Stress Singularity Analysis at an Interfacial Corner between Dissimilar Crystals and Evaluation of Mixed Modes Fracture Criteria Using Molecular Statics

Horiike, Koichi; Ikeda, Tôru; Matsumoto, Ryosuke; Miyazaki, Noriyuki

doi:10.2472/jsms.59.908

J. Soc. Mat. Sci., Japan

2010

DOI: 10.2472/jsms.59.908

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Stress Singularity Analysis at an Interfacial Corner between Dissimilar Crystals and Evaluation of Mixed Modes Fracture Criteria Using Molecular Statics

Koichi Horiike¹,

Tôru Ikeda²,

Ryosuke Matsumoto³

et al.

Abstract: The asymptotic solution of an interfacial corner between dissimilar crystals is expressed by the theory of anisotropic linear elasticity. However, it is not elucidated if the stress field obtained by the molecular analysis corresponds with the anisotropic linear elastic solution. We analyzed the stress fields around interfacial corners between dissimilar crystals using the molecular statics, and compared them with the asymptotic solutions. The stress intensity factor (SIF) is one of the basic fracture mechanic… Show more

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Cited by 3 publications

References 12 publications

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Singular Stress Fields in Anisotropic Bonded Joints Considering Interface Stress and Interface Elasticity

Koguchi

Suzuki

2014

Journal of Applied Mechanics

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Surface stress and surface elasticity are related to the organization of surface morphology, surface patterns, and surface atomic structures. As the size of the structure approaches the nanometer level, the surface-to-volume ratio increases. Generally the surface energy in deformable solids depends on the surface strain. The surface stress and elasticity influence the distribution of bulk stress near the surface. Interface stress and elasticity also exist at material interfaces and determine the interface properties. In the present study, the singular stress at a wedge corner in an anisotropic two-dimensional joint under tensile loading is analyzed using the molecular dynamic (MD) method and the anisotropic elasticity theory using a boundary condition with interface stress and interface elasticity. Not only the interface stress but also surface stress on the free surface are considered as a special case of an interface. The interface stress and interface elasticity are obtained through the MD analysis. In the case of a two-dimensional joint, the interface stress and elasticity depend on the distance from the wedge corner. In the analysis of anisotropic elasticity, the eigenequation used to determine the order of the stress singularity is newly derived using a boundary condition that considers the interface stress and interface elasticity. The order of the stress singularity varies with distance from the wedge corner. The stress distribution near the wedge corner can be expressed by the relation between the order of the stress singularity and the distance from the wedge corner.

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Singular Stress Fields in Anisotropic Bonded Joints Considering Interface Stress and Interface Elasticity

Koguchi

Suzuki

2014

Journal of Applied Mechanics

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Analysis of singular stress field in nanoscaled dissimilar material joints using the anisotropic elasticity theory considering interface properties

Koguchi

Tanaka

2017

Transactions of the JSME (In Japanese)

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In recent advanced semiconductor products, elements of thickness and width are frequently in nanoscale. As the size of elements reduces to nanometer, a ratio of surface to volume increases. Surface properties, such as surface stresses and surface elasticity, influence on the distributions of bulk stresses near the surface. In the present study, the singular stress at the corner in an anisotropic two-dimensional multi-wedge joint consisting of three kinds of material is analyzed using molecular statics (MS) method and the anisotropic elasticity theory with a boundary condition considering interface properties. The joints are composed of Ni, Au and Cu. Several joints with different wedge angles at the interface are analyzed. Distributions of atomic stress calculated by the MS method are compared with those by the theory. In the results of the MS analysis, stress jumps exist at the interface in the circumferential direction of the stress distribution around the stress singular point. It is supposed that these are attributed to the influence of interface stresses. Then, interface stresses and elastic properties at the interfaces are investigated using the MS method. The obtained interface properties are used in the stress analysis using the Stroh's formalism. Finally, the theoretical analysis considering the interface properties can be expressed the jumps of stress at the interfaces.

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Estimating the critical stress intensity factor for an interfacial corner equivalent to an interfacial crack using the molecular statics and cohesive zone model

Abumi

Ikeda

Koganemaru

2021

Transactions of the JSME (In Japanese)

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The stress intensity factors (SIFs) for an interfacial corner, which are compatible with that for a crack, can describe the singular stress field around the corner. However, due to the difference of the singular order with the angle of a corner and the combination of materials, we cannot compare the SIFs of interfacial corners to that with different singular orders. In this study, we estimated the fracture toughness (critical SIF) of jointed interfacial corners with different opening angles and different combinations of materials using the molecular statics method and cohesive zone model. The critical SIFs were normalized using those of interfacial cracks with the same combinations of materials. Regarding the relationships between the normalized critical SIF and the singular order for the numerical experiments using both the molecular statics method and cohesive zone model, the normalized SIF increased exponentially with decreasing singular order. The relationship between the singular order and the critical SIF obtained by the molecular statics or the cohesive model was almost unique regardless of the combination of materials and jointed angles. In other words, it is possible to translate the critical SIFs of a jointed interfacial corner to that of interfacial crack. However, the slopes of the relationship obtained by the molecular statics and the cohesive zone model did not correspond. This might be because only the molecular statics method considers the influence of crystal structure factors such as slip and dislocation. The interactions between atoms of the molecular statics and cohesive zone model along the interfaces are different. The relationship between the singular order and the critical SIF of actual jointed interfacial corner must be investigated experimentally in further research.

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Stress Singularity Analysis at an Interfacial Corner between Dissimilar Crystals and Evaluation of Mixed Modes Fracture Criteria Using Molecular Statics

Cited by 3 publications

References 12 publications

Singular Stress Fields in Anisotropic Bonded Joints Considering Interface Stress and Interface Elasticity

Singular Stress Fields in Anisotropic Bonded Joints Considering Interface Stress and Interface Elasticity

Analysis of singular stress field in nanoscaled dissimilar material joints using the anisotropic elasticity theory considering interface properties

Estimating the critical stress intensity factor for an interfacial corner equivalent to an interfacial crack using the molecular statics and cohesive zone model

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