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Article
Publication date: 4 July 2016

Chuan Liu, Ying Luo, Min Yang and Qiang Fu

The purpose of this paper is to clarify the effect of material hardening model and lump-pass method on the thermal-elastic-plastic (TEP) finite element (FE) simulation of residual…

Abstract

Purpose

The purpose of this paper is to clarify the effect of material hardening model and lump-pass method on the thermal-elastic-plastic (TEP) finite element (FE) simulation of residual stress induced by multi-pass welding of materials with cyclic plasticity.

Design/methodology/approach

Nickel-base alloy and stainless steel, which are used in J-type weld for manufacturing the nuclear reactor pressure head, can easily harden during multi-pass welding. The J-weld welding experiment is carried out and the temperature cycle and residual stress are measured to validate the TEP simulation. Thermal-mechanical sequence coupling method is employed to get the welding residual stress. The lumped-pass model and pass-by-pass FE model are built and two materials hardening models, kinematic hardening model and mixed hardening model, are adopted during the simulations. The effects of material hardening models and lumped-pass method on the residual stress in J-weld are distinguished.

Findings

Based on the kinematic hardening model, the stresses simulated with the lumped-pass FE model are almost consistent with those obtained by the pass-by-pass FE model; while with the mixed hardening material model, the lumped-pass method has great effect on the simulated stress.

Practical implications

A computation with mixed isotropic-kinematic material seems not to be the appropriate solution when using the lumped-pass method to save the computation time.

Originality/value

In the simulation of multi-pass welding residual stress involved in materials with cyclic plasticity, the material hardening model should be carefully considered. The kinematic hardening model with lump-pass FE model can be used to get better simulation results with less computation time. The results give a direction for welding residual stress simulation for the large structure such as the reactor pressure vessel.

Details

Engineering Computations, vol. 33 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1996

Eiji Nakamachi and Xianghuai Dong

Describes the development of a dynamic‐explicit type finite‐element formulation based on elastic/crystalline‐viscoplastic theory to predict the dynamic forming limits of sheet…

Abstract

Describes the development of a dynamic‐explicit type finite‐element formulation based on elastic/crystalline‐viscoplastic theory to predict the dynamic forming limits of sheet metal. Formulates an evolution equation governing all the slip stages of a single crystal, by modifying Pierce and Bassani’s crystalline plasticity models. Interprets precisely the experimentally observed hardening evolution. Takes account of the importance of the strain rate and temperature sensitivity of the material in predicting dynamic plastic instability. Analyses the deformation and strain localization in a rectangular sheet under stretching, in relation to the plane strain assumption, using the numerical results to demonstrate the influences of tension force and temperature on strain localization, and to show the temperature dependence of shear band formation. Demonstrates that the deviation of tension direction from the axis of symmetry of a single crystal causes non‐simultaneous sliding between primary and conjugate slip systems, resulting in S‐shaped non‐symmetrical deformation.

Details

Engineering Computations, vol. 13 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 November 2018

Aref Mehditabar and Gholam H. Rahimi

This study aims to explain the characterization of cyclic behavior of a tube made of functionally graded material (FGM) under different combinations of internal pressure and…

Abstract

Purpose

This study aims to explain the characterization of cyclic behavior of a tube made of functionally graded material (FGM) under different combinations of internal pressure and cyclic through-thickness temperature gradients.

Design/methodology/approach

The normality rule, nonlinear kinematic hardening Chaboche model and Von Mises yield criterion were used to model the constitutive behavior of an FG tube in the incremental form. The material properties and hardening parameters of the Chaboche model vary according to the power-law function in the radial direction. The backward Euler integration scheme combined with return mapping algorithm which relies on the solution of a nonlinear equation performs the numerical procedure. The algorithm is implemented within the user subroutine UMAT in ABAQUS/standard.

Findings

The published works on FG components considering only the mechanical and physical properties as a function of spatial coordinate and nonlinear kinematic hardening parameters have not been considered to be changed continuously from one surface to another. Motivated by this, the present paper has deliberately been targeted to tackle this kind of problem to simulate the cyclic behavior of an FG tube as accurately as possible. In addition, to classify various behaviors the FG tube under cyclic thermomechanical loadings, Bree’s interaction diagram as an essential tool in designing of the FG pressure vessels in many engineering sectors is presented.

Originality/value

Provides a detailed description of the FG parameters of Chaboche kinematic hardening parameters in the adopted constitutive equations. In this paper, the significant effects of internal pressure values, kinematic hardening models and also FG inhomogeneity index related to the hardening rule parameters on plastic deformation of the FG tube are illustrated. Finally, the various cyclic behaviors of the FG tube under different combinations of thermomechanical loading are fully explored.

Details

Engineering Computations, vol. 36 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 September 2011

Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Abstract

Purpose

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Design/methodology/approach

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

Findings

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

Research limitations/implications

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Practical implications

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

Originality/value

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

Article
Publication date: 3 August 2015

Mark Messner, Armand Beaudoin and Robert Dodds

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element…

Abstract

Purpose

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework.

Design/methodology/approach

Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes.

Findings

A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation.

Research limitations/implications

The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions.

Practical implications

The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D.

Originality/value

In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.

Details

Engineering Computations, vol. 32 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 July 2016

Jerzy Barglik

As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and…

Abstract

Purpose

As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and simultaneous hardening processes and exemplary results of computations and measurements. The upper critical temperature Ac3 is determined from the Time Temperature Austenization diagram for investigated steel.

Design/methodology/approach

Computation of coupled electromagnetic, thermal and hardness fields is based on the finite element methods, while the hardness distribution is determined by means of experimental dependence derived from the continuous cooling temperature diagram for investigated steel.

Findings

The presented results may be used as a theoretical background for design of inductor-sprayer systems in continual and simultaneous arrangements and a proper selection of their electromagnetic and thermal parameters.

Research limitations/implications

The both models reached a quite good accuracy validated by the experiments. Next work in the field should be aimed at further improvement of numerical models in order to shorten the computation time.

Practical implications

The results may be used for designing induction hardening systems and proper selection of field current and cooling parameters.

Originality/value

Complete mathematical and numerical models for continuous and simultaneous surface induction hardening including dual frequency induction heating of gear wheels. Experimental validation of achieved results. Taking into account dependence of the upper critical temperature Ac3 on speed of heating.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 35 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 September 1999

Jürgen Fuhrmann and Dietmar Hömberg

We discuss a model that is capable of describing the solid‐solid phase transitions in steel. It consists of a system of ordinary differential equations for the volume fractions of…

1301

Abstract

We discuss a model that is capable of describing the solid‐solid phase transitions in steel. It consists of a system of ordinary differential equations for the volume fractions of the occuring phases coupled with a nonlinear energy balance equation to take care of the latent heats of the phase changes. This model is applied to simulate surface heat treatments, which play an important role in the manufacturing of steel. Two different technologies are considered: laser and induction hardening. In the latter case the model has to be extended by Maxwell’s equations. Finally, we present numerical simulations of laser and induction hardening applied to the steel 42CrMo4.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 May 2020

Divyanshu Kumar Lal and Arghya Das

Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress…

Abstract

Purpose

Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.

Design/methodology/approach

Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.

Findings

Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.

Originality/value

Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.

Details

Engineering Computations, vol. 37 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 1986

H. Burlet and G. Cailletaud

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the…

Abstract

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the initial stress method is implemented in a two‐dimensional finite element code (ZEBULON). The procedure is tested on examples including mechanical and thermal loading. Some remarks are made on the maximum increment size, the relative efficiency of ‘radial return’ and ‘secant stiffness method’ is discussed. Finally, the possibilities of the model concerning ratchetting, cyclic hardening and softening are shown.

Details

Engineering Computations, vol. 3 no. 2
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 6 March 2017

Jerzy Barglik and Albert Smalcerz

Modeling of induction surface hardening strongly depends on accuracy of material properties data and their temperature characteristics. However, it is especially complicated in…

Abstract

Purpose

Modeling of induction surface hardening strongly depends on accuracy of material properties data and their temperature characteristics. However, it is especially complicated in case of the magnetic permeability dependent not only on temperature but also on the magnetic strength. This paper aims to estimate the influence of the magnetic permeability on modeling of coupled physical fields describing the process. Investigations are provided for the gear wheels made of the steel C45E.

Design/methodology/approach

Computation of coupled electromagnetic temperature and hardness fields is based on FEM methods. The Flux 3D software is applied for the numerical simulation of coupled electromagnetic and temperature fields. The QT Steel software is applied for a determination of the hardness and microstructure distributions.

Findings

Obtained results may be used as a kind of background for the design of induction surface hardening systems.

Research limitations/implications

The presented calculation model provided quite a good accuracy of hardness distribution validated by the experiments. Next work in the field should be aimed at taking into account a dependence of the magnetic permeability on the field current frequency.

Originality/value

Mathematical model of induction surface hardening with taking into account time dependence on the magnetic permeability on temperature and magnetic strength is elaborated. Experimental validation of hardness distribution is provided. A quite reasonable convergence between simulations and measurements was achieved.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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