fracture and microstructural study of bovine bone under mixed mode i ii loading

Abstract Understanding the fracture behavior and associated crack growth mechanism in bone material is an important issue for biomechanics and biomaterial researches. Fracture of bone often takes place due to complex loading conditions which result in combined tensile-shear (i.e. mixed mode) fracture mechanism. Several parameters such as loading type, applied loading direction relative to the bone axis, loading rate, age and etc., may affect the mixed mode fracture resistance and damage mechanism in such materials. In this research, a number of mixed mode I/II fracture experiments are conducted on bovine femur bone using a sub-sized test configuration called "compact beam bend (CBB)" specimen to investigate the fracture toughness of bone under different mode mixities. The specimen is rectangular beam containing a mid-edge crack that is loaded by a conventional three-point bend fixture. The results showed the dependency of bone fracture toughness on the state of mode mixity. The fracture surfaces of broken CBB specimens under different loading conditions were studied via scanning electron microscopy (SEM) observations. Fracture surface of all investigated cases (i.e. pure mode I, pure mode II and mixed mode I/II) exhibited smooth patterns demonstrating brittle fracture of bovine femur. The higher density of vascular channels and micro-cracks initiated in the weakened area surrounded by secondary osteons were found to be the main cause of the decreased bone resistance against crack growth and brittle fracture

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semicircular bend specimen is herein presented. The specimen is semicircular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied

Evaluation of Mode I Fracture Toughness Assisted by the Numerical Determination of K-Resistance

The fracture toughness of a rock often varies depending on the specimen shape and the loading type used to measure it. To investigate the mode I fracture toughness using semi-circular bend (SCB) specimens, we experimentally studied the fracture toughness using SCB and chevron bend (CB) specimens, the latter being one of the specimens used extensively as an International Society for Rock Mechanics (ISRM) suggested method, for comparison. The mode I fracture toughness measured using SCB specimens is lower than both the level I and level II fracture toughness values measured using CB specimens. A numerical study based on discontinuum mechanics was conducted using a two-dimensional distinct element method (DEM) for evaluating crack propagation in the SCB specimen during loading. The numerical results indicate subcritical crack growth as well as sudden crack propagation when the load reaches the maximum. A K-resistance curve is drawn using the crack extension and the load at the point of evaluation. The fracture toughness evaluated by the K-resistance curve is in agreement with the level II fracture toughness measured using CB specimens. Therefore, the SCB specimen yields an improved value for fracture toughness when the increase of K-resistance with stable crack propagation is considered

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily overconsolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as the critical distance. This fracture criterion is known as the Point Method, and is part of the Theory of Critical Distances, which is utilized in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, ó0, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, óc and ót. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (óc/ót=3-50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low confining stresses.The work presented was initiated during a research project on “Structural integrity assessments of notch-type defects", for the Spanish Ministry of Science and Innovation (Ref.: MAT2010-15721)

Confining pressure effects on stress intensity factors: A 3D finite element analysis

At great depths of earth, fracture in rock masses occurs under the influence of confining pressure. However, most of the previous rock fracture studies deal only with ambient conditions and ignore the effects of multiaxial stresses induced because of applying the confining pressure. In this paper, the influence of confining pressure on the mixed mode stress intensity factors (KI and KII) is investigated for a test specimen. A large number of 3D finite element models were analyzed for investigating the effect of various confining pressure levels on the fracture behaviour of brazilian disc specimen. In the finite element models a uniformly distributed confining pressure in the range of 0 MPa to 20 MPa is applied to all sides of the test specimen. It is shown that the confining pressure has a significant effect on the mode I stress intensity factor, but the mode II stress intensity factor is completely independent of the applied confining pressure. A comparison between the confined and unconfined conditions shows that the effective mixed mode stress intensity factor increases by increasing the value of confining pressure for all mode mixities.Keywords: confining pressure; mixed mode; stress intensity factors; brazilian disc; numerical method. A des profondeurs importantes de la terre, la rupture dans les masses de roches se produit sous l'influence de la pression de confinement. Cependant, la plupart des études précédentes de rupture de roche traitent seulement dans des conditions ambiantes et ignorent les effets des efforts multiaxiaux induits en raison de l'application de la pression de confinement. Dans cette étude, l'influence de la pression sur les facteurs d'intensité de contrainte en modes mixtes (KI et KII) est étudiée pour un spécimen d'essai. Un grand nombre de modèles finis de l'élément 3D ont été analysés pour étudier l'effet de divers niveaux de confinement de pression sur le comportement de rupture du spécimen brésilien sous la forme de disque. Pour les modèles d'éléments finis, une pression uniformément distribuée dans l'intervalle de 0 à 20 MPa est appliquée sur tous les côtés du spécimen d'essai. Il est montré que la pression de confinement a un effet significatif sur le facteur d'intensité de contrainte en mode I, mais celui de mode II est complètement indépendant de la pression de confinement appliquée. Une comparaison entre les conditions de confiné et non confiné indique que le facteur d'intensité de contrainte en mode mixte augmente avec la valeur de la pression de confinement quelque soit le mode mixte considéré.Mots clés: pression de confinement; mode de rupture mixte; facteurs d'intensité de contraintes; Disque brésilien ; méthode numérique.