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.

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.

Analysis of the Contact Deformation of Tread Blocks

1992 ◽  
Vol 20 (4) ◽  
pp. 230-253 ◽  
Author(s):  
T. Akasaka ◽  
K. Kabe ◽  
M. Koishi ◽  
M. Kuwashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Behavior ◽  
Contact Deformation ◽  
The Finite Element Method ◽  
The Road ◽  
Loss Of Contact ◽  
Tread Rubber ◽  
Good Agreement ◽  
Rubber Block

Abstract The deformation behavior of a tire in contact with the roadway is complicated, in particular, under the traction and braking conditions. A tread rubber block in contact with the road undergoes compression and shearing forces. These forces may cause the loss of contact at the edges of the block. Theoretical analysis based on the energy method is presented on the contact deformation of a tread rubber block subjected to compressive and shearing forces. Experimental work and numerical calculation by means of the finite element method are conducted to verify the predicted results. Good agreement is obtained among these analytical, numerical, and experimental results.

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 Study of Influence of Width to Thickness Ratio in Sheet Metals on Bendability under Ambient and Superimposed Hydrostatic Pressure

2021 ◽  
Vol 2 (3) ◽  
pp. 542-558
Author(s):  
Mohammadmehdi Shahzamanian ◽  
David Lloyd ◽  
Amir Partovi ◽  
Peidong Wu
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Ratio ◽  
Fracture Strain ◽  
Stress Triaxiality ◽  
Volumetric Strain ◽  
Thickness Ratio ◽  
Sheet Metals ◽  
The Finite Element Method ◽  
Bending Strain ◽  
Good Agreement

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.

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