The grain microstructure of molten pool during the solidification of TC4 titanium alloy in the single point laser cladding was investigated based on the CAFE model which is the cellular automaton (CA) coupled with the finite element (FE) method. The correct temperature field is the prerequisite for simulating the grain microstructure during the solidification of the molten pool. The model solves the energy equation by the FE method to simulate the temperature distribution in the molten pool of the single point laser cladding. Based on the temperature field, the solidification microstructure of the molten pool is also simulated with the CAFE method. The results show that the maximum temperature in the molten pool increases with the laser power and the scanning rate. The laser power has a larger influence on the temperature distribution of the molten pool than the scanning rate. During the solidification of the molten pool, the heat at the bottom of the molten pool transfers faster than that at the top of the molten pool. The grains rapidly grow into the molten pool, and then the columnar crystals are formed. This study has a very important significance for improving the quality of the structure parts manufactured through the laser cladding forming.
Currently, the laser cladding technology has become the new breakthrough of the complex structure parts for aviation manufacturing process. In the laser cladding technology, the high input heat can make the surface of the substrate and the laser cladding material melt and then the molten pool is formed. It avoids the disadvantages of high machining allowances in the traditional process, long computer numerically controlled (CNC) machining time, low material utilization, long production cycles and high manufacturing cost [
Principle of the laser cladding forming.
The solidification of the molten pool is a very complex and unbalanced rapid solidification process. It is difficult to observe the growth of grains during the solidification of molten pool experimentally because of the high temperature and the rapid solidification rate affected by the size of the molten pool and the material features. With the development of the computer science, the numerical simulation technology is a good method to analyze the growth of grains in the solidification of molten pool. It contributes to revealing the evolution of microstructures and improving the quality of the workpiece in the laser cladding forming.
The researches on the microstructure simulation have achieved many significant accomplishments since the end of the last century [
Cellular automaton (CA) which is a kinetic and stochastic model scattered in time, space, and state has been widely used in solidification and recrystallization of the material science in recent decades [
Shang et al. [
In this paper, compared with the experimental microstructures, a model combining the cellular automaton and the finite element method was developed to simulate the growth of the grain occurring in the molten pool during the single point laser cladding based on the temperature distribution.
The temperature distribution has a significant impact on the grain microstructure in the molten pool. The heat transfer model [
The enthalpy is defined in this paper to solve the release of the latent heat during the solidification of the molten pool:
In terms of the nucleation of the solidification in the molten pool, the paper considers only the heterogeneous nucleation. For simulating the growth of the grain, a continuous nucleation model which was proposed by Rappaz and Gandin [
Gaussian distribution of nucleation sites is assumed to account for the heterogeneous nucleation in the molten pool:
Gaussian distribution for nucleation sites.
The parameters of the Gaussian distribution for nucleation sites have a deep effect on the growth of the grains. The area of the columnar crystal increases with the mean nucleation undercooling. The increase of the standard deviation undercooling results in the decrease of the grains which have the minimum area but the uniformity of these grains deceases firstly and then increases. The maximum nucleation density contributes to the decrease of the grain size.
In the present paper, the Kurz-Giovanola-Trivedi (KGT) model [
The relationship between the undercooling,
In order to accelerate the calculation, the paper fitted the KGT model in the process of the realistic simulation. And then the growth velocity of the grain tip can be obtained:
Calculation parameters of grain tip growth kinetics coefficients.
Elements | Initial concentration |
Partition coefficient |
Liquidus slope |
Diffusion coefficient in liquid |
Gibbs-Thomson coefficient (K·m) |
---|---|---|---|---|---|
Al | 6.1 | 0.9 | −1190 | 10−9 | 2 × 10−7 |
V | 4.2 | 0.8 | −1500 | ||
Fe | 0.15 | 0.07 | −2000 |
The finite element (FE) enmeshments can calculate the heat flow and the temperature gradients in the laser rapid forming. Based on the result of the macroscopic finite element, the cellular automaton (CA) units which are square cells with smaller sizes perform the calculations to simulate the growth of the grains in the laser rapid forming. In order to combine the CA and FE calculations, three nonzero interpolation coefficients
CA cell,
Obviously, the temperature of the finite element units has a deep effect on the temperature of the CA units. The relationship on temperature between the finite element and the cellular automaton is shown as follows [
Figure
Geometry model and mesh of the single point laser cladding.
In order to ensure the accuracy of the results in the simulation of the grain growth, the parameter database is created about the material of the solved model. The material used in this study is TC4 titanium alloy including 6.1 wt% Al, 4.2 wt% V, and few impurity elements. The liquidus temperature is 1718°C and the solidus temperature is 1649°C. The material physical properties including conductivity, density, enthalpy, and fraction-solid are shown in Figure
Thermophysical perimeters of TC4 titanium alloy, (a) conductivity, (b) density, (c) enthalpy, and (d) fraction.
The energy transfers from the molten pool to the surroundings in single point laser cladding through the base. The temperature field is three-dimensional erratic heat-transfer model in the solidification of the molten pool. The temperature distribution at a time is selected as the initial condition [
The heat convection between the solving model and the surrounding fluid medium is another boundary condition in the heat transfer process [
The correct temperature field is the prerequisite for simulating the grains microstructure during the solidification of the molten pool. Figure
Temperature distribution on conditions that the laser power is 2000 W and the scanning time is 3 s.
In order to illustrate the temperature distribution in the single point laser cladding, the temperature at different positions on the
Temperature curves at different parts in the molten pool during the single point laser cladding.
Temperature curves at different positions in the molten pool during the solidification.
Figure
Figures
Temperature distribution curves on the
Temperature distribution curves on the
Based on the CAFE model, the grain microstructure was simulated during the solidification of TC4 titanium alloy in the single point laser cladding. The laser power is 2000 W and the scanning time is 3 s.
The growth of the grain has a close relationship with the temperature distribution of the molten pool in the single point laser cladding. Figure
Simulation results of the grain microstructure at different times, (a) 3.3 s, (b) 3.4 s, (c) 3.5 s, and (d) 3.6 s.
At the beginning of the solidification, the heat at the bottom of the molten pool transfers faster than that at the top of the molten pool because the bottom contacts with the microthermal base while the top of the pool is exposed in the surrounding medium. The cells on the wall of the molten pool grow up to the grains which are random orientation in the way of the heterogeneous nucleation. During the process of the grain growth, the faster growing grains are perpendicular to the temperature gradients in the molten pool. The grains on the other directions were inhibited to grow. The maximum temperature gradient in the molten pool is 2500 × 106°C/m. So the grains rapidly grow into the molten pool and then the columnar crystals are formed. Figure
Fraction solid of the molten pool during the solidification at different times, (a) 3.0 s, (b) 3.1 s, (c) 3.3 s, and (d) 3.6 s.
Figure
(a) Experimental microstructure of the global molten pool; (b) experimental microstructure of the local molten pool.
In the laser cladding forming experiments, the input laser energy varies in different process parameters which have the great influence on the depths of the molten pools. Based on the microstructure experiments; Table
Depths of the molten pools on different laser process parameters (unit: mm).
Scanning time | Laser power | |||
---|---|---|---|---|
|
|
|
| |
|
0.305 | 0.358 | 0.579 | 0.595 |
|
0.516 | 0.411 | 0.653 | 0.668 |
|
0.589 | 0.600 | 0.726 | 0.740 |
The paper established the CAFE model to simulate the grain structure during the solidification of Ti-6Al-4V alloy in the molten pool of the single point laser cladding. The model solves the heat transfer equation in the molten pool by FE method to calculate the temperature distribution. And then the growth of the grains in the molten pool was simulated based on the temperature field. The maximum temperature in the molten pool increases with the laser power and the scanning rate. On condition of the constant scanning time, the range of the maximum temperature is from 1894°C to 2445°C with the increase of the laser power. In addition, the laser power has a larger influence on the temperature of the molten pool than the scanning rate. The growth of the grain has a close relationship with the temperature distribution of the molten pool in the single point laser cladding. During the process of the grain growth, the faster growing grains are perpendicular to the temperature gradients in the molten pool. As the solidification continues, the columnar crystals grow bigger and there is little sign of the isometric crystals. The mean radius of the grains in the simulation is 0.138 mm. This study has very important significance for improving the quality of the structure parts manufactured from the laser cladding forming and the future related research work. The CAFE model is a useful tool for studying the solidification microstructure changing in the laser cladding forming.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by the National Natural Science Foundation of China (no. 51205261). The authors appreciate the Key Laboratory of Fundamental Science for National Defense of Aeronautical Digital Manufacturing Process and Shenyang Aerospace University.