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Povzetek: After the continuous hot-rolling process, steel bars are immediately placed on the cooling bed. At the beginning of the cooling, the material is at high temperatures, and the yield strength is low. Due to thermal load, yield strength can be exceeded, and permanent plastic strains start accumulating, resulting in possible unwanted shape changes and residual stresses. The present paper aims to develop a thermo-mechanical model for studying and eliminating undesirable phenomena before the products leave the cooling bed. The governing equations are solved for the two-dimensional slice in a strong form, and a modified version of the radial basis function generated finite difference (RBF-FD) method [1]. The initial bar geometry is obtained from the existing meshless hot-rolling simulation system [2]. The thermal and mechanical models are one-way coupled, i.e. the temperature solution represents a driving force for the stress and strain solution. The temperature field is obtained with explicit propagation in time. The convective and radiative heat fluxes on the boundary are updated at each time step using the ray tracing procedure to determine the radiative heat flux. The mechanical part is solved by considering the small strain elasto-plasticity, where the isotropic von Mises temperature-dependent hardening is employed. The global system of nonlinear equations of the mechanical part is solved by the Newton-Raphson method. The closest point projection method is used to solve the constitutive relations. A sensitivity study is performed on the influence of cooling intensity on a rectangular steel bar’s temperature, stress and strain field. We defined the most influential factors for defect formation. For the first time, a novel meshless RBF-FD method is successfully used for solving such a complex industrial problem. The model will be perspectively upgraded from the slice to the three-dimensional model to enable also bending.
Ključne besede: cooling bed, steel bars, thermo-mechanics, strong form, meshless method
Objavljeno v DiRROS: 21.03.2024; Ogledov: 83; Prenosov: 48
Celotno besedilo (1,62 MB)
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Povzetek: A hybrid version of the strong form meshless Radial Basis Function-Finite Difference (RBF-FD) method is introduced for solving thermo-mechanics. The thermal model is spatially discretised with RBF-FD, where trial functions are polyharmonic splines augmented with polynomials. For time discretisation, the explicit Euler method is employed. An extension of RBF-FD, the hybrid RBF-FD, is introduced for solving mechanical problems. The model is one-way coupled, where temperature affects displacements. The thermo-elastoplastic material response is considered where the stress field is generally non-smooth. The hybrid RBF-FD, where the finite difference method is used to discretise the divergence operator from the balance equation, is shown to be successful when dealing with such problems. The mechanical model is introduced in a plane strain and in a generalised plane strain (GPS) assumption. For the first time, this work presents a strong form RBF-FD for GPS problems subjected to integral form constraints. The proposed method is assessed regarding h-convergence and accuracy on the benchmark with heating an elastoplastic square. It is proven to be successful at solving one-way coupled thermo-elastoplastic problems. The proposed novel meshless approach is efficient, accurate, and robust. Its use in an industrial situation is provided in Part 2 of this paper.
Ključne besede: thermo-mechanical modelling, von Mises small strain plasticity, hybrid radial basis function generated finite differences, polyharmonic splines
Objavljeno v DiRROS: 28.02.2024; Ogledov: 124; Prenosov: 66
Celotno besedilo (2,69 MB)
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