Theoretical investigations into heat transfer in laser-welded steel sheets

Piekarska, W.; Кубяк, М.

doi:10.1007/s10973-012-2486-0

Cited by 39 publications

(22 citation statements)

References 24 publications

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“…Dilatometric and microstructural analysis supported by microhardness measurement were applied to evaluate dilatometric samples. Both CCT diagrams of S355 steel, obtained in dilatometric research for different cooling rates v 8/5 , where v 8/5 = (800÷500)/t 8/5 and t 8/5 is a cooling time in the range of 800÷500°C and final volumetric fractions of phases (final structure composition of analyzed steel) for specified cooling rates are shown in Figure 1 [15]. Fig.…”

Section: Experiment Cct Diagram Of S355 Steelmentioning

confidence: 99%

“…1. CCT diagram and phase fractions of S355 steel [15] 3. Analytical methods of phase transformations analysis.…”

Section: Experiment Cct Diagram Of S355 Steelmentioning

confidence: 99%

“…Despite these limitations, analytical formulas are invaluable in assessing the weldability and welding conditions, largely eliminating costly and labor-intensive technology research. Particularly, the use of the combined analytical methods and results of numerical analysis seems to be very attractive [11,[13][14][15][16][17]. Results obtained by analytical methods are often used in the initial analysis of material properties, preceding experimental studies and during the development of mathematical models.…”

Section: Introductionmentioning

confidence: 99%

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Application of analytical methods for predicting the structures of steel phase transformations in welded joints

Piekarska¹,

Goszczyńska²,

Saternus³

2015

J. Appl. Math. Comput. Mech.

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Abstract. The paper presents the feasibility the prediction of phase structures of the medium carbon S355 steel under the transformations running in welding process by using analytical methods. The relationships proposed here allow to specify start and finish temperatures of phase transformations in the case of formation of bainite, ferrite, pearlite and martensite structures at various cooling rates v 8/5 (t 8/5 ) as well. Continuous-Cooling-Transformation (CCT) diagram and volumetric fractions of each steel phases possible to occur are determined in function of cooling rates. Analytically obtained values are compared with results obtained by dilatometric research. Correctness of applied analytical methods in this field has been verified when the structure compositions formed in the heat affected zone (HAZ) of electric arc butt-welded sheets made of the S355 steel were predicted.

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Section: Experiment Cct Diagram Of S355 Steelmentioning

confidence: 99%

“…1. CCT diagram and phase fractions of S355 steel [15] 3. Analytical methods of phase transformations analysis.…”

Section: Experiment Cct Diagram Of S355 Steelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of analytical methods for predicting the structures of steel phase transformations in welded joints

Piekarska¹,

Goszczyńska²,

Saternus³

2015

J. Appl. Math. Comput. Mech.

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“…If the explicit effect of component segregation is neglected one can consider it indirectly using one of the models involving solidification between the solidus and liquidus temperatures. They are widely used to model various technological processes containing solidification such as continuous casting or welding [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Skrzypczak

Węgrzyn-Skrzypczak

Winczek

2015

Archives of Metallurgy and Materials

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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...

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“…This approach is found in the description of the temperature field during welding processes using analytical and numerical methods [1][2][3][4][5][6][7]. The shape of the fusion lines during arc weld surfacing exhibit shape irregularity, which is difficult to restore by means of the description of the temperature field obtained by using the analytical method and the single-distributed heat source model.…”

Section: Introductionmentioning

confidence: 99%

Modelling of a temporary temperature field during arc weld surfacing of steel elements taking into account heat of the weld

Winczek¹,

Rygal²

2015

J. Appl. Math. Comput. Mech.

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Abstract. In this work, a model of a temperature field in a steel element during a singlepass arc weld surfacing is presented. Analytical solution for half-infinite body model is obtained by aggregating temperature increments caused by applying liquid metal and heat radiation of a moving electrode. The assumptions are Gaussian distributed heat sources of applied metal and the weld and of an electric arc heat source. Computations of the temperature field were carried out during arc weld surfacing of cuboidal steel element. The results are presented as temporary and maximum temperature distribution in the element's crosssection and thermal cycles at selected points. The accuracy of the solution is verified comparing a calculated fusion line to that obtained experimentally.

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Theoretical investigations into heat transfer in laser-welded steel sheets

Cited by 39 publications

References 24 publications

Application of analytical methods for predicting the structures of steel phase transformations in welded joints

Application of analytical methods for predicting the structures of steel phase transformations in welded joints

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Modelling of a temporary temperature field during arc weld surfacing of steel elements taking into account heat of the weld

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