A Corotational Flow Rule for Rigid Plastic Hardening Materials Based on Logarithmic Strain Tensor

2002 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mehdi Yeganeh ◽  
Alireza Saidi
Keyword(s):  
Yield Criterion ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Cauchy Stress ◽  
Logarithmic Strain ◽  
Rigid Plastic ◽  
Corotational Rate ◽  
Plastic Hardening ◽  
Von Mises

In this paper a flow rule for rigid plastic hardening materials based on von Mises yield criterion is introduced. This flow rule relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. Using different corotational rates in the proposed flow rule, the deviatoric Cauchy stress tensor is calculated for rigid plastic isotropic, kinematic and combined hardening materials in the simple shear problem at large deformations. For the purpose of verification, the results for different corotational rates are compared with the results presented in referenced articles.

Elastic-Plastic Modeling of the Hardening Materials Based on an Eulerian Strain Tensor and a Proper Corotational Rate

2005 ◽  
Author(s):  
Reza Naghdabadi ◽  
Kamyar Ghavam
Keyword(s):  
Kinematic Hardening ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Governing Equations ◽  
Plastic Part ◽  
Elastic Plastic ◽  
Eulerian Strain ◽  
Corotational Rate ◽  
Conjugate Stress

In this paper a model for analyzing elastic-plastic kinematic hardening materials is introduced, based on the additive decomposition of the corotational rate of an Eulerian strain tensor In this model, the elastic constitutive equation as well as the flow rule and the hardening equation is expressed in terms of the elastic and plastic parts of the corotational rate of the mentioned Eulerian stain tensor and its conjugate stress tensor. In the flow rule, the plastic part of the corotational rate of the Eulerian strain tensor is related to the difference of the deviatoric part of the conjugate stress and the back stress tensors. A proportionality factor is used in this flow rule which must be obtained from a consistency condition based on the von Mises yield criterion. A Prager type kinematic hardening model is used which relates the corotational rate of the back stress tensor to the plastic part of the corotational rate of the Eulerian strain tensor. Also in this paper a proper corotational rate corresponding to the Eulerian strain tensor is introduced. Finally the governing equations for the analysis of elastic-plastic kinematic hardening materials are obtained. As an application, these governing equations are solved numerically for the simple shear problem and the stress and back stress components are plotted versus the shear displacement. The results are compared with those, which are available in the literature.

A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

2003 ◽  
Vol 70 (5) ◽  
pp. 649-654 ◽  
Author(s):  
Y.-Q. Zhang ◽  
H. Hao ◽  
M.-H. Yu
Keyword(s):  
Plane Stress ◽  
Yield Criterion ◽  
Strength Criterion ◽  
Rigid Plastic ◽  
Strength Criteria ◽  
Special Cases ◽  
Characteristic Theory ◽  
Characteristic Methods ◽  
Von Mises ◽  
Suitable Characteristic

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.

scholarly journals A Method for Determining the Workability Diagram by Varying Friction Conditions in the Upsetting of a Cylinder between Flat Dies

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1411
Author(s):  
Dejan Movrin ◽  
Mladomir Milutinovic ◽  
Marko Vilotic ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Ductile Fracture ◽  
Yield Criterion ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Medium Carbon Steel ◽  
New Method ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Workability Diagram

This paper aims to develop a method for determining the workability diagram by varying frictional conditions in the cylinder upsetting test. The method is based on a known theoretical relationship between the average stress triaxiality ratio and in-surface strains if the initiation of fracture occurs at a traction-free surface. This relationship is valid for any rigid/plastic strain hardening material obeying the Mises-type yield criterion and its associated flow rule, which shows the wide applicability of the method. The experimental input to the method is the strain path at the site of fracture initiation. Neither experimental nor numerical determination of stress components is required at this site, though the general ductile fracture criterion involves the linear and quadratic invariants of the stress tensor. The friction law’s formulation is neither required, though the friction stress is the agent for varying the state of stress and strain at the site of ductile fracture initiation. The upsetting tests are carried out on normalized medium-carbon steel C45E, for which the workability diagram is available from the literature. Comparison of the latter and the diagram found using the new method shows that the new method is reliable for determining a certain portion of the workability diagram.

scholarly journals An ellipticity domain for the distortional Hencky logarithmic strain energy

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150510 ◽  
Author(s):  
Ionel-Dumitrel Ghiba ◽  
Patrizio Neff ◽  
Robert J. Martin
Keyword(s):  
Elastic Energy ◽  
Strain Energy ◽  
Strain Tensor ◽  
Energy Criterion ◽  
Logarithmic Strain ◽  
Hencky Energy ◽  
Von Mises ◽  
Deviatoric Part

We describe ellipticity domains for the isochoric elastic energy F ↦ ∥ dev n log ⁡ U ∥ 2 = ∥ log ⁡ F T F ( det F ) 1 / n ∥ 2 = 1 4 ∥ log ⁡ C ( det C ) 1 / n ∥ 2 for n =2,3, where C = F T F for F ∈ GL + ( n ). Here, dev n log U = log U − ( 1 / n )   tr ( log U ) ⋅ 1 is the deviatoric part of the logarithmic strain tensor log ⁡ U . For n =2, we identify the maximal ellipticity domain, whereas for n =3, we show that the energy is Legendre–Hadamard (LH) elliptic in the set E 3 ( W   H iso , LH , U , 2 3 ) := { U ∈ PSym ( 3 ) | ∥ dev 3 log ⁡ U ∥ 2 ≤ 2 3 } , which is similar to the von Mises–Huber–Hencky maximum distortion strain energy criterion. Our results complement the characterization of ellipticity domains for the quadratic Hencky energy W   H ( F ) = μ ∥ dev 3 log ⁡ U ∥ 2 + ( κ / 2 ) [ tr ( log ⁡ U ) ] 2 , U = F T F with μ >0 and κ > 2 3 μ , previously obtained by Bruhns et al.

Elastic-Plastic Modeling of Kinematic Hardening Materials Based on F=FeFp Decomposition and the Logarithmic Strain Tensor

Volume 1 ◽  
2004 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Flow Rule ◽  
Deformation Gradient Tensor ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Corotational Rate ◽  
Stress Components ◽  
Shear Problem

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material.

scholarly journals Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nelli Aleksandrova
Keyword(s):  
Structural Steel ◽  
Yield Criterion ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Open Hole ◽  
Practical Engineering ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Material Compressibility

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies.

Theoretical Analysis for the Redrawing of Cylindrical Cups through Conical Dies without Pressure Sleeves

1968 ◽  
Vol 10 (2) ◽  
pp. 141-152 ◽  
Author(s):  
B. Fogg
Keyword(s):  
Yield Criterion ◽  
Minimum Energy ◽  
Present Theory ◽  
Detailed Examination ◽  
Flow Rule ◽  
Stress Equilibrium ◽  
Die Profile ◽  
The Difference ◽  
Process Work ◽  
Von Mises

A theory for the redrawing of cylindrical cups through conical dies is presented. In the absence of a pressure sleeve a zone of unconstrained drawing exists prior to the conical zone and the principle of minimum energy is used to establish the extent of the zone and the associated deformation and stresses. A linearization of the von Mises yield criterion for plane stress problems is adopted and use of the flow rule associated with this criterion allows the variation of thickness across an element to be taken into account in the solution of the stress equilibrium equation; the strains can also be determined without resorting to numerical integration. Because the deformation during redrawing takes place in a series of discrete steps, work-hardening can be conveniently included in the analysis. Bending and unbending contribute significantly to the process work and a more detailed examination of the mechanism is justified. The present theory allows the effects of friction, die angle and die intersection radius to be examined but the punch load/redrawing ratio relation has been considered for only one die profile and clearance. The results for the redrawing of 70/30 brass cups with and without interstage annealing are compared with experimental redrawing loads and whilst excellent agreement exists for the near-limiting redrawing ratios, the theory considerably over-estimates the punch loads at the smaller ratios. A possible reason for the difference is discussed.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

ADAPTIVE INCREMENTAL FINITE ELEMENT PROCEDURE FOR SOLVING ELASTOPLASTIC FRICTIONAL CONTACT PROBLEMS SUBJECTED TO NORMAL AND TANGENTIAL LOADS

2014 ◽  
Vol 06 (03) ◽  
pp. 1450031 ◽  
Author(s):  
W. S. ABDALLA ◽  
S. S. ALI-ELDIN ◽  
M. R. GHAZY
Keyword(s):  
Finite Element ◽  
Frictional Contact ◽  
Programming Model ◽  
Yield Criterion ◽  
Contact Problems ◽  
Flow Rule ◽  
Friction Behavior ◽  
Elastoplastic Behavior ◽  
Coulomb’S Friction ◽  
Von Mises

This paper presents a numerical model for analyzing the stresses and displacements of deformable bodies in contact with the presence of friction and material nonlinearity. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (ICPM) under inequality contact constraints and friction conditions. The classical Coulomb's friction law and the Prandtl–Reuss flow rule with the von Mises yield criterion are used to simulate the interface friction conditions and the elastoplastic behavior of the contacting bodies, respectively. The Lagrange multiplier approach is adopted for imposing the contact constraints. Furthermore, an effective adaptive incremental procedure is developed for solving the elastoplastic frictional contact problems. Examples for the frictional contact having advancing and receding nature are analyzed. The obtained results prove the ability of the developed procedure to investigate the sequence of different events during monotonic application of external loads. In addition, the results elucidate the effect of external side force on the friction behavior in the presence of plastic deformation. Good agreement has been found with published results.

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