The typical engineering stress–strain responses for coquina, sandstone, and foam from the quasi-static compression tests are shown in Fig. 4. In general, the stress–strain curves for all the materials reveal linear response up to their peak compressive strengths. Sandstone, exhibited a medium compressive strength of 46.8 ± 3.2 MPa. On the other hand, the coquina had a very low strength of 5.6 ± 0.6 MPa. The commercial cellular foam had a peak strength of around 2.8 ± 0.03 MPa. Similarly, it was determined that the elastic moduli for the coquina and foam (151 ± 17 and 99 ± 0.3 MPa) were an order of magnitude lower than that of the sandstone (4404 ± 20 MPa). The low modulus along with low-density of coquina are primarily due to its highly porous microstructure and weak bonding of the constituent particles. The above values are summarized in Table 2.
Once the peak strength was reached, both coquina and sandstone experienced a sharp drop in strength (typical of brittle failure). The sandstone failed catastrophically at only ~1.5 % strain and the strength dropped sharply to zero after reaching its maximum compressive strength of 46.8 MPa (see Fig. 4a and b). On the contrary, after reaching its peak strength coquina displayed continued deformation at a residual strength close to 0.9 ± 0.1 MPa (16 % of peak strength). This deformation continued in an oscillatory manner over a large strain as seen in Fig. 4c. Thus, coquina was able to sustain applied loads over a strain up to ~50 %. This behavior can be treated as a pseudo-ductility which enhances its energy absorbing capacity. Finally, beyond the peak strength of the foam, continued deformation at approximately a constant strength of ~3.0 MPa ensued over a large strain range similar to coquina (see Fig. 4d). Comparing the mechanical behaviors of coquina and foam, one can see that these materials exhibit ‘ductility’ and the ability to sustain load (i.e., residual strength) when stressed beyond their peak strength.
In order to elucidate the deformation mechanisms responsible for the observed stress–strain behavior, the in situ damage during quasi-static loading was captured by time-lapse photography (see Fig. 5). By examining the deformation characteristics during testing, clear differences in the failure behavior between the sandstone, coquina, and foam were observed and correlated to the strength and energy absorption capabilities of the materials. In the case of both the sandstone and coquina, as the applied force reached a maximum, several cracks were first initiated near the loading surfaces. For sandstone, several dominant cracks grew axially causing a catastrophic failure, as shown in Fig. 5a, followed by a rapid strength drop. At this point, the failure could be heard audibly, followed by large cracks fully propagating through the entire length of the sample and a few large fragments being ejected at high velocity. This behavior in sandstone was marked by a sudden energy release during loading which was reflected in the sudden strength drop in the stress–strain data (Fig. 4b). For the coquina, the sudden strength drop, seen in Fig. 4c, occurred as the top layer and some peripheral material crumbled (localized failure), and eventually fell off (see Fig. 5b). Under increased displacement, the remaining core material continued to sustain the load until further crumbling of the peripheral material occurred. This intermittent increase and decrease in load caused progressive crushing of coquina and periodic load oscillations. Thus, rather than demonstrating a catastrophic mode of failure, the coquina exhibited progressive crushing, i.e., gradual release of strain energy. Lastly, the foam deformation was characterized by localized crushing of the open foam cells near the loading surfaces. With increased displacement, further pore crushing occurred in the specimen until the foam eventually became an incompressible solid (see Fig. 5c). Thus, coquina and foam exhibited similar behaviors in terms of progressive crushing but through different energy absorbing mechanisms. In coquina, the loosely bonded shell fragments de-bonded and were crushed upon application of load, whereas, in foam, the struts of the cell walls buckled and crushed. Furthermore, the crushing behavior of the coquina is much more non-uniform due to the highly defective and heterogeneous microstructural make-up, which gives rise to oscillatory residual strength behavior, whereas the highly homogeneous porous structure in foam gives rise to a constant residual strength with continued deformation. Additionally, due to the brittle nature of the coquina, the failure process is marked by fracture and fragmentation rather than cell wall buckling in the foam.
Post-mortem fragment analysis of the test specimens, shown in Fig. 6, exemplified that the failure of the sandstone is marked by formation of long axial cracks and large columnar fragments. On the other hand, the progressive crushing behavior of the fragmented shells in coquina led to comminution of the specimen. Lastly, the foam displayed primarily pore crushing, during which, the cellular structure collapsed, and thus resulted in a dense solid of crushed foam.
The stress–strain responses of coquina, sandstone, and foam under dynamic compression (250, 600, and 7000/s, respectively) are displayed in Fig. 7. Similar to the static compression testing, the sandstone yielded a notably higher dynamic failure strength compared to that of the coquina, 87.6 ± 1.9 versus 8.3 ± 1.8 MPa, respectively. Additionally, the dynamic strength values for both materials were greater than their respective static strength values (see Table 2), suggesting that both materials showed strain rate sensitivity in strength for the strain rate regime examined in this investigation. This behavior is attributed to the fact that increased loading rate resulted in shorter time for cracks to initiate and grow while the applied stress continued to rise. This led to a greater compressive strength to failure. Note from the stress–strain responses in Fig. 7 that the sandstone exhibited a typical brittle failure mode (strength fell rapidly after reaching the peak value), while the coquina showed a more complex behavior. Thus, rather than failing catastrophically, the coquina showed a residual strength which is ~34 % of the peak strength. Also, unlike the sudden drop at peak strength during quasi-static loading (see Fig. 4c), the failure was much more gradual, with residual strength oscillating between 1 and 3 MPa. Lastly, the stress–strain response for foam was found to be similar to its static compressive response (Fig. 4d). The peak strength under dynamic load was around 2.4 ± 0.7 MPa. Beyond its elastic limit, the foam exhibited a nearly constant residual strength at almost the same peak strength. These values suggested that foam exhibits low rate-sensitivity in strength, whereas both sandstone and coquina revealed a significant increase in strength with strain rate for the examined strain rate range.
Deformation Mechanisms under Dynamic Loading
The fracture morphology under dynamic compression loading was analyzed from the high-speed images shown in Fig. 8. For the sandstone, a large number of shear-dominated cracks rapidly grew and caused a significant dilatation of the specimen. It is well known that brittle materials exhibit axial cracking during uniaxial compression loading . This was clearly observed for the sandstone during static loading (Fig. 4), but not during dynamic loading. Due to the abundance of porosity in sandstone, multiple cracks nucleated simultaneously under dynamic loading. Instead of primarily axial crack growth, a greater number of small cracks grew at an angle, characteristic of a quasi-ductile response due perhaps to inertial confinement afforded by the increased strain rate. Additionally, the sandstone reached catastrophic failure more rapidly (less than 100 μs) compared to the coquina (more than 200 μs). This behavior is reflected in the stress–strain curves in Fig. 7, where the peak strength was reached in a shorter strain range in sandstone than in coquina. This is attributed to the greater density and elastic modulus of sandstone. The greater level of microstructural interconnectivity and stronger interparticle bonding in the sandstone allowed for rapid stress transmission during dynamic loading and higher crack propagation velocities. For the coquina, the failure occurred by multiple crack initiation and propagation similar to its static behavior where numerous cracks were initiated in the specimen periphery leading to comminution and removal of the peripheral material. This behavior is further amplified by the highly heterogeneous microstructure of the coquina (e.g., abundance of pores and particle boundaries) where the crack path is expected to be more tortuous which delays catastrophic failure and leads to gradual softening of the entire coquina specimen as reflected in the stress–strain response in Fig. 7c. For the case of foam, the observed deformation mechanism is still crushing of the porous cells. The cell walls crumble gradually at a constant stress level over a long strain range. It appears that this deformation mechanism in foam is not strain rate dependent process because the stress level in both static and dynamic loading is almost the same (see Table 2).
Post-mortem examination of the dynamic compression test specimens, shown in Fig. 9, demonstrated enhanced fragmentation and pulverization of the sandstone compared to its static behavior. Due to rapid loading of the specimen, less time was available for long cracks to grow and propagate during dynamic loading. Thus, a large number of small cracks were formed, leading to increased comminution of the sandstone. The formation of conical fragments near the loading surfaces was the result of increase in friction between the sandstone and the steel bars under the dynamic loading. The deformation of the coquina and foam did not differ drastically from their static behaviors. Similar to static loading, coquina experienced comminution and fragmentation due to progressive crushing, while the foam failed by cellular crushing and compaction.
By computing the area under each stress–strain curve, the energy density, or energy per unit volume, consumed in the deformation process for each material was determined. These values are given in Table 2. During static compression, coquina had 2 times the energy absorption capability (0.59 ± 0.18 J cm−3) compared to that of sandstone (0.29 ± 0.05 J cm−3), but only half the absorption capacity of foam (1.25 J cm−3), as seen in Fig. 4. Despite having a high compressive strength, sandstone did not absorb high energy density due to its limited strain to failure range (1.5 %) and catastrophic brittle fracture. On the other hand, coquina and foam exhibited much lower compressive strength, but deformed over a larger strain exceeding 50 %. Despite having a greater peak strength, the coquina had half the energy density of the foam due to a lower residual strength and greater strength-drop beyond its peak strength. It is worth noting that the energy density calculations are not able to capture the true energy per unit volume absorbed during the post-failure response of coquina. Due to the continuous loss of peripheral material with increased strain (see Fig. 5b), the residual strength of the coquina refers to the load sustained by the remaining central column of coquina material. However, the calculations were performed considering the original volume of the specimen. With at least half of the cross-sectional area diminishing during deformation as seen in Fig. 5b, the energy consumed is at least twice that calculated, suggesting that coquina may in fact absorb significantly more specific energy than a characteristically brittle sedimentary rock such as sandstone.
The absorbed energy densities during dynamic loading for the sandstone and coquina were calculated to be 0.12 ± 0.07 and 0.11 ± 0.02 J cm−3, respectively. However, the coquina spread out the impact stresses appreciably over a larger strain range. It is presumed that such a response would be preferred for mitigating impact loads, producing a “softer” response than the typical catastrophic brittle response seen for sandstone. Compared to foam, the coquina still demonstrated a reduced capacity for energy absorption during dynamic loading. This is because of the instantaneous fracture of the coquina as soon as the dynamic load was applied where as in static loading the coquina was able to sustain nearly 50 % strain due to the continuous displacement of the piston in the machine. However, the dynamic loading caused instantaneous fracture and resulted in small strain values and low specific energy absorption. The foam withstood the same level of strain and exhibited similar crushing behavior in both static and dynamic loading, and yielded almost the same energy absorption in both cases as shown in Table 2.
Clearly, foam had the largest energy absorbed during deformation followed by coquina and sandstone. The brittle fracture and large fragmentation in sandstone results in small amount of energy absorbed during the deformation, whereas, progressive material shredding in coquina gives rise to large strain and higher energy absorption, especially at quasistatic loading. Due to small specimen thickness in dynamic loading, the progressive crushing of coquina could not be observed, Finally, the energy absorbed in the foam is the greatest due to its progressive crushing and ductile stress–strain response over a large strain range. In the impact experiments, the understanding developed above will be utilized to rationalize the ball impact response of each of the materials.
Ball Impact Experiments
The damage developed in sandstone, coquina, and foam due to ball impact (analogous to a cannonball impact event) was captured by high-speed imaging, as shown in Fig. 10. Clear differences were observed between the response of three materials. The ball impact on the sandstone at 75 m/s caused the rock to catastrophically shatter into many fragments due to the formation of a number of long cracks which appear as radial cracks on the impact surface. Upon impact, the strong bonding between the sand particles is suddenly released causing a rapid release of energy. Once structural cohesion is lost, the large fragments were ejected off. It was found that these fragments flew away at a velocity of approximately 20 m/s. At the same time, the ball rebounded at ~8 m/s. The images also revealed that the ball was in contact with the sandstone for less than 10 µs. The impact response was more characteristic of a hard material, typically observed for brittle materials under dynamic impact. Thus, energy dissipation in the sandstone was due to nearly instantaneous fragmentation.
On the other hand, the impact of the steel ball at 60 m/s on coquina was completely absorbed by the coquina and the ball itself was embedded in the coquina rock without forming any visible large cracks in the surrounding material at the time of the impact. Additionally, no rebound of the ball was observed. The impact response was characteristic of a soft material impact (quasi-ductile), owing to its highly porous structure (full of innumerable heterogeneous interfaces, pores, and other defects) and weak bonding between neighboring particles. Thus, as the ball advanced into the coquina, slow energy absorption occurred due to local crushing, but no large cracks were formed. Additionally, the significant particle comminution ahead of the projectile was evidenced in the high-speed images by the high-velocity ejecta which was expelled from the impact site, typical of an impact on brittle materials [16, 17]. The fine particle ejecta oppose the impacting ball and also erodes the impactor surface.
Finally, a ball impact on the foam at 82 m/s revealed that the ball was entirely absorbed and captured by the material. The ball was found to be embedded deeply in the foam without any damage extending to the surrounding area. Similar to coquina, deformation was highly localized to the impact site and was accommodated by localized crushing of foam cells beneath the impacting ball.
Post-mortem analysis of the recovered steel balls gave further insight into the nature of the interaction between the debris created and the incoming projectile. The impact surface of the ball, shown in Fig. 11 revealed evidence of wear and erosion due to the debris generated from sandstone and coquina. The frictional damage to the ball appeared as radial scratches and grooves on the ball as a result of the comminuted material passing by the ball at high velocity. No wear marks were observed on the steel balls which impacted foam (not shown for brevity). In Fig. 11a minor pitting of the surface is seen due to the impact on the hard sandstone, which dulls the surface. Figure 11b shows long grooves formed due to erosive action of debris from coquina as well as fine comminuted material adhered to the ball surface. Thus, it would be anticipated that increased frictional energy dissipation in coquina would lend itself to enhanced impact performance.