Inverse finite element modelling and identification of constitutive parameters of UHS steel based on Gleeble tensile tests at high temperature

The authors are grateful to the publisher, Taylor & Francis, for letting the manuscript being archived in this Open Access repository. This is an electronic version of an article that was published in Inverse Problems in Science and Engineering© 2011 Copyright: Taylor & Francis. Inverse Problems in Science and Engineering is available online at: http://www.tandfonline.com/doi/abs/10.1080/17415977.2010.518288International audienceThe rheological behaviour of an ultra high strength (UHS) steel is investigated by Gleeble tensile tests at low-deformation rates and high temperature, from 1200°C to solidus temperature. Results show that large thermal gradients exist in specimens, resulting in heterogeneous deformation, which makes the identification of constitutive parameters difficult from the directly deduced nominal stress-strain curves. The advantages of an inverse identification method - associating a direct finite element model of Gleeble tests and an optimization module - are demonstrated in such conditions. The constitutive parameters identified by this technique have been successfully applied to additional tests, more complex in nature than those used for the identification of parameters. However, such tests combining successive loading and relaxation stages have revealed some limitations of the considered constitutive model

Finite Element Modelling Of Tensile Test For Micro-Alloyed Low Carbon Steel At High Temperature

International audienceIn view of the numerical inverse identification of constitutive models, a forward numerical modelling of Gleeble tension tests is conducted. A coupled electrical--thermal--mechanical model is proposed for the resolution of electrical, energy and momentum conservation equations by means of finite element method. In momentum equation, the mixed rheological model in multi--phase region (e.g. δ--ferrite and γ austenite (δ+γ mixture)) is developed to consider the δ/γ phase transformation phenomenon for micro--alloyed low carbon steel at high temperature. Experimental and numerical results reveal that significant thermal gradients exist in specimen along longitudinal and radial directions. Such thermal gradients will lead to phase fraction gradient in specimen at high temperature, such as δ fraction gradient or liquid fraction gradient. All these gradients will contribute to the heterogeneous deformation of specimen and severe stress non--uniform distribution, which is the major difficulty for the identification of constitutive models, especially for the simple identification method based on nominal stress--strain. The proposed model can be viewed as an important achievement for further inverse identification methods, which should be used to identify constitutive parameters for steel at high temperature in the presence of thermal gradients

A Coupled Electrical-Thermal-Mechanical Modeling of Gleeble Tensile Tests for Ultra-High-Strength (UHS) Steel at a High Temperature

International audienceA coupled electrical-thermal-mechanical model is proposed aimed at the numerical modeling of Gleeble tension tests at a high temperature. A multidomain, multifield coupling resolution strategy is used for the solution of electrical, energy, and momentum conservation equations by means of the finite element method. Its application to ultra-high-strength steel is considered. After calibration with instrumented experiments, numerical results reveal that significant thermal gradients prevail in Gleeble tensile steel specimen in both axial and radial directions. Such gradients lead to the heterogeneous deformation of the specimen, which is a major difficulty for simple identification techniques of constitutive parameters, based on direct estimations of strain, strain rate, and stress. The proposed direct finite element coupled model can be viewed as an important achievement for subsequent inverse identification methods, which should be used to identify constitutive parameters for steel at a high temperature in the solid state and in the mushy state

Numerical Simulation of Macrosegregation with Solid Deformation During the Solidification of Steel Ingots Using a Single-Phase/Two-Phase Integrated Model

Macrosegregation, a serious defect formed during the solidification of steel ingots, impairs the performance of the final components. To predict macrosegregation caused by thermal-solutal convection and solid deformation, a volume-averaged single-phase/two-phase integrated model is developed. During the deformation stage, the two-phase model coupling the solid deformation and liquid flow in the mushy zone is utilized. Before or after the deformation stage, the motion of the solid phase is neglected, and the single-phase model is solved. A 450 kg steel ingot punching test is considered for application. The results show that when the solid shell of the ingot is being punched, the solid phase in the mushy core at punching height is compressed, and a relative liquid flow is induced. This in turn causes a transition of positive segregation to negative segregation in the compressed mushy core of the ingot. According to numerical sensitivity tests of different punching parameters, as the punching start time and punching velocity increase, the effect of punching on macrosegregation will be smaller. It is demonstrated that the single-phase/two-phase integrated model can predict macrosegregation in the steel ingots which are deformed during solidification

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Grain structure and macrosegregation are two main factors determining mechanical properties of components and are strongly coupled during alloy solidification. A two-dimensional (2D) cellular automaton (CA)⁻finite element (FE) model is developed to achieve a direct macroscopic modeling of grain structure and macrosegregation during the solidification of binary alloys. With the conservation equations of mass, momentum, energy, and solute solved by a macroscopic FE model and the grain structure described by a microscopic CA model, a two-way coupling between the CA and FE models is applied. Furthermore, the effect of the fluid flow on the dendrite tip growth velocity is considered by modified dendrite tip growth kinetics. The CAFE model is applied to a quasi-2D benchmark solidification experiment of a Sn⁻3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously. It is demonstrated that the model has a capacity to describe the undercooling ahead of the growth front. The growth directions of columnar grains, grain sizes, and columnar-to-equiaxed transition (CET) position are obviously modified by the fluid flow, and obvious segregated channels almost aligned with the orientations of the columnar grains are found. Qualitatively good agreement is obtained between the predicted segregation profiles and experimental measurements

Numerical simulation on multiple pouring process for a 292 t steel ingot

A ladle-tundish-mould transportation model considering the entire multiple pouring (MP) process is proposed. Numerical simulation is carried out to study the carbon distribution and variation in both the tundish and the mould for making a 292 t steel ingot. Firstly, the fluid flow as well as the heat and mass transfer of the molten steel in the tundish is simulated based on the multiphase transient turbulence model. Then, the carbon mixing in the mould is calculated by using the species concentration at the tundish outlet as the inlet condition during the teeming process. The results show a high concentration of carbon at the bottom and a low concentration of carbon at the top of the mould after a MP process with carbon content high in the first ladle and low in the last ladle. Such carbon concentration distribution would help reduce the negative segregation at the bottom and the positive segregation at the top of the solidified ingot

Transient Modeling of Grain Structure and Macrosegregation during Direct Chill Casting of Al-Cu Alloy

Grain structure and macrosegregation are two important aspects to assess the quality of direct chill (DC) cast billets, and the phenomena responsible for their formation are strongly interacted. Transient modeling of grain structure and macrosegregation during DC casting is achieved with a cellular automaton (CA)–finite element (FE) model, by which the macroscopic transport is coupled with microscopic relations for grain growth. In the CAFE model, a two-dimensional (2D) axisymmetric description is used for cylindrical geometry, and a Lagrangian representation is employed for both FE and CA calculations. This model is applied to the DC casting of two industrial scale Al-6.0 wt % Cu round billets with and without grain refiner. The grain structure and macrosegregation under thermal and solutal convection are studied. It is shown that the grain structure is fully equiaxed in the grain-refined billet, while a fine columnar grain region and a coarse columnar grain region are formed in the non-grain-refined billet. With the increasing casting speed, grains become finer and grow in a direction more perpendicular to the axis, and the positive segregation near the centerline becomes more pronounced. The increasing casting temperature makes grains coarser and the negative segregation near the surface more pronounced

Analysis of segregation solute redistribution and centerline in continuously cast thin slab

A model has been built to calculate the solute redistribution in continuously cast thin slab and the effect of the fluid flow in mush on the centerline segregation was analyzed. The corresponding simulation program was developed by applying the SIMPLER algorithm. The momentum, energy and species conservation equations were solved simultaneously. The macro-segregation of a 3-D thin slab with 900 mm x 50 mm cross section was simulated. The obtained results show that negative segregation forms near the slab surface and severe centerline segregation forms in the mid-thickness plane. The species concentration in the centerline of the slab increases obviously at the final solidification stage