1 Introduction

Recently, the attention of some researchers has been drawn to alloys based on the Al-Ca eutectic, in which calcium is partially replaced by other eutectic-forming elements, including Fe, Ni, Ce, and La. This allows, on the one hand, creating complex eutectics with a very fine microstructure, which has a positive effect on their mechanical properties, and on the other hand, increasing the working temperatures of the alloy (Ref 1,2,3,4,5,6).

Severe plastic deformation (SPD) is an effective method for improving the mechanical properties of metals and alloys. Recent advances in this field are summarized in papers (Ref 7, 8). In particular, the processing of eutectic aluminum alloys using SPD methods provides a significant improvement in the strength–ductility balance (Ref 9,10,11,12,13,14,15,16). The best strength–ductility balance was achieved through the high-pressure torsion (HPT) processing alloys with a volume fraction of the eutectic particles of no more than 15-20% (Ref 10, 12). Thus, in the Al-4Ca-1.3Fe-0.8Mn alloy, the yield strength of 684 MPa, the ultimate tensile strength of 770 MPa, and the relative elongation of 5% were achieved (Ref 10). In binary Al–Ca alloys of eutectic composition (corresponding to 7.6 wt.% Ca), as well as in ternary eutectic alloys based on the Al-Ca-M system (where M is La, Ce, and Fe), the fraction of particles is significantly higher (approximately two times) compared to eutectic Al-Ce, Al-La, Al-Ni, et al. (Ref 5, 11, 12). This results in very high grain and interphase boundary densities during HPT processing, which causes high stress concentration (Ref 17), and contributes to severe embrittlement of the alloys (Ref 18). Restoration of ductility is possible through annealing, but the achieved strength–ductility balance is comparable to HPT-processed traditional binary eutectic alloys such as Al-La and Al-Ce (Ref 18). Thus, for the HPT processing of alloys based on the Al-Ca system, it is preferable to use hypoeutectic compositions with an optimal fraction of the eutectic phase.

A good strength–ductility balance of Al-Ca-based alloys with eutectic composition was achieved by equal-channel angular pressing (ECAP) (Ref 11, 19). Thus, ECAP of the Al-6Ca-3Ce eutectic alloy (four passes at a temperature of 200 °C) provided the yield strength, ultimate tensile strength, and relative elongation of the alloy of 208, 239 MPa, and 5%, respectively. The main advantage of ECAP, compared to HPT, is the possibility of processing more massive workpieces. At the same time, the strength of alloys processed by ECAP is significantly lower than those processed by HPT.

There are only a few works aimed at studying hypoeutectic Al-Ca-based alloys processed by SPD (Ref 3, 9, 10). These works considered complex alloys of the Al-Ca-La-Mn and Al-Ca-Fe-Mn systems, which made it difficult to interpret the results. In addition, the authors (Ref 3) limited themselves to measuring the microhardness after HPT. Thus, further efforts are required to achieve a high strength–ductility balance in ternary hypoeutectic alloys based on the Al-Ca-M system (where M is La, Ce, and Fe) using SPD technique.

In this work, a ternary hypoeutectic alloy Al-3Ca-3Ce (wt.%) was considered, and a comparative study of the effects of HPT and ECAP on the microstructure and strength–ductility balance of the alloy, as well as on their relationship, was carried out.

2 Materials and Methods

The Al-3Ca-3Ce (wt.%) alloy, initially taken in the cast state, was investigated. Ingots of about 200 mm in length and about 22 mm in diameter were obtained, which are turned to a diameter of 20 mm.

Two types of samples for deformation treatment were prepared from the ingots using a precision 2-axis wire-cut electrical discharge machine:

  1. i.

    Disks 1.8 mm thick and 20 mm in diameter. The final thickness of 1.6 mm was achieved by sanding with P600 abrasive paper. These samples were used for HPT;

  2. ii.

    Cylindrical samples 90 mm long and 20 mm in diameter. These samples were used for ECAP.

HPT was carried out at room temperature, a pressure of 6 GPa for three turns. The HPT setup had a constrained geometry of the dies. ECAP was performed under isothermal conditions with an angle between the channels of 110°. Before ECAP, the sample was heated in a muffle furnace to a temperature of 180-200 °C for 20 min; the die was heated to the same temperature. The die channel was treated with carbon grease for better sample sliding. Then, the sample was placed in the channel and pressed through the channel four times using a vertical press with a punch. An auxiliary copper sample was used to push the sample through the channel. After each pass, the sample was rotated 90° around the axis in one direction. In addition, after each pass, the presence of defects (cracks) on the workpiece’s surface was visually assessed. After the last pass, the sample was cooled in air.

Optical microscopy (NIM-100 microscope) and transmission electron microscopy (JEM-2100 JEOL microscope) were used to characterize the microstructure of the samples. The Vickers microhardness measurements were carried out using Micromet 5101 Buehler tester at a load of 0.5 N. The tensile mechanical properties were determined using an INSTRON-5966 machine and a series of three miniature flat specimens with a gauge size of 5 × 1.5 × 1 mm. The strain rate was 0.002 s−1. Fractographic analysis was performed using a TESCAN Vega 3 SBH scanning electron microscope. X-ray diffraction analysis was performed in the range of angles 2θ from 20° to 120° using a Bruker diffractometer and CuKα radiation with a wavelength of 1.54178 Å. In addition, the specific electrical conductivity of the samples was measured using the eddy-current method using a VE-27NC tester.

3 Results

3.1 Characteristics of the as-cast Al-3Ca-3Ce Alloy

The photographs of the as-cast sample microstructure were obtained using an optical microscope at different magnifications: × 200 and × 1000 (Fig. 1). The images clearly show the branches of dendrites with the eutectic between them. The main eutectic phases in the Al-Ca-Ce system are the Al4(Ca,Ce) and Al11(Ce,Ca)3 compounds (Ref 5). Dendrites are a solid solution based on aluminum (considering the lack of solubility of calcium and cerium in aluminum, we can talk about technically pure aluminum). According to work (Ref 19), the Al4(Ca,Ce) phase predominates in the alloy. The average size of the dendritic branches was 6 ± 2 μm; while the microstructure is characterized by some heterogeneity, expressed in the presence of areas with smaller and larger dendrites. Using the Image Expert Pro 3 package, the average percentage of dendrites was determined to be 55%, which is close to the theoretical value (Ref 5). At high magnifications ( × 1000), the individual eutectic particles were resolved: their average size was 1.8 μm. The microhardness of the alloy in the initial state was 51 ± 2 HV.

Fig. 1
figure 1

(a, b) Microstructure of the Al-3Ca-3Ce alloy as-cast

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3.2 Effect of ECAP on the Microstructure of the Al-3Ca-3Ce Alloy

The microstructures of the ECAP-processed samples in longitudinal and cross sections are shown in Fig. 2, 3, respectively. In the longitudinal direction, a strong distortion of the dendrite shape was observed. A barely noticeable tendency for the dendrites to be elongated at a certain angle to the pressing direction was found. In this case, the shape and size of the dendrites varied over a wide range, which may be due to the heredity of the initial ingot heterogeneity. In the cross section, the microstructure was even more heterogeneous. Both areas with elongated dendrites (Fig. 3a, d) and areas without a predominant orientation of dendrites (Fig. 3b, c) were observed. Just as in the longitudinal section, the shape and size of the dendrites varied over a wide range. At high magnifications, fragmentation of the dendrites was obvious (Fig. 3f). The fraction of dendrites increased from 55 to 70%, which can be explained by mass transfer; however, the average size of dendrites did not change significantly and was 5 ± 2 μm.

Fig. 2
figure 2

(a-d) Microstructure of the Al-3Ca-3Ce alloy after ECAP in longitudinal section

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Fig. 3
figure 3

(a-f) Microstructure of the Al-3Ca-3Ce alloy after ECAP in cross section

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3.3 Effect of ECAP and HPT on the Mechanical Properties of the Al-3Ca-3Ce Alloy

To assess the uniformity of hardening during ECAP, the microhardness of the sample was measured in longitudinal and cross sections. In the cross section, the microhardness was measured along the diameter, and in the longitudinal section—both along the center line of the sample and at a depth of 1 mm from the surface. The measurement step in all cases was 1 mm (three measurements per point). In all measured areas, the microhardness was the same and amounted to 62 ± 2 HV, which indicates a very high uniformity of hardening of the material, despite the microstructure heterogeneity. The obtained microhardness values were 20% higher compared to as-cast state.

To assess the uniformity of hardening during HPT, the microhardness was measured along the diameter of the disk-shaped sample with a step of 1 mm (three measurements per point). HPT resulted in an increase in microhardness and its gradient distribution along the sample’s radius (Fig. 4). In the direction from the center to the periphery, the microhardness values increased from 64 ± 1 to 192 ± 4 HV. Thus, the maximum microhardness at the periphery of the sample was 3.8 times higher than in as-cast state. In the center of the sample, the microhardness increased by 25%.

Fig. 4
figure 4

Microhardness value distribution along the diameter of the Al-3Ca-3Ce alloy sample before and after HPT

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Comparing the microhardness after HPT and ECAP, it is evident that the maximum values of microhardness after HPT are three times higher than after ECAP. At the same time, the values of microhardness after HPT, averaged over the entire surface of the sample, are only two times higher than after ECAP.

Table 1 summarizes the mechanical properties of the Al-3Ca-3Ce alloy in different conditions during tensile testing. The tensile curves are shown in Fig. 5.

Table 1 Mechanical properties of the Al-3Ca-3Ce alloy in different conditions
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Fig. 5
figure 5

Tensile stress-strain curves of the Al-3Ca-3Ce alloy samples in different conditions: 1—as-cast, 2—ECAP, 3—HPT

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Both ECAP and HPT improved the strength–ductility balance of the alloy. ECAP increased the yield strength and ultimate tensile strength by 2.4 and 1.3 times, respectively, compared to as-cast state. At the same time, the relative elongation slightly decreased. Moreover, the spread of mechanical properties inherent to the alloy in the cast state significantly decreased, which is expressed in a decrease in standard deviations by more than three times. HPT increased the yield strength and ultimate tensile strength by 5.7 and 3.7 times, respectively, compared to as-cast state. At the same time, the relative elongation increased by 1.5 times. The maximum values of the yield strength, ultimate tensile strength, and relative elongation after HPT were 418, 529 MPa, and 17%, respectively. Thus, the strength after ECAP was 2.3-2.8 times lower, and the ductility was two times lower than after HPT. The tendency of the alloy to strain hardening decreased in the following order: as-cast, HPT, and ECAP, which is expressed in an increase in the ratio YS/UTS. Uniform elongation (REUNIF) decreased after ECAP and HPT.

The fracture surfaces of the tensile specimens are shown in Figure 6. At the macro-level, the fracture surface of the as-cast alloy specimen was flat without any pronounced reduction in area (Fig. 6a). At the micro-level, a ductile dimple fracture was observed, with the dimple sizes corresponding to the size of the dendritic branches, and the dimple contours repeating the dendritic structure of the alloy (Fig. 6b). Very small dimples less than 1 μm in size were observed in the eutectic region (Fig. 6c). The fracture surface of the ECAP-processed specimen was also flat at the macro-level, but the reduction in area was more pronounced (Fig. 6d). The fracture mechanism was also ductile, but the size and distribution of the dimples were predominantly uniform (Fig. 6e, f), which is explained by the more uniform microstructure of the alloy after ECAP. The most developed fracture surface relief and the most pronounced reduction in area were characteristic of the HPT-processed specimen (Fig. 6g). The fracture surface was uniform, consisting of very small dimples of about 1 μm in size (Fig. 6h, i). Thus, the fracture surfaces correlated well with the microstructure of the samples as well as with the tensile curves.

Fig. 6
figure 6

(a, d, g) General view and (b, c, e, f, h, i) patterns of fracture surfaces of tensile specimens of Al-3Ca-3Ce alloy in different conditions: (a-c) as-cast; (d-f) ECAP and (g-i) HPT

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3.4 Electron Microscopic Studies of Al-3Ca-3Ce Alloy After ECAP and HPT

To explain the change in the mechanical properties of the samples after different deformation treatments, electron microscopic studies were carried out using the TEM method. The obtained microstructure images for ECAP- and HPT-processed alloy are shown in Figure 7, 8, respectively. During ECAP, small grains in the micron range (average size 1.3 ± 0.3 μm) with predominantly high-angle boundaries were formed in aluminum dendrites (Fig. 7a). In contrast, in the eutectic areas, the sub-microcrystalline structure with predominantly low-angle boundaries was formed (Fig. 7b, c). The presence of low-angle boundaries is evidenced by the blurring of reflections in the electron diffraction pattern, as well as by the analysis of dark-field images (Fig. 7e). In addition, individual grains with high-angle boundaries were found in the areas of the former eutectic (Fig. 7f). The average grain (subgrain) size was 320 ± 27 nm (the predominant size was 100-470 nm). Judging by the light contrast, the dislocation density was relatively low. The eutectic particles were crushed mainly by cleavage mechanism. The average length and width of the particles were 470 ± 23 nm and 230 ± 7 nm.

Fig. 7
figure 7

Microstructure of the Al-3Ca-3Ce alloy sample after ECAP: (a) general bright-field image; (b, c) bright-field image of the eutectic areas; (d) dark-field image in particle reflections; (e, f) dark-field images in aluminum reflections

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Fig. 8
figure 8

Microstructure of the Al-3Ca-3Ce alloy sample after HPT: (a, c, d) general view bright-field images; (b) dark-field image in particle reflections

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As a result of HPT, a nano- and sub-microcrystalline structure was formed with a predominance of high-angle misorientations with a moderately high density of crystalline defects, and the eutectic particles were crushed (Fig. 8a, c). Nanosized particles are clearly visible in the dark-field TEM image (Fig. 8b). The contrast in the bright-field images indicates an increased level of internal stresses (Fig. 8d). The microstructure was dominated by grains (subgrains) 20-190 nm in size (average size 128 ± 10 nm) and particles 10-30 nm in size (average size 18 ± 8 nm).

In addition, the presence of intermetallic particles in the alloy after SPD treatments is confirmed by clear lines in the x-ray diffraction pattern, corresponding to the Al4Ca phase (Fig. 9a). Given the absence of ternary phases for the Al-Ca-Ce system in the x-ray databases and based on the literature data (Ref 5), it can be concluded that the Al4(Ca,Ce) phase is present.

Fig. 9
figure 9

(a) X-ray patterns for the Al-3Ca-3Ce alloy sample after ECAP and HPT and (b) enlarged fragments with (400)Al line

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To further calculate the dislocation density in the alloy after ECAP and HPT, x-ray diffraction analysis was carried out (Fig. 9b). The calculation of the dislocation density was carried out according to Equation (1):

$$\rho = \delta /\left( {b \times d} \right)$$
(1)

where: δ is the full width at half maximum; b is Burgers vector (0.286 nm); and d is the crystallite size. For the calculation, the (400)Al line corresponding to the angle 2θ ~ 99.5° was selected.

According to the calculation, the dislocation density in the alloy after ECAP was 1012-1013 m−2, and after HPT, it was 1013-1014 m−2. These values are in good agreement with earlier studies (Ref 12, 19).

3.5 Electrical Properties of Al-3Ca-3Ce Alloy

The results of measuring the electrical properties of the Al-3Ca-3Ce alloy in different conditions are presented in Table 2. A slight tendency for the electrical conductivity to decrease was observed in the following series: as-cast, ECAP, and HPT. The smallest spread of the values was characteristic of the alloy after ECAP, and the largest was for the alloy as-cast, which may be associated with its residual porosity. Thus, in all conditions, the alloy was characterized by close values of electrical conductivity, which amount to 44-47% IACS. This, in turn, corresponds to the level of electrical conductivity of typical structural aluminum alloys (Ref 20), as well as calcium-containing aluminum alloy (Ref 21).

Table 2 Electrical properties of the Al-3Ca-3Ce alloy in different conditions
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4 Discussion

4.1 Effect of ECAP on the Microstructure and Mechanical Properties of the Al-3Ca-3Ce Alloy

In this work, the ECAP processing of the Al-3Ca-3Ce alloy resulted in the distortion of the dendrite shape, which is typical for such alloys (Ref 9, 11, 19). This is primarily a consequence of the non-uniform distribution of micro-stresses and micro-strains in the workpiece, which is characteristic of severe plastic deformation processes (Ref 22,23,24,25). However, the observed distortion of the dendrite shape was less pronounced than in the eutectic Al-6Ca-3Ce alloy after the same processing (Ref 19). This can be explained as follows: The structure of the Al-Ca-Ce-based alloys consists of two components (dendritic areas and eutectic areas), which are deformed differently. The eutectic is deformed worse than the dendrites. During ECAP, both structural components are deformed simultaneously. Due to the different deformation capacity, a non-uniform stress–strain state arises between them; this additionally leads to the distortion of the dendrite shape. In the Al-6Ca-3Ce alloy, the fraction of eutectic is higher than in the Al-3Ca-3Ce alloy. This increases the non-uniformity of the stress–strain state between the eutectic areas and the dendrites, which in turn leads to a stronger distortion of the latter. At the same time, the strength of the Al-6Ca-3Ce alloy is only 20% greater than that of the Al-3Ca-3Ce alloy, although the relative elongation is two times less. Moreover, despite the strong non-uniformity of the microstructure after ECAP (Fig. 2, 3), the Al-3Ca-3Ce alloy is characterized by uniform hardening (uniform distribution of microhardness values in the sample’s volume). It follows from this that the interphase boundaries do not have a serious effect on the mechanical properties. Consequently, the main effect on the strength of the Al-Ca-Ce-based alloys after ECAP is exerted by the substructure and eutectic particles. It is clear that the strengthening mechanisms in the former dendrite and former eutectic areas will differ. Based on the results of microstructural studies, it can be stated that the main strengthening mechanisms of the Al-3Ca-3Ce alloy after ECAP are: (i) strengthening from high-angle boundaries of the fine-crystalline structure of former dendrites (σHAB), (ii) strengthening from low-angle boundaries of the sub-microcrystalline structure of the former eutectic (σLAB), and (iii) Orowan strengthening from crushed eutectic particles (σOr). The total strengthening of the alloy can be calculated using the rule of mixtures as the sum of the strengthening mechanisms acting in the former dendrite and former eutectic areas, taking into account their volume fractions. Thus, the total theoretical strength (yield strength) of the alloy after ECAP can be approximately estimated by the following relationship:

$$\sigma = \sigma_{0} + \left( {1{-}\alpha } \right) \times \sigma_{{{\text{HAB}}}} + \alpha \times (\sigma_{{{\text{LAB}}}} + \sigma_{{{\text{Or}}}} )$$
(2)

where \(\sigma_{0}\) is the frictional or Peierls stress (10 MPa), α—fraction of eutectic.

Grain boundary strengthening (σHAB) was calculated using a classical Hall–Petch equation (Ref 26),

$$\sigma_{{{\text{HAB}}}} = Kd^{ - 1/2}$$
(3)

where K is a coefficient, and d is the grain size. Taking into account the dependence of the K on the grain size, in the specified range of grain sizes K = 0.1 (Ref 27).

Calculating strengthening from subgrain boundaries (σLAB) is more complex and involves different approaches. The first approach is based on calculating the contribution of low-angle boundaries through the dislocation density,

$$\sigma_{{{\text{LAB}}}} = M\alpha Gb\sqrt {\rho_{0} + \rho_{{{\text{LAB}}}} }$$
(4)

where M ( = 3.07) is the Taylor factor, α is a constant ( = 0.24) (Ref 28), G is the shear modulus (26,000 MPa), b is the Burgers vector (0.286 nm), ρ0 is the dislocation density between the boundaries, ρLAB is the dislocation density stored in the low-angle dislocation boundaries that contribute as dislocation strengthening. It must be pointed out here that the Taylor factor value 3.07 refers to un-textured aluminum (Ref 29, 30). However, Equation (4) is not easy to apply due to the complexity of calculating the dislocation density ρ0 and ρLAB.

The second approach is based on the use of a relationship similar to the Hall—Petch relationship,

$$\sigma_{{{\text{LAB}}}} = Kd^{ - 1/2}$$
(5)

where K is a coefficient, and d is the subgrain size. In this case, it is difficult to find the value of the coefficient K for low-angle boundaries of aluminum in the literature, but it is considered to be 2-10 times smaller than the coefficient K for high-angle boundaries. In this paper, the coefficient K is taken to be equal to 0.05.

The precipitation hardening (σOr) was estimated according to the well-known Orowan equation (Ref 13),

$$\sigma_{{{\text{Or}}}} = \frac{0.4MGb}{{\pi \lambda \left( {1 - v} \right)^{1/2} }}{\text{In}}\left( \frac{d}{b} \right)$$
(6)

where ν is the Poisson’s ratio ( = 0.331), d is the mean particle size, λ is the effective inter-particle spacing. This latter was calculated as

$$\lambda = \frac{3\pi d}{4}\left( {\frac{1}{2}\left( {\frac{2\pi }{{3f_{{\text{v}}} }}} \right)^{1/2} - 1} \right)$$
(7)

where fV is the volume fraction of particles.

The calculated contribution of different strengthening mechanisms to the overall strengthening of the Al-3Ca-3Ce alloy under ECAP is presented in Table 3. It can be seen that the difference between the theoretical and experimental yield strength exceeds 40%, which is explained by the interaction of different strengthening mechanisms in the complex structure of the alloy, as well as the difficulty of calculating the exact value of the inter-particle distance.

Table 3 Contribution of different strengthening mechanisms to the overall strengthening of the Al-3Ca-3Ce alloy under ECAP
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Considering that the quantitative characteristics of the grain and subgrain microstructure of the Al-3Ca-3Ce and Al-6Ca-3Ce alloys are similar, and the dislocation density is relatively low in both alloys, the small difference in the strength of the alloys (about 20%) is associated with a larger fraction of eutectic in the Al-6Ca-3Ce alloy structure, i.e., with increased dispersion strengthening. At the same time, the mean free path of dislocations decreases, which naturally leads to a decrease in ductility (relative elongation).

4.2 Effect of HPT on the Microstructure and Mechanical Properties of the Al-3Ca-3Ce Alloy

The main strengthening mechanisms of the Al-3Ca-3Ce alloy after HPT are: (i) strengthening from high- and low-angle boundaries of the nano- and sub-microcrystalline structure (σHAB and σLAB), (ii) dislocation strengthening (σdisl), and (iii) Orowan strengthening from crushed eutectic particles (σOr). The structure of the alloy after HPT is predominantly homogeneous. Considering that high-angle boundaries predominate in the alloy structure, strengthening from low-angle boundaries can be neglected. Thus, the overall theoretical strength of the alloy after HPT can be estimated by the following relationship:

$$\sigma = \sigma_{0} + \sigma_{{{\text{HAB}}}} + \sigma_{{{\text{Or}}}} + \sigma_{{{\text{disl}}}}$$
(8)

The strengthening from high-angle boundaries (σHAB) can be calculated using Equation (3), the Orowan strengthening can be calculated using Equation (6), and dislocation strengthening–using Equation (9). Taking into account the dependence of the K on the grain size, in the specified range of grain sizes K = 0.07 (Ref 27). The volume fraction of particles in the alloy (taking into account the volume fraction of eutectic) is 0.12. The calculated contribution of different strengthening mechanisms to the overall strengthening of the Al-3Ca-3Ce alloy during HPT is presented in Table 4. Good agreement between the theoretical and experimental yield strengths is evident (the difference was less than 10%).

$$\sigma_{{{\text{disl}}}} = M\alpha Gb\sqrt \rho$$
(9)

where M ( = 3.07) is the Taylor factor, α is a constant ( = 0.33) (Ref 13), G is the shear modulus (26,000 MPa), b is the Burgers vector (0.286 nm), and ρ0 is the dislocation density.

Table 4 Contribution of different strengthening mechanisms to the overall strengthening of the Al-3Ca-3Ce alloy under HPT
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The difference in mechanical properties after various deformation treatments is due to the different microstructure of the alloy formed under ECAP and HPT conditions. HPT provides ultra-high degrees of strain and a high rate of accumulation of dislocation density, which promotes dynamic recrystallization. The degrees of strain and the rate of accumulation of dislocations during ECAP are lower; furthermore, the ECAP process is carried out at elevated temperatures, facilitating recovery. Thus, during HPT, a nano- and sub-microcrystalline structure is formed with a predominance of high-angle misorientations with a relatively low density of crystalline defects, and the eutectic particles are crushed to the nanolevel. This ensures a combination of ultra-high strength and high ductility. ECAP does not ensure the formation of a developed ultrafine-grained microstructure. The alloy after ECAP is characterized by a heterogeneous structure: fine-crystalline structure with a predominance of high-angle boundaries and a sub-microcrystalline structure with a predominance of low-angle boundaries and a low density of dislocations; while the eutectic particles are crushed. This ensures a combination of moderately high strength and ductility. It is important to note that the alloy after both HPT and ECAP is characterized by a combination of good strength and ductility, which is associated with structural accommodation (Ref 10, 31,32,33).

Taking into account the gradient distribution of microhardness along the radius of the disk-shaped sample processed by HPT, it is obvious that the tensile specimen’s gauge part was also characterized by a gradient distribution of microhardness. During electrical discharge cutting of the tensile specimen, the positioning accuracy was 1 mm. Knowing the position of the tensile specimen’s gauge part relative to the disk and superimposing it on the graph from Fig. 3, it is possible to determine the microhardness of the tensile specimen’s gauge part. Thus, the tensile specimen’s gauge part was located at a distance from the center of the disk within 5 to 8 mm. These areas corresponded to a microhardness gradient from 127 to 187 HV. The microhardness of the gauge part of the specimen cut closer to the periphery varied from 133 to 187 HV, and the gauge part of the specimen cut closer to the center–from 127 to 159 HV. The difference in the strength of the two specimens was small: 9% in the ultimate tensile strength and less than 2% in the yield strength. Thus, gradient hardening did not lead to heterogeneity in mechanical properties. Moreover, a number of studies have noted the positive effect of gradient hardening (or gradient microstructures) on the strength-ductility balance of the material (Ref 31, 34, 35).

4.3 Evaluation of the Ductility Reserve of Al-3Ca-3Ce Alloy

According to the tensile test conducted, the uniform elongation in Al-3Ca-3Ce alloy after ECAP and HPT is insignificant and amounted to about 3%. However, the shape of the stress–strain curve after the maximum load deserves attention (Fig. 5). This part of the curve is almost parallel to the x-axis up to a strain of approximately 5% for the HPT specimen and approximately 7% for the ECAP specimen. In other words, there is no sharp load drop after maximum load, but rather quasi-stable plastic flow, which is characteristic of this alloy processed by SPD, as noted earlier (Ref 10). Thus, the alloy exhibits moderately high ductility. Moreover, in combination with high strength, one can fairly speak of a high strength–ductility balance.

As is known, the reserve of ductility of a material can be estimated by comparing the values of the uniform strain (eu) and the strain hardening exponent (n) (Ref 36). A significant difference between eu and n (eu <  < n) indicates an early loss of stability of plastic flow, for example, due to the formation of cracks in a heterogeneous microstructure during deformation. The values of the true stress, S = σ × (1 + ε) and the true strain, e = ln(1 + ε) were determined in the uniform plastic deformation area up to the moment of the load drop on the stress-strain curve. The S-e stress–strain curves corresponded to the Hollomon’s equation, S = K × en. The parameters were determined using the least squares method as the coefficients of the linear regression equation, ln(S) = ln(K) + n × ln(e).

Figure 10 shows the relationship between the values of eu and n for the specimens of all conditions under tension. It can be seen that the initial as-cast specimen has the largest values of both eu and n, while eu <  < n. This indicates that the localization of deformation and necking occurs due to the early loss of stability of plastic flow. In addition, it should be noted that large scatter was found in the values of eu for the as-cast specimens, which may be associated with some porosity. For specimens after HPT, both eu and n decrease, while the ratio eu <  < n is maintained. For specimens after ECAP, both eu and n are the smallest, while eu = n. This indicates that the material shows optimal ductility and that premature localization of deformation is avoided. Although the uniform elongation of the alloy after ECAP is small, it is the maximum possible uniform elongation for an alloy with a given microstructure.

Fig. 10
figure 10

The relationship between eu and n for the for tensile specimens of Al-3Ca-3Ce alloy after various treatments

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4.4 Effect of ECAP and HPT on Electrical Properties of the Al-3Ca-3Ce Alloy

In all conditions, the Al-3Ca-3Ce alloy was characterized by relatively high values of electrical conductivity (Table 2). This can be explained as follows: Given the insolubility of Ca and Ce in solid aluminum, the scattering of conductive electrons by solute atoms can be neglected. The most significant obstacle to electron flow in the cast alloy is the irregularly distributed clusters of the Al4(Ca, Ce) particles within the alloy’s volume, with a higher specific resistance than that of the metal matrix, forming a kind of network along the boundaries of the dendrites. This reduces the electrical conductivity of the alloy compared to pure aluminum. As a result of SPD, the grain is refined, and the Al4(Ca, Ce) particles are crushed and distributed more evenly within the alloy’s volume. This has a dual effect on electrical conductivity. On the one hand, the destruction of the intermetallic network contributes to an increase in the free path of conduction electrons, on the other hand, the scattering frequency of conduction electrons will increase. Moreover, an increase in the density of crystalline defects in the alloy after SPD should lead to a decrease in electrical conductivity. Apparently, the expected decrease in electrical conductivity due to an increase in the density of crystalline defects and refinement of the microstructure is compensated by an increase in electrical conductivity due to the intermetallic network destruction in the cast alloy. As a result, the electrical conductivity of the alloy after SPD remains, approximately, the same as that of the cast alloy. The positive effect of SPD on the electrical conductivity of aluminum alloys has been recorded in a number of studies (Ref 15, 37).

4.5 Comparative Effect of ECAP and HPT on the Microstructure and Mechanical Properties of Hypoeutectic and Eutectic Al-M Alloys (where M is Ca, Ce)

It is of interest to compare the mechanical properties of the hypoeutectic Al-3Ca-3Ce alloy obtained in this study with the literature data for similar alloys of eutectic composition. Thus, the achieved strength–ductility balance of the Al-3Ca-3Ce alloy after HPT is similar to that of the eutectic Al-10Ce alloy, the yield strength, the ultimate tensile strength, and the relative elongation of which were 456, 495 MPa, and 17%, respectively (Ref 12). This can be explained by the same number of particles in both alloys. At the same time, the eutectic Al-6Ca-3Ce alloy after HPT was in an embrittled state (Ref 18). This is due to the high volume fraction of particles in this alloy, which contributes to high stress concentration. In the case of ECAP processing, as noted above, the Al-6Ca-3Ce alloy had a slightly higher strength, but significantly lower ductility, compared to the Al-3Ca-3Ce alloy: the yield strength, the ultimate tensile strength, and the relative elongation of which were 208, 239 MPa, and 5% (Ref 19). Due to the higher ductility, the achieved strength–ductility balance of the Al-3Ca-3Ce alloy exceeded that of the eutectic Al-6Ca-3Ce alloy.

5 Conclusions

A comparative analysis of the effects of ECAP (200 °C for four passes) and HPT (room temperature for 3 turns) on the microstructure and its relationship with the strength–ductility balance of the hypoeutectic Al-3Ca-3Ce alloy (wt.%) was performed. The following was found:

  • The yield strength, the ultimate tensile strength, and the relative elongation of the alloy as-cast were 73, 142 MPa, and 11%, respectively. Both ECAP and HPT improve the strength–ductility balance of the alloy. ECAP led to an increase in the yield strength and ultimate tensile strength by 2.4 and 1.3 times, respectively, compared to as-cast state; at the same time, the relative elongation slightly decreased (to 9%). HPT resulted in an increase in the yield strength and ultimate tensile strength by 5.7 (up to 418 MPa) and 3.7 times (up to 529 MPa) compared to the as-cast state; the relative elongation increased by 1.5 times (up to 17%). Thus, the strength after ECAP was 2.3-2.8 times lower, and the ductility was two times lower than after HPT. The fracture of tensile alloy specimens in all conditions occurred entirely by the ductility dimple mechanism.

  • The difference in the mechanical properties of the alloy after ECAP and HPT is due to the different microstructure of the alloy. HPT resulted in the formation of a nano- and sub-microcrystalline structure with a predominance of high-angle misorientations, while the eutectic particles were crushed to a nanosize. The alloy after ECAP was characterized by a heterogeneous structure, namely, the areas of fine-crystalline structure with a predominance of high-angle boundaries and the areas of sub-microcrystalline structure with a predominance of low-angle boundaries and the presence of crushed particles.

  • The alloy in all conditions was characterized by good electrical conductivity, amounting to 44-47% IACS.