Evaluation of microstructural evolution of Mg–4Al– x RE in SIMA process based on statistical approach

Abstract

Strain induced melt activation (SIMA) for achieving as nearly as possible a spheroidal semisolid structure with minimum entrapped second phase is more practically/economically advantageous compared to other techniques. One prerequisite towards arriving at an effective SIMA process is the use of appropriate methodology for the evaluation/prediction of pertinent factors in such processes. In the present work, the effects of alloying element, induced strain and holding time on three responses, namely, shape factor, particle size diameter and fraction of liquid, were investigated using response surface methodology based on a central composite design. According to statistical analysis and the developed polynomial equation models, it was found that all the first order terms of the independent parameters as well as second order term of alloying element are statistically significant for all the responses. In the case of shape factor, the second order term of time and the interactive term of induced strain and alloying element have statistical significance.

Keywords

Strain induced melt activation Response surface methodology Magnesium alloy Rare earth

Introduction

Nowadays, semisolid forming has become widely investigated and commercially practiced due to its noteworthy advantages over other conventional forming processes. The significant features of semisolid forming are the remarkable reduction of microsegregation, higher microstructural homogeneity, almost complete elimination of shrinkage porosity and lower forming efforts.^1–4 There is a wide variety of different semisolid forming techniques that aim to achieve as nearly as possible a spheroidal semisolid structure with minimum entrapped second phase.^5–8 Among these techniques, strain induced melt activation (SIMA), which was developed by Young et al.,⁹ is more practical due to its simplicity and low equipment cost especially in industrial scale. In addition, it is applicable to various metals and/or alloys including aluminium, magnesium, copper and ferrous alloys.

The SIMA process involves three stages: casting of the alloy to produce a dendritic structure, deformation of the specimens to induce a residual plastic strain and reheating the deformed specimen to a semisolid temperature to attain a globular structure. In this procedure, processing parameters, such as induced strain, isothermal holding time and alloy composition, have significant effects on the microstructure evolution during partial remelting.^10–12 It has been reported that dendrite skeleton structure starts to vanish by increasing the holding time, which results in spherodised solid particles, while, if the holding time is insufficient, the agglomeration of solid particles would occur.^13,14 Furthermore, many researchers believe that shape factor increases by an increase in holding time;^10,15 however, there is an optimum condition (time and induced strain) for alloys to achieve its peak of sphericity. Although there are some studies on the effect of process parameters^15–22 on the microstructural evolution of SIMA processed alloys, hardly any focused on effect of alloying elements.^23–25 For instance, Chen et al.²³ reported that the addition of Mg accelerates the microstructural evolution of ZA27 zinc alloy, while rare earth (RE) elements have a deceleration effect.

Generally, previous investigations on pertinent parameters influencing the microstructural evolution of SIMA processed alloys have been conducted using the ‘one factor at a time’ methodology,^11,18,21 which cannot disclose any important interactions that might exist among the factors.²⁶ To the authors’ best knowledge, there is no through work describing the simultaneous effect of the pertinent parameters and their probable interaction on the microstructural evolution of SIMA processed alloys. Recently, statistical experiment design techniques, such as response surface methodology (RSM), have been widely applied in many engineering and research issues.^27–30 Response surface methodology is an effective mathematical and statistical tool that can concurrently examine several factors at different levels and produce a correlation model between the factors and the response. On the other hand, fractional factorial design of experiments, such as central composite design (CCD), can give information regarding parameter interactions using less experimentation as well as giving reliable information about first order interactions.²⁶

The aim of the present study is to ascertain and quantify the effect of pertinent parameters as well as the probable interactions between these parameters (i.e. induced strain, isothermal holding time and alloying elements) and the responses (i.e. shape factor, solid particle diameter and fraction of liquid) during microstructural evolution of SIMA processed Mg–4Al alloy using RSM. A half fractional factorial CCD was chosen as the design matrix since it allows reliable identification of first order interaction between factors and provides second order polynomial models.

Experimental

Materials and processing

The three alloys designed for this investigation have the nominal chemical composition of Mg–4 wt-Al– wt-RE (x = 0, 2 and 4). Commercial purity magnesium (99·95 wt-), aluminium (99·99 wt-) and a mischmetal mainly composed of 55 wt-La, 32 wt-Ce, 10 wt-Nd and 3 wt-Pr were used to prepare the alloys. Melting was carried out in an electrical resistance furnace (3 kW) under a covering flux (50MgCl₂, 20KCl, 15MgO and 15CaF₂) to protect the melt from oxidation. The melt was held at 720°C for 20 min and mechanically stirred for 2 min before the addition of alloying elements. Rare earth metals were added as mischmetal to the molten alloy, stirred again and held for 15 min. After addition of mischmetal, the melt was held at 720°C for 20 min to make sure that the RE elements were completely dissolved. Pouring of the melt was accomplished into a cylindrical steel die of 30 mm diameter and 250 mm height, which was already preheated up to 250°C. The specimens were machined into round samples with a height of 20 mm and diameter of 20 mm diameter. The samples were then subjected to hot compression at 250±3°C followed by immediate water quenching. The applied strains were 0·15, 0·25, 0·35 and 0·45. Graphite powder was used as a lubricant between the specimen and compression dies so as to minimise the friction.

The hot deformed specimens were heated to 605±1°C (in a salt bath of 63·5KCl and 36·5MgCl₂) and held for 10, 20, 30, 40 and 50 min followed by quenching. The microstructure of the as cast and heat treated samples was studied by optical microscopy and scanning electron microscopy. The specimens for microstructural studies were polished and etched using Nital 1 solution. Ten representative areas for each sample were subjected to microstructural quantitative analyses using Clemex Image Analyzer (version 3·5). In this regard, shape factor, solid particle size and fraction of liquid (including both the liquid that entrapped within and existed between α-Mg solid particle) were measured. For each sample, solid particles were separated subsequently by measuring its perimeter, area, and minor and major axis. The average of minor and major axis was considered as a solid particle size. For evaluation of liquid fraction, a colour filter was used to separate the bright area (solid particles) from the dark ones (liquid indications). In addition, shape factor was calculated in each case in accordance to 4πA/P², in which A is the area of the α-Mg solid particle and P is the perimeter.

Experimental design for RSM

Seventeen runs consisting of six star points (star distance was 0) and four centre points were generated by the principle of RSM using MINITAB Release 15. To develop a second order polynomial model, a CCD with multiple linear regression was employed to estimate the model coefficients of the three selected factors with each factor set at its high level (+1), low level (−1) and medium level (0). The levels used for these three factors, according to a CCD, are listed in Table 1.

Table 1

Experiments designed by employing CCD approach

Run numbers	Factors			Response
Run numbers	Alloying element/	Induced strain/	Holding time/min	Shape factor	Particle diameter/μm	Fraction of liquid
1	0	15	10	0·18	51	0·07
2	4	15	10	0·48	58	0·05
3	0	45	10	0·82	51	0·18
4	4	45	10	0·74	48	0·16
5	0	15	50	0·76	70	0·14
6	4	15	50	0·76	72	0·24
7	0	45	50	0·96	67	0·35
8	4	45	50	0·88	57	0·35
9	0	30	30	0·8	54	0·16
10	4	30	30	0·75	60	0·22
11	2	15	30	0·69	68	0·15
12	2	45	30	0·99	58·8	0·35
13	2	30	10	0·62	57	0·12
14	2	30	50	0·92	70	0·39
15	2	30	30	0·80	63	0·26
16	2	30	30	0·80	63	0·26
17	2	30	30	0·80	63	0·26

All the experiments were performed with two replicates, and the results for the response were reported as a mean value of each two responses in a randomised order to avoid systematic bias. Finally, a quadratic polynomial regression model (equation (1)) was employed to estimate and predict the response value over a range of input factors’ values²⁶ 1 where Y is the dependent response variable (i.e. shape factor and fraction of liquid and solid particle size); b₀ is the intercept term; and b_i, b_ii and b_ij are the measures of the effect of variable X_i, and X_iX_j respectively. X_i and X_j represent the independent variables, and k is the number of these factors. The variable X_iX_j represents the first order interaction between X_i and X_j (i<j).

The analysis of variance (ANOVA) for quadratic model was performed at 5 confidence level (p<0·05). The significance and the magnitude of the effects estimations for each variable and all their possible linear and quadratic interactions were also determined. All the analysis was carried out using MINITAB Release 15.

Results and discussion

Optical micrographs of as cast and SIMA processed Mg–4Al alloy containing 0, 2 and 4 wt- of RE are illustrated in Fig. 1a and b. As it can be seen, shape and size of the dendrites were changed by increasing the RE elements, while interdendritic arm spacing remains identical (20±1 μm), which can be attributed to attainment of constitutional undercooling.¹⁰ After holding at semisolid temperature, the irregular solid particles appear, which is due to the absence of induced strain (Fig. 1c), while by increasing the strain, the fine and spherodised solid particles are formed under the same conditions (Fig. 1d). It has to be noted that addition of RE elements would result in finer α-Mg solid particles with elimination of entrapped liquid within (Fig. 1e). Moreover, liquid fraction and α-Mg solid particle diameter increases by an increase in holding time (Fig. 1f).

Table 1 lists the values of shape factor and fraction of liquid and solid particle size at each of the 17 combinations of factor levels (the values given are the mean of two independent experiments). The values of the regression coefficients are presented in Table 2. As can be seen, all the first order terms of the independent parameters as well as second order term of alloying element are statistically significant for all the responses. In the case of shape factor, the second order term of time together with the interactive term of strain and alloying element are statistically significant.

Table 2

Values of regression coefficients calculated for all responses after SIMA process*

Independent factor	Shape factor				Solid particle diameter/μm				Fraction of liquid
Independent factor	RC	SE	T	p value	RC	SE	T	p value	RC	SE	T	P
Constant	0·820141	0·0099	82·431	0·000	62·847	0·8029	78·277	0·000	0·26783	0·00848	0·008479	0·000
Alloying element (AE)	0·040000	0·00735	5·440	0·001	2·400	0·5934	4·045	0·005	0·01790	0·00627	2·857	0·024
Strain (st)	0·148000	0·00735	20·128	0·000	−3·920	0·5934	−6·606	0·000	0·07990	0·00627	12·751	0·000
Time t	0·146000	0·00735	19·856	0·000	6·900	0·5934	11·629	0·000	0·08970	0·00627	14·315	0·000
AE×AE	−0·057746	0·01420	−4·065	0·005	−4·834	1·1463	−4·217	0·004	−0·07620	0·01211	−6·295	0·000
st×st	0·012254	0·01420	0·863	0·417	0·566	1·1463	0·494	0·636	−0·01620	0·01211	−1·339	0·223
t×t	−0·067746	0·01420	−4·769	0·002	0·666	1·1463	0·581	0·579	0·01480	0·01211	1·222	0·261
AE×st	−0·007500	0·00822	−0·912	0·392	0·250	0·6634	0·377	0·717	−0·01438	0·00701	−2·052	0·079
AE×t	−0·017500	0·00822	−2·129	0·071	0·000	0·6634	0·000	1·000	0·01563	0·00701	2·230	0·061
st×t	−0·075000	0·00822	−9·123	0·000	−1·000	0·6634	−1·507	0·175	0·01062	0·00701	1·517	0·173

*RC, regression coefficient; SE, standard error.

The low values of P determined for the regression (p<0·001), as well as the fact that the lack of fit of the model is not significant (p>0·05), reveal the suitability of the model (Table 3).

Table 3

Analysis of variance table

	Shape factor					Solid particle diameter (μm)					Fraction of liquid
	df	SS	MS	f	p value	df	SS	MS	f	p value	DF	SS	MS	f	P
Total	16	0·543188				16	796·235				16	0·18009
Regression	6	0·536101	0·536101	126·08	0·000	9	791·990	87·999	145·11	0·000	4	0·17187	0·042968	62·70	0·000
Linear	3	0·448200	0·448200	210·81	0·000	3	629·764	209·921	346·16	0·000	3	0·14750	0·049168	71·75	0·000
Square	2	0·042901	0·042901	30·27	0·000	3	75·726	25·242	41·62	0·000	1	0·02436	0·024368	35·56	0·000
Interaction	1	0·045000	0·045000	63·50	0·000	3	86·500	28·833	47·55	0·000
Residual error	10	0·007087	0·007087			7	4·245	0·606			12	0·00822	0·000685
Lack of fit (model error)	8	0·006887	0·006887	8·61	0·108	5	4·058	0·812	8·70	0·106	10	0·00802	0·000802	8·02	0·116
Pure error (replicate error)	2	0·000200	0·000200			2	0·187	0·093			2	0·00020	0·000100
R ²

*df: degree of freedom; SS: sum of squares; MS: mean squares.

According to the calculated values of the regression coefficients (Table 2), a polynomial equation for fraction of liquid is proposed as follows 2 where time is the holding time at semisolid temperature and AE and st are the percentage of alloying elements and induced strain respectively. As it can be observed, liquid fraction increases by an increase in both holding time and induced strain; this can be ascribed to the diffusion dependent phenomena. The thermally aligned induced vacancies and the lattice distortion operate as conduit channels for alloying elements. Thus, an increase in induced strain leads to higher number of channels. The effect of alloying elements on liquid fraction is reflected in casting grain size increasing and chemical inhomogeneity reduction.²⁴ These effects appear in equation (2) by three linear and a quadratic term by negative coefficient. In addition, the induced strain and holding time have more significant effect on the formed liquid than the alloying elements (Fig. 2).

Figure 2 shows the main effects plots corresponding to shape factor of the solid particles. As one can see, an increase in both time and strain results in an increase in shape factor, which can be further confirmed by equation (3) 3 Based on Ostwald ripening mechanism, the main mechanism of solid coarsening in semisolid slurries,³ large globules grow at the expense of vanishing of the small ones to reduce their interfacial free energy. The rate of coarsening is defined by the following equation³ 4 where , , k and t are the average diameter of globules, the average diameter of initial globules, the coarsening rate and the holding time respectively. Therefore, each phenomenon that results in diffusion acceleration would increase the ripening and consequently the sphericity of globules.

It is clear that shape factor of the globules increases by addition of RE metals (equation (3)). Figure 3 shows the linescan analysis through a solid globule. As seen, the saturation of alloying elements at solid/liquid interface can result in hindering of atomic diffusion rate.^25,31 On the other hand, the addition of RE elements would lead to replacing equiaxed dendrites by sharp and narrow ones.³¹ Consequently, the rosette type microstructure needs less time for spherodising than the fully dendritic microstructure. It seems that these two effects results in the appearance of an interactive term in equation (3); the first one (enrichment of alloying elements at the interface) decreases the diffusion rate, while the shape of the dendrites enhances the spherodising rate. The statistical analysis of the developed models shows that the regression coefficient term of alloying element in solid particle diameter response has a negative sign, while in the case of the other two responses, this coefficient is positive; this can be attributed to shape of initial dendrites and flow of solute atoms between particles of different sizes.¹⁰ As a matter of knowledge, an increase in both induced strain and holding time at the semisolid temperature range results in increasing shape factor. In the present study, it is statistically confirmed that both these parameters have the same effect on shape factor by coefficient of 0·15.

Surface and contour plots of the shape factor with respect to induced strain and holding time are depicted in Figs. 4 and 5 respectively. As it can be seen, the effect of holding time on the shape factor at the lower induced strain is much more than that at the higher one; likewise, it is the case that happens for induced strain. In other words, at lower holding time, induced strain plays a more important role compared to one at higher holding time. Since spherodisation is a diffusional process, each factor that affects the kinetic of diffusion would result in acceleration of spherodising. As mentioned before, induced strain enhances the lattice defects/dislocations, which can act as diffusional channels. On the other hand, the holding time has a positive effect on the spherodisation process (Fig. 2), and increasing the holding time results in higher diffusion. Consequently, the salient effect of induced strain gradually drops at higher holding time.

It has been reported that the induced strain has a reciprocal effect on solid particle diameter and shape factor;^32–36 i.e. there are optimum values of induced strain and holding time for each alloy under which the maximum sphericity and minimum particle size can be achieved. On the other hand, Luo et al.³⁶ stated that the degree of spherodisation strongly depends on liquid fraction. In the case of AZ91D, Czerwinski et al.³⁴ showed that shape factor increases from 0·61 to 0·65 by an increase in liquid fraction from 0·42 to 0·57; however, it decreases from 0·64 to 0·47 when liquid fraction further increases from 0·78 to 0·96. This behaviour in AM60 magnesium alloy has been related to two coarsening and melting phenomena.³⁷ At high liquid fraction, melting trend is dominant and leads to a diminution in average grain size, while coarsening trend and agglomeration result in a reduction in shape factor. According to our statistical analysis, the relation between solid particle diameter and operating factors can be proposed by the following equation: 5 It can be seen that the induced strain has a negative effect on average solid particle diameter; this is due to the formation of more defects such as vacancies and dislocations during strain induction and the consequent refining of the particle size.³⁶ Furthermore, it has been reported³⁸ that by increasing the compression ratio, the breaking up mechanisms become active and the grain size rapidly decreases by increasing the compression ratio (Fig. 6).

In addition, although particle size increases linearly by amount of alloying elements (positive sign of the regression coefficient), it is reduced by its quadratic term (negative sign of the regression coefficient). This reciprocal effect might be due to two reasons: addition of RE metals would result in enlargement of grain size, which has a negative effect on reducing particle size during partial melting, and these elements are surface active species, which can hinder the diffusion rate. On the other hand, since the particle growth is a diffusional phenomenon, the addition of RE elements would have negative impact on the growth mechanism. Thus, solid particles grow slower by introducing the alloying elements to the melt.

Conclusions

The induced strain leads to finer and spherodised solid particles. In addition, the liquid fraction increases by increasing the holding time. Moreover, the results obtained via CCD coupled with RSM in the evaluation of microstructural evolution of Mg–4Al–xRE in SIMA process indicate that the following.

All the first order terms of the independent parameters as well as second order term of alloying element are statistically significant for all the responses. In the case of shape factor, the second order term of time together with the interactive term of induced strain and alloying element are statistically significant.

According to the estimated values of the regression coefficients, three polynomial equations for three responses were proposed

The ascending effects holding time and induced strain on the liquid fraction were justified by the diffusion dependent phenomena.

The appearance of interactive term in shape factor polynomial equation was ascribed to the saturation of alloying elements at solid/liquid interface (resulting in hindering of atomic diffusion rate) and the presence of RE elements (leading to replacing equiaxed dendrites by sharp and narrow ones).

Footnotes

Acknowledgement

This experimental research was carried out at Sharif University of Technology, and one of the authors would like to thank Professor H. Ashuri for his valuable and helpful discussions.

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