Mathematical and numerical model of solidification process of pure metals

The work concerns the numerical modelling of coupled thermal and mechanical phenomena occurring in the laser beam welding process. Commercial Abaqus FEA engineering software is adopted to numerical computations in order to perform a comprehensive analysis of thermo-mechanical phenomena. Created in Fortran programming language additional numerical subroutines are implemented into Abaqus solver, used to describe the power intensity distribution of the movable laser beam heat source. Temperature dependent thermomechanical properties of X5CrNi18-10 steel are adopted in the numerical analysis of stress and strain states. Mathematical and numerical models are verified on the basis of a comparison between selected results of computer simulations and experimental studies on butt-welded joints.Numerical simulations are presented for steel sheet with a thickness of 2 mm. Temperature distributions, the shape and size of melted zone as well as residual stress and deformations are presented for analyzed elements. Numerically determined deflections are compared with the measured deflection of welded joint.

Section: Mathematical Modelmentioning

confidence: 99%

Numerical Prediction Of Deformations In Laser Welded Sheets Made Of X5CrNi18-10 Steel

Piekarska

Кубяк

Saternus

et al. 2015

“…Temperature field during material melting and solidification is affected by the latent heat of fusion. Macro models describing solidification process for both pure metals [20][21][22][23] and alloys [24][25][26][27][28] can be found in the literature. Mostly, one domain approach is used with fuzzy solidification front in the model where latent heat is included into effective heat capacity.…”

Section: Thermal Phenomenamentioning

confidence: 99%

Numerical Modelling Of Thermal And Structural Phenomena In Yb:YAG Laser Butt-Welded Steel Elements

Кубяк¹,

Piekarska²,

Stano³

et al. 2015

MODELOWANIE NUMERYCZNE ZJAWISK CIEPLNYCH I STRUKTURALNYCH W ELEMENTACH STALOWYCH SPAWANYCH DOCZOŁOWO WIĄZKĄ LASERA Yb:YAGThe numerical model of thermal and structural phenomena is developed for the analysis of Yb:YAG laser welding process with the motion of the liquid material in the welding pool taken into account. Temperature field and melted material velocity field in the fusion zone are obtained from the numerical solution of continuum mechanics equations using Chorin projection method and finite volume method. Phase transformations in solid state are analyzed during heating and cooling using classical models of the kinetics of phase transformations as well as CTA and CCT diagrams for welded steel. The interpolated heat source model is developed in order to reliably reflect the real distribution of Yb:YAG laser power obtained by experimental research on the laser beam profile.On the basis of developed numerical models the geometry of the weld and heat affected zone are predicted as well as the structural composition of the joint.Keywords: Laser welding, heat transfer, phase transformations, numerical modelling, Kriging method Praca dotyczy modelowania numerycznego zjawisk cieplnych i strukturalnych w procesie spawania laserem Yb:YAG z uwzględnieniem ruchu ciekłego materiału w jeziorku spawalniczym. Pole temperatury i pole prędkości ciekłej stali w strefie przetopienia otrzymano z numerycznego rozwiązania równań mechaniki ośrodków ciągłych metodą projekcji Chorina i metodą objętości skończonych. Przemiany fazowe w stanie stałym analizowano podczas nagrzewania i chłodzenia bazując na klasycznych modelach kinetyki przemian fazowych oraz wykresach CTA i CTPc-S. W celu wiarygodnego odzwierciedlenia rzeczywistego rozkładu mocy lasera Yb:YAG opracowano model interpolowany źródła, wykorzystujący badania doświadczalne profilu wiązki laserowej. Na podstawie opracowanych modeli numerycznych prognozowano geometrię spoiny i strefy wpływu ciepła oraz skład strukturalny złącza.

“…In the third step the solution of the equation (35) gives the real velocity field u f +1 . The numerical treatment of the equation (4) was discussed in details in [35,36]. The reinitialization of the level set function as well as the calculation of the heat fluxes on the solid and liquid sides of Γ LS were the same as in [36].…”

Section: Numerical Modelmentioning

confidence: 99%

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Skrzypczak

Węgrzyn-Skrzypczak

Winczek

2015

The paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin's projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.Keywords: Pure Metal, Solidification, Sharp Interface, Natural Convection, Finite Element Method, Level Set Method Praca porusza problematykę modelowania kierunkowego krzepnięcia czystego metalu. Podczas tego procesu obserwuje się formowanie ostrego frontu krzepnięcia w postaci powierzchni separującej ciecz i ciało stałe w przypadku trójwymiarowym lub krzywej w przypadku płaskim. Położenie oraz kształt interfejsu krzepnięcia zmieniają się w czasie a wartości prędkości lokalnych zależą od różnicy intensywności strumieni ciepła po stronie ciała stałego i cieczy. Krzepnięcie z ostrym frontem należy do grupy procesów z przemianami fazowymi, które warunkowane są zmianami temperatury, ciśnienia, itp. Przejście fazowe z jednego stanu w drugi...