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.     

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.     

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.     

Application of fracture mechanics to failure in manatee rib bone

BACKGROUND: The Florida manatee (Trichechus manatus latirostris) is listed as endangered by the U.S. Department of the Interior. Manatee ribs have different microstructure from the compact bone of other mammals. Biomechanical properties of the manatee ribs need to be better understood. Fracture toughness (K(C)) has been shown to be a good index to assess the mechanical performance of bone. Quantitative fractography can be used in concert with fracture mechanics equations to identify fracture initiating defects/cracks and to calculate the fracture toughness of bone materials. METHOD OF APPROACH: Fractography is a standard technique for analyzing fracture behavior of brittle and quasi-brittle materials. Manatee ribs are highly mineralized and fracture in a manner similar to quasi-brittle materials. Therefore, quantitative fractography was applied to determine the fracture toughness of manatee ribs. RESULTS: Average fracture toughness values of small flexure specimens from six different sizes of manatees ranged from 1.3 to 2.6 MPa(m)(12). Scanning electron microscope (SEM) images show most of the fracture origins were at openings for blood vessels and interlayer spaces. CONCLUSIONS: Quantitative fractography and fracture mechanics can be combined to estimate the fracture toughness of the material in manatee rib bone. Fracture toughness of subadult and calf manatees appears to increase as the size of the manatee increases. Average fracture toughness of the manatee rib bone materials is less than the transverse fracture toughness of human and bovine tibia and femur.     

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.

     

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.     

Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behavior

Bone is a hierarchical material exhibiting different fracture mechanisms at each length scale. At the submicroscale, the bone is composed of mineralized collagen fibrils (MCF). At this scale, the fracture processes in cortical bone have not been extensively studied in the literature. In this study, the influence of MCF size and orientation on the fracture behavior of bone under both transverse and longitudinal loading was investigated using novel 3D models of MCF networks with explicit representation of extra-fibrillar matrix. The simulation results showed that separation between MCFs was the main cause of damage and failure under transverse loading whereas under longitudinal loading, the main damage and failure mechanism was MCF rupture. When the MCF network was loaded in the transverse direction the mechanical properties increased as the orientation of fibrils deviated farther from the main fibril orientation whereas the opposite trend was observed under longitudinal loading. The fracture energy was much larger in longitudinal than transverse loading. MCF diameter variation did not affect the mechanical properties under longitudinal loading but led to higher mechanical properties with increasing MCF diameter under transverse loading. The new modeling framework established in this study generate unique information on the effect of MCF network spatial arrangement on the fracture behavior of bone at the submicroscale which is not currently possible to measure via experiments. This unique information may improve the understanding of how structural alterations at the submicroscale due to disease, age-related changes, and treatments affect the fracture processes at larger length scales.     

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.     

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.     

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.     

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.     

The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics

This paper reports on some theoretical work which used fracture mechanics concepts to draw conclusions about the nature of the so-called 'cellular transducer': the means by which bone cells detect the presence of damage and thus initiate remodelling and adaptation activities. Using analytical and numerical methods, we estimated the strains and displacements around cracks of the typical size, shape and orientation that normally occur in compact bone. We predicted that it is not possible for osteocytes or their processes to be fractured as a result of direct tensile strains, because the strains generated are much less than the expected failure strains of cellular material. We proposed a new failure mechanism by which osteocyte processes spanning the crack are cut by shearing motions between the crack faces. We predicted that failures of this type can occur. Failures begin to occur if crack lengths become greater than normal (100 microm), so this could act as a signal to initiate repair processes for individual cracks. Very large numbers of cell processes (greater than 1000) will fail if the crack length and/or applied stress reach dangerous levels (300 microm and 60 Mpa, respectively) at which point bone deposition may be required to prevent stress fractures. Similar results also occurred if we proposed a different mechanism of damage detection, involving cells' ability to detect the high levels of strain that occur near crack tips. This work, though based on theoretical mechanics considerations, suggests some biological experiments which might confirm our findings.     

Effect of temperature on the fracture toughness of compact bone

Bone is a composite composed mainly of organics, minerals, and water. Many researchers have studied effects such as crack velocity, density, orientation, storage media, porosity, and age on the fracture toughness (K(C), also called critical stress intensity factor) of compact bone. Most of these studies were conducted at room temperature. Considering that the body temperature of animals is greater than room temperature, and that bone has a large volumetric percentage of organics and water (generally, 55-65%), it is hypothesized that temperature has a significant effect on the fracture toughness of compact bone. Single-edge V-notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37, and 50 degrees C in four-point flexure. The fracture toughness values of bovine femur and manatee rib were found to decrease from 7.0 to 4.3MPam(1/2) and from 5.5 to 4.0MPam(1/2), respectively, as temperature increased over a temperature range of 50 degrees C. The results support the hypothesis that temperature has a significant effect on the fracture toughness of compact bone. Therefore, we suggest that study on fracture toughness of bone should be done at physiologically relevant temperatures.     

Fracture toughness and work of fracture of hydrated, dehydrated, and ashed bovine bone

Bone, a tri-phase composite, consists of nano-sized apatite minerals, an organic component, and water. Heat-treated bovine cortical bone has been proposed as a candidate for void-filling bone substitute. However, the toughness of heat-treated bone is not yet fully studied. Fracture toughness (K(c)) and work of fracture (W(f)) of hydrated, dehydrated, and ashed bovine bone were estimated using a single-edge V-notched beam method. Thermal gravimetric analysis and differential thermal analysis were used to determine the temperature at which the organics and water were removed. Dehydrated specimens were obtained by placing the samples in a 60 degrees C vacuum oven for 24h or a 110 degrees C furnace for 2h. Ashed specimens were obtained by heat-treating samples at 600 degrees C for 24h. K(c) of bovine specimens decreased from 5.5MPa.m(1/2) for hydrated bone, to 3.8MPa.m(1/2) for dehydrated specimens, and to 0.36MPa.m(1/2) for ashed specimens. W(f) decreased from 7.1 to 1.1kJ/m(2) for dehydrated specimens, and to 0.04kJ/m(2) for ashed specimens. The main reasons for the significant decreases in K(c) and W(f) may be attributed to water's ability in stabilizing collagen structure and to the organics' ability in making bone more ductile. Because of the large decrease in fracture toughness and work of fracture, we suggest that ashed bone is not appropriate for load-bearing bone substitute in areas where bone experiences loadings in flexure.     

Fatigue microcracks that initiate fracture are located near elevated intracortical porosity but not elevated mineralization

In vivo microcracks in cortical bone are typically observed within more highly mineralized interstitial tissue, but postmortem investigations are inherently limited to cracks that did not lead to fracture which may be misleading with respect to understanding fracture mechanisms. We hypothesized that the one fatigue microcrack which initiates fracture is located spatially adjacent to elevated intracortical porosity but not elevated mineralization. Therefore, the spatial correlation between intracortical porosity, elevated mineralization, and fatigue microdamage was investigated by combining, for the first time, sequential, nondestructive, three-dimensional micro-computed tomography (micro-CT) measurements of each in cortical bone specimens subjected to compressive fatigue loading followed by a tensile overload to fracture. Fatigue loading resulted in significant microdamage accumulation and compromised mechanical properties upon tensile overload compared to control specimens. The microdamage that initiated fracture upon tensile overload was able to be identified in all fatigue-loaded specimens using contrast-enhanced micro-CT and registered images. Two-point (or pair) correlation functions revealed a spatial correlation between microdamage at the fracture initiation site and intracortical porosity, but not highly mineralized tissue, confirming the hypothesis. This difference was unique to the fracture initiation site. Intracortical porosity and highly mineralized tissue exhibited a significantly lower and higher probability, respectively, of being located spatially adjacent to all sites of microdamage compared to the fracture initiation site. Therefore, the results of this study suggest that human cortical bone is tolerant of most microcracks, which are generally compartmentalized within the more highly mineralized interstitial tissue, but a single microcrack of sufficient size located in spatial proximity to intracortical porosity can compromise fracture resistance.     

Assessment of cortical bone fracture resistance curves by fusing artificial neural networks and linear regression

Bone injures (BI) represents one of the major health problems, together with cancer and cardiovascular diseases. Assessment of the risks associated with BI is nontrivial since fragility of human cortical bone is varying with age. Due to restrictions for performing experiments on humans, only a limited number of fracture resistance curves (R-curves) for particular ages have been reported in the literature. This study proposes a novel decision support system for the assessment of bone fracture resistance by fusing various artificial intelligence algorithms. The aim was to estimate the R-curve slope, toughness threshold and stress intensity factor using the two input parameters commonly available during a routine clinical examination: patients age and crack length. Using the data from the literature, the evolutionary assembled Artificial Neural Network was developed and used for the derivation of Linear regression (LR) models of R-curves for arbitrary age. Finally, by using the patient (age)-specific LR models and diagnosed crack size one could estimate the risk of bone fracture under given physiological conditions. Compared to the literature, we demonstrated improved performances for estimating nonlinear changes of R-curve slope (R² = 0.82 vs. R² = 0.76) and Toughness threshold with ageing (R² = 0.73 vs. R² = 0.66).     

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.     

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.     

Experimental validation of a microcracking-based toughening mechanism for cortical bone

It has been proposed that cortical bone derives its toughness by forming microcracks during the process of crack propagation (J. Biomech. 30 (1997) 763; J. Biomech. 33 (2000) 1169). The purpose of this study was to experimentally validate the previously proposed microcrack-based toughening mechanism in cortical bone. Crack initiation and propagation tests were conducted on cortical bone compact tension specimens obtained from the antlers of red deer. For these tests, the main fracture crack was either propagated to a predetermined crack length or was stopped immediately after initiating from the notch. The microcracks produced in both groups of specimens were counted in the same surface area of interest around and below the notch, and crack growth resistance and crack propagation velocity were analyzed. There were more microcracks in the surface area of interest in the propagation than in initiation specimens showing that the formation of microcracks continued after the initiation of a fracture crack. Crack growth resistance increased with crack extension, and crack propagation velocity vs. crack extension curves demonstrated the characteristic jump increase and decrease pattern associated with the formation of microcracks. The scanning electron micrographs of crack initiation and propagation displayed the formation of a frontal process zone and a wake, respectively. These results support the microcrack-based toughening mechanism in cortical bone. Bone toughness is, therefore, determined by its ability to form microcracks during fracture.     

Propagation of surface fatigue cracks in human cortical bone

An understanding of how fatigue cracks grow in bone is of importance as fatigue is thought to be the main cause of clinical stress fractures. This study presents new results on the fatigue-crack growth behavior of small surface cracks (approximately 75-1000 microm in size) in human cortical bone, and compares their growth rates with data from other published studies on the behavior of both surface cracks and many millimeter, through-thickness large cracks. Results are obtained with a cyclically loaded cantilever-beam geometry using optical microscopy to examine for crack growth after every 100-500 cycles. Based on the current and previous results, small fatigue cracks appear to become more resistant to fatigue-crack growth with crack extension, analogous to the way the fracture resistance of cortical bone increases with crack growth. Mechanistically, a theory attributing such behavior to the development of bridges in the wake of the crack with crack growth is presented. The existence of such bridges is directly confirmed using optical microscopy.