Effect of the third stress invariant on the characteristic curves of a material

1972 ◽  
Vol 4 (4-6) ◽  
pp. 471-475
Author(s):  
A. F. Kregers
Keyword(s):  
Characteristic Curves ◽  
The Third ◽  
Third Stress Invariant ◽  
Stress Invariant

scholarly journals A GTN-like Model for Plastic Porous Materials

2014 ◽  
Vol 4 (6) ◽  
pp. 734-738
Author(s):  
L. Siad ◽  
S. C. Gangloff
Keyword(s):  
Constitutive Model ◽  
Yield Function ◽  
Isotropic Hardening ◽  
Extended Version ◽  
Gtn Model ◽  
Hardening Model ◽  
The Third ◽  
Third Stress Invariant ◽  
Stress Invariant ◽  
Good Agreement

An extended version of the well-known Gurson-Tvergaard-Needleman (GTN) isotropic hardening model is presented in this paper. The yield function of the proposed constitutive model possesses the distinctiveness to explicitly depend upon the third stress invariant. The presented constitutive model is used to analyze the necking of a round tensile bar. As long as softening initiation of specimen is not reached, the obtained numerical results highlight similarities and good agreement with those provided by the use of the GTN model. However, discrepancy shows up as soon as specimen failure starts.

On the Development and Identification of Phenomenological Damage Models - Application to Industrial Wire Drawing and Rolling Processes

2013 ◽  
Vol 554-557 ◽  
pp. 213-226 ◽  
Author(s):  
Trong Son Cao ◽  
Christian Bobadilla ◽  
Pierre Montmitonnet ◽  
Pierre Olivier Bouchard
Keyword(s):  
Stress Tensor ◽  
Damage Model ◽  
Stress Triaxiality ◽  
Wire Drawing ◽  
Damage Models ◽  
The Third ◽  
Third Stress Invariant ◽  
Lode Angle ◽  
Stress Invariant ◽  
Angle Parameter

The continuum thermodynamics-based Lemaitre damage model is nowadays widely used to deal with coupled damage analyses for various mechanical applications (e.g. forming process simulations). However, such a model, which only accounts for the stress triaxiality (the ratio between the first and the second invariants of stress tensor) has been found to give incorrect results under shear dominated loading (in terms of damage location as well as risk of crack). Several recent studies have demonstrated the importance of the third stress invariant in damage prediction; the Lode angle parameter is generally used to include it. The idea is to describe completely the stress state in damage model’s formulations, which is defined by the equivalent stress, the stress triaxiality ratio and the Lode angle parameter. This later parameter has proved to have an important influence on ductile damage under low stress triaxiality. Xue’s coupled damage model accounts for the third invariant of the deviatoric stress tensor, allowing a better balance between respective effects of shear and elongation on damage. Some extensions of more physically based damage models, such as the Gurson-Tvergaard-Needleman model, have also been presented to account for this influence of the third stress invariant. In the present work, the phenomenological damage models have been implemented in Forge® Finite Element (FE) software to investigate ductile damage occurring during industrial forming processes. This paper presents the comparative study of Xue’s model and Lemaitre’s model. A complete procedure is detailed to identify the material and damage parameters from experimental mechanical tests on high carbon steel. This identification process has been carried out both for Lemaitre’s coupled damage model and Xue’s coupled damage model. Application to wire drawing followed by flat rolling shows that in such shear-inducing processes, these models predict damage at different locations, due to their different emphasis on shear with respect to elongational strain damage.

Thermoviscoplasticity Theory Incorporating the Third Deviatoric Stress Invariant

2015 ◽  
Vol 51 (1) ◽  
pp. 85-91 ◽  
Author(s):  
M. E. Babeshko ◽  
Yu. N. Shevchenko ◽  
N. N. Tormakhov
Keyword(s):  
Deviatoric Stress ◽  
The Third ◽  
Stress Invariant

Lode Dependences for Isotropic Pressure-Sensitive Elastoplastic Materials

1990 ◽  
Vol 57 (3) ◽  
pp. 498-506 ◽  
Author(s):  
J. P. Bardet
Keyword(s):  
Experimental Investigations ◽  
Present Communication ◽  
Modified Model ◽  
True Triaxial ◽  
The Third ◽  
Pressure Sensitive ◽  
Isotropic Pressure ◽  
Elastoplastic Materials ◽  
Lode Angle ◽  
Stress Invariant

Experimental investigations indicate that the third stress invariant; Lode angle α affects significantly the behavior of pressure sensitive materials. The present communication presents a formulation to account for α in isotropic pressure-sensitive elastoplastic materials. Seven Lode dependences are reviewed. A new one, referred to as LMN, in proposed to generalize Lade and Duncan, and Matsuoka and Nakai failure surfaces. The formulation is general enough to introduce α into the isotropic elastoplastic modes which are only developed in terms of first and second-stress invariants. As an illustration, several Lode dependences are introduced into Roscoe and Burland model. The performance of the modified model is estimated by comparing experimental and analytical results in the case of true triaxial loadings on normally consolidated clay.

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