F.A.M. Pereira

The double cantilever beam test applied to mode I fracture characterization of cortical bone tissue

The primary objective of this work was to analyse the adequacy of the Double Cantilever Beam (DCB) test in determining fracture toughness under pure mode I loading of cortical bone tissue. A new data reduction scheme based on specimen compliance and the crack equivalent concept was used to overcome the difficulties inherent in crack monitoring during its growth. It provides a complete resistance curve, which is fundamental in estimating the fracture energy. A cohesive zone model was used to simulate damage initiation and propagation, thus assessing the efficacy of the proposed testing method and data reduction scheme. Subsequently, the DCB test was applied to evaluate the mode I fracture energy of hydrated and thermally dehydrated cortical bone tissue from young bovine femur, in the tangential-longitudinal propagation system. The results obtained demonstrate the efficacy of the DCB test and the proposed data reduction scheme on the bone fracture characterization under mode I loading.

Bone fracture characterization using the end notched flexure test

A miniaturized version of the end notch flexure test was used in the context of pure mode II fracture characterization of bovine cortical bone. To overcome the difficulties intrinsic to crack length monitoring during its propagation an equivalent crack method was employed as data reduction scheme. The proposed method was validated numerically by means of a finite element analysis including a cohesive zone modeling and subsequently applied to experimental results to determine the fracture energy of bone under pure mode II loading. Finally, a cohesive law representative of fracture behavior of each specimen was determined employing an inverse method, considering a trapezoidal shape for the softening law. The consistency of the obtained results leads to the conclusion that the trapezoidal law is adequate to simulate fracture behavior of bone under mode II loading. The proposed testing setup and the employed data reduction scheme constitute powerful tools in which concerns fracture characterization of bone under pure mode II loading and can be viewed as the main outcomes of this work.

Fracture characterization of bone under mode II loading using the end loaded split test

Fracture energy release rate under mode II loading of bovine cortical bone is determined using a miniaturized testing device of the end loaded split test. The energy release rate is evaluated by means of a data reduction scheme based on specimen compliance, beam theory and crack equivalent concept. Experimental tests were carried out to evaluate the Resistance curve which provides a successful method to characterize fracture behavior of quasi-brittle materials like bone. A numerical analysis including a cohesive damage model was used to validate the procedure. It was demonstrated that the end loaded split test and proposed data reduction scheme provide a valuable solution for mode II fracture characterization of bone.

Mixed-mode I+II fracture characterization of human cortical bone using the Single Leg Bending test

Mixed-mode I+II fracture characterization of human cortical bone was analyzed in this work. A miniaturized version of the Single Leg Bending test (SLB) was used owing to its simplicity. A power law criterion was verified to accurately describe the material fracture envelop under mixed-mode I+II loading. The crack tip opening displacements measured by digital image correlation were used in a direct method to determine the cohesive law mimicking fracture behavior of cortical bone. Cohesive zone modeling was used for the sake of validation. Several fracture quantities were compared with the experimental results and the good agreement observed proves the appropriateness of the proposed procedure for fracture characterization of human bone under mixed-mode I+II loading.

Bone fracture characterization under mixed-mode I+II loading using the single leg bending test.

Fracture under mixed-mode I+II was induced in bovine cortical bone tissue using a developed miniaturized version of the single leg bending test (SLB). Due to the difficulty in crack length monitoring in the course of the test, an equivalent crack method based on specimen compliance and beam theory was adopted as a data reduction scheme. The method was applied to the experimental results in order to obtain the Resistance curves in each loading mode. The determined fracture energy is well described by an energetic power law whose exponent is below one, which means that the linear energetic criterion is not applicable to this material. The proposed procedure was numerically validated by means of a cohesive mixed-mode I+II damage model with bilinear softening. It was concluded that the miniaturized version of the SLB test is adequate for mixed-mode I+II fracture characterization of bone for a constant mode ratio.

Fracture characterization of human cortical bone under mode II loading using the end-notched flexure test

Fracture characterization of human cortical bone under mode II loading was analyzed using a miniaturized version of the end-notched flexure test. A data reduction scheme based on crack equivalent concept was employed to overcome uncertainties on crack length monitoring during the test. The crack tip shear displacement was experimentally measured using digital image correlation technique to determine the cohesive law that mimics bone fracture behavior under mode II loading. The developed procedure was validated by finite element analysis using cohesive zone modeling considering a trapezoidal with bilinear softening relationship. Experimental load-displacement curves, resistance curves and crack tip shear displacement versus applied displacement were used to validate the numerical procedure. The excellent agreement observed between the numerical and experimental results reveals the appropriateness of the proposed test and procedure to characterize human cortical bone fracture under mode II loading. The proposed methodology can be viewed as a novel valuable tool to be used in parametric and methodical clinical studies regarding features (e.g., age, diseases, drugs) influencing bone shear fracture under mode II loading.

Identification of transverse elastic properties of the diaphysis of cortical bone

An inverse identification method is proposed to determine transverse elastic properties of cortical bone of diaphysis of long bones. Compression tests on tubular diaphysis disks are carried out. The approach couples the digital image correlation technique with the finite element updating method. An optimisation algorithm is used to minimize the numerical-experimental response for the elastic properties of the model. Diaphysis of tibia, femur and humerus is tested. In a first approximation, cortical bone tissue is considered transversely isotropic. A transverse elastic modulus of 8.2, 8.9 and 7.0 GPa is identified for tibia, femur and humerus tissue, respectively, with a typical scatter for biological materials. The response of the diaphysis disk to compression loading is however less sensitive to the Poisson’s ratio; hence, this parameter is more difficult to evaluate in practice for the proposed configuration. DOI: https://doi.org/10.24243/JMEB/2.5.172

Mode I fracture characterization of human bone using the DCB test

Purpose – Fracture characterization of human cortical bone under pure mode I loading was performed in this work. The purpose of this paper is to validate the proposed test and procedure concerning fracture characterization of human cortical bone under pure mode I loading. Design/methodology/approach – A miniaturized version of the double cantilever beam (DCB) test was used for the experimental tests. A data reduction scheme based on crack equivalent concept and Timoshenko beam theory is proposed to overcome difficulties inherent to crack length monitoring during the test. The application of the method propitiates an easy determination of the Resistance-curves (R-curves) that allow to define the fracture energy under mode I loading from the plateau region. The average value of fracture energy was subsequently used in a numerical analysis with element method involving cohesive zone modelling. Findings – The excellent agreement obtained reveals that the proposed test and associated methodology is quite effec...