Creep contributes to the fatigue behavior of bovine trabecular bone.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.     

Systematic error in mechanical measures of damage during four-point bending fatigue of cortical bone

Accumulation of fatigue microdamage in cortical bone specimens is commonly measured by a modulus or stiffness degradation after normalizing tissue heterogeneity by the initial modulus or stiffness of each specimen measured during a preloading step. In the first experiment, the initial specimen modulus defined using linear elastic beam theory (LEBT) was shown to be nonlinearly dependent on the preload level, which subsequently caused systematic error in the amount and rate of damage accumulation measured by the LEBT modulus degradation. Therefore, the secant modulus is recommended for measurements of the initial specimen modulus during preloading. In the second experiment, different measures of mechanical degradation were directly compared and shown to result in widely varying estimates of damage accumulation during fatigue. After loading to 400,000 cycles, the normalized LEBT modulus decreased by 26% and the creep strain ratio decreased by 58%, but the normalized secant modulus experienced no degradation and histology revealed no significant differences in microcrack density. The LEBT modulus was shown to include the combined effect of both elastic (recovered) and creep (accumulated) strain. Therefore, at minimum, both the secant modulus and creep should be measured throughout a test to most accurately indicate damage accumulation and account for different damage mechanisms. Histology revealed indentation of tissue adjacent to roller supports, with significant sub-surface damage beneath large indentations, accounting for 22% of the creep strain on average. The indentation of roller supports resulted in inflated measures of the LEBT modulus degradation and creep. The results of this study suggest that investigations of fatigue microdamage in cortical bone should avoid the use of four-point bending unless no other option is possible.     

Near-terminal creep damage does not substantially influence fatigue life under physiological loading

Cortical bone specimens were damaged using repeated blocks of tensile creep loading until a near-terminal amount of creep damage was generated (corresponding to a reduction in elastic modulus of 15%). One group of cortical bone specimens was submitted to the near-terminal damage protocol and subsequently underwent fatigue loading in tension with a maximum strain of 2000 με (Damage Fatigue, n=5). A second group was submitted to cyclic fatigue loading but was not pre-damaged (Control Fatigue, n=5). All but one specimen (a damaged specimen) reached run-out (10 million cycles, 7.7 days). No significant differences in microscopic cracks or other tissue damage were observed between the two groups or between either group and additional, completely unloaded specimens. Our results suggest that damage in cortical bone allograft that is not obvious or associated with a stress riser may not substantially affect its fatigue life under physiologic loading.     

Analysis of creep strain during tensile fatigue of cortical bone

During fatigue tests of cortical bone specimens, at the unload portion of the cycle (zero stress) non-zero strains occur and progressively accumulate as the test progresses. This non-zero strain is hypothesised to be mostly, if not entirely, describable as creep. This work examines the rate of accumulation of this strain and quantifies its stress dependency. A published relationship determined from creep tests of cortical bone (Journal of Biomechanics 21 (1988) 623) is combined with knowledge of the stress history during fatigue testing to derive an expression for the amount of creep strain in fatigue tests. Fatigue tests on 31 bone samples from four individuals showed strong correlations between creep strain rate and both stress and "normalised stress" (sigma/E) during tensile fatigue testing (0-T). Combined results were good (r(2)=0.78) and differences between the various individuals, in particular, vanished when effects were examined against normalised stress values. Constants of the regression showed equivalence to constants derived in creep tests. The universality of the results, with respect to four different individuals of both sexes, shows great promise for use in computational models of fatigue in bone structures.     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

A phenomenological model for predicting fatigue life in bovine trabecular bone

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.     

Strain rate dependence of the mechanical properties of reindeer antler and the cumulative damage model of bone fracture

Carter and Caler have produced a 'cumulative damage' model for the fracture of bone, based on creep experiments on human bone, which has been corroborated by monotonic tensile tests on bone, loaded at various strain rates. Monotonic tensile tests on reindeer's antler, which has a lower modulus of elasticity than human bone, produce very similar results. Unlike human bone, reindeer antler always shows a large post-yield strain, and it is possible to distinguish pre-yield and post-yield behaviour. The 'final stiffness' (ultimate stress/ultimate strain) is invariant with strain rate. This is confirmation that bone fractures when a certain amount of damage has accumulated. However, reindeer antler shows a considerable post-yield increase in stress. This is difficult to accommodate in a cumulative damage model.     

Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low density trabecular bone

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.     

Creep does not contribute to fatigue in bovine trabecular bone

In both cortical and trabecular bone loaded in fatigue, the stress-strain loops translate along the strain axis. Previous studies have suggested that this translation is the result of creep associated with the mean stress applied in the fatigue test. In this study, we measured the residual strrain (corresponding to the translation of the stress-strain loops) in fatigue tests on bovine trabecular bone and compared it to an upper bound estimate of the creep strain in each test. Our results indicate that the contribution of creep to the translation of the stress-strain loops is negligible in bovine trabecular bone. These results, combined with models for fatigue in lower density bone, suggest that that creep does not contribute to the fatigue of normal human bone. Creep may make a significant contribution to fatigue in low-density osteoporotic bone in which trabeculae have resorbed, reducing the connectivity of the trabecular structure.     

A fatigue damage model for the cement-bone interface

Loss of fixation at the cement-bone interface can contribute to clinical loosening of cemented total hip replacements. In this study, the fatigue damage response was determined for cement-bone constructs subjected to shear fatigue loading. A typical three-phase fatigue response was observed with substantial early damage, followed by a long constant damage rate region and a final abrupt increase in damage to fracture. All of the damage resulted from creep (permanent) deformation during fatigue loading and there was no loss in cyclic stiffness. Using a Von Mises equivalent stress/strain concept, a general damage model was developed to describe the fatigue creep response of the cement-bone interface under either shear or tensile fatigue loading. Time to failure was highly correlated (r2=0.971) with equivalent creep strain rate and moderately related (r2=0.428) with equivalent initial strain for the two loading regimes. The equivalent creep strain at failure (0.052+/-0.018) was found to be independent of the applied equivalent stress. A combination of the creep damage model (to describe the damage process) with a constant final equivalent strain (as a failure criteria) could be used to assess the cement-bone failure response of cemented implant systems.     

Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.     

Fatigue of immature baboon cortical bone

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

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.     

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.     

Time-dependent circumferential deformation of cortical bone upon internal radial loading

Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.     

Tensile fatigue failure of acrylic bone cement

Tensile fatigue tests of acrylic bone cement were conducted under strain control in a wet environment at 37 degrees C. A constant strain rate of 0.02s-1 was used, resulting in physiologic loading frequencies. Comparison of the tensile fatigue data with the results of previous tension-compression fatigue tests indicates that fatigue failure is governed primarily by the maximum cyclic tensile strain. The compressive portion of the loading cycle has little effect on the number of cycles to failure. A new empirically derived equation is introduced to describe the influence of mean strain and strain amplitude on fatigue endurance. The results emphasize the critical role tensile strains may play in cement failure and loosening of total joint replacements.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

Continuum damage mechanics (CDM) modelling demonstrates that ligament fatigue damage accumulates by different mechanisms than creep damage

Ligaments can be subjected to creep and fatigue damage when loaded to higher than normal stresses due to injury of a complementary joint restraint. Continuum damage mechanics (CDM) assumes that diffuse damage accumulates in a material, thereby reducing the effective cross-sectional area and leading to eventual rupture. The objective of this study was to apply CDM modelling to ligament creep and fatigue to reveal mechanisms of damage. Fatigue was modelled by cyclically varying the stress in the creep model. A few novel approaches were used. First, area reduction was not assumed equal to modulus reduction; thus, allowing damaged fibres to potentially contribute to load-bearing through the extracellular matrix. Modulus ratio was related to area reduction using residual strength. Second, damage rate was not assumed constant but rather was determined directly from the modulus ratio change with respect to time. Third, modulus ratio was normalized to maximum modulus to avoid artificial calculation of negative damage. With this approach, the creep time-to-rupture was predicted with -4% error at 60% UTS and -13% error at 30% UTS. At 15% UTS, no test was undertaken experimentally for a duration as long as the 24 days predicted theoretically. Oscillating the time-dependent damage in the creep model could not completely explain the fatigue behaviour because the fatigue time-to-rupture was predicted with over 1300% error at all stresses. These results suggest that a cycle-dependent damage mechanism, in addition to a time-dependent one, was responsible for fatigue rupture. Cycle-dependent damage may be an important consideration for rehabilitation activities following injury of a complementary ligament restraint.     

Some viscoplastic characteristics of bovine and human cortical bone

Multiple cycle tensile creep tests were performed on human and bovine cortical bone specimens. The tests enabled total strain to be decomposed into elastic, linear viscoelastic, creep and permanent plastic components. The results indicate that a stress threshold exists; above which time dependent effects dominate material response and below which the behavior is primarily linear viscoelastic, with time effects playing only a secondary role. A constant stress above the threshold produces a constant steady state creep rate, with the magnitude of the creep rate being an exponential function of the stress magnitude. Additionally, it was found that a major portion of the inelastic strain is always recovered on unloading and that the accumulation of creep strain increases the material compliance on subsequent loadings below the threshold. These two factors suggest that a damage mechanism is responsible for the nonlinear behavior.