procedure for alignment of ECT specimens is described in Ref. [22]. Similar to Ref. [22], all ECT specimens were tested in displacement control at a loading rate of 0.25 mm/min.

2.4. Test procedure The tests conducted in this work represent a continuation of the experimental studies described in Refs. [9,22]. In these studies, ‘‘damage progression tests’’ were performed on 24-ply SST and 32-ply ECT specimens of the types described above. Here, specimens were tested to various percentages below the load or displacement at which planar delamination growth was expected to occur, after which they were unloaded and the near-tip regions were sectioned and inspected via optical microscopy. For both SST and ECT specimens, it was found that transverse matrix cracks initiate prior to macroscopic delamination advance, and that the sequence of events prior to delamination growth is quite similar in both specimen types. In the present work, 48-ply SST damage progression tests were first performed. Damage progression tests were only performed on the 48-ply specimens, as similar tests on 24-ply SST [9] and ECT specimens [22] had already been conducted. Following this, a series of delamination toughness tests were performed. These tests were stopped immediately after the onset of macroscopic delamination growth. The region containing transverse crack or delamination growth in these specimens was then inspected using X-ray CT and/or optical microscopy. Optical microscopy was performed on transversely cut sections as in Refs. [9,22]. That is, while other researchers have commonly conducted post-test fractographic examination of the delamination plane of fractured mode III specimens [e.g., 1–4,7,21,26], the authors have found that viewing sections transverse to the delamination plane allows for an improved reconstruction and understanding of the fracture process [9,22]. For the examinations using optical microscopy, the cut sections were potted in epoxy, polished, and cleaned according to Ref. [28], and photomicrographs were taken using an inverted optical microscope. This provides a very fine level of resolution, but only at a limited number of locations per specimen. Conversely, X-ray CT provides a three-dimensional view of the entire cracked region, but at a somewhat lower resolution. Combining the information from these two techniques with the knowledge gained from the damage progression testing allowed the evolution of events leading to macroscopic

Bolt

Upper load block/grip

Lower load block/grip

Specimen

Load tab

Alignment blocks

Specimen

Load pin

(a)

(b) Fig. 2. Test fixtures used. (a) SST and (b) ECT.

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delamination advance to be determined. The observed sequence of events was then compared for the two different thickness SST specimens, and for the SST and ECT specimens. Following the above, ‘‘extended growth tests’’ were conducted, which were similar to the delamination toughness tests, although here an extended amount of delamination growth was allowed to occur in order to determine how the cracked surfaces evolve as a function of the amount of planar delamination growth. The SST extended growth tests yielded 14– 16 mm of planar delamination growth (in the x-direction, Fig. 1a). Only limited work was done in this area for the ECT, and the ECT specimen that was evaluated evidenced only a few millimeters of growth (in the y-direction, Fig. 1b). These specimens were inspected using the same techniques as those used for the delamination toughness test specimens, and comparisons were made between results from the various specimen types. 3. Specimen response and data reduction Typical load versus displacement responses from 24-ply and 48-ply SST specimens are presented in Fig. 3a. The curves from the two specimens display similar amounts of ‘‘global nonlinearity.’’ It has previously been shown that no planar crack advance is associated with this nonlinearity prior to the maximum load, Pmax [23], although transverse matrix cracks do initiate as the load approaches Pmax [9]. The apparent toughness, i.e., the toughness as obtained from the test, which may not be representative of a true material property, was determined following the same finite element-based approach and using similar finite element models as those described previously [8]. A typical load versus displacement response from an ECT specimen with a/b = 0.2 is presented in Fig. 3b. Initially, the load versus deflection response is essentially linear. The point of nonlinearity onset (PNL) was determined following the procedure described in Ref. [1], and corresponds to a load slightly larger than that required for microcracks to initiate ahead of the preimplanted Teflon insert [22]. The maximum load in the test, Pmax, corresponds to the onset of planar delamination advance. The dashed line represents extrapolation of the linear portion of the load–displacement curve and is intended to illustrate the extent of the nonlinearity. The ‘‘CC range’’ of Fig. 3b refers to the range of load and displacement used to determine compliance in the reduction of data to obtain apparent toughness. This was performed using a multi-specimen compliance calibration procedure and is described in Ref. [22]. 4. Damage progression and delamination toughness tests 4.1. Apparent fracture toughness Delamination toughness tests were carried out on four specimens each of the SST 24- and 48-ply geometries, and on 12 specimens of ECT geometries with initial delamination lengths from a/b = 0.1–0.35. Apparent toughness was calculated as described in Refs. [9,22]. The apparent value of GIIIc was similar for SST specimens of both thicknesses and was approximately 850 J/m2. The apparent toughness for ECT specimens averaged across all delamination lengths was approximately 1200 J/m2. The coefficient of variation for each of the three geometries was on the order of 6%. This indicates that each test and specimen geometry produces consistent results. However, these apparent toughnesses clearly depend on the test geometry and therefore cannot be interpreted as a true material property. They are presented here solely for qualitative comparison and to aid in subsequent assessments of crack surface evolution.

2.0

/RDGN1

Pmax

SST



48-ply



/RDGN1

2.5

1.5

24-ply

1.0

ECT

Pmax PNL





CC range: 0.44-1.33kN 

0.5

0.0 0.0

0.2

0.4

0.6

'LVSODFHPHQWPP

0.8

1.0

 







'LVSODFHPHQWPP

(a)

(b)

Fig. 3. Load deflection plots for (a) SST and (b) ECT.

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4.2. Transverse crack initiation and progression Fig. 4 presents photomicrographs from damage progression tests of a 48-ply SST specimen and an ECT specimen. These and subsequent photomicrographs were obtained by making a transverse cut exposing the y–z plane of SST specimens (Fig. 1a) and the x–z plane of ECT specimens (Fig. 1b). Both images in Fig. 4 are from section cuts immediately ahead of the Teflon insert tip. These specimens were loaded to approximately 85% of Pmax, which corresponds to approximately 70% of the apparent GIIIc. The dark grey region in the center of each image is the resin rich layer in-between the two center-most plies and immediately ahead of the Teflon insert tip. Both images clearly show interlaminar microcracks initiating well before the maximum load is reached. There is essentially no difference between the image of Fig. 4a in comparison to the analogous view of a 24-ply SST specimen [9]. Fig. 5 presents photomicrographs from delamination toughness tests of a 48-ply SST specimen and of an ECT specimen. Both images are from cuts made just ahead of the original Teflon insert tip and within the newly delaminated region. The delamination fronts of all other SST specimens – both 24-ply and 48-ply – looked similar to that shown in Fig. 5a. Here, the thick, jagged path running horizontally is the interlaminar delamination, which remained essentially at the midplane. There are approximately three plies visible on each side of the midplane. In the ECT specimen shown in Fig. 5b, delamination growth occurred one ply below the midplane, at a 90/45 interface. In both images, transverse matrix cracks that span more than one ply and which are oriented at approximately 45° can be seen intersecting the interlaminar delamination. The horizontal arrows above and below the images show the directions of the applied shear stress, from which it is observed that the transverse cracks are oriented essentially perpendicular to the direction of the maximum principal tensile stress near the tip of the Teflon insert. As described in Refs. [9,22] and may be observed in Figs. 4 and 5, as the applied load reaches an appreciable percentage of Pmax during either an SST or ECT test, microcracks such as those shown in Fig. 4 first occur in the resin interlayer at the specimen’s midplane. These microcracks initiate just ahead of the tip of the Teflon insert along the entire delamination front. As the magnitude of the load increases, a subset of these microcracks grow into transverse cracks that run through the adjacent plies, i.e., in the planes shown in Fig. 4, as well as into the uncracked region. As the load approaches Pmax in the SST test, some of these growing transverse cracks display horizontal branches at or near the specimen’s midplane, just ahead of the Teflon insert tip. These horizontal branches link and produce the macroscopic observation of planar delamination advance preceded by transverse cracking, as shown in Fig. 5a [9]. Figs. 4a, 5a, and similar photomicrographs from other SST specimens indicated that there was no difference in this process for the 24-ply and 48-ply specimens. As the load approaches Pmax in the ECT test, the growth of the transverse cracks proceeds as described above through the two central 90° plies [22].

microcracks

microcracks

10 µ m

10 µ m

(a)

(b)

Fig. 4. Typical photomicrographs ahead of the insert tip prior to delamination growth in (a) 48-ply SST and (b) ECT specimens.

transverse cracks transverse cracks

midplane delamination delamination

200 µ m

200 µ m

(a)

(b)

Fig. 5. Typical photomicrographs ahead of the insert tip subsequent to delamination growth in (a) SST and (b) ECT specimens.

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However, further progression in the z-direction is hindered by the bounding 45° plies. At this point, the transverse cracks generally turn, resulting in delamination growth at one of the 90/45 interfaces as shown in Fig. 5b. 4.3. Analysis of transverse cracking The photomicrographs shown in Fig. 5 represent only small percentages of the specimens’ widths, B (SST) or lengths, l (ECT). Therefore, analyses were performed to quantify the transverse crack length, spacing and angles immediately ahead of the Teflon insert tip in the three specimen types. These were performed on representative SST delamination toughness specimens of 24 and 48 plies, and on ECT delamination toughness specimens with a/b = 0.1 and 0.35. For SST specimens, the entire delamination front was used, and every visible crack was included in the analysis. Due to their larger crack front lengths, only one-half of the length (l/2), from the edge to the center-point, was analyzed for the ECT specimens. Here, l is used rather than L, because no transverse cracks were observed outside of the ECT loading pins. This resulted in 30–80 measureable cracks for each specimen. For all specimens, the length and angle to the horizontal direction of each crack were measured, as well as the spacing between cracks. The results of this analysis are presented in Table 1. First, considering the SST specimens at the two different thicknesses, the spacing in-between the transverse cracks and their angles are reasonably similar, but the transverse crack lengths in the 48-ply specimens are quite a bit larger than in the 24-ply specimens. The greater thickness of the 48-ply specimens and the fact that the transverse cracks must arrest before reaching the traction-free upper and lower surfaces are responsible for this effect. Interestingly, this produced no appreciable influence on the apparent toughness, i.e., as described previously, no noticeable difference in apparent GIIIc between SST specimens of the two thicknesses was observed. Next, considering the ECT geometries at the two different insert lengths, these specimens show transverse cracks that are essentially the same in terms of their length, spacing and angle. The relatively small standard deviations in Table 1 indicate that there was little variation in transverse crack length in these specimens. The average crack length measured for the ECT specimens is equal to that of a transverse crack traversing the two center plies at a 45° angle. Thus, although some transverse cracks are shorter and some do penetrate a small distance through one or both 45° plies, the majority of the transverse cracks in the ECT specimen extended through the center two plies and were arrested at the adjacent interfaces. Comparing SST and ECT geometries, it can be seen that there is much less variation in transverse crack length and spacing in the ECT specimens. Moreover, on average, the ECT specimens have somewhat shorter transverse crack lengths, somewhat closer crack spacing, and transverse crack angles closer to 45°. The shorter transverse crack length is likely influenced by the constraints of the neighboring 45° plies in the ECT. The closer crack spacing is related: the transverse cracks locally reduce the magnitude of the maximum principal tensile stress that led to their creation. Smaller transverse cracks produce less stress relief; this means that, a short distance away, the maximum principal tensile stress again reaches the critical value required for another transverse crack to form [11,15,29,30]. Thus, the constraint on transverse crack size leads to both smaller transverse cracks and smaller spacing between them. 5. Crack surface evolution 5.1. Split shear torsion test 5.1.1. 24-ply SST One SST specimen of each thickness was utilized for an extended delamination growth test. The results for the 24-ply specimen are presented in Fig. 6 in the form of a sequence of images at different (x-direction) distances ahead of the insert tip, all of which are representative of the central region of the specimen’s width. Fig. 6a and b present photomicrographs from cross-sections 0.5 mm and 2 mm ahead of the insert tip, respectively. Fig. 6c presents an X-ray CT image that is also from the cross-sectional plane 2 mm ahead of the insert tip, and the inset of Fig. 6c shows the location at which the photomicrograph of Fig. 6b was taken. The images in Fig. 6c–f were obtained by X-ray CT, and all display the specimen’s full 3 mm thickness. Note that the concentric arcs centered near the upper right corner of each of Fig. 6c–f are artifacts of the X-ray CT process. In Fig. 6a–e, the thick dark line near the specimen’s centerline is the delamination, which is no longer evident in Fig. 6f. The X-ray CT images showed planar delamination growth for the first 16 mm ahead of the insert tip, and the transverse matrix cracks extended an additional 2 mm beyond this. A comparison of all images in Fig. 6 shows that the transverse matrix crack spacing increases with increasing distance ahead of the Teflon insert tip. As their spacing increases, however, so do their lengths. That is, there is a coarsening process,

Table 1 Summary of transverse matrix crack data immediately ahead of the teflon insert tip: averages (standard deviations); crack length and spacing in mm. Geometry

SST 24-ply

SST 48-ply

ECT a/b = 0.1

ECT a/b = 0.35

Crack length Crack spacing Crack angle

0.42 (0.27) 0.95 (0.26) 36.7° (7.2°)

0.68 (0.53) 0.85 (0.34) 37.6° (6.9°)

0.34 (0.05) 0.57 (0.19) 43.5° (5.1°)

0.33 (0.07) 0.52 (0.19) 43.9° (6.3°)

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(a)

0.4 mm

0.4 mm

(b)

(c)

1.5 mm

1.5 mm

(d)

1.5 mm

(e)

1.5 mm

(f)

Fig. 6. Images obtained from 24-ply SST specimen. (a) and (b) by optical microscopy, (c)–(f) by X-ray CT. Distances ahead of insert tip: (a) 0.5 mm, (b) 2 mm, (c) 2 mm, (d) 7 mm, (e) 11 mm, (f) 16 mm.

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with, on average, many small, closely-spaced transverse cracks where planar delamination growth first initiates from the insert tip, and which gradually change to fewer, larger transverse cracks as the planar delamination grows. Further, as is most evident in the last few images in the sequence, the angles of the transverse cracks become increasingly shallow, and in some cases begin to develop a slight s-shape, as planar delamination growth progresses. The planar delamination remains at the midplane across the width of the specimen over the entire extent of growth. As noted previously, from examinations of the many specimens with different delamination lengths in this work and in Refs. [8,9], the transverse cracks always clearly precede the planar delamination in growing into the uncracked region. In terms of the shape of the evolving structure across the specimen’s width, the delamination advanced across the full width of the specimen for the first 12 mm of growth, and transverse matrix cracks covered the full width for the first 14 mm. From 12 mm to 16 mm the delamination is thumbnail-shaped, with the tip at 16 mm and the outer edges at 12 mm. The transverse crack profile, i.e., if one were to consider their lengths in x across the width y (cf. Fig. 1a), is also thumbnail-shaped, and extends approximately 2 mm ahead of the delamination front at all width locations. Superposed onto this is the coarsening behavior described above. Quantitative assessments of coarsening, presented subsequently, utilized only the X-ray CT data. This was due to the different accuracies inherent in the microscopy versus X-ray CT evaluations. That is, a comparison of Fig. 6b and c indicates that the X-ray CT is able to find larger transverse matrix cracks, but the smaller ones, such as near the right side of Fig. 6b, are not visible. Additionally, X-ray CT imaging also slightly under-estimates the length of each crack. However, quantitative comparisons made from these and similar figures indicated that the X-ray CT’s accuracy was quite good for cracks above approximately 1 mm in length. 5.1.2. 48-ply SST Fig. 7 presents a sequence of images for the 48-ply specimen, all of which were obtained by X-ray CT. These images show the entire 6 mm thickness, and are at similar distances ahead of the Teflon insert tip as those presented in Fig. 6d–f. A comparison of the images shows that, particularly for the two longest delamination lengths, the transverse crack length is greater in the 48-ply than in the 24-ply specimens, and the spacing between cracks is also greater. This former result is consistent with the results in Table 1. Also, the ‘‘thumbnail portion’’ of the 48-ply specimen was somewhat smaller than in the 24-ply

(a)

1.5 mm

(b)

1.5 mm

(c)

1.5 mm Fig. 7. X-ray CT images from 48-ply SST specimen. Distances ahead of insert tip: (a) 6 mm, (b) 10 mm, (c) 14 mm.

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specimen. As in the 24-ply specimen, the full width delamination ended 12 mm ahead of the insert tip. The region from 12 mm to 14 mm was thumbnail-shaped, i.e., the tip progressed 2 mm less into the uncracked region than in the 24-ply specimen. As in the case of the 24-ply specimen, the transverse crack profile was also thumbnail-shaped and extended approximately 2 mm ahead of the delamination front at all width locations, with similar coarsening behaviors. 5.1.3. SST graphical crack analysis In order to compare coarsening behaviors in the different thickness SST specimens, graphical crack analysis was conducted on the X-ray CT images in the same manner that was utilized with photomicrographs to generate Table 1. Every visible crack in each image was counted and measured, and these measurements were taken in increments every 0.5–1.0 mm ahead of the Teflon insert tip until no transverse cracks were visible. Fig. 8 presents plots of the average transverse crack length (Fig. 8a) and the number of transverse cracks (Fig. 8b) versus distance ahead of the insert tip. As SST specimens are all the same width, the number of transverse cracks will be directly related to the average crack spacing. It is therefore noteworthy that the first data points in Fig. 8b (0.5 mm ahead of the insert tip) show a different trend than the data in Table 1 (immediately ahead of the insert tip). However, there is specimen-to-specimen variation in the number of transverse cracks that are measured, and there is some imprecision measuring these cracks using both optical microscopy and X-ray CT, particularly near the Teflon insert tip where the cracks are very small and difficult to see. Therefore, and as noted previously with respect to Table 1, it is likely the transverse crack spacing is similar for 24-ply and 48-ply specimens close to the insert tip. The vertical line on each plot in Fig. 8 denotes the distance ahead of the insert after which there was no longer a full planar delamination. Beyond this point, the data are obtained only for the transverse cracks in the center region of the specimen that continued advancing. Fig. 8 indicates that transverse crack lengths are similar in the two specimen thicknesses for the first 5 mm ahead of the Teflon insert tip, but that there are more transverse cracks in the 24-ply specimen. Note that the transverse cracks within this region are fairly small, so the length and number results may be somewhat influenced by the resolution of the X-ray CT. Starting at a distance of 5 mm beyond the insert tip there is a divergence between the two sets of data in Fig. 8a: here, the transverse cracks in the 48-ply specimens continue to grow in length at a reasonably similar rate, whereas there is only a small additional increase in length of the transverse cracks in the 24-ply specimen. The divergence occurs when the average crack length is approximately 1.5 mm, or 50% of the 24-ply specimen’s thickness. As described previously, it is likely that this occurs due to the proximity to the 24-ply specimen’s free surface. In contrast, the difference in the two data sets remains fairly constant in Fig. 8b, where more transverse matrix cracks are observed in the 24-ply specimen at any distance ahead of the insert tip. Both data sets show a gradual decrease in the number of cracks due to the coarsening process. 5.2. Edge crack torsion test

Transverse Crack Length (mm)

3.0

48 ply 24 ply

2.5 2.0 1.5 No full planar delaminaon

1.0 0.5 0.0

Number of Cracks (per 25.4 mm)

Because the average transverse crack lengths are much smaller in ECT than in SST specimens, a high resolution X-ray CT was utilized in order to accurately view crack surface evolution. This system covers only a small distance in the direction of growth (y-direction in Fig. 1b). Therefore, an ECT specimen with a/b = 0.3 was X-ray CT scanned in two locations: immediately ahead of the insert tip, and 1.7 mm ahead of the insert tip. These results are presented in Fig. 9, where the arrows included in Fig. 9b and c are used to indicate the location of the 90/45 interfaces. Fig. 9a and b are both immediately ahead of the insert tip. Fig. 9a is an expanded view of the inset of Fig. 9b. The dark, horizontal jagged line is right at the insert tip, at the specimen’s midplane. Thus, it may be observed that there is some growth at this location, which consists of many connected small transverse cracks at approximately 45° to the horizontal direction, plus a few relatively large transverse cracks at this same angle.

48 ply 24 ply

30 25

No full planar delaminaon

20 15 10 5 0

0

5

10

15

Distance Ahead of Insert Tip (mm)

(a)

20

0

5

10

15

20

Distance Ahead of Insert Tip (mm)

(b)

Fig. 8. Crack surface evolution data for SST. (a) Average transverse crack length. (b) Number of transverse cracks detected.

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(a)

100 μm

(b) 200 μm

(c) 200 μm

Fig. 9. X-ray CT images from an ECT specimen with a/b = 0.3. Images (a) and (b) are immediately ahead of the insert tip, (c) is 1.7 mm ahead of the insert tip.

Fig. 9c is from the cross-sectional plane that is 1.7 mm ahead of the insert tip. An intermediate image to Fig. 9b and c would appear similar to that shown in Fig. 5b, where delamination growth is evident at the 90/45 interface. However, at a distance of just 1.7 mm ahead of the insert tip, delamination advance no longer occurs. Small transverse cracks are also no longer evident. Rather, there appears to be crack coarsening analogous to that seen in the SST specimens, although shown here on a much finer scale and with higher resolution. One or two of the small transverse cracks of Fig. 9b appears to have extended, and the larger transverse cracks in Fig. 9b have grown in size, while the majority of the smaller cracks have arrested. As seen in Fig. 9c, the transverse cracks which extended have progressed through the two central 90° plies into the uncracked region, and the upper and lower bounding 45° plies are still constraining most, but not all, additional transverse crack growth. 6. Discussion 6.1. Effect of material and laminate architecture As described in the introduction, results from the literature indicate that planar cracks in homogeneous and geologic materials subjected to anti-plane shear loading initially advance in the same manner as growth that initiates from the tip of the insert in SST and ECT specimens. That is, propagation of the planar crack initially occurs through the development of an echelon of cracks oriented at approximately 45° to the original plane. The subsequent evolution of the fracture surface in homogeneous and geologic materials subjected to anti-plane shear has most commonly been studied under loadings that also produce some amount of crack opening or in which crack face compression occurs. Under these conditions, certain combinations of the spacing, length and orientation of the extending echelon array has been shown to cause some of the echelon cracks to be in regions of decreased stress and to arrest, and others to be in more dominant stress regions and to extend [13,15]. This produces coarsening. Typically, this is also accompanied by an overall twisting of the crack path from its original plane to one that ultimately aligns with the echelon array [15,19,31,32]. All of these mechanisms lead toward the expected final transition to a single mode I crack. For the SST specimen, however, the crack surface evolution is different. One important reason for this is that the laminate’s free surfaces bound the length of the transverse cracks. Thus, the energy-absorbing capacity of the transverse crack array is limited in comparison to homogenous materials. In addition, the longitudinal (0°) fibers constrain the original delaminated surface from gradually twisting to align itself with the transverse cracks, i.e., a significant amount of fiber breakage would have to occur in order for this to be accommodated. These observations indicate that it is unlikely that the SST will display a twisting crack path similar to that which often occurs in homogeneous materials. Rather, considering that the SST specimen contains a relatively weak interlaminar interface, the mechanism displayed – of the delamination extending along the interlaminar interface in the wake of the transverse crack array – would appear to be the most energetically favored. A comparison of the SST specimen’s behavior to that observed in the ECT specimen shows the distinct role played by the laminate’s architecture. Transverse matrix crack initiation has been shown to initiate identically in SST and ECT specimens Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013

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[9,22]. However, the similarities in matrix crack coarsening and growth in the two specimen types are limited to the plies adjacent to the midplane interface. Note that the two midplane 90° plies in the ECT specimen have a combined thickness of approximately 0.24 mm. By comparison to Table 1 and Fig. 8a, this is less than the average transverse crack length in the SST specimen just ahead of the Teflon insert tip. Thus, although the initial coarsening behavior may be identical in SST and ECT specimens, the effect of the bounding 45° plies very quickly limits the maximum transverse crack length in the ECT specimen. While the transverse cracks tend to primarily terminate at the upper 90/45 interface in the ECT specimen, at the lower 90/45 interface they link up and form a new delamination [22]. This new delamination initiates quite close to the tip of the insert, and delamination growth then proceeds along the lower 90/45 interface without extensive transverse cracking beyond the central two plies. No comparable migration occurs in the SST specimens, where delamination growth remains at the midplane. Thus it can be seen that altering the laminate architecture can both limit transverse crack length as well as shift the interface of a planar delamination. That is, in specimens of both types, there remains a coupling between the matrix cracking and planar delamination, but the evolution of the fracture surface remains heavily dependent on laminate architecture. 6.2. Application to mode III delamination toughness testing and prediction From the preceding discussions, it is clear that ‘‘mode III delamination’’ in polymeric fiber reinforced SST specimens consists of the linking and coalescence of a series of mode I transverse matrix cracks. The process in the ECT specimen is similar, but somewhat complicated by the migration of the delamination to the lower 90/45 interface. However, growth behaviors in both specimens certainly bear some resemblance to what occurs during mode II delamination toughness testing of unidirectional specimens, where a ‘‘mode II delamination’’ also consists of a linking and coalescence of mode I events. The difference is that the plies bounding the delamination in a unidirectional mode II specimen constrain the microcracking to the interlaminar region, whereas in conventional mode III specimens the bounding plies allow the microcracks to develop into intralaminar transverse cracks. For SST, these transverse cracks progress through the adjacent plies until they approach the free surfaces, whereas for ECT they are arrested when they reach the closest 45° plies. The result is an apparent mode III toughness that depends upon test geometry [9,22]. One partial solution to the above situation would be the development of a toughness test for pure mode III interlaminar delamination that is analogous to what is performed for mode II. It is likely that, for both SST and ECT specimens, stacking sequences could be chosen for which the microcracks will be constrained to the interlaminar region at the specimen’s midplane and macroscopically mode III delamination advance within this region will occur. This should produce a geometry-independent value of GIIIc for some range of bounding ply angles. This would be similar to the approach currently used for both mode I and mode II testing, as these tests will also produce different toughnesses if the ply angle is changed significantly from 0° [33]. For many purposes, this will produce satisfactory results. However, it would not address the larger issue that delamination growth in practical structural geometries that experience anti-plane shear loading will often occur similarly to that observed herein. For this more general situation, a more robust delamination growth prediction methodology is required. This would require prediction of the competing failure modes of transverse matrix cracking, delamination advance, and other potential events, and would need to allow for the simultaneous or consecutive progression of more than one of these failure modes to occur as part of a sequential failure assessment. Here, it is possible that ECT and/or SST tests with stacking sequences chosen to allow some amount of transverse cracking and/or delamination migration to adjacent interfaces will provide important characterization or validation data. 7. Conclusions A study was conducted to determine the manner in which the coupled system of a delamination and multiple transverse cracks evolves and advances in mode III split shear torsion and edge crack torsion delamination toughness tests. Ultrasonic inspection, X-ray computed tomography and optical microscopy were utilized to view the fracture surface evolution both before and after the onset of planar delamination growth. The three-dimensional fracture surfaces from the two test types were compared to each other and to analogous results from homogeneous and geologic materials. Three clear differences emerged that caused the fracture surface evolution in composite laminates to differ from that in homogeneous materials. The first is that composite laminates contain energetically preferential fracture paths along interlaminar interfaces. The second is that the laminate’s fibers constrain the fracture surface from twisting. The third is that the amount by which transverse cracks can extend in a laminate is determined by the proximity of the preimplanted insert to other distinct interfaces: that of the free surfaces in SST specimens and of the 90/45 interfaces in ECT specimens. This third issue is primarily responsible for the different behaviors evidenced by the two types of specimens examined, whereas all three issues contribute to the different surface evolution in the unidirectional SST specimens studied herein in comparison to that which has been observed in homogeneous materials. In addition to the above, the insights from this and previous supporting works were used to make observations and suggestions regarding mode III delamination toughness testing and delamination growth predictions. Regarding the former issue, it was suggested that alternate stacking sequences for either or both specimens could likely be selected that would prevent the growth of transverse cracks, and that specimens of this type could be used to obtain a true mode III delamination Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013

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Please cite this article in press as: Horner AL et al. Three-dimensional crack surface evolution in mode III delamination toughness tests. Engng Fract Mech (2015), http://dx.doi.org/10.1016/j.engfracmech.2015.07.013