Structural (
Abstract
In this chapter, the welding method applied for modelling the temperature field and phase transformations is presented. Three-dimensional and temporary temperature field for butt welding with thorough penetration was determined on the basis of analytical methods of an integral transformation and Green’s function. Structural changes of heating and cooling, proceeding in a weld (in the heat-affected zone), were described using the existing formulations of phase transformations. Considerations were illustrated by an example, for which analysis of temperature fields, developed by a moving heat source, and calculations of the distribution of particular phases (structures) were carried out. Metallographic studies of the butt joints, which were arc welded under a flux, were carried out in the empirical part of this work. Their results enabled the verification of the numerical simulation results of the phase transformations.
Keywords
- butt-welded joint
- temperature field
- HAZ
- phase transformations
- numerical modelling
- metallographic examination
1. Introduction
Welding is characterised by many specific features associated with variable temperatures and variable physical and mechanical properties of the welding material. The moving heat source, characteristic of welding, partial melts the joint surface and fuses an electrode. The electrode fills a joint space with liquid metal. Hence, welding elements are subjected to varying temperature ranges, that is, from ambient to that of a liquid metal.
Crystallisation and solidification, segregation of alloy elements and solutes and structural changes caused by intensive cooling occur extensively. Thermal and mechanical states and microstructure directly state about the quality of the welding joint.
Modelling the temperature field during welding was first initiated by Rosenthal [1] and Rykalin [2], who supposed the point and linear models of heat source, respectively. The adoption of a point heat source, as in the above-mentioned studies, yields results with respect to the points located near the centre of the weld, which are significantly different from the actual temperature values. Therefore, Eagar and Tsai [3] proposed a two-dimensional (2D) Gaussian-distributed heat source model and developed a solution of temperature field in a semi-infinite steel plate. Subsequently, Goldak et al. [4] introduced a double ellipsoidal three-dimensional heat source model. There are two ways of modelling the temperature field during welding: analytical [5–14] and numerical (the finite difference methods, infinitesimal heat balances and finite element method) [15–30]. The welding methods and types of joints can be studied through these approaches [6, 20, 21, 31–33]. The construction of numerical models with heightening complexity allows more essential factors for the exact description of the structural changes in the welded steel.
2. Temperature field in the butt-welded joint with thorough penetration
Welding is characterised by an application of the movable, concentrated heat source, which in turn makes the temperature field movable in time and space:
Studies are being conducted to develop models of temperature field. Such models should have a real-time shape and temperature gradients based on the geometrical dimension of the welding element and also time. Referring to the formulated problem, the solution of heat equation for isotropic medium is essential to determine a temporary temperature field:
Analytical method, proposed by Geissler and Bergmann [34, 35], was chosen to solve this differential equation. A short description of the method, described in detail in the above-mentioned studies, is presented below.
The following assumptions were accepted in the calculations:
quantities characterising the material properties, such as thermal conductivity, temperature compensation and thermal capacity, are constant (independent from temperature),
heat waste by convection and radiation is negligible,
reciprocal interaction of temperature field and phase changes is not taken into account,
heat of fusion is not taken into consideration.
A sample with thickness of
According to Geissler and Bergmann [34, 35], the solution of Eq. (2) can be written as a superposition of Green’s function. This leads to the following convolution of integrals as a general expression of temperature
A three-dimensional temperature field with the possibility of acceptance of different geometries of samples as well as the shape of the heat source can be determined from Eq. (3).
In the case of the Gauss model of heat source, we have
where the power of source is denoted by
An infinitely long bar with the above-mentioned dimensions of cross-section was accepted in the considered example (Figure 1).
This can be written in the Cartesian coordinate system as follows:
Boundary conditions defining the surface and Green’s function were taken from the study by Carslaw and Jaeger [36]. Green’s function takes the following form:
The relationship of movement of the welding heat source to the welding element is included in
Temperature distribution can be calculated after substituting Green’s function and Eq. (4) into Eq. (10). The integral over a range of variables can be evaluated, which yields the following result:
3. Kinetics of phase transformations in a solid state
Heating processes of steel lead to the transformation of a primary structure into austenite, while cooling leads to the transformation of austenite into ferrite, pearlite, bainite and martensite. Structural changes of a welded joint, connected with its cooling (also with hardening), develop heterogeneous image of material structure, which influences the state of stress after welding. The zone with a yield point lesser or greater than that of an indigenous material can occur in the welded joint.
Mechanical properties of the joint mostly depend on the type of welding material (its primary structure and chemical constitution of steel) and the characteristics of heat cycles accompanying welding. Temperature levels attained during heating, the hold time at a particular temperature and velocity of cooling in the 800–500°C range determine the type of structure present in the joint during and after welding.
Figure 3 shows the distribution characteristics of the weld joint zone of structural carbon steel [37] with a schematic of the fragment of an iron-carbon system and fragment of the TTT-welding diagram. Together, it is categorised into the following zones:
fusion zone, which undergoes a thorough penetration and is characterised by the dendritic structure of solidification,
partial joint penetration, where material is in a semi-fluid state and creates the border between the melted material and the material being converted into austenite,
the course-grained structure, the so-called overheating zone,
proper transformation, where perfect conversion of primary structure into austenite occurs,
partial transformation between temperature A1 at the beginning of austenisation and A3 at the end of austenisation, where only a part of the structure changes into austenite,
recrystallisation.
Several studies have focused on the description and numerical modelling of steel phase transformations. These studies have been reviewed by Rhode and Jeppson [38].
The type of a newly created phase depends heavily on the kinetics of heating and cooling processes. Kinetics of those processes is described by Johnson-Mehl-Avrami’s and Kolomogorov’s (JMAK) rules [39]. The amount of austenite
In welding processes, the volume fractions of particular phases during cooling depend on the temperature, cooling rate, and the share of austenite (in the zone of incomplete conversion 0≤
The quantitative description of dependence of the material structure and quality on temperature and transformation time of overcooled austenite during surfacing is made using the time-temperature-transformation diagram during continuous cooling, which combines the time of cooling
Quantitatively, the progress of phase transformation is estimated by volumetric fraction
The fraction of martensite formed below the temperature
4. Thermal and phase transformation strains
Changes in temperature during welding cause deformations associated with the thermal expansion and deformation of the material resulting from the structural phase transformation. Deformation during the whole thermal cycle is the total deformation created during heating and cooling [44]:
Heating leads to an increase in the material volume, while transformation of the initial structure (ferritic, pearlitic or bainitic) in austenite causes shrinkage which is associated with different densities of the given structures. Then, the strain caused during heating is calculated as follows:
During cooling, the total strain (similarly as during heating) is the sum of strains associated with thermal expansion (in this case, the shrinkage of the material) as well as structural strains. Volumetric increase can be attributed to the high density of austenite (highest among the hardening structures such as martensite, bainite, ferrite and pearlite). The strain caused during cooling can be described by the following relation [44]:
where
while
where
5. The example of calculation of temperature field and phase transformations in welded flats
In the considered example, it is assumed that the welded material is steel S235 with the following material constants: specific heat
The speed and power of the movement source are assumed to be
The quantities
On the basis of the maximum temperature field achieved in particular areas of the weld joint, specific heat-affected zones were determined (Figure 9) specified by limit temperatures
The analysis of the cooling speed
Changes in temperature and volume fraction of the individual structural components at the selected points in the cross-section (comp. Figure 9) are shown in Figure 20.
Point
In strain calculations, linear expansion coefficients of the particular structural elements were assumed and structural stresses (Table 1) were determined on the basis of the author’s own dilatometric research [46].
Austenite | 2.178 × 10−5 | 1.986 × 10−3 | |
Ferrite | 1.534 × 10−5 | γB→A | 1.440 × 10−3 |
Pearlite | 1.534 × 10−5 | 3.055 × 10−3 | |
Bainite | 1.171 × 10−5 | 4.0 × 10−3 | |
Martensite | 1.36 × 10−5 |
Dilatometric graphs (thermal and structural strains as a function of temperature) for selected points of the section (comp. Figure 9) are shown in Figure 21. In Figure 21a, a dilatometric graph for point
Dilatometric graph in point
6. Verification of the results of numerical simulation of phase transitions with the results of metallographic research
In order to verify the results of the numerical calculations, metallographic tests of the butt-welded joint were carried out. For this purpose, two flats with identical geometry as calculated, that is, two flats with a thickness of 0.012 m and width of 0.1 m, were welded. The material of the flats was steel S235. Before making the joint, sheet chamfering was conducted. Then, welding was carried out with the submerged arc welding method, under welding flux Taste-3 and with SPG
Next, the images of structures of individual areas are presented. In the area of the weld (Figure 25), we observe the ferritic-pearlitic structure with a small amount of supercooled pearlite and island bainite in the dendritic system characteristic of solidified structures. In the heat-affected zone (Figure 26), ferrite, pearlite and pearlite balls supercooled with a number of non-metallic inclusions are visible. Primary structure of the parent material (Figure 27) consists of ferrite and pearlite in the band system (hardly visible).
The results of metallographic tests show high conformity with the results of numerical simulation and testify to the correctness of the developed numerical model.
7. Conclusion
The proposed model for determining temperature field allows to obtain characteristic zones of the weld joint with shapes and dimensions similar to the real ones. Metallographic verification of the results of numerical simulation of phase transitions also provided satisfactory results.
Analysis of phase transformations occurring during the welding process allowed determination of the quantitative composition of the cooling structures in the weld area (in the heat-affected zone).
This approach allows for an accurate tracking of changes in phase participations and the course of thermal and phase strains, which enable to determine, within the framework of thermoplasticity theory, welding stresses temporary and residual welding stresses.
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