Determination of thermal stress distribution in a model microelectronic device encapsulated with alumina filled epoxy resin using fluorescence spectroscopy

A method for measuring residual and applied stresses in particulate polymer systems, which utilizes the piezo-spectroscopic effect of the optical fluorescence of filled particles, is presented. Fluorescence piezo-spectroscopy (PS) is non-destructive and provides microscopic lateral resolution upon using an optical microprobe system. Epoxy resin filled with α-alumina particles is used in this study. Stress values are obtained by frequency shift measurement of the characteristic optical fluorescence lines produced by Cr³⁺ impurities in alumina. The relationships between peak frequency shift of these lines and stress are derived by using a 4-point-bending test. The peak frequency shift shows linear correlation with tensile stress, while a non-linear relation between peak frequency shift and stresses is found in the compressive stress region. To a first order approximation, residual stresses were calculated by the frequency shift divided by the linear correlation coefficient in the tensile stress region. As an application of the PS method, we determined micron order residual stress distributions in a model plastic encapsulated silicon substrate for microelectronic devices and compared the stress data with those calculated using a two-dimensional finite element analysis of the device. The experimental results were in good agreement with the tensile stress components that have been obtained by theoretical calculation. Therefore, PS techniques can be used to measure residual stresses in polymer compounds utilizing the information obtained from the fluorescence lines of a dispersed ceramic powder.     

Measured orientation and internal stress distributions in melt-spun fibers

In this investigation, experimentally measured radial birefringence profiles are compared to internal stress distributions as predicted by a mathematical model. A direct indicator of the degree of molecular orientation, fiber birefringence, is found to correlate well with the stress distributions as calculated from radial temperature variations. In an initial study of glass fibers, no radial birefringence profiles are found, indicating that any residual stresses present are small. In polystyrene fibers, however, large radial variations in birefringence are observed and are shown to be directly related to the calculated internal stresses.     

Edge Stresses in Alumina/Zirconia Laminates

Using the technique of fluorescence piezospectroscopy, we determine the distribution of thermal residual stresses across the edges of three laminated alumina/zirconia composites. We develop a methodology for separating the measured stress state into microstresses that result from grain-to-grain thermal mismatch and macrostresses that result from lamination-induced thermal mismatch between individual plies. Comparison between the measured edge-stress distributions and those calculated based on a simple force-superposition model shows good agreement, indicating that the laminate system is well approximated as linear elastic. Given the experimental confirmation of significant edge stresses in multi-ply laminates, the possibility of failure initiating at composite edges must be considered in the design of surface-compressed laminate structures with the aim of mediating the detrimental effect of surface flaws.     

Coupled Thermomechanical Multiscale Modeling of Alumina Ceramics to Predict Thermally Induced Fractures Under Laser Heating

This study is concerned with thermally induced fractures and failure of high weight percentage alumina ceramics. A 3D coupled thermomechanical multiscale model has been developed to simulate thermally induced fractures. In laser heating of alumina ceramics, the temperature and stress distributions have been predominantly correlated with the interfacial glass phase within alumina microstructure. A coupled thermomechanical analysis with traction–separation law has been implemented in the finite element framework as a cohesive zone model (CZM). The alumina grains are modeled as thermomechanical continuum elements separated by CZM. A thermal and mechanical analysis has been conducted using Molecular Dynamics methods to obtain the thermal conductivities and parameterize traction–separation laws for the interface of alumina ceramics at different temperatures. The coupled thermal‐mechanical analysis achieved through a finite element model in Abaqus is compared with experimental results in laser‐heating tests. The model is successful in predicting temperature distributions and thermal fractures, which could help assist in selecting proper conditions in alumina applications and fabrication processes.     

Micromechanical Stresses in SiC-Reinforced Al2O3 Composites

Applying an Eshelby approach, the internal micromechanical stresses within an SiC-inclusion-reinforced (platelet to whisker geometries) polycrystalline alumina matrix composite were calculated. The results are compared to the experimental residual stress measurements of a SiC-whisker-reinforced Al₂O₃ by Predecki, Abuhasan, and Barrett and found to be in excellent agreement. The calculations are then extended to SiC-reinforced composites with polycrystalline mullite, silicon nitride, and cordierite matrices. It is concluded that the internal stresses are significantly influenced by the inclusion geometry as well as the thermoelastic differences between the inclusion and the matrix and also the volume fraction.     

Phenomenological Theory of High Permittivity in Fine-Grained Barium Titanate

The anomalously high permittivity in fine-grained ceramic barium titanate is explained by the absence of 90° twinning within the grains, giving rise to internal stresses as the ceramic cools below the Curie temperature. Using the Devonshire phenomenological thermodynamic method and a simplified model, the stresses involved are calculated. At these stress levels, the reduced strain calculated on this model agrees well with X-ray data for the fine-grained material. The limitations and possible developments of the proposed model are discussed.     

Slip and Twinning in Polycrystalline Alumina (α-Al2O3) Deformed under Hydrostatic Pressure between 600° and 1000°C

The microstructure of polycrystalline alumina deformed under hydrostatic pressure and at low temperature is investigated by transmission electron microscopy. Deformation occurs mainly by prism plane slip and rhombohedral twinning. Introduction of hydrogen leads to a significant decrease in the yield stress. In large grain size alumina deformed with hydrogen, accommodation of twinning involves dislocation reactions in the twin boundary and in the grains rather than by cracking. Prism plane dislocations decompose into basal dislocations by cross slip probably due to a decrease of Peierls stress for basal slip in the presence of hydrogen.     

Residual-Stress-Induced Grain Pullout in a 96% Alumina

A comparison of the surface and bulk microstructures of two 96% aluminas indicates that the residual stresses arising from thermal expansion mismatch created by crystallization of the amorphous boundary phase, when combined with stresses created during grinding, can lead to excessive pullout of the alumina grains. However, neither source of residual stress is, by itself, sufficient to cause such pullout. Residual stresses resulting from crystallization of the boundary glass are expected to play a significant role in determining the abrasive wear resistance of these materials.     

Residual Stresses in Machined MgO Crystals

The residual stresses introduced in MgO crystals by grinding on {100} surfaces in 〈100〉 directions were measured using photoelastic techniques. Grinding was conducted with two wheels; a 100-grit diamond wheel removed material by brittle fracture, and a 46-grit alumina wheel caused plastic flow and burnishing. Both wheels introduced a discrete, highly deformed layer adjacent the machined surface. In all cases the machined surfaces were under a residual tensile stress which became compressive within the deformed region. Beneath the deformed layer the residual stress patterns were distinctly different. In crystals ground with the alumina wheel the stresses became tensile again within 0.5 mm of the ground surface, whereas the subsurface stresses in crystals ground with the diamond wheel remained compressive to distances ≥1 mm. These residual stress distributions are discussed in terms of a simple model based on the superposition of mechanically and thermally induced stresses.     

矩形截面容器实验研究与应力分析

矩形容器作为非回转型容器,其应力分布较回转型容器复杂,对一实际矩形容器进行应力测试实验,得到该容器不同部位的应力值,并通过国标给出的强度条件进行强度校核,同时将结果与新颁布的GB 150-2011中规定的矩形截面容器的应力计算公式的计算结果进行对比分析,为容器的优化设计提供指导.     

Simulation of crack propagation in Alumina particle-dispersed SiC composites

Addition of alumina particles to silicon carbide results in strongly improved toughness values. In order to come to a better understanding of this phenomenon, crack propagation is simulated for a 20 vol% alumina particles-dispersed silicon carbide composite material using the Body Force Method. Special emphasis is paid to the influence of graded compositions. Numerically obtained crack paths are compared to crack paths generated experimentally by Vickers indentations. Moreover, mechanical properties of the investigated material were measured experimentally. Microstructural toughness variations as well as the direction of crack propagation are found to be strongly influenced by residual stresses due to the mismatch between thermal expansion coefficients of alumina and silicon carbide and by the actual crack location. According to tensile residual stresses in the radial direction cracks approaching a particle are deviated circumferentially in the matrix around the particle. Moreover, the failure behavior of cracks propagating into a zone of increasing or decreasing volume fraction of alumina particles is found to behave differently as residual stress fields superimpose in the case of particle clustering. ©.     

Influence of Surface Residual Stress State on Crack Path Evolution in Polycrystalline Alumina

The residual stress distribution in polycrystalline alumina is estimated by an object-oriented finite element method. By combining the microstructural image, individual grain orientation, and the crystal elastic properties, the residual stress distribution under a plane stress assumption is obtained by an analysis cooling of the sample through 1000°C. Furthermore, the residual stresses associated with grain boundary areas are investigated and discussed in the context of the concomitant influence on the observed crack path.     

Micro- and macroscopic thermal expansion of stabilized aluminum titanate

The lattice expansion of aluminum titanate (AT) obtained by firing a mixture of alumina, rutile, strontium and calcium carbonate and silica was measured using neutron and laboratory X-ray diffraction. The microscopic data are compared with macroscopic measurement completed by dilatometry.A powder and a compact rod sample were compared to assess the influence of micro residual stresses locked into the solid structure at grain level, which could possibly be relieved upon grinding.Results show good correlation between neutron and X-ray diffraction techniques. They also show that a compact material behaves differently than a powder, contrary to what happens for other porous ceramics such as cordierite. The integrity factor model was used to rationalize the results and predict grain level stresses in all crystal directions and all phases (AT, Strontium aluminum silicate, alumina and residual glass). Calculation show that the AT c-axis is always under compression while all other crystal directions and phases are under tension. Those micro-stresses do not undermine the macroscopic mechanical properties of the material and confer to it its interesting properties like low thermal expansion and enhanced strain tolerance.     

Dependencies of microstructure and stress on the thickness of GdBa2Cu3O7 ? δ thin films fabricated by RF sputtering

GdBa₂Cu₃O_{7 − δ} (GdBCO) films with different thicknesses from 200 to 2,100 nm are deposited on CeO₂/yttria-stabilized zirconia (YSZ)/CeO₂-buffered Ni-W substrates by radio-frequency magnetron sputtering. Both the X-ray diffraction and scanning electron microscopy analyses reveal that the a-axis grains appear at the upper layers of the films when the thickness reaches to 1,030 nm. The X-ray photoelectron spectroscopy measurement implies that the oxygen content is insufficient in upper layers beyond 1,030 nm for a thicker film. The Williamson-Hall method is used to observe the variation of film stress with increasing thickness of our films. It is found that the highest residual stresses exist in the thinnest film, while the lowest residual stresses exist in the 1,030-nm-thick film. With further increasing film thickness, the film residual stresses increase again. However, the critical current (I_c) of the GdBCO film first shows a nearly linear increase and then shows a more slowly enhancing to a final stagnation as film thickness increases from 200 to 1,030 nm and then to 2,100 nm. It is concluded that the roughness and stress are not the main reasons which cause the slow or no increase in I_c. Also, the thickness dependency of GdBa₂Cu₃O_{7 − δ} films on the I_c is attributed to three main factors: a-axis grains, gaps between a-axis grains, and oxygen deficiency for the upper layers of a thick film.     

Cavitation wear of structural oxide ceramics and selected composite materials

The usage of ceramic materials in the applications endangered by intensive cavitation could limit erosion phenomena. In the presented work, cavitation erosion resistance of commonly used (in structural application), oxide phases (α-alumina, tetragonal zirconia) were investigated. Additionally, the behaviour under cavitation conditions of two composite materials, based on alumina and zirconia matrices, was tested.Significant difference in cavitation wear mechanisms for alumina and tetragonal zirconia materials was observed. Alumina was degraded by removing the whole grains from the large surface subjected to cavitation. Degradation of zirconia proceeded locally, along ribbon-like paths of removed grains. Cavitation wear of composites was strongly dependent on the residual stress state in the material. Alumina/zirconia composite with compressive stresses in the matrix showed a significant improvement of cavitation resistance. The zirconia/tungsten carbide composite with relatively high level of tensile stresses in the matrix was the worst of all investigated materials.     

Facet–Defacet Transition of Grain Boundaries in Alumina

Grain boundaries in pure alumina powder compacts sintered at 1400°C are smoothly curved, indicating that they have atomically rough structures. When these specimens are heat-treated at temperatures between 900° and 1100°C, a small fraction of the grain boundaries develop either hill-and-valley or kinked shapes with flat segments. Some of these flat boundary segments lie on the {011[Twomacr]} plane of one of the grain pairs. These grain boundaries thus appear to become singular at these temperatures. When a corundum crystal with a basal surface is sintered in alumina powder at 1400°C, all grain boundaries formed between the corundum basal surface and small grains, as well as those between the small grains, are smoothly curved, indicating their rough structure. When heat-treated at 900°C for 3 days, about 30% of the grain boundaries between the corundum basal surface and the small grains develop kinks with flat boundary segments, and some of these flat segments lie on the basal plane of the corundum. When heat-treated again at 1400°C, all grain boundaries are curved, indicating that they become reversibly rough. These observations show that at least some of the grain boundaries in alumina undergo roughening-singular transitions at temperatures between 900° and 1100°C.     

Improved Fracture Behavior of Alumina Microstructural Composites with Highly Textured Compressive Layers

Alumina‐based microstructural composites combining equiaxed and textured layers were fabricated to examine how cracks propagate and the mechanical properties are affected as a function of the residual stress and volume fraction of texture in a multilayer structure. By combining equiaxed and highly textured alumina layers of varying thermal expansion, the embedded textured layers were placed under compressive residual stresses as high as ?670 MPa. Composites with a near constant maximum failure stress of up to 300 MPa were shown to be almost independent of the initial defect size as result of the compressive residual stress in the textured layers. An apparent fracture toughness of up to 10.1 MPa·m^1/2 was obtained for composites with an equiaxed to textured volume ratio of 7.4:1. The high compressive stress in the textured layers arrested cracks, whereas the weak bonding parallel to the basal surfaces of the textured alumina grains caused cracks to deflect within the textured layers. The coupling of these two mechanisms resulted in crack arrest and a maximum work of fracture of ~1200 J/m² or almost 50 times higher than equiaxed alumina. We believe that embedding textured layers having compressive stresses below the surface of multilayer composites represent an important strategy for designing flaw‐tolerant materials with pronounced crack growth resistance and a high work of fracture.     

Yield behavior of rubber-modified epoxy adhesives under multiaxial stress conditions

In rubber-modified epoxy resins, a damage zone is generated in the vicinity of the crack tip due to the cavitation of rubber particles, which improves fracture toughness dramatically. Hence, in evaluating the stress distribution in adhesive joints with rubber-modified adhesives, the void formation and growth should be taken into account. In most studies, however, the adhesive layer is still considered as a continuum material governed by the von Mises yield criterion. For many ductile materials, Gurson's model is used for the stress analysis, in which the void formation and growth is taken into account. In a previous study, using adhesively bonded scarf and torsional butt joints, the effect of stress triaxiality on the yield stress in the adhesive layer was investigated. In this study, these experimentally-obtained yield stresses were compared with those obtained by a finite element method, where Gurson's constitutive equations were applied to the adhesive layer. As a result, the calculated yield stresses agreed well with the experimentally-obtained yield stresses. This indicates that Gurson's model is a useful tool for estimating stress distributions in adhesive joints with rubbermodified adhesives.     

Wet Erosive Wear of Alumina Densified with Magnesium Silicate Additions

A study was made of the wet erosive wear of polycrystalline alumina of mean grain size >1 μm, containing up to 10 wt% of magnesium silicate sintering aid. For pure polycrystalline alumina, the dominant wear mechanism was grain-boundary microfracture, leading to partial or complete grain removal. In the case of the liquid-phase-sintered materials, wear rates could be as low as 25% of those of pure alumina of the same mean grain size, and the main material removal mechanism was transgranular fracture combined with tribochemical wear. The use of Cr³⁺ photoluminescence line broadening showed much higher levels of local stress in the magnesium silicate-sintered materials (∼450 MPa) than in the pure-alumina materials (∼200 MPa). Grain-boundary compressive hoop stresses, caused by the thermal expansion mismatch between a continuous magnesium silicate film and the alumina grains, provided an explanation for the improved wear resistance of the alumina sintered with magnesium silicate.     

A quantitative evaluation method for particle orientation structure in alumina powder compacts

A quantitative evaluation method was developed to analyze weak-moderate particle orientation in alumina green compacts based on the optical anisotropy measured with a polarized light microscope. Alumina compacts of various structures were prepared in high magnetic fields 0–10 T by a casting method. The compact was made transparent with an immersion liquid, and the retardation of polarized light through it was measured quantitatively using a polarized light microscope with a Berek compensator. The degree of particle orientation was defined as the ratio of birefringence of the compact to that of alumina single crystal perpendicular to the c-axis. The degrees of orientation thus evaluated were compared to those calculated from X-ray diffraction analysis for samples with high orientation, and were found to agree very well.