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

Characterization of damage mechanisms in cortical bone: Quantification of fracture resistance, critical strains, and crack tortuosity

One step towards understanding bone fragility and degenerative diseases is to unravel the links between fracture resistance and the compositional and structural characteristics of cortical bone. In this study, we explore an optical method for automatic crack detection to generate full fracture resistance curves of cortical bone. We quantify fracture toughness, critical failure strains at the crack tip, and crack tortuosity in three directions and analyze how they relate to cortical bone microstructure. A three-point bending fracture test of single-edge notched beam specimens in three directions (cracks propagating transverse, radial and longitudinal to the microstructure) from bovine cortical bone was combined with 2D-digital image correlation. Crack growth was automatically monitored by analyzing discontinuities in the displacement field using phase congruency analysis. Fracture resistance was analyzed using J-R-curves and strains were quantified at the crack tip. Post-testing, a subset of specimens was scanned using micro-tomography to visualize cracks and to quantify their tortuosity. Both fracture toughness and crack tortuosity were significantly higher in the transverse direction compared to the other directions. Similar fracture toughness was found for radial and longitudinal directions, albeit 20% higher crack tortuosity in the radial specimens. This suggests that radial crack deflections are not as efficient toughening mechanisms. Strains at crack initiation were ∼0.4% for all tissue orientations, while at fully developed damage process zones failure strains were significantly higher in the transverse direction (∼1.5%). Altogether, we present unique quantitative data including different aspects of bone damage in three directions, illustrating the importance of cortical bone microstructure.

Micromechanical modelling of transverse fracture behaviour of lamellar bone using a phase-field damage model: The role of non-collagenous proteins and mineralised collagen fibrils

At the tissue-scale and above, there are now well-established structure-property relationships that provide good approximations of the biomechanical performance of bone through, for example, power-law relationships that relate tissue mineral density to elastic properties. However, below the tissue-level, the individual role of the constituents becomes prominent and these simple relationships tend to break down, with more detailed theoretical and computational models are required to describe the mechanical response. In this study, a two-dimensional micromechanics damage-based representative volume element (RVE) of lamellar bone was developed, which included a novel implementation of a phase-field damage model to describe the behaviour of non-collagenous proteins at mineral-mineral and mineral-fibril interface regions. It was found that, while the stiffness of the tissue was governed by the relative proportion of extra-fibrillar mineral and mineralised collagen fibrils, the strength and toughness of the tissue in transverse direction relied on the interactions occurring at mineral-mineral and mineral-fibril interfaces, highlighting the prominence of non-collagenous proteins in determine fracture-based processes at this scale. While fractures tended to initiate in mineral rich areas of the extra-fibrillar mineral matrix, it was found that the presence of mineralised collagen fibrils at low density did not provide a substantial contribution to crack propagation behaviour under transverse loading. However, at physiological volume fraction (VfMCF=50%), different scenarios could arise depending on the relative strength value of the interphase around the MCFs ( [Formula: see text] ) to the interphase between individual minerals ( [Formula: see text] ): (i) When [Formula: see text] , MCFs appear to facilitate crack propagation with MCF-mineral debonding being the dominant failure mode; (ii) once γ>1, the MCFs hinder the microcracks, leading to inhibition of crack propagation, which can be regarded as an energy dissipation mechanism. The effective fracture properties of the tissue also experience a sudden increase in fracture work density (J-integral) once the crack is arrested by MCFs or severely deflected. Collectively, the predicted behaviour of the model compared well to those reported through experimental and computational methods, highlighting its potential to provide further understanding into the mechanistic response of bone ultrastructure alterations related to the structural and compositional changes resulting from disease and aging.

Effect of ribose incubation on physical, chemical, and mechanical properties of human cortical bone

Raman spectroscopy (RS) is sensitive to the accumulation of advanced glycation end-products (AGEs), and it measures matrix-sensitive properties that correlate with the fracture toughness of human cortical bone. However, it is unclear whether sugar-mediated accumulation of AGEs affects the fracture toughness of human cortical bone in a manner that is consistent with the negative correlations between amide I sub-peak ratios and fracture toughness. Upon machining 64 single-edge notched beam (SENB) specimens from cadaveric femurs (8 male and 7 female donors between 46 years and 61 years of age), pairs of SENB specimens were incubated in 15 mL of phosphate buffered saline with or without 0.1 M ribose for 4 weeks at 37 °C. After acquiring 10 Raman spectra per bone specimen (n = 32 per incubation group), paired SENB specimens were loaded in three-point bending at a quasi-static or a high loading rate approximating 10-4 s-1 or 10-2 s-1, respectively (n = 16 per incubation group per loading rate). While 2 amide I sub-peak ratios, I1670/I1640 and I1670/I1610, decreased by 3-5% with a 100% increase in AGE content, as confirmed by fluorescence measurements, the ribose incubation to accumulate AGEs in bone did not affect linear elastic (KIc) nor non-linear elastic (KJc) measurements of bone's ability to resist crack growth. Moreover, AGE accumulation did not affect the change in these properties when the loading rate changed. Increasing the loading rate increased KIc but decreased KJc. Ribose incubation did not affect mineral-related RS properties such as mineral-to-matrix ratios, Type B carbonate substitutions, and crystallinity. It did however increase the thermal stability of demineralized bone (differential scanning calorimetry), without affecting the network connectivity of the organic matrix (i.e., maximum slope during a hydrothermal isometric tension test of demineralized bone). In conclusion, RS is sensitive to AGE accumulation via the amide I band (plus the hydroxyproline-to-proline ratio), but the increase in AGE content due to ribose incubation was not sufficient to affect the fracture toughness of human cortical bone.

Causative or associative: A critical review of the role of advanced glycation end-products in bone fragility

The accumulation of advanced glycation end-products (AGEs) in the organic matrix of bone with aging and chronic disease such as diabetes is thought to increase fracture risk independently of bone mass. However, to date, there has not been a clinical trial to determine whether inhibiting the accumulation of AGEs is effective in preventing low-energy, fragility fractures. Moreover, unlike with cardiovascular or kidney disease, there are also no pre-clinical studies demonstrating that AGE inhibitors or breakers can prevent the age- or diabetes-related decrease in the ability of bone to resist fracture. In this review, we critically examine the case for a long-standing hypothesis that AGE accumulation in bone tissue degrades the toughening mechanisms by which bone resists fracture. Prior research into the role of AGEs in bone has primarily measured pentosidine, an AGE crosslink, or bulk fluorescence of hydrolysates of bone. While significant correlations exist between these measurements and mechanical properties of bone, multiple AGEs are both non-fluorescent and non-crosslinking. Since clinical studies are equivocal on whether circulating pentosidine is an indicator of elevated fracture risk, there needs to be a more complete understanding of the different types of AGEs including non-crosslinking adducts and multiple non-enzymatic crosslinks in bone extracellular matrix and their specific contributions to hindering fracture resistance (biophysical and biological). By doing so, effective strategies to target AGE accumulation in bone with minimal side effects could be investigated in pre-clinical and clinical studies that aim to prevent fragility fractures in conditions that bone mass is not the underlying culprit.

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.

Experimental evaluation of fracture properties of bovine hip cortical bone using elastic-plastic fracture mechanics

BACKGROUND

Understanding the fracture mechanics of bone is very important in both the medical and bioengineering field. Bone is a hierarchical natural composite material of nanoscale collagen fibers and inorganic material.

OBJECTIVE

This study investigates and presents the fracture toughness of bovine cortical bone by using elastic plastic fracture mechanics.

METHODS

The J-integral was used as a parameter to calculate the energies utilized in both elastic deformation (Jel) and plastic deformation (Jpl) of the hipbone fracture. Twenty four different types of specimens, i.e. longitudinal compact tension (CT) specimens, transverse CT specimens, and also rectangular unnotched specimens for tension in longitudinal and transverse orientation, were cut from the bovine hip bone of the middle diaphysis. All CT specimens were prepared according to the American Society for Testing and Materials (ASTM) E1820 standard and were tested at room temperature.

RESULTS

The results showed that the average total J-integral in transverse CT fracture specimens is 26% greater than that of longitudinal CT fracture specimens. For longitudinal-fractured and transverse-fractured cortical specimens, the energy used in the elastic deformation was found to be 2.8-3 times less than the energy used in the plastic deformation.

CONCLUSION

The findings indicate that the overall fracture toughness measured using the J-integral is significantly higher than the toughness calculated by the stress intensity factor. Therefore, J-integral should be employ to compute the fracture toughness of cortical bone.

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.

Evaluation of fracture properties of cancellous bone tissues using digital image correlation/wedge splitting test method

The fracture mechanics (FM) parameters of cancellous bone tissues are very important from a clinical point of view especially for the bone cement augmentation. From the literature review, one can observe that the experimental determination of fracture mechanic parameters of cancellous bone are still lacking. This can be due to the conditions associated with the unstable crack propagation in the cancellous bone and lack of tools to extract and measure the parameters (like crack opening displacement (COD) and crack length) in the course of fracture tests, which are necessary to evaluate the fracture properties. To address above mentioned, a platform was developed integrating an optical measurement technique like digital image correlation (DIC) with classical wedge splitting test (WST) method to extract precise and real crack tip positions, crack opening displacement (COD) at each load step. These indeed used for the evaluation of the fracture mechanic properties (fracture toughness, specific fracture energy (G_f)) of the cancellous bone. Two approaches were used to evaluate the fracture mechanic properties of the bone. The first method is based on the global approach, which was widely used in the literature and the second method is based on the local approach. In this local approach, the local fracture energy (G_i) during the course of the test was evaluated, which give access to local fracture mechanics. The results evaluated by both the methods were in good accordance and compared with available literature. In addition, an attempt made to retrieve the real crack tip position at each load step during the test.

Fracture Mechanism and Fracture Toughness at the Interface between Cortical and Cancellous bone

Objective The micro-structure at the interface of cortical and cancellous bone is quite complicated. The fracture mechanism at this location is necessary for understanding the comprehensive fracture of whole bone. The goal of this study is to identify fracture toughness in terms of J integral and fracture mechanism at the interface between cortical and cancellous bone. Materials and Methods For this purpose, single edge notch bend (SENB) specimens were prepared from bovine proximal femur according to ASTM-E399 standard. Bone samples were prepared such that half of the sample width consist of cortical bone and other half of the width was cancellous bone; this interfacial bone is referred as corticellous bone. Elastic-plastic fracture mechanics was used to measure fracture toughness. The J integral (both elastic and plastic) was used to quantify the fracture toughness. Results The plastic part of J integral value (Jpl) of corticellous specimen was 9310 Jm-2, and shown to be 27 times of the J integral of the elastic part (Jel), 341 Jm-2. The total J integral of the corticellous bone was found to be 9651 Jm-2, which is close to two times of the cortical bone, 4731 Jm-2. Conclusions Present study observed that, J integral of corticellous bone is higher than cortical bone since, more energy is required for plastic deformation of corticellous bone due to crack branches and slowdown at the interface between cortical and cancellous bone.

Experimental and numerical comparisons between finite element method, element-free Galerkin method, and extended finite element method predicted stress intensity factor and energy release rate of cortical bone considering anisotropic bone modelling

Stress intensity factor and energy release rate are important parameters to understand the fracture behaviour of bone. The objective of this study is to predict stress intensity factor and energy release rate using finite element method, element-free Galerkin method, and extended finite element method and compare these results with the experimentally determined values. For experimental purpose, 20 longitudinally and transversely fractured single-edge notched bend specimens were prepared and tested according to ASTM standard. All specimens were tested using the universal testing machine. For numerical simulations (finite element method, element-free Galerkin method, and extended finite element method), two-dimensional model of cortical bone was developed by assuming plane strain condition. Material properties of the cortical bone were considered as anisotropic and homogeneous. The values obtained through finite element method, element-free Galerkin method, and extended finite element method are well corroborated to experimentally determined values and earlier published data. However, element-free Galerkin method and extended finite element method predict more accurate results as compared to finite element method. In the case of the transversely fractured specimen, the values of stress intensity factor and energy release rate were found to be higher as compared to the longitudinally fractured specimen, which shows consistency with earlier published data. This study also indicates element-free Galerkin method and extended finite element method predicted stress intensity factor and energy release rate results are more close to experimental results as compared to finite element method, and therefore, these methods can be used in the different field of biomechanics, particularly to predict bone fracture.

Studies on the Stress-Strain Relationship Bovine Cortical Bone Based on Ramberg–Osgood Equation

Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

Hydoxyapatite/beta-tricalcium phosphate biphasic ceramics as regenerative material for the repair of complex bone defects

Bone is a composite material composed of collagen and calcium phosphate (CaP) mineral. The collagen gives bone its flexibility while the inorganic material gives bone its resilience. The CaP in bone is similar in composition and structure to the mineral hydroxyapatite (HA) and is bioactive, osteoinductive and osteoconductive. Therefore synthetic versions of bone apatite (BA) have been developed to address the demand for autologous bone graft substitutes. Synthetic HA (s-HA) are stiff and strong, but brittle. These lack of physical attributes limit the use of synthetic apatites in situations where no physical loading of the apatite occurs. s-HA chemical properties differ from BA and thus change the physical and mechanical properties of the material. Consequently, s-HA is more chemically stable than BA and thus its resorption rate is slower than the rate of bone regeneration. One solution to this problem is to introduce a faster resorbing CaP, such as β-tricalcium phosphate (β-TCP), when synthesizing the material creating a biphasic (s-HA and β-TCP) formulation of calcium phosphate (BCP). The focus of this review is to introduce the major differences between BCP and biological apatites and how material scientists have overcome the inadequacies of the synthetic counterparts. Examples of BCP performance in vitro and in vivo following structural and chemical modifications are provided as well as novel ultrastructural data. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 2493-2512, 2018.

Fragility Assessment of Bovine Cortical Bone Using Scratch Tests

Bone is a complex hierarchical material with five distinct levels of organization. Factors like aging and diseases like osteoporosis increase the fragility of bone, making it fracture-prone. Owing to the large socio-economic impact of bone fracture in our society, there is a need for novel ways to assess the mechanical performance of each hierarchical level of bone. Although stiffness and strength can be probed at all scales - nano-, micro-, meso-, and macroscopic - fracture assessment has so far been confined to macroscopic testing. This limitation restricts our understanding of bone fracture and constrains the scope of laboratory and clinical studies. In this research, we investigate the fracture resistance of bone from the microscopic to the mesoscopic length scales using micro scratch tests combined with nonlinear fracture mechanics. The tests are performed in the short longitudinal orientation on bovine cortical bone specimens. A meticulous experimental protocol is developed and a large number (102) of tests are conducted to assess the fracture toughness of cortical bone specimens while accounting for the heterogeneity associated with bone microstructure.

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.

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.

•

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

•

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

•

Toughening mechanisms are observed at the microscopic scale.

•

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.

Elastic-plastic fracture toughness and rising JR-curve behavior of cortical bone is partially protected from irradiation-sterilization-induced degradation by ribose protectant

OBJECTIVE

This study tested the hypothesis that pre-treating cortical bone with ribose would protect the rising fracture resistance curve behavior and crack initiation fracture toughness of both bovine and human cortical bone from the degrading effects of γ-irradiation sterilization.

MATERIALS AND METHODS

A ribose pre-treatment (1.8 M for bovine, and 1.2 M for human, in PBS at 60 °C for 24 h) was applied to single-edge notched bending fracture specimens prior to sterilization with a 33 kGy dose of γ-irradiation. Fracture resistance curves were generated with a single specimen method using an optical crack length measurement technique. The effect of the treatment on overall fracture resistance behavior, crack initiation fracture toughness, and tearing modulus was compared with non-irradiated and conventionally irradiation sterilized controls. Hydrothermal isometric tension testing was used to examine collagen network connectivity and thermal stability to explore relationships between collagen network quality and fracture resistance.

RESULTS

The ribose pre-treatment successfully protected the crack growth initiation fracture toughness of bovine and human bone by 32% and 63%, respectively. The rising JR-curve behavior was also partially protected. Furthermore, collagen connectivity and thermal stability followed similar patterns to those displayed by fracture toughness.

CONCLUSIONS

This paper demonstrates that the fracture toughness of irradiation-sterilized bone tissue can be partially protected with a ribose pre-treatment. This new approach shows potential for the production and clinical application of sterilized allografts with improved mechanical performance and durability.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Mixed-mode I+II fracture characterization of human cortical bone using the Single Leg Bending test

Mixed-mode I+II fracture characterization of human cortical bone was analyzed in this work. A miniaturized version of the Single Leg Bending test (SLB) was used owing to its simplicity. A power law criterion was verified to accurately describe the material fracture envelop under mixed-mode I+II loading. The crack tip opening displacements measured by digital image correlation were used in a direct method to determine the cohesive law mimicking fracture behavior of cortical bone. Cohesive zone modeling was used for the sake of validation. Several fracture quantities were compared with the experimental results and the good agreement observed proves the appropriateness of the proposed procedure for fracture characterization of human bone under mixed-mode I+II loading.

γ-Irradiation sterilized bone strengthened and toughened by ribose pre-treatment

OBJECTIVE

This study tested the hypothesis that a ribose-based pre-treatment would protect the strength, ductility and toughness of γ-irradiation sterilized cortical bone.

METHODS

Experiment 1: The effects of ribose pre-treatment (1.8M in PBS at 60°C for 24h) prior to 33 kGy of irradiation on strength, ductility and toughness (beams in three-point bending) and fracture toughness (J-integral at instability in single edge notched (bending)) were tested against matched non-irradiated and irradiated controls from bovine tibiae. Experiment 2: Three-point bending tests were conducted using beams from human femora (males, 59-67 years). Bone collagen thermal stability and network connectivity were examined using hydrothermal isometric tension testing.

RESULTS

Ribose pre-treatment protected the strength, ductility and toughness of irradiation sterilized bovine and human specimens to differing degrees. Their ultimate strength was not detectably different from non-irradiated control levels; toughness in bovine and human specimens was protected by 57 and 76%, respectively. Untreated human bone was less affected by irradiation and ribose pre-treatment was more effective in human bone than bovine bone.

CONCLUSIONS

This paper presents the first proof-of-principle that irradiation-sterilized bone with improved mechanical properties can be produced through the application of a ribose pre-irradiation treatment, which provides a more stable and connected collagen network than found in conventionally irradiated controls.

The role of nanoscale toughening mechanisms in osteoporosis

Strength is the most widely reported parameter with regards to bone failure. However, bone contains pre-existing damage and stress concentration sites, perhaps making measures of fracture toughness more indicative of the resistance of the tissue to withstand fracture. Several toughening mechanisms have been identified in bone, prominently, at the microscale. More recently, nanoscale toughness mechanisms, such as sacrificial-bonds and hidden-length or dilatational band formation, mediated by noncollagenous proteins, have been reported. Absence of specific noncollagenous proteins results in lowered fracture toughness in animal models. Further, roles of several other, putative influencing, factors such as closely bound water, collagen cross-linking and citrate bonds in bone mineral have also been proposed. Yet, it is still not clear if and which mechanisms are hallmarks of osteoporosis disease and how they influence fracture risk. Further insights on the workings of such influencing factors are of high importance for developing complementary diagnostics and therapeutics strategies.

Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone

As a composite material, cortical bone accumulates fatigue microdamage through the repetitive loading of everyday activity (e.g. walking). The accumulation of fatigue microdamage is thought to contribute to the occurrence of fragility fractures in older people. Therefore it is beneficial to understand the relationship between microcrack accumulation and the fracture resistance of cortical bone. Twenty longitudinally orientated compact tension fracture specimens were machined from a single bovine femur, ten specimens were assigned to both the control and fatigue damaged groups. The damaged group underwent a fatigue loading protocol to induce microdamage which was assessed via fluorescent microscopy. Following fatigue loading, non-linear fracture resistance tests were undertaken on both the control and damaged groups using the J-integral method. The interaction of the crack path with the fatigue induced damage and inherent toughening mechanisms were then observed using fluorescent microscopy. The results of this study show that fatigue induced damage reduces the initiation toughness of cortical bone and the growth toughness within the damage zone by three distinct mechanisms of fatigue-fracture interaction. Further analysis of the J-integral fracture resistance showed both the elastic and plastic component were reduced in the damaged group. For the elastic component this was attributed to a decreased number of ligament bridges in the crack wake while for the plastic component this was attributed to the presence of pre-existing fatigue microcracks preventing energy absorption by the formation of new microcracks.

Fracture analysis for biological materials with an expanded cohesive zone model

In this study, a theoretical framework for simulation of fracture of bone and bone-like materials is provided. An expanded cohesive zone model with thermodynamically consistent framework has been proposed and used to investigate the crack growth resistance of bone and bone-like materials. The reversible elastic deformation, irreversible plastic deformation caused by large deformation of soft protein matrix, and damage evidenced by the material separation and crack nucleation in the cohesive zone, were all taken into account in the model. Furthermore, the key mechanisms in deformation of biocomposites consisting of mineral platelets and protein interfacial layers were incorporated in the fracture process zone in this model, thereby overcoming the limitations of previous cohesive zone modeling of bone fracture. Finally, applications to fracture of cortical bone and human dentin were presented, which showed good agreement between numerical simulation and reported experiments and substantiated the effectiveness of the model in investigating the fracture behavior of bone-like materials.

Bone embrittlement and collagen modifications due to high-dose gamma-irradiation sterilization

Bone allografts are often used in orthopedic reconstruction of skeletal defects resulting from trauma, bone cancer or revision of joint arthroplasty. γ-Irradiation sterilization is a widely-used biological safety measure; however it is known to embrittle bone. Irradiation has been shown to affect the post-yield properties, which are attributed to the collagen component of bone. In order to find a solution to the loss of toughness in irradiated bone allografts, it is important to fully understand the effects of irradiation on bone collagen. The objective of this study was to evaluate changes in the structure and integrity of bone collagen as a result of γ-irradiation, with the hypothesis that irradiation fragments collagen molecules leading to a loss of collagen network connectivity and therefore loss of toughness. Using cortical bone from bovine tibiae, sample beams irradiated at 33kGy on dry ice were compared to native bone beams (paired controls). All beams were subjected to three-point bend testing to failure followed by characterization of the decalcified bone collagen, using differential scanning calorimetry (DSC), hydrothermal isometric tension testing (HIT), high performance liquid chromatography (HPLC) and gel electrophoresis (SDS-PAGE). The carbonyl content of demineralized bone collagen was also measured chemically to assess oxidative damage. Barium sulfate staining after single edge notch bending (SEN(B)) fracture testing was also performed on bovine tibia bone beams with a machined and sharpened notch to evaluate the fracture toughness and ability of irradiated bone to form micro-damage during fracture. Irradiation resulted in a 62% loss of work-to-fracture (p≤0.001). There was significantly less micro-damage formed during fracture propagation in the irradiated bone. HPLC showed no significant effect on pentosidine, pyridinoline, or hydroxypyridinoline levels suggesting that the loss of toughness is not due to changes in these stable crosslinks. For DSC, there was a 20% decrease in thermal stability (p<0.001) with a 100% increase (p<0.001) in enthalpy of denaturation (melting). HIT testing also showed a decrease in thermal stability (20% lower denaturation temperature, p<0.001) and greatly reduced measures of collagen network connectivity (p<0.001). Interestingly, the increase in enthalpy of denaturation suggests that irradiated collagen requires more energy to denature (melt), perhaps a result of alterations in the hydrogen bonding sites (increased carbonyl content detected in the insoluble collagen) on the irradiated bone collagen. Altogether, this new data strongly indicates that a large loss of overall collagen connectivity due to collagen fragmentation resulting from γ-irradiation sterilization leads to inferior cortical bone toughness. In addition, notable changes in the thermal denaturation of the bone collagen along with chemical indicators of oxidative modification of the bone collagen indicate that the embrittlement may be a function not only of collagen fragmentation but also of changes in bonding.

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.

Fracture patterns of the growth plate and surrounding bone in the ovine knee joint at different ages

Fractures of the growth plate region were performed with cadaver specimens obtained from the ovine distal femur and proximal tibia. Specimens of 6 different ages, ranging from 1 week to 4 years, were investigated in order to determine changes in the fracture characteristics. Mechanical properties (crack resistance and notch tensile strength), supported by microscopy of the distal tibia (thickness of growth plate and its zones, trabecular bone volume ratio) were determined. The crack propagated through different regions depending on age, which was observed both in microscopy and mechanical tests. In specimens of younger animals the fracture typically went through trabecular bone, often parallel to the growth plate, and only sometimes through the growth plate cartilage. Specimens of older animals fractured directly through the growth plate cartilage, while trabecular bone was not affected at all. Adult specimens had significantly higher mechanical values than the young ones. The results reveal the underlying mechanical properties that induce different fracture patterns of the epiphyseal growth plate at different stages of growth. The possibility of fractures through trabecular bone parallel to the growth plate in newborns and infants should be considered when clinical radiographs of paediatric fractures are analysed and classified.

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.

Extended Finite Element models of introcortical porosity and heterogeneity in cortical bone

Due to changes in the bone quality during ageing the fracture risk increases. The influence of the different parameters affecting bone quality is not well understood. The Finite Element method offers the opportunity to determine the individual contribution of a parameter by changing single parameters. In this study, the ABAQUS extended Finite Elements Method (xFEM) was applied to simulate the crack propagation in compact bone samples using the quadratic nominal stress as crack criterion. Micro computed tomography images of compact-tension samples machined from a 19 and an 81 years old donor were used to generate Finite Element meshes consisting of linear tetrahedrons via Mimics. Cavities were modelled only in the estimated crack area to avoid a high number of degrees of freedom. Crack area was meshed with a higher number of smaller elements. The other areas were meshed with a small number of larger elements. The changes in the material constants due to the simplification of the model were taken into account by using effective material parameters in these partitions. Our results show that age-related loss in bone toughness results from increased porosity and loss in heterogeneity of material level properties.

Early or delayed operation, which is more optimal for kyphoplasty? A retrospective study on cement leakage during kyphoplasty

PURPOSE

To retrospectively assess the optimal operating time for kyphoplasty as far as the cement leakage during kyphoplasty is concerned.

MATERIALS AND METHODS

One hundred and six patients with a total of 117 osteoporotic vertebral compression fractures (VCFs) were enrolled in our study. According to the time of kyphoplasty, they were divided into two groups: group 1 (early operation group, who received the operation within 14 days after fracture, n=46) and group 2 (delayed operation group, who received the operation between 15 and 28 days after fracture, n=71). Preoperative and postoperative visual analogue scale (VAS) and Oswestry Disability Index (ODI) scores were compared 3 days after surgery within each group and between the two groups. The radiographic outcomes were evaluated by the restoration rate (RR) of the treated vertebrae. The outcome of cement leakage was assessed after surgery using X-ray and computed tomography (CT) scans. Leaks of cement were classified into three types: those via the basivertebral vein (type B), via the segmental vein (type S) and through a cortical defect (type C).

RESULTS

The mean VAS and ODI scores decreased significantly from pre-surgery to post-surgery in each group, as did the RR (p>0.05). There was no significant difference postoperatively on VAS and ODI scores (p>0.05) between the two groups. However, significant differences were observed postoperatively on RR (p=0.045) and vertebrae with leakage (p=0.038). In addition, there was a significant difference on leakage site of type C between the two groups (p=0.032).

CONCLUSION

Both early and delayed operations of kyphoplasty can achieve satisfactory clinical and radiographic outcomes for osteoporotic VCFs. The risk of cement leakage during kyphoplasty will decrease obviously in delayed operation; so delayed operation, perhaps 2 weeks after fracture, is more safe and optimal than early operation as far as cement leakage is concerned, especially for vertebrae with cortical defects. But early operation of kyphoplasty is more effective in vertebral height restoration.

Characterization of the effects of x-ray irradiation on the hierarchical structure and mechanical properties of human cortical bone

Bone comprises a complex structure of primarily collagen, hydroxyapatite and water, where each hierarchical structural level contributes to its strength, ductility and toughness. These properties, however, are degraded by irradiation, arising from medical therapy or bone-allograft sterilization. We provide here a mechanistic framework for how irradiation affects the nature and properties of human cortical bone over a range of characteristic (nano to macro) length-scales, following x-ray exposures up to 630 kGy. Macroscopically, bone strength, ductility and fracture resistance are seen to be progressively degraded with increasing irradiation levels. At the micron-scale, fracture properties, evaluated using insitu scanning electron microscopy and synchrotron x-ray computed micro-tomography, provide mechanistic information on how cracks interact with the bone-matrix structure. At sub-micron scales, strength properties are evaluated with insitu tensile tests in the synchrotron using small-/wide-angle x-ray scattering/diffraction, where strains are simultaneously measured in the macroscopic tissue, collagen fibrils and mineral. Compared to healthy bone, results show that the fibrillar strain is decreased by ∼40% following 70 kGy exposures, consistent with significant stiffening and degradation of the collagen. We attribute the irradiation-induced deterioration in mechanical properties to mechanisms at multiple length-scales, including changes in crack paths at micron-scales, loss of plasticity from suppressed fibrillar sliding at sub-micron scales, and the loss and damage of collagen at the nano-scales, the latter being assessed using Raman and Fourier Transform Infrared spectroscopy and a fluorometric assay.

Effect of aging on the transverse toughness of human cortical bone: evaluation by R-curves

The age-related deterioration in the quality (e.g., strength and fracture resistance) and quantity (e.g., bone-mineral density) of human bone, together with increased life expectancy, is responsible for increasing incidence of bone fracture in the elderly. The present study describes ex vivo fracture experiments to quantitatively assess the effect of aging on the fracture toughness properties of human cortical bone specifically in the transverse (breaking) orientation. Because bone exhibits rising crack-growth resistance with crack extension, the aging-related transverse toughness is evaluated in terms of resistance-curve (R-curve) behavior, measured for bone taken from a wide range of age groups (25-74 years). Using this approach, both the ex vivo crack-initiation and crack-growth toughness are determined and are found to deteriorate with age; however, the effect is far smaller than that reported for the longitudinal toughness of cortical bone. Whereas the longitudinal crack-growth toughness has been reported to be reduced by almost an order of magnitude for human cortical bone over this age range, the corresponding age-related decrease in transverse toughness is merely ~14%. Similar to that reported for X-ray irradiated bone, with aging cracks in the transverse direction are subjected to an increasing incidence of crack deflection, principally along the cement lines, but the deflections are smaller and result in a generally less tortuous crack path.

The long-term effects of water fluoridation on the human skeleton

Municipal water fluoridation has notably reduced the incidence of dental caries and is widely considered a public health success. However, ingested fluoride is sequestered into bone, as well as teeth, and data on the long-term effect of exposure to these very low doses of fluoride remain inconclusive. Epidemiological studies suggest that effects of fluoride on bone are minimal. We hypothesized that the direct measurement of bone tissue from individuals residing in municipalities with and without fluoridated water would reveal a relationship between fluoride content and structural or mechanical properties of bone. However, consonant with the epidemiological data, only a weak relationship among fluoride exposure, accumulated fluoride, and the physical characteristics of bone was observed. Analysis of our data suggests that the variability in heterogenous urban populations may be too high for the effects, if any, of low-level fluoride administration on skeletal tissue to be discerned.

Wedge Indentation Fracture of Cortical Bone: Experimental Data and Predictions

The fracture of bone due to indentation with a hard, sharp object is of significance in surgical procedures and certain trauma situations. In the study described below, the fracture of bovine bone under indentation was measured experimentally and predicted using the theory of critical distances (TCDs), a theory, which predicts failure due to cracking in the vicinity of stress concentrations. The estimated indentation fracture force was compared with the experimental results in three different cutting directions. Under indentation, the material experiences high levels of compression and shear, causing cracks to form and grow. The direction of crack growth was highly dependent on the bone’s microstructure: major cracks grew in the weakest possible structural direction. Using a single value of the critical distance (L=320 μm), combined with a multiaxial failure criterion, it was possible to predict the experimental failure loads with less than 30% errors. Some differences are expected between the behavior of human bone and the bovine bone studied here, owing to its plexiform microstructure.

On the effect of X-ray irradiation on the deformation and fracture behavior of human cortical bone

In situ mechanical testing coupled with imaging using high-energy synchrotron X-ray diffraction or tomography is gaining in popularity as a technique to investigate micrometer and even sub-micrometer deformation and fracture mechanisms in mineralized tissues, such as bone and teeth. However, the role of the irradiation in affecting the nature and properties of the tissue is not always taken into account. Accordingly, we examine here the effect of X-ray synchrotron-source irradiation on the mechanistic aspects of deformation and fracture in human cortical bone. Specifically, the strength, ductility and fracture resistance (both work-of-fracture and resistance-curve fracture toughness) of human femoral bone in the transverse (breaking) orientation were evaluated following exposures to 0.05, 70, 210 and 630 kGrays (kGy) irradiation. Our results show that the radiation typically used in tomography imaging can have a major and deleterious impact on the strength, post-yield behavior and fracture toughness of cortical bone, with the severity of the effect progressively increasing with higher doses of radiation. Plasticity was essentially suppressed after as little as 70 kGy of radiation; the fracture toughness was decreased by a factor of five after 210 kGy of radiation. Mechanistically, the irradiation was found to alter the salient toughening mechanisms, manifest by the progressive elimination of the bone's capacity for plastic deformation which restricts the intrinsic toughening from the formation "plastic zones" around crack-like defects. Deep-ultraviolet Raman spectroscopy indicated that this behavior could be related to degradation in the collagen integrity.