MATHEMATICAL SIMULATION
OF THE WELDABILITY OF MODERN STRUCTURAL STEELS
by
Prof. V.Makhnenko (E.O.Paton Electric Welding Institute, Kyiv, Ukraine),
Prof. P.Seyffarth (SLV, Rostock, Germany)
ABSTRACT
The prediction of characteristic weldability problems (risk of hot and cold cracking, assuring required mechanical and functional properties of welded joints) of modern structural steels using mathematical simulation for various technological variants and welding conditions is closely related to the capability to quite reliably model the whole number of physical phenomena, which accompany the welding process and specify the quality of welded joints, such as heat- and mass-transfer, chemical composition of the penetration zone, microstructural changes in the weld metal and the near-weld region, local concentrations of diffusive hydrogen, the kinetics of volumetric effects and changes of mechanical properties, stresses and plastic strains in heating and cooling etc. In the majority of cases, only the integral account of the phenomena mentioned allows development of models which are more or less comply with modern views concerning the risk of hot and cold crack formation and ensurance of the specified level of mechanical and functional properties in weldments.
The given report considers the use of such integral approach concerning the multi-pass fusion welding of a compound butt weld in thick-walled shells (tubes) of ferritic and austenitic steels. By using mathematical simulation, the study is made of the development of thermal fields, dimensions of the penetration zone, of chemical composition of a multi-pass weld, of the microstructure and properties of the penetration zone and the near-weld area, of the kinetics of high-temperature plastic strains in the penetration zone and accordingly of the risk of hot cracking, the kinetics of microstructural changes and stresses in the near-weld region of the ferritic steel element and of the risk of cold crack formation.
Fundamentals
Currently, a large experience is accumulated on mathematical simulation of various physical phenomena which accompany the welding process and significantly influence the weldability i.e. the occurrence of imperfections (hot and cold cracks), and receiving of required functional properties in welded joints [1-5]. There are a number of works that propose mathematical models and criteria to assess the risk of hot and cold crack formation in welding modern structural steels and to evaluate the functional properties [4,6].
The present work implements these approaches to predict the weldability of butt welded joints of thick-walled tubes (see Fig.1) of austenitic (316L) and ferritic (A508) steels in multi-pass thin-layer argon TIG-welding into a deep groove. The filler metal was a Ni-based alloy (Inconel 690). Chemical composition of materials is given in Table 1.
Table 1 Chemical Composition of Parent and Filler Materials
Material
/ Element, %wt.C / Mn / Si / Cr / Ni / Mo / Nb / Al / Ti
A508 / 0.162 / 1.350 / 0.296 / 0.196 / 0.700 / 0.504 / 0.006 / 0.017 / 0.0
Inconel 690 / 0.030 / 0.100 / 0.150 / 30.00 / 60.00 / 0.010 / 0.021 / 0.0 / 0.330
316L / 0.030 / 1.600 / 0.500 / 17.00 / 12.00 / 0.500 / 0.0 / 0.0 / 0..0
The basic idea of the prediction consists in the following. Based on the given groove shape, welding conditions, and heat transfer, a temperature field is calculated, where are coordinates of the joint's points; is time. At relatively high welding rates, a scheme of fast moving heat source can be used and the problem can be solved in terms of axial symmetry. This considerably reduces the amount of calculations. Based on the known temperature field for each welding pass, the penetration zones of the base metals (I and II) and of previous cladded layer (III) are defined. Based on sections , and - the filler's section in the welding run – a mean chemical composition of the penetration zone at the given run is specified
, , (1)
where is chemical composition of the -th zone, .
Based on the magnitudes of for the given penetration zone and using Schaeffler's diagram with experimental data indicated on it relating to the material's susceptibility to hot, cold cracks, and embrittlement (Fig.2), the computer-aided calculations are carried out of occurrences of hot and/or cold cracks in the penetration zone as well as of its expected functional properties. The susceptibility to hot (crystalline or liquation) cracking according to Fig.2 is a necessary but not sufficient condition for their occurrence. Certain deformational conditions in a brittleness temperature range (BTR) of the given alloy (a penetration zone) are needed as well. These conditions can be formulated as follows
, (2)
where is active normal plastic deformation accumulated in a given point of the BTR in the direction of ; is critical deformation at hot crack formation having a normal to the crack's plane. The condition (2) is sufficient to specify the crack formation in a given point. However, its usage is complicated by limited data on . Using for that purposes relatively simple Varenstrain's tests [7] is promising to overcome these difficulties. In absence of rather reliable data on , condition (2) can be used for comparison of alternative technologies assuming that the higher , the higher the probability of hot crack formation [8].
Similarly, for alloys susceptible to cold crack formation according to Fig.2, the following sufficient condition of their formation at the cooling of the penetration zone is proposed
, (3)
where are normal stresses (residual ones) responsible for cold crack formation characterized by the normal ; is critical magnitude of these stresses for the corresponding microstructure, hydrogen content etc. [8].
It can be stated a priori, that , i.e. at , the cold cracks with the normal do not occur.
Condition (3) is also applicable outside the penetration zone. However traditionally it was used only rarely, since in engineering practice the determination of and until recently was very difficult.
Currently, numerical predictions of the -magnitudes in the potential areas of cold crack formation in welding structures of modern steels do not yield a problem [5,9]. That sharply increases an interest to using of condition (3) and stipulates experimental determination of [7]. Here of large importance is accounting for microstructural changes in the near-weld region caused by welding, since they can significantly affect both the and the .
This problem is given a special consideration in the present work. Regarding the penetration zones in high-alloyed chromium-nickel steel, the Schaeffler's diagram (or the WRC-1992 diagram [10]) allows to calculate the final expected microstructures after complete cooling depending on the equivalents of chromium (Creq) and nickel (Nieq). For the Schaeffler's diagram
. (4)
The calculated microstructure is characterized by the weight shares of corresponding phases – austenite (), -ferrite (), and martensite (). The kinetics of changes in for this area can be represented in terms of temperature changes only, i.e.
, , at ,
, , at , (5)
, , at ,
where is a solidus temperature of a given alloy; is a temperature of a start of the martensite transformation; is a temperature of an end of this transformation;
, . (6)
is calculated using a relationship [11]:
At
, (7)
where at 21, 10.5, 16.8; at , 10.5, 16.8; at 27, 7.8, 9.5.
A value of for the chromium-nickel alloys under consideration with accounting for (6) can be evaluated using the relationship [11]
. (8)
Prediction of a microstructure in a heat-affected zone (HAZ) of ferritic steel is based on the following relationships:
at , , if ; (9)
at ; if ,
where is defined using a diagram of non-isothermal austenite transformation for the given steel at corresponding heating and cooling cycles. Usually, the characteristics of this cycle include a maximum temperature of heating , a cooling time in the temperature range of 800 oC through 500 oC, . The available experience [12-14] demonstrates that at plain thermal cycles the magnitudes of can be rather accurately predicted (in engineering sense) by using , when two points of austenite transformation diagram are known, namely and corresponding to cooling times from 800 oC to 500 oC at which and , respectively.
In [12], the following relationship has been proposed for these purposes:
, (10)
where , , , , . Here, ,, and designate a ferrite-pearlite, pearlite, and bainite phases, respectively. Concerning the function in (9), it is more convenient to use it in a form of (6) by replacing a subscript by . Then the magnitudes of and for the given steel can be obtained using its austenite transformation diagram.
By having defined the magnitudes of in an arbitrary point of a material at the moment , an entire line of mechanical and thermal-physical properties of the material can be determined
, (11)
where is the value of the -th property of the -th phase at the temperature .
A function of free relative elongations
, (12)
where is a specific volume of the-th phase at temperature , in cm3/g. According to experimental data from [15]
,
, (13)
.
The approach introduced has been used in development of a computer program in which temperature fields, stresses, and strains were defined with taking account of the relationships described between thermal and mechanical properties and the microstructure in the penetration zone and HAZ. The numerical solution is obtained by successive observations of temperatures, stresses, and strains using corresponding algorithms shown in [8,9,14].
Results of Calculations.
Below given are calculation results for the welded joint in Fig.1. Geometry dimensions were as follows: mm, mm, mm, mm, mm, mm. One-sided welding was used. The geometry of a groove is shown in Fig.1, b. Here, mm, , mm, mm, mm, mm, mm, mm with . Welding conditions were such that effective specific heat input in the section of each deposited layer was 1.04 kJ/mm2. The layers were 1.5 mm thick. Base metal of the element I was steel A508, that of element II – steel 316L. The filler material was Inconel 690 shown in Table 1. Mechanical properties were taken from [14]. Fig.3 illustrates the results of calculations of dimensions and shape of a penetration zone for pass No.20. Also shown are dimensions of the penetration zone, and average chemical composition in terms of and , and expected final microstructure at , revealing high susceptibility to hot cracking. Assessment of the risk of formation of these cracks at various points of the weld has been based on criterion (2). The BTR for crystalline cracks has been assumed in the range of 1260 through 1200 oC. For presentation purposes and comparison on the risks of hot crack formation characterized by the normal , a ten-point scale has been introduced. The magnitudes of are defined depending on ratio, as follows
. (14)
Fig.4 illustrates the magnitudes of () for hot cracks after the 20th pass at . From these data it follows that the risks are higher than . The risks are insignificant.
Data in Fig.5 demonstrate the changes of microstructure in the near-weld region of the detail of ferritic steel having initial microstructure , , . It can be seen that without preheating (oC), the microstructure is mainly that of martensite. However, the thickness of this region along coordinate is in the limits of 1 mm. Preheating at 350 oC sharply changes the martensite content in the near-weld region. This, in turn, should effect the risk of cold crack formation. To quantitatively describe the risk mentioned, the criterion (3) is used combined with the condition that cold cracks do not occur if the value of in a given point is less than a certain threshold value depending on the hydrogen content. For presentation's sake, the combined criterion of cold crack formation is introduced, namely
, (15)
where and are some characteristics of steel A508 depending on the hydrogen content [16]. Below given are calculated data of corresponding to and MPa. Fig.6 illustrates these data for the near-weld region after a 20th pass at oC in a ten-point scale, when the -unit is tied with the as follows:
,MPa / 0-23 / 23-34 / 34-51 / 51-76 / 76-114 / 114-171 / 171-256 / 256-384 / 384-577 / >577/ 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
For the cases of oC . It is seen, that the risk of cold crack formation at oC is the highest for the cracks characterized by . However, small thicknesses of the layer in which such cracks are possible stipulate the possibility of occurrences of only small cracks having lengths in the limits of 1 mm. Concerning the cracks with normals and , their lengths along the weld line can be rather significant.
By knowing chemical composition, microstructure, residual stresses and strains, a whole number of functional properties of the welded joint can be predicted [6]. Without considering this in details, it only should be mentioned that at our current knowledge of material's behavior due to the welding thermo-deformational cycles the method described deserves special attention for comparative evaluations of different weldability problems. As an illustration, Table 2 compares numerical results after the 20th pass for the real welded joint considered and for its model (small-scale specimen) which differ only in their dimensions, as shown in Fig.1: mm, mm, mm, mm. Other dimensions are the same for both cases.