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.

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.

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.

scholarly journals Elastomeric Impression Materials: A Comparison of Accuracy of Multiple Pours

2011 ◽  
Vol 12 (4) ◽  
pp. 272-278 ◽  
Author(s):  
Dheeraj Kumar ◽  
Anand U Madihalli ◽  
K Rajeev Kumar Reddy ◽  
Namrataa Rastogi ◽  
NT Pradeep
Keyword(s):  
Clinical Significance ◽  
Dimensional Stability ◽  
Central Hole ◽  
Central Incisor ◽  
Impression Material ◽  
Maxillary Central Incisor ◽  
Dimensional Changes ◽  
The Third ◽  
Impression Materials ◽  
Time Periods

ABSTRACT Aim The aim of the present study is to compare the various elastomeric impression materials in terms of accuracy and dimensional stability, with respect to obtaining multiple casts from a single elastomeric impression at various times of pours. Materials and methods Three master dies were prepared for the impression making, two of these were made of brass containing a central hole with undercuts. The third die simulated a conventionally prepared typodont maxillary central incisor. Three elastomeric impression materials were chosen for the study. Each impression was poured at various time periods. Casts thus obtained were evaluated under a traveling microscope to evaluate various dimensional changes. Results Addition silicones provided dies which were shorter in height and bigger in diameter. Polyethers provided dies which were shorter in both height and diameter. Condensation silicones showed insignificant changes from the master die at the immediate pour but deteriorated rapidly after that in subsequent pours. Conclusion None of the impression material showed a consistent behavior up to the fourth pour. They occasionally showed deviation from the pattern, but all these values were statistically insignificant. Polyethers showed lesser ability than both the addition silicones as well as the condensation silicones to recover from induced deformation. Clinical significance Addition silicones as well as the condensation silicones have better ability to recover from induced deformation when compared to polyether. How to cite this article Kumar D, Madihalli AU, Reddy KRK, Rastogi N, Pradeep NT. Elastomeric Impression Materials: A Comparison of Accuracy of Multiple Pours. J Contemp Dent Pract 2011;12(4):272-278.

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

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