Víctor D. Fachinotti

Thermomechanical model of a continuous casting process

A model for the analysis of thermal stresses arising at the early stage of a continuous casting process is proposed. The model is used to simulate the casting of round billets assuming axial symmetry. Thermal analysis takes into account phase-change in the material and heat transfer through the mould. The heat balance equation is solved using an Eulerian formulation for the billet domain, while the mould is analyzed using a Lagrangian one. Heat transfer from billet to mould is simulated assuming non-linear heat conduction through the air gap formed between them. Air conductivity is taken as a function of temperature. Two mechanical models are built assuming elastoplastic and viscoplastic hardening materials. Both Lagrangian and Arbitrary Lagrangian Eulerian (ALE) techniques have been implemented and compared. In the latter, advection of the history-dependent material parameters is taken into account using an appropriate finite volume integration scheme. Stresses and strains obtained with both models are compared, showing a good agreement.

Constitutive models of steel under continuous casting conditions

Abstract We review in this paper a series of constitutive equations that describe the behavior of steels at elevated temperatures, laying emphasis upon continuous casting processes. The different laws are situated in an appropriate thermodynamic context, enabling the straightforward multiaxial generalization of uniaxial relationships proposed on a pure experimental basis. Plastic and viscoplastic standard materials are mainly considered, including models that split the instantaneous and creep components of the irreversible deformation. Unified models without a yield criterion are also treated. Predictions of different models for steels with the same carbon content are shown throughout the work.

Phasewise numerical integration of finite element method applied to solidification processes

Abstract Phase change is a very complex physical phenomenon that governs a lot of industrial situations. Due to the inherent difficulties that arise in manufacturing activities they need a numerical treatment using models to predict the behavior of the different phases involved in the process. Historically, solidification problems were solved considering only the solution of an energy balance with isothermal phase change including conduction and or convection in the material. Nowadays computational fluid dynamics is becoming a well-suited numerical technique to investigate all kind of transport phenomena, especially when coupled fields are involved. This trend has addressed the research in solidification problems towards the solution of models combining incompressible Navier–Stokes equations coupled with heat and mass transfer including phase change. In this paper we present a phasewise discontinuous numerical integration method to solve thermal phase change problems in a fast and accurate way. Moreover, this methodology was extended to coupled fluid flow and energy balance equations with success and in a future work we will apply to binary alloy solidification with macrosegregation.

Visco-plastic constitutive models of steel at high temperature

Abstract Two constitutive elasto-visco-plastic models are adopted to simulate the behavior of plain carbon steel at high temperature, specifically at the austenitic range (950–1300°C), being particularly appropriate for the numerical simulation of casting and hot-working processes. The response in hardening, creep and non-uniform loading conditions is analyzed and compared with experimental data. An efficient numerical integration scheme is proposed and its accuracy is evaluated using iso-error maps. The consistent isothermal tangent matrix is computed and the final models are implemented into an FEM code. Several tests are performed to evaluate the accuracy and robustness of the integration scheme. Finally an application concerning the analysis of the thermal stresses produced at the early stage of a steel continuous casting process is shown.

Linear tetrahedral finite elements for thermal shock problems

Purpose – The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.Design/methodology/approach – The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which ensures an oscillation‐free solution.Findings – The proposed “diffusion‐split” method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well ...

Optimization-based design of a heat flux concentrator

To gain control over the diffusive heat flux in a given domain, one needs to engineer a thermal metamaterial with a specific distribution of the generally anisotropic thermal conductivity throughout the domain. Until now, the appropriate conductivity distribution was usually determined using transformation thermodynamics. By this way, only a few particular cases of heat flux control in simple domains having simple boundary conditions were studied. Thermal metamaterials based on optimization algorithm provides superior properties compared to those using the previous methods. As a more general approach, we propose to define the heat control problem as an optimization problem where we minimize the error in guiding the heat flux in a given way, taking as design variables the parameters that define the variable microstructure of the metamaterial. In the present study we numerically demonstrate the ability to manipulate heat flux by designing a device to concentrate the thermal energy to its center without disturbing the temperature profile outside it.

Optimization-based design of heat flux manipulation devices with emphasis on fabricability

In this work, we present a new method for the design of heat flux manipulating devices, with emphasis on their fabricability. The design is obtained as solution of a nonlinear optimization problem where the objective function represents the given heat flux manipulation task, and the design variables define the material distribution in the device. In order to facilitate the fabrication of the device, the material at a given point is chosen from a set of predefined metamaterials. Each candidate material is assumed to be a laminate of materials with high conductivity contrast, so it is a metamaterial with a highly anisotropic effective conductivity. Following the discrete material optimization (DMO) approach, the fraction of each material at a given finite element of the mesh is defined as a function of continuous variables, which are ultimately the design variables. This DMO definition forces the fraction of each candidate to tend to either zero or one at the optimal solution. As an application example, we designed an easy-to-make device for heat flux concentration and cloaking.

A Diffusion‐Split Method To Deal With Thermal Shocks Using Standard Linear Tetrahedral Finite Elements

The thermal analysis using linear standard tetrahedral finite elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe way to directly discourage the use of these elements. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which assures an oscillation‐free solution. The performance of this method is evaluated by means of test case with analytical solution, as well as an industrial application, for which a well‐behaved numerical solution is available.

Optimization-based design of an elastostatic cloaking device

We present a new method for the design of devices to manipulate the displacement field in Elastic materials. It consists of solving a nonlinear optimization problem where the objective function defines the error in matching a desired displacement field, and the design variables determine the required material distribution within the device. In order to facilitate fabrication, the material at a given point of the device is chosen from a set of predefined materials, giving raise to a discrete optimization problem that is converted into a continuous one using the Discrete Material Optimization technique. The candidate materials maybe simple, isotropic materials, but the device made of them behaves as a whole as a metamaterial, enabling the manipulation of the displacement field in ways that are inconceivable in nature. As an example of application, a device for elastostatic cloaking or unfeelability is designed.