On Infinitesimal Plastic Shear Deformation after Finite Plastic Tensile Loading and Partial Unloading

1988 ◽  
pp. 501-504
Author(s):  
Akhtar S. Khan ◽  
Xinwei Wang
1996 ◽  
Vol 428 ◽  
Author(s):  
D. Beckers ◽  
H. Schroeder ◽  
I. Eppler ◽  
W. Schilling

AbstractAl and Al- alloys are commonly used as interconnect materials in integrated electronic devices. Stress induced voiding and degradation of metal lines by electromigration are closely related to the stresses in the lines.We have studied the strain and stress evolution during thermal cycling, isothermal relaxation and due to electromigration in passivated Al and AlSi(1%)Cu(0.5%) lines by Xray diffraction with variation of experimental parameters such as the aspect ratio and the electrical current density. Furthermore the extent of voiding and plastic shear deformation has been determined from the experimental metal strains with the help of finite element calculations.Main results are: 1) During thermal cycling the voiding is less than 2.10-3. The extent of plastic shear deformation increases with increasing line width and with decreasing flowstress. 2) During isothermal relaxation void growth occurs but no significant change in the plastic shear deformation. 3) An electric current in the lines causes no measurable additional change of the volume averaged stresses up to line failure.


Author(s):  
Roger W. Chan ◽  
Thomas Siegmund

Previous empirical studies have shown that vocal fold tissues exhibit nonlinear viscoelastic behaviors under different loading conditions. Hysteresis and strain rate-dependence of stress-strain curves have been observed for different layers of vocal fold tissues when subjected to cyclic tensile loading [1,2]. Nonlinear viscoelastic response has also been described for vocal fold tissues subjected to constant strain and constant stress tests under both tensile loading and large-strain shear deformation conditions [3,4]. These findings cannot be adequately described by many of the traditional constitutive formulations of linear and quasilinear viscoelasticity. For instance, models based on Y. C. Fung’s quasilinear viscoelastic theory typically apply two separate functions to describe the time dependence and the strain dependence of stress (e.g., the reduced relaxation function G(t) and the elastic response σe(ε), respectively), and combine the two functions by the Boltzmann superposition principle [5]. Such formulations assume that time dependence and strain dependence can be separated. However, recently obtained stress relaxation data of vocal fold tissues under various magnitudes of applied shear strain indicated that they are not separable, as relaxation became slower with increasing strain [4]. This paper attempts to characterize some nonlinear viscoelastic behaviors of vocal fold tissues under tensile and shear deformation conditions based on an implementation of the Bergstrom-Boyce model [6,7].


Nature ◽  
1988 ◽  
Vol 336 (6194) ◽  
pp. 52-54 ◽  
Author(s):  
T. Dunstan ◽  
J. R. F. Arthur ◽  
A. Dalili ◽  
O. O. Ogunbekun ◽  
R. K. S. Wong

1996 ◽  
Vol 436 ◽  
Author(s):  
I. Eppler ◽  
H. Schroeder ◽  
U. Burges ◽  
W. Schilling

AbstractPassivated metal lines, commonly used in integrated circuits, show thermally induced stresses due to the difference of the thermal expansion coefficients of the lines and their surroundings. These stresses cause voidage and plastic flow of the lines. Aim of the analysis was to derive equations connecting experimentally measured strains or stresses by the X-ray diffraction and wafer curvature techniques with the magnitude of voidage and plastic shear deformation of the lines.Using the concepts of linear elasticity the volume averaged stresses of an array of parallel interconnects embedded in a passivation layer on a flat substrate are analysed. Equations are derived connecting the volume averaged stresses in the metal and in the passivation with the “Heigen-strains” of the metal which characterize the true (stress free) thermal strains and plastic deformation strains of the metal. The coefficients entering these equations are determined from (elastic) finite element method (FEM) calculations performed for various geometries and aspect ratios of the metal lines. Choosing the proper values of the coefficients allows the eigen- strains to be determined from the experimental data.By comparison of the evaluated eigen-strains with the purely elastic eigen-strains ΔαΔT the extent of voidage and/or plastic shear deformation of passivated metal lines caused by thermally induced stresses can be determined model independently.


2011 ◽  
Vol 64 (1) ◽  
pp. 81-84 ◽  
Author(s):  
X.D. Wang ◽  
Q.P. Cao ◽  
J.Z. Jiang ◽  
H. Franz ◽  
J. Schroers ◽  
...  

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