Elastic-Plastic Tension-Torsion in a Circular Bar of Rate-Sensitive Material

1979 ◽  
Vol 46 (2) ◽  
pp. 311-316 ◽  
Author(s):  
S. A. Meguid ◽  
J. D. Campbell
Keyword(s):  
Yield Criterion ◽  
Effective Strain ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Sensitive Material ◽  
Linear Partial Differential Equations ◽  
Partial Pivoting ◽  
Interaction Curves ◽  
Circular Bar ◽  
Von Mises

A theoretical and numerical investigation is made of the behavior of a circular bar of elastic-viscoplastic material subjected to either proportional or nonproportional straining in tension and torsion. The tensile properties of the material are assumed to be adequately represented by the empirical formula of Bodner and Symonds, which is based on experimental results for mild steel. The analysis employs Perzyna’s generalization of von Mises’ yield criterion, and the associated plastic flow rule. Elastic compressibility is taken into account. The stresses, strains, and loading paths are determined for four prescribed straining paths; the results were obtained by solving numerically, using Crout’s method with partial pivoting, a system of six simultaneous quasi-linear partial differential equations of hyperbolic type. Closed-form analytical solutions are also obtained for the stresses, load, and torque corresponding to fully plastic conditions; interaction curves are plotted relating load and torque under these conditions, for quasi-static straining and for a range of finite effective strain rates.

A Semi-Analytical 3-D Solution for Bending Under Tension

2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Bending Under Tension ◽  
Associated Flow Rule

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.

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%.

Limit Loads of Circular Plates Under Combined Loading

1973 ◽  
Vol 40 (3) ◽  
pp. 799-802 ◽  
Author(s):  
H. M. Haydl ◽  
A. N. Sherbourne
Keyword(s):  
Yield Criterion ◽  
Yield Condition ◽  
Combined Loading ◽  
Stress Fields ◽  
Collapse Load ◽  
Circular Plates ◽  
Limit Loads ◽  
Title Problem ◽  
Interaction Curves ◽  
Von Mises

Limit loads of circular plates under combined transverse and in-plane loading are given for the von Mises yield condition. Ivanov’s approximation to the Ilyushin yield surface is used. Collapse load interaction curves and stress fields are given for simply supported and clamped plates. The results are compared with existing solutions for the title problem based on the Tresca yield criterion.

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.

scholarly journals AVALIAÇÃO DO DESEMPENHO DO MÉTODO CPPM EM ANÁLISES ELASTOPLÁSTICAS

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Maria Paz Duque Gutiérrez ◽  
William Taylor Matias Silva
Keyword(s):  
Projection Method ◽  
Yield Criterion ◽  
Flow Rule ◽  
Analytical Formulation ◽  
Strain Behavior ◽  
Nonlinear Responses ◽  
Von Mises ◽  
Closest Point Projection ◽  
Point Projection ◽  
Nonlinear Hardening

RESUMO: O método de projeção do ponto mais próximo (CPPM, closest point projection method) é amplamente utilizado quando se apresentam respostas não lineares no comportamento dos materiais. Este artigo destina-se ao detalhamento e formulação analítica do método e avaliar com exemplos simples seu desempenho utilizando distintas leis de endurecimento não lineares para definir a evolução das deformações plásticas. O método é implementado sob uma cinemática de deformações infinitesimais. É considerado que o material possui propriedades elásticas constantes. O critério de escoamento de von Mises é utilizado com uma regra associativa de fluxo para descrever o comportamento tensão-deformação do material. A principal contribuição deste trabalho é verificar a robustez do método e apresentar explicação completa da formulação analítica. ABSTRACT: The closest point projection method is widely used when nonlinear responses occur in the behavior of the materials. The aim of this work is detailing its analytical formulation with simple examples and evaluates the performance of the method using different nonlinear hardening laws to define the evolution of plastic deformation. The method is implemented under a kinematic of infinitesimal strains, it is considered a material with constant elastic properties, the von Mises yield criterion and an associative flow rule is used to describe the stress - strain behavior of the material. The main contribution of this work is to verify the robustness of the method and the complete explanation of the analytical formulation. RESUMEN. El método de proyección al punto más próximo (CPPM, closest point projection method) es ampliamente utilizado cuando se presentan respuestas no lineales en el comportamiento de los materiales. Se pretende con este trabajo detallar su formulación analítica y evaluar con ejemplos simples el desempeño del método utilizando diferentes leyes de endurecimiento no lineales para definir la evolución de las deformaciones plásticas. El método es implementado bajo una cinemática de deformaciones infinitesimales. Se considera un material con propiedades elásticas constantes, se emplea el criterio de fluencia de von Mises y una regla asociativa de flujo para describir el comportamiento tensión - deformación del material. La principal contribución de este trabajo es la verificación de la robustez del método y la explicación completa de la formulación analítica.

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.

Bending and Twisting of Pipes With Strain Hardening

1984 ◽  
Vol 106 (2) ◽  
pp. 188-195 ◽  
Author(s):  
J. H. Lau ◽  
T. T. Lau
Keyword(s):  
Effective Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Small Deformation ◽  
Form Solution ◽  
Simultaneous Action ◽  
Deformation Analysis ◽  
Engineering Practice ◽  
Strain Diagram ◽  
Interaction Curves

A closed-form solution is presented for the small deformation analysis of a straight thin-walled circular cylinder subjected to the simultaneous action of bending and twisting moments. Dimensionless interaction curves and charts which relate the variables, bending moment, curvature, maximum effective strain, twisting moment, and shear strain are also provided for engineering practice convenience. The average stress-strain diagram of the cylinder is described by two straight lines. The result presented herein is not only a good approximation of a wide class of piping materials, but also provides a standard tool for estimating the accuracy of different direct schemes such as numerical integration, finite-difference, and finite-element methods.

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