Residual stress measurement in filament-evaporated aluminium films on single crystal silicon wafers

Shadow Moire interferometry was used to determine the residual stresses in thin, filament-evaporated aluminium films deposited on (100) p-type, 10.16 cm diameter, 0.05 cm thick, circular single crystal silicon wafers. The aluminium film thicknesses ranged from 70 to 780 nm. Benchmark experiments on wafers without aluminium films showed that wafers possess in-plane residual stresses; the centre of the wafer is under tensile stresses of the order of 30 M Pa and these stresses decrease toward the edge of the wafers to approximately 10 M Pa. The deposition of aluminium films increases these tensile residual stresses by 3 to 15 M Pa depending on the film thickness. The increase in the stress is attributed to the stresses in the films.     

Determination of mechanical properties of electroplated Ni thin film using the resonance method

This paper addresses a relatively simple method of measuring the mechanical properties such as Young's modulus and residual stress of electroplated Ni thin film using the resonance method of Atomic Force Microscope. Thin layer of nickel to be measured is electroplated onto the tip side of AFM silicon cantilever and plating thicknesses were measured at the end of each plating step. The measured Young's modulus of nickel at the end of each plating step ranged from 148.04 GPa to 159.90 GPa with the maximum standard deviation of 3.47. The end deflection of electroplated AFM cantilever is also measured as a function of the plated Ni thickness, which is converted into the film stress by appropriate mechanics.     

Interracial Bonding Strength of TiN Film Coated on Si3N4 Ceramic Substrate

The fraction of TiN/Si3N4 in the cross section was observed with scanning electric microscope （SEM）, and residual stresses of TiN coated on the surface of Si3N4 ceramic were measured with X-ray diffraction （XRD）.The hardness of TiN film was measured, and bonding strength of TiN film coated on Si3N4 substrate was measured by scratching method. The formed mechanism of residual stress and the failure mechanism of the bonding interface in the film were analyzed, and the adhesion mechanism of TiN film was investigated preliminarily. The results show that residual stresses of TiN film are all behaved as compressive stress, and TiN film is represented smoothly with brittle fracture, which is closely bonded with Si3N4 substrate. TiN film has high hardness and bonding strength of about 500 MPa, which could satisfy usage requests of the surface of cutting Si3N4 ceramic.     

A small cantilever beam test for determination of creep properties of materials

The application of small specimen creep test techniques in the evaluation of creep properties of materials in‐service has been increasing. To obtain the creep data accurately and conveniently, a new creep test method with small cantilever beam specimens is proposed. Analytical equations are derived that can convert the load to equivalent uniaxial stress and the displacement rate to equivalent uniaxial strain rate. Three types of the cantilever beam specimens are designed. The optimal configuration of the cantilever beam specimens is recommended with the aid of finite element method, which is further validated by the cantilever beam and uniaxial specimen tests. The results show that parameters obtained from the cantilever beam tests correspond reasonably well with those from uniaxial tests at low stress levels. With a relatively large equivalent gauge length, the cantilever beam specimen allows the small creep strain rate data obtained with a high accuracy.     

Der Einfluß von thermozyklischer Beanspruchung auf den Eigenspannungszustand in elektronenstrahlgedampften Wärmedämmschichten aus Zirkonoxid

Influence of Thermal Cycling on Residual Stresses in Zirconia Thermal Barrier Coatings Produced by Electron Beam – Physical Vapor Deposition. Flat specimens and aircraft turbine engine blades were coated with partially stabilized zirconia by electron beam - physical vapor deposition. Residual stresses of these thermal barrier coatings were measured before and after thermal cycling by x-ray stress analysis. All flat specimens and blades showed compressive residual stresses. Stress values in the longitudinal direction were significantly greater than those measured in the transverse direction. No changes of stress states and line widths were observed after thermal cycling. The specimens showed considerable differences in texture which made evaluation of the stress measurements difficult and which may have influenced degradation behaviour during thermal cycling.     

The hydrostatic pressure‐induced stresses in double‐coated optical fibers

Abstract

Hydrostatic pressure‐induced stresses in double‐coated optical fibers are analyzed. The lateral pressure, radial stress, tangential stress and axial stress in the optic fiber are found. The normal stresses in the optical fiber are proportional to the hydrostatic pressure, and are determined by the material properties of the primary and secondary coating, and their thicknesses. Additionally, microbending losses induced by hydrostatic pressure in double‐coated optical fibers are discussed.     

Schwingfestigkeit laserstrahlgeschweißter Dünnblechproben aus Stahl nach lokalen Konzepten

Fatigue strength of laser beam welded thin sheet specimens in steel according to local approaches An investigation into the fatigue strength of laser beam welded thin sheet specimens in steel performed several years ago is re-evaluated according to local approaches based on structural stresses, stress intensity factors, J-integral and notch stresses. The re-evaluation is restricted to the tensile-shear and peel-tension specimens with a keyhole weld. Data from the literature are set in comparison. Re-evaluating the tensile-shear specimen, the equivalent stress intensity factor according to Erdogan and Sih resulted as the parameter best suited for characterising the technical endurance limit of the specimens. It takes the effect of sheet thickness on the strength into account whereas the structural stress does not. But unsolved difficulties occurred when comparing the strength values in the tensile-shear and peel-tension specimens. The J-integral approach evolved as inappropriate in both cases. The notch stress approach is unsufficiently developed up to now in respect of thin sheet specimens. An extension of the investigation is recommended with a larger number of test specimens, a higher quality of manufacture and a more differentiated evaluation.     

Optimum Design of Thick-Walled Multi-Layered CFRP Pipes to Reduce Process-Induced Residual Stresses

Process-induced residual stresses may cause cracking in thick-walled multi-layered CFRP pipes during the curing of the pipes, significantly affecting the ultimate structural performance. Several factors influence the amount of the residual stresses, such as thermal and elastic properties of CFRP, and stacking sequences and dimensions of pipes. This paper deals with the optimum design of thick-walled multi-layered CFRP pipes by minimising the process-induced residual stresses under some constraints of structural stiffnesses. An analytic model based on quasi-static thermoelasticity is adopted for the calculation of the residual stresses in the multi-layered CFRP pipes. The numerical results of optimisation show that, in the case of cross-ply pipes, the residual stresses can be reduced to a certain level by controlling ply thicknesses. However, in real process conditions, the optimised pipes are susceptible to cracking because the transverse residual stress is still large in a strength-based sense. To further suppress the residual stresses, the effects of stacking sequence, wall thickness and axial pre-tension on the optimum solutions are carefully examined.     

A rational elasto‐plastic spatially curved thin‐walled beam element

Torsion is one of the primary actions in members curved in space, and so an accurate spatially curved‐beam element needs to be able to predict the elasto‐plastic torsional behaviour of such members correctly. However, there are two major difficulties in most existing finite thin‐walled beam elements, such as in ABAQUS and ANSYS, which may lead to incorrect predictions of the elasto‐plastic behaviour of members curved in space. Firstly, the integration sample point scheme cannot capture the shear strain and stress information resulting from uniform torsion. Secondly, the higher‐order twists are ignored which leads to loss of the significant effects of Wagner moments on the large twist torsional behaviour. In addition, the initial geometric imperfections and residual stresses are significant for the elasto‐plastic behaviour of members curved in space. Many existing finite thin‐walled beam element models do not provide facilities to deal with initial geometric imperfections. Although ABAQUS and ANSYS have facilities for the input of residual stresses as initial stresses, they cannot describe the complicated distribution patterns of residual stresses in thin‐walled members. Furthermore, external loads and elastic restraints may be applied remote from shear centres or centroids. The effects of the load (and restraint) positions are important, but are not considered in many beam elements. This paper presents an elasto‐plastic spatially curved element with arbitrary thin‐walled cross‐sections that can correctly capture the uniform shear strain and stress information for integration, and includes initial geometric imperfections, residual stresses and the effects of the load and restraint positions. The element also includes elastic restraints and supports, which have to be modelled separately as spring elements in some other finite thin‐walled beam elements. Comparisons with existing experimental and analytical results show that the elasto‐plastic spatially curved‐beam element is accurate and efficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Micron-sized fracture experiments on amorphous SiOx films and SiOx/SiNx multi-layers

In this study miniaturized monolithic cantilevers of thermally grown silicon oxide and multi-layer cantilevers of plasma enhanced chemical vapor deposited silicon oxide and nitride were mechanically characterized. In order to determine the fracture stress as well as the fracture toughness, un-notched and focused ion beam pre-notched cantilevers were tested. While the thickness of the monolithic cantilevers was varied from 280 nm to 2380 nm, the individual sub-layer thickness of the multi-layer cantilevers was adjusted to 50 nm. Bending experiments reveal a small increase of the fracture stresses with decreasing cantilever thicknesses. For the multi-layer stacks the tensile stress at fracture slightly exceeds the strength values of the corresponding monolithic materials. Furthermore, it is demonstrated that the specimens pre-notched by focused ion beam do not show significant changes in fracture toughness with varying pre-notch size. This makes the applied test a reproducible technique to determine fracture toughness of brittle films.     

Energy release rates of bi-material interface crack including residual thermal stresses: Application of crack tip element method

Crack tip element method is applied to the formulation of the energy release rate associated with interfacial crack growth of laminates with residual thermal stresses using the Timochenko beam model. Special attention is paid to the energy release rates of double cantilever beam and mixed-mode bending tests of bi-material specimens, and mode-I and mode-II energy release rates are formulated including residual thermal stresses. The derived results are verified by the comparison to finite element analysis, and the effect of residual thermal stresses on the mode mixity of the double cantilever beam and mixed-mode bending tests is discussed.     

Numerical and experimental validation of residual stresses of laser‐welded joints and their influence on the fatigue behaviour

In this work laser‐welded tube‐tube specimens made of aluminium alloys AlMg3.5Mn and AlSi1MgMn T6 were experimentally tested under constant and variable amplitude loading, under pure axial and pure torsion loading. In order to evaluate the influence on fatigue behaviour of the residual stresses, because of the welding process, some specimens were subjected to postweld heat treatment and then were tested. The numerical analyses, using finite element (FE), were carried out to obtain a reliable estimation of the residual stress in the specimen. The numerical results were in a good agreement with experimental ones obtained by means of hole‐drilling method. Finally, the residual stress distribution was superimposed to stress distribution because of fatigue loads obtained by FE analyses applying local concept, to calculate the stresses in the crack initiation zone and to understand the different types of failure that occurred in as‐welded and relieved specimens.     

变截面梁的应力计算及其分布规律研究

为了合理计算预应力混凝土变截面箱形梁的剪应力,客观反映其应力分布状况,首先推导了任意变截面梁剪应力计算的一般公式,在此基础上,考虑箱形梁的梁高、底板厚度、腹板厚度沿跨度的变化,导出了变截面箱形梁的剪应力实用计算公式。应用导出的公式,结合矩形及箱形变截面悬臂梁算例,分析了变截面梁的应力分布状况。研究结果表明,变截面梁横截面上的最大剪应力并不发生在截面重心轴处,而是在重心轴以下区域或梁底缘处;变截面箱形梁的底板受有很大剪应力作用,为了合理设计变截面箱形梁,不应采用薄底板,而且应加强其配筋及构造处理。     

Tensile and high cycle fatigue test of copper thin film

This paper presents the results of tensile and high cycle fatigue tests for copper thin film. Copper films coated by Sn are often used in various electro devices. Especially, when the film is used in tape carrier package (TCP), the film is repeatedly exposed to mechanical or(and) thermal stresses which results often in the failure of the component. Therefore, to guarantee the reliability of the electrical devices using a film, tensile and fatigue characteristics of the film are important. In this study, to obtain the tensile and fatigue characteristics of the film, the specimen was fabricated by an etching process to make a smooth specimen of 2000 μm width, 8000 μm length and 15.26 μm thickness. The tensile and high cycle fatigue tests were performed with the specimen using the test machine developed by the authors. These specimens had measured values of Young's modulus (72 GPa) and a 0.2 % offset yield and an ultimate strength of 358 MPa and 462 MPa, respectively. A closed‐loop feedback control of the magnetic‐electric actuator allowed load‐controlled fatigue tests with 20 Hz frequency, in ambient environment and at two levels of mean stresses. The fatigue strength coefficient and exponent at 0.5 times of the ultimate tensile strength were 431 MPa and ‐0.0843, respectively. The fatigue strength coefficient and exponent at 0.6 times of the ultimate tensile strength were 371 MPa and ‐0.0923, respectively. The Goodman method is recommended when the fatigue life of thin film with mean stress will be estimated. The fatigue strength coefficient and exponent of copper thin film modified using Goodman method were 910 MPa and ‐0.0896, respectively.     

A modified layer-removal method for residual stress measurement in electrodeposited nickel films

Combining the traditional layer-removal method with a cantilever beam model, a modified layer-removal method is developed and used to measure residual stress in single and multi-layer electrodeposited nickel films with thickness of 2.5 μm. The out-of-plane displacement of the free tip of a cantilever beam is measured by the digital speckle correlation method. The results show that residual stress in a single semimat nickel film is compressive, while in a multi-layer system composed of dark, semimat and holophote nickel, residual stress in the surface layer is tensile. Residual stress decreases gradually with the increase of etching depths of single and multi-layer films. These findings are in qualitative agreement with nanoindentation tests, which confirms the reliability of the modified layer-removal method.     

Influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors

The influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors has been analyzed under the framework of thermodynamic theory and Fick's second law. A self-consistent diffusion equation involving the coupling effects of residual stress and diffusion-induced stress is developed. Effects of thickness ratio, modulus ratio, diffusivity ratio and residual stress gradient of film and substrate on the curvature of bilayered cantilever are then discussed with the help of finite difference method. Results reveal that the curvature of bilayered cantilever increases with decreasing the diffusivity ratio and modulus ratio of substrate to film at a given time. Case study of the polysilicon/palladium hydrogen sensor has been finally carried out using the above developed bending theory.     

受初应力作用的轴向运动功能梯度梁的动力学分析

基于Euler梁模型研究了初始应力作用下轴向运动功能梯度材料梁的横向振动问题。假设材料性质沿梁的厚度方向按幂指数形式连续变化,利用Hamilton原理建立了系统的控制方程,应用复模态法求得了其固有频率和模态函数,接着分析了轴向运动速度、梯度指数、初应力大小等因素对梁的动力响应的影响。结果表明:梯度指数和轴向速度的增大都会导致固有频率降低,轴向初应力的增大则使得固有频率升高。     

Consideration of influence factors between small‐scale specimens and large components on the fatigue strength of thin‐plated block joints in shipbuilding

Shipbuilding in blocks, as being usual on all larger shipyards, requires that the blocks will finally be welded together manually or semi‐automatically, that is, with butt‐welds in transverse direction that have to withstand relatively high dynamical loads. Modern shipbuilding aims at lightweight construction with thin plates that may have a plate thickness down to 4 mm. Previous investigations showed that manually produced butt‐welds in such thin structures did not reach the calculated fatigue life as required in the rules. Up to the present, this problem has not yet been solved, and it is questioned if all influence factors on the fatigue behaviour of real structures are correctly considered as no damage cases at butt joints that are known yet. In the investigation described here, results from small‐scale specimens tested with cyclic loads will be transferred to large components, considering the effects of recorded pre‐deformations induced by welding as well as measured differences in residual stresses between small‐scale specimens and large components, thus clarifying how far for instance a detrimental stress ratio should be taken into account by the rules for thin plates.     

Effect of thick DLC coating on fatigue behaviour of magnesium alloy in laboratory air and demineralised water

Rotating bending fatigue tests have been performed using Diamond‐like carbon (DLC) coated specimens of a wrought magnesium alloy, AZ80A, in laboratory air and demineralised water and the effect of DLC coating on fatigue and corrosion fatigue behaviour was studied. Three film thicknesses of 3.5 μm, 13 μm, and 25 μm (two‐layer film) were evaluated and particular attention was paid to the role of thick DLC coating. In laboratory air, the fatigue strengths of the DLC‐coated specimens were higher than that of the substrate specimen and increased with increasing film thickness. This was because hard DLC coating with good adhesion suppressed the crack initiation due to cracking of inclusions or cyclic slip deformation on the substrate surface. In demineralised water, the fatigue strength of the 3.5‐μm DLC‐coated specimen was the same as that of the substrate specimen due to the penetration of the water through pre‐existing film defects, while the 13‐μm and 25‐μm DLC‐coated specimens showed increased corrosion fatigue strength with increasing film thickness and also exhibited nearly the same fatigue strength as in laboratory air except for a few premature failed specimens, indicating a potential of thick DLC coating or two‐layer coating for complete improvement of corrosion fatigue strength in aqueous environments.     

Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method

The transverse vibration of a rotary tapered microbeam is studied based on a modified couple stress theory and Euler–Bernoulli beam model. The governing differential equation and boundary conditions are derived according to Hamilton's principle. The generalized differential quadrature element method is then used to solve the governing equation for cantilever and propped cantilever boundary conditions. The effect of the small-scale parameter, beam length, rate of cross-section change, hub radius, and nondimensional angular velocity on the vibration behavior of the microbeam is presented.