Comparison of the effects of hydrostatic pressure and the third invariant of deviatoric stress tensor on non-linear viscoelastic deformation in cellulose nitrate

1980 ◽  
Vol 15 (7) ◽  
pp. 1609-1613 ◽  
Author(s):  
T. Nishitani ◽  
Y. Murayama
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Tensor ◽  
Cellulose Nitrate ◽  
Deviatoric Stress ◽  
Viscoelastic Deformation ◽  
The Third ◽  
Third Invariant ◽  
Non Linear ◽  
Linear Viscoelastic ◽  
Deviatoric Stress Tensor

Effects of Third Invariant of Deviatoric Stress Tensor on Transient Creep of Thick-Walled Tubes

1974 ◽  
Vol 96 (3) ◽  
pp. 207-213 ◽  
Author(s):  
S. Murakami ◽  
Y. Yamada
Keyword(s):  
Mild Steel ◽  
Stress Tensor ◽  
Equivalent Stress ◽  
Transient Creep ◽  
Deviatoric Stress ◽  
The Third ◽  
Third Invariant ◽  
Stress Functions ◽  
Thin Walled ◽  
Deviatoric Stress Tensor

Creep theories with the effect of the third invariant of the deviatoric stress tensor and their accuracy as applied to practical problems are discussed. Constitutive equations for transient creep are first formulated by assuming creep potentials of the Prager-Drucker and the Bailey-Davis type together with the associated equivalent stress functions. Strain-hardening and time-hardening hypotheses are assumed. Experimental results hitherto reported for thin-walled tubes are discussed according to these equations. Then, the creep of a thick-walled tube of mild steel is analyzed and compared with experiments.

Study on Character of Triaxial Extension Strength of Compacted Clay

2011 ◽  
Vol 243-249 ◽  
pp. 2183-2187
Author(s):  
Jun Xin Liu ◽  
Zhong Fu Chen ◽  
Wei Fang Xu
Keyword(s):  
Stress Tensor ◽  
Triaxial Compression ◽  
Deviatoric Stress ◽  
Stress Deviator ◽  
Strength Ratio ◽  
Compacted Clay ◽  
The Third ◽  
Third Invariant ◽  
Coulomb Criterion ◽  
Triaxial Extension

For soils, failure occurs with lower deviatoric stress under the same pressure (the first invariant of stress tensor) in TXE compared with the strength of the triaxial compression, which is indicated that the strength of soils strongly depends on the third invariant of stress deviator; Although in the traditional Mohr-Coulomb criterion it can be reflected in difference of strength between triaxial extension and compression under the same pressure, it’s nothing to do with the pressure for the strength ratio between triaxial extension and compression. By TXC and TXE, changes of deviatoric stress and the ratio with the pressure were studied

Residual Stress Analysis of the Autofrettaged Thick-Walled Tube Using Nonlinear Kinematic Hardening

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
G. H. Farrahi ◽  
George Z. Voyiadjis ◽  
S. H. Hoseini ◽  
E. Hosseinian
Keyword(s):  
Plastic Deformation ◽  
Residual Stresses ◽  
Stress Tensor ◽  
Kinematic Hardening ◽  
Deviatoric Stress ◽  
Material Behavior ◽  
Behavior Modeling ◽  
The Third ◽  
Deviatoric Stress Tensor ◽  
Stress Invariant

Recent research indicates that accurate material behavior modeling plays an important role in the estimation of residual stresses in the bore of autofrettaged tubes. In this paper, the material behavior under plastic deformation is considered to be a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. The yield surface is assumed to depend on the first stress invariant and the Lode angle parameter which is defined as a function of the second and the third invariants of the deviatoric stress tensor. Furthermore for estimating the unloading behavior, the Chaboche's hardening evolution equation is modified. These modifications are implemented by adding new terms that include the effect of the first stress invariant and pervious plastic deformation history. For evaluation of this unloading behavior model a series of loading-unloading tests are conducted on four types of test specimens which are made of the high-strength steel, DIN 1.6959. In addition finite element simulations are implemented and the residual stresses in the bore of a simulated thick-walled tube are estimated under the autofrettage process. In estimating the residual stresses the effect of the tube end condition is also considered.

Mechanical Behavior of Nonlinear Visco-Elastic Celluloid Under Superimposed Hydrostatic Pressure

1978 ◽  
Vol 100 (3) ◽  
pp. 271-276 ◽  
Author(s):  
T. Nishitani
Keyword(s):  
Hydrostatic Pressure ◽  
Deformation Behavior ◽  
Proportional Loading ◽  
Distinctive Features ◽  
The Third ◽  
Third Invariant ◽  
Stress Strain Relation ◽  
Tubular Specimens ◽  
Deviatoric Stress Tensor ◽  
Good Agreement

The behavior of polymers is significantly influenced by hydrostatic pressure. In this paper, the effects of hydrostatic pressure and the third invariant of the deviatoric stress tensor on the nonlinear visco-elastic deformation of celluloid are first discussed in connection with experiments of torsion of tubular specimens and tension of uniaxial specimens. The distinctive features of the deformation behavior in creep and for proportional loading (namely, uniform rate of stress increase with time) under superimposed hydrostatic pressure are investigated by using the nonlinear visco-elastic celluloid. The stress-strain relation of the nonlinear visco-elastic media with regard to the effect of the hydrostatic pressure is deduced from the invariant theory with an hypothesis of creep potential. The deduced relation gives fairly good agreement with the actual observations.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

Effect of J3 on Creep and Relaxation in a Plate With a Central Hole

1977 ◽  
Vol 99 (1) ◽  
pp. 76-79
Author(s):  
R. P. Goel
Keyword(s):  
Central Hole ◽  
Relaxation Phenomena ◽  
The Third ◽  
Relaxation Problem ◽  
Third Invariant ◽  
Creep Problem ◽  
Deviatoric Stress Tensor ◽  
Theoretical Results ◽  
Lower Contact ◽  
Walled Cylinder

Mises type of creep equations have been used widely to study creep and relaxation phenomena. In a study by Murakami and Yamada [1] inclusion of J3, the third invariant of the deviatoric stress tensor, in the Mises type creep theories helped explain the deviations between experimental and theoretical results of a thick-walled cylinder creeping under an internal pressure. Similarly, the present study investigates the effects of including J3 in the creep constitutive equations on creep and relaxation in a circular plate with a central hole. The results show that inclusion of J3 in the creep equations tends to predict higher values of Σθ (tangential stress) in the creep problem and lower values of Σθ and Σr in the relaxation problem. Lower value of Σr in the relaxation problem implies a lower contact force at the interface of a press-fitted joint.

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