5.3.1 Chevron Notch Test
Figure5.3apresents typical load-displacement curves obtained from chevron notch test on the three different seashells. All specimens initially displayed a linear response followed by a nonlinear part beyond the point marked by an arrow. The onset of nonlinearity indicates the beginning of crack propagation. Surprisingly in case of top shell and pearl oyster the failure was not catastrophic, rather a relatively stable crack extension was observed in the course of in-situ imaging. The thickness of the beams for each type of nacre was designed in such a way that the beams remain elastic when the load reaches maximum.
Therefore, inevitable slight variations in the thickness of the cantilever beams led to significant differences in stiffness across the samples (the bending stiffness of a beam scales with (thickness)3). Among the three, top shell displayed the highest maximum load (ca. 40 N) reached in the fracture test while red abalone failed at a load nearly one order of magnitude lower.
The interlaminar fracture toughness of the three nacres was calculated from the maximum load Fmax, and the elastic properties and geometry of the chevron notch specimen [22], using:
JIC¼F2max 1 2wðaÞ
@C
@a
min
¼F2maxImin (5.1)
WhereCandwdenote the compliance and width of the specimen at crack lengtha, respectively. The maximum load can be obtained from experiment, however the value ofIminneeds to be determined numerically or experimentally. In this study, a three- dimensional model of the chevron specimens was built using the commercial finite element software ABAQUS (v. 6.9, ABAQUS Inc., Providence, RI). The specimens were modeled as a transversely isotropic material (Ez¼30 GPa, Ep¼70 GPa,Gzp¼10 GPa, andvp ¼vzp¼0:2 [23]) with plane of isotropy being parallel to the fracture surface of the specimens. Appropriate boundary conditions were applied along the two symmetry planes of the model, and the compliance of the system was determined at different crack lengths.Imin was then determined for each sample geometry. Finally, the interlaminar toughness of the specimens was determined using Eq.5.1, yieldingJIC¼20514J/m2for top shell,JIC¼69 16J/m2for pearl oyster, andJIC ¼111J/m2for red abalone. These results are reported in Fig.5.3b, and for comparison the
“cross-laminar” fracture toughness (crack propagation across the direction of the tablets) is also included (the values were taken from fracture tests performed previously [13]). Interfacial fracture toughness is generally considered to be lower than the fracture toughness across the tablet layers, because of a variety of toughening mechanisms which are believed to be active primarily when the crack is traveling across the layers [13]; a crack extending through the interface is assumed to encounter only a weak barrier from the organic glue and brittle nano-bridges. Initial fracture toughness across the layers is, however, expected to be controlled
Fig. 5.3 (a) Typical load-displacement curves of the different shells obtained from chevron notch test.Arrows indicate the onset of crack propagation in each specimen; (b) interlaminar fracture toughness (average and standard deviation). The cross-laminar fracture toughness is also shown (Data from [13])
34 R. Rabiei et al.
by fracture toughness characteristics at the interface since crack initiation at any direction is mostly initiated by interface delamination. A comparison between these three toughness characteristics is shown in Fig.5.3bwhich suggests consistency between these hypotheses and the experiment. However for top shell, the interlaminar toughness is higher compared to the initial toughness across the layers. These surprising observations are further explored in the following sections.
5.3.2 In-situ “Half Chevron” Geometry
In order to further investigate the behavior of a crack propagating along the interfaces of the structure, in-situ fracture tests were carried out under optical microscope using half chevron notch specimens. Figure5.4displays optical images taken from the polished surface of the specimens during the crack growth along the tablets interfaces. Despite the presence of a sharp razor blade notch in the red abalone sample (Fig.5.4a), the crack tends to follow a growth line which is closer to the crack tip. A growth line is a ~20mm thick layer of organic material which separates two mesolayers of abalone shell [24]. It is believed that the growth line forms during a period in which mineral growth lessens due to an interruption of feeding [24].
Fracture tests across the tablets have shown that growth lines might cause a crack deflection thereby leading to an increased overall toughness due to the conflict between the weakest path (growth line) and maximum mechanical driving force (crack path) [24]. The high toughness is generally achieved when these two paths are perpendicular. Growth lines in red abalone function analogous to the cement lines surrounding osteons in cortical bone. The cement lines in bone deflect the intersecting cracks up to 90, thus increase the overall toughness of bone [2]. Crack deflection at the cement lines is believed to be the most potent toughening mechanism in bone [25]. However, these weak layers have an adverse effect on the overall toughness when they are lined up with the mechanical driving force in a certain configuration, as is the case for interfacial fracture of red abalone. This explains why the work of fracture in red abalone is significantly lower than those of pearl oyster and top shell, in which no growth line was observed to interfere with the main crack.
Interestingly, uncracked ligament bridging and crack deflection were observed for both pearl oyster and top shell (Fig.5.4b, c). An uncracked ligament bridge is an intact part of the material which bridges the crack walls sustaining a portion of the load, and therefore increases the ability of the material to resist fracture, i.e. higher fracture toughness.
Fig. 5.4 In-situ optical images taken from (a)redabalone, (b)pearloyster, and (c)topshell.Black arrowsin (a) indicate thegrowth line, and in (b) and (c) show uncracked ligament bridges. (d) SEM micrograph of the top shell specimen showing junction opening (black arrows) at an area close to the crack wall (white arrow)
5 Interfacial Fracture Toughness of Nacre 35
Uncracked ligament bridging is a well-understood mechanism observed in a wide range of materials including bone, dentine, metals and composites [26–28]. Additionally for top shell, a diffuse relatively whiter “process zone” ahead of the crack tip was captured through in-situ differential interference contrast (DIC) imaging on the polished surface of the fracture sample.
Stress whitening, a visual indication of inelastic deformation (here tablet sliding and junction opening), is a well- documented phenomenon in nacre and bone [13,29], which can lead to tremendous amplification in toughness [21]. In this case the process zone of top shell is likely to highly contribute to its superior toughness compared to the other two types of nacre. Figure5.4dpresents an SEM micrograph of the crack wall from a polished fracture sample of top shell in which junction opening (i.e. inelastic deformation) is clearly visible. The size of the process zone measured from this image is about 10mm, which is almost 40 times smaller than the measured size of the process zone in across direction [13]. From a fracture mechanics perspective, toughness originates from two competitive sources: extrinsic and intrinsic toughening mechanisms. Extrinsic toughening mechanisms, including crack deflection and uncracked ligament bridging, generally act at some distance from the crack tip, whereas intrinsic toughening mechanism which here originates from the toughness of the organic phase surrounding the aragonite tablets operates ahead of the crack tip only. Therefore, the overall interlaminar fracture toughness of top shell (~200 J/m2) is a resultant of both toughening mechanisms. Stress whitening was not clearly noticeable for pearl oyster compared to top shell. Furthermore, post-mortem SEM imaging on fracture surface from the two shells (Fig.5.5) revealed more pronounced crack deflection in top shell resulting in larger energy dissipation and higher toughness. Interestingly in both cases, occasional brittle tablet fracture was evident possibly as a result of an abrupt change in the crack path, i.e. crack kinks out of the interface.
5.3.3 Fracture Toughness Estimation for the Organic Interface
The apparent interlaminar fracture toughness measured from the test includes all the toughening mechanisms including bridging and process zone, and a direct measurement of the intrinsic toughness of the interfaces was not possible. Instead, an estimate of the toughness was obtained from the size of the process zone using linear elastic fracture mechanics (LEFM) analysis. Ahead of the crack tip biaxial tension dominates, and tablet sliding may be initiated ifsxx reaches the tensile Fig. 5.5 Post-mortem SEM micrographs from fracture surface of (a,b)pearloyster, and (c,d)topshell, showing crack deflection to different extents. Tablet fracture (marked byarrows) is evident in both cases at higher magnification images
36 R. Rabiei et al.
strength of nacre along the tablets, and before interlaminar fracture occurs. The asymptotic stress field can then be related to the size of the inelastic region, considering that the maximum height of that region occurs at an angley¼30 ;from the crack line. This leads to the simple expression [30]:
KIC¼2 ffiffiffiffiffiffi pph
0:79 sS (5.2)
UsingsS ¼60 MPa [31] andh ¼10mm (measured from the SEM imaging, Fig.5.4d) leads toKIC ¼0.43MPa ffiffiffiffi pm
. This can be converted to an energy form usingJIC¼ ð1v2ÞK2IC=Efor plane strain condition whereE¼30 GPa [31] is the elastic modulus of nacre across the direction of the tablets. This leads to a value ofJIC¼5.5 J/m2for the intrinsic plus process zone toughness of the interface. As for pearl oyster and red abalone, the fact that no process zone larger than a few tablets width was observed implies a higher bound of 0.4 ~ 1 J/m2for the intrinsic toughness of their organic interface.
These values are in good agreement with the previously reported data computed from the deformation properties of organic proteins reflected in nacre cohesive law [5]. This measured toughness value is comparable to the toughness of the mineral [32], despite the fact that in minerals toughness is achieved by high tensile strength while in the interface toughness is achieved by high deformability. Although powerful toughening mechanisms are present at the molecular level of the interface [17], the confinement of these proteins is so severe (20–30 nm interfaces) that toughening mechanisms associated with volumetric energy dissipation remain insignificant [33]. This analysis therefore suggests a low intrinsic toughness for the interfaces and highlights that some powerful toughening mechanisms resulting from the staggered structure of nacre must be at work in order to produce its tremendous toughness at the macroscale.