Micromechanics fracture in osteonal cortical bone: a study of the interactions between microcrack propagation, microstructure and the material properties

A two-dimensional micromechanical fibre reinforced composite materials model for osteonal cortical bone is presented. The interstitial bone is modelled as a matrix, the osteons are modelled as fibres, and the cement line is presented as interface tissue. The interaction between osteons and microcracks is evaluated by linear elastic fracture mechanics theory, followed by a determination of the stress intensity factor at the vicinity of the microcrack tips. The results indicate that bone microstructural heterogeneity greatly influences fracture parameters. Furthermore, microstructural morphology and loading conditions affect growth trajectories, the microcrack propagation trajectory deviates from the osteon under tensile loading, and osteon penetration is observed under compressive loads.     

The behaviour of microcracks in compact bone

This paper summarises four separate studies carried out by our group over the past number of years in the area of bone microdamage. The first study investigated the manner by which microcracks accumulate and interact with bone microstructure during fatigue testing of compact bone specimens. In a series of fatigue tests carried out at four different stress ranges between 50 and 80 MPA, crack density increased with loading cycles at a rate determined by the applied stress. Variations in the patterns of microdamage accumulation suggest that that at low stress levels, larger amounts of damage can build up without failure occurring. In a second study using a series of four-pont bending tests carried out on ovine bone samples, it was shown that bone microstructure influenced the ability of microcracks to propagate, with secondary osteons acting as barriers to crack growth. In a third study, the manner by which crack growth disrupts the canalicular processes connecting osteocytes was investigated. Analysis of individual cracks showed that disruption of the canalicular processes connecting osteocytes occurred due to shear displacement at the face of propagating microcracks, suggesting that this may play some role in the mechanism that signals bone remodelling. In a fourth in vivo study, it was shown that altering the mechanical load applied to the long bones of growing rats causes microcrack formation. In vivo microdamage was present in rats subjected to hindlimb suspension with a higher microcrack density found in the humeri than the femora. Microdamage was also found in control animals. This is the first study to demonstrate in vivo microcracks in normally loaded bones in a rat model.     

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.     

Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.     

Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.     

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.     

Fatigue of immature baboon cortical bone

Strain-controlled uniaxial fatigue and monotonic tensile tests were conducted on turned femoral cortical bone specimens obtained from baboons at various ages of maturity. Fatigue loading produced a progressive loss in stiffness and an increase in hysteresis prior to failure, indicating that immature primate cortical bone responds to repeated loading in a fashion similar to that previously observed for adult human cortical bone. Bone fatigue resistance under this strain controlled testing decreased during maturation. Maturation was also associated with an increase in bone dry density, ash fraction and elastic modulus. The higher elastic modulus of more mature bone meant that these specimens were subjected to higher stress levels during testing than more immature bone specimens. Anatomical regions along the femoral shaft exhibited differences in strength and fatigue resistance.     

Visualization of a phantom post-yield deformation process in cortical bone

A prominent opacity is evident in the process zone of notched thin wafers of bone loaded in tension. Being recoverable upon unloading, this opaque zone can be stained only when the sample is under load, unlike the classically reported forms of damage which take up the stain in the unloaded state. Furthermore, despite the stain uptake, microcracks are absent in the stained area examined by high magnification optical microscopy and atomic force microscopy (AFM). Therefore, the size scale and the electric charge of the features involved in the process zone were probed at the submicron level by using a wide range of fluorescent dyes of different molecular weights and charges. It was observed that negatively charged dyes penetrate the process zone and that dyes greater than 10 kDa (about 10–20 nm in size) were unable to label the process zone. Digital image correlation (DIC) measurements indicated that the opacity initiates at about 1% principal strain and the strain accumulates up to 14%. While the opacity was largely recoverable upon unloading, the core regions which experienced large strains had permanent residual strains up to 2%, indicating that the observed deformation phenomenon can be interlocked within bone matrix without the formation of microcracks. Based on the similarity of size and their known affinity for negatively charged species, exposure of mineral nanoplatelets is proposed as prime candidates. Therefore, the deformation process reported here may be associated with debonding of mineral crystals from the neighboring collagen molecules. Overall, post-yield deformation of bone at the micron scale takes place by large strain events which are accommodated in bone matrix by the generation of nanoscale positively charged interfaces.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

Fracture mechanics of bone with short cracks

Tensile fracture experiments were performed upon specimens of wet mature bovine Haversian bone, with short, controlled notches. Stress concentration factors were found to be significantly less than values predicted using a maximum stress criterion in the theory of elasticity. Results were also modeled with the aid of linear elastic fracture mechanics. Agreement of experiment with theory was better in this case, however deviations were seen for short notches. Two mechanisms were evaluated for the behavior: plasticity near the crack tip, and effects of the Haversian microstructure, modelled by Cosserat elasticity, a generalized continuum theory. Plastic zone effects were found to be insignificant. Cosserat elasticity, by contrast, predicted stress concentration factors which better approximated observed values. To explore strain redistribution processes, further experiments were conducted upon notched specimens in torsion at small strain. They disclosed a strain redistribution effect consistent with Cosserat elasticity. These microelastic effects were attributed to the Haversian architecture of bone. The implications of the results are that bone resists the effect of stress raisers such as fatigue microcracks and surgical sawcuts to a much greater extent than anticipated on the basis of its elastic or elastoplastic properties.     

Microdamage propagation in trabecular bone due to changes in loading mode

Microdamage induced by falls or other abnormal loads that cause shear stress in trabecular bone could impair the mechanical properties of the proximal femur or spine. Existing microdamage may also increase the initiation and propagation of further microdamage during subsequent normal, on-axis, loading conditions, resulting in atraumatic or "spontaneous" fractures. Microdamage formation due to shear and compressive strains was studied in 14 on-axis cylindrical bovine tibial trabecular bone specimens. Microdamage was induced by a torsional overload followed by an on-axis compressive overload and quantified microscopically. Fluorescent agents were used to label microdamage and differentiate damage due to the two loading modes. Both the microcrack density and diffuse damage area caused by the torsional overload increased with increasing shear strain from the center to the edge of the specimen. However, the mean microcrack length was uniform across the specimen, suggesting that microcrack length is limited by microstructural features. The mean density of microcracks caused by compressive overloading was slightly higher near the center of the specimen, and the diffuse damage area was uniform across the specimen. Over 20% of the microcracks formed in the initial torsional overloading propagated during compression. Moreover the propagating microcracks were, on average, longer than microcracks formed by a single overload. As such, changes in loading mode can cause propagation of microcracks beyond the microstructural barriers that normally limit the length. Damage induced by in vivo off-axis loads such as falls may similarly propagate during subsequent normal loading, which could affect both remodeling activity and fracture susceptibility.     

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.     

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.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

The role of the lamellar interface during torsional yielding of human cortical bone

Fragility fractures are a result of alterations in bone quantity, tissue properties, applied loads, or a combination of these factors. The current study addresses the contribution of cortical bone tissue properties to skeletal fragility by characterizing the shear damage accumulation processes which occur during torsional yielding in normal bone. Samples of human femoral cortical bone were loaded in torsion and damaged at a post-yield twist level. The number of microcracks within osteons, interstitial tissue, and along cement lines were assessed using basic fuchsin staining. Damage density measures (number of cracks/mm2) were correlated with stiffness degradation and changes in relaxation. Damaged samples exhibited a wide variation in total microcrack density, ranging from 1.1 to 43.3 cracks/mm2 with a mean density of 19.7 +/- 9.8 cracks/mm2. Lamellar interface cracks comprised more than 75% of the total damage, indicating that the lamellar interface is weak in shear and is a principal site of shear damage accumulation. Damage density was positively correlated with secant stiffness degradation, but only explained 22% of the variability in degradation. In contrast, damage density was uncorrelated with the changes in relaxation, indicating that a simple crack counting measure such as microcrack density was not an appropriate measure of relaxation degradation. Finally, a nonuniform microcrack density distribution was observed, suggesting that internal shear stresses were redistributed within the torsion samples during post-yield loading. The results suggested that the lamellar interface in human cortical bone plays an important role in torsional yielding by keeping cracks physically isolated from each other and delaying microcrack coalescence in order to postpone the inevitable formation of the fatal crack.     

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.     

The many adaptations of bone

Studies concerned with the "adaptations" in bones usually deal with modelling taking place during the individual's lifetime. However, many adaptations are produced over evolutionary time. This survey samples some adaptations of bone that may occur over both length scales, and tries to show whether short- or long-term adaptation is important. (a) Woven and lamellar bone. Woven bone is less mechanically competent than lamellar bone but is frequently found in bones that grow quickly. (b) Stress concentrations in bone. Bone is full of cavities that potentially may act as stress concentrators. Usually these cavities are oriented to minimise their stress-concentrating effect. Furthermore, the "flow" of lamellae round the cavities will still further reduce their stress-concentrating effect, but the elastic anisotropy of bone will, contrarily, tend to enhance it in normal loading situations. (c) Stiffness versus toughness. The mineral content of bone is the main determinant of differences in mechanical properties. Different bones have different mineral contents that optimise the mix of stiffness and toughness needed. (d) Synergy of whole bone architecture and material properties. As bone material properties change during growth the architecture of the whole bone is modified concurrently, to produce an optimum mechanical behaviour of the whole bone. (e) Secondary remodelling. The formation of secondary osteones in general weakens bone. Various suggestions that have been put forward to account for secondary remodelling: enabling mineral homeostasis; removing dead bone; changing the grain of the bone; taking out microcracks. (f) The hollowness of bones. It is shown how the degree of hollowness is adapted to the life of the animal.     

A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone

Targeted remodeling is activated by fatigue microcracks and plays an important role in maintaining bone integrity. It is widely believed that fluid flow-induced shear stress plays a major role in modulating the mechanotransduction process. Therefore, it is likely that fluid flow-induced shear stress plays a major role in the initiation of the repair of fatigue damage. Since no in vivo measurements of fluid flow within bone exist, computational and mathematical models must be employed to investigate the fluid flow field and the shear stress occurring within cortical bone. We developed a computational fluid dynamic model of cortical bone to examine the effect of a fatigue microcrack on the fluid flow field. Our results indicate that there are alterations in the fluid flow field as far as 150 microm away from the crack, and that at distances farther than this, the fluid flow field is similar to the fluid flow field of intact bone. Through the crack and immediately above and below it, the fluid velocity is higher, while at the lateral edges it is lower than that calculated for the intact model, with a maximum change of 29%. Our results suggest that the presence of a fatigue microcrack can alter the shear stress in regions near the crack. These alterations in shear stress have the potential to significantly alter mechanotransduction and may play a role in the initiation of the repair of fatigue microcracks.     

Determinants of Microdamage in Elderly Human Vertebral Trabecular Bone

Previous studies have shown that microdamage accumulates in bone as a result of physiological loading and occurs naturally in human trabecular bone. The purpose of this study was to determine the factors associated with pre-existing microdamage in human vertebral trabecular bone, namely age, architecture, hardness, mineral and organic matrix. Trabecular bone cores were collected from human L2 vertebrae (n = 53) from donors 54–95 years of age (22 men and 30 women, 1 unknown) and previous cited parameters were evaluated. Collagen cross-link content (PYD, DPD, PEN and % of collagen) was measured on surrounding trabecular bone. We found that determinants of microdamage were mostly the age of donors, architecture, mineral characteristics and mature enzymatic cross-links. Moreover, linear microcracks were mostly associated with the bone matrix characteristics whereas diffuse damage was associated with architecture. We conclude that linear and diffuse types of microdamage seemed to have different determinants, with age being critical for both types.     

Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods

The key parameters determining the elastic properties of an unidirectional mineralized bone fibril-array decomposed in two further hierarchical levels are investigated using mean field methods. Modeling of the elastic properties of mineralized micro- and nanostructures requires accurate information about the underlying topology and the constituents’ material properties. These input data are still afflicted by great uncertainties and their influence on computed elastic constants of a bone fibril-array remains unclear. In this work, mean field methods are applied to model mineralized fibrils, the extra-fibrillar matrix and the resulting fibril-array. The isotropic or transverse isotropic elastic constants of these constituents are computed as a function of degree of mineralization, mineral distribution between fibrils and extra-fibrillar matrix, collagen stiffness and fibril volume fraction. The linear sensitivity of the elastic constants was assessed at a default set of the above parameters. The strain ratios between the constituents as well as the axial and transverse indentation moduli of the fibril-array were calculated for comparison with experiments. Results indicate that the degree of mineralization and the collagen stiffness dominate fibril-array elasticity. Interestingly, the stiffness of the extra-fibrillar matrix has a strong influence on transverse and shear moduli of the fibril-array. The axial strain of the intra-fibrillar mineral platelets is 30–90% of the applied fibril strain, depending on mineralization and collagen stiffness. The fibril-to-fibril-array strain ratio is essentially ~1. This study provides an improved insight in the parameters, which govern the fibril-array stiffness of mineralized tissues such as bone.