Predicting the Volume Fraction of Martensite in Welded Mild Steel Joint Reinforced with Titanium Alloy Powder

Alain Ngenzi^1*, Stephen A. Akinlabi², Anthony K. Muchiri³

¹Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya.
²Department of Mechanical and Construction Engineering, Northumbria University, Newcastle, UK.
³Department of Mechatronic Engineering, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya.

DOI: 10.4236/mnsms.2023.132002                

Abstract

Welded mild steel is used in different applications in engineering. To strengthen the joint, the weld can be reinforced by adding titanium alloy powder to the joint. This results in the formation of incomplete martensite in a welded joint. The incomplete martensite affects mechanical properties. Therefore, this study aims to predict the volume fraction of martensite in reinforced butt welded joints to understand complex phenomena during microstructure formation. To do so, a combination of the finite element method to predict temperature history, and the Koistinen and Marburger equation, were used to predict the volume fraction of martensite. The martensite start temperature was calculated using chemical elements obtained from the dilution-based mixture rule. The curve shape of martensite evolution was observed to be relatively linear due to the small quantity of martensite volume fraction. The simulated result correlated with experimental work documented in the literature. The model can be used in other powder addition techniques where the martensite can be observed in the final microstructure.

Keywords

Finite Element Analysis, Martensite Volume Fraction, Dilution, Koistinen and Marburger Equation

1. Introduction

Mild steel’s excellent malleability and weldability make it popular for various applications such as cookware, machine parts, and construction [1] . Welding mild steels can have some processing irregularities that need analysis. A weak zone of the welded joint is often observed because heat makes the welded area undergo microstructural change [2] . Studies related to the strength of the forming joint of material during welding have become an area of interest. Consequently, many methods have been proposed to strengthen steel joints, including metal powder addition in welding [3] . Often, the execution of this method is to use the metal powder, which has mostly different chemical compositions with base metal, as reinforcement, filled into the groove, and a heat source is applied to form the joint. In addition to that, the heat can be provided by the conventional arc welding technique, particularly Gas Metal Arc Welding (GMAW) [3] . The final microstructure phases are obtained at the joint, using the metal addition in welding, depending on the chemical element of metal powder and the base metal. For example, it was shown that welding mild steel reinforced with titanium alloy powder in the joint using GMAW resulted in the formation of the intermetallic compound and martensite phases in the final microstructure [4] . It was due to the mismatch in the chemical composition of base metals and the reinforced powder. The intermetallic compound and martensite phase in the joint have been experimentally investigated in the dissimilar joint. Kumar and Balasubramanian [5] noted that the martensite and intermetallic compound lower the strength of the joint between stainless steel and titanium. In addition, Nikulina et al. [6] showed that the martensite formation in the welded dissimilar joint between high-carbon steel and chrome-nickel steel could give rise to failure through fatigue cracking. It is because of the high dislocation density and residual stresses that characterize the martensite.

As the experimental work consumes time and is expensive, numerical methods have been developed to predict the formation of the martensite phase when there is a mismatch of chemical composition in the joint. Esfahani et al. [7] predicted the martensite volume fraction in the dissimilar joint formed between the carbon steel and austenitic stainless using the Schaeffler diagram. The martensite phase was also observed by Prabakaran et al. [8] using the Schaeffler diagram after welding the AISI 1018 low alloy steel and AISI 316 austenitic stainless steel sheet. On the other hand, Sun et al. [9] predicted the volume fraction of martensite in three passes of welding for low alloy steel plate and the SD3 steel as electrode using the dilution-based mixture rule and the Koistinen and Marburger (KM) equation. Dupont and Kusko [10] applied the dilution base mixture rule to predict the martensite start temperature to understand the martensite formation in austenite to ferrite dissimilar welds considering separately the chemical compositions of the nickel-based electrode. Sun et al. [9] developed a thermal metallurgical and mechanical model to analysis the effect of the tempering on the microstructure, hardness and residual stress on the joint. The materials used to form the weldment were SA508 Cr.3 Cl.1 steel and S3 and SDX wire steels for base metal and filler respectively. The martensite volume fraction was predicted using the dilution-based mixture rule. From those numerical analyses, the Schaeffler diagram has the limitation of not considering the nitrogen pickup, which sometimes occurs in GMAW [11] . Still, an alternative to this may be the dilution-based mixture rule.

From the literature, it has been seen that there are still limitations on work that deals with predicting the martensite on the reinforced joint; therefore, the present paper focuses on predicting the volume fraction of martensite in welded steel joint reinforced with titanium alloy powder. First, the thermal transient is simulated to predict the temperature history at the welded zone, Barbier’s equation for determining martensite start temperature (M_s) is adopted, and the dilution effect is considered so that the new chemical element can be determined. Secondly, the KM equation is used to determine the volume fraction of martensite. The contribution of this study is to understand the impact of adding titanium alloy powder in the mild steel groove in predicting the martensite phase.

2. Methodology

2.1. Finite Element Analysis

Thermal analysis simulation during the GMAW welding process necessitates three-dimensional modeling. The ANSYS non-linear finite element code is used in this context due to its modeling flexibility and ability to obtain full field numerical solutions. The moving heat source, written in APDL command language, has been inputted for analysis runs. The following sections are steps of finite element method.

2.1.1. Governing Equation and Heat Source Model

To calculate the temperature history, the researchers employed Fourier’s equation for three-dimensional heat conduction [12] . This equation is a partial differential equation that includes temperature-dependent material properties and can be expressed as follows:

$k\frac{{\delta }^{2}T}{\delta x^2}+k\frac{{\delta }^{2}T}{\delta y^2}+k\frac{{\delta }^{2}T}{\delta z^2}+\frac{\delta Q}{\delta t}=\rho C\frac{\delta T}{\delta t}$ (2.1)

The equation above includes several variables and coefficients. The variable Q represents the volumetric internal energy generation, while T represents temperature. The spatial coordinates are denoted by x, y, and z, and time is represented by t. Additionally, the equation incorporates several coefficients: $\rho$ represents the density of the material, C represents specific heat, and k represents the thermal conductivity coefficient.

During welding, the electrode is moving along a direction. Therefore a moving heat source has to be employed. The modified Gaussian heat source model, which its frame is represented by the Gaussian function shown in Figure 1 is adopted and it is used to simulate the thermal history at different points along the welded zone [13] .

$Q_s\left(x\mathrm{,}y\mathrm{,}t\right)=\frac{3q_s}{\pi r_0^2}{\text{e}}^{\left(-3\frac{r^2}{d_0^2}\right)}$ (2.2)

Q denotes the rate of heat input. The effective radius of the welding arc is

Figure 1. Gaussian heat source model [14] .

represented by $r_0$ , and the diameter of the welding arc is represented by $d_0$ . r is calculated by:

$r={\left(x-x_0\right)}^2+{\left(y-vt-y_0\right)}^2$ (2.3)

where $x_0$ and $y_0$ represent the distance of the heat source from the reference coordinate system’s origin along the x- and y-axes, respectively. The welding arc travel speed is given by v, and the travel time is given by t.

2.1.2. Mesh

In this analysis, the geometrical model was divided into two parts and the hexahedral element was used. The first part is the fusion zone and its surrounding area. The second is for the rest of the area where no high temperature occurred (see Figure 3). Due to the high temperature subjected to the first area, a mesh convergence study is based on the maximum temperature attained after the simulation process at a node. The node located 7 mm from the origin along the reinforced welded joint (see Figure 6) was chosen for the mesh convergence study. Different maximum temperatures were obtained in the simulation as the mesh size was varied. As the size kept varying, the maximum temperature became constant, as is shown in Figure 2. Subsequently, the mesh size of 0.8 mm was chosen to reduce the computational time taken during the simulation. From the mesh convergence results, the first area was sized 0.8 mm, and the remaining area was sized 3 mm. The geometrical model was discretized into 18,072 elements and 90,730 nodes (see Figure 3).

2.1.3. Boundary Conditions

Boundary conditions specify the relationship between the domain and the external environment. In welding, boundary conditions are the external specific heat flux which is applied on the top of the specimen and heat losses due to radiation and convection are applied at all faces of the specimen. Each boundary can be described with mathematical description of thermal boundary conditions.

Figure 2. Mesh convergence.

Figure 3. Discretized geometrical model.

The specific heat flux was considered to be Modified Gaussian heat source model discussed in previous section. The equation for convection $q_c$ and radiation $q_e$ are written as [15] :

$q_c=h\cdot \left(T-T_0\right)$ (2.4)

$q_e=\stackrel{\dot{}}{\epsilon }\cdot \xi \cdot \left(T^4-T_0^4\right)$ (2.5)

The temperature of the room is denoted as $T_0$ , while the convection coefficient and emissivity coefficient for all surfaces of the plate are represented by h and $\epsilon$ , respectively. $\xi$ is the Stefan Boltzmann constant. In thermal analysis, thermal material properties also called the temperature-dependent material properties contribute to the distribution of temperature during the welding process. Those properties are density, thermal conductivity, and specific heat. As each material has their thermal property, Table 1 shows the properties of mild steel, and Table 2 shows that titanium alloy powder was considered to be the same material properties of Ti-6Al-4V. The thermal properties of the electrode were considered to be the same as mild steel because they have small differences in chemical composition. The ANSYS workbench solver did the interpolation to determine the intermediate values of the two tables.

Table 1. Thermal properties for mild steel [16] .

Table 2. Thermal properties for titanium alloy powder [17] .

2.2. Formation of Martensite

Phase Transformation

In low-carbon steel, the final microstructure is formed when the temperature is starting to cool down from the austenite finish temperature. From that period, the ferrite phase occurs in different types. First, the allotriomorphic ferrite occurs in the austenite boundary, and as the temperature keeps cooling down, the Widmanstatten ferrite forms. The ferrite formation period is usually in the range of 800˚C to 500˚C [18] . If retained austenite is remained, it becomes either bainite or martensite. When titanium alloy is added to the groove, the titanium particle reacts with the iron particles and forms the intermetallic compound. The presence of titanium alloy powder can lead to the creation of titanium carbide, which then influences the formation of the martensite phase in the welded zone [19] . Considering that the intermetallic and martensite phase cannot be predicted using the same model, this paper only concentrates on predicting the martensite phase occurring in a reinforced butt joint.

The martensite phase transformation is diffusionless, which may occur in non-isothermal phenomena such as welding. The martensite formation can start when the cooling temperature is below the $M_s$ and end at a martensite finish temperature ( $M_f$ ). Usually, the Ms can vary below 500˚C, and the $M_f$ can even go to room temperature or below. In addition to that, in case the $M_s$ is more than 400˚C, the $M_f$ would be located above the ambient temperature [20] .

The formation of martensite can then be modeled by Koistinen and Marburger (KM) equation [21] . The disadvantage of this model is the parabolic shape during the evolution of martensite [22] . The equation is written as follow:

$V_M=1-\exp \left[-A_m\cdot \left(M_s-T\right)\right]$ (2.6)

where $V_M$ is the volume fraction of martensite, $M_s$ is the martensite start temperature, T is temperature, $A_m$ is the constant rate. The value of the constant rate depends on the type of steel. In low-carbon steel, the value is usually equal to 0.011 [23] .

It was found that the $M_s$ varies with the chemical composition of materials. For that reason, many researchers have developed different regression models to predict the $M_s$ base on the chemical composition of the material. Considering that the titanium may affect the Ms, the equation employed has to consider the titanium for determining $M_s$ . Barbier [24] created a model that can be used to determine the $M_s$ . Barbier’s equation is written as following:

$\begin{array}{c}{M}_s=545-{601.2}^{*}\left(1-\exp \left(-{0.868}^{*}\text{C}\%\right)\right)-{34.4}^{*}\text{Mn}\%-13.7\text{Si}\%\\ -9.2\text{Cr}\%-17.3\text{Ni}\%-15.4\text{Mo}\%+10.8\text{V}\%+4.7\text{Co}\%\\ -1.4\text{Al}\%-16.3\text{Cu}\%-361\text{Nb}\%-2.44\text{Ti}\%-3448\text{B}\%\end{array}$ (2.7)

where C, Mn, Si, Cr, Mo, V, Co, Al, Cu, Nb, Ti, and B are values of weight percentage for each chemical composition on Table 3 was taken from literature [4] .

Table 3. Chemical composition of titanium alloy, mild steel and due elements to dilution.

It is unreasonable to consider the weight percentage of only the chemical composition of the base metal, whereas the reinforced particle has different chemical compositions from the mild steel. Therefore the mixing degree of the two metals, so-called dilution, was considered. The dilution helps to determine the new chemical elements in the fusion zone [25] . The dilution calculation assumes a homogeneous mixture between two alloys and that the dilution is constant in the welded zone. The dilution is calculated using Equation (2.8) [26] .

$D=\frac{B}{A+B}\ast 100$ (2.8)

where B is the melted cross-sectional area of the reinforcement and base metal and A donates the cross-sectional area where titanium alloy filled as shown in Figure 4. In Figure 4, the red cross-sectional area was considered for determining the dilution.

To calculate the weight percentage of a new chemical element by considering the effect of dilution, therefore the mixture rule is used, and the equation is written as follows [25] :

$W=W_B\ast D+W_A\left(1-D\right)$ (2.9)

where D is the dilution; W is the weight percentage of chemical composition; W_B and W_A are the weight percentage of the chemical element in the base metals and titanium alloy powder respectively. Equations (2.8) and (2.9) assume that the loss of material due to evaporation is insignificant. Hence, they cannot be used to predict the behavior of alloying elements that have a high vapor pressure, such as magnesium in aluminum alloys [27] .

Figure 4. Dilution parameters.

2.3. Thermal Analysis

2.3.1. Weld Pool Geometry

The transient thermal analysis was used to predict the weld pool shape of weldments. The simulated weld pool geometry can be compared to the actual weld geometry obtained through optical microscopy tests to validate the simulation method’s effectiveness [28] .

To determine the simulated weld pool geometry, a cross-section of the weld joint is cut, and the temperature fields in this cross-section are examined to record the temperature contours [29] . The area where the temperature was above the melting point of mild steel for unreinforced joints and titanium alloy for the reinforced joint was defined as the weld pool geometry.

Figure 5(a) compares the simulation result and experiment result for the unreinforced joint. The red area is for the simulation result, and the white area is for the experiment. The two areas were the weld pool geometry, due to the observed temperature being above the melting point of mild steel, 1430˚C. They were compared to each other and found a good agreement between them. Figure 5(b) compares the simulation and experiment results for the reinforced joint. The same areas were identified as it was done in the unreinforced joint by considering the temperature higher than melting point of titanium, 1600˚C. They were also compared to each other and found a good agreement between them. The inaccuracy of the weld bead height shown in those figures is affected by the predetermined bead height used in the simulated model. The bead height was taken as 2 mm.

The dimensions of interest are the depth of penetration and width of the weld pool, measured along the x and y axes of the cross-section. The weld pool is defined as areas with temperatures above titanium’s melting point.

Table 4 presents the measured dimensions of the simulated and experimental butt joint geometries, indicating good agreement between the experimental and

(a)(b)

Figure 5. Comparison simulation result and experimental result. (a) Unreinforced weld pool geometry; (b) Reinforced weld pool.

Table 4. Comparison of weld pool geometry dimensions of unreinforced and reinforced joint from experiment and simulation results.

simulated values for the depth of penetration and the weld pool width. The high relative error was 10%. This error may have occurred because it was challenging to accurately replicate the actual conditions in which the process takes place. Factors such as material physical parameters may have contributed to the difficulty in matching real conditions [28] .

2.3.2. Temperature History

To collect the thermal history in the joint, a temperature probe was inserted at different distances along the weld joint, as shown in Figure 6. Thermal history was measured at four different points to observe the variation in temperature in the reinforced welded zone and unreinforced welded joint. In Figure 8, the curve shows the peak temperature has been above the melting point of mild steel, 1430˚C. It can be observed that the peak of temperature at each point is different. The observation means that as the welding heat source moves, it causes the heat to transfer from one point to another.

This movement of heat can be observed by the high temperature of the next adjacent node after the previous node has reached its peak temperature. Furthermore, the peak temperature of the next adjacent node is higher than that of the previous one, which suggests that heat is being accumulated. In Figure 7, the curve shows that the peak temperature has been above the melting point of titanium alloy powder, 1600˚C. Comparing Figure 7 and Figure 8 shows that by adding the titanium inside the groove, the titanium alloy powder slows the cooling. Titanium has a low thermal conductivity, making it retain heat for a long time compared to mild steel. It is observed even in the figures where the cooling rate from 2000˚C to 500˚C was 39.985 s and 41.768 s for unreinforced and reinforced welded joints, respectively.

Figure 6. Distances at which the temperature probe was inserted.

Figure 7. Temperature history at different points along reinforced welded zone.

Figure 8. Temperature history at different points along unreinforced welded zone.

2.4. Martensite Phase

The determination of the martensite volume fraction was started by calculating the dilution effect using Equation (2.8). This gave a value of 96%. Then the value was used in Equation (2.9) to determine the new weight percentage of chemical element in the reinforced welded zone, as shown in Table 3. The new weight percentage was used to determine the martensite start temperature using Equation (2.7) and the obtained value was 476˚C. The obtained value of M_s can be in agreement with the microstructure observed in optical micrograph. Because, in the microstructure, the lath martensite was observed and this type of martensite starts to form at a high temperature [30] . To finalize the determination of V_M parameters, the temperature was extracted from the thermal history of one point in the reinforced butt joint. The random choice of the point was because, below the martensite start temperature, the curves of points have the same cooling rate (see also Figure 7).

The chosen temperature was employed to simulate the martensite volume fraction. The evolution of martensite volume fraction was plotted in Figure 9. The C-shaped curve was expected when the KM equation is used [31] . However, due to a small volume fraction of martensite that was observed in the final microstructure, the curve was quite linear. This was also confirmed by skrotzki [32] who stated that the evolution of martensite volume fraction is quite linear when it is in the range of 6% to 60% of the volume fraction. The course of martensite phase was also in agreement with the work done by Heinze et al. [33] who predicted the martensite volume fraction by considering the prior austenite grain size. By Considering Figure 9, it is seen that the volume fraction of martensite can be predicted at different temperature. The volume fraction of martensite was 23% in the final microstructure of the reinforced butt joint. The results obtained were compared with the experimental work done by Odiaka et al. [4] (see Table 5). It was noticed that the difference between experiment and simulation results was 4.2 weight percentages. This may be because of the assumption made on the bead height. It can be concluded that the simulation results correlated with experimental work.

Figure 9. Simulation of volume fraction martensite.

Table 5. Comparison of experimental and simulation result of volume fraction of martensite in reinforced butt welded joint.

3. Conclusion

The present study was to predict the volume fraction of martensite in welded steel butt joint reinforced with titanium alloy powder. The model employed the finite element method to predict the thermal history at the welded joint which acts as driving force on the diffusionless kinetic phase transformation equation, KM equation, to predict the volume fraction of martensite. Dilution base mixture rule was then considered in determining the martensite start temperature. The results obtained were in good agreement with experimental work, with a deviation of 4.2%. This shows that the model can be used in other powder addition techniques where the martensite can be observed in the final microstructure. To increase the accuracy of predicting martensite formation, future research can concentrate on separately utilizing the diverse temperature-dependent material properties of the base metal and filler.

Acknowledgements

The author responsible for the correspondence wishes to express gratitude to the Pan African University, Institute for Basic Sciences, Technology and Innovation (PAUSTI) for their support in conducting this research.

Authors’ Contribution

Conceptualization: AN, SAA and AKM, methodology: AN, SAA, and AKM, software: AN, validation AN, SAA, and AKM, data curation AN, formula analysis AN, SAA, and AKM, resources: AN, SAA and AKM, writing original draft preparation: AN, SAA and AKM, writing review and editing AN, supervision: SAA and AKM, project administration AN.

Data Availability

The real data used to illustrate the developed model is within the manuscript.

Conflicts of Interest

The manuscript has been reviewed and approved by all authors for publication in its current form.

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