Finite Element Simulation of Carbide Precipitation in Austenitic Stainless Steel 304

A three dimensional transient finite element model with Gaussian heat source was proposed to predict the heat transfer in Gas Tungsten Arc Welding (GTAW) of stainless steel 304 and experimental tests were conducted to study chromium carb ide precipitation and to verify the developed model. The position of chromium carbide precipitation band and its relation to welding parameters were studied. The results showed, increasing the heat input of weld, increases the distance in which precipitation in austenite grain boundaries occurs. After measurement of carbide-band distance from weld centre and using obtained time-temperature curves of the developed model, the distance of carbide-band from the weld centre line was simulated. Finally, good agreement was observed between experimental and simulat ion results in terms of pred iction of thermal history and carbide precip itation.


Introduction
During weld ing of stainless steels, local sensitized zones oft en develop . Th is is because o f ch ro miu m carb ide fo rmat ion at g rain boundaries , resu lt ing in ch ro miu m depletion at regions adjacent to the grain boundaries [1][2][3][4][5][6]. Chro miu m depletion creates many local galvanic cells and if chro miu m content gets less than 12% wt., sensitivity to intergranular corrosion in the mentioned areas will occurs [7]. The sensitivity o f austenitic stainless steels contain more than 0.05%wt. carbon is often due to heat affected zone and named weld decay [ 8,9].Chro miu m has a very co mp os itio nal ten dency to carbo n at 650-85 0℃ ; if austenitic stainless steel is held for more than the specific time at the above mentioned temperature range, carbon rich chromiu m carbides often in the form of M 23C6 at austenite g rains bo und aries will b e fo rmed [8, 1 0]. Req u ired sensitization t ime of stainless steels is usually shown as C-shape curves in wh ich Carbon-Time -Temperatu re is being shown [11]. Sample of curves for stainless steel 304 has been shown in Figure 1 [7]. Chemical co mposit ion, thermal cycle, internal or external stresses as well as service loadings; welding operations or previous transformat ion and the environ ment where the part is used are four main effect ive fact o rs o f s ens it iv ity [10]. A n aly tical and numerical methods are used widely to investigate thermal and mechanical behaviour of welds. Rosenthal proposed the first process of analytical solution in welding which contained simplify ing assumptions such as point heat source, constant thermophysical properties of material and steady-state heat flow [12]. Many computerized models have been proposed for studying two and three-dimensional heat flow during weld ing processes. In those models many of Rosenthal's numerical solution hypotheses have been changed; for instance, Kou et al. [13] studied the heat transfer during the welding of 3.2 mm thick 6061 alu minum sheet. Masubuchi et al. [14] ut ilized thermal analysis to study the residual stresses. Lee et al. [15] simu lated the heat transfer in similar and d issimilar joints between structural steels. Teng et al. [16] investigated the effect of speed, sample d imension, external restraint and preheat on heat transfer and residual stresses. Taljat et al. [17] studied the heat flow and residual stresses in GTAW process and noticed the effects of solid-state transformat ions. Lu et al. [18] proposed a model to study current distribution, power and heat flo w in GTAW welding process. Teng et al. [19] also suggested a model to evaluate the effect of sequence on the distribution of heat and residual stresses in SAW process. Despite the importance of weld decay phenomenon in austenitic stainless steels and its close relationship with thermal cycle, it seems that no numerical model has been proposed to study the relation of these phenomena yet. Therefore there is a need of an investigation these issues. This paper reports a thermal simu lation of GTAW of austenitic stainless steel 304 to study chromiu m carbide precip itation and its relationship to weld ing parameters.

Experimental
All Six 160×80×3mm samp les of stainless steel 304 were p repared; the surfaces were cleaned with acetone and bead-on-plate automatic GTAW welds without any filler metal were made at the centre of samples. Used physical and chemical p roperties of steel sheet were respectively according to the Tables 1 and 2. Applied weld ing parameters for the samples are in Table 3. The diameter of applied W-%2Th electrode was 1.6 mm, the internal diameter of ceramic nozzle was 12 mm, argon gas flo w was 5 lit re/ minute and the arc length was 0.75 mm. Welding o f all samples were done on a copper block, then transverse section at the centre of samp les were p repared fo r macroscopic study. After usual metallographic stages in macrostructural revealing of sections, electroetch technique with % 10 o xa lic acid solution, voltage of 6 V and 15 second was used, photos of appeared sections were taken by utilizing stereograph microscope, and the optical microscope was used to calculate the distance of carbide band in all of the specimens.

Mathematical Model
Modelling of heat source is the most important point for thermal simulat ion of weld. The amount and the technique of heat distribution are effect ive factors for the size of weld pool and heat affected zone (HAZ). The amount of heat input fro m arc, heat distribution in the sample and the travel speed of heat source are the important parameters to formulate and modeling the heat source. Usual methods of source modeling in weld ing include: d istribution of surface heat flu x, distribution of volumetric heat flu x and comb ination of above two mentioned models. The amount of heat given to the work piece in unit of time is being calculated according to equation (1): In the above relation (I) is current intensity, (V) is voltage and (η) is arc efficiency. There are other factors such as kind of shielding gas, arc length, geo metry of electrode, shape and dimensions of ceramic nozzle and type of work piece that affect on η [20].In welding with low current and h igh voltage, if the heat energy is assumed as surface thermal flu x, satisfactory results will be obtained. Arc can mix up the surface of weld pool and affects the distribution of surface heat energy. According to Lu et al. currents more than 225A mix up the weld pool surface; it can assumed a flat free surface for weld pool at lower currents [18].In the present study, energy distribution of static arc with surface thermal flu x is defined according to equation (2) in which the heat energy is assumed to be Gaussian: In the above, (Q) is the welding input energy, (r) is the distance from the center of heat source and (r′) is the Gaussian distribution parameter [21]. The amount of η is set 0.6 in equation (1) and r' is set 1.5 mm. Finite element method and ANSYS software as well as two types of elements are used to analyse the model. To simu late the bulk model, SOLID90 (volu me thermal element) was used and SURF152 (surface element) was utilized to simu late the surface heat flu x. It is worth noting that in the finite element analysis, 3680 elements and 19220 nodes have been emp loyed. Convection effects on the top and bottom surfaces of sheet considered with convection coefficients of h=15 W/ (m 2 K) for the surface in contact with air and h=800 W/ (m 2 K) for the surface in contact with copper sheet. Radiat ion of surfaces was abandoned and transient heat flow was analysed in different welding conditions. To account for heat transfer due to flu id flow in the weld pool, the thermal conductivity was assumed to increase linearly above the melting po int by a factor of about three [17]. For modelling of heat source movement at time intervals, after apply ing heat on considered nodes, source was transferred to the front nodes. For solving the governing equations a finite element base program, ANSYS was employed. Equation 3 shows the governing heat conduction equation: Where T is the temperature, K is the thermal conductivity, C is the specific heat, ρ is the density and Q is the rate of heat generation per unit volume (Q=0 fo r this case) and t represents welding time. Heat flu x at the top surface is given by the equation 4 (as a boundary condition). The imposed boundary conditions are illustrated in Figure 2.   Table 4 and for instance, experimental and simulated weld section of sample 4 are shown in Figure 4. According to Table 4, increasing the current and resulted welding heat input causes weld pools dimensions will get greater.

Results and Discussion
One of the simulat ion results is time-temperature curves of different points. These curves can estimate the cooling rate and the staying time of different points around the weld pool in sensitizat ion temperature range. To verify the model, precise formed carb ide band zone near the surface of samples was investigated. The concerning results are shown in Table 5.   Comparison of experimental and simulated weld pool dimensions for specimen 4   Figure 6. According to the C-shape curves at 650-850℃ which is sensitizat ion range in austenitic stainless steel, a min imu m maintenance time is needed for steel to be sensitized and chro miu m carbide to be precipitated at austenite grain boundaries. In these curves, according to the cooling rate of a point which is 4 mm far fro m weld (Curve A), needed time for carbide boundary formation is prepared and carbide precip itation is happened. For points with distances less than 4 mm in specimen 4 (Curve B), because of high cooling rate, the minimu m time of boundary formation doesn't exist and even in points with greater distances than 4 mm (Cu rve C), carbide boundary doesn't form because points' temperature does not reach to maximu m needed level. The effect of welding parameters on carbide boundary formation distance from the centre of weld pool is another important factor. Regarding the obtained results, with increasing weld ing heat input, the carbide band's distance is increased. When heat input is increased, the effective temperature range for chro miu m carbide to precipitate at austenite boundaries will be moved to farther distances relative to weld pool centre. For co mparison, the effects of increasing the current and its effect on the temperature distribution in specimens 1 and 6 are shown in Figure 7.

Conclusions
In the present study a thermal model was developed to model heat transfer and carbide precipitation in weld ing of austenitic stainless steel 304. The results show that the proposed model has capability to predict the dimensions of weld pool and thermal history of different points of the welded samp les and increasing the current results in the increased weld heat input and increased dimensions of weld pool. Since chromiu m carb ide precipitation occurs at the specified temperature range, the developed finite element model can anticipate the occurrence area of th is phenomenon. At a specific current, since the cooling rate of points adjacent to weld is increased and there is not enough time for the formation of chro miu m carb ide, the phenomenon doesn't happen; at the farther points from weld line, the carbide band doesn't occur because of maximu m temperature limit doesn't approach to 650-850℃ .When the current is increased and temperature d istribution method is changed, sensitization temperature range will be moved to the further distances fro m weld line. Consequently, carbide band is formed at more distant regions and the current developed model anticipates this change easily. The possible future works are modeling of this phenomenon when filler metal is used and the effect of heat treatment on carbide precipitation.