A Study on the Fracture Behavior of Inhomogeneous Biological Materials and Interfaces

Alternative Title
Dhaneshwar Mishra
Mishra, Dhaneshwar
Alternative Author(s)
Dhaneshwar Mishra
Seung-Hyun Yoo
일반대학원 기계공학과
The Graduate School, Ajou University
Publication Year
Fracture study
Alternative Abstract
Material inhomogeneity is common in every walk of life. Whether the materials are manmade or natural/biological; they are inherently inhomogeneous. Present days’ trend of material development focuses on composites which are made up of various layers and have inherent inhomogeneity with many interfaces. Interfaces and inhomogeneity are the most susceptible to failure. In another side, biological materials are inherently inhomogeneous and have interfaces but designed in such a way that the load transfer takes place so nicely such that mostly cracks are arrested at interfacial layers. Most common example of this case is dentine enamel junction (DEJ), which is an interfacial layer that connects very brittle enamel and relatively tougher dentine of tooth. This interfacial layer arrests/bridges the cracks which grows from enamel towards dentine. Knowing this aspect of materials in use for various applications, it is worthwhile to study fracture behavior of inhomogeneous materials especially the biological materials and interfaces so that future material development can be mimicked from the understanding of design of materials and interfaces in nature. This thesis has two goals, first goal is to study inhomogeneous materials for its fracture behavior by developing closed form solution and the second aim is to understand this aspect in the biological materials and interfaces. To achieve these goals, a coated circular inclusion embedded in an infinite matrix has been analyzed in the framework of two-dimensional isotropic linear elasticity. A closed-form solution has been obtained for the case of far-field uniaxial tension using Muskelishvili’s complex potential method. The solutions for the stress and strain distributions for all three regions, i.e., matrix, coating, and inclusion, have been obtained for various coating-to-matrix shear modulus ratios, while keeping the fiber and matrix shear moduli the same. Test cases for inclusion without the coating and hollow inclusion have also been studied. The energy release rate has been evaluated using the path-independent M-integral, which is used to calculate the energy release rate for the self-similar expansion of defects surrounded by the closed contour of the integral. The results for the stress and strain concentrations along with the energy release rate due to this material inhomogeneity were analyzed to yield a better understanding of the mechanics of materials with inhomogeneity. The analytical results obtained in closed form has been realized for fracture behavior study for biological material human tooth layers, namely enamel and dentine and the interfacial layer dentine enamel junction (DEJ) by finite element tool ABAQUS considering their various microconstituent, orientations of cracks and crack bridging capability of the interfacial layer DEJ. The crack growth has been simulated for various crack geometry for enamel and DEJ by extended finite element analysis (XFEA) considering their functionally graded structure. Fracture toughness of these layers has been evaluated in terms of J-integral which is measure of energy release rate. The critical value of energy release rate can be characterized as fracture toughness. In case of enamel and DEJ, this has been found to be location dependent in place of constant material property as in homogeneous elastic materials. The crack arresting/bridging behavior of DEJ has been simulated by introducing one-D spring elements. The stiffness of these spring elements found to be 1% of the Young’s modulus of DEJ at that location which can achieve crack closure within a distance of 10-15μ from the enamel surface. Dentine is the inner layer of tooth which is mineralized tissue made up of dentinal tubules and collagen. These dentinal tubules have been used for fluid circulation that ultimately makes it tougher. Permeability and porosity are important parameters to contribute for failure of dentine because of internal fluid circulation in the dentinal tubules. The fluid circulation i.e. rate of permeation increases with increase in pore size that makes the dentine like bio-composite hydrated and provide resistance to fracture. Thus it is important to understand fracture toughening behavior of dentine like bio-composite in terms of porosity and permeability change. The first study on dentine has been focused on evaluating fracture toughness for different values of porosity and permeability by finite element analysis tool ABAQUS for continuum model of dentine and its unit cell model to understand the heirachical aspect of biological materials. It has been observed that the fracture toughness increases with increase in porosity when simulation is carried out at continuum level with isotropic and elastic material properties. At the cell level, this is not true as we found that up to 10% of porosity, the J-Integral and strain energy density increases and thereafter it decreases. This explains role of the bonding of dentinal tubules at continuum level on fracture strength of dentine composite. In second analysis, dentine composite is modeled at unit cell level considering its constituents peri-tubular and inter-tubular dentine. The micro-constituents of both peri-tubular and inter-tubular dentines, the collagen fibers and apatite minerals have been considered while modeling the unit cell model of dentine composite. The fracture toughness has been evaluated with various fraction of collagen fraction in both peri-tubular and inter-tubular dentine. It is found that fracture toughness of dentine composite increases with increase in collagen fraction. This is in agreement with the result for elastic modulus which decreases with increase in collagen fraction as presented in literatures. It can be described as decrease in elastic modulus resulted to decrease in brittleness which refers to increase in toughness. Collagen has very important role in shaping up mechanical properties and toughening of biomaterials like bone, dentine composite and so on. This study helps to understand fracture behavior of inhomogeneous materials especially the biological materials which is characterized as inherent inhomogeneous and hierarchical materials and can help to understand how these materials becomes tougher and stiffer even though made up of softer and brittle micro constituents like protein and minerals. This work can also be helpful to understand the biological interfaces in terms of its fracture behavior and crack arresting/bridging nature such that future material design and development can be benefited with the better understanding of these natural interfaces. Dhaneshwar Mishra

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Graduate School of Ajou University > Department of Mechanical Engineering > 3. Theses(Master)
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