Experimental evaluation of cohesive laws components of mixed-mode I + II fracture characterization of cortical bone

Mixed-mode I + II fracture characterization of cortical bone tissue is addressed in this work. The mixed-mode bending test was used to impose different mode ratios. An equivalent crack length data reduction method was considered to obtain the strain energy release rate components. Crack opening and shear displacements were measured by means of digital image correlation. These quantities were then integrated to propose a direct evaluation of cohesive laws. The components of the cohesive laws for each mixed-mode loading were obtained by the uncoupled and Hogberg ¨ ’s methods. The later provided consistent evolution of strain energy release rate and peak stresses components in function of mode-ratio, revealing its appropriateness regarding the fracture characterization of cortical bone under mixed-mode I + II loading.The first and second author acknowledges the Portuguese Foundation for Science and Technology, under the project UIDB/04033/2020. The third and fifth authors acknowledge the ‘Laboratorio' Associado de Energia, Transportes e Aeronautica’ (LAETA) for the financial support by the project UID/EMS/50022/2019 and the financing of FCT/MCTES through national funds (PIDDAC) and UIDB/00667/2020 (UNIDEMI). The fourth author acknowledges the Portuguese Foundation for Science and Technology, under the project PTDC/EME-SIS/28225/2017

Fracture Characterisation of bonded joints between cortical bone tissue and bone cement

The process of evolution has led to the creation of fantastic materials. Bone is one of these materials and has a complex, anisotropic, hierarchical and heterogeneous microstructure, characterised by an excellent mechanical performance. However, as it is an almost fragile material, it often ends up fracturing. These fractures decrease the patient's quality of life and entail high costs for the health system. In order to deal with these fractures, the BoFraPla project arose, which aims to develop a fibrous system for fixing bone fractures. Therefore, in the scope of the activities of this project, the present dissertation emerges, proposing to mechanically characterise the bond between the bone and bone cement. From a thorough literature review, it was found that although the bone cement has been used for more than fifty years, there are few references to its mechanical characterisation and none were found that have made a clear characterisation of the fracture process between the bone and the cement. Hence, in this report, a pure mode I characterisation (tension) through a Double Cantilever Beam (DCB) test and another pure mode II characterisation (shear) through an End-Notched Flexure (ENF) test are presented. In order to overcome the difficulties in monitoring the crack length during the laboratory tests, a method based on the equivalent crack length was used. With this method, the resistance curve was drawn for each specimen and, in most of them, the existence of thresholds was remarkable, which allowed a correct measurement of the fracture energy for each test. In order to validate the results obtained, numerical simulations were performed with cohesive models. Through the results, it was possible to determine that the chosen tests, the defined dimensions and the adopted procedure, can be used to characterise the fracture of these two materials in the studied loading modes.O processo de evolução natural levou à existência de materiais fantásticos. O osso é um destes materiais e apresenta uma microestrutura complexa, anisotrópica, hierárquica e heterogénea, caracterizada por um excelente desempenho mecânico. Contudo, como se trata de um material quase frágil, inúmeras vezes acaba por fraturar. Estas fraturas diminuem a qualidade de vida do paciente e acarretam elevados custos para o sistema de saúde. Com vista ao tratamento destas fraturas, surgiu o projeto BoFraPla, que se propõe a desenvolver um sistema fibroso de fixação de fraturas ósseas. Assim, no âmbito das atividades deste projeto, surge a presente dissertação que se propõe a caracterizar mecanicamente a ligação entre o osso e um cimento ósseo. A partir de uma profunda revisão bibliográfica apurou-se que, apesar do cimento ósseo ser utilizado há mais de cinquenta anos, existem poucas referências à sua caracterização mecânica, não sendo encontrada nenhuma que fizesse uma clara caracterização do processo de fratura entre o osso e o cimento. Assim, neste relatório é apresentada uma caracterização em puro modo I (tensão), através de um ensaio Double Cantilever Beam (DCB) e outra caracterização em puro modo II (cisalhamento), através de um ensaio End-Notched Flexure (ENF). Para colmatar as dificuldades de monitorização do comprimento de fenda durante os ensaios laboratoriais, recorreu-se a um método baseado no comprimento de fenda equivalente. Com este método foi traçada a curva de resistência para cada provete, sendo notória a existência de patamares na sua maioria, o que permite uma correta medição da energia de fratura para cada ensaio. Com vista a validar os resultados obtidos, foram realizadas simulações numéricas com modelos coesivos. Através dos resultados, foi possível apurar que os ensaios escolhidos, as dimensões definidas e o procedimento adotado, podem ser utilizados para caracterizar à fratura entre estes dois materiais nos modos de carregamento estudados

On the evaluation of strain energy release rate of cement-bone bonded joints under mode II loading

Bone cements based on poly(methylmethacrylate) (PMMA) are primarily used in joint replacement surgeries. In the fixation of joint replacement, the self-curing cement fills constitutes a very important interface. To understand and improve the interaction between cortical bone and bone cement it is essential to characterize the mechanical properties of cement-bone bonded joints in full detail. In this study, the end-notched flexure test was used in the context of pure mode II fracture characterisation of cement-bone bonded joints. A data reduction scheme based on crack equivalent concept was employed to overcome the difficulties inherent to crack length monitoring during damage propagation. A finite element method combined with a cohesive zone model was first used to validate numerically the adopted method. The procedure was subsequently applied to experimental results to determine the fracture toughness of cement-bone bonded joints under pure mode II loading. The consistency of the obtained results leads to the conclusion that the adopted procedure is adequate to carry out fracture characterisation of these joints under pure mode II loading. The innovative aspect of the present work lies in the application of cohesive zone modelling approach to PMMA-based cement-bone bonded joints

Mixed-mode I+II fracture characterization of bovine bone tissue using the SLB test

Fracture of bone in vivo generally occurs as a result of multiaxial loaded conditions, which leads tocomplex mixed-mode stress-states involving the combination of tension, compression and shear. As a resultof this the characterization of the mixed-mode crack propagation assumes a high level of importance.In this work we analysed the adequacy of a miniaturized version of the single leg bending test (SLB) tocharacterize the mixed-mode I+II fracture behaviour of young bovine bone tissue. Hence, a new datareduction scheme based on specimen compliance and crack equivalent concept was used to overcome thedifficulties inherent to crack monitoring during its growth. The method was applied to the experimentalresults in order to obtain the Resistance-curves in each mode. It was concluded that the developed versionof SLB test is adequate for mixed-mode fracture characterization of bone, since it permits to obtain acomplete Resistance-curve though revealing an almost constant mode ratio

Experimental fracture resistance study for cracked bovine femur bone samples

Crack growth and brittle fracture is one of the major failure modes in bone materials and therefore understanding the fracture behavior and affecting parameters on the crack growth resistance of bone is necessary for biomechanics researchers. In this paper, mode I fracture toughness value for the left and right femur bones of same bovine were measured experimentally using several single edge notch bend beam specimens (SENB) subjected to three-point bend loading in dry condition. The SENB specimens were cut along the longitudinal axis of bone but from different hoop directions. Fracture toughness results of sample prepared from the frontal part of bone were higher than the back or side sections. Depending on the location of sample, the fracture toughness of femur bone was varied from 5 to 10 MPa . Furthermore, the results obtained for similar location of both left and right femur bones were nearly identical. The fracture energy (Gf) of the tested specimens was also measured and it was found that a linear relation can be fitted to the (KIc)2 versus Gf results of the tested bovine bone

Mode II Fracture of Cortical Bone Tissue

In this work a numerical study has been performed to verify the adequacy of the End Notched Flexure (ENF) test todetermine the fracture toughness under mode II loading of cortical bovine bone tissue. In this work a detailed numericalanalysis using the finite element method and a cohesive damage model was performed in order to optimize thespecimen geometry when applied to bone fracture characterization under mode II loading. A data reduction schemebased on specimen compliance and crack equivalent concept was used to overcome the difficulties inherent to crackmonitoring during its growth. It was verified that a judicious selection of the geometry allows a rigorous estimation oftoughness in mode II

Mode II Characterization of Cortical Bone Tissue using the ELS Test

A miniaturized testing device of the end load split (ELS) test was conceived to evaluate fracture energy release rateunder pure mode II loading of young bovine cortical bone tissue. Since crack length is not possible to monitor duringpropagation, classical methods cannot be applied to determine fracture energy in this material. Hence, an equivalentcrack technique, which does not necessitate the crack length surveillance, was used to assess the equivalent crackextent. The applied data reduction scheme is based on the specimen compliance, beam theory and crack equivalentconcept, providing the assessment of the energy release rate. The method was dully validated through a numericalanalysis, by means cohesive zone modeling