1. Introduction
The effort to obtain steels with higher mechanical properties is also associated with attempts to reduce grain size, as the yield strength (the Hall-Petch equation) and other mechanical properties are dependent on grain size. In addition to other changes caused by welding processes, a change in grain size, especially in a high-temperature heat-affected zone (HAZ) area, is a very negative phenomenon. For thermomechanically processed steels, these phenomena are unfavorable and, unfortunately, irreversible. Considerable attention therefore needs to be paid to the issue of grain growth in the HAZ of welded joints. Grain size is important, not only for the material mechanical properties but also for the course of transformation processes. An austenitic transformation leads to longer times and increases the risk of martensite formation.
Changes in grain size occur during transformation processes, recrystallization processes, and long-term temperature exposures. The thermodynamic driving force of grain growth is the reduction of surface Gibbs free energy. Grain growth leads to a reduction in the grain boundary area and, thus, to a reduction in the amount of free energy. The change of grain size is related to changes in temperature and is also dependent on the proportional amount of the relevant phase. The following basic rules apply to grain growth [
1]:
Grain growth occurs by moving grain boundaries rather than coalescing.
The motion of the grain boundary is interrupted, and the direction of motion may suddenly change.
Grain can grow into another at the expense of its volume.
Grain consumption rates at the expense of others are often increased when grains are almost consumed.
The curved border usually migrates to its center of curvature.
If the grain boundaries of one phase meet at angles other than 120° grains with an acute angle are consumed so that the angle approaches 120°.
The first models based on these physical foundations were developed in the early 1950s (Smith. 1952; Burke and Turnbul, 1952) [
1]. However, there was a big difference between theoretically and experimentally determined values. In 1980, a new approach based on computer simulations was applied, and processes that were difficult to observe experimentally (such as the volume change rate of individual grains) could now be observed on the basis of simulation calculations. Several simulation methods have been developed over the years, with the “Monte Carlo Potts model” being the most used. A description of this method is given in [
2,
3]. The general relationship for grain growth is given by (1), and the constant
K is expressed by (2) [
4].
In Equations (1) and (2), D is the current grain size, D0 is the initial grain size, K is the proportionality constant that depends on the thermodynamic temperature T and the activation energy Q required for grain growth, R is a universal gas constant, t is a soaking time at a given temperature, and m is a material exponential coefficient.
It has been shown experimentally that the values of the coefficient
m are in the range of 2–5. The value of
m = 2 is valid if the grain growth process is exclusively controlled by diffusion. The value of
m = 4 is used in the case of combination precipitation and diffusion along the grain boundary. As is shown below, other factors also affect grain growth [
4,
5].
As was already mentioned above, grain growth is dependent on the exposure temperature and the soaking time at this temperature, but it is also affected by other phenomena such as secondary precipitation. It has been found experimentally that the partial growth of grains already occurs after the transformation temperature has been reached. However, a noticeable grain growth in steels is only evident at temperatures above 900 °C [
6,
7]. At the same time, as temperature rises, grain growth rate increases, but there are a number of factors that slow down its growth kinetics. Most often, there is growth slowdown due to the presence of other particles that prevent the grain boundaries from moving. These are mainly very small oxides, sulfides, nitrides, carbides, or silicate particles [
4]. These particles may already be present in the material, or they may precipitate along grain boundaries at the exposure temperature. Thanks to them, restoring forces (Zener drag forces) act against the grain growth direction and arise at the borders [
4]. As a result, the grain size limit, for which the grain growth driving force is in balance with Zener drag forces, can be determined. This dimension is defined by Equation (3) as following [
8]:
In Equation (3),
Rcrit defines the grain size limit expressed as the critical grain radius,
A is the material constant for a given steel type,
r is the particle mean radius preventing grain motion, and
f is the volume fraction of these particles. The influence of Zener forces on the fixation of grain boundaries can be observed, especially at lower temperatures when all particles preventing the motion of grain boundaries are present. At higher temperatures, these particles gradually dissolve, and the Zener drag forces decrease [
8].
In his work, Górka described the influence of temperature cycles on the mechanical properties of the S700MC steel [
9]. The maximum value of a temperature cycle was 1250 °C. An important conclusion of this work was the fact that, due to performed temperature cycles, all realized cooling conditions (
t8/5—the time required to cool the sample from 800 to 500 °C for the given temperature cycle) revealed a significant decrease in the impact strength at the test temperature of −30 °C. In another publication [
10], the same author studied the effect of a simulated temperature cycle on the properties and structure of the HAZ of S700MC 10 mm thick steel plates. The simulation was prepared for both a simple and complex temperature cycle. The heat treatment results were studied by a Charpy pendulum impact test, a static tensile test, a hardness measurement, and metallographic analysis.
An analysis of the results proved that the temperature cycles during welding strongly influence the structural and phase changes in a HAZ. A rapid decrease of toughness in the affected material is associated with the separation processes of MX-type phases and the dissolution of Nb carbides and V carbonitrides in austenite during heating. Checking the amount of heat input into the joint area during welding makes it possible to reduce the unfavorable precipitation processes in the weld and HAZ, which ensures adequate joint strength. Similar conclusions were made by Górka in his work [
11].
In [
12], Górka dealt with the assessment of the microstructure and properties of the S700MC heat-affected zone after heating to 1250 °C and cooling by specified cooling rates as following:
t8/5 = 3, 5, 10, 15, 30, 60, and 120 s. The influence of temperature cycle parameters was evaluated by a metallographic analysis, a hardness evaluation, a Charpy impact test, and a static tensile test. It was determined that for all
t8/5 values, the impact strength values were very low, and the austenite transformation conditions were not a reliable basis to evaluate the weldability of this group of steels. Similar results were provided by study [
13], where the author focused on the evaluation of S700MC weldability by various welding methods. Lahtinen et al. [
14] dealt with the weldability of 8 mm sheets from two types of high-strength fine-grained steels—namely, S700MC and S690QL. Two-layer welded joints made by MAG technology with four different heat input values from 0.7 to 1.4 kJ·mm
−1, which corresponded to values
t8/5 = 5, 10, 15, and 20 s. Tests carried out on all materials included the determination of ultimate tensile strength, hardness profiles (HV5), Charpy impact tests, and microstructure analysis by scanning electron microscopy (SEM). The most notable differences in the mechanical properties of welded joints among tested materials were observed in Charpy impact tests, mostly close to the melting boundary, whereas the heat-treated steel was more vulnerable to heat affected zone (HAZ) embrittlement than TMCP steel. Rahman et al., in their work [
15], dealt with S700MC-steel austenite-grain-size, which has a direct influence on the course of austenite transformation during cooling. They described a model of non-isothermal grain growth which includes the influence of the Zener effect. The study confirmed that the grain growth kinetics of a HAZ strongly depend on precipitates dissolution kinetics.
Numerical simulations have provided a significant contribution to the optimization of welding conditions. Kik et al. [
16] dealt with the application of simulation computations for a T-weld made by laser and hybrid methods for sheets of 10 mm thickness. The simulation program SYSWELD was used in these computations, and possibilities of its application are now presented.
The SYSWELD simulation program is based on Equations (1) and (2), and computations are based on Equation (4), this expressing the grain growth rate.
This computational relationship is intended for cases where the amount of austenite in the structure is constant or decreases. In cases where the austenite content of the structure increases, two situations may arise:
In the second case, the grain size computation is carried out in accordance with Equation (5). In Equation (5), the λ value expresses the current ratio of austenite in the structure and the λ value of the transformation rate of this phase. In cases where austenite is no longer formed (λ ≤ 0), Equation (4) is applied [
17].
For the purpose of simulation computations, input data are necessary to predict the finite states of the structure and properties in the welded joint area. Therefore, it is not necessary to determine and describe all phenomena and processes during individual temperature cycles. However, it is necessary to obtain data for the prediction of finite states on the basis of realized experiments. This is also the background for the method for determining HAZ grain size values for S700MC steel.