In this paper an analysis of phenomena of laser welding of steel thin-walled element is presented. Coupled mathematical and numerical models of thermal phenomena, mechanical and phase transitions in solid and liquid state are proposed. To the modeling of phase transformation in the solid state the macroscopic model based on the analysis of the CTP diagrams are used. In the simulation of thermal phenomena the solution of heat transport equations with melting and solidification model is applied. Mechanical phenomena using the stress model for a elastic-plastic range and the isotropic strengthening of material are simulated. In order to solve analyzed problem the software using the finite element method (3D problem)has been developed. The influence of the individual elements of the model on the stress field and the plastic deformation field of welded steel element is determined. A comparative analysis of the results of numerical calculations for the case: the dependence of material properties on the temperature, the inclusion of phase transformation in the solid state, the dependence of the yield strength on the phase composition of the material are made.
A. Kulawik and A. Bokota
Modelling of Heat Treatment of Steel Elements with the Movement of Coolant
A mathematical and numerical model of hardening process using the generalized finite difference method for the movement of fluid and heat transport have been proposed in this paper. To solve the Navier-Stokes equation the characteristic based split scheme (CBS) has been used. The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless method. To determine of the phase transformation the macroscopic model built on the basis of CCT diagrams for continuous cooling of medium-carbon steel has been used. The temporary temperature fields, the phase transformation, thermal and structural strains for the heat treated element and the fields of temperature and velocity for the coolant have been determined. The comparative analysis of the results of calculations for the model without taking into account movement of coolant has been carried out. The effect of the notch in the shaft on the cooling rates and fields of the kinetics of the phase transformations has been presented.
R. Bęczkowski, J. Wróbel and A. Kulawik
In the paper, the regeneration process of the material in grade C45 using the MAG welding was analysed. The effect of preheating on the properties of the regenerated layers was determined. Preheating technology was used to facilitate the process of regeneration and minimize the risk of imperfections. The use of numerical methods allows one to observe the direction of changes in the properties, structures and emerging stresses and accompanying strains of the elements depending on the temperature applied for preheating. Modeling of the stress state in the element made of medium carbon steel during the regeneration process was performed on original software based on the finite element method. The implemented numerical model consists of three basic elements – thermal phenomena, mechanical phenomena and phase transformations in the solid state. The performed numerical analysis made determining the optimum heating conditions possible, so that the material in the area of joint didn’t show tendency to create structural notches associated with the stress state.
J. Wróbel, A. Kulawik and A. Bokota
In the paper the use of the artificial neural network to the control of the work of heat treating equipment for the long axisymmetric steel elements with variable diameters is presented. It is assumed that the velocity of the heat source is modified in the process and is in real time updated according to the current diameter. The measurement of the diameter is performed at a constant distance from the heat source (Δz = 0). The main task of the model is control the assumed values of temperature at constant parameters of the heat source such as radius and power. Therefore the parameter of the process controlled by the artificial neural network is the velocity of the heat source. The input data of the network are the values of temperature and the radius of the heated element. The learning, testing and validation sets were determined by using the equation of steady heat transfer process with a convective term. To verify the possibilities of the presented algorithm, based on the solve of the unsteady heat conduction with finite element method, a numerical simulation is performed. The calculations confirm the effectiveness of use of the presented solution, in order to obtain for example the constant depth of the heat affected zone for the geometrically variable hardened axisymmetric objects
A. Bokota, A. Kulawik, R. Szymczyk and J. Wróbel
In the paper the complex model of hardening of the hot-work tool steel is presented. Model of estimation of phase fractions and their kinetics is based on the continuous heating diagram (CHT) and cooling diagram (CCT). Phase fractions which occur during the continuous heating and cooling (austenite, pearlite or bainite) are described by Johnson-Mehl (JM) formula. To determine of the formed martensite the modified Koistinen-Marburger (KM) equation is used. Model takes into account the thermal, structural, plastic strains and transformation plasticity. To calculate the plastic strains the Huber-Mises plasticity condition with isotopic hardening is used. Whereas to determine transformations induced plasticity the Leblond model is applied. The numerical analysis of phase compositions and residual stresses in the hot-work steel (W360) element is considered.