FRACTURE TOUGHNESS AT THE INTERFACE BETWEEN CORTICAL BONE AND CANCELLOUS BONE

Introduction

Bone fracture toughness is an important parameter in resistance of bone to monotonic and fatigue failure. Earlier studies on bone fracture toughness were focused on either cortical or cancellous bone, separately [1, 2]. Reported fracture toughness values indicated that cortical bone is tougher to break as compared to cancellous bone. In order to understand complete fracture of a whole bone, the interface between cortical and cancellous bone (named as corticellous bone) might play a crucial role and is interesting topic of research. The goal of this study was to identify fracture toughness in terms of J integral and fracture mechanism of the corticellous bone.

Material and Methods

Corticellous bone samples (single edge notch bend specimen or SENB) were prepared from bovine proximal femur according to ASTM E399-90 standard (Fig.1). For corticellous bone, samples were prepared in such way that approximately half of the sample width consist of cortical bone and another half is cancellous bone. Precaution was taken while giving notch and pre-crack to corticellous bone that pre-crack should not enter from cortical to cancellous portion. All specimens were tested using a universal testing machine (Tinius Olsen, ± 100 N) under displacement rate of 100 µm/min until well beyond yield point. The fracture toughness parameter in terms of critical stress intensity (K_IC) was calculated according to ASTM E399-90 as given by,

Where, P = applied load in kN, S = loading span in cm, B = specimen thickness in cm, W = specimen width in cm, a = total crack length, f(a/W) = geometric function. After the fracture test the J integral of each specimen was calculated using following equation. [ASTM E1820].

Where, J_el is J integral of the elastic deformation, J_pl is J integral of the plastic deformation, E′=E for plane stress condition and E′= E/(1−ν²) for plane strain condition (E is elastic modulus; ν is Poisson's ratio), b_o = W−a_o, height of the un-cracked ligament, and A_pl is the area of the plastic deformation part in the load–displacement curve.

Result and Discussion

The fracture toughness in terms of critical stress intensity (K_IC) of corticellous bone was found to be 2.45 MPa.m^1/2. The plastic part of J integral, J_pl value of corticellous specimen was 9310 Jm⁻², and shown to be 27 times of the J_el value, 341 Jm⁻2. Total J integral of corticellous bone was found to be 9651 Jm⁻². When crack travels through cortical portion and reaches at the interface, crack branching occurred and further it slows down (Fig.2). Indeed, more energy is required in plastic than elastic deformation.

Conclusion

J integral of corticellous bone is found to higher which is due to plastic deformation and crack branches at the interface between cortical and cancellous bone.

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