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.     

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.     

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     

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.     

Analysis of micro fracture in human Haversian cortical bone under transverse tension using extended physical imaging

We propose a procedure to investigate local stress intensity factors at the scale of the osteons in human Haversian cortical bone. The method combines a specific experimental setting for a three‐point bending millimetric specimen and a numerical method using the eXtended Finite Element Method (X‐FEM). The interface between the experimental setting and the numerical method is ensured through an imaging technique that analyses the light microscopy observations to import the geometrical heterogeneity of the Haversian microstructures, the boundary conditions and appearing crack discontinuities into the numerical model. The local mechanical elastic Young's moduli are measured by nano‐indentation, and the Poisson ratios are determined by an imaging technique of the stress–strain fields. The model is able to access three scales of measurement: the macro scale of the material level (mm), the micro scale inside the Haversian material for stress–strain fields (10–100µm), and the sub‐micro scale for the crack opening profiles (1–10µm ) and fracture parameters (stress intensity factors). The model is applied to several patients at different aging stages. Copyright © 2009 John Wiley & Sons, Ltd.     

Local criteria for ductile fracture

Strain distributions in specimens suitable for studying the initiation of fracture are reviewed, and distributions are developed for the steady-state propagation of cracks in plane strain lension of fully plastic materials. The functional forms of local fracture criteria are discussed for different metallurgical mechanisms. It is concluded that:

1. pure Mode I (normal) fracture is unlikely to exist except in cleavage.
2. there is both theoretical and experimental evidence for the development of both: sharp and flat-bottomed cracks.
3. simultaneous diffuse and concentrated (Dugdale-Muskhelishvili) flow fields can occur in torsion of longitudinally grooved bars if the stress-strain curve has a maximum which causes band formation, so that a displacement criterion becomes appropriate for final fracture.

     

A note on fracture criteria for interface fracture

Several criteria for interface fracture are examined and compared to test results obtained from glass/epoxy specimens. These include two energy release rate criteria, a critical hoop stress criterion and a critical shear stress criterion. In addition, approximate plastic zone size and shape within the epoxy are determined for these tests.     

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.     

Orientation and loading condition dependence of fracture toughness in cortical bone

The fracture toughness at crack initiation were determined for bovine cortical bone under tension (mode I), shear (mode II), and tear (mode III). A total of 140 compact tension specimens, compact shear specimens and triple pantleg (TP) specimens were used to measure fracture toughness under tension, shear, and tear, respectively. Multiple-sample compliance method was utilized to measure the critical strain energy release rate (G_c) at the a/W=0.55 (crack length, a, to specimen width, W, ratio). The critical stress intensity factor (K_c) was also calculates from the critical loading (P_c) of the specimens at the a/W=0.55. The effect of the anisotropy of bone on its resistance to crack initiation under shear and tear loading was investigated as well. Fracture toughness of bone with precrack orientations parallel (designed as longitudinal fracture) and vertical (designed as transverse fracture) to the longitudinal axis of bone were compared. In longitudinal fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 644±102, 2430±836, and 1723±486 N/m, respectively. In transverse fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 1374±183, 4710±1284, and 4016±948 N/m, respectively. An unpaired t-test analysis demonstrated that the crack initiation fracture toughness of bone under shear and tear loading were significantly greater than that under tensile loading in both longitudinal and transverse fracture (P<0.0001 for all). Our results also suggest that cortical bone has been “designed” to prevent crack initiation in transverse fracture under tension, shear, and tear.     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

Comparison of different failure criteria for fiber-reinforced plastics in terms of fracture curves for arbitrary stress combinations

For fiber-reinforced plastics exists a big number of different criteria for the failure prediction. The intention of this paper is to compare the TSAI-HIL-, the LaRC04- and PUCK’s criterion in terms of their fracture curves for a unidirectional glass-fiber reinforced composite layer. Therefore after the implementation of these three criteria, the two-dimensional fracture curves for all possible stress combinations, which can be derived from a general spatial stress tensor, are computed. In this way, the characteristics of the criteria, similarities and differences and possible weak points become obvious.     

Anisotropy and failure criteria for concrete

Summary The migration of water within fresh concrete to produce the phenomenon known as “water gain” appears to have received far too little attention, particularly as regards failure theories which assume that concrete exhibits isotropic behaviour. It is shown that concrete is anisotropic when subjected to either tensile or compressive stresses. Reliable comparisons of tension and compression test results must therefore relate the direction of testing the specimens to the vertical direction at casting. The design of cast in-situ columns, for example, based on normal cube test results can be particularly unsafe. The effects of anisotropic behaviour upon failure envelopes for biaxial states of stress are also considered.

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Résumé La migration d'eau à travers le béton frais, qui produit le phénomène du ressuage, ne parait pas avoir suscité une attention suffisante, particulièrement en ce qui concerne les théories de la rupture qui dépendent de l'hypothèse d'un comportement isotropique du béton. On montre ici que le béton est anisotropique lorsqu'il est soumis à une contrainte en traction ou en compression. Une étude comparative sérieuse des résultats d'essais en traction et en compression doit par conséquent relier la direction de l'essai des éprouvettes à la direction verticale au moment du coulage. Le calcul de poteaux coulés in-situ d'après les résultats de l'essai normal sur cube peut, par exemple, être particulièrement inadéquat. On considère aussi les effets du comportement anisotropique sur les enveloppes de rupture pour la condition de contrainte biaxiale.

     

Numerical simulation of the slant fracture of a helicopter's rotor hub with ductile damage failure criteria

The main rotor hub is one of the most critical components in helicopter structures. Thus, to assess the behaviour of the component, a fatigue test until failure has been carried out on a real Ti–6Al–4V hub. A fracture mechanics analysis is used to estimate the critical crack dimensions. Subsequently, the slant fracture due to a propagating fatigue crack has also been simulated numerically with an explicit finite element model, using the Bao–Wierzbicki ductile damage criterion. Fracture toughness and failure calibration of Ti alloy have been carried out to obtain reliable results. The numerical fracture surface obtained has been compared with the experimental one.     

A study of fracture criteria for ductile materials

In order to establish a ductile fracture criterion, several potential fracture parameters were investigated by comparing numerical simulations of crack extension with available experimental data. Based on the comparison, a fracture criterion, the Global-Local Fracture Criterion (GLFC), was proposed. The J-integral is employed as a global parameter to characterize the initial stage of crack extension. In the subsequent steady state crack growth, the fracture criterion is switched to a local parameter characterizing the crack tip stress or strain. The accuracy of the proposed fracture criterion in predicting ductile fracture behavior was verified.     

Fatigue failure criteria for combined cyclic stress

Failure criteria for combined cyclic stress are represented in terms of parametric families of failure surfaces in stress space. Quadratic approximations and symmetry arguments are employed in systematic fashion to construct isotropic failure criteria for general three dimensional states of cyclic stress. Particular attention has been directed to the important cases of normal stress-shear stress (bending-torsion) and biaxial stress cyclings. It is shown that failure criteria for cycling with and without mean stress (reversed cycling) have different forms, the latter admitting simpler representations.

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Résumé On représente des critères de rupture pour des contraintes cycliques combinées en termes de familles paramétriques de surfaces de rupture dans l'espace où agissent les contraintes. Des approximations quadratiques et des arguments symétriques sont utilisés de manière systématique pour établir des critères de rupture isotrope dans le cas général d'états tridimensionnels de contraintes cycliques. Une attention particulière a été consacrée à deux cas importants: des variations de contraintes normales, contraintes de cisaillement (flexion-torsion) et des variations de contraintes biaxiales. On montre que les critères de rupture dans le cas de variations de contraintes avec ou sans contraintes moyennes (sollicitation alternée) présentent différentes formes et que les représentations les plus simples sont associées aux contraintes alternées.

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Supported by the Naval Air Systems Command, Washington, D.C. and the Office of Naval Research, Structural Mechanics Branch, Arlington, VA under Contract N00014-78-C-0544 with the University of Pennsylvania.