Contribution, development and morphology of microcracking in cortical bone during crack propagation

A fracture mechanics study of cortical bone is presented to investigate the contribution, development morphology of microcracking in cortical bone during crack propagation. Post-hoc analyses of microcrack orientation, crack propagation velocity and fracture surface roughness were conducted on previously tested human and bovine bone compact tension specimens. It was found that, consistent with its higher toughness, bovine bone formed significantly more longitudinal, transverse and inclined microcracks than human bone. However, in human bone more of the microcracks that formed were longitudinal than transverse or inclined, a feature that would optimise bone's toughness. Crack propagation velocity in human and bovine bone displayed the same characteristic pattern with crack extension, where an increase in velocity is followed by a consequent decrease and vice versa. On the basis of this pattern, a model or crack propagation has been proposed. It provides a detailed account of mocrocrack formation and contribution towards the propagation of a fracture crack. Analyses of fracture surfaces indicated that, consistent with its higher toughness, bovine bone displays a rougher surface than human bone but they both have the same basic fractured element, i.e. a mineralised collagen fibril.     

Equine cortical bone exhibits rising R-curve fracture mechanics

Previous studies of the fracture properties of cortical bone have suggested that the fracture toughness increases with crack length, which is indicative of rising R-curve behavior. Based on this indirect evidence and the similarity of bone to ceramic matrix composites, we hypothesized that bone would exhibit rising R-curve behavior in the transverse orientation and that the characteristics of the R-curves would be regionally dependent within the cortex due to variations in bone microstructure and toughening mechanisms. To test these hypotheses, we conducted R-curve experiments on specimens from equine third metacarpal bones using standard fracture mechanics testing methods. Compact type specimens from the dorsal and lateral regions in the middle of the diaphysis were oriented for crack propagation transverse to the longitudinal axis of the bone.The test results demonstrate that equine cortical bone exhibits rising R-curve behavior during transverse crack propagation as hypothesized. Statistical analyses of the crack growth initiation toughness, K0, the peak toughness, Kpeak, and the crack extension at peak toughness, deltaa, revealed significant regional differences in these characteristics. Specifically, the lateral cortex displayed higher crack growth initiation and peak toughnesses. The dorsal cortex exhibited greater crack extension at the peak of crack growth resistance. Scanning electron microscopy revealed osteon pullout on fracture surfaces from the dorsal cortex and but not in the lateral cortex. Taken together, the significant differences in R-curves and the SEM fractography indicate that the fracture mechanisms acting in equine cortical bone are regionally dependent.     

Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements

Fracture mechanics studies have characterized bone's resistance to fracture in terms of critical stress intensity factor and critical strain energy release rate measured at the onset of a fracture crack. This approach, although useful, provide a limited insight into fracture behavior of bone because, unlike classical brittle materials, bone is a microcracking solid that derives its resistance to fracture during the process of crack propagation from microfracture mechanisms occurring behind the advancing crack front. To address this shortfall, a crack propagation-based approach to measure bone toughness is described here and compared with crack initiation approach. Post hoc analyses of data from previously tested bovine and antler cortical bone compact specimens demonstrates that, in contrast to crack initiation approach, the crack propagation approach successfully identifies the superior toughness properties of red deer's antler cortical bone. Propagation-based slope of crack growth resistance curve is, therefore, a more useful parameter to evaluate cortical bone fracture toughness.     

Anisotropy of age-related toughness loss in human cortical bone: a finite element study

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.     

Cortical bone tissue resists fatigue fracture by deceleration and arrest of microcrack growth

Knowledge of kinetics of fatigue crack growth of microcracks is important so as to understand the dynamics of bone adaptation, remodeling, and the etiology of fatigue-based failures of cortical bone tissue. In this respect, theoretical models (Taylor, J. Biomech., 31 (1998) 587-592; Taylor and Prendergast, Proc. Instn. Mech. Engrs. Part H 211 (1997) 369-375) of microcrack growth in cortical bone have predicted a decreasing microcrack growth rate with increasing microcrack length. However, these predictions have not been observed directly. This study investigated microcrack growth and arrest through observations of surface microcracks during cyclic loading (R=0.1, 50-80MPa) of human femoral cortical bone (male, n=4, age range: 37-40yr) utilizing a video microscopy system. The change in crack length and orientation of eight surface microcracks were measured with the number of fatigue cycles from four specimens. At the applied cyclic stresses, the microcracks propagated and arrested in generally less than 10,000 cycles. The fatigue crack growth rate of all microcracks decreased with increasing crack length following initial identification, consistent with theoretical predictions. The growth rate of the microcracks was observed to be in the range of 5x10(-5) to 5x10(-7)mmcycle(-1). In addition, many of the microcracks were observed not to grow beyond 150 microm and a cyclic stress intensity factor of 0.5MNm(-3/2). The results of this study suggest that cortical bone tissue may resist fracture at the microscale by deceleration of fatigue crack growth and arrest of microcracks.     

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

     

Fracture toughness and fatigue crack propagation rate of short fiber reinforced epoxy composites for analogue cortical bone

Third-generation mechanical analogue bone models and synthetic analogue cortical bone materials manufactured by Pacific Research Laboratories, Inc. (PRL) are popular tools for use in mechanical testing of various orthopedic implants and biomaterials. A major issue with these models is that the current third-generation epoxy-short fiberglass based composite used as the cortical bone substitute is prone to crack formation and failure in fatigue or repeated quasistatic loading of the model. The purpose of the present study was to compare the tensile and fracture mechanics properties of the current baseline (established PRL "third-generation" E-glass-fiber-epoxy) composite analogue for cortical bone to a new composite material formulation proposed for use as an enhanced fourth-generation cortical bone analogue material. Standard tensile, plane strain fracture toughness, and fatigue crack propagation rate tests were performed on both the third- and fourth-generation composite material formulations using standard ASTM test techniques. Injection molding techniques were used to create random fiber orientation in all test specimens. Standard dog-bone style tensile specimens were tested to obtain ultimate tensile strength and stiffness. Compact tension fracture toughness specimens were utilized to determine plane strain fracture toughness values. Reduced thickness compact tension specimens were also used to determine fatigue crack propagation rate behavior for the two material groups. Literature values for the same parameters for human cortical bone were compared to results from the third- and fourth-generation cortical analogue bone materials. Tensile properties of the fourth-generation material were closer to that of average human cortical bone than the third-generation material. Fracture toughness was significantly increased by 48% in the fourth-generation composite as compared to the third-generation analogue bone. The threshold stress intensity to propagate the crack was much higher for the fourth-generation material than for the third-generation composite. Even at the higher stress intensity threshold, the fatigue crack propagation rate was significantly decreased in the fourth-generation composite compared to the third-generation composite. These results indicate that the bone analogue models made from the fourth-generation analogue cortical bone material may exhibit better performance in fracture and longer fatigue lives than similar models made of third-generation analogue cortical bone material. Further fatigue testing of the new composite material in clinically relevant use of bone models is still required for verification of these results. Biomechanical test models using the superior fourth-generation cortical analogue material are currently in development.     

Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study

The extent to which increased intracortical porosity affects the fracture properties of aging and osteoporotic bone is unknown. Here, we report the development and application of a microcomputed tomography based finite element approach that allows determining the effects of intracortical porosity on bone fracture by blocking all other age-related changes in bone. Previously tested compact tension specimens from human tibiae were scanned using microcomputed tomography and converted to finite element meshes containing three-dimensional cohesive finite elements in the direction of the crack growth. Simulations were run incorporating age-related increase in intracortical porosity but keeping cohesive parameters representing other age-related effects constant. Additional simulations were performed with reduced cohesive parameters. The results showed a 6% decrease in initiation toughness and a 62% decrease in propagation toughness with a 4% increase in porosity. The reduction in toughnesses became even more pronounced when other age-related effects in addition to porosity were introduced. The initiation and propagation toughness decreased by 51% and 83%, respectively, with the combined effect of 4% increase in porosity and decrease in the cohesive properties reflecting other age-related changes in bone. These results show that intracortical porosity is a significant contributor to the fracture toughness of the cortical bone and that the combination of computational modeling with advanced imaging improves the prediction of the fracture properties of the aged and the osteoporotic cortical bone.     

Compliance calibration for fracture testing of equine cortical bone

An experimental compliance calibration method for measuring crack length in fracture toughness tests of cortical bone was developed. Calibration tests were conducted on twenty compact type fracture specimens machined from the mid-diaphysis of five pairs of equine third metacarpal bones. Specimens were oriented for crack propagation in a direction transverse to the longitudinal axis of the bone. Specimen compliance was determined from the load vs. crack opening displacement record over a range of crack lengths from 0.48 to 0.75 times the specimen width. The results demonstrate that the compliance calibration method developed for isotropic materials can be used to determine crack length in bone, which is transversely isotropic. However, specimens from lateral and dorsal regions exhibited significantly different compliance calibrations even after differences in elastic modulus were taken into account in the normalized compliance.     

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.     

Effect of specimen thickness on fracture toughness of bovine patellar cartilage

Fracture toughness and crack tip opening angle were measured for bovine patellar cartilage using modified single-edged notch specimens of two thicknesses. There was no difference in fracture toughness between thin (0.7 mm) versus relatively thick (2.7 mm) specimens, but the crack tip opening angle at initiation of crack propagation was larger for the thin specimens (106 deg) than for the thick specimens (70 deg). Fracture toughness of the bovine patellar cartilage (1.03 kJ/m2) was not statistically different than that reported previously for canine patellar cartilage (1.07 kJ/m2) employing the same methods. Large variation in measurements for both bovine and canine cartilage are in part attributable to variation between individual animals, and are consistent with variation in other mechanical property measurements for articular cartilage. The observed reduction in crack tip opening angle with increased specimen thickness is consistent with behavior of some engineering materials, and demonstrates that specimen thickness influences fracture behavior for bovine patellar cartilage.     

Influence of loading condition and anatomical location on human cortical bone linear micro-cracks

Human cortical bone fracture toughness depends on the anatomical locations under quasi-static loading. Recent results also showed that under fall-like loading, cortical bone fracture toughness is similar at different anatomical locations in the same donor. While cortical bone toughening mechanisms are known to be dependent on the tissue architecture under quasi-static loading, the fracture mechanisms during a fall are less studied. In the current study, the structural parameters of eight paired femoral diaphyses, femoral necks and radial diaphyses were mechanically tested under quasi-static and fall-like loading conditions (female donors, 70 ± 14 y.o., [50–91 y.o.]). Synchrotron radiation micro-CT imaging was used to quantify the amount of micro-cracks formed during loading. The volume fraction of these micro-cracks was significantly higher within the specimens loaded under a quasi-static condition than under a loading representative of a fall. Under fall-like loading, there was no difference in crack volume fraction between the different paired anatomical locations. This result shows that the micro-cracking toughening mechanism depends both on the anatomical location and on the loading condition.     

Cohesive finite element modeling of age-related toughness loss in human cortical bone

Although the age-related loss of bone quality has been implicated in bone fragility, a mechanistic understanding of the relationship is necessary for developing diagnostic and treatment modalities in the elderly population at risk of fracture. In this study, a finite element based cohesive zone model is developed and applied to human cortical bone in order to capture the experimentally shown rising crack growth behavior and age-related loss of bone toughness. The cohesive model developed here is based on a traction–crack opening displacement relationship representing the fracture processes in the vicinity of a propagating crack. The traction–displacement curve, defining the cohesive model, is composed of ascending and descending branches that incorporate material softening and nonlinearity. The results obtained indicate that, in contrast to initiation toughness, the finite element simulations of crack growth in compact tension (CT) specimens successfully capture the rising R-curve (propagation toughness) behavior and the age-related loss of bone toughness. In close correspondence with the experimentally observed decrease of 14–15% per decade, the finite element simulation results show a decrease of 13% in the R-curve slope per decade. The success of the simulations is a result of the ability of cohesive models to capture and predict the parameters related to bone fracture by representing the physical processes occurring in the vicinity of a propagating crack. These results illustrate that fracture mechanisms in the process zone control bone toughness and any modification to these would cause age-related toughness loss.     

Fracture in human cortical bone: local fracture criteria and toughening mechanisms

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.     

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.     

Fracture-toughening mechanisms responsible for differences in work to fracture of hydrated and dehydrated dentine

This study investigates the nature of deformation and differences in the mechanisms of fracture and properties of dentine where there has been a loss of moisture, as may occur with removal of the pulp in the endodontic treatment of teeth. Controlled fracture toughness testing was conducted on bovine teeth to determine the influence of hydration on the work of fracture of dentine. Significant differences (p<0.01) were observed between the fracture toughness of hydrated (554+/-27.7J/m2) and dehydrated (113+/-17.8J/m2) dentine. Observations of the crack tip region during crack extension revealed extensive ligament formation occurred behind the crack tip. These ligaments provide considerable stability to the crack by significantly increasing the work of fracture, thereby acting as a fracture-toughening mechanism. Micro-cracking, reported as a fracture-toughening mechanism in bone, is also clearly seen. A zone of in-elastic deformation may occur as hydrated specimens revealed upon crack extension, a region about the tip that appeared to suck water into the structure and to exude water behind the crack tip. In dehydrated dentine, no in-elastic zone was observed. Micro-cracking is present though the cracks are smaller, straighter and with less opening than hydrated dentine. Only limited ligament formation just behind the crack tip was observed. These differences resulted in a significantly lower work of fracture with unstable brittle fracture characteristics. Based on these results, several fracture-toughening mechanisms were identified in dentine, with micro-cracking not considered the most important. These findings may be relevant for bone, a similar mineralised hydrated tissue.     

The effect of moisture absorption on the fatigue crack propagation resistance of acrylic bone cement.

In vivo, bone cement is subject to cyclic loading in a fluid environment. However, little is known about the effect of moisture absorption on the fatigue crack propagation resistance of bone cement. The effect of moisture absorption at 37 degrees C on the fatigue crack propagation resistance of a common bone cement (Endurance, DePuy, Orthopaedics, Inc.) was examined. Preliminary fracture toughness tests were conducted on disk-shaped, vacuum-mixed cement specimens (compact tension type) that were cyclically pre-cracked. Plain-strain fracture toughness K(IC) (MPa square root(m)) was determined. To study the effect of moisture absorption four treatment groups, with different soaking periods in Ringer's at 37 degrees C, of Endurance cement were tested. The specimens weights prior to and following soaking showed a significant increase in mean weight for specimens soaked for 8 and 12 weeks. Linear regression analysis of log(da/dN) vs. log (deltaK) was conducted on the combined data in each fatigue test group. Soaking bone cement in Ringer's at 37 degrees C for 8 and 12 weeks lead to an improvement in fatigue crack propagation resistance, that may be related to water sorption that increases polymer chain mobility, with enhanced crack tip blunting. It may be more physiologically relevant to conduct in vitro studies of fatigue and fracture toughness of bone cements following storage in a fluid environment.     

Advances in the fracture mechanics of cortical bone

As cortical bone is a semi-brittle solid, its fracture is dependent not only on the magnitude of the applied stress, but also on the nature of any intrinsic or introduced cracks. Consequently a variety of fracture mechanics techniques have been utilised to evaluate the fracture toughness of cortical bone, including the single edge notched, centre notched cylindrical and compact tension methods, and values have been established for the critical stress intensity factor (Kc) and the critical strain energy release rate (Gc). The Kc and Gc values obtained depend on the orientation of the cortical bone, as well as on bone density, the velocity of crack propagation and specimen geometry. The significance of these fracture mechanics parameters for cortical bone is critically reviewed.     

Material heterogeneity,microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.