Re-evaluating the toughness of human cortical bone

Fracture of the porcine aorta. Part 1: symconCT fracture testing and DIC

Tissue failure and damage are inherent parts of vascular diseases and tightly linked to clinical events. Additionally, experimental set-ups designed to study classical engineering materials are suboptimal in the exploration of vessel wall fracture properties. The classical Compact Tension (CT) test was augmented to enable stable fracture propagation, resulting in the symmetry-constraint Compact Tension (symconCT) test, a suitable set-up for fracture testing of vascular tissue. The test was combined with Digital Image Correlation (DIC) to study tissue fracture in 45 porcine aorta specimens. Test specimens were loaded in axial and circumferential directions in a physiological solution at 37∘ C. Loading the aortic vessel wall in the axial direction resulted in mode I tissue failure and a fracture path aligned with the circumferential vessel direction. Circumferential loading resulted in mode I-dominated failure with multiple deflections of the fracture path. The aorta ruptured at a principal Green-Lagrange strain of approximately 0.7, and strain rate peaks that develop ahead of the crack tip reached nearly 400 times the strain rate on average over the test specimen. It required approximately 70% more external work to fracture the aorta by circumferential than axial load; normalised with the fracture surface, similar energy levels are, however, observed. The symconCT test resulted in a stable fracture propagation, which, combined with DIC, provided a set-up for the in-depth analysis of vascular tissue failure. The high strain rates ahead of the crack tip indicate the significance of rate effects in the constitutive description of vascular tissue fracture. STATEMENT OF SIGNIFICANCE: This paper represents a significant step forward in understanding the fracture properties of porcine aorta. Inspired by the Compact Tension test, we developed an ad hoc experimental protocol to investigate stable crack propagation in soft materials, providing new insights into the mechanical processes that lead to the rupture of vascular tissue. The set-up enables the assessment of strains and strain rates ahead of the crack tip, and our findings could improve the clinical risk assessment of vascular pathologies as well as optimize medical device design.

A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments

Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.

A critical evaluation of cortical bone fracture toughness testing methods

Cortical bone fracture mechanics which quantifies the tissue's resistance to fracture is widely regarded as important to finding key determinants of bone fragility and fracture. Currently, the most widely used fracture mechanics approach is the J-integral resistance (J-R) curve as defined in ASTM E1820 standard. This standard employs an unloading compliance (UC) method to estimate crack extension, necessary for fracture toughness and resistance curve (R-curve) quantification. Further, this UC method requires a series of unload-reload cycles to be conducted during the fracture test. However, cortical bone violates some assumptions on which the UC method is based, which are: no energy loss during the unload-reload cycles and any change in unloading compliance is only due to crack extension. Consequently, the aim of this study was to examine the impact of the UC method on the accuracy of fracture toughness measurement for bovine cortical bone. Ten pairs of single edged notched bend specimens were prepared from the posterior diaphysis of bovine tibiae and underwent three-point bending fracture tests. The paired specimens were divided into two groups: a cyclic loaded group and a monotonic loaded group. Further, crack extension was determined by the UC method for the cyclic group and by an optical method for both the cyclic and monotonic groups. From these, three different approaches were used to generate J-R curves from which three fracture toughness parameters were computed and compared between the three approaches. This comparison allowed the impact of crack extension estimation by the UC method as well as the unload-reload cycles on the accuracy of the fracture toughness measures to be assessed. Results show that the UC method underestimates crack extension by an average error of 73%. In addition, the combined effects from crack extension estimation using the UC method and the unload-reload cycles lead to a significant overestimation of the specimen's fracture toughness measures. This highlights the need for more studies to establish a standardized approach to cortical bone fracture testing.

Fracture behaviour and toughening mechanisms of dry and wet collagen

The growing interest to the use of collagen films for biomedical applications motivates the analysis of their fracture behaviour in different environments. Studies revealed the decreased mechanical strength and stiffness as well as increased plasticity in water compared to collagen specimens tested in air. However, the fracture behaviour of pure collagen films in both air and water has not been reported so far. In this paper, the entire process of mode-I loading of single-edge notched tension (SENT) specimens was recorded and analysed. In case of in-air (dry) specimens, cracks propagated rapidly in a brittle fashion while large plastic deformations were observed in aqua prior to failure due to crack opening and a blunting mechanism in wet specimens. The fracture-toughness parameters for pure collagen in air and in aqua were estimated using linear-elastic (K_I and G_I) and elasto-plastic (J_I) fracture-mechanics approaches, respectively, following the force-displacement response and deformational behaviour. G_IC and J_I were 1365 ± 112 J/m² and 2500 ± 440 J/m², respectively. Scanning electron microscopy was used to observe the structural changes linked to collagen fibrils in the crack-tip area and the fracture surface. For in-air specimens, the former mostly exhibited extrinsic toughening (usually at micro scale) acting behind the crack-tip, while in-aqua intrinsic toughening acting ahead of a crack tip was found. Fractography of in-air specimens showed no occurrence of voids while multiple micro-voids were found for in-aqua specimens. STATEMENT OF SIGNIFICANCE: The fracture toughness and crack propagation of both mineralised (bone, dentine) and non-mineralised (skin) tissues has been extensively investigated over the past decades. Though these tissues are rich in collagen, the fracture properties of pure collagen have not been quantified yet at macroscale. Considering the applications of collagen films in tissue regeneration, it is essential to perform investigations of their fracture behaviour in both dry and wet conditions. Determining the effect of environment on the fracture behaviour of collagen and understanding its toughening mechanism are essential for prevention of failures during application. Moreover, this would give an insight for fabrication of tougher collagen-based biomaterials for biomedical uses.

A review on experimental and numerical investigations of cortical bone fracture

This paper comprehensively reviews the various experimental and numerical techniques, which were considered to determine the fracture characteristics of the cortical bone. This study also provides some recommendations along with the critical review, which would be beneficial for future research of fracture analysis of cortical bone. Cortical bone fractures due to sports activities, climbing, running, and engagement in transport or industrial accidents. Individuals having different diseases are also at high risk of cortical bone fracture. It has been observed that osteon orientation influences cortical bone fracture toughness and fracture mechanisms. Apart from this, recent studies indicate that fracture parameters of cortical bone also depend on many factors such as age, sex, temperature, osteoporosis, orientation, location, loading condition, strain rate, and storage facility, etc. The cortical bone regains its fracture toughness due to various toughening mechanisms. Owing to these factors, several experimental, clinical, and numerical investigations have been carried out to determine the fracture parameters of the cortical bone. Cortical bone is the dense outer surface of the bone and contributes to 80%–82% of the skeleton mass. Cortical bone experiences load far exceeding body weight due to muscle contraction and the dynamics of motion. It is very important to know the fracture pattern, direction of fracture, location of the fracture, and toughening mechanism of cortical bone. A basic understanding of the different factors that affect the fracture parameters and fracture mechanisms of the cortical bone is necessary to prevent the failure and fracture of cortical bone. This review has summarized the advancement considered in the various experimental techniques and numerical methods to get complete information about the fracture mechanisms of cortical bone.

Computational homogenisation based extraction of transverse tensile cohesive responses of cortical bone tissue

The numerical assessment of fracture properties of cortical bone is important in providing suggestions on patient-specific clinical treatments. We present a generic finite element modelling framework incorporating computational fracture approaches and computational homogenisation techniques. Finite element computations for statistical volume elements (SVEs) at the microscale are performed for different sizes with random osteon packing with a fixed volume fraction. These SVEs are loaded in the transverse direction under tension. The minimal SVE size in terms of ensuring a representative effective cohesive law is suggested to be 0.6 mm. Since cement lines as weak interfaces play a key role in bone fracture, the effects of their fracture properties on the effective fracture strength and toughness are investigated. The extracted effective fracture properties can be used as homogenised inputs to a discrete crack simulation at macroscopic or structural scale. The extrinsic toughening mechanisms observed in the SVE models are discussed with a comparison against experimental observations from the literature, giving beneficial insights to cortical bone failure.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Assessment of Elastic-Plastic Fracture Behavior of Cortical Bone Using a Small Punch Testing Technique

The fracture properties of cortical bone are directly coupled to its complex hierarchical structure. The limited availability of bone material from many anatomic locations creates challenges for assessing the effect of bone heterogeneity and anisotropy on fracture properties. The small punch technique was employed to examine the fracture behavior of cortical bone in terms of area under the curve values obtained from load-load point displacement behavior. Fracture toughness of cortical bone was also determined in terms of J-toughness values obtained using a compact tension (CT) test. Area under the curve values obtained from the small punch test were correlated with the J-toughness values of cortical bone. The effects of bone density and compositional parameters on area under the curve and Jtoughness values were also analyzed using linear and multiple regression analysis. Area under the curve and J-toughness values are strongly and positively correlated. Bone density and %mineral content are positively correlated with both area under the curve and J-toughness values. The multiple regression analysis outcomes support these results. Overall, the findings support the hypothesis that area under the curve values obtained from small punch tests can be used to assess the fracture behavior of cortical bone.

Bone collagen network integrity and transverse fracture toughness of human cortical bone

Greater understanding of the determinants of skeletal fragility is highly sought due to the great burden that bone affecting diseases and fractures have on economies, societies and health care systems. Being a complex, hierarchical composite of collagen type-I and non-stoichiometric substituted hydroxyapatite, bone derives toughness from its organic phase. In this study, we tested whether early observations that a strong correlation between bone collagen integrity measured by thermomechanical methods and work to fracture exist in a more general and heterogeneous sampling of the population. Neighboring uniform specimens from an established, highly characterized and previously published collection of human cortical bone samples (femur mid-shaft) were decalcified in EDTA. Fifty-four of the original 62 donors were included (26 male and 28 females; ages 21-101 years; aging, osteoporosis, diabetes and cancer). Following decalcification, bone collagen was tested using hydrothermal isometric tension (HIT) testing in order to measure the collagen's thermal stability (denaturation temperature, T_d) and network connectivity (maximum rate of isometric tension generation; Max.Slope). We used linear regression and general linear models (GLMs) with several explanatory variables to determine whether relationships between HIT parameters and generally accepted bone quality factors (e.g., cortical porosity, pentosidine content [pen], pyridinoline content [pyd]), age, and measures of fracture toughness (crack initiation fracture toughness, K_init, and total energy release/dissipation rate evaluated at the point of unstable fast fracture, J-int) were significant. Bone collagen connectivity (Max.Slope) correlated well with the measures of fracture toughness (R² = 24-35%), and to a lesser degree with bound water fraction (BW; R² = 7.9%) and pore water fraction (PW; R² = 9.1%). Significant correlations with age, apparent volumetric bone mineral density (vBMD), and mature enzymatic [pyd] and non-enzymatic collagen crosslinks [pen] were not detected. GLMs found that Max.Slope and vBMD (or BW), with or without age as additional covariate, all significantly explained the variance in Kinit (adjusted-R² = 36.7-49.0%). Also, the best-fit model for J-int (adjusted-R² = 35.7%) included only age and Max.Slope as explanatory variables with Max.Slope contributing twice as much as age. Max.Slope and BW without age were also significant predictors of J-int (adjusted-R² = 35.5%). In conclusion, bone collagen integrity as measured by thermomechanical methods is a key factor in cortical bone fracture toughness. This study further demonstrates that greater attention should be paid to degradation of the overall organic phase, rather than a specific biomarker (e.g. [pen]), when seeking to understand elevated fracture rates in aging and disease.

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 micro-damage process zone during transverse cortical bone fracture: No ears at crack growth initiation

OBJECTIVE

Apply high-resolution benchtop micro-computed tomography (micro-CT) to gain greater understanding and knowledge of the formation of the micro-damage process zone formed during traverse fracture of cortical bone.

METHODS

Bovine cortical bone was cut into single edge notch (bending) fracture testing specimens with the crack on the transverse plane and oriented to grow in the circumferential direction. We used a multi-specimen technique and deformed the specimens to various individual secant modulus loss levels (P-values) up to and including maximum load (Pmax). Next, the specimens were infiltrated with a BaSO₄ precipitation stain and scanned at 3.57-μm isotropic voxel size using a benchtop high resolution-micro-CT. Measurements of the micro-damage process zone volume, width and height were made. These were compared with the simple Irwin's process zone model and with finite element models. Electron and confocal microscopy confirmed the formation of BaSO₄ precipitate in micro-cracks and other porosity, and an interesting novel mechanism similar to tunneling.

RESULTS

Measurable micro-damage was detected at low P values and the volume of the process zone increased according to a second order polynomial trend. Both width and height grew linearly up to Pmax, at which point the process zone cross-section (perpendicular to the plane of the crack) was almost circular on average with a radius of approximately 550µm (approximately one quarter of the unbroken ligament thickness) and corresponding to the shape expected for a biological composite under plane stress conditions.

CONCLUSION

This study reports details of the micro-damage fracture process zone previously unreported for cortical bone. High-resolution micro-CT enables 3D visualization and measurement of the process zone and confirmation that the crack front edge and process zone are affected by microstructure. It is clear that the process zone for the specimens studied grows to be meaningfully large, confirming the need for the J-integral approach and it does not achieve steady state at Pmax in most specimens. With further development, this approach may become valuable towards better understanding the role of the process zone in cortical bone fracture and the effects of relevant modifications towards changes in fracture toughness in a cost effective way.

Strain rate influence on human cortical bone toughness: A comparative study of four paired anatomical sites

Bone fracture is a major health issue worldwide and consequently there have been extensive investigations into the fracture behavior of human cortical bone. However, the fracture properties of human cortical bone under fall-like loading conditions remains poorly documented. Further, most published research has been performed on femoral diaphyseal bone, whereas it is known that the femoral neck and the radius are the most vulnerable sites to fracture. Hence, the aim of this study is to provide information on human cortical bone fracture behavior by comparing different anatomical sites including the radius and the femoral neck acquired from 32 elderly subjects (50 - 98 y.o.). In order to investigate the intrinsic fracture behavior of human cortical bone, toughness experiments were performed at two different strain rates: standard quasi-static conditions, and a higher strain rate representative of a fall from a standing position. The tests were performed on paired femoral neck, femoral, tibial and radius diaphyseal samples. Linear elastic fracture toughness and the non-linear J-integral method were used to take into account both the elastic and non-elastic behavior of cortical bone. Under quasi-static conditions, the radius presents a significantly higher toughness than the other sites. At the higher strain rate, all sites showed a significantly lower toughness. Also, at the high strain rate, there is no significant difference in fracture properties between the four anatomical sites. These results suggest that regardless of the anatomical site (femur, femoral neck, tibia and radius), the bone has the same fracture properties under fall loading conditions. This should be considered in biomechanical models under fall-like loading conditions.

Ovarian hormone depletion affects cortical bone quality differently on different skeletal envelopes

The physical properties of bone tissue are determined by the organic and mineral matrix, and are one aspect of bone quality. As such, the properties of mineral and matrix are a major contributor to bone strength, independent of bone mass. Cortical bone quality may differ regionally on the three skeletal envelopes that compose it. Each of these envelopes may be affected differently by ovarian hormone depletion. Identifying how these regions vary in their tissue adaptive response to ovarian hormones can inform our understanding of how tissue quality contributes to overall bone strength in postmenopausal women. We analyzed humeri from monkeys that were either SHAM-operated or ovariectomized. Raman microspectroscopic analysis was performed as a function of tissue age based on the presence of multiple fluorescent double labels, to determine whether bone compositional properties (mineral/matrix ratio, tissue water, glycosaminoglycan, lipid, and pyridinoline contents, and mineral maturity/crystallinity) are similar between periosteal, osteonal, and endosteal surfaces, as well as to determine the effects of ovarian hormone depletion on them. The results indicate that mineral and organic matrix characteristics, and kinetics of mineral and organic matrix modifications as a function of tissue age are different at periosteal vs. osteonal and endosteal surfaces. Ovarian hormone depletion affects the three cortical surfaces (periosteal, osteonal, endosteal) differently. While ovarian hormone depletion does not significantly affect the quality of either the osteoid or the most recently mineralized tissue, it significantly affects the rate of subsequent mineral accumulation, as well as the kinetics of organic matrix modifications, culminating in significant differences within interstitial bone. These results highlight the complexity of the cortical bone compartments, add to existing knowledge on the effects of ovarian hormone depletion on local cortical bone properties, and may contribute to a better understanding of the location specific action of drugs used in the management of postmenopausal osteoporosis.

Microscopic assessment of bone toughness using scratch tests

Bone is a composite material with five distinct structural levels: collagen molecules, mineralized collagen fibrils, lamellae, osteon and whole bone. However, most fracture testing methods have been limited to the macroscopic scale and there is a need for advanced characterization methods to assess toughness at the osteon level and below. The goal of this investigation is to present a novel framework to measure the fracture properties of bone at the microscopic scale using scratch testing. A rigorous experimental protocol is articulated and applied to examine cortical bone specimens from porcine femurs. The observed fracture behavior is very complex: we observe a strong anisotropy of the response with toughening mechanisms and a competition between plastic flow and brittle fracture. The challenge consists then in applying nonlinear fracture mechanics methods such as the J-integral or the energetic Size Effect Law to quantify the fracture toughness in a rigorous fashion. Our result suggests that mixed-mode fracture is instrumental in determining the fracture resistance. There is also a pronounced coupling between fracture and elasticity. Our methodology opens the door to fracture assessment at multiple structural levels, microscopic and potentially nanometer length scale, due to the scalability of scratch tests.

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We measure bone toughness at the osteon level using microscopic scratch tests.

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Scratch tests induce a ductile-to-brittle transition in cortical bone.

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Toughening mechanisms are observed at the microscopic scale.

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The J-integral and the size effect law are employed to predict the fracture energy.

Assessment of compressive failure process of cortical bone materials using damage-based model

The main failure factors of cortical bone are aging or osteoporosis, accident and high energy trauma or physiological activities. However, the mechanism of damage evolution coupled with yield criterion is considered as one of the unclear subjects in failure analysis of cortical bone materials. Therefore, this study attempts to assess the structural response and progressive failure process of cortical bone using a brittle damaged plasticity model. For this reason, several compressive tests are performed on cortical bone specimens made of bovine femur, in order to obtain the structural response and mechanical properties of the material. Complementary finite element (FE) model of the sample and test is prepared to simulate the elastic-to-damage behavior of the cortical bone using the brittle damaged plasticity model. The FE model is validated in a comparative method using the predicted and measured structural response as load-compressive displacement through simulation and experiment. FE results indicated that the compressive damage initiated and propagated at central region where maximum equivalent plastic strain is computed, which coincided with the degradation of structural compressive stiffness followed by a vast amount of strain energy dissipation. The parameter of compressive damage rate, which is a function dependent on damage parameter and the plastic strain is examined for different rates. Results show that considering a similar rate to the initial slope of the damage parameter in the experiment would give a better sense for prediction of compressive failure.

An inset CT specimen for evaluating fracture in small samples of material

In evaluations on the fracture behavior of hard tissues and many biomaterials, the volume of material available to study is not always sufficient to apply a standard method of practice. In the present study an inset Compact Tension (inset CT) specimen is described, which uses a small cube of material (approximately 2×2×2mm(3)) that is molded within a secondary material to form the compact tension geometry. A generalized equation describing the Mode I stress intensity was developed for the specimen using the solutions from a finite element model that was defined over permissible crack lengths, variations in specimen geometry, and a range in elastic properties of the inset and mold materials. A validation of the generalized equation was performed using estimates for the fracture toughness of a commercial dental composite via the "inset CT" specimen and the standard geometry defined by ASTM E399 (2006). Results showed that the average fracture toughness obtained from the new specimen (1.23±0.02MPam(0.5)) was within 2% of that from the standard. Applications of the inset CT specimen are presented for experimental evaluations on the crack growth resistance of dental enamel and root dentin, including their fracture resistance curves. Potential errors in adopting this specimen are then discussed, including the effects of debonding between the inset and molding material on the estimated stress intensity distribution. Results of the investigation show that the inset CT specimen offers a viable approach for studying the fracture behavior of small volumes of structural materials.

Micro-CT finite element model and experimental validation of trabecular bone damage and fracture

Most micro-CT finite element modeling of human trabecular bone has focused on linear and non-linear analysis to evaluate bone failure properties. However, prediction of the apparent failure properties of trabecular bone specimens under compressive load, including the damage initiation and its progressive propagation until complete bone failure into consideration, is still lacking. In the present work, an isotropic micro-CT FE model at bone tissue level coupled to a damage law was developed in order to simulate the failure of human trabecular bone specimens under quasi-static compressive load and predict the apparent stress and strain. The element deletion technique was applied in order to simulate the progressive fracturing process of bone tissue. To prevent mesh-dependence that generally affects the damage propagation rate, regularization technique was applied in the current work. The model was validated with experimental results performed on twenty-three human trabecular specimens. In addition, a sensitivity analysis was performed to investigate the impact of the model factors' sensitivities on the predicted ultimate stress and strain of the trabecular specimens. It was found that the predicted failure properties agreed very well with the experimental ones.

Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests

There is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element (FE) analysis applied to experimental data of mechanically loaded single trabecular bone tissue obtained from non-invasive imaging techniques for the investigation of the damage initiation and growth of bone tissue. FE analysis of this type of bone has mainly focused on linear and non-linear analysis to evaluate the bone's failure properties. However, there is a lack of experimentally validated FE damage models at trabecular bone tissue level allowing for the simulation of the progressive damage process (initiation and growth) till complete fracture. Such models are needed to perform enhanced prediction of the apparent failure mechanical properties needed to assess the fracture risk of bone organs. In the current study, we develop a FE model based on a continuum damage mechanics (CDM) approach to simulate the damage initiation and propagation of a single trabecula till complete facture in quasi-static regime. Three-point bending experiments were performed on single bovine trabeculae and compared to FE results. In order to validate the proposed FE mode, (i) the force displacement curve was compared to the experimental one and (ii) the damage distribution was correlated to the measured one obtained by digital image correlation based on stress whitening in bone, reported to be correlated to microdamage. A very good agreement was obtained between the FE and experimental results, indicating that the proposed damage investigation protocol based on FE analysis and testing is reliable to assess the damage behavior of bone tissue and that the current damage model is able to accurately simulate the damaging and fracturing process of single trabeculae under quasi static load.

A novel videography method for generating crack-extension resistance curves in small bone samples

Assessment of bone quality is an emerging solution for quantifying the effects of bone pathology or treatment. Perhaps one of the most important parameters characterising bone quality is the toughness behaviour of bone. Particularly, fracture toughness, is becoming a popular means for evaluating bone quality. The method is moving from a single value approach that models bone as a linear-elastic material (using the stress intensity factor, K) towards full crack extension resistance curves (R-curves) using a non-linear model (the strain energy release rate in J-R curves). However, for explanted human bone or small animal bones, there are difficulties in measuring crack-extension resistance curves due to size constraints at the millimetre and sub-millimetre scale. This research proposes a novel “whitening front tracking” method that uses videography to generate full fracture resistance curves in small bone samples where crack propagation cannot typically be observed. Here we present this method on sharp edge notched samples (<1 mm×1 mm×Length) prepared from four human femora tested in three-point bending. Each sample was loaded in a mechanical tester with the crack propagation recorded using videography and analysed using an algorithm to track the whitening (damage) zone. Using the “whitening front tracking” method, full R-curves and J-R curves could be generated for these samples. The curves for this antiplane longitudinal orientation were similar to those found in the literature, being between the published longitudinal and transverse orientations. The proposed technique shows the ability to generate full “crack” extension resistance curves by tracking the whitening front propagation to overcome the small size limitations and the single value approach.

Bone fracture characterization using the end notched flexure test

A miniaturized version of the end notch flexure test was used in the context of pure mode II fracture characterization of bovine cortical bone. To overcome the difficulties intrinsic to crack length monitoring during its propagation an equivalent crack method was employed as data reduction scheme. The proposed method was validated numerically by means of a finite element analysis including a cohesive zone modeling and subsequently applied to experimental results to determine the fracture energy of bone under pure mode II loading. Finally, a cohesive law representative of fracture behavior of each specimen was determined employing an inverse method, considering a trapezoidal shape for the softening law. The consistency of the obtained results leads to the conclusion that the trapezoidal law is adequate to simulate fracture behavior of bone under mode II loading. The proposed testing setup and the employed data reduction scheme constitute powerful tools in which concerns fracture characterization of bone under pure mode II loading and can be viewed as the main outcomes of this work.

Dilatational band formation in bone

Toughening in hierarchically structured materials like bone arises from the arrangement of constituent material elements and their interactions. Unlike microcracking, which entails micrometer-level separation, there is no known evidence of fracture at the level of bone's nanostructure. Here, we show that the initiation of fracture occurs in bone at the nanometer scale by dilatational bands. Through fatigue and indentation tests and laser confocal, scanning electron, and atomic force microscopies on human and bovine bone specimens, we established that dilatational bands of the order of 100 nm form as ellipsoidal voids in between fused mineral aggregates and two adjacent proteins, osteocalcin (OC) and osteopontin (OPN). Laser microdissection and ELISA of bone microdamage support our claim that OC and OPN colocalize with dilatational bands. Fracture tests on bones from OC and/or OPN knockout mice (OC(-/-), OPN(-/-), OC-OPN(-/-;-/-)) confirm that these two proteins regulate dilatational band formation and bone matrix toughness. On the basis of these observations, we propose molecular deformation and fracture mechanics models, illustrating the role of OC and OPN in dilatational band formation, and predict that the nanometer scale of tissue organization, associated with dilatational bands, affects fracture at higher scales and determines fracture toughness of bone.

The importance of microstructural variations on the fracture toughness of human dentin

The crack growth resistance of human dentin was characterized as a function of relative distance from the DEJ and the corresponding microstructure. Compact tension specimens were prepared from the coronal dentin of caries-free 3rd molars. The specimens were sectioned from either the outer, middle or inner dentin. Stable crack extension was achieved under Mode I quasi-static loading, with the crack oriented in-plane with the tubules, and the crack growth resistance was characterized in terms of the initiation (K(o)), growth (K(g)) and plateau (K(p)) toughness. A hybrid approach was also used to quantify the contribution of dominant mechanisms to the overall toughness. Results showed that human dentin exhibits increasing crack growth resistance with crack extension in all regions, and that the fracture toughness of inner dentin (2.2 ± 0.5 MPa·m(0.5)) was significantly lower than that of middle (2.7 ± 0.2 MPa·m(0.5)) and outer regions (3.4 ± 0.3 MPa·m(0.5)). Extrinsic toughening, composed mostly of crack bridging, was estimated to cause an average increase in the fracture energy of 26% in all three regions. Based on these findings, dental restorations extended into deep dentin are much more likely to cause tooth fracture due to the greater potential for introduction of flaws and decrease in fracture toughness with depth.

Analysis of micro fracture in human Haversian cortical bone under compression

A procedure to investigate local stress intensity factors in human Haversian cortical bone under compression is presented. The method combines a customised experimental setting for micro-compression tests of millimetric bone specimens and a finite element contact model conforming to the bone morphology that tracks advancing microcracks. The non-interpenetration conditions along the crack edges are ensured by penalty constraints of which the parameters are optimised for minimum contact pressure error with respect to the crack orientations. A cohesive crack opening law is implemented in the wake of the crack tips to remain consistent with the progressive tearing of collagen fibrils. The displacement solution is searched by a Newton-Raphson scheme containing a double loop first on the displacements and second on the frictional contact and cohesive condition updates at the crack interfaces. The experimental Dirichlet boundary conditions are acquired by digital image cross-correlation of bone light microscopy observations and then imported into the model. The local mechanical elastic moduli are measured by nanoindentation and microextensometry. The comparison of the macroscopic stress-strain numerical response with the experiment reveals the existence of narrow diffuse damaged zones near the major cracks where the local stress intensity factors can be calculated.

Interaction of microstructure and microcrack growth in cortical bone: a finite element study

Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behaviour in cortical bone. This study aims to develop a computational mechanics approach to evaluate microscale fracture mechanisms in bone. In this study, finite element models based on actual human cortical bone images that allow for arbitrary crack growth were utilised to determine the crack propagation behaviour. The simulations varied the cement line and osteon strength and fracture toughness in different bone microstructures to assess the crack propagation trajectory, stress-strain relationship and nonlinear strain energy density. The findings of this study provide additional insight into the individual influence of microstructural features and their properties on crack growth behaviour in bone using a computational approach.

Measurement of the toughness of bone: a tutorial with special reference to small animal studies

Quantitative assessment of the strength and toughness of bone has become an integral part of many biological and bioengineering studies on the structural properties of bone and their degradation due to aging, disease and therapeutic treatment. Whereas the biomechanical techniques for characterizing bone strength are well documented, few studies have focused on the theory, methodology, and various experimental procedures for evaluating the fracture toughness of bone, i.e., its resistance to fracture, with particular reference to whole bone testing in small animal studies. In this tutorial, we consider the many techniques for evaluating toughness and assess their specific relevance and application to the mechanical testing of small animal bones. Parallel experimental studies on wild-type rat and mouse femurs are used to evaluate the utility of these techniques and specifically to determine the coefficient of variation of the measured toughness values.

The true toughness of human cortical bone measured with realistically short cracks

Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for 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.

How tough is bone? Application of elastic-plastic fracture mechanics to bone

Bone, with a hierarchical structure that spans from the nano-scale to the macro-scale and a composite design composed of nano-sized mineral crystals embedded in an organic matrix, has been shown to have several toughening mechanisms that increases its toughness. These mechanisms can stop, slow, or deflect crack propagation and cause bone to have a moderate amount of apparent plastic deformation before fracture. In addition, bone contains a high volumetric percentage of organics and water that makes it behave nonlinearly before fracture. Many researchers used strength or critical stress intensity factor (fracture toughness) to characterize the mechanical property of bone. However, these parameters do not account for the energy spent in plastic deformation before bone fracture. To accurately describe the mechanical characteristics of bone, we applied elastic-plastic fracture mechanics to study bone's fracture toughness. The J integral, a parameter that estimates both the energies consumed in the elastic and plastic deformations, was used to quantify the total energy spent before bone fracture. Twenty cortical bone specimens were cut from the mid-diaphysis of bovine femurs. Ten of them were prepared to undergo transverse fracture and the other 10 were prepared to undergo longitudinal fracture. The specimens were prepared following the apparatus suggested in ASTM E1820 and tested in distilled water at 37 degrees C. The average J integral of the transverse-fractured specimens was found to be 6.6 kPa m, which is 187% greater than that of longitudinal-fractured specimens (2.3 kPa m). The energy spent in the plastic deformation of the longitudinal-fractured and transverse-fractured bovine specimens was found to be 3.6-4.1 times the energy spent in the elastic deformation. This study shows that the toughness of bone estimated using the J integral is much greater than the toughness measured using the critical stress intensity factor. We suggest that the J integral method is a better technique in estimating the toughness of bone.

Fracture length scales in human cortical bone: The necessity of nonlinear fracture models

Recently published data for fracture in human humeral cortical bone are analyzed using cohesive-zone models to deal with the nonlinear processes of material failure. Such models represent the nonlinear deformation processes involved in fracture by cohesive tractions exerted by the failing material along a fracture process zone, rather than attributing all damage to a process occurring at a single point, as in conventional linear-elastic fracture mechanics (LEFM). The relationship between the tractions and the net displacement discontinuity across the process zone is hypothesized to be a material property for bone. To test this hypothesis, the cohesive law was evaluated by analyzing published load vs. load-point displacement data from one laboratory; the calibrated law was then used to predict similar data taken for a different source of bone using a different specimen geometry in a different laboratory. Further model calculations are presented to illustrate more general characteristics of the nonlinear fracture of bone and to demonstrate in particular that LEFM is not internally consistent for all cases of interest. For example, the fracture toughness of bone deduced via LEFM from test data is not necessarily a material constant, but will take different values for different crack lengths and test configurations. LEFM is valid when the crack is much longer than a certain length scale, representative of the length of the process zone in the cohesive model, which for human cortical bone ranges from 3 to 10mm. Since naturally occurring bones and the specimens used to test them are not much larger than this dimension for most relevant orientations, it is apparent that only nonlinear fracture models can give an internally consistent account of their fracture. The cohesive law is thus a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality. The analysis of fracture data also requires proper representation of the approximately orthotropic elasticity of the bone specimen; if the specimen is incorrectly assumed to be isotropic, the initial measured compliance cannot be reproduced to within a factor of four and the fracture toughness deduced from the measured work of fracture will be overestimated by approximately 30%.