# Microstructural simulation of friction stir welding using a cellular automaton method: a microstructure prediction of AZ91 magnesium alloy

- Parviz Asadi
^{1}Email author, - Mohammad Kazem Besharati Givi
^{1}and - Mostafa Akbari
^{2}

**10**:20

https://doi.org/10.1186/s40712-015-0048-5

© Asadi et al. 2015

**Received: **5 June 2015

**Accepted: **19 July 2015

**Published: **13 August 2015

## Abstract

### Background

Recently, some researchers have simulated FSW using FEM and studied the influence of process parameters and tool geometry on material flow, welding force, and temperature and strain distributions during friction stir processing. Additionally, in terms of microstructure modeling, various approaches such as the Cellular Automaton (CA) model have been developed to simulate microstructural evolution during plastic deformation processes.

### Method

In this work, a finite element model (FEM) is established to study the microstructure evolution during friction stir welding (FSW) of AZ91 magnesium alloy. To this aim, first, the hot compression tests at different temperatures and strain rates were carried out to achieve the flow stress curves. Then, the hardening parameter, the recovery parameter and the strain rate sensitivity were calculated according to flow stress results and using the Kocks−Mecking model. Next, a continuum based thermo-mechanically coupled rigid-viscoplastic FEM model was proposed in Deform-3D software to simulate the FSW of AZ91 magnesium alloy. To evaluate microstructure of the weld zone a model is proposed based on the combination of Cellular Automaton and Laasraoui-Jonas models.

### Results

Temperature history, strain distribution and welding force are achieved through thermomechanical model and microstructure and grain size distribution are achieved by microstructure evolution model. The effects of rotational and traverse speeds on the grain size and microstructure of weld zone are considered.

### Conclusion

There is a good agreement between results of numerical models and experiments in the aspects of welding forces, temperature history and grain size. Additionally, the proposed microstructure evolution model can simulate accurately the dynamic recrystallization (DRX) process during FSW and its resulted microstructure.

### Keywords

FSW simulation Microstructural evolution DRX Cellular automaton Laasraoui-Jonas model## Background

AZ91, a magnesium alloy, is one of the most commercially and commonly used magnesium alloys. This alloy, containing 9 wt% Al, 1 wt% Zn, and 0.2–0.3 wt% Mn as major alloying elements, contains a good combination of castability, mechanical strength, and ductility (Suresh et al. 2009). This has made AZ91 a popular light metal alloy especially among automotive industries whose aim is manufacturing lightweight vehicles (Srinivasan et al. 2010). However, the use of AZ91 in different industries is not yet extended comparing to its competitors such as aluminum alloys and plastics, partially due to the difficulty in controlling its microstructure (Asadi et al. 2010a).

Friction stir welding (FSW) as a relatively new welding technique has gained wide applications in different industries such as aerospace, automotive, and maritime. It has been utilized to weld and process different aluminum (Heidarzadeh et al. 2015), Mg (Asadi et al. 2012; 2010b; Motalleb-nejad et al. 2014; Faraji and Asadi 2011), and Cu (Farrokhi et al. 2013) alloys, some of which are classified as practically unweldable alloys in use of conventional welding methods.

Recently, some researchers have simulated FSW using a finite element model (FEM). Buffa et al. (2013; 2012; 2006) simulated friction stir welding using a 3D finite element method. Their model effectively determines the relationships between the tool forces and process parameters. Shojaeefard et al. (2013) studied the influence of pin profile and shoulder diameter on material flow, welding force, temperature, and strain distributions. Marzbanrad et al. (2014) investigated the effect of tool pin profile, and Asadi et al. (2011a;Tutunchilar et al. 2012a) studied the effect of the process parameters on material flow, temperature, and strain distributions during friction stir processing.

It is clear that the grain size in the weld zone has a great influence on the mechanical properties of weld such as hardness, tensile strength, plasticity, and toughness properties, and therefore, fine-grain structure could enhance these properties (Asadi et al. 2010b; Farrokhi et al. 2013; Heidarzadeh et al. 2014). Since it is difficult and time consuming to investigate experimentally the microstructure of weld, numerical simulations could be very applicable in different manufacturing processes (Liu et al. 2013; Wang et al. 2010). In terms of microstructure modeling, various approaches such as the cellular automaton (CA), the Monte Carlo model, and the phase field model have been developed to simulate microstructural evolution during processes (Liu et al. 2013). Although all these models successfully simulate microstructural evolution, most of the CA model is employed because of its length scale calibrations and straightforward time. Discrete spatial and temporal evolution of complex systems via applying local or global deterministic or probabilistic transformation rules to the location of a lattice is the main algorithm of the CA method. Many researchers have shown that CA offers a computationally efficient framework for simulation of microstructural evolution (Liu et al. 2013).

Timoshenkov et al. simulated the microstructure evolution in steel using CA for thermo-mechanical treatment. Tsai et al. (2010) predicted the morphologies in the solidification process for Cu-0.6Cr (mass fraction, %) alloy and Wang et al. (2010) simulated the dynamic recrystallization (DRX) characteristic in hot compression of steel using the CA method. They stated that the CA model can simulate the nucleation and growth kinetics of dynamically recrystallized grains in hot working process. Besides these advantages, this method could not consider solely the effects of the process parameters on DRX and the relationship between the nucleation sites and the distribution of dislocation density (Liu et al. 2013).

In fact, dislocation density plays a crucial role in nucleation and therefore, in microstructural evolution during DRX (Qian and Gou 2004). In order to evaluate the dislocation density, many models have been developed, such as the Laasraoui-Jonas (LJ) model (Laasraoui and Jonas 1991), the Kocks-Mecking (KM) model (Mecking and Kocks 1981), and the Estrin-Mecking (EM) model (Yazdipour et al. 2007). These models are internal variable dislocation density models and deal with calculation of flow stress and evaluation of dislocation density during hot deformation processes. Additionally, the modified LJ model (Gourdet and Montheullet 2003) considers the effects of grain boundary migration on dislocation density. Therefore, the modified LJ model grants a more realistic evolution for dislocation density. Li et al. (2012) used the LJ model to simulate the microstructural evolution during hot extrusion of Mg-Al-Ca-based alloy. Similarly, Liu et al. (2013) simulated the DRX for hot compression of AZ31 magnesium alloy.

In the present study, a model is developed to simulate the microstructural evolution of AZ91 magnesium alloy during FSW. To this aim, first, the flow stress curves are obtained via the hot compression tests carried out at different temperatures and strain rates. Then, the hardening parameter, the recovery parameter, and the strain rate sensitivity are calculated according to flow stress results. Next, a continuum based thermo-mechanically coupled rigid-viscoplastic FEM model for the FSW process is proposed in Deform-3D software coupled with the combination of CA and LJ models for microstructural evolution and dislocation density computation. The relationship between the nucleation rate and the dislocation density as well as between critical strain, critical dislocation density, and DRX are investigated. Next, the optical-microscope images from weld zone and base metal are used to validate the microstructure predicting model. Furthermore, nucleation and grain growth are shown by the micro-images extracted from simulation. Finally, the effect of the process parameters on grain size is studied.

## Methods

The methods of this research include some experimental investigations and tests, numerical model for the process simulation, and the microstructure evolution formulation for modeling of dynamic recrystallization. All these methods are described in below.

### Experimental setup

Chemical composition of the AZ91 magnesium alloy used in this study

Element | Al | Zn | Mn | Si | Cu | Ni | Fe | Mg |

Weight percentage | 9.1 | 0.68 | 0.21 | 0.085 | 0.0097 | 0.001 | 0.0029 | Bal. |

The welded specimens were cut in transverse sections and prepared by standard metallographic techniques. The etching solution was composed of 5 mL acetic acid, 5 mL HCl, 6 g picric acid, 7 mL nitric acid, 100 mL ethanol, and 10 mL water for 1–2 s. Microstructural observations of the samples were carried out by optical microscopy (OM), and a linear intercept method was employed to measure the average grain size (*d* = 1.74 L; L is the linear intercept size).

In order to acquire the flow stress of the AZ91 Mg alloy, hot compression test was conducted at different temperatures among 200–450 °C and strain rates of 0.001, 0.01, 0.1 and 1 s^{−1}. The hot compression test specimens were 15 mm in height and 10 mm in diameter.

### Numerical model of friction stir welding

Due to the ability of accurate modeling of severe plastic deformation (SPD) processes, Deform-3D^{™} software is employed to simulate the FSW (Tutunchilar et al. 2012a). To simplify the problem, the tool was selected as a rigid material and workpiece was supposed to be a rigid-viscoplastic material.

The Arrhenius equation was chosen to determine the relationship between the strain rate, the flow stress, and the temperature (Asadi et al. 2011a).

### Microstructure evolution model

The microstructural evolution during FSW of AZ91 magnesium alloy is simulated using the combination of CA and LJ methods in Deform-3D software which are coupled to the thermo-mechanically, rigid-viscoplastic FEM model of FSW.

Evidently, the dislocation density is the most effective factor on nucleation and microstructure evolution during hot deformation processes (Liu et al. 2013; Qian and Gou 2004). Therefore, besides the temperature history, calculation of dislocation density is crucial in microstructure evolution of the FSW process. The temperature history will be achieved via the FSW FEM model. However, the dislocation density calculation requires coupled models (such as CA and LJ).

#### Dislocation density calculation

*ρ*

_{ i }is the dislocation density in the ith grain;

*h*, the strain hardening parameter;

*r*, the recovery coefficient parameter;

*ε*, the strain; and

*dV*, the volume swept by grain boundary movement. To precisely calculate the amount of parameters in LJ model (Eq. 1) the KM model is also used:

*K*

_{1}is the constant denoting the work hardening and

*K*

_{2}is the softening parameter for dislocation annihilation.

#### Nucleation and growth during DRX

*ṅ*represents the nucleation rate;

*ΔH*, the activation energy, acquirable by the flow curves;

*R*, the gas constant;

*T*

_{abs}, absolute temperature; and

*C*, a constant. The relationship reveals that by increasing the process temperature and strain rate, the nucleation number raises.In the metals with medium to low stacking fault energy such as Mg, the DRX onsets when the dislocation density reaches a critical value (Liu et al. 2013; Roberts and Ahlblom 1978). Generally, nuclei predominantly nucleate along the grain boundaries in which sufficient stored energy is present by a critical dislocation density:

*b*represents the Burger’s vector;

*l*, the dislocation free path;

*M*, the grain boundary mobility;

*τ*, the dislocation line energy; and

*γ*

_{ i }, the grain boundary energy, which can be computed by Eq. 5 (Xiao et al. 2008):

*γ*

_{m}is the high angle grain boundary energy which can be described by Equation 6;

*θ*

_{ i }, is the misorientation among the ith recrystallized grain and its neighbor; and

*θ*

_{m}, the misorientation between high angle boundaries.

*v*is the Poisson ratio.The grain boundary migration velocity is influenced by the net pressure on the boundary and can be described as:

*v*

_{ i }represents the grain boundary migration velocity;

*M*, the grain boundary mobility;

*r*

_{ i }, the ith recrystallized grain radius; and

*F*

_{ i }, the driving force is attainable through Eq. 7.

#### Cellular automaton method

*F*

_{ i }) is positive. The growth velocity (

*v*

_{i}) can be obtained through Eqs. 7 and 8 for each time step. The radius of the ith recrystallized grain represents the volume swept by the grain boundary. Then, the dislocation density can be calculated by Eq. 1 for each time step. These computations are terminated, when the pre-set strain is reached.The cells in which recovery happens are random (Peckzak and Luton 1993), and to select certain number of lattices

*N*

_{r}for recovery occurrence in each time step, the following equation is selected:

*N*

_{1}and

*N*

_{2}represent the number of rows and columns in cells and

*K*is the material constant (Peckzak and Luton 1993).

#### Work hardening and recovery parameters

*h*) and the recovery coefficient parameter (

*r*) can be calculated through Eqs. 10 and 11 (Gourdet and Montheullet 2003):

*m*, the strain rate sensitivity;

*ΔH*

_{b}, the activation energy for self-diffusion;

*h*

_{0}, the hardening parameter (in Eq. 10); and

*r*

_{0}, the recovery parameter (in Eq. 11).

*h*

_{0},

*r*

_{0}, and

*m*are achieved as: 1.34e13, 15.6, and 0.2, respectively (for more details see ref. (Liu et al. 2013; Guangyin et al. 2001; Unigovski 2009)). The material parameters used in the simulation process are summarized in Table 2.

Materials parameters for AZ91 magnesium alloy used in simulation model

Material parameter | Value |
---|---|

Primary dislocation density, | 0.01 (Liu et al. 2013) |

Shear modulus, | |

Activation energy for self-diffusion, \( \varDelta {H}_{\mathrm{b}}\frac{kJ}{\mathrm{mol}} \) | 140 (Guangyin et al. 2001) |

Activation energy, \( \varDelta H\frac{kJ}{\mathrm{mol}} \) | 147 |

Material constant in Eq. 9, | 6030 (Liu et al. 2013) |

Shear friction factor, | 0.4 |

Hardening parameter, | 1.34e13 |

Recovery parameter, | 15.6 |

Strain rate sensitivity, | 0.2 |

## Results and discussion

As cited before, the temperature and strain distributions in the weld zone are crucial factors in determining the grain size of the weld nugget. Therefore, the temperature history and strain distribution during FSW will be reported in this paper. Then, the microstructural properties of the weld zone such as microstructural image, grain size, and nucleation sites will be considered as well as the effect of the process parameters on these properties.

### Temperature history and strain distribution during FSW

It is well-accepted that frictional heat and plasticizing action formed by the FSW tool over the process causes the joining of two parts. Generation of a certain amount of frictional heat along with the presence of a high hydrostatic pressure along the joint line are the crucial requirements during the FSW to keep the processing material in a well-plasticized region with a suitable temperature, and finally to form a sound weld.

*w*/

*v*) the heat generation will be increased.

It can be seen that an increase in the rotational speed or a decrease in the traverse speed results in an increase in the amount of strain. Indeed by increasing the rotational speed to traverse speed ratio (*w*/*v*), the tool pin rotation rate in a certain distance increases, leading to a rise in strain of material under processing.

### Microstructure evolution during FSW

It is well-known that DRX during FSW will cause the generation of fine equiaxed grains in the stir zone. Process parameters, tool geometry, welding material composition, temperature history, vertical pressure, and active cooling are the effective factors on the microstructure and grain size of the weld (Besharati Givi and Asadi 2014). In this paper, the effects of FSW on the microstructure of base metal as well as the effects of process parameters on the microstructure of stir zone are discussed by simulation results.

Song et al. (2014) simulated the microstructure evolution during FSW of titanium alloy using CA model and reported that their established model is more suitable for hot compression process. However, they did not compare the grain size with an experimental microstructure and did not report any simulated microstructure of the weld zone.

As cited before, by increasing the *w*/*v*, the heat generation is increased and therefore the grain growth and grain size will be increased. The *w*/*v* ratio for Fig. 8a, b is \( \frac{710}{50}=14.2 \), and it is \( \frac{1400}{25}=56 \) for Fig. 8c, d. In this case, the grain size is increased from 13.3 μm in Fig. 8b to 29 μm in Fig. 8d.

Comparing the microstructures for base metal and weld zone (Figs. 7 and 8), and as reported widely in literature, the grain size is reduced drastically by FSW (from 130 μm in base metal to 10–30 μm in the weld zone). The combination of high temperature, as a result of frictional heat, and high strain rate, due to the severe plastic deformation, leads to generation of fine recrystallized grains in the stir zone (Fig. 8) (Asadi et al. 2012; 2010b). Therefore, the grain refinement occurs by the DRX including nucleation and growth. The presented model can precisely reveals the changes in microstructure during the DRX process.

In each step (Fig. 9a–e), the figures on the left side and middle shows the microstructure of stir zone and the figure on the right side illustrates the dislocation accumulation map of that step. The darker points in the dislocation accumulation map represent the areas with higher dislocation density. Noting to the dislocation accumulation maps at different steps, it can be concluded that, by nucleation and growth, white points form inside the dark areas in the map and onset to consume them. Therefore, little by little, the dark areas reduce demonstrating the reduction of dislocation density.

It should be stated that by deformation progress, the dislocation density goes beyond a critical value and the DRX initiates. Then, the new grains with zero dislocation density start to grow. On the other side, the simultaneous work hardening generates dislocation density inside the DRX grains and thus, the driving force for grain boundary migration drops down as far as the growth stops. On the other words, the driving force for the grain growth reduces gradually as its dislocation density inside the grain increases with deformation progress and finally the grain growth ceases. Also in another case, if the DRX grain sticks into another, both grains cease to grow at the clash point, while free sections of their boundaries can continue the growth. Additionally, in very high deformation rates, the DRX grain’s boundaries again can become nucleation sites, if its dislocation density reaches the critical value for nucleation (Liu et al. 2013; Song et al. 2014).

*w*/

*v*results in a rise in the amount of generated heat and peak temperature, leading to acceleration of grain growth step, and thus, the final microstructure will contain larger grains (Salekrostam et al. 2010; Tutunchilar et al. 2012b).

## Conclusions

In this work, a finite element model is established to study the microstructure evolution during FSW of AZ91 magnesium alloy. The hardening parameter, the recovery parameter, and the strain rate sensitivity, required for the model, are calculated according to flow stress results. A continuum based thermo-mechanically coupled rigid-viscoplastic FEM model is proposed in Deform-3D software to simulate the FSW of AZ91. To evaluate microstructure of the weld zone, a model is proposed based on the combination of cellular automaton and Laasraoui-Jonas models. Results show that the simulated microstructure of the weld zone has a good agreement with that of the experiments. The proposed model can simulate the dynamic recrystallization process during friction stir welding and predict the grain size and microstructure of the weld zone precisely. The simulated grain size under different process parameters reveals that by increasing the *w*/*v* parameter, the grain size increases.

## Declarations

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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