Investigation of temperature cycles by real experiment and numerical simulation of welded joints from austenitic steel and aluminium

Various research methods are used in the field of scientific research. The most frequently used methods are real experiment and computer modeling. A real experiment requires equipping the laboratory with very expensive equipment. The implementation of experiments in laboratories requires knowledgeable professional personnel to operate the devices. Therefore, when investigating phenomena, the real experiment is gradually being replaced by a numerical experiment using computer technology. Computer modeling with appropriate software provides convenient investigation of technical phenomena in various areas of technological processes. Realization of experiments by computer modeling is more flexible when solving technical processes. The content of the article is a description of the investigation of temperature cycles. The experiment described in this paper focused on measuring the temperature cycles of the butt and fillet welds made of austenitic steel and aluminum. The temperature cycles were investigated via a real experiment and modelling: 1/under laboratory conditions, measured using thermocouples located in the heat-affected zone (HAZ), 2/by numerical experiment performed in the ANSYS program using FEM. Numerical simulation was used to investigate the welding process. When modeling the temperature cycles, we compared the calculated temperatures in the nodes of the model, which corresponded to the places where the thermocouples were placed in the real experiment. Results from both experiments are shown graphically.


Introduction
In the real experiments were the weld joints made by a fusion welding with two welding methods: GMAW and GTAW.During the action of the concentrated heat flow during welding, the temperature gradient increases.This is followed by rapid cooling and solidification of the weld joint.There is a rapid change in temperature in the welded material, from the ambient temperature up to the melting point of the material being welded.The crucial and most researched in fusion welding, is the area in the close proximity to the weld, which is called the heat affected zone (HAZ).The priority in the fusion welding process is to examine the temperature cycle.A rapid change in the wide range of temperature in the HAZ can cause a change in the material structure.This can initiate a significant change in the mechanical properties, such as strength, toughness, ductility as well as others, of the welded materials [1].Those changes may pose an increased risk of stressing the weld joint, in terms of both, stresses and change in the weld shape, resulting in the weld failure and material destruction [2].
In the GMAW and GTAW fusion welding method, the heat source is move [3].Quasi-stationary process for moving heat source during welding can be solved analytically and the FEM in program ANSYS [4].In the FEM numerical experiment, the moving heat source can be modeling according to the Gaussian distribution or to the Goldak double ellipsoid [5,6].In all experiments, it is always necessary to evaluate the obtained results.In the contribution therefore is the comparison and evaluation of the results from the real experiment and the numerical simulation [7].With computer modeling it is possible to obtain more complex results in the HAZ in the numerical simulation of FEM in the ANSYS program.

Methods of solving temperature cycles in a weld joint
The range of changes and temperature distributions in the material being welded can be examined by various methods.From the point of view of the process studied, problem can be stationary and nonstationary, linear and non-linear.Temperature cycle solutions are divided into direct and indirect.Methods of solving can be divided into three basic areas of solution: numerical, analytical and experimental.The most commonly used methods are experimental methods.To investigate the temperature cycles, we chose a conventionalreal experiment on the one hand, and a numerical experiment on the other hand.
Classical experiments are performed under laboratory conditions, while the numerical ones are based on a computer simulation of the process examined.The experimentally obtained data are further analysed and processed into the final result.

Materials
It is important for practice to know the temperature cycles in the welding process.Their shape depends on the welding technology and the base material of the weld.The experiment was performed on the samples of austenitic steel X 10CrNi 18-8 used to make a butt weld and a fillet weld.The experimental sample of the fillet weld was made of aluminium of 99.5 % purity.

Real experiment
An integral part of the experimental research implementation was the theoretical readiness of the research team and the technical equipment.The most important device for our experimental solution of temperature cycles was the Quantum X MX840 data acquisition unit shown in Figure 1.
The universal measuring device Quantum X has 8 inputs that support 12 different types of sensors.Scheme of the measuring unit connection to the computer and the object of measurement to measure one variable can be direct, as shown in Figure 1a.Connection of two Quantum X universal -type measuring systems via a switch is shown in Figure 1b.For recording and evaluating the measured values, a special computer program is used.To measure the temperature cycles in the experimental sample, it was necessary to attach thermocouples to the Quantum X universal measuring system.Principle of the measurement is described in detail in [8].Based on the shape, dimensions and thickness of the material to be welded, it is important to correctly determine the type of weld.For the experimental sample made of austenitic steel X 10CrNi 18-8 for butt and fillet welds, the Gas Metal Arc Welding method is suitable.The Gas Tungsten Arc Welding method is suitable for welding an experimental sample made of 99.5 % purity aluminium.
Thermocouples were attached to the bottom of each experimental sample at HAZ locations (Figure 2), where the welding process was conducted.The welding process was performed at the ambient temperature of 20 °C.The experimental samples were welded at the welding parameters corresponding to the sample material and the shape of the weld (Table 1).

Numerical simulation
Numerical experiment also requires the correct definition of the problem.Solution to a thermal problem is possible if the designed geometric model is assigned with the material properties of the base material and the filler that form the material model.An integral part of the thermal task is the heat balance with the appropriate distribution of the heat flow and the conditions of unambiguity that define the mathematical model of the thermal problem.

Mathematical model
The defined problem of thermal task is solved by FEM, i. e. by dividing the investigated area into the final number of elements of appropriate shape and size.Then the mathematical model becomes a set of linear equations with the variable function Ti, which is the function at the node, corresponding to the total number of nodes.Solution to the thermal problem using the finite element method will result in the form of a matrix [10,11]: where: [K]global matrix of thermal conductivity, [C]global matrix of thermal capacity, {T}vector of the nodal temperatures, {F}global residual vector, Tvector of temperature change versus time at nodal points.
Mathematical model of the heat problem solution by numerical simulation is the Fourier-Kirchhoff differential equation of heat conduction given by the general relation in the form [12,13,14]: [W.m 3 ] -volumetric density of internal heat sources, λ (T, t)tensor of coefficients of thermal conductivity of materials in the x, y, z directions in t time at T temperature.
The initial and boundary conditions as an integral part of the mathematical model design represent a necessary and sufficient condition for solving the differential heat conduction equation.
Boundary condition of the 3 rd can express the cooling of an unevenly heated material.Intensity of heat flow by convection depends on the value of the coefficient of heat transfer h [W.m 2 .K 1 ].The boundary condition of the 3 rd applies to the surface cooling of the heated material during fusion welding, regarding the effects of radiation, convection and conduction, and thus determining the total heat transfer coefficient in the shape showed below [12,14]: where hc [W.m 2 .K 1 ] is the total coefficient of heat transfer by convection and radiation.The initial state of the weldment is applied to determine the initial conditions for numerical simulation.In terms of the common operating conditions, the temperature of the examined weldment complies with the ambient temperature.Thus, at the initial time t = 0 s, the temperature of 20 °C is considered.
Further important stage in solving the temperature issues via numerical simulation is the balance of the thermal energy generated during the fusion process of welding.An important parameter is the determination of the actual heat input .Q for the welding methods utilising electric arc.Heat flow is defined by means of the volume elements.The distribution of heat flow in both, the weld area and the HAZ during welding can be performed in several ways.The Gaussian distribution of heat flow density takes a circular surface heat source.Representing a double ellipsoid under the welding arc, the Goldak's model of the moving heat source is the most widely used [15].
The solution of the thermal problem in the welding process in the ANSYS program is carried out by the Newton-Rapson's method as a non-stationary and non-linear task.The procedure of a thermal problem solution by numerical simulation can be summarised in the diagram as shown in Figure 3 [16].

Material model
The weld must exhibit the properties identical or similar to those of the welded material, in order to retain the mechanical properties.For the welding process, it is necessary to determine the filler according to the chemical composition of the base material.To solve the optimum temperature cycle, it is necessary to determine thermophysical properties of the base material and filler, depending on the temperature change: λ(T), cp(T) and ρ(T).

Results of temperature cycles the weld joint
In the current section, the values of temperatures measured by thermocouples during a real experiment as well as the temperatures calculated by numerical simulation during the whole welding process until cooling the weldment to the ambient temperature are graphically processed.
The results of solution to thermal problem of both weld types take the form of the temperature curves.The temperature curves illustrate the temperature distribution at any time of the welding process.

GEOMETRIC MODEL
Characterising the shape and dimensions of welded part

MATERIAL PROPERTIES
of the base and filler materials

MATHEMATICAL MODEL of thermal problem Initial, boundary conditions
Heat balance

Gaussian
Heat Source Goldak's Heat Source q q(r) r r q m . . .

Results of experimental measurements
During the experiment, all temperatures were measured using thermocouples as a function of time.Each welded material corresponds to different welding parameter therefore the heating and cooling rate of the individual experimental samples is different.
Graphical representation of temperature cycles of the experimental sample No. 1, a fillet weld made of austenitic steel X 10CrNi 18-8, is shown in Figure 4.The maximum temperature measured by thermocouple 1 was 1100 °C.Thermocouple 2 recorded the maximum temperature of 580 °C.The graph in Figure 6 shows the measured temperature values of the experimental sample No. 3, butt weld made of austenitic steel X 10CrNi 18-8.The maximum temperature measured by thermocouple 1 was 780 °C.Thermocouple 2 recorded the maximum temperature of 700 °C.

Results of the weld joint numerical simulation of temperature cycles
The results of solution to thermal problem of both weld types take the form of the temperature curves.The temperature curves illustrate the temperature distribution at any time of the welding process.
The temperature curves during welding and cooling the weldment of austenitic steel X 10CrNi 18-8 is illustrated in Figure 7 for the fillet weld or Figure 9 for the butt weld.Figure 7 graphically shows the maximum temperature value of the fillet weld from the weld site and in its close vicinity.At the selected point of HAZ, node 1, the maximum temperature reached the value of 1130 °C.On the opposite side of the fillet weld, i. e. in HAZ without weld, in Node 2, the maximum temperature attained the value of 600 °C.The graph in Figure 8 shows the temperature cycles calculated by numerical simulation of the aluminium fillet weld.The indicated temperature cycles in the selected HAZ nodes correspond to those during the steady welding process.The maximum temperature calculated was 375.9 °C in Node 1 or 372.5 °C in Node 2.

Figure 8.
The temperature values calculated in numerical simulation -Al [17].
Figure 9 shows the maximum value of the butt weld temperature in the selected HAZ nodes.The obtained temperature cycles calculated by numerical simulation indicate that the maximum temperature of approximately 820 °C is attained when fabricating a butt weld.In Node 2, the maximum temperature attained the value of 750 °C.

Figure 9.
The temperature values calculated in numerical simulation [17].

Evaluation of the temperature cycle of a weld joint
The Figure 10 shows the is others measured by thermocouples stored at 1 and 2 for the fabricated fillet welds made of austenitic steel X 10CrNi 18-8, and the temperature values calculated in numerical simulation in the nods No. 1 and 2. Both graphs illustrate a big difference in the maximum temperatures and the cooling rates.The difference is due to a uniformly moving heat source at the weld side, which warmed the material to a higher temperature.There is no direct contact of the heat source with the material on the opposite side of the fillet weld, and therefore the temperatures there are lower.
The graphs in Figure 10 show that the cooling rate at the weld side is higher, which is also expressed by the abrupt curve of the temperature decrease, denoted as Node 1.On the no-weld side, the cooling rate is slower, denoted as Node 2 in Figure 10.At the time of about 800 seconds, the cooling rate is slowed down and stabilized on both sides of the fillet weld.The correlation coefficient of compliance between the measured and calculated temperatures reached the value of 0.978.Figure 11 shows are measured isotherms by thermocouples stored at 1 and 2 for the fabricated butt welds made of aluminium of 99.5 % purity.It also illustrates the temperature values calculated in numerical simulation in the nods No. 1 and 2. The heating and cooling rates during the welding process are very high.At approximately about 800 s after finishing the welding cycle and equalisation of the welding temperatures, the cooling rate becomes steady, retarded and nearly equal at both, the selected HAZ nodes and in place of thermocouples.The correlation coefficient of compliance between the measured and calculated temperatures reached the value of 0.812.Figure 12 shows the measured isotherms by the thermocouples stored at 1 and 2 and for the fabricated butt welds made of austenitic steel X 10CrNi 18-8.It also illustrates the temperature values calculated in numerical simulation in the nods No. 1 and 2. In such a case, the heating and cooling rates during the welding process are very high.At about approximately 600 s after finishing the welding cycle and equalisation of the welding temperatures, the cooling rate becomes steady, retarded and nearly equal at both, the selected HAZ nodes and in the place of thermocouples.The correlation coefficient of compliance between the measured and calculated temperatures reached the value of 0.916.

Discussion
Several factors may influence the results of experimental thermocouple measurements:  real material properties of the base and additive materials,  manual welding method causing a non-uniform welding speed,  thermocouples placed in the HAZ at the bottom of the base material,  natural convection and imperfect insulation of the sample during welding,  natural human factor causing a certain error in measurement.
The result attained in the numerical experiment of thermal task using the FEM numerical simulation and experimental measurements are presented as temperature cycles.The temperature cycles express distribution of the temperature in the form of a curve at particular location and moment of the welding and the following cooling process up to the equalisation of temperature throughout the weldment volume.
Advantage of the above-mentioned solution is that it enables to obtain instantaneous temperature at any time and place for any welded part of various shapes and thus predict the resulting material properties, i.e.to manufacture the required type of weldment by any fusion welding technology.The result attained from numerical simulation is the temperature distribution throughout the model volume depending on time.HAZ is therefore a crucial and carefully investigated area of the welding process.
Following are the factors affecting the extent and properties of HAZ in the fusion welding process:  Material properties of the base material and filler depending on the changing temperature, the coefficient of thermal conductivity in particular;  Geometric dimensions of the material being welded, thickness in particular;  Suitable selection of the initial and boundary conditions;  Size and shape of the weld;  Heat input determined by the welding parameters.Compliance of the measured values of temperature cycles in the real experiment with those calculated by numerical simulation at the same places is significant, especially for the fillet weld made of austenitic steel X 10CrNi 18-8; the difference in compliance is 2.2 %.As for butt weld of austenitic steel X 10CrNi 18-8, the difference in compliance is 8.4%.The experiment with the fillet weld made of pure aluminium showed the largest difference in values compliance up to 18.8 %.This large difference may be due to the incorrect sample insulation in the real experiment, as well as uneven heat flux in manual welding.From a practical point of view, obtaining the temperature cycles by numerical experiment is more advantageous, as it provides wider range of the obtained results applications.In the numerical experiment, the material properties of a given model as well as the initial and boundary conditions can be flexibly adapted, while the real experiment requires additional preparation and implementation of further experimental investigations.

Conclusion
General solution of thermal problems was concentrated on the field of melt welding technology, particularly the thermal processes taking place in both, the base material and filler during welding.The attained results were expressed as the temperature fields generated in the base material during the process of welding.Also significant is the heat affected zone (HAZ) where the welding material is heated to high temperatures.Moreover, when heated to very high temperatures close to the weld, the material being welded undergoes the change in both, its structure and mechanical properties.It is therefore important to investigate the temperature fields in the related area regarding the further utilisation of the weld.
With numerical simulation, it is possible to achieve a solution in a relatively short time even for complex processes taking place in fusion welding processes.In the engineering approach to solving the given problem, the effort is to:  inclusion of all factors that may influence the given problem. Neglecting those factors that are assumed to have little or no influence on the desired result of the solution.
The obtained results can be optimized and implemented on a real system.The reasons for using simulations are as follows:  It is possible to solve even very complex systems with simulation, which cannot be solved by analytical methods and procedures. Simulation allows us to study the behavior of the system in real time, accelerated or slowed down time. With the help of a simulation model, it is possible to "simulate" a real process in a relatively short time, which can take several days or months depending on the complexity of the process under investigation. The very experience of creating a model can lead to a proposal for improving the management or structure of the system. Simulation of the investigated process or system enables a more comprehensive view of the studied problem. The simulation directly affects the creator and user of the model to go beyond the limits of their expertise and strive for a comprehensive view of the process under investigation. With the help of simulation, it is possible to check different variants of the solution, thus minimizing the risks of wrong decisions. Once created, the model can be used in other applications.
The goal of numerical methods is to create an efficient and suitable algorithm applicable to the solution and investigation of various phenomena from various fields of science and technology.

Figure 5
Figure 5 shows the measured temperature values of the experimental sample No. 2, fillet welds made of Al -purity 99.5 %.The maximum temperature measured by thermocouple 1 was 350 °C.Thermocouple 2 recorded the maximum temperature of 330 °C.

Figure 10 .
Figure 10.The temperature values measured and calculated in numerical simulation.

Figure 11 .
Figure 11.The temperature values measured and calculated in numerical simulation -Al.

Figure 12 .
Figure 12.The temperature values measured and calculated in numerical simulation.
weld austenitic steel Node 2 butt weld austenitic steel Thermocouple 1 butt weld austenitic steel Thermocouple 2 butt weld austenitic steel