Relaxation capacity of cartilage is a critical factor in rate- and integrity-dependent fracture

Articular cartilage heals poorly but experiences mechanically induced damage across a broad range of loading rates and matrix integrity. Because loading rates and matrix integrity affect cartilage mechanical responses due to poroviscoelastic relaxation mechanisms, their effects on cartilage failure are important for assessing and preventing failure. This paper investigated rate- and integrity-dependent crack nucleation in cartilage from pre- to post-relaxation timescales. Rate-dependent crack nucleation and relaxation responses were obtained as a function of matrix integrity through microindentation. Total work for crack nucleation increased with decreased matrix integrity, and with decreased loading rates. Critical energy release rate of intact cartilage was estimated as 2.39 ± 1.39 to 2.48 ± 1.26 kJ m−2 in a pre-relaxation timescale. These findings showed that crack nucleation is delayed when cartilage can accommodate localized loading through poroviscoelastic relaxation mechanisms before fracture at a given loading rate and integrity state.

www.nature.com/scientificreports/ PVE relaxation was not clearly made. It is difficult to find the link by combining previous studies because failure was not investigated from pre-to post-relaxation timescales and PVE relaxation corresponding to the failure was not examined. Furthermore, the effect of solid matrix integrity on rate-dependent cartilage failure is currently missing in the literature. To summarize, mechanically mediated cartilage failure can be hypothesized to depend on loading rates and solid matrix integrity 37,38 . The current study tests this hypothesis by investigating crack nucleation in cartilage as a function of solid matrix integrity across pre-to post-relaxation time scales (Fig. 1C).
In this study, crack nucleation in intact and GAG-depleted cartilage was induced across a broad range of loading rates through microindentation. GAG-depleted cartilage simulated the early stages of OA 39,40 . Microindentation with a sharp axisymmetric probe enabled localized crack nucleation with smaller standard deviations in comparison to macroscopic testing 36,41 . Crack nucleation was identified as a sudden drop in load and was characterized by the critical load, displacement, and total work at onset of failure. In addition, PVE relaxation responses of intact and GAG-depleted cartilage were measured with the same testing system used for crack nucleation. Finally, crack nucleation results combined with the relaxation responses provided total work required for crack nucleation in intact and GAG-depleted cartilage across pre-to post-relaxation timescales. Relaxationdependent crack surfaces were visualized via an optical microscope. These experimental results demonstrated that crack nucleation in intact and GAG-depleted cartilage was governed by how quickly cartilage was able to accommodate localized loading through PVE relaxations.

Results
Crack nucleation depends on solid matrix integrity and loading rates. The effects of loading rates on cartilage failure as a function of integrity were investigated by inducing crack nucleation in intact and GAGdepleted cartilage with a microscale tip at multiple loading rates (0.005-5 mm s −1 ) ( Fig. 2A). The moment of crack nucleation was identified through a sudden drop in the load response and was quantified with critical parameters (Fig. 2): critical load, L C , critical displacement, D C , critical total work, W C , and critical time, T C . All of the loading conditions except for GAG-depleted cartilage at 0.005 mm s −1 achieved crack nucleation. Loading rates and GAG depletion significantly affected critical parameters (Fig. 2B). For all loading rates, the recorded loads were higher for intact cartilage than those for GAG-depleted cartilage ( Fig. 2B and Fig. S1A) due to GAG-depletion induced loss of compressive stiffness. GAG depletion approximately increased critical loads by 30-45% at matching loading rates (5-0.05 mm s −1 : p < 0.01). For both intact and GAG-depleted tissues, critical loads at the onset of crack nucleation decreased as the loading rates increased (Intact and GAG-depleted: p < 0.0001) (Fig. 2C). Critical load of intact cartilage at 0.005 mm s −1 (7.08 ± 0.97 N) was approximately 4 times higher on average than that at 5 mm s −1 (1.86 ± 0.37 N). Critical load of GAG-depleted cartilage at 0.05 mm s −1 (6.61 ± 0.96 N) was approximately 3 times higher on average than that at 5 mm s −1 (2.46 ± 0.27 N). GAG depletion increased critical displacement by approximately 55-100% at corresponding loading rates (5-0.05 mm s −1 : p < 0.001). Critical displacements of intact and GAG-depleted cartilage decreased with increasing loading rates (intact and GAG-depleted: p < 0.0001) (Fig. 2C). Critical displacement of intact cartilage at 0.005 mm s −1 (0.78 ± 0.07 mm) was nearly 4 times larger on average than that at 5 mm s −1 (0.20 ± 0.02 mm). Critical displacement of GAG-depleted cartilage decreased nearly 3 times on average from 0.05 mm s −1 (0.91 ± 0.06 mm) to 5 mm s −1 (0.32 ± 0.03 mm). GAG depletion increased total work required for crack nucleation by approximately 80-150% across all of the loading rates (5-0.05 mm s −1 : p < 0.001). For both intact and GAG-depleted cartilage, critical total work sharply decreased as loading rates increased (intact and GAG-depleted: p < 0.0001) (Fig. 2D). Critical work of intact cartilage at 0.005 mm s −1 (1.41 ± 0.27 mJ) was nearly 11 times larger on average than that at 5 mm s −1 (0.13 ± 0.04 mJ). Critical work of GAG-depleted cartilage went down nearly 6 times from 0.05 mm s −1 (1.42 ± 0.26 mJ) to 5 mm s −1 (0.25 ± 0.04 mJ). GAG depletion delayed critical time by approximately 55-100% across all of the loading rates (5-0.05 mm s −1 : p < 0.001). Critical times of intact and GAGdepleted cartilage decreased with increasing loading rates (intact and GAG-depleted: p < 0.0001) (Fig. 2E). Critical time of intact cartilage at 0.005 mm s −1 (155.17 ± 13.04 s) was around 3900 times larger on average than that at 5 mm s −1 (0.04 ± 0.004 s). Critical time of GAG-depleted cartilage increased around 300 times from 5 mm s −1 (0.06 ± 0.01 s) to 0.05 mm s −1 (18.16 ± 1.09 s).
GAG-depleted cartilage relaxes faster than intact cartilage. Integrity-dependent cartilage relaxation was examined by measuring relaxation responses of intact and GAG-depleted cartilage via a microscale tip at a constant displacement (Fig. 3A). The relaxation response of GAG-depleted cartilage was distinct from that of intact cartilage (Fig. 3B). The peak load of intact cartilage (2.12 ± 0.26 N) at an unrelaxed state (after 0 s of relaxation) was nearly 6.5 times higher on average than that of GAG-depleted cartilage (0.33 ± 0.05 N) ( Fig. 3B and Fig. S1B). The equilibrium load of intact cartilage (0.18 ± 0.03 N) at a relaxed state (after 200 s of relaxation) was 9 times higher on average than that of GAG-depleted cartilage (0.02 ± 0.005 N) ( Fig. 3B and Fig. S1B). GAGdepleted cartilage showed much faster relaxation than intact cartilage (50-90% of the total relaxation: p < 0.01) (Fig. 3B,C). Relaxation times were determined as time required to reach a certain percentage of the total relaxation based on a normalized experimental relaxation curve (Fig. 3B,C). For intact cartilage, relaxation times at 50, 70, and 90% of the total relaxation were 1.29 ± 0.12 s, 3.18 ± 0.29 s, and 13.07 ± 1.17 s, respectively (p < 0.0001). For GAG-depleted cartilage, relaxation times at 50, 70, and 90% of the total relaxation corresponded to 0.47 ± 0.14 s, 1.40 ± 0.44 s, and 8.04 ± 2.74 s, respectively (p < 0.0001). Intact cartilage showed higher elastic moduli compared to GAG-depleted cartilage (unrelaxed and relaxed: p < 0.001) ( Fig. 3D and Fig. S1B). Elastic moduli of intact cartilage at unrelaxed and relaxed states were 28.06 ± 3.23 MPa and 2.33 ± 0.40 MPa, respectively. Elastic moduli of GAG-depleted cartilage at unrelaxed and relaxed states were 4.56 ± 0.74 MPa and 0.25 ± 0.07 MPa, respectively. Some discrepancies in unrelaxed (instantaneous) and relaxed (equilibrium) moduli of intact and GAG-depleted Relaxation as a function of solid matrix integrity governs crack nucleation behavior. A relationship between crack nucleation in intact and GAG-depleted cartilage and PVE relaxation degree was investigated by linking critical time for crack nucleation with relaxation time (Fig. 4A). For intact cartilage, critical time   (Fig. 2E) was shorter than 50% relaxation time (Fig. 3C), and thus crack nucleation was induced in a pre-relaxation timescale. Conversely, critical time at 0.05 mm s −1 and 0.005 mm s −1 in intact cartilage belonged to a post-relaxation timescale. For GAG-depleted cartilage, critical time at 5 mm s −1 was shorter than 50% relaxation time, and therefore crack nucleation was generated in a pre-relaxation timescale. Critical time at 0.5 mm s −1 and 0.05 mm s −1 was within a post-relaxation timescale for GAG-depleted cartilage.
For both intact and GAG-depleted cartilage, much less critical total work was needed to induce crack nucleation in a pre-relaxation timescale compared to a post-relaxation time scale. Crack nucleation in GAG-depleted cartilage occurred at much higher relaxation degrees and critical total work than in intact cartilage. Although the critical total work curves ( Fig. 4A) visualized an important role of PVE relaxation degree in crack nucleation, there were sources for possible shifts of the curves. The loading ramp rate before the relaxation period ( Fig. 3B) was not instantaneous loading to prevent the onset of crack nucleation during the ramp loading. Analyzing the average relaxation time with a previous study 43 suggested that the relatively slow loading ramp rate could shift the curves for intact and GAG-depleted tissues toward higher relaxation degrees by about 1% and about 3%, respectively. In addition, the dependence of bulk PVE relaxation responses on a contact radius between the indenter and tissue can cause the shifts of the curves. This dependence results from PE relaxation because it depends on the square of a contract radius, controlling the PE diffusion length 19,44 . The comparison between the current study at a microscale length with our previous study at a macroscopic length showed that although the ratio of the square of contact radii at the two length scales was about 66, the ratio of average relaxation times between the two studies was only about 5 for intact and about 1 for GAG-depleted cartilage, respectively. Based on this comparison, as the ratio of a contact radius during the relaxation measurement to a contact radius experienced during crack nucleation tests was small (intact: < about 6 and GAG-depleted: < about 8), the effect of indentation depth on relaxation times would be minor.

Cracks become longer and more branched with greater relaxation degrees. A transition in
crack shapes from pre-to post-relaxation timescales was investigated via optical images of cracks stained with India ink (Fig. 4B,C). Crack lengths of intact cartilage increased from 430 ± 60 µm in a pre-relaxation timescale Similarly, crack lengths of GAG-depleted cartilage were rate-dependent (p < 0.01) and slightly increased from 715 ± 135 µm in a pre-relaxation timescale (5 mm s −1 ) to 750 ± 190 µm in a post-relaxation timescale (0.05 mm s −1 ) (Fig. 4B). The maximum crack length for GAG-depleted cartilage was 1060 ± 215 µm at 0.5 mm s −1 . The crack lengths (715 ± 135 µm) of GAG-depleted cartilage in a pre-relaxation timescale may be overestimated because possible sequential crack propagation was observed after the major crack nucleation. However, we were able to induce a single major crack nucleation event for intact and GAG-depleted cartilage at other loading rates without sequential crack events. The number of branches increased from two in a pre-relaxation timescale (5 mm s −1 ) to three in a postrelaxation timescale (0.05 mm s −1 ) (p < 0.0001) ( Fig. 4C and Fig. S2B). For GAG-depleted cartilage loaded at 0.005 mm s −1 , no evidence of crack nucleation was observed; i.e., no sudden load drops in microindentation response and no crack opening observed after staining.

Discussion
Poroviscoelastic relaxation at slow loading rates delays cartilage fracture. PVE relaxation mechanisms play a crucial role in determining the onset of cartilage failure, supported by critical total work combined with crack images showing that crack nucleation in intact and GAG-depleted cartilage was relaxationdependent. When crack nucleation in intact and GAG-depleted cartilage occurred in a post-relaxation timescale (Fig. 4A) where critical time (Fig. 2E) was larger than 50% relaxation time (Fig. 3B,C), critical total work was nearly an order of magnitude higher than that in a pre-relaxation timescale. This was because cartilage had  www.nature.com/scientificreports/ sufficient time to accommodate localized microindentation strains and thus distribute stresses over larger tissue volumes. This stress-diffusion process, as quantified by the degree of PVE relaxation, led to delays in crack nucleation 36 . Besides, a substantial portion of applied mechanical work was consumed by the PVE relaxation; specifically by the solid matrix rearrangement and solid-fluid frictional interactions. In contrast, microindentation over a pre-relaxation timescale led to localized stress and strains in the vicinity of the probe and thus provided strain energy with minimal losses to be used directly for crack nucleation. As a result, critical total work in a pre-relaxation timescale was much smaller. A transition in crack branches from pre-to post-relaxation timescales reiterated that PVE relaxation played a crucial role in crack nucleation in intact and GAG-depleted cartilage (Fig. 4B,C). In addition, the finding about critical total work across a broad range of relaxation degree (Fig. 4A) showed that critical total work was more sensitive to relaxation degree in a post-relaxation timescale. This could be because kinematic fibril rearrangement actively occurred in a post-relaxation timescale (intact: ≥ 85% relaxation degree and GAG-depleted: ≥ 65% relaxation degree) with the large exudation of fluid in the vicinity of the tip, resulting in the compaction of the tissue. These findings suggested that physical activities occurring over timescales shorter than relaxation time constants of the tissue would make cartilage significantly more vulnerable to failure.
Accelerated relaxation capacity delays cartilage fracture at given loading rates. GAG depletion allowed for access to the effects of PVE relaxation timescales on crack nucleation, reiterating that the relaxation degree governed crack nucleation even at different degrees of solid matrix integrity. GAG depletion accelerated cartilage PVE relaxation (Fig. 3B,C). This could be due to accelerated PE relaxation, resulting from the increased pore size of cartilage, or from possible alteration in time constants of intrinsic VE relaxation, resulting from altered nonfibrillar matrix density and collagen matrix configuration 6,24,28,42 . Crack nucleation in GAGdepleted cartilage required higher critical total work and relaxation degree than intact cartilage at corresponding loading rates (Fig. 4A). It has been reported that the collagen network in tension dominantly governed cohesive strength of cartilage rather than PGs with GAG side chains 5,6,45 . Consequently, the current findings, combined with the previous studies, indicated that accelerated PVE relaxation after GAG depletion delayed an increase in stress underneath the microscale tip 36 by rapidly accommodating localized loading at given loading rates. This rapid accommodation of GAG-depleted cartilage by accelerated PVE relaxation was likely to originate from the enhanced freedom of collagen fibril rearrangement in the absence of confined non-fibrillar matrixes, resulting in increased critical total work, critical load, and critical displacement for crack nucleation.
Estimations of critical energy release rates from crack morphologies in the pre-relaxation timescale. In the pre-relaxation timescale, GAG-depleted cartilage was likely to require less energy per unit fracture surface area than intact cartilage. The consistent line shapes of cracks in intact and GAG-depleted cartilage in pre-relaxation timescales (Fig. 4C) allowed for quick estimates of critical energy release rates via the energy-balance model of sharp-tipped punch penetration 46,47 . Detailed information about the model is given in the supplementary text and Fig. S3

Relaxation-dependent crack branching provides insight into cartilage failure.
Relaxation degree before crack nucleation affected crack lengths and morphologies. Crack lengths increased and more crack branching occurred from pre-to post-relaxation timescales (Fig. 4B,C and S2). Our observations as well as the literature suggested that cracks should nucleate at a single-line cut due to stress intensities. Subsequent release of energy during propagation of cracks could cause instabilities and fragmentation, especially when single-line cracks cannot increase free surfaces to balance large strain energies to be released. This mismatch can occur in ballistic loading cases as well as in quasistatic perforation of thin shells and plates 51,52 . Dynamic crack propagation and branching cannot be observed in our test setup. Besides, even though we varied loading rates to 5 mm s −1 , those speeds are still orders of magnitude lower than shear wave speeds, C S , of the tissue (C S = √ G/ρ ~ 1-10 m/s where G: shear modulus and ρ : density of the medium). Thus, a quasistatic loading scenario was more applicable to our microindentation-based crack nucleation tests. For slow loading cases studied (a post-relaxation timescale), the sphero-conical indenter penetrated significantly larger depths than fast loading cases (a pre-relaxation timescale) (Fig. 2C). At those depths, significant tensile strains accumulated due to the stretching of collagen fibers around the sharp tip (see the model in the supplementary material). This kinematic stretching combined with large strain energy accumulated in a post-relaxation timescale led to the splitting of the single-line cut in a three-branch crack as shown in Fig. 4C. Note that kinematic alignments and stretching of collagen fibers were limited in a pre-relaxation timescale (see SEM images in our previous work 36 ). Therefore, single-line cuts could create sufficient crack area to balance corresponding energy releases. To the best of the authors' knowledge, the current study is the first to report crack branching in cartilage. Despite being beyond the scope of this study, understanding the factors driving crack branching in cartilage could offer translational benefits given the tissue's limited healing ability. www.nature.com/scientificreports/ Estimated threshold flaw sizes of cartilage provide insight into catastrophic fracture due to pre-existing cracks. Another measure of cartilage's toughness is its tolerance to pre-existing cracks. Soft materials such as elastomers and double-network hydrogels exhibit excellent stretchability when pre-existing cracks have lengths below a threshold flaw size estimated as the ratio of toughness to work to rupture 53 . As noted above, the microindentation-based crack nucleation tests can readily deliver work to rupture (referred to as critical work above). However, this work is an apparent quantity affected by dissipation, strain energy density, and deformed volume. Since microindentation localizes large strains in the vicinity of the contact scaling with a contact radius, strain energy densities, S D , can be approximated by the ratio of the measured work to rupture, W C , to the cube of contact radius, a, ( S D ∼ W C a 3 ). Note that strain energy densities are non-homogenous under the indenter, and so the approximation should be treated as an averaged quantity. Besides, dissipated energy is included in that estimate, and thus, it should be treated as an upper boundary of critical strain energy densities (work to fracture). The work to fracture based on critical total work (Fig. S4) and the critical energy release rates (fracture energy) of intact and GAG-depleted cartilage in a pre-relaxation timescale (supplementary text and Fig. S3) allowed us to estimate their threshold flaw sizes (Fig. 5). These thresholds for intact cartilage at 5 mm s −1 and 0.5 mm s −1 were 78.16 ± 48.91 µm and 99.49 ± 55.53 µm, respectively. The threshold for GAG-depleted cartilage at 5 mm s −1 was 63.47 ± 41.32 µm with 1.17 ± 0.62 kJ m −2 critical energy release rate (105.55 ± 138.65 µm with 2.09 ± 2.99 kJ m −2 ). Those threshold flaw sizes are larger than cartilage's structural features (chondrocytes: ~ 13 µm 54 , spacing between GAG chains: ~ 3 nm 55 , and spacing between collagen fibrils: ~ 100 nm 56 ). Therefore structural features are unlikely to lead to a flaw-sensitive region where the tissue's toughness is compromised. However, load-induced cracks with lengths larger than those thresholds were observed in the literature 30,57 . Those pre-existing flaws can accelerate the catastrophic failure of cartilage. We did not report similar thresholds at post-relaxation timescales since the crack morphology and potential substrate effects blur estimation of critical strain energy release rates (fracture energy) and work to fracture.
Crack nucleation results improve understanding of cartilage failure during physiological activities. The current findings about relaxation-and integrity-dependent crack nucleation can provide insight into cartilage failure under physiological activities. Bulk strain rates of intact and GAG-depleted cartilage (5 mm s −1 ) in a pre-relaxation timescale were 3.35 ± 0.25 s −1 and 3.29 ± 0.21 s −1 , respectively, and fall within the lower bound of the strain rates during walking, jumping, and running 28,58,59 . Bulk strain rates of intact (0.005 mm s −1 ) and GAG-depleted (0.05 mm s −1 ) cartilage in a post-relaxation timescale were 0.0032 ± 0.0003 s −1 and 0.032 ± 0.029 s −1 , respectively, and could represent human resting. Bulk strain rates were estimated by dividing the ratio of critical displacement to thickness by critical time. The interpretation of the current findings with the bulk strain rates suggested that when load-associated time during physiological activities is in a prerelaxation timescale, cartilage failure could easily occur with relatively small total work.

Figure 5.
Comparison of intact and GAG-depleted cartilage with other materials in terms of the fracture energy, work to fracture, and length of flaw sensitivity. The diagonal lines represent the length of flaw sensitivity, calculated by dividing fracture energy (critical energy release rates) by work to fracture. The mechanical properties of other materials were from previous studies 53, [65][66][67][68][69] . The conversion of the mechanical properties into this plot was explained in a previous study 53 . The data points of intact and GAG-depleted cartilage were obtained from a pre-relaxation timescale, and the detailed process was included in the supplementary text, Fig. S3

Limitations
This study filled gaps in knowledge related to the link between cartilage failure and PVE relaxations, but limitations should be explored further. The experimental conditions were different from in vivo conditions. One of the possible differences could be the pre-compression levels of cartilage by body weight 60 at the moment of mechanically mediated crack nucleation. Since the unrelaxed and relaxed elastic moduli of GAG-depleted cartilage were lower than those of intact cartilage (Fig. 3D), the pre-compression levels of GAG-depleted cartilage would be higher compared to those of intact cartilage. However, the current findings with the fully hydrated cartilage thickness under no initial compression allowed us to compare crack nucleation in cartilage as a function of solid matrix integrity from pre-to post-relaxation timescales. The fundamental comparison could lay the foundation for understanding more complicated cases in in vivo conditions through experiments and simulations. Minor cracks in the initial stages of indentation might not be captured due to the noise floor in the load cell. Given the rigid kinematic constraint imposed by the indenter tip with a tip radius of 100 μm, these minor cracks were expected to have a crack length much smaller than the tip radius. As cartilage is a hydrated material, the identification of these minor cracks with an optical microscope is challenging. Moreover, these pre-existing flaws were smaller than the threshold flaw sizes of intact and GAG-depleted cartilage, and therefore we do not anticipate much compromise on cartilage failure responses in our measurements. In this sense, crack nucleation investigated in this study was defined as a major crack nucleation event that was detected with the current instrument. In order to distinguish between minor and major crack nucleation events, experimental instruments with higher force and displacement resolutions are required. Cartilage integrity was only controlled by depleting GAGs and non-fibrillar components via trypsin digestion, and thus the current study did not explore the effect of other fibrillar components (e.g., collagen fibrils) on relaxation-dependent cartilage failure. Cartilage relaxation behavior depends on temperature with accelerated relaxation at higher tempertures 61 , so testing at different temperatures would be expected to shift the time at which the pre-and post-relaxation timescales occur. As the indenter geometry governs stress distributions in the vicinity of the indenter tip, it can affect the numerical values of the crack nucleation results and the transition timescale from pre-to post-relaxation regimes 36,44 .

Conclusions
In conclusion, this work examined a link between rate-dependent crack nucleation and PVE relaxation as a function of cartilage integrity. An axisymmetric micro-indenter effectively generated rate-dependent crack nucleation in intact and GAG-depleted cartilage at known locations from pre-to post-relaxation timescales. Rate-dependent crack nucleation was governed by the degree of PVE relaxation at given cartilage integrity. The degeneration of solid matrix integrity by GAG depletion allowed access to a different PVE relaxation timescale, significantly decreased relaxation time, and increased critical total work for cartilage failure. These results indicated that GAG depletion enhanced the capacity of kinematic fibril rearrangement and fluid diffusion at given loading rates and thus delayed rupture of a collagen network and crack nucleation. For both intact and GAG-depleted cartilage, crack nucleation at the fast and slow loading rates occurred in pre-and post-relaxation timescales, respectively, and total work for crack nucleation rapidly increased toward a post-relaxation timescale. These results showed that cartilage in the vicinity of the tip experienced relatively large PVE relaxation, accompanied by kinematic fibril rearrangement and fluid diffusion, at the slow loading rates, resulting in delayed crack nucleation. The dependence of rate-dependent crack morphology on the degree of relaxation before failure provided further evidence for relaxation-governed rate-dependent crack nucleation in intact and GAG-depleted cartilage. These findings from pre-to post-relaxation timescales underlined the importance of PVE relaxation mechanisms in rate-dependent cartilage failure and provided new insight into the onset of load-induced cartilage damage. Also, these findings can be useful information for designing cartilage-like tough and dissipative hydrogel materials across a wide range of loading rates.

Methods
Sample preparation. Patellae of 20 porcine joints were harvested from a local abattoir (14 animals, 5-6 months old, sex unknown and assumed random) to prepare 100 full-thickness cartilage samples ( Fig. 2A). Samples were randomized across the ten test conditions such that no two samples in a given test condition were from the same animal. Six mm diameter cylindrical cores were obtained using a biopsy punch and a scalpel. A bottom surface parallel to an articular surface was created by removing subchondral bone with a microtome, allowing an indenter to be placed perpendicular to the articular surface.  0024 s), and the sampling rate at a loading rate of 0.005 mm s −1 was 50 Hz (every 0.02 s). The broad loading rates were selected to induce crack nucleation from pre-to post-relaxation timescales of intact and GAG-depleted cartilage. Rupture of intact and GAG-depleted cartilage was identified as a sudden drop in the measured load response (Fig. 2B). In this study, the first detectable load drop with the current instrument was defined as major crack nucleation. The indentation displacement was prescribed based on preliminary data so that only a single major crack was nucleated for all of the cases except for GAG-depleted cartilage at 5 mm s −1 . Maintaining single crack nucleation in GAG-depleted cartilage at 5 mm s −1 failed because sequential crack events were too close to the major crack event. Crack nucleation was quantified with critical load, L C , displacement, D C , and total work, W C , and critical time, T C (Fig. 2). The critical total work was obtained from the integral of load-displacement curves from zero to the critical displacement (trapezoidal integration with Origin 2018 (OriginLab, Northampton, MA)). The critical time was defined as the time required for crack nucleation and was determined by dividing the critical displacement by the corresponding loading rate. Ten tests for each loading rate were conducted at the center of 10 samples.
Relaxation responses of cartilage. Relaxation responses of intact and GAG-depleted cartilage were measured by conducting indentation tests on the articular surface. Tests were performed on the instrument with the sphero-conical indenter used for the crack nucleation tests. The indenter was moved down to a displacement of 0.3 mm (~ 18% of the average sample thickness) at a loading rate of 0.1 mm s −1 and then held for 200 s while the load response was measured. GAG-depleted cartilage was prepared in the same way as that for the crack nucleation tests. A total of 10 tests for each matrix integrity were performed at the center of 10 samples. Times required to reach 50, 70, and 90% of total relaxation were calculated from the results of the relaxation responses. The total relaxation was defined from maximum load to equilibrium load while the displacement was held constant. The equilibrium load was determined at 200 s of relaxation, beyond which load relaxation rates became negligibly small (~ 10 −4 N s −1 ) compared to the initial rates (~ 1.5 N s −1 for intact cartilage and ~ 0.6 N s −1 for GAG-depleted cartilage). Unrelaxed and relaxed elastic moduli of intact and GAG-depleted tissues were calculated at the maximum (0 s of relaxation) and equilibrium (200 s of relaxation) loads through a linear elastic solution for a rigid cone indenter 64 . Pre-and post-relaxation regimes (or timescales) were divided based on the time required to reach 50% of total relaxation.
Brightfield images of cracks. Cracks induced by microindentation tests were assessed through brightfield images. India ink was dropped on the articular surface and gently cleaned with DPBS and a delicate task wiper (Kimtech, Orange, TX). Then the articular surface was imaged using a IX-71 inverted microscope at 4 × (Olympus, Tokyo, Japan). Crack lengths and number of crack branches were measured manually using the segmented line tool in ImageJ (version 1.52a, National Institutes of Health). Each crack was measured three times and averaged to obtain the final crack length.
Statistical analysis. The Kruskal-Wallis test was used to determine the dependence of crack nucleation results (critical load, critical displacement, critical total work, critical time, crack lengths, and the number of branches) on loading rates, and relaxation time on relaxation degree. The Mann-Whitney U test was used to statistically compare experimental results (critical load, critical displacement, critical total work, critical time, relaxation times, and elastic moduli) from intact and GAG-depleted cartilage. Non-parametric tests were used as the number of samples was small. All statistical analysis was performed using MATLAB (The MathWorks, Inc., Natick, MA). A significance level of 5% was used for all tests.

Data availability
Data are available upon reasonable request from the corresponding author.