N. Dourado

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.

Estimate of resistance-curve in wood through the double cantilever beam test

Abstract Numerical and experimental studies involving the double cantilever beam test to estimate the resistance-curve under mode I loading in wood (Pinus pinaster Ait. – RL fracture system) are presented. Two data reduction schemes based on the specimen compliance and crack equivalent concept are proposed to obtain accurate values of fracture energy. The methods do not require crack length monitoring and mitigate the influence of scatter of wood elastic properties on the measured fracture energy. A finite element analysis to validate the proposed methodologies was performed. Good agreement was achieved in both cases, especially for one case. Experimental tests were also carried out to determine the fracture energy of this wood species. Application of both data reduction schemes provided consistent values.

Determination of cohesive laws in wood bonded joints under mode I loading using the DCB test

Abstract The cohesive laws (CLs) have been investigated by means of direct and inverse methods concerning wood bonded joints under pure mode I. The experimental results were obtained by tests with double cantilever beam. The direct method is based on the differentiation of the relation between strain energy release rate and crack opening displacement at the crack tip. An equivalent crack method was used to evaluate the strain energy release rate in the course of the test without monitoring the crack length, which is difficult to observe exactly. The crack opening displacement was determined by postprocessing local displacements measured by digital image correlation. The inverse method requires a previous assumption of the CL shape, and as such, a trilinear law with bilinear softening relationship was selected. The cohesive parameters were identified by an optimization procedure involving a developed genetic algorithm. The idea is to minimize an objective function that quantifies the difference between the experimental and the numerical load-displacement curves resulting from the application of a given law. A validation procedure was performed based on a numerical analysis with finite elements. Both methods in focus provided good agreement with the experimental data. It was observed that CLs adopted by the inverse method are consistent with the ones obtained with the direct method.

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 I Loading

A miniaturized version of the double cantilever beam (DCB) test is used to determine the fracture energy in human cortical bone under pure mode I loading. An equivalent crack length based data-reduction scheme is used with remarkable advantages relative to classical methods. Digital image correlation (DIC) technique is employed to determine crack opening displacement at the crack tip being correlated with the evolution of fracture energy. A method is presented to obtain the cohesive law (trapezoidal bilinear softening) mimicking the mechanical behavior observed in bone. Cohesive zone modeling (CZM) (finite-element method) was performed to validate the procedure showing excellent agreement.

Wood fracture characterization under mode I loading using the three-point-bending test. Experimental investigation of Picea abies L.

Mode I fracture characterization was performed in wood using the single-edge-notched beam loaded in three-point-bending (SEN-TPB). A data reduction scheme based on equivalent linear elastic fracture mechanics concept was used to evaluate the Resistance-curve instead of classical methods. The method is founded on assessment of an equivalent crack from specimen compliance using beam theory and the existence of a stress relief region in the crack vicinity. Crack length monitoring is unnecessary during the loading process, providing a complete Resistance-curve which is essential for a clear identification of the fracture energy. Experimental results were obtained from fracture tests involving geometrically similar SEN-TPB specimens of different sizes. It was observed that the smallest tested specimen is inadequate to estimate the fracture energy due to fracture process zone confinement. Contrarily, the other two are suitable for such purpose. An inverse method was used to determine a bilinear cohesive law representative of wood material fracture. It was concluded that a unique cohesive law is able to mimic the fracture behaviour of considered specimen sizes.

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...