Stress That Counteracts Electromigration: Threshold Versus Kinetic Approach

1994 ◽  
Vol 356 ◽  
Author(s):  
E. Glickman ◽  
N. Osipov ◽  
A. Ivanov
Keyword(s):  
Plastic Flow ◽  
Material Properties ◽  
Effective Viscosity ◽  
Threshold Stress ◽  
Stress Gradient ◽  
Material Constant ◽  
Induced Stress ◽  
Net Flux ◽  
Constant Yield ◽  
Coble Creep

AbstractThe paper analyzes electromigration (EM) conditions and material properties that determine the maximum EM induced stress, σa, and stress gradient, ∇σ, which counteract EM flow in interconnects.The first systematic data on the drift velocity vs. stripe length, L, current density, j, and temperature are presented for Al lines. In contrast to the conventional approach to the Blech problem with σa taken to be a material constant (“yield strength”), the observations suggest that σa increases with j. The stress adjustment is shown to result from the imperative coupling of the net flux of material directed to the downwind end of the stripe with the flux of plastic flow (creep) responsible for stress relaxation. The effect of parameters of the constitutive equation assumed to describe the plastic flow kinetics, namely that of strain rate exponent, threshold stress, and creep, effective viscosity, on the stress cya is considered. To account for the creep viscosity, η, obtained unpassivated aluminum stripes from EM experiments, a model for the attachment-controlled Coble creep is suggested.

scholarly journals Comparison Between the Hyperelastic Behavior of Fresh and Frozen Equine Articular Cartilage in Various Joints

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Hyeon Lee ◽  
William D. Campbell ◽  
Kelcie M. Theis ◽  
Margaret E. Canning ◽  
Hannah Y. Ennis ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Material Properties ◽  
Statistical Models ◽  
Solid Phase ◽  
Material Constant ◽  
Hyperelastic Material ◽  
Aggregate Modulus ◽  
Significant Difference ◽  
Fluid Load ◽  
Hyperelastic Model

Abstract Fresh and frozen cartilage samples of the fetlock, carpus, and stifle were collected from 12 deceased horses. Half were measured immediately following extraction, and half were frozen for seven days and then measured. Seven indentations (various normalized displacements) were implemented with an indention rate of 0.1 mm/s. Solid phase aggregate modulus (Es), hyperelastic material constant (α), and fluid load fraction (F′) of equine articular cartilage were assessed using the Ogden hyperelastic model. The properties were statistically compared in various joints (fetlock, carpus, and stifle), and between fresh and frozen samples using various statistical models. There was no statistical difference between the fetlock and carpus in the aggregate modulus (p = 0.5084), while both were significantly different from the stifle (fetlock: p = 0.0017 and carpus: p = 0.0406). For the hyperelastic material constant, no statistical differences between joints were observed (p = 0.3310). For the fluid load fraction, the fetlock and stifle comparison showed a difference (p = 0.0333), while the carpus was not different from the fetlock (p = 0.1563) or stifle (p = 0.3862). Comparison between the fresh and frozen articular cartilage demonstrated no significant difference among the joints in the three material properties: p = 0.9418, p = 0.7031, and p = 0.9313 for the aggregate modulus, the hyperelastic material constant, and the fluid load fraction, respectively.

scholarly journals Model of layered flow of viscous-plastic Bingham fluid in the extruder channel

2018 ◽  
Vol 80 (2) ◽  
pp. 58-63
Author(s):  
A. V. Gukasyan
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Plastic Flow ◽  
Significant Influence ◽  
Effective Viscosity ◽  
Piston Flow ◽  
Layered Flow ◽  
Discharge Pressure ◽  
Pressure Characteristics

The analysis is carried out and the presence of a zone of a piston flow, which has a significant influence both on the process of extrusion, and on the determination of the discharge-pressure characteristics of the screw, is established. It is noted that the effective viscosity has a physical meaning if the shear rate to which it corresponds is indicated. The effective viscosity is considered to consist of two components: the plastic viscosity corresponding to the viscosity of the Newtonian fluid and the structural viscosity that characterizes the shear resistance caused by the tendency of the solid particles contained in the Bingham liquid to form a structure. The effective viscosity is introduced into many hydrodynamic equations if the shear rate to which it corresponds is known. In the auger channel there are zones of forced flow created by the dynamic shear stress and the reverse flow of the head resistance created by the overpressure. The shear rate in the auger channel is marked by considerable heterogeneity and determines the complex nature of the shear deformation of the material during extrusion. Regardless of the pressure amplitude, the rigid core can not completely disappear, because for very small dimensions of the nucleus the pressure value must be very large, and with the disappearance of the plastic flow it must become infinite. Thus, the dependence of the shear stress on the shear rate for the flow of a Bingham viscoplastic fluid is always nonlinear for any values of the shear rate. An important element in the calculation of the discharge-pressure characteristics of the extrusion process is the localization of the plastic flow in the screw channel. As a result of the analysis of the model of the layered flow of viscoplastic Bingham liquid in the extruder channel, it is established that there is a zone of piston flow that exerts a significant influence both on the process of extrusion and on the determination of the discharge and pressure characteristics of the screw.

scholarly journals Numerical Modeling of the Effect of Randomly Distributed Inclusions on Fretting Fatigue-Induced Stress in Metals

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 836 ◽  
Author(s):  
Qingming Deng ◽  
Nadeem Bhatti ◽  
Xiaochun Yin ◽  
Magd Abdel Wahab
Keyword(s):  
Material Properties ◽  
Volume Ratio ◽  
Fatigue Behaviour ◽  
Fretting Fatigue ◽  
Volume Element ◽  
Homogeneous Material ◽  
The Finite Element Method ◽  
Multiple Cracking ◽  
Induced Stress ◽  
Peak Shear Stress

The analysis of fretting fatigue plays an important role in many engineering fields. The presence of heterogeneity may affect the performance of a machine or a structure, including its lifetime and stability. In this paper, the effect of randomly distributed micro inclusions on the fretting fatigue behaviour of heterogeneous materials is analysed using the finite element method (FEM) for different sizes, shape and properties of inclusions. The effect of micro inclusions on macroscopic material properties is also considered by representative volume element (RVE). It is shown that the influence of micro inclusions on macroscopic material properties cannot be ignored, and the shape and size of the inclusions have less effect on the macroscopic material properties as compared to the material properties of inclusion and volume ratio. In addition, various parameters of inclusions have little effect on the peak tensile stress, which remains almost the same as homogeneous material. Peak shear stress occurs at many places inside the specimen, which can result in multiple cracking points inside the specimen, as well as at the contact surface. Moreover, the stress band formed by the stress coupling between adjacent inclusions may have an important influence on the direction of crack growth.

PREDICTION OF CRANKSHAFT FATIGUE LIMIT LOAD BY CRACK-MODELING TECHNIQUE

2011 ◽  
Vol 10 (01) ◽  
pp. 127-134 ◽  
Author(s):  
XIAO PING CHEN ◽  
XIAO LI YU ◽  
RU FU HU ◽  
JIAN FENG LI
Keyword(s):  
Stress Intensity ◽  
Fatigue Limit ◽  
Material Properties ◽  
Threshold Stress ◽  
Limit Load ◽  
Processing Technology ◽  
Modeling Technique ◽  
Threshold Stress Intensity ◽  
Stress Intensity Range ◽  
Different Types

In this paper, combining the previous crankshaft fatigue test data with Crack-Modeling Technique, the threshold stress intensity range, ΔKth of crankshaft can be derived. The calculated threshold, ΔKth takes the effect of material properties and processing technology into account. Then, using the threshold, ΔKth, we can predict the fatigue limit load of the different types of crankshafts with the same material properties and processing technology by Crack-Modeling Technique. This study shows that the standard crack may be a good equivalent to the crankshaft stress concentration and the prediction of the crankshaft fatigue limit load is accurate.

scholarly journals Analysis on the Behavior of Nonpropagating Fatigue Cracks under Steep Stress Gradients

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hao Wu ◽  
Qiuying Lu
Keyword(s):  
Material Properties ◽  
Notch Root ◽  
Fatigue Cracks ◽  
Stress Gradient ◽  
Local Stress ◽  
Characteristic Size ◽  
Short Crack ◽  
Stress Gradients ◽  
Applied Loading ◽  
Experimental Values

A mechanism for the formation of nonpropagating fatigue cracks ahead of a notch root is presented. The stress gradients near the elongated notch root along with the propagation of short crack and the resulting nonpropagating crack lengthsanpcare estimated. The local stress which is higher than the unnotched material fatigue limitS0initiates the crack from a notch root and local steep stress gradient as a very important element leads to the nonpropagating crack. The value ofanpcdepends on the material properties, and specimen geometry as well as applied loading. The characteristic size of the short cracka0which depends on the material properties associates with the fatigue stress concentration factorKf. The estimated values ofanpcare in fairly good agreement with the experimental values available.

EFFECT OF RANDOM SYSTEM PROPERTIES ON INITIAL BUCKLING OF COMPOSITE PLATES RESTING ON ELASTIC FOUNDATION

2008 ◽  
Vol 08 (01) ◽  
pp. 103-130 ◽  
Author(s):  
ACHCHHE LAL ◽  
B. N. SINGH ◽  
RAKESH KUMAR
Keyword(s):  
Elastic Foundation ◽  
Material Properties ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Material Constant ◽  
Random System ◽  
Pasternak Model ◽  
Random System Properties

In this paper, the effects of randomness in the material properties and foundation stiffness parameters on the elastic buckling of laminated composite plate resting on elastic foundation subjected to uniform in-plane edge compression are studied. Higher order shear deformation theory has been used for the plates. The interaction between the plate and foundation is included in the formulation of a two-parameter Pasternak model. A C0finite element method is used for treating the random eigenvalue problem. The uncertain lamina material properties and the foundation stiffness parameters are modeled as independent basic random variables. A mean-centered first order perturbation technique is adopted to examine the stochastic characteristics of the buckling load. From the results presented for laminated composite plates resting on elastic foundations with different boundary conditions, the influence of variation of material constant, foundation stiffness parameters, edge in-plane forces, side-to-thickness ratio, plate aspect ratio, and variation in standard deviation of material properties on the buckling response has been investigated. The results have been compared with those available in the literature and from an independent Monte Carlo simulation.

A Parametric Investigation on the Neo-Hookean Material Constant

2014 ◽  
Vol 915-916 ◽  
pp. 853-857 ◽  
Author(s):  
Siti Hajar Mohd Yusop ◽  
Mohd Nor Azmi Ab Patar ◽  
Anwar P.P. Abdul Majeed ◽  
Jamaluddin Mahmud
Keyword(s):  
Constitutive Equation ◽  
Material Properties ◽  
Parametric Study ◽  
Strain Energy ◽  
Deformation Behaviour ◽  
Strain Energy Function ◽  
Material Constant ◽  
Hyperelastic Materials ◽  
Material Parameters ◽  
To Come

This paper assesses the Neo-Hookean material parameters pertaining to deformation behaviour of hyperelastic material by means of numerical analysis. A mathematical model relating stress and stretch is derived based on Neo-Hookeans strain energy function to evaluate the contribution of the material constant, C1, in the constitutive equation by varying its value. A systematic parametric study was constructed and for that purpose, a Matlab programme was developed for execution. The results show that the parameter (C1) is significant in describing material properties behaviour. The results and findings of the current study further enhances the understanding of Neo-Hookean model and hyperelastic materials behaviour. The ultimate future aim of this study is to come up with an alternative constitutive equation that may describe skin behaviour accurately. This study is novel as no similar parametric study on Neo-Hookean model has been reported before.

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