Effect of collagen damage induced by heat treatment on the mixed-mode fracture behavior of bovine cortical bone under elevated loading rates

International Journal of Fracture - The fracture resistance of bone has been attributed to a competition of sub-micron lengthscale intrinsic mechanisms, including plasticity conferred by collagen...     

Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness

This study was concerned with the mechanics and micromechanisms of diffuse (ultrastructural) damage occurrence in human tibial cortical bone specimens subjected to tension–tension fatigue. A nondestructive technique was developed for damage assessment on the surfaces of intact compact tension specimens using laser scanning confocal microscopy. Results indicated that diffuse damage initiates as a result of fractures in the inter-canalicular regions. Subsequent growth of those microscopic flaws demonstrated multiple deflections from their paths due to 3D spatial distribution of microscopic porosities (lacunae–canalicular porosities) and the stress-concentrating effects of lacunae. Damage dominating effects in the early stages of fatigue had been verified by the observed variations of the fracture toughness due to artificially induced amounts of damage. Toughening behavior was observed as a function of diffuse damage. © 2001 Kluwer Academic Publishers     

Some fatigue damage measures for longitudinal elements based on the Wohler field

In this paper, the problem of selecting damage measures and ways of accumulating damage due to a fatigue load history is dealt with. First, a statistical model and a normalization procedure, that allow using a reference stress level or a reference random variable for analysing the fatigue data coming from tests at different stress ranges, are presented. Next, some desirable properties for a damage measure are discussed and several alternative damage measures are investigated based on these properties. It is shown how several damage measures, such as the Palmgren–Miner number, do not satisfy these properties. On the contrary, the standardized logarithm of the number of cycles, which coincides with the standardized Palmgren–Miner number, a Weibull reference variable and a probability based damage measure are demonstrated to satisfy these properties and to be good alternatives for a damage measure. It is shown that the most convenient damage measures are obtained by assuming that two pieces subjected to different stress level tests suffer the same damage if, at the end of the corresponding tests, they have the same probability of failure. The problem of extending the damage measure below the zero-percentile area (where fatigue failure does not occur) is also analysed. Finally, the damage accumulation problem for non-constant stress range load histories is discussed, and formulae for calculating the associated damage are given. For the sake of illustration, several examples of different load types are also given.     

The nature of fatigue damage in bone

Bone is unusual among structural materials as it is alive and capable of self-repair. Fatigue-induced microdamage is repaired by bone remodelling, but if damage accumulates too quickly, or remodelling is deficient, fatigue failure may result. Fatigue is thought to contribute to both stress and fragility fractures which are of major clinical importance. Despite this, we do not fully understand the nature of fatigue damage in bone. Human rib sections, containing microcracks stained with basic fuchsin, were serially sectioned and microcracks identified and reconstructed in three dimensions using computer software. Microcracks were elliptical in shape, 400 μm long and 100 μm wide, typical of a transversely isotropic material. Chelating agents which bind Ca²⁺ were found to label microcracks in rib, as well as mineralising bone surfaces and resorption sites, suggesting that microcracks are Ca²⁺ ion-lined discontinuities in the hydroxyapatite matrix. Ca²⁺ ions were exposed by scratching the surface of bovine bone specimens and labelled with chelating agents in sequence. The optimal four agent sequence was: alizarin, xylenol orange, calcein and calcein blue. Two dye sequences were used to differentiate between pre-existing and test-induced microdamage in bovine samples fatigue tested in compression and longer sequences labelled microcrack growth. Microcrack dimensions can be used to calculate stress intensity values and, together with fatigue test data, can aid theoretical models to predict fatigue failure in bone.     

Crack velocity dependence of longitudinal fracture in bone

An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G _c) and critical stress intensity factor (K _c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10^–5 m sec^–1 produced increases in G _c (from 1736 to 2796 J m^–2), K _c (from 4.46 to 5.38 MN m^–3/2) and W. At crack velocities >23.6×10^–5 m sec^–1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec^–1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.     

Microstructural aspects of the fracture process in human cortical bone

Fracture toughness tests were conducted in the transverse and longitudinal directions to the osteonal orientation of human femoral cortical bone tissue to investigate the resulting damage patterns and their interaction with the microstructure. The time history of damage accumulation was monitored with acoustic emission (AE) during testing and was spatially observed histologically following testing. The fracture toughness of the transverse specimens was almost two times greater than the fracture toughness of the longitudinal specimens (3.47 MNm^–3/2 vs. 1.71 MNm^–3/2, respectively). The energy content of the AE waveforms of transverse specimens were greater than those of the longitudinal specimens implying higher fracture resistance in the transverse crack growth direction. The results showed that the propagation of the main crack involved weakening of the tissue by ultrastructural (diffuse) damage at the fracture plane and formation of linear microcracks away from the fracture plane for the transverse specimens. For the longitudinal specimens, the growth of the main crack occurred in the form of separations at lamellar interfaces. The lamellar separations generally arrested at the cement lines. Linear microcracks occurred primarily in the interstitial tissue for both crack growth directions.     

Mechanistic fracture criteria for the failure of human cortical bone

A mechanistic understanding of fracture in human bone is critical to predicting fracture risk associated with age and disease. Despite extensive work, a mechanistic framework for describing how the microstructure affects the failure of bone is lacking. Although micromechanical models incorporating local failure criteria have been developed for metallic and ceramic materials, few such models exist for biological materials. In fact, there is no proof to support the widely held belief that fracture in bone is locally strain-controlled, as for example has been shown for ductile fracture in metallic materials. In the present study, we provide such evidence through a novel series of experiments involving a double-notch-bend geometry, designed to shed light on the nature of the critical failure events in bone. We examine how the propagating crack interacts with the bone microstructure to provide some mechanistic understanding of fracture and to define how properties vary with orientation. It was found that fracture in human cortical bone is consistent with strain-controlled failure, and the influence of microstructure can be described in terms of several toughening mechanisms. We provide estimates of the relative importance of these mechanisms, such as uncracked-ligament bridging.     

Transverse fatigue crack propagation behavior in equine cortical bone

Stress fractures stem from the initiation and propagation of fatigue cracks through bone, and fatigue damage may play a role in many other orthopaedic problems, such as hip fractures in the elderly. The objective of this investigation was to measure fatigue crack propagation rates in cortical bone. Specific aims were to determine fatigue crack growth rate, da/dN, as a function of alternating stress intensity factor, K, for equine third metacarpal cortical bone tissue; to determine whether the resulting data followed the Paris law; and to test the hypothesis that crack growth rates differ between dorsal and lateral regions. Compact type specimens oriented for transverse crack growth were subjected to fatigue under Mode I loading. The da/dN vs. K data for the dorsal specimens revealed a Paris law exponent of 10.4 (R ² = 0.82), comparable to that for ceramics. These data also exhibited an apparent threshold stress intensity factor of 2.0 MPa · m^1/2. It was not possible to obtain similar results for lateral specimens because all cracks deviated from the desired transverse path and ran longitudinally in spite of the use of side grooves to constrain the crack path. However, the results for lateral specimens were not due to a failure of the test method, but reflect dramatic differences in fatigue crack propagation resistance between the two cortical regions. These results are consistent with clinical observations that stress fractures in the third metacarpus typically occur in the mid-diaphysis of the dorsal cortex, but not in the lateral cortex.     

疲劳荷载对橡胶混凝土损伤和断裂性能的影响

虽然橡胶混凝土塑性和疲劳性能较好,但由于掺入橡胶,其在疲劳荷载下离散性增大,损伤过程及最终的断裂机制均不明确.为研究橡胶混凝土在疲劳荷载下的损伤和断裂性能,基于声发射开展了不同橡胶掺量的混凝土在疲劳荷载下的三点弯曲疲劳断裂试验.计算有效裂缝长度,分析疲劳荷载下不同橡胶掺量的混凝土裂缝长度a的变化规律,并利用裂缝长度a和...     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.     

A combined finite element method and continuum damage mechanics approach to simulate the in vitro fatigue behavior of human cortical bone

The fatigue of bone, in particular the associated modulus degradation and accumulation of permanent strain, has been implicated as the cause of femoral neck fractures and the migration of total joint replacements. The objective of this study was to develop a technique to simulate the tensile fatigue behavior of human cortical bone. A combined continuum damage mechanics (CDM) and finite element analysis (FEA) approach was used to predict the number of cycles to failure, modulus degradation and accumulation of permanent strain of human cortical bone specimens. The simulation of fatigue testing of eight dumb-bell specimens of cortical bone were performed and the predictions compared with existing experimental data. The predictions from the finite element models were in close agreement with the experimental data. The models predicted similar development of modulus degradation and permanent strain as observed in the experimental tests. The technique is capable of predicting the accumulation of permanent strain without the need for simulating every single load step. These findings suggest that the complex fatigue behavior of human cortical bone can be simulated using the described approach and forms the first step for simulating the more complex mechanisms associated with femoral neck fractures and implant migration.     

On the assessment of brittle-elastic cortical bone fracture in the distal radius

The primary objective of this work is to outline a simple methodology for the evaluation of the risk of cortical bone fracture in the distal radius in the event of a fall from standing height onto an outstretched hand. The approach involves conducting an elastic finite element (FE) analysis wherein the cortical bone is considered to be a transversely-isotropic material and, subsequently, verifying the admissibility of the stress field. The latter is based on a proposed macroscopic fracture criterion, which takes into account the anisotropic nature of the cortical tissue. The methodology is illustrated by a numerical example, which involves FE simulation of an experimental test designed to produce a Colles’ fracture of the radius.     

Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

Evaluation of the fatigue fracture resistance of unfilled and filled polytetrafluoroethylene materials

Polytetrafluoroethylenes (PTFEs) and their composites are a special class of fluorocarbons with very high chemical resistance and wide service temperature. This makes them good candidate materials for load-bearing components exposed to harsh environments, including some space applications. In the present work, fatigue crack propagation (FCP) behavior of four materials from the fluorocarbon family, including PTFE without filler (virgin PTFE), PTFE with 15% glass fiber, PTFE with 15% graphite particles, and PTFE with 25% glass fiber, were studied. Tension/tension FCP experiments were carried out using single-edge notch (SEN) specimens under load control. The maximum stress was kept constant at 8 MPa for each material at a frequency of 3 Hz. The minimum to maximum stress ratio was 0.27. FCP data such as the number of cycles, crack length, and hysteresis loops were recorded in order to establish the crack speed, the energy release rate, J*, and the change in work Wi. Parameters that characterize the resistance of PTFEs to FCP have been successfully determined by the modified crack layer (MCL) model. These parameters are , the specific energy of damage, which reflects the FCP resistance of the PTFE materials, and the dissipative characteristic of the materials, . It has been found that the MCL model describes the behavior of the PTFEs over the entire range of the energy release rate and discriminates the subtle effects introduced by changing the filler type and dosage as well as the processing conditions. The values of the specific energy of damage have been found to decrease by increasing the dosage of the fiberglass fillers. Graphite particulate filler also reduced the value of more than fiberglass filler for the same dosage. Microscopic analysis of the fracture surface in the stable crack propagation region of each material revealed that there exists a strong correlation between the value of and the amount of damage energy manifested by different mechanisms and species during the fatigue process.     

A fracture mechanics and mechanistic approach to the failure of cortical bone

The fracture of bone is a health concern of increasing significance as the population ages. It is therefore of importance to understand the mechanics and mechanisms of how bone fails, both from a perspective of outright (catastrophic) fracture and from delayed/time‐dependent (subcritical) cracking. To address this need, there have been many in vitro studies to date that have attempted to evaluate the relevant fracture and fatigue properties of human cortical bone; despite these efforts, however, a complete understanding of the mechanistic aspects of bone failure, which spans macroscopic to nanoscale dimensions, is still lacking. This paper seeks to provide an overview of the current state of knowledge of the fracture and fatigue of cortical bone, and to address these issues, whenever possible, in the context of the hierarchical structure of bone. One objective is thus to provide a mechanistic interpretation of how cortical bone fails. A second objective is to develop a framework by which fracture and fatigue results in bone can be presented. While most studies on bone fracture have relied on linear‐elastic fracture mechanics to determine a single‐value fracture toughness (e.g., K_c or G_c), more recently, it has become apparent that, as with many composites or toughened ceramics, the toughness of bone is best described in terms of a resistance‐curve (R‐curve), where the toughness is evaluated with increasing crack extension. Through the use of the R‐curve, the intrinsic and extrinsic factors affecting its toughness are separately addressed, where ‘intrinsic’ refers to the damage processes that are associated with crack growth ahead of the tip, and ‘extrinsic’ refers to the shielding mechanisms that primarily act in the crack wake. Furthermore, fatigue failure in bone is presented from both a classical fatigue life (S/N) and fatigue‐crack propagation (da/dN) perspective, the latter providing for an easier interpretation of fatigue micromechanisms. Finally, factors, such as age, species, orientation, and location, are discussed in terms of their effect on fracture and fatigue behaviour and the associated mechanisms of bone failure.     

Microstructural influences on fatigue and fracture resistance in high strength structural materials

A concise review is given of microstructural influences on fatigue strength, fatigue crack propagation, fracture toughness, and stress corrosion in high strength aluminium alloys, titanium alloys, and steels.     

Influence of z-pin length on the delamination fracture toughness and fatigue resistance of pinned composites

The effect of z-pin length on the mode I and mode II delamination toughness and fatigue resistance of z-pinned carbon-epoxy composites is investigated. Experimental testing and mechanical modelling reveals that both the mode I fracture toughness and fatigue resistance increase with the z-pin length due to increased bridging traction loads generated by elastic stretching and pull-out of the pins. The opposite trend occurs for mode II toughness, which decreases with increasing z-pin length due to lower traction loads arising from restrictions on the shear-induced rotation and pull-out of the pins. The mode II fatigue resistance is increased by z-pinning, although it is not dependent on the z-pin length. Increasing the z-pin length beyond a critical size also changes the mode I and mode II delamination fracture and fatigue processes from single to multiple cracking. The effect of z-pin length on the delamination toughening and fatigue strengthening mechanisms is determined.     

Effects of interfacial debonding on fatigue damage of cemented hip prostheses

Abstract

Clinical studies on retrieved cement mantles have pointed out that the cemented hip prostheses failed after long‐term use due to debonding at the cement‐stem interface and local fractures in the cement mantles. These were linked to fatigue damages of cement mantles proved by fatigue experiments. In this paper, a numerical approach based on finite element analysis and continuum damage mechanics is proposed to investigate the fatigue behavior of cement mantles during gait cycles. Results reveal that the major sites for failure initiation are at the proximal medial regions and at the distal prostheses tip. Such fatigue failures not only result in the corruption of cementstem interfaces, but also greatly affect the stress distribution and damage rate of the proximal cement mantles in subsequent loading cycles. The interfacial debonding rate increases from 2.5% to 15% with gait loadings from five to twenty million cycles. Meanwhile, owing to the partial debonding of interface, the cement stresses on the remaining regions increase by 91% to 871% when compared with those generated with a fully bonded interface, which in turn accelerates the fatigue damage accumulation rate of the cement mantle from 5.99 % to 21.5%.