Three-dimensional thermomechanical coupled FEM analysis of static recrystallisation during two-pass tube tension reducing process

Abstract

In this paper, a thermal dynamic numerical method was carried out to model the austenite static recrystallisation behaviour of steel 33Mn2V used in new non-quenched/tempered oil well tubes at different deformation temperatures, strain rates, deformation amounts and initial microstructures. Based on the MARC/AutoForge software, a three-dimensional thermomechanical coupled elastoplastic finite element model (FEM) was applied to simulate static recrystallisation amount of the two-pass tube tension reducing process of steel 33Mn2V for oil well. The distribution law of static recrystallisation inside the workpiece is analysed. It is indicated that the simulation results are much reliable through comparison with experimental data.     

Formulation of a thin shell finite element with continuity C 0 and convected material frame notion

 This paper presents a formulation for a new family of thin shell finite elements. The element is formulated by using a convected material frame notion which offers an interesting framework to take into account large transformations. Bending behaviour is calculated from the Love–Kirchhoff assumptions and from a finite difference technique between adjacent elements. We therefore called this element SFE for semi-finite-element. This method allows us to keep C ⁰ continuity without introducing other variables than the 3 classical displacements, which reduces computational time. In this paper, a full formulation of this element is described more precisely. It takes into account the coupling effect between both membrane and bending behaviour. Various sample solutions that illustrate the effectiveness of the element in linear and nonlinear analysis are presented, with some sheet metal forming examples. Received 10 January 2001     

On the computation of two-dimensional stress intensity factors using the boundary element method

General two-dimensional linear elastic fracture problems are investigated using the boundary element method. The √r displacement and 1/√r traction behaviour near a crack tip are incorporated in special crack elements. Stress intensity factors of both modes I and II are obtained directly from crack-tip nodal values for a variety of crack problems, including straight and curved cracks in finite and infinite bodies. A multidomain approach is adopted to treat cracks in an infinite body. The body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion. Numerical results, compared with exact solution whenever possible, are accurate even with a coarse discretization.     

A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis

A simple model based on experimental observations of the yarn-parallel biaxial extension of PVC-coated polyester fabric cruciform specimens is proposed. In situ loading conditions are considered. The material behaviour is assumed to be plane stress orthotropic for a particular load ratio, while the elastic properties can vary with the load ratio in order to represent the complex interaction between warp and fill yarns. A linear relationship is experimentally found between elastic moduli and normalized load ratios for a wide range of PVC-coated polyester (Type I to Type IV). Two new parameters corresponding to the moduli variations are introduced to complement the existing plane stress orthotropic model. Theoretical results show that only five biaxial tests are required to accurately describe the material response with the proposed material model. Finally, the model was integrated in a commercial finite element software. It is shown that the proposed material model significantly increases the accuracy of the finite element predictions compared to the standard orthotropic linear material model with almost identical computation times.     

Treatment of material discontinuities in finite element computations

We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by Steven.¹ Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.     

Material modelling for dynamic strain ageing phenomenon of alloy 20MnMoNi55

Dynamic strain ageing (DSA) is observed in the tensile behaviour of 20MnMoNi55. The DSA phenomenon contributes extra hardening for a certain combination of straining rate and temperature. At temperature ranging from 200°C to 400°C and a straining rate of 10^?4–10^?2?s^?1, alloy 20MnMoNi55 exhibits DSA. In the present work, DSA stresses are calibrated as a function of strain, strain-rate and temperature. Modification of the Johnson–Cook material model by incorporating DSA has been attempted. The modified flow stress model is used in finite element computation to simulate the material behaviour for a wide range of temperature and strain-rates including the DSA regime. The simulated results are in good agreement with the experimental results.     

Experimental Characterisation of Aluminium 6082 at Varying Temperature and Strain Rate

Abstract: This article describes the experimental methodology used in overcoming the challenges of performing tests and recording results on specimens, which are suitable for such a wide range of test conditions. Uniaxial tensile tests were conducted on aluminium alloy 6082‐T352 at varying temperatures and strain rates to validate testing techniques and to determine the effect of these parameters upon this material. The applied strain rate varied over several orders of magnitude – using a screw‐driven tensometer for quasi‐static loading (6.9 × 10^?4 s^?1), a hydraulic piston rig for moderate strain rate (4.0 × 10¹ s^?1) and a tensile Hopkinson bar for high strain rate (1.5 × 10³ s^?1). Temperature was varied using a heat gun, and the air temperature was measured using a thermocouple in the hot air stream. Specimen temperature is determined by finite element modelling, and this correlates well with other work. Although it would have been possible to improve the design of individual tests for specific test conditions, an important objective was to conduct the entire series of tests in as consistent a manner as possible. The procedure for characterising the stress–strain behaviour for this material under these different loading conditions is also considered in some detail, as the real material behaviour deviates from simplified elasto‐plastic material models. Results presented for Al 6082 samples show a slight increase in yield stress with increasing strain rate, and a decrease in yield stress with increasing temperature.     

A super element model for non-linear analysis of stiffened box structures

A numerical model for non-linear static and dynamic analysis of stiffened box structures is presented. The model is based on a new super element formulation which provides complete C¹ continuity for both plate and beam elements. Geometric and material non-linearities are included and the temporal equations are solved by the implicit Newmark-β method with Newton-Raphson subiteration. The new formulation has been applied to the static, vibration and transient analysis of various structures such as flat plates, folded plates and rectangular boxes. Both isotropic and beam stiffened structures are considered and the results obtained are compared with other available solutions. It is observed that the new super element formulation can provide reasonable solutions to both linear and non-linear problems of stiffened box structures. The mathematical formulation of the model is presented in this paper, while the numerical verifications are given in the companion paper.¹     

A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved.     

MATERIAL MODELLING FOR TRANSIENT DYNAMIC ANALYSIS OF REINFORCED CONCRETE STRUCTURES

Reinforced concrete is a composite structural material which has been the subject of extensive research since it was first used. When considering the rational properties, the research has mainly centred on the behaviour of the concrete, that of the reinforcing steel and the interaction between the steel and the surrounding concrete subject to static loading. The behaviour of reinforced concrete, and, in particular, that of the concrete itself when subject to dynamic loading has been less thoroughly studied. This paper proposes a material model for the concrete which includes the effect of high strain rate upon both the stiffness of the material and upon the crushing strength. It proposes expressions for the yield and failure surfaces of the concrete which account for the effects of high strain rate and then incorporates this material model into an existing finite element program to compare with a series of test results. The paper illustrates that this improved material model can now produce a displacement/time history for reinforced concrete elements which is very close to that observed in tests on elements which are far outside the elastic range.     

Numerical computations of three-dimensional thin panel structures

A finite element model for analysing static problems of three-dimensional thin panel constructions is presented. The potential energy of stretching of each panel is represented by the classical Lagrange formulation of two-dimensional elasticity and in the finite element discretization piecewise linear u, v displacements are used. The potential energy of bending of each panel is represented in the finite element discretization by Hellan and Herrmann's model, i.e. piecewise constant moments and piecewise linear w-displacements are used. The physical appropriateness of the model is verified for different assemblages of panels, and in all cases good numerical results are obtained.     

Finite cover method for linear and non‐linear analyses of heterogeneous solids

We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non‐linear mechanical behaviour of heterogeneous solids and structures. The name ‘FCM’ is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non‐linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermal deformation vector for a bilinear temperature distribution in an anisotropic quadrilateral membrane element

This paper presents a thermal-structural deformation vector for an anisotropic quadrilateral membrane element. The elastic properties of the element are based on linear stress assumptions and were developed by Robinson¹. A general bilinear temperature field within the element is chosen in order to obtain a thermal deformation capability for the element commensurate with its elastic capability. A pseudo shear term is developed to account for part of the thermal deformation. The element is suitable for finite element analysis of advanced aircraft structures under elevated temperature environments and is particularly well suited for analysis of regions with severe temperature gradients such as occur in the vicinity of local heat sources and sinks. An example problem is included to demonstrate the behaviour of the element.     

Identification of damage and cracking behaviours based on energy dissipation mode analysis in a quasi-brittle material using digital image correlation

Characterizing the crack stability to predict the behaviour of ceramics designed for industrial use is a challenging issue. It requires accurate crack tip detection during the controlled crack propagation of notched bending tests. Different indirect methods are available, like for instance the compliance technique. Recently, techniques based on digital image correlation (DIC) have emerged: finite-element DIC (FE-DIC) with a finite element decomposition of the displacement field, integrated-DIC (I-DIC) based on Williams?? series decomposition of the displacement field and regularized-DIC (R-DIC) for mechanical constraints. These full-field techniques enable the quantification of the crack length and the stress intensity factor K ^I . In this paper, these four methods are compared in terms of measurements of crack lengths and stress intensity factors during a notched bending test. The tested material is a damageable quasi-brittle ceramic at room temperature. The non linearity of the stress-strain law of this microcraked ceramic results in a complex behaviour that is not captured by the compliance method during the bending test. Therefore the linear elastic compliance method leads to a different estimation of crack lengths and stress intensity factors compared to DIC methods. On the other hand, the R-DIC approach handles the non linear material constitutive behaviour. It allows a deeper analysis of the mechanical fields, the energy dissipation and the damage mechanisms during the crack propagation.     

Experimental and numerical analysis of flexural and impact behaviour of glass/pp sandwich panel for automotive structural applications

Cost and recyclability are among the primary factors on exploiting the engineering materials for their new applications. In this context, glass/pp-based sandwich panel has been studied experimentally and numerically with the aims of its potential applications in the automotive structures. The first part of this work presents the experimental results achieved for the load-carrying capacity of panels using three-point bend tests for its static flexural behaviour. Static behaviour is studied to compare the top-roller diameter effect on the flexural behaviour of the panels and shows a significant difference in the results. Impact behaviour of the panels is explored using three different types of impactor end-shapes that generate different levels of damage in the material with the same level of impact energy. The second part of this paper deals with the development of numerical models for the three-point bend and impact behaviour of the panels using a commercial finite element code of Abaqus. Strain energy-based homogenisation technique is employed to determine the equivalent orthotropic properties of complex circular honeycomb core material. The finite element models predict to a good level of the static and impact behaviour of the material when compared with the experiments.     

Rebound behaviour of spheres for plastic impacts

This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity V_i to the yield velocity V_y which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Young's Modulus E^* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(V_i/V_y)/(E^*/Y)]^−1/2.     

Collapse of thin shell structures—stress resultant plasticity modelling within a co‐rotated ANDES finite element formulation

Due to the very non‐linear behaviour of thin shells under collapse, numerical simulations are subject to challenges. Shell finite elements are attractive in these simulations. Rotational degrees of freedom do, however, complicate the solution. In the present study a co‐rotated formulation is employed. The deformation of the shell is decomposed in to a contribution from large rigid body rotation and a strain producing term. A triangular assumed strain shell finite element is used. Hence, a high performance elastic element is combined with the co‐rotated formulation. In the co‐rotated co‐ordinate system the plasticity is accounted for by a simplifyed Ilyushin stress resultant yield surface. The stress update is determined from the backward Euler difference, and a consistent geometrical and material tangent stiffness is derived. Comparison with other published analysis results show that the present formulation gives acceptable accuracy. Copyright © 1999 John Wiley & Sons, Ltd.     

New crack‐tip elements for XFEM and applications to cohesive cracks

An extended finite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3‐node triangular elements and quadratic 6‐node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton–Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended finite element method are compared to reference solutions and show excellent agreement. Copyright © 2003 John Wiley & Sons, Ltd.