scholarly journals Studies on the Residual Stress and Strain Gradients in Poly-SiGe Nanocantilevers

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Tesleem B Asafa
Keyword(s):  
Strain Gradient ◽  
Stress Gradient ◽  
Local Stress ◽  
Stress And Strain ◽  
Fast Method ◽  
Stress Evolution ◽  
Strain Gradients ◽  
Study Results ◽  
Evolution Study ◽  
Gradient Measurement

One of the fundamental structural requirements for Micro/Nano-ElectroMechanical (M/NEM) devices is low strain gradient. Measurement of strain gradients is time consuming, therefore finding a simple and fast method is necessary. In this paper, a comparative study of the strain gradients in poly-SiGe nanocantilevers measured experimentally and obtained using finite element modelling (FEM) approach is reported.  Arrays of nanocantilevers were fabricated from 100 nm thick poly-SiGe films via lithography. Then, strain gradients were calculated from the tip deflections and cantilevers’ lengths. In the modelling study, similar cantilevers were modelled with COMSOL Multiphysics as superposition of smaller layers in which each layer sustained local stress obtained from stress evolution study. Results showed that the average strain gradients obtained from the experimental and FEM studies differ by ~5% and ~6% for film A and B, respectively with standard deviations lying between ±0.004 and ±0.009/µm. While this study established that stress gradient is responsible for the calculated strain gradient, it also emphasises that both parameters are proportional. Key words: Poly-SiGe, Strain gradient, FEM, COMSOL.

scholarly journals The Influence of the Strain and Stress Gradient in Determining Strain Fatigue Characteristics for Oscillatory Bending

Materials ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 173 ◽  
Author(s):  
Andrzej Kurek ◽  
Justyna Koziarska ◽  
Tadeusz Łagoda
Keyword(s):  
Aluminum Alloys ◽  
Compression Test ◽  
Strain Gradient ◽  
Stress Gradient ◽  
Fatigue Tests ◽  
Model Verification ◽  
Bending Test ◽  
Stress And Strain ◽  
Fatigue Characteristics ◽  
Gradient Surface

In this study, we created a new model to determine strain fatigue characteristics obtained from a bending test. The developed model consists of comparing the stress and strain gradient surface ratio for bending and tensile elements. For model verification, seven different materials were examined based on fatigue tests we conducted, or data available in the literature: 30CrNiMo8, 10HNAP, SM45C, 16Mo3 steel, MO58 brass, and 2017A-T4 and 6082-T6 aluminum alloys. As a result, we confirmed that the proposed method can be used to determine strain fatigue characteristics that agree with the values determined on the basis of a tensile compression test.

scholarly journals Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models

2017 ◽  
Vol 25 (7) ◽  
pp. 1429-1449 ◽  
Author(s):  
Samuel Forest ◽  
Karam Sab
Keyword(s):  
Strain Gradient ◽  
Finite Deformation ◽  
Stress Gradient ◽  
Higher Order ◽  
Second Order ◽  
Stress And Strain ◽  
Dynamical Equations ◽  
Generalized Continua ◽  
Micromorphic Theory ◽  
Gradient Models

Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presented, together with its relation to the second-order micromorphic model. The linearization of the combination of stress and strain gradient models is then shown to deliver formulations related to Eringen’s and Aifantis’s well-known gradient models involving the Laplacians of stress and strain tensors. Finally, the structures of the dynamical equations are given for strain and stress gradient media, showing fundamental differences in the dynamical behaviour of these two classes of generalized continua.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

Reliability Simulation and Forecast Based on Virtual Prototype for the Running System of Complicated Equipments

2014 ◽  
Vol 543-547 ◽  
pp. 195-198
Author(s):  
Li Jun Cao ◽  
Hui Bin Hu ◽  
Gui Bo Yu ◽  
Shu Hai Wang
Keyword(s):  
Probability Density ◽  
Local Stress ◽  
Virtual Prototype ◽  
Probability Density Distribution ◽  
Stress And Strain ◽  
Load Spectrum ◽  
Density Distribution Function ◽  
Running System ◽  
Maintenance Cycle ◽  
Damage Theory

The running system is the key part to finish training or battle tasks of complicated equipments. But formidable working conditions influence the measurement of load spectrums and it is difficult to analyze and forecast the reliability of running system. Actual vehicle experiments and virtual prototype are firstly combined to obtain complete load spectrum of running system. According to the materials S-N curve, stress and strain spectrums can be computed. Nominal stress method and local stress and strain method are combined with probability density accumulation damage theory to compute the probability density distribution function. Then, the reliability of running system can be forecasted, which provide adequate reference for the maintenance cycle confirmation and mission reliability prediction.

A Chemomechanical Model for Stress Evolution and Distribution in the Viscoplastic Oxide Scale During Oxidation

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Hailong Wang ◽  
Shengping Shen
Keyword(s):  
Oxide Scale ◽  
Maximum Stress ◽  
Stress Gradient ◽  
Oxidation Time ◽  
Stress Evolution ◽  
Oxide Interface ◽  
Temperature Oxidation ◽  
Substrate Interface ◽  
Oxide Substrate ◽  
Chemomechanical Model

Using the location-dependent growth strain, a chemomechanical model is developed for the analysis of the stress evolution and distribution in the viscoplastic oxide scale during high-temperature oxidation. The problem of oxidizing a semi-infinite substrate is formulated and solved. The numerical results reveal high compressive stress and significant stress gradient. The maximum stress is at the oxide/substrate interface and the minimum stress at the oxygen/oxide interface in short oxidation time, while the maximum stress is no longer at the oxide/substrate interface in long oxidation time. The stress evolutions at different locations are also presented. The predicted results agree well with the experimental data.

scholarly journals Influence of Orthotropy on Biomechanics of Peri-Implant Bone in Complete Mandible Model with Full Dentition

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xi Ding ◽  
Sheng-Hui Liao ◽  
Xing-Hao Zhu ◽  
Hui-Ming Wang
Keyword(s):  
Orthotropic Material ◽  
Tooth Enamel ◽  
Local Stress ◽  
Isotropic Case ◽  
Stress And Strain ◽  
Isotropic Model ◽  
Bone Interface ◽  
Multiple Data ◽  
Cad Models ◽  
The Impact

Objective.The study was to investigate the impact of orthotropic material on the biomechanics of dental implant, based on a detailed mandible with high geometric and mechanical similarity.Materials and Methods.Multiple data sources were used to elaborate detailed biological structures and implant CAD models. In addition, an extended orthotropic material assignment methodology based on harmonic fields was used to handle the alveolar ridge region to generate compatible orthotropic fields. The influence of orthotropic material was compared with the commonly used isotropic model and simplified orthotropic model.Results.The simulation results showed that the values of stress and strain on the implant-bone interface almost increased in the orthotropic model compared to the isotropic case, especially for the cancellous bone. However, the local stress concentration was more obvious in the isotropic case compared to that in orthotropic case. The simple orthotropic model revealed irregular stress and strain distribution, compared to the isotropic model and the real orthotropic model. The influence of orthotropy was little on the implant, periodontal ligament, tooth enamel, and dentin.Conclusion.The orthotropic material has significant effect on stress and strain of implant-bone interface in the mandible, compared with the isotropic simulation. Real orthotropic mechanical properties of mandible should be emphasized in biomechanical studies of dental implants.

Nonlinear semi-analytical nonlocal strain-gradient dynamic response investigation of phase-transition-induced transversely graded hierarchical viscoelastic nano/microplates

2019 ◽  
Vol 233 (15) ◽  
pp. 5388-5409 ◽  
Author(s):  
M Shariyat ◽  
F Farrokhi
Keyword(s):  
Strain Gradient ◽  
Viscoelastic Model ◽  
Functionally Graded ◽  
Special Technique ◽  
Stress And Strain ◽  
Transient Vibration ◽  
Size Dependent ◽  
Integration Schemes ◽  
Series Type ◽  
Nonlocal Strain Gradient

A functionally graded Boltzmann hierarchical viscoelastic model with both stress- and strain-gradient nonlocalities is developed and implemented to extract results that are more precise than results of Eringen's nonlocal elasticity model. The available size-dependent vibration analyses of the nano/microplates have focused on the frequency analysis and even not the time-dependent transient vibration analyses. In the present research, the forced and transient responses of the microplates are studied comprehensively, for the first time, using a three-element standard solid viscoelastic model. The studied transversely symmetric graded viscoelastic microplate and the relevant function of the material properties variations contain notable hints as well. Furthermore, the resulting new sixth-order nonlocal strain gradient integrodifferential equations are solved by a special technique that includes an analytical spatial Navier series-type solution and a trapezoidal and Runge–Kutta integration schemes, in time domain. Finally, the influences of the stress- and strain-gradient nonlocality parameters and the viscoelasticity parameters on the dynamic behaviors of the viscoelastic FGM microplates are investigated in details. Results show that the effects of the strain gradient nonlocality on the viscodynamic results may be much remarkable than those of the length scale nonlocality, in microscales.

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