Numerical Simulation of Thermal Phenomena and Phase Transformations in Laser-Arc Hybrid Welded Joints

Abstract

The paper concerns mathematical and numerical modelling of temperature field with convective motion of liquid metal in the melted zone taken into account and numerical estimation of structure composition of a plate made of S355 steel, butt-welded by laser-arc hybrid welding technique. Coupled transport phenomena, including heat transfer and fluid flow in the melted zone, were described respectively by transient heat transfer equation with convective term and Navier-Stokes equation. Latent heat associated with the material's state changes and latent heat of phase transformations in solid state were taken into consideration in the solution algorithm. The kinetics of phase transformations and volumetric fractions of arising phases were calculated on the basis of the Johnson-Mehl-Avrami (JMA) and Koistinen-Marburger (KM) classic mathematical models. In modelling of phase transformations during heating continuous heating transformation (CHT) diagram was used, whereas continuous cooling transformation (CCT) diagram was used in modelling of phase transformations during cooling of welded steel.Transient heat transfer equation was solved using finite element method in Petrov-Galerkin formulation and Navier-Stokes equation was solved in Chorin's projection method. The solution algorithms were implemented in ObjectPascal programming language.Keywords: Laser-arc hybrid welding, heat transfer, fluid flow, phase transformations, structure composition, numerical modelling Praca zawiera numeryczne modelowanie pola temperatury oraz prognozowanie numeryczne składu strukturalnego płasko-wnika wykonanego ze stali S355, spawanego doczołowo techniką hybrydową laser-łuk elektryczny. Model pola temperatury uwzględnia ruch ciekłego metalu w jeziorku spawalniczym. Sprzężone zjawiska transportu ciepła i cieczy w strefie przetopienia opisywane są równaniem nieustalonego przewodzenia ciepła z członem konwekcyjnym i równaniem Naviera-Stokesa. W algorytmie numerycznym uwzględniono ciepła związane ze zmianą stanu skupienia materiału i ciepła przemian fazowych w stanie stałym. Kinetykę przemian fazowych w stanie stałym oraz algorytmy numeryczne wyznaczania ułamków objętościowych powstających faz oparto na równaniach Johnsona-Mehla-Avramiego (JMA) i Koistinena-Marburgera (KM). W modelowaniu przemian nagrzewania wykorzystano wykres ciągłego nagrzewania (CTPc A ), natomiast w modelowaniu przemian chłodzenia wykorzystano spawalniczy wykres przemian austenitu (CTPc-S) spawanej stali. Do rozwiązania równania nieustalonego przewodzenia ciepła zastosowano metodę elementów skończonych w sformuło-waniu Petrov-Galerkina, a równanie Naviera-Stokesa rozwiązano metodą projekcji Chorina. Algorytmy analizy rozważanych zagadnień zaimplementowano w języku programowania ObjectPascal.

Modelling and Analysis of Phase Transformations and Stresses in Laser Welding Process / Modelowanie I Analiza Przemian Fazowych I Naprężeń W Procesie Spawania Laserowego

“…Latent heat of fusion, evaporation and latent heat of phase transformations in solid state [33][34][35] …”

Numerical and Experimental Study of Phase Transformations in Welding Processes / Badania Numeryczne I Doświadczalne Przemian Fazowych W Procesach Spawania

“…and boundary conditions of Dirichlet, Neumann and Newton type, taking into account a heat loss due to convection and radiation [12]: (10) where α is a convective coefficient (assumed as average value α=50 W/m 2 K), ε=0.5 is a radiation coefficient, σ is Stefanboltzmann constant and q=q(r,0) is the heat flux towards the top surface of welded workpiece (z=0) in the source activity zone, T 0 =293 K is an ambient temperature.…”

“…The analysis of the kinetics of phase transformation is carried out by well known mathematical models found in the literature and Continuous-Cooling Transformations (CCT) diagrams. The analysis of phase transformations in the heating process in most cases is carried out for constant Ac 1 and Ac 3 temperatures, whereas the effect of the maximum heating temperature is substantially omitted [11][12][13][14][15][16].…”

Theoretical investigations into heat transfer in laser-welded steel sheets

“…Generated heats during transformation of austenite into ferrite, pearlite, bainite and martensite in cooling process [24] are included into effective heat capacity.…”

“…A fraction g i for diffusive phase transformations (austenite into ferrite, pearlite and bainite) is determined by Johnson-Mehl-Avrami (JMA) equation [24,27,28] …”