Determination of tensile properties and residual stresses of Ni-Co thin films

This paper reports tensile properties and residual stresses of Ni-Co thin films. To measure elastic (and plastic) properties, direct tensile tests using dog-bone type specimens are performed first. Assuming that residual stresses vary linearly through the film thickness, bending and membrane residual stress components are measured using cantilever beam and T-structure beam specimens, respectively. Averaged values of Young’s modulus, yield strength and tensile strength are found to be about 163GPa, 1,700MPa and 2,000MPa, respectively. The membrane and bending residual stress components are found to be about 825MPa and 47MPa, respectively.     

Effect of tip geometry of atomic force microscope on mechanical responses of bovine articular cartilage and agarose gel

The objective of this study is to investigate the effect of different Atomic Force Microscope (AFM) tip geometries (sharp-conical and spherical tips) on the microscale Young’s modulus of bovine articular cartilage and agarose gel that is calculated by the method of the average point-wise modulus. The measurements of the microscale Young’s moduli of 3% agarose gel under a conical AFM tip (20.9±4.9 kPa) and under a spherical AFM tip (17.5±3.0 kPa), averaged over an indentation depth of 600 nm, were comparable. However, the microscale Young’s moduli of articular cartilage, as measured with a conical AFM tip (116.9±62.9 kPa), were significantly higher than the corresponding values under a spherical AFM tip (30.9±14.3 kPa). The results of the current study suggest that the AFM tip geometry affects the microscale measurements of the mechanical properties on the surfaces of biological materials. The findings of the study can help to elucidate more accurately the microscale mechanical properties on the surface layers of diverse biological materials including tissue-engineered cartilages with different material characteristics.     

A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

In this paper, based on the exact analytical solution of axisymmetric deformation of the circular membrane fixed at its edge under the action of uniformly-distributed loads, we propose a new method to be able to simultaneously determine Poisson’s ratio and Young’s modulus of elasticity for thin films. We also present a set of exact formulas used for simultaneously determining Poisson’s ratio and Young’s modulus of elasticity for free-standing thin films or coating thin films without residual stresses or pre-tension. This method has the advantages of simplicity and reliability, and it doesn’t involve the substrate effect.     

微桥结构Ni膜杨氏模量和残余应力研究

采用MEMS(MicroelectromechanicalSystems)技术研制了镍(Ni)膜微桥结构试样,应用陶瓷压条为承力单元,与纳米压痕仪XP系统的Berkovich三棱锥压头相结合,解决了较宽Ni膜微桥加载问题。测量了微桥载荷与位移的关系,并结合微桥力学理论模型得到了Ni膜微桥的杨氏模量及残余应力,其值分别为190.5GPa和146MPa,与应用纳米压痕仪直接测得的带有Si基底的Ni膜杨氏模量186.8±7.34GPa相吻合。     

A method to calculate the reliability of the gas pipeline segment under axial compression

An algorithm is presented for probabilistic calculation of the gas pipeline strength reliability for the case when the ultimate strength of the pipe steel, compressing force, gas pressure, Young’s modulus, temperature drop, pipe thickness, and diameter are distributed normally.     

Calibration of AFM cantilever spring constants

In this paper we present two simple, reliable and readily applicable methods for calibrating cantilevers and measuring the thickness of thin gold films. The spring constant calibration requires knowledge of the Young's modulus, density of the cantilever and resonant frequency. The thickness of thin gold layers was determined by measuring changes in the resonant frequency and Q-factor of beam shaped AFM cantilevers before and after coating.The techniques for measuring the spring constant and thin film thickness provide accuracy on the order of 10-15%.     

Prediction of residual stress distribution in multi-stacked thin film by curvature measurement and iterative FEA

In this study, residual stress distribution in multi-stacked film by MEMS (Micro-Electro Mechanical System) process is predicted using Finite Element method FEMi. We develop a finite element program for residual stress analysis (RESA) in multi-stacked film. The RESA predicts the distribution of residual stress field in multi-stacked film. Curvatures of multistacked film and single layers which consist of the multi-stacked film are used as the input to the RESA. To measure those curvatures is easier than to measure a distribution of residual stress. To verify the RESA. mean stresses and stress gradients of single and multilayers are measured. The mean stresses are calculated from curvatures of deposited wafer by using Stoney’s equation. The stress gradients are calculated from the vertical deflection at the end of cantilever beam. To measure the mean stress of each layer in multi-stacked film, we measure the curvature of wafer with the left film after etching layer by layer in multi-stacked film.     

Performance analysis of piezoelectric bimorph generator

In this paper, the theoretical model and simulation of the performance of a piezoelectric (PZT) bimorph generator is introduced. The generator consists of two piezoelectric plates bonded on a substrate metal plate. For an effective electromechanical coupling coefficient (EECC) and the generated energy, the analytical formulae are established with the thickness ratio and the Young’s modulus ratio as variables. After giving correlative material parameters, the EECC and generated energy can be computed. The results show that there is a optimal thickness ratio for a piezoelectric bimorph generator to achieve the maximum EECC and electrical energy. The EECC and generated energy decrease with an increase of the Young’s modulus ratio. In addition, the influence of mechanical source on electrical energy generation and power output is also considered.     

Developing a bio-mechanotronic probing system for estimating soft tissue Young’s modulus in vivo

In many medical applications such as rehabilitation, clinical palpation, and manipulation of organs, it is important to characterize soft-tissue properties accurately. This paper presents a bio-mechatronic probing system that could be used for estimating soft tissue Young’s modulus in vivo. The system employs an electromagnetic spatial displacement sensor. The accuracy and reliability of the system were investigated. In addition, the effect of indentation rate on the variation of the values of the measured effective Young’s modulus was also studied. A series of elastomers with different Young’s modulus (ranged from 13.08 to 36.19 kPa) were assessed with both the probing system and a Hounsfield material testing machine. Intra-individual and inter-individual variations of the system were tested by five independent operators. The probing system was applied to assess the effective Young’s modulus of human body parts in vivo. Fifteen healthy female subjects with age of 22.5 ± 4.3 years old were included for the in vivo test. The system was shown to be highly accurate (R ² = 0.995) in comparison with the results obtained by the mechanical testing machine and had good reliability (intra-individual variation = 5.43%, inter-individual variation = 5.99%). The average effective Young’s modules of the region of umbilicus were 13.33 and 10.71 kPa for two different sites, respectively. Based on the results obtained, it is believed that this probing system was an accurate and reliable tool for rapidly assessing the mechanical properties of human body tissues in vivo.     

脉冲激光沉积薄膜的残余应力测量

为了测量脉冲激光沉积法制备的小面积薄膜的残余应力,并解决Stoney公式在特定情况下误差较大的问题,本文提出了一种基于悬臂梁结构和数值计算的薄膜残余应力测量方法。该方法以初始曲率为零的原子力显微镜探针作为衬底梁,在衬底梁上使用脉冲激光沉积方法沉积被测薄膜,并记录衬底梁在薄膜沉积前后的翘曲形貌变化,再结合薄膜厚度、衬底梁几何尺寸、所涉及材料的杨氏模量与泊松比等其他参数,借助数值计算对实验数据进行分析,得出被测薄膜的残余应力。使用该方法测出:基于脉冲激光沉积法在高温环境下制备的二氧化钒薄膜的残余应力为-340 MPa,与文献报道的结果相符。本文提出的基于悬臂梁结构和数值计算的薄膜残余应力测量方法具有适用范围广、准确度好、实验成本低的优点。     

Thermal design criteria for long-term durability of ceramic catalyst substrates

The automotive industry has traditionally used ceramic honeycomb substrates as catalyst carriers. The long-term durability of a passenger car’s converter is assessed by examining the thermal stresses resulting from the temperature variations experienced under various driving conditions. These thermal stresses constitute the majority of the total stress that the ceramic catalyst substrate experiences while in service. The radial and axial temperature distributions were measured, and the thermal stress was calculated by using the thermal expansion coefficient according to the measured temperature. The threshold stress was determined from the fatigue constant, the required lifetime and the duration of the short term strength tests. The radial temperature variation was higher than the axial temperature variation, and the axial stress was higher than the radial stress because the thermal stress is dependent on the elastic modulus. The radial and axial stresses exist below the threshold thermal stress over the entire engine speed range.     

Stress Analysis on Layered Materials in Point Elastohydrodynamic-Lubricated Contacts

For multilayered or coated substrates in elastohydrodynamic-lubricated (EHL) contacts, the subsurface stress distributions under a normal load combined with shear traction have been analyzed in this article through computer simulations. The Papkovich-Neuber potentials and Fourier transform are adopted to deduce the pressure–displacement, pressure–stress, and shear traction–stress response functions in frequency domain for the coated substrates, and to calculate distributions of pressure and subsurface stress. The results from the analysis of EHL contacts on coated substrates are compared with those from dry contact model in which shear traction is assumed to obey Coulomb’s law. Effects of the Young’s modulus of coatings, the properties of lubricants, and the magnitude of traction are discussed. Similar to the results in dry contacts, hard coatings in lubricated cases tend to increase the von Mises stress, whereas soft coatings decrease the stress. Shear traction makes the max von Mises stress increasing and moving closer to surface. However, the changes in subsurface stress due to shear traction are less obvious in lubricated contacts. Comparison between EHL and dry contact models reveals that lubrication can reduce the von Mises stress in the coating layer due to smaller shear traction. The analyses show that pressure, film thickness, and subsurface stress distributions are influenced by surface coatings, sliding velocity, rheological models, and pressure–viscosity behaviors.     

Evaluation of cellulose electro-active paper made by tape casting and zone stretching methods

Cellulose has been discovered as a smart material that can be used as sensor and actuator material. In this paper, cellulose smart material termed as electro-active paper (EAPap) is prepared by an automated process that includes tape casting and zone stretching. To evaluate characteristics of the EAPap, its Young’s modulus and piezoelectric charge constant are measured depending on the orientation angle, in comparison with the manually fabricated EAPap results. The zone stretching method can effectively align the cellulose fibers in the EAPap so as to improve its Young’s modulus as well as piezoelectric charge constant. The 0 degree oriented sample shows its maximum Young’s modulus and the 45 degree oriented sample exhibits the maximum piezoelectric charge constant. This 45 degree is associated with its shear piezoelectricity. The actuator performance of EAPap is evaluated by measuring its bending displacement depending on the orientation angle and the excitation voltage. The 45 degree oriented sample exhibits the maximum bending displacement. Details of the material preparation, the automation process, characterization and the actuator performance are addressed. This automated process that includes tape casting and zone stretching is suitable for mass production of the EAPap.     

Measuring Non-Uniform Residual Stress in Thin Plates by a Proposed Hole-Drilling Strain Gauge Method

In this paper, a new proposed through hole-drilling strain gauge method is developed to determine the magnitudes and directions of the principal residual stresses, and the stress gradients in the directions of the principal residual stresses of the in-plane non-uniform biaxial residual stresses in thin plates. The variation of the residual stresses in the directions of the principal residual stresses at the region close to the measured point can be predicted simultaneously with the calculated gradients. Two thin butt-welded specimens were prepared in this study to verify the accuracy of the proposed method in comparison with the Kabiri’s method by using two different gauge layouts of rosettes. The experimental results show that the percentage of the relative errors between the proposed method and the Kabiri’s method are all within 9.4%. Thus, the proposed method shows good accuracy in the determination of the in-plane non-uniform biaxial residual stresses in thin plates.     

Study of the effect of imperfect tips on nanoindentation by FEM

In this paper, the imperfect tip effect of the Ti film on Si substrate on nanoindentation with Berkovich probe tip was investigated with the finite element method (FEM). In the literature, we found the effects of tip deformation and tip radius on nanoindentation were investigated frequently, but the imperfect centerline of tip has never been studied. In this work, at first, the Ti film on Si substrate was conducted with a high-resolution nanomechanical test. The Young’s modulus of Ti films can be obtained by using the Oliver and Pharr method while the nanoindentation depth is smaller than 20% of the film thickness for avoiding the substrate effect. Second, the FEM was employed to determine the yield stress of thin films because it cannot be found from nanoindentation. Finally, the load-depth of nanoindentation was compared between the experimental data and numerical results. The results show while choosing the suitable yield stress of films, the load-depth curves of numerical simulation were very close to the experimental curves with the imperfect effect being ignored. Moreover, it is concluded while the imperfect angles of tip were considered that the larger imperfect angles |θ _x | orθ _x , the smaller displacement on nanoindentation.     

Atomic-scale finite-element model of tension in nanoscale thin film

In this paper, a 2D atomic-scale finite-element model of tension in nanoscale thin film is developed in which Morse’s potential energy function is used to model the interactive forces between atoms. The model is fed into the finite-element package LS-DYNA and both a single integration point and an explicit solution method are used for solving the tension process rapidly to investigate the size effect of different film thicknesses and the effect of different atomic vacancy ratios on nanoscale thin film under tension. The results show that since the applied displacement is exerted at both ends for different thickness of a perfect crystal, a neutral line is formed at the middle of the material. The material slides along the easiest slip direction to cause a “necking” feature on both sides. The stress initially increases with the gradual increase of strain and thicker film shows a larger tensile stress. After the film experiences the peak stress, the stress then decreases with the gradual increase of strain. While the applied displacement is applied at both ends for different vacancies, a neutral line is formed at the middle of material, but this is not apparent due to the random scattered vacancies. The material slides along the easiest slip direction from left to right, and the stress concentration areas near the constrained ends form “necking” features. Stresses are not zero at zero strain. Tension tests for different vacancy ratios show different maximum stresses. Film with a larger vacancy ratio shows a lower stress at the same strain. As the vacancy ratio of the film under tension increases, the strength and elastic modulus reduces.     

Study on residual stress in viscoelastic thin film using curvature measurement method

Using LSM (laser scanning method), the radius of curvature due to thermal deformation in polyimide film coated on Si substrate is measured. Since the polyimide film shows viscoelastic behavior, i.e., the modulus and deformation of the film vary with time and temperature, we estimate the relaxation modulus and the residual stresses of the polyimide film by measuring the radius of curvature and subsequently by performing viscoelastic analysis. The residual stresses relax by an amount of 10% at 100°C and 20% at 150°C for two hours.     

Reliability-based topology optimization with uncertainties

This research proposes a reliability-based topology optimization (RBTO) using the finite element method. RBTO is a topology optimization based on probabilistic (or reliability) constraints. Young’s modulus, thickness, and loading are considered as the uncertain variables and RBTO is applied to static and eigenvalue problems. The RBTO problems are formulated and a sensitivity analysis is performed. In order to compute probability constraints, two methods—RIA and PMA— are used. Several examples show the effectiveness of the proposed method by comparing the classical safety factor method.     

On analysis and measurement of residual stresses in the bending of sheet metals

A new method for evaluating distribution of residual stresses in bent sheet metals is presented. Due to the non-uniform distribution of strain and stress across thickness, springback on unloading induces residual stress in a bent specimen. The authors have formulated the problem and shown that the springback and residual stresses can be expressed as a function of geometric parameters and material properties of sheet metals, e.g. bending curvature, thickness, Young's modulus, work-hardening index, etc. The layer-removing method was used to determine the residual stresses in the study. By simulating the layer-removing process, analytical measurement of the residual stress was made. The analytical results were compared with the experimental data measured, and a good agreement was found.     

High-throughput characterization of stresses in thin film materials libraries using Si cantilever array wafers and digital holographic microscopy

We report the development of an advanced high-throughput stress characterization method for thin film materials libraries sputter-deposited on micro-machined cantilever arrays consisting of around 1500 cantilevers on 4-inch silicon-on-insulator wafers. A low-cost custom-designed digital holographic microscope (DHM) is employed to simultaneously monitor the thin film thickness, the surface topography and the curvature of each of the cantilevers before and after deposition. The variation in stress state across the thin film materials library is then calculated by Stoney's equation based on the obtained radii of curvature of the cantilevers and film thicknesses. DHM with nanometer-scale out-of-plane resolution allows stress measurements in a wide range, at least from several MPa to several GPa. By using an automatic x-y translation stage, the local stresses within a 4-inch materials library are mapped with high accuracy within 10 min. The speed of measurement is greatly improved compared with the prior laser scanning approach that needs more than an hour of measuring time. A high-throughput stress measurement of an as-deposited Fe-Pd-W materials library was evaluated for demonstration. The fast characterization method is expected to accelerate the development of (functional) thin films, e.g., (magnetic) shape memory materials, whose functionality is greatly stress dependent.