Effect of Si Addition on Microstructure and Mechanical Properties of Al–1.5%Mn Alloys

Abstract

Al–1.5 mass%Mn was chosen as the base alloy, and 1.0 and 3.3Si were added to the base alloys, keeping the same values in the ΔMk of s-orbital energy level as those of Al–1.5Mn–0.8 and 2.4Mg alloys with superior tensile properties for as-cast applications. The Si addition or increment in the base alloy showed strengthened tensile behavior of the 0.2% proof stress (σ_0.2) of 67 MPa and ultimate tensile strength (σ_UTS) of 160 MPa, although there was reduced in fracture strain (ε_f) to 9%. The increase and decrease in flow stress and strain, respectively, resulted from the increment in degree of solid solution strengthening by the increase of ΔMk of the alloys. There was a good linear relationship between the nanoindentation hardness or rate of elastic deformation work in the α-Al phase and σ_0.2 of the alloys. The dislocation density of Al–1.5Mn–xSi alloys increased linearly as the ΔMk-magnitude increased, compared with that of the base alloy. The behavior in the flow stress variation qualitatively agreed with that of dislocation density. There was a linear relationship between the lattice constant and Mk_α in Al–1.5Mn–Si/Mg alloys. As the Mk_α changed, the σ_0.2 of the alloys also increased and its increment rate was similar in both Si and Mg addition alloys. It may be considered that the trend of change in the lattice constant, σ_0.2, work hardening amount and dislocation density was predominantly consistent with that in the Mk_α or ΔMk_α showing the indication of solid solution hardening level of the α-Al phase, and the effect of difference of third elements such as Si and Mg on their mechanical properties could be ignored in tensile examination procedures in this study.

1. Introduction

Currently, there is no doubt that the automotive industry is the most important consumer of cast aluminum alloys because of their good casting properties and can be made into complex shapes.^1–3) Up to now, the cast Al–Si series alloys are the most widely used alloys, particularly for automotive applications.^4–7) However, most cast Al–Si alloys have an elemental content close to the eutectic composition⁸⁾ and have to be heat-treated after solidification to achieve the purpose of strengthening the alloy.⁹⁾ In light of reducing the production cost, the application of the Al alloys in as-cast condition has attracted great attention in recent years.^1,2,10,11) For example, the Castasil^®-37 (Al–9 mass%Si–Mn–Mo–Zr) showed the 0.2% proof stress (σ_0.2) of 80–110 MPa, ultimate tensile strength (σ_UTS) of 200–250 MPa and the fracture strain (ε_f) of 10–14% in the as-cast condition.¹⁰⁾ The alloy compositions are referred to in mass percent unless otherwise noted. And this as-cast alloy has been applied to the automobile parts, such as reinforcement for convertible soft-top, shock tower, suspension-strut dome, internal door parts and longitudinal carrier.¹¹⁾ Thus, how to make traditional Al alloys continue to develop in the new century, how to develop new alloys to meet various needs, making the traditional alloy materials of Al alloys glow with new brilliance is an important issue for us.

The Al–Mn series alloys¹²⁾ are widely used in industry because they have moderate mechanical strength, high ductility and excellent corrosion resistance. It can be considered that some of a little number of elements can be added to the alloys for achieving solid solution strengthening.^13–16) In the previous study,¹⁵⁾ Al–1.5Mn was used as the base alloy, the Zn, Ca, Mg and Ti were chosen as alloying elements, and the relationship between mechanical properties and ΔMk value (the compositional average value of s-orbital energy level in the alloy) was experimentally investigated in details. The composition of promising alloy was decided to Al–1.5Mn–2.4Mg with the ΔMk value of 0.029 on the basis of the relationship between tensile properties and ΔMk value as the indication of the solid solution strengthening level of the alloy. This as-cast alloy as champion data showed the σ_0.2 of 135 MPa, σ_UTS of 270 MPa and ε_f of 18%, as well as excellent corrosion resistance in the NaCl solution, which led to the as-cast applications for automobile structural parts.

The d-electrons concept based on the theoretical calculation of electronic structure theory proposed by Morinaga et al.^17,18) has been applied to the design of the high-performance alloys such as Al,^15,19–21) Bi,^22,23) Ni^24–27) and Ti,^28,29) and some physical or chemical properties of the designed alloys were successfully predicted by this concept.¹⁵⁾ The bond order (Bo) and the d-orbital level of the transitional alloying element (Md) have been used in this concept. Bo is a measure of the strength of the covalent bond between atoms. And Md is related to charge transfer. It has also been found that Md is related to the electronegativity and atomic radius of the element.¹⁵⁾ Both electronegativity and atomic radius are classical parameters that have been used to describe the nature of chemical bonds between the atoms in the solids.²⁰⁾ For Al alloys of s, p simple metal, the ΔMk values are defined by taking the compositional averages of s-orbital energy level as mentioned in detail in section 2, which is easy to use in practical application, compared with other alloy design methods.^30–32)

In the present study, for the development of low-cost Al alloys, the Al–1.5Mn was chosen as the base alloy, and 1.0 and 3.3Si were added to it, keeping the same ΔMk values as those of Al–1.5Mn–0.8 and 2.4Mg¹⁵⁾ alloys, respectively. The relationship among their microstructures, mechanical properties and electron parameter was experimentally investigated on Al–1.5Mn–Si alloys, and it was also compared with the Al–1.5Mn–Mg alloys showing the applicability of the as-cast due to superior tensile properties.

2. Electron Parameter for the Determination of Alloy Compositions

The parameter used in the compositional optimizations of Al alloys had been obtained from the electronic approach to alloy design.^19–21) The electron parameter, Mk_i, is an s-orbital energy level existing above the Fermi energy level of an iAl₁₈ cluster, containing an alloying element i and its surrounding Al atoms.²⁰⁾ So far, various parameters have been proposed to describe the alloying behavior, but the electronegativity and the atomic radius of elements were chosen here because they represent well the nature of chemical bonds between the atoms in the solids.²⁰⁾ There was a good correlation between the electronegativity or atomic radius and the Md parameter of d-orbital energy level on transition metals, as mentioned in section 1. For s, p simple metals like Al, the d-orbital energy level was no longer effective in the transition metal-based alloys. The Mk_i, which is an s-orbital energy level exciting above the Fermi energy level, and it was obtained by the discrete variational Xα³³⁾ (DV-Xα) cluster calculation. Consequently, alloying effects are inevitably involved in Mk_i.²⁰⁾ It is well known that the energy level obtained by the DV-Xα cluster calculation represents the electronegativity itself.^19,20) The Mk_i value of each alloying element which was calculated on the iAl₁₈ cluster model in the case of FCC Al is listed in Table 1.^19,20) The Mk_i value decreased with increasing electronegativity, whereas it increased with an increasing atomic radius of elements, as shown in Fig. 1.^19,20) In addition, the p-orbital energy level may be considered instead of the s-orbital energy level, but a spherical symmetrical s-orbital was probably better than a directional p-orbital for investigating the mechanical properties of Al alloys.²⁰⁾

Table 1 List of Mk_i values of alloying elements in the FCC Al cluster.^19,20)

Fig. 1

Relationship between Mk_i values and the (a) electronegativity, (b) atomic radius of elements: ○ non-transition metals and ● transition metals.^19,20)

Most of the elements have a higher Mk_i value than Al except for the Si, Zn, Ga, and Ge. For alloys, two kinds of the average values of the s-orbital energy level, Mk_t and ΔMk values were defined by taking the compositional average, using eqs. (1) and (2).   

\begin{equation} \mathit{Mk}_{t} = \varSigma x_{i}\mathit{Mk}_{i} \end{equation} (1)

  

\begin{equation} \varDelta \mathit{Mk} = \varSigma x_{i}|\mathit{Mk}_{i} - \mathit{Mk}_{m}| \end{equation} (2)

Where x_i is the mole fraction of component i in the alloy, Mk_i and Mk_m are the Mk value for component i and Al, respectively. In the case when all the elements in the alloy have a higher (or lower) Mk_i value than Al, these two averages differ only by a constant bias of Mk_m value of 3.344 and hence there is no essential difference between them. However, when the elements with higher and lower Mk_i values are mixed in the alloy, the two average values have different meanings.²⁰⁾

In this study, Si addition alloys were designed on the basis of the Al–1.5Mn alloy, keeping the same ΔMk values as those of Al–1.5Mn–0.8 and 2.4Mg¹⁵⁾ alloys, respectively. There were the opposite alloying vectors between Al to Si and Al to Mg, as shown in Fig. 1, because the same alloying effect is respected due to the same vector, as the alloying vector is considered in the selection of alloying elements.^25,28) The ΔMk values of 0.8 and 2.4Mg addition alloys showing the applicability of the as-cast due to superior tensile properties, were 0.015 and 0.029, respectively. Therefore, the ΔMk values of 1.0 and 3.3Si addition alloys were 0.015 and 0.029, respectively. The Mk_t values of 1.0 and 3.3Si addition alloys were also 3.346 and 3.331, respectively. The Al–1.5Mn–xSi (x: 0.0, base; 1.0; 3.3) alloys were also designed in this study, as mentioned above.

3. Experimental Methods

Both the Al–Mn and Al–Si master alloys were used for preparing experimental alloys, and the targeted concentrations of 0.0, 1.0 and 3.3 of Si were achieved by Al addition. The constant melting temperatures were kept at 963∼993 K for 1.2 ks. Then, the melt was poured into a steel mold preheated at 423 K. The ingots were cooled to room temperature in the steel mold. The size of the cast ingots was 190 mm × 23 mm × 39 mm.

Specimens for microstructural observations were performed using optical microscopy (OM) and transmission electron microscopes (TEM, JEM-2010, JEOL, Japan). The image-pro software was employed to measure the volume fractions and the secondary dendrite arm spacings of the experimental alloys. The secondary dendrite arm spacings were measured by using OM images with an accurate scale bar. The line intercept method³⁴⁾ was used to measure the secondary dendrite arm spacings, and at least 100 dendrites were taken to determine the secondary dendrite arm spacings.

X-ray diffraction (XRD) patterns of the experimental alloys were obtained by using an X-ray diffractometer (D/max-2500PC, Rigaku, Japan) with Cu radiation (λ = 0.15418 nm, 40 kV, 200 mA) at a scanning step size of 0.001°, and silicon was used as an internal standard. The lattice constants were calculated from the interplanar spacing of the (111), (200), (220), (311) and (222) planes based on Bragg’s law. The minimal scanning step size of 0.001° was selected for the determination of the angular accuracy of the lattice constant. Therefore, there are five significant figures in the lattice constant for the experimental alloys.

Tensile test specimens with a diameter of 6 mm and a gauge length of 60 mm were machined from the cast ingots. The tests of tensile were performed at an initial strain rate of 6.7 × 10⁻⁴ s⁻¹ at room temperature with a testing machine (DCS-R-5000, SHIMADZU, Japan). The tensile strain was accurately measured by using an extensometer until the necking.

To reveal dislocation behavior in 1, 5 and 10% flow stress levels in tensile tests, 1, 5 and 10% plastic strains in cold rolling were applied to the Al–1.5Mn–xSi specimens with annealing at 453 K for 3.6 ks. The dislocation density was measured by the equal thickness fringe method using areas with a thickness of more than 100 nm in TEM specimens. The dislocation density (ρ) was estimated, using eq. (3). The values of ρ were measured in arbitrary cross-sections of more than fifty areas per one specimen.   

\begin{equation} \rho = n/A \end{equation} (3)

Where n and A are the numbers of dislocation and area in an arbitrary cross-section, respectively.

The nanoindentation experiments were conducted on the α-Al phase of each alloy by an instrument (ENT-1100a, Elionix, Japan) using a Berkovich diamond indenter at room temperature. The measurements were performed at the holding load of 30 mN (load controlled), loading up in 30 s, holding for 10 s at the peak load and unloading in 30 s on each specimen. The nanoindentation hardness (H_IT) was calculated using the Oliver-Pharr method³⁵⁾ as shown in eqs. (4) and (5), respectively, according to load-depth curves.   

\begin{equation} H_{\textit{IT}} = P_{\textit{max}}/A_{p} \end{equation} (4)

  

\begin{equation} A_{P} = 23.46 \times h_{c}^{2} \end{equation} (5)

Where H_IT is the nanoindentation hardness of the α-Al phase, P_max is the maximum indentation load, A_P is the projected area of the indentation and h_c is the depth of indentation.

4. Results and Discussion

4.1 Microstructures

The OM images of the experimental alloys are shown in Fig. 2. Dendritic structures with different size were obtained in alloys, and these dendritic structures predominantly consisted of the α-Al phase. The volume fractions of the α-Al phase in the base, 1.0 and 3.3Si addition alloys were 99.3, 98.6 and 96.1%, respectively, and other parts were defined as the eutectic consisting of the α-Al and Al₆Mn, or the α-Al, Al₁₂Mn₃Si and Si in the base or Si addition alloys, respectively. The measured secondary dendrite arm spacings in the base, 1.0 and 3.3Si addition alloys were 104.3, 98.7 and 43.1 µm, respectively, which meant that the secondary dendrite arm spacings decreased with the increment of Si addition. The number of nucleation sites of the α-Al grain increased due to the increment of Si addition. More, the melting points of alloys decreased with the increment of Si content. The slower diffusion rate of the solute elements led to the small secondary dendrite arm spacings. The compositions of the α-Al phase varied with the Si content, as listed in Table 2, which was caused by the change in the partition ratio between the α-Al phase and the eutectic for each element. The partition ratio of Mn and Si in the α-Al phase was exchanged by the increment of Si content, which led to the small amount of Mn in 3.3Si addition alloy. The difference in Mk_a values among three alloys is smaller than that in Mk_t, as shown in Table 2. It may be considered that enough solid solution degree was achieved in alloys. The Mk_α value of each alloy was defined by compositions measured in the α-Al phase listed in Table 2, and this value might correspond to the solid solution strengthening level of the α-Al phase.

Fig. 2

OM images of the (a) Base, (b) 1.0Si and (c) 3.3Si addition experimental alloys.

Table 2 The Mk_t and ΔMk values of experimental and reference¹⁵⁾ alloys, and their compositions in the α-Al phase.

Figure 3 shows the relationship between ΔMk values and the lattice constant, Mk_α or Mk_t values of the experimental alloys. The lattice constant decreased linearly with the increase in ΔMk values. It is considered that the decrease in lattice constant was related to the amounts of solid solution elements in the α-Al phase. The base alloy with ΔMk value of 0.008 showed the same value between the Mk_α and Mk_t, which meant the formation of the α-Al phase by the perfect solution of added elements in it. In contrast, 1.0 and 3.3Si with ΔMk values of 0.015 and 0.029 showed different values between Mk_α and Mk_t, which meant the decision of compositions of both the α-Al phase and the eutectic by a certain partition ratio of each element, or both the existence of solid solubility limit of each element in the α-Al phase and the increase of the eutectic.

Fig. 3

Relationship between ΔMk values and the lattice constant, Mk_α or Mk_t values of the experimental alloys.

4.2 Mechanical properties

The nominal tensile stress-strain curves of the experimental alloys are plotted in Fig. 4, and the nominal tensile stress-strain curves of the A1070 and Al–1.5Mn–6.0Mg were reported previously¹⁵⁾ and obtained from this study for reference. The A1070 specimens were annealed enough to obtain the lowest strength. The base alloy showed the strengthened plastic deformation behavior, compared with the A1070. The values of the σ_0.2, σ_UTS and ε_f were 47 MPa, 95 MPa and 18% in the base alloy, respectively. The 1.0Si addition alloy showed strengthened tensile behavior with the σ_0.2 of 61 MPa, σ_UTS of 148 MPa and ε_f of 18%, compared with the base alloy. The 3.3Si addition alloy showed the highest value throughout all flow stress, however, the ε_f was reduced to 9%. Serration in stress-strain curves on Si addition alloys are remarkable, which suggests Portevin-Le Chatelier effect,³⁶⁾ probably due to the presence of hindrances including predominantly distributed Si atoms in the α-Al phase for dislocation migration. The increase in flow stress meant the increase of strength properties due to the increment of solid solution strengthening level and dislocation strengthening in alloys, caused by the increase in ΔMk value of alloys, as well as Al–1.5Mn–xMg¹⁵⁾ alloys. The Si addition increased the tensile strength and decreased the ε_f of the alloys. Both Al₁₂Mn₃Si and Si phases in the eutectic area were distributed along the grain boundary and the cracks were propagated along the interface of both their phases and the α-Al phase during the tensile test and the ε_f of 3.3Si addition alloys with a large amount of their phases had a significant reduction. In addition, some shrinkage defects were observed in the base and Si addition alloys. However, the cracks were propagated along the interface of the Al₁₂Mn₃Si or Si and the α-Al phase in the eutectic area during the tensile test. As a consequence, shrinkage defects were not regarded as the factor influencing the tensile properties.

Fig. 4

Nominal tensile stress-strain curves of the experimental alloys. ^*The nominal tensile stress-strain curves of the A1070 and Al–1.5Mn–6.0Mg were reported previously¹⁵⁾ and obtained from this study, for reference.

To investigate the effects of the strengthening α-Al phase as the predominant phase on the mechanical properties, the nanoindentation experiments were carried out using the experimental alloys and A1070. Figure 5 shows the typical load (P)-depth (h) curves obtained from the nanoindentation experiments. The P-h curves had similar behaviors, regardless of the alloys. The α-Al phase of the 3.3Si addition alloy showed the lowest depth at the constant load, which could be attributed to solid solution strengthening. This also meant that the highest solid solution strengthening of the α-Al phase could be achieved by the Si addition or the decrease of Mk_a value as shown in Fig. 3.

Fig. 5

Load-depth curves of the nanoindentation experiments of the experimental alloys and A1070.

Form the P-h curves, the nanoindentation hardness and rate of elastic deformation work were obtained from the Oliver-Pharr method.³⁵⁾ The rate of elastic deformation work was defined by the ratio of the elastic deformation work to the total deformation work, which meant the possibility for the prediction of σ_0.2-magnitude by this rate. Figure 6 shows the good linear relationship between the nanoindentation hardness, the rate of elastic deformation work of the α-Al phase and σ_0.2 of the experimental alloys and A1070. It may be considered that the tensile properties such as flow stress and the ε_f as mentioned above were predominantly explained by using the solid solution strengthening level of the α-Al phase, although there were a few effects of eutectic in Al–1.5Mn–xSi alloys.

Fig. 6

Relationship between the nanoindentation hardness, the rate of elastic deformation work of the α-Al phase and the σ_0.2 of the experimental alloys and A1070. The σ_0.2 values were obtained from the stress-strain curves of the experimental alloys and A1070 as shown in Fig. 4.

4.3 Dislocation behavior

To reveal dislocation behavior in 1, 5 and 10% flow stress in tensile tests, 1, 5 and 10% plastic strains in cold rolling were applied to the Al–1.5Mn–xSi specimens with annealing at 453 K for 3.6 ks. TEM was employed to observe their dislocation behaviors. Figure 7 shows the typical dislocation behaviors obtained from the dark-fields of the α-Al phase because the flow stress levels were mainly decided by the solid solution strengthening level of the α-Al phase as shown in Fig. 6. The 1% plastic deformation of the base alloy resulted in the formation of dense dislocation entanglements which were arranged in the α-Al phase.¹⁵⁾ The characteristic dislocation cell structure could be only observed in the 1% strained base alloy, because of the increase of dislocation mobility. The dislocation of the 1.0 and 3.3Si addition alloys was more uniformly and densely distributed in the α-Al phase at the same levels of plastic strain, compared to that of the base alloy. Dislocation mobility in 1.0 and 3.3Si addition alloys were lower due to trapping of dislocations by homogeneously distributed solute elements in the α-Al phase, which resulted in uniform distribution of dislocations.

Fig. 7

TEM dark-field images on 1, 5 and 10% plastic strained specimens of the experimental alloys.

The value of dislocation density on 1, 5 and 10% of plastic strained specimens are shown in Fig. 8. The dislocation density was measured in alloys with a strain of 1, 5 and 10%, although the cell structure was partially observed in the base alloy. The dislocation density of the experimental alloys and A1070¹⁵⁾ varied linearly with ΔMk value. The flow stress value in 1, 5 and 10% strains were read out in the tensile curves shown in Fig. 4. Figure 9 shows a good relationship between ΔMk values and the flow stress corresponds to 1, 5 and 10% strain of the experimental alloys and A1070.¹⁵⁾ Here, in the tensile tests, the A1070 specimen was un-uniformly deformed at 10% strain, and the center in gauge length showed the constriction, as shown in Fig. 4. Since the value in ε_f of the 3.3Si addition alloy was 9.0%, the value of 154 MPa in fracture stress was used as the 10% flow stress level, for convenience. The behavior of the flow stress variation qualitatively agreed with that of dislocation density as shown in Fig. 8, which meant the possibility for the prediction of flow stress levels by the solid solution strengthening and dislocation strengthening of the α-Al phase, using ΔMk or Mk_α value.

Fig. 8

Relationship between ΔMk values and dislocation density on 1, 5 and 10% plastic strained specimens of the experimental alloys and A1070.¹⁵⁾

Fig. 9

Relationship between ΔMk values and the flow stress correspond to 1, 5 and 10% strain of the experimental alloys and A1070.¹⁵⁾

The effectiveness of this prediction method was firmly demonstrated by examining various data on the mechanical properties of both the Al–1.5Mn–xSi and Al–1.5Mn–xMg¹⁵⁾ alloys. Although the dislocation density has a good relationship with ΔMk value, in particular, how to physically understand this parameter within the framework of dislocation theory is unknown. It may be assumed that the dislocation theory is constructed by both elastic interaction and interaction based on the shear-modulus effect. The yield stress of FCC solid solution alloys has been interpreted as due to the hindering effects of solute atoms on dislocation motion.³⁷⁾ The effects may be due either to the pinning of dislocations and solute atoms.³⁸⁾ It is unclear which effect is more dominant in Al–1.5Mn–xSi alloys, but, according to pinning model, the solute-dislocation interactions may be attributable mainly to the elastic interaction as Cottrell effect and the interaction caused by shear-modulus effect.³⁹⁾

4.4 Relationship between Mk values and mechanical properties in Al–1.5Mn–xSi/Mg alloys

Previously, the compositional optimization of Al–Mn–X alloys has been reported in the literature.¹⁵⁾ Mg showed a higher Mk_i value than that of Al, however, Si showed a lower Mk_i value than Al, as shown in Fig. 1. Both alloying vectors of Si and Mg showed the near amount and opposite direction, as the alloying vectors were determined from Al to alloying elements i.^25,26) A certain interaction between Mg and Si may be implicit in the Mk_t values, regardless of the ΔMk values, as defined by eqs. (1) and (2). Table 2 shows the Mk_t and ΔMk values of the experimental and reference¹⁵⁾ alloys. The addition of Si and Mg in the base alloy meant the tension and compression stress fields around their substitutional elements, respectively.

For instance, the Mk_t value of 3.3Si addition alloy was 3.331, which was lower than that of the base alloy (3.352). In contrast, the 2.4Mg addition alloy which was keeping the same ΔMk value (0.029) with that of the 3.3Si addition alloy showed a higher Mk_t value (3.373) than that of the base alloy. The α-Al phase served as the dominating phase, it would have a direct impact on the properties in the experimental alloys, as shown in Figs. 3 and 6. It is necessary to establish a relationship between microstructural or mechanical properties and the Mk_α of the α-Al phase in the Al–1.5Mn–xSi alloys.

The addition of Si and Mg in the base alloy led to different types of lattice distortion caused by the substitutional solid solution of Si or Mg in the α-Al phase. Figure 10 shows the relationship between Mk_α values and the lattice constant, σ_0.2 of the experimental and reference¹⁵⁾ alloys. Here, the Al–1.5Mn–6.0Mg alloy was prepared for a reference over the solid solubility limit. It was apparent that the lattice constant values of Si and Mg addition alloys showed an increasing trend of negative and positive directions centering on the base alloy, respectively. It was also found that there was a linear relationship between Mk_α values of the α-Al phase and the lattice constant in Al–1.5Mn–xSi/Mg alloys, regardless of the kinds of the third element. In addition, as the Mk_α values changed the σ_0.2 of the alloys also increased, compared with the base alloy. The increment rate of σ_0.2 represented by θ₁ and θ₂ was similar in Fig. 10. Further, the relationship between ΔMk_α values and working hardening amount of the experimental and reference¹⁵⁾ alloys is also shown in Fig. 11. There was also a good linear relationship between ΔMk_α and the working hardening amount in their alloys.

Fig. 10

Relationship between Mk_α values and the lattice constant values, σ_0.2 of the Al–1.5Mn–xSi and Al–1.5Mn–xMg¹⁵⁾ alloys.

Fig. 11

Relationship between ΔMk_α values and working hardening amount of the experimental and reference¹⁵⁾ alloys.

The relationship between Mk_α and dislocation density of the experimental and reference¹⁵⁾ alloys is also shown in Fig. 12. There was a good relationship between Mk_α and dislocation density, regardless of kinds of alloys. The Si and Mg had low and high Mk_i values, or small and large atomic radius, or large and small electronegativity, respectively, as shown in Fig. 1. The elastic interaction is caused by the difference in atomic size between the solute and the solvent atoms. In contrast, the charge transfer occurs based on the difference in electronegativity between the solute and the solvent atoms. The charge transfer between the solute and the solvent atoms may contribute to the bond strength between them. The dislocation density of Si and Mg addition alloys increased in the proportion to the Mk_α value, compared with the base alloy. In the one-parametrical model in flow stress curves, the proof stress (σ_p) depends only on the total dislocation density (ρ) which is considered as the single internal variable of material according to eq. (6)^40,41)   

\begin{equation} \sigma_{p} = aGb(\rho)^{1/2} \end{equation} (6)

Fig. 12

Relationship between Mk_α values and dislocation density of the experimental and reference¹⁵⁾ alloys.

Where G is the shear modulus, a is constant and b is the Burger vector. It was considered on the basis of the assumption in eq. (6) as evidence, that the interaction between the σ_0.2 and dislocation density or hindrance for dislocation migration at the certain could be explained by the Mk_α value. This might lead to an indication of the solid solution strengthening level using the Mk_α value for ternary Al–1.5Mn–xSi/Mg system alloys.

It may be considered that the trend of change in the lattice constant, σ_0.2 and working hardening amount was predominantly consistent with that in the Mk_α or ΔMk_α, showing the indication of solid solution strengthening level of the α-Al phase, and the effect of difference of third elements such as Mg and Si with higher and lower Mk_i values on their mechanical properties could be ignored in tensile tests procedures in this study, although the effect of Mn was not discussed in this study. The σ_0.2 values of 1.0 and 3.3Si addition alloys with the Mk_t values of 3.346 and 3.331, respectively, can be predicted by the Mk_α value. It is considered that the decrease in the Mk_α value to 3.330 is necessary according to the relation between the σ_0.2 and Mk_α as shown in Fig. 10, for the achievement of the σ_0.2 of 135 MPa. This σ_0.2 value was obtained from the Al–1.5Mn–2.4Mg alloy with the Mk_α value of 3.372 in the development for as-cast applicability. However, more than 3.3Si addition in this system alloys is useless because it exceeded the solid solubility limit of Si in the α-Al phase and the brittle phase appeared in the alloys, as shown in Fig. 3. It may be concluded that the application of automobile structural parts of Al–1.5Mn–Si system alloys is difficult, compared with Al–1.5Mn–Mg alloys which keeping the same ΔMk value with the Al–1.5Mn–Si alloys in the as-cast condition in this study.

5. Conclusions

1. (1)    Dendritic structures with different size were obtained in alloys, and these dendritic structures predominantly consisted of the α-Al phase. The compositions of the α-Al phase varied with the Si contents, which caused the change in the partition ratio between the α-Al phase and eutectic for each element. The lattice constant decreased linearly with the increase in ΔMk values.
2. (2)    The 3.3Si addition alloy showed the strengthened tensile behavior with the σ_0.2 of 67 MPa and σ_UTS of 160 MPa, although the ε_f was reduced to 9%. The increase and decrease in flow stress and strain, respectively, resulted from the increment of solid solution strengthening level, caused by the increase in ΔMk values of the alloys.
3. (3)    The α-Al phase of 3.3Si addition alloy showed the lowest nanoindentation depth, which resulted in the achievement of the highest solid solution strengthening in it by 3.3Si addition or the decrease of Mk_α value. There was a good linear relation between the nanoindentation hardness, rate of elastic deformation work in the α-Al phase and σ_0.2 of alloys.
4. (4)    The dislocation density of Al–1.5Mn–xSi alloys increased linearly as the ΔMk-magnitude increased, compared with that of the base alloy. The behavior in the flow stress variation qualitatively agreed with that of dislocation density, which meant to the applicability for prediction of flow stress levels meaning the degree of solid solution strengthening and dislocation strengthening of the α-Al phase, using ΔMk or Mk_α.
5. (5)    There was a linear relationship between the lattice constant and Mk_α values in Al–1.5Mn–Si/Mg alloys, regardless of the kinds of third elements. As the Mk_α values changed, the σ_0.2 of the alloys also increased and its increment rate was similar in both Si and Mg addition alloys. In contrast, there was a good relationship between the ΔMk_α values and the working hardening amount. It may be considered that the trend of change in the σ_0.2, work hardening amount and dislocation density was predominantly consistent with that in the Mk_α or ΔMk_α showing the indication of solid solution hardening level of α-Al phase, and the effect of difference of third elements such as Si and Mg with lower and higher Mk_i values on their mechanical properties could be ignored in tensile examination procedures in this study.

Acknowledgments

This study was financially supported by the Japan Foundry Engineering Society Found. Simultaneously, we thank S. Sakamoto and Zongxian Su at Hiroshima University for their experimental assistance.

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