Fracture Properties of LPCVD Silicon Nitride and Thermally Grown Silicon Oxide Thin Films From the Load-Deflection of Long Si3N4 and SiO2/Si3N4 Diaphragms

The bulge test is successfully extended to the determination of the fracture properties of silicon nitride and oxide thin films. This is achieved by using long diaphragms made of silicon nitride single layers and oxide/nitride bilayers, and applying comprehensive mechanical model that describes the mechanical response of the diaphragms under uniform differential pressure. The model is valid for thin films with arbitrary z-dependent plane-strain modulus and prestress, where z denotes the coordinate perpendicular to the diaphragm. It takes into account the bending rigidity and stretching stiffness of the layered materials and the compliance of the supporting edges. This enables the accurate computation of the load-deflection response and stress distribution throughout the composite diaphragm as a function of the load, in particular at the critical pressure leading to the fracture of the diaphragms. The method is applied to diaphragms made of single layers of 300-nm-thick silicon nitride deposited by low-pressure chemical vapor deposition and composite diaphragms of silicon nitride grown on top of thermal silicon oxide films produced by wet thermal oxidation at 950 degrees C and 1050 degrees C with target thicknesses of 500, 750, and 1000 mn. All films characterized have an amorphous structure. Plane-strain moduli E-ps and prestress levels sigma(0) of 304.8 +/- 12.2 GPa and 1132.3 +/- 34.4 MPa, respectively, are extracted for Si3N4, whereas E-ps = 49.1 +/- 7.4 GPa and sigma(0) = -258.6 +/- 23.1 MPa are obtained for SiO2 films. The fracture data are analyzed using the standardized form of the Weibull distribution. The Si3N4 films present relatively high values of maximum stress at fracture and Weibull moduli, i.e., sigma(max) = 7.89 +/- 0.23 GPa and m = 50.0 +/- 3.6, respectively, when compared to the thermal oxides (sigma(max) = 0.89 +/- 0.07 GPa and m = 12.1 +/- 0.5 for 507-nm-thick 950 degrees C layers). A marginal decrease of sigma(max) with thickness is observed for SiO2, with no significant differences between the films grown at 950 degrees C and 1050 degrees C. Weibull moduli of oxide thin films are found to lie between 4.5 +/- 1.2 and 19.8 +/- 4.2, depending on the oxidation temperature and film thickness.

Creep behavior of woven roving grp beam in three-point bending

The creep and relaxation behaviour of laminated glass fibre reinforced plastics (GRP) in three-point bending were studied both experimentally and analytically. Creep and relaxation experiments were carried out on eight types of specimens, consisting of glass fibre fabric reinforced epoxy beams. While the bending deflexion and creep strains were measured in the creep tests, the load and relaxation strain were recorded in the relaxation tests. Marked creep effects were seen in the tests, where the environment temperature was 50°C and the period of the measurement was 60 min. An attempt to predict the creep deflexion and relaxation behaviour was made. The transverse shear effect on creep deflexion was taken into account. The predicted results were compared with experimental ones. They were found to be in reasonable agreement, but the linearization assumption, upon which the relaxation behaviour analysis was based, appears to lead to larger inaccuracies in the results.

Lattice type of fracture model for concrete

Concrete is usually described as a three-phase material, where matrix, aggregate and interface zones are distinguished. The beam lattice model has been applied widely by many investigators to simulate fracture processes in concrete. Due to the extremely large computational effort, however, the beam lattice model faces practical difficulties. In our investigation, a new lattice called generalized beam (GB) lattice is developed to reduce computational effort. Numerical experiments conducted on a panel subjected to uniaxial tension show that the GB lattice model can reproduce the load-displacement curves and crack patterns in agreement to what are observed in tests. Moreover, the effects of the particle overlay on the fracture process are discussed in detail. (C) 2007 Elsevier Ltd. All rights reserved.

The interlaminar fracture-behavior and toughening mechanisms of new carbon-fiber-reinforced bismaleimide composites

The interlaminar fracture behaviour of carbon fibre-reinforced bismaleimide (BMI) composites prepared by using a new modified BMI matrix has been investigated by various methods. Laminates of three typical stacking sequences were evaluated. Double cantilever beam, end-notch flexure and edge-delamination tension tests were conducted under conventional conditions and in a scanning electron microscope. The strain energy release rates in Mode I and Mode III G(lc) and G(llc), as well as the total strain energy release rate, G(mc), have been determined and found to be higher than those for laminates with an epoxy matrix. Dynamic delamination propagation was also studied. The toughening mechanisms are discussed.

Micro- and macroscopic characterizations of the viscoelastic fracture of resin-based fibre composites

Micro- and macroscopic characterizations of the viscoelastic fracture of a unidirectional carbon-fibre-reinforced epoxy composite are presented. First, the micro-cracking behavior of the material is studied by the use of scanning electron microscopy; the in situ creep cracking process is observed and the crack propagation is measured. In order to obtain insight into the mechanisms of the observed creep cracking, macroscopic investigations were also carried out. Finite-element method simulations were carried out to calculate the stress distribution and the variation of stresses with time. A theoretical analysis of the orthotropy of viscoelastic fracture behavior of the material is also conducted.

Internal resonance of an L-shaped beam with a limit stop .2. Forced vibration

A limit stop is placed at the elbow of an L-shaped beam whose linear natural frequencies are nearly commensurable. As a result of this hardening device the non-linear system exhibits multiple internal resonances, which involve various degree of coupling between the first five modes of the beam in free vibration. A point load is so placed as to excite several modes and the resulting forced vibration is examined. In the undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with multiple branches and interactions between the first four modes. The amplitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Consequently parts of the resonance curve may be eliminated, with the resulting response comprising different distinctive branches. (C) 1996 Academic Press Limited

Plastic stress-strain fields and blunting effects during large deformations

Plastic stress-strain fields of two types of steel specimens loaded to large deformations are studied. Computational results demonstrate that, owing to the fact that the hardening exponent of the material varies as strain enlarges and the blunting of the crack tip, the well known HRR stress field in the plane strain model can only hold for the stage of a small plastic strain. Plastic dilatancy is shown to have substantial effects on strain distributions and blunting. To justify the constitutive equations used for analysis and to check the precision of computations, the load-deflection of a three-point bend beam and the load-elongation of an axisymmetric bar notched by a V-shaped cut were tested and recorded. The computed curves are in good accordance with experimental data.

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre-matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.

基于工程地质力学的岩土工程加固理论、技术与实践

In the engineering reinforcement of-rock and soil mass, engineers must consider how to obtain better reinforcing effect at the cost of less reinforcing expense, which, in fact, is the aim of reinforcement design. In order to accomplish the purpose, they require not only researching the material used to reinforce and its structure, but also taking into account of several important geological factors, such as the structure and property of rock and soil mass. How to improve the reinforcing effect according to engineering geomechanical principle at the respect of the reinforcement of engineering soil and rock mass is studied and discussed in this paper. The author studies the theory, technology and practice of geotechnical reinforcement based on engineering geomechanics, taking example for the soil treatment of Zhengzhou Airport, the effect analysis of reinforcement to the slope on the left bank of Wuqiangxi Hydropower Station and the reinforcing design of the No. 102 Landslide and unique sand-slide slope on the Sichuan-Tibet Highway. The paper is comprised of two parts for the convenience of discussion. In the first part, from the first chapter to the fifth chapter, trying to perform the relevant research and application at the viewpoint of soil mass engineering geomechanics, the author mainly discusses the study of reinforcing soft ground soil through dynamical consolidation and its application. Then, in the second part, from the sixth chapter to the eleventh chapter, the study of new technologies in the rock slope reinforcement and their application are discussed. The author finds that not only better reinforcing effect can be gained in the research where the principle and method of rock mass engineering geomechanics is adopted, but also new reinforcing technologies can be put forward. Zhengzhou Airport is an important one in central plains. It lies on Yellow River alluvial deposit and the structure of stratum is complex and heterogeneous. The area of airport is very large, which can result in differential settlement easily, damage of airport and aircraft accident, whereas, there are no similar experiences to dispose the foundation, so the foundation treatment become a principal problem. During the process of treatment, the method of dynamic compaction was adopted after compared with other methods using the theory of synthetic integration. Dynamic compaction is an important method to consolidate foundation, which was successfully used in the foundation of Zhengzhou Airport. For fill foundation, controlling the thickness of fill so as to make the foundation treatment can reach the design demand and optimum thickness of the fill is a difficult problem. Considering this problem, the author proposed a calculation method to evaluate the thickness of fill. The method can consider not only the self-settlement of fill but also the settlement of the ground surface under applied load so as to ensure the settlement occurred during the using period can satisfy the design demand. It is proved that the method is correct after using it to choose reasonable energy of dynamic compaction to treat foundation. At the same time, in order to examine the effect of dynamic compaction, many monitor methods were adopted in the test such as static loading test, modulus of resilience test, deep pore pressure -test, static cone penetration test and the variation of the pore volume measurement. Through the tests, the author summarized the discipline of the accumulation and dissipation of pore pressure in Yellow River alluvial deposit under the action of dynamic compaction, gave a correct division of the property change of silt and clay under dynamic compaction, determined the bearing capacity of foundation after treatment and weighted the reinforcing effect of dynamic consolidation from the variation of the soil particle in microcosmic and the parameter of soil mass' density. It can be considered that the compactness of soil is in proportion to the energy of dynamic compaction. This conclusion provided a reference to the research of the "Problem of Soil Structure-the Central Problem of Soil Mechanics in 21 Century ". It is also important to strengthen rock mass for water conservancy and electric power engineering. Slip-resistance pile and anchoring adit full of reinforced concrete are usually adopted in engineering experience to strengthen rock mass and very important for engineering. But there also some deficiency such as the weakest section can't be highlighted, the monitor is inconvenient and the diameter of pile and adit is very large etc. The author and his supervisor professor Yangzhifa invented prestressed slip-resistance pile and prestressed anchoring adit full of reinforced concrete, utilizing the advantage that the prestressed structure has better anti-tensile characteristic (this invention is to be published). These inventions overcome the disadvantages of general slip-resistance pile and anchoring adit full of reinforced concrete and have the functions of engineering prospecting, strengthening, drainage and monitor simultaneous, so they have better strengthened effect and be more convenient for monitor and more economical than traditional methods. Drainage is an important factor in treatments of rock mass and slop. In view of the traditional drainage method that drainage pore often be clogged so as to resulted in incident, professor Yangzhifa invented the method and setting of guide penetration by fiber bundle. It would take good effect to use it in prestressed slip-resistance pile and anchoring adit full of reinforced concrete. In this paper, the author took example for anchoring adit full of reinforced concrete used to strengthen Wuqiangxi left bank to simulate the strengthened effect after consolidated by prestressed slip-resistance pile, took example for 102 landslide occurred along Sichuan-Tibet highway to simulate the application of slip-resistance pile and the new technology of drainage. At the same time the author proposed the treatment method of flowing sand in Sichuan-Tibet highway, which will benefit the study on strengthening similar engineering. There are five novelties in the paper with the author's theoretical study and engineering practice: 1. Summarizing the role of pore water pressure accumulation and dissipation of the Yellow River alluvial and diluvial soil under the action of dynamical consolidation, which has instructive significance in the engineering construction under the analogical engineering geological conditions in the future. It has not been researched by the predecessors. 2. Putting forward the concept of density D in microcosmic based on the microcosmical structure study of the soil sample. Adopting D to weight the reinforcing effect of dynamic consolidation is considered to be appropriate by the means of comparing the D values of Zhengzhou Airport's ground soil before with after dynamically consolidating reinforcement, so a more convenient balancing method can be provided for engineering practice. 3. According to the deep research into the soil mass engineering geology, engineering rock and soil science, soil mechanics, as well as considerable field experiments, improving the consolidating method in airport construction, from the conventional method, which is dynamically compactmg original ground surface firstly, then filling soil and dynamically layer-consolidating or layer-compacting at last to the upgraded method, which is performing dynamical consolidation after filling soil to place totally at the extent of the certain earth-filling depth. The result of the dynamical consolidation not only complies with the specifications, but also reduces the soil treatment investment by 10 million RMB. 4. Proposing the method for calculating the height of the filled soil by the means of estimating the potential displacement produced in the original ground surface and the filled earth soil under the possible load, selecting the appropriate dynamically-compacting power and determining the virtual height of the filled earth soil. The method is proved to be effective and scientific. 5. According to the thought of Engineering Geomechanics Metal-Synthetic Methodology (EGMS), patenting two inventions (to the stage of roclamation, with Professor Yang Zhi-fa, the cooperative tutor, and etc.) in which multi-functions, engineering geological investigation, reinforcement, drainage and strength remedy, are integrated all over in one body at the viewpoint of the breakage mechanism of the rock slope.

Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.

Composite materials dynamic fracture studies by generalized Shmuely difference algorithm

The generalized Shmuely Difference Algorithm (GSDA) is presented here to analyze the dynamic fracture performance of orthogonal-anisotropic composite materials, such as glass fibre reinforced phenolplast. The difference recurrence Formulae and boundary condition difference extrapolation formulae are derived and programmed. The dynamic stress intensity factors (DSIF) of the isotropic and anisotropic centrally cracked plates are computed respectively using GSDA and compared with that published previously. GSDA is proved effective and reliable. Copyright (C) 1996 Elsevier Science Ltd.

Fracture properties of silicon carbide thin films by bulge test of long rectangular membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mu m were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 +/- 47 and 201 +/- 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 +/- 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 +/- 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 +/- 0.88 and 3.16 +/- 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mu m-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mu m-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws.

Bulge testing and fracture properties of plasma-enhanced chemical vapor deposited silicon nitride thin films

The mechanical properties and fracture behavior of silicon nitride (SiNx) thin film fabricated by plasma-enhanced chemical vapor deposition is reported. Plane-strain moduli, prestresses, and fracture strengths of silicon nitride thin film; deposited both oil a bare Si substrate and oil a thermally oxidized Si substrate were extracted using bulge testing combined with a refined load-deflection model of long rectangular membranes. The plane-strain modu i and prestresses of SiNx thin films have little dependence on the substrates, that is, for the bare Si substrate, they are 133 +/- 19 GPa and 178 +/- 22 MPa, respectively, while for the thermally oxidized substrate, they are 140 +/- 26 Gila and 194 +/- 34 MPa, respectively. However, the fracture strength values of SiNx films grown on the two substrates are quite different, i.e., 1.53 +/- 0.33 Gila and 3.08 +/- 0.79 GPa for the bare Si substrate a A the oxidized Si substrate, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over the edge, Surface, and volume of the specimens and fitted with the Weibull distribution function. For SiNx thin film produced oil the bare Si Substrate, the Volume integration gave a significantly better agreement between data and model, implying that the volume flaws re the dominant fracture origin. For SiNx thin film grown on the oxidized Si substrate, the fit quality of surface and edge integration was significantly better than the Volume integration, and the dominant surface and edge flaws could be caused by buffered HF attacking the SiNx layer during SiO2 removal. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Fracture properties of PECVD silicon nitride thin films by long rectangular memrane bulge test

Bulge test combined with a refined load-deflection model for long rectangular membrane was applied to determine the mechanical and fracture properties of PECVD silicon nitride (SiNx) thin films. Plane-strain modulus E-ps prestress s(0), and fracture strength s(max) of SiNx thin films deposited both on bare Si substrate and on SiO2-topped Si substrate were extracted. The SiNx thin films on different substrates possess similar values of E-ps and s(0) but quite different values of s(max). The statistical analysis of fracture strengths were performed by Weibull distribution function and the fracture origins were further predicted.

Fracture properties of silicon carbide thin films charcterized by bulge test of long membranes

The mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates were characterized using bulge testing combined with a refined load-deflection model for long rectangular membranes. Plane-strain modulus E-ps, prestress so, and fracture strength s(max) for 3C-SiC thin films with thickness of 0.40 mu m and 1.42 mu m were extracted. The E, values of SiC are strongly dependent on grain orientation. The thicker SIC film presents lower so than the thinner film due to stress relaxation. The s(max) values decrease with increasing film thickness. The statistical analysis of the fracture strength data were achieved by Weibull distribution function and the fracture origins were predicted.