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Hydrostatic stress

About: Hydrostatic stress is a research topic. Over the lifetime, 1568 publications have been published within this topic receiving 37773 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a planar electron backscattered diffraction analysis showed that the void was initiated at the triple junction of the grain boundaries, not at the junction of twin boundary and grain boundary.
Abstract: In a crystallographic study of stress induced voiding of copper interconnect, the planar electron backscattered diffraction analysis showed that the void was initiated at the triple junction of the grain boundaries, not at the junction of the twin boundary and grain boundary. By using stepwise cross-sectional crystalline investigation for the void, it was possible to rebuild 3D crystalline structure near the void. From the stress calculation based on the measured crystalline structures, the hydrostatic stress was highly concentrated at the triple junction of the twin boundary and grain boundary, but experimentally, there was no voiding at that. The voiding in the copper interconnect may depend mainly on the boundary instability.
03 May 2013
TL;DR: In this article, the authors investigated the characteristic of stress singularity fields at a vertex on an interface in two-and three-dimensional bonded joints and showed that the stress distribution in the region near the vertex can be expressed as a function of distance from a stress singular point.
Abstract: The authors have been investigated the characteristic of stress singularity fields at a vertex on an interface in two- and three-dimensional bonded joints [1,2,3]. It is well known that stress distribution in stress singularity fields can be expressed as a function of distance from a stress singular point. In two-dimensional joints, an angular variation for the stress distribution in a polar coordinate system with an origin at the stress singular point can be expressed analytically based on the theory of elasticity [4,5,6,7]. On the contrary, in three-dimensional joints[8], an angular variation of stress distribution in a spherical coordinate system cannot be clearly expressed until now. For instance, stress singularity line which is a cross line with an interface and a side free surface will affect on the stress distribution near the vertex. Generally, stress distribution in the stress singularity region can be expressed as follows.
Dissertation
01 Jan 2018
TL;DR: In this paper, numerical simulations and experimental investigations related to the growth and formation of tin whiskers on tin-coated copper substrates were performed using 3D x-ray diffraction.
Abstract: Tin whiskers are hair-like single crystals that spontaneously grow from tin-coated surfaces. Whiskers are commonly found in electronic components, where tin coatings are used in, e.g., soldering applications, and to protect components from corrosion. Whiskers are known to cause short-circuits leading to failure of electronic components. The exact mechanisms responsible for whisker formation and growth are not fully understood. It is, however, believed that whiskers grow as a way to relax stress in the tin coating and that compressive stress gradients drive the growth. The stress in the coating is mainly caused by the formation and growth of the intermetallic compound Cu6Sn5 in the interface region between the copper substrate and the tin layer.This thesis presents numerical simulations and experimental investigations related to the growth and formation of tin whiskers on tin coated copper substrates. The aim of the experimental work has been to verify the existence of a compressive stress gradient and to characterise the microstructure around tin whiskers in 2D as well as 3D. This was realised using different x-ray diffraction methods, namely scanning Laue microdiffraction, differential aperture x-ray microscopy (DAXM), and scanning 3D x-ray diffraction (3DXRD). Laue microdiffraction was used to study the evolution of the microstructure around two whiskers over a period ranging from 4 to 21 months of ageing. The hydrostatic stress field in the tin coating was estimated by assuming plane stress conditions. It was found that the stress field was highly inhomogeneous.It was possible to identify ridges of high compressive stress leading to the whisker. These ridges, which have not been observed previously, are potentially driving diffusion of tin from specific regions of the coating towards the root of the whisker.DAXM and 3DXRD were used to study the microstructure around a whisker in three dimensions. Using DAXM, through-depth variations of the deviatoric strain field were measured for the first time. Deep in the coating, where the \ce{Cu6Sn5} is present, the deviatoric strain was high. This indicates that the growth of the intermetallic phase causes plastic deformation of the tin coating. A novel scanning 3DXRD tomography technique was used to map out intragranular variations in the unit cell parameters and the grain orientations with sub-micrometre resolution. A short (4 micrometre) radial gradient in hydrostatic stress was observed around the root of the whisker.This gradient together with long-range diffusion from specific regions could provide the driving force for whisker growth.From the 3DXRD data, it was also possible to determine the location of Cu6Sn5 in the sample. A large grain of Cu6Sn5 was found right below the whisker which seems to have caused distortion of the nearby tin grains. We also studied the evolution of the microstructure during heat treatment. The heat treatment encouraged the formation of the intermetallic phase and also led to coarsening of the tin grains.The numerical simulations in this thesis are based on a multiphase field model. This model is one of few phase field models existing that includes diffusion as well as elastic and plastic deformation. The model was used to study the growth of Cu6Sn5 during room temperature ageing, specifically the effect of the curvature of the intermetallic layer on the stress and plastic deformation of the tin coating was investigated. It was found that a high curvature led to localisation of plastic deformation in the region above the highly curved grain. (Less)
Book ChapterDOI
01 Jan 2015
TL;DR: In this article, a criterion to predict crack initiation in unidirectional laminae subjected to multiaxial cyclic loading is proposed based on experimental observations concerning the damage mechanisms occurring at the microscopic scale, of which the evolution leads to the initiation of a macro crack.
Abstract: In this chapter, a criterion to predict crack initiation in unidirectional laminae subjected to multiaxial cyclic loading is proposed. The criterion is based on experimental observations concerning the damage mechanisms occurring at the microscopic scale, of which the evolution leads to the initiation of a macro-crack. In particular, two stress parameters have been identified as representative of the driving forces for the damage evolution at the microscale. These parameters, that is the local maximum principal stress and the local hydrostatic stress in the matrix, are expressed in terms of local stresses in the matrix, calculated by means of finite element analyses of a fiber/matrix unit cell subjected to periodic boundary conditions. Applications of the proposed criterion to fatigue results from the literature show that only two scatter bands can be successfully used to predict the cycles spent for crack initiation in unidirectional laminae under multiaxial loading.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202246
202134
202047
201948
201839