Influence of Severe Plastic Deformation by Extrusion on Microstructure, Deformation and Thermal Behavior under Tension of Magnesium Alloy Mg-2.9Y-1.3Nd

Abstract

The microstructural investigation, mechanical properties, and accumulation and dissipation of energies of the magnesium alloy Mg-2.9Y-1.3Nd in the recrystallized state and after severe plastic deformation (SPD) by extrusion are presented. The use of SPD provides the formation of a bimodal structure consisting of grains with an average size 15 µm and of ultrafine-grained grains with sizes less than 1 µm and volume fractions up to 50%, as well as of the fine particles of the second Mg₂₄Y₅ phases. It is established that grain refinement during extrusion is accompanied by an increase of the yield strength, increase of the tensile strength by 1.5 times, and increase of the plasticity by 1.8 times, all of which are due to substructural hardening, redistribution of the phase composition, and texture formation. Using infrared thermography, it was revealed that before the destruction of Mg-2.9Y-1.3Nd in the recrystallized state, there is a sharp jump of temperature by 10 °C, and the strain hardening coefficient becomes negative and amounts to (−6) GPa. SPD leads to a redistribution of thermal energy over the sample during deformation, does not cause a sharp increase in temperature, and reduces the strain hardening coefficient by 2.5 times.

1. Introduction

Recently, there has been an increasing interest in biodegradable metals, which are used in various fields of medicine. Particular attention is attracted to magnesium alloys [1,2,3,4,5,6,7,8] having certain advantages which distinguish them favorably from other materials used in the manufacturing of implants. One of the most important advantages is the ability of magnesium alloys to be resorbed in the human body. This feature makes it possible to avoid surgical operations, which are otherwise needed for removing implants [9,10]. Moreover, magnesium implants demonstrate good biocompatibility and may have antitumor effects. The latter are due to magnesium’s ability to release hydrogen during biodegradation, which has a cytopathogenic effect on tumor cells [11,12]. Finally, magnesium alloys have an optimal modulus of elasticity (40–45 GPa), similar to that of the native bone [13,14]. Alloying of magnesium with rare earth metals (RE), such as Y, Nd, Gd, Ce, Dy, etc., leads to the enhancement of strength characteristics, and to increases in plasticity and corrosion resistance [15,16,17,18]. However, in some cases, the achieved level of strength properties does not meet the necessary requirements. This may to some extent limit the use of these materials in implantology.

In view of the above, various deformation methods were proved to be very promising, including severe plastic deformation (SPD), for example, equal-channel angular pressing (ECAP), abc-forging, rotational forging, extrusion, etc. These methods allow one to obtain a high level of mechanical properties in metals by grinding grain to an ultrafine-grained (UFG) state [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. In this case, it becomes possible to significantly improve the mechanical properties of alloys. Of particular importance is that this can be done without additional alloying with elements, which reveal toxic properties and are thus inapplicable, for example, in biomedicine.

Various investigations were conducted to study the microstructure and physico-mechanical properties of the medical materials in which the UFG structure is formed. This applies primarily to studies of ‘pure titanium’ VT1-0, VT1-00, Grade 1, Grade 2, and, to a lesser extent, to titanium and magnesium alloys [30,31]. However, it is worth noting that the use of SPD methods, such as ECAP and abc-forging, does not always lead to the formation of the UFG state in magnesium alloys. As a rule, one obtains a finely dispersed structure with an average grain size of about 1 μm. Therefore, the development of methods and technological regimes of deformation for obtaining the UFG state in magnesium alloys remains an urgent task. In addition, the issues related to obtaining the UFG structure in bulk magnesium alloy samples by SPD are complex and have not yet been fully resolved.

Understanding the mechanisms of plastic deformation and destruction under various types of loading is important for developing new UFG alloys. Strain localization plays a special role, since it determines the features of degradation and destruction of real samples [32,33,34,35]. At the same time, the issues related to identification of the mechanisms leading to the destruction of UFG alloys remain poorly understood and require a more detailed analysis.

There are various approaches developed for estimating the criteria of the strength and fracture of materials. One of them is the method of complete diagrams, which makes it possible to find a characteristic for estimating the ultimate damage in the plastic part of the complete tensile diagram after any preloading. The latter has the meaning of the specific work expended for failure. This method also allows one to develop a new criterion for crack resistance [35]. Another approach is based on the evaluation of the accumulation and dissipation of energy during plastic deformation using the method of infrared (IR) thermography.

The IR thermography method [36] has been proved to be very convenient for analyzing the processes in which a material reaches its critical state. This method allows one to analyze the temperature variations of samples throughout the whole range of deformations. It also makes it possible to investigate the evolution of structural defects within materials in real time. As has been shown in Refs. [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56], despite the absence of external signs of deformation, the shear bands are formed at different stages of deformation. In the same works, it was noted that the accumulation and dissipation of energy develop non-linearly and depend on the loading conditions. It should however be noted that investigations of deformation processes by IR thermography were carried out mainly on steels, aluminum, and titanium alloys in the coarse-grained state [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56].

In some of our previous works [57,58,59,60,61], comparative studies of the evolution of the temperature distributions, as well as of the peculiarities of energy accumulation and dissipation during the deformation of VT1-0, Zr–1Nb, and Ti–45Nb alloys in the CG and UFG states, were carried out. According to our results, the distribution of the temperature field on the surface of the deformed samples depends on the samples’ structural states, the presence of defective structures, and the mechanical and thermophysical properties of the alloys under study.

The aim of the present work is to study how the extrusion deformation processing of a magnesium alloy of the Mg-Y-Nd system affects the microstructure, mechanical properties, and tensile deformation behavior.

2. Materials and Research Methods

For the present study we used a commercial magnesium Mg-Y-Nd alloy with the following elemental content: Mg-2.9Y-1.3Nd (wt.%): Mg 95.0; Y 2.9; Nd 1.3; Fe ≤ 0.2; Al ≤ 0.6, manufactured by continuous mold casting [62,63]. In order to refine the grain and thus improve the mechanical properties, the samples were subjected to SPD by extrusion. The alloy billets were deformed by reverse extrusion at a speed of 0.5 mm/s, and the temperature of the billet and the extruder wall was 350 °C. The diameter of the bars was successively reduced from 60 to 14 mm. The accumulated logarithmic degree of deformation as a result of deformation processing of the samples was e = 1.46. This parameter was determined as the logarithm of the ratio of the initial to the final thicknesses of the sample at each pressing.

The magnesium alloy was investigated in both the extruded and recrystallized states. The recrystallized state in the Mg-2.9Y-1.3Nd alloy was achieved by annealing at a temperature of 525 °C for 8 h in argon with subsequent cooling in air.

The mechanical tests were performed out on the universal servohydraulic test stand Instron (Instron European Headquarters, High Wycombe, UK). The uniaxial tension of flat samples was conducted at a constant strain rate of 0.01 s⁻¹. To measure the temperature distributions on the surface of the samples, as well as to evaluate the samples’ dimensions and shapes including the formation of necks during deformation, we used an infrared radiometric imager FLIR SC 7700M. This allowed obtaining the true deformation σ_true(ε_true) and temperature ΔT(ε_true) curves, as well as determining the work of plastic deformation A_p(ε_true), the specific amount of the heat dissipated during deformation (Q), and the energy stored during deformation (Es). The respective calculation methodology was described elsewhere [57,60].

The true stress σ_true was evaluated using the formula:

$${\sigma }_{true}=\frac{F(1+{\epsilon }_{eng})}{S_0},$$

(1)

where $F$ is the load applied to the sample, S₀ is the initial cross-section area of the sample, S₀ = a₀ × b₀, where a₀ and b₀ are the width and the thickness of the sample, ε_eng is the engineering deformation, and ${\epsilon }_{eng}=\frac{\mathsf{\Delta }l}{l_0}$ where Δl and l₀ are the elongation and the initial length of the gauge section of the sample, respectively. The true stress in the “neck” zone was calculated as follows:

$${\sigma }_{true}=\frac{F}{S_i},$$

(2)

where S_i = a_i × b_i is the apparent cross-sectional area in the “neck” of the sample corresponding to the i-th IR thermogram and a_i and b_i are the width and the thickness of the sample in the “neck” region for the i-th thermogram. The latter are related by the equation b_i = b₀ × a_i/a₀

The true deformation ε_true was determined thus:

$${\epsilon }_{true}=\mathit{ln}(1+{\epsilon }_{eng}),$$

(3)

The total specific work of deformation was estimated using the true strain curves thus:

$$A={\int }_0^{{\epsilon }_{max}}{\sigma }_{ture}{d\epsilon }_{ture},$$

(4)

where ε_max is the maximum deformation of the sample before fracture.

The work of plastic deformation A_p is defined thus:

A_p = A − A_e,

(5)

where A_e is the work of elastic deformation.

Then, the energy stored during plastic deformation (E_s) can be defined thus:

E_s = A_p − Q

(6)

Using the data obtained by the infrared thermography method, the specific amount of heat released during the deformation process (Q) was estimated by using the obvious formula:

$$Q=c\frac{m}{V}\mathsf{\Delta }t.$$

(7)

Here, c, m, and V are the specific heat of the sample material, the sample mass, and the sample volume, respectively, and Δt is the average temperature change on the sample surface during its deformation.

The microstructure and phase composition of the samples were studied using the optical microscope AXIOVERT-200MAT (Carl Zeiss, Industrielle Messtechnik GmbH, Oberkochen, Germany), a transmission electron microscope (TEM) (JEOL JEM 2100, JEOL Ltd., Akishima, Tokyo, Japan), and an X-ray diffraction analysis unit using CuKα radiation (Bruker D8 Advance, Karlsruhe, Germany, λ = 1.54 Å). The measurements were fulfilled in the 2θ range of 10–90°, with a scan step of 0.01° and an acquisition time of 1 s. The phase was identified using the cards from the database of the International Center for Diffraction Data (ICDD) PDF4+. To calculate the average size of structural elements (grains, subgrains, fragments) we used the standard secant method [64].

The microhardness was evaluated according to the Vickers on the microhardness tester Duramin 5 (Struers, Ballerup, Denmark). To measure the elastic modulus, we used the nanohardness tester DUH 211S (Shimadzu, Chiyoda-ku, Tokyo, Japan). The modulus value was obtained by pressing the indenter into the sample surface with the simultaneous building up of the ‘load-unload’ kinetic diagram. The measurements were performed at a load of 200 g. The loading, unloading, and holding time was 10 s. The elastic modulus was calculated by means of graphical derivation of the unloading branch on the diagram [65].

The microstructure of the fracture surface and the texture of the samples were investigated by applying the technique of scanning electron microscopy (SEM) by means of an electron microscope (LEO EVO 50 Carl Zeiss, Oberkochen, Germany) equipped with a backscattered electron diffraction (EBSD).

3. Results and Discussion

Figure 1 shows the microstructure of the Mg-2.9Nd-1.3Y alloy in the recrystallized state. As we can see, the microstructure is uniform over the entire volume of the sample with equiaxed grains of the main α-phase of magnesium (HCP lattice). The average grain size is the same in the longitudinal and in the transverse sections and amounts to 35 µm (Figure 1a). The dislocation substructure is represented by individual dislocations and dislocation loops. The dislocation density is low and amounts to only 3·10⁹ cm⁻². In the α-grains of magnesium there are evenly distributed particles of the intermetallic phase (Figure 1b,c) with a high content of yttrium (9–30 wt.%).

The intermetallic particles were identified by X-ray microanalysis of the elemental content as Mg₂₄Y₅ (BCC lattice). The Mg₂₄Y₅ particles, having the form of irregular polyhedrons, were 0.2 to 1 μm in size. Furthermore, the microstructure images show another type of intermetallic phases enriched in Y and Nd, appearing inside or along the grain boundaries. According to [66,67], in the Mg-Y-Nd alloys, these phases are identified as precipitates of intermetallic phases: eutectic equilibrium β-phase (Mg₁₄Nd₂Y, FCC lattice), precipitates of the β′-phase (Mg₁₂NdY, orthorhombic lattice) of globular morphology, and a plate of the β1-phase (Mg₃NdY, FCC lattice). Discharges of the β-phase are localized along the grain boundaries in the form of a grid of up to 0.8–2 μm in thickness (Figure 1b). The average size of the β′-phase (Mg₁₂YNd) globules is 0.3 µm and the length and the width of the β1-phase plates are within the ranges of 0.3–0.9 µm and 0.02–0.08 µm, respectively.

After extrusion, the refinement of the microstructure occurs in the Mg-2.9Nd-1.3Y alloy. The microstructure has a bimodal character. In the longitudinal section, there are grains 20–25 µm in size, as well as smaller grains 0.5–2 µm in size (Figure 2a). The shapes of most grains are close-to-equiaxed. The fraction of ultrafine-grained grains is about 50%. The average grain sizes for the longitudinal and the cross sections are 14 and 17 µm, respectively. On the TEM images of the microstructure, one observes grain and subgrain boundaries with a clear contrast. These contain an increased density of lattice dislocations in the inner region (Figure 2b). The dislocation density is 4·10¹⁰ cm⁻². As in the recrystallized state, the structure (Figure 2b–d) contains particles of Mg₂₄Y₅, β-phase (Mg₁₄Nd₂Y), precipitates of β′-phase (Mg₁₂NdY), globular morphology, and plates of the β1-phase (Mg₃NdY)).

According to the results of the microdiffraction analysis, the Mg₂₄Y₅ particles have an increased yttrium content (30 wt.%). Their sizes are in the range 0.3–0.7 µm. The volume fraction of particles of the second Mg₂₄Y₅ phase does not exceed 5%. In the extruded alloy, the Mg₂₄Y₅ particles are in the form of irregular polyhedrons and are located in the bodies of the grains (Figure 2c). The content of yttrium in the discharge of β-, β′- and β1-phases is (9–11) wt.%, and that of neodymium is (4–6) wt.%. The average size of globules of the β′-phase (Mg₁₂YNd) is 0.2 µm. The length and the width of the β1-phase plates are within the ranges of 0.06–0.3 µm and 0.03–0.04 µm, respectively. Note that the plates of the β1-phase are oriented in the same direction. The eutectic β-phase (Mg₁₄Nd₂Y) is represented by an irregularly shaped polyhedral and localized along the grain boundaries in the form of a network of precipitates of 0.1–0.3 µm in thickness. In the extruded state, one observes a decrease of the linear dimensions of the particles in the Mg₂₄Y₅ intermetallic compounds, as well as of the β-phase and β1-and β′-phases.

Figure 3 shows the diffraction patterns for Mg-2.9Nd-1.3Y alloys (a, b) in the recrystallized and the extruded states. For both states, high-intensity reflections from the α-phase of magnesium and low-intensity reflections from the Mg₂₄Y₅ intermetallics were found. The intensity of reflections from the intermetallic phases for the recrystallized state is t higher than that for the alloy after extrusion. This may indicate a certain increase of the volume fraction of the phases and Mg₂₄Y₅ as a result of annealing. For the extruded state of the alloys, redistributions of the reflection intensity (100) and (101) are observed, indicating the reorientation of the grains and formation of a texture. The volume fraction of the secondary phase particles could not be determined by an X-ray diffraction analysis because of their small amount.

Figure 4 shows EBSD misorientation maps and inverse pole figures for magnesium alloy Mg-2.9Y-1.3Nd in various structural states. On the EBSD maps, the grains are colored according to their crystallographic orientations (the color code is given in the next). On the maps for the two states, one can notice the granular nature of the microstructure. The structure for the extruded state is dominated by a weak crystallographic texture of the <001> type. The inverse pole figures are presented for different external sections in the crystal: longitudinal X0, transverse Y0, and normal (axial) Z0 in three main planes (0001), (01–10), (11–20). As one can see, in the recrystallized state, the inverse pole figures have clear maxima (Figure 4a), and the maximum reflection density is not concentrated near a particular crystallographic direction. This may point to the formation of an annealing texture [68,69]. After the extrusion of the magnesium alloy, the inverse pole figures become blurred, and the pole density maximum changes its position (Figure 4b). For the main directions of the crystal lattice, high pole densities are observed. The maximum density occurs in the direction <001> for the longitudinal Y0 and <010> for the normal Z0 sections. This indicates a pronounced texture. The texture of the extruded magnesium alloy Mg-2.9Y-1.3Nd is quite diffuse. Note that the total intensity of the peaks in the extruded state is much higher than that in the case of annealing.

The plasticity of magnesium alloys should be analyzed taking into account the texture factor [70]. The presence of texture changes the activity of the main deformation systems in the basal {0001}, prismatic {1010}, and pyramidal {1122} systems, as well as {1012} twinning. The texture formed after deformation activates the basal and pyramidal sliding, as well as the twinning. At the same time, it hinders the dislocation slide for prismatic planes. On the contrary, the texture for the recrystallized state activates the basal slide and weakens the activity of the prismatic slide. The overall effect of prismatic and pyramidal slide activation is superior to that of the basal slide activation after extrusion. Thus, it can be argued that the extrusion of an alloy significantly increases both its strength and its plasticity. In addition, the higher relative elongation of the magnesium alloy in the extruded state, compared to in the recrystallized state, can be explained by a slightly lower fraction of second phase particles.

In Figure 5 we demonstrate the conditional engineering curves for Mg-2.9Y-1.3Nd alloy samples in the recrystallized (1) and the extruded (2) states. Using the ‘engineering stress—engineering strain’ diagrams, the following ultimate strength characteristics of Mg-2.9Y-1.3Nd alloys under uniaxial tension conditions can be determined: conditional yield strength σ_YS, ultimate strength σ_UTS, and maximum plastic deformation before failure ε_f. The corresponding values are collected in

Table 1. Mechanical properties of Mg-2.9Y-1.3Nd alloy.

State/Property	σYS, MPa	σUTS, MPa	εf, %	Hμ, MPa	E, GPa
Recrystallized state	150 ± 7	230 ± 8	12 ± 1	860 ± 60	33.9 ± 0.5
Extruded state	220 ± 9	340 ± 10	21 ± 1	1210 ± 70	35.0 ± 0.5

. There we also present the microhardness Hμ and the Young’s modulus E for the alloy under study. The results indicate that the grain refinement during extrusion is accompanied by an increase of mechanical properties: the conditional yield strength, tensile strength by 1.5 times, and plasticity by 1.8 times. Moreover, the deformation processing of the Mg-2.9Y-1.3Nd alloy by extrusion leads to an increase in microhardness by a factor of 1.2 and does not cause any significant change in the Young’s modulus of the magnesium alloy (Table 1).

The increase in strength is determined by strain hardening associated with the accumulation of dislocation density and by the contribution of the dispersed particles from the second Mg₂₄Y₅ phase localized along the grain boundaries. The decrease of strength in the recrystallized state should be assigned to an increase of the grain size and to a decrease of the dislocation density. According to the results of Ref. [70], during deformation at temperatures above 225 °C in the basal slide mechanism in the magnesium alloy, this is realized. In this case, the dislocation slide occurs along the basis planes if these planes are ‘conveniently’ oriented with respect to the direction of the applied stress. In addition, at higher temperatures, the gliding of prismatic and pyramidal systems also becomes possible. This mechanism is preferable for obtaining the optimal combination of the strength and plastic properties of magnesium alloys.

The increase in plasticity after deformation is caused by the activation of an additional mechanism of the dislocation slide, i.e., the slide predominantly along prismatic planes and not along the base planes as in the equilibrium state [71]. The increase of the plasticity strength of the magnesium alloys is associated with the evolution of the dislocation substructure and with the formation of textures as a result of the deformation processing of alloys. This finding agrees with the results obtained by other authors for the magnesium alloys MA2-1 and WE43 after SPD [72,73]. The reason for this may be the formation of a bimodal structure and texture in the Mg-Y-Nd alloy during extrusion, as well as the substructural hardening of the matrix α-phase and redistribution of the phase composition (secondary phases β, - β′-, and β1, and the Mg₂₄Y₅ particles).

Figure 6a,b show the SEM images of the fracture surfaces of the alloy in the extruded and recrystallized states. For the alloy sample after extrusion, on the fracture surface, there are areas of “pitted” microrelief typical of ductile fracture (Figure 6a). The microrelief consists of large “pits” with an average size 20 µm and a heteroaxial shape and smaller pits with an average size of less than 5 µm.

The fracture surface of the alloy after extrusion has a uniform structure, and this may indicate the macroplastic nature of the fracture. The fracture surface of the sample for the recrystallized state has a “rough” faceted structure (Figure 6b). The fracture microrelief consists mainly of large smooth and flat fragments of 30–100 µm in size. There are protrusions and chips at the boundaries of the fragments. Note that there are areas of pit fracture between the flat fragments. The brittle nature of the fracture is evidenced by the presence of chips and protrusions of the facets. The presence of flat facets with characteristic flow lines is typical of brittle fracture. For both states, there are pores that appeared during the plastic deformation.

Figure 7 shows the true deformation curves σ_true(ε_true) and the corresponding dependences of the strain hardening coefficient θ(ε_true) = dσ_true/dε_true for the Mg-2.9Y-1.3Nd alloy in the recrystallized (1) and the extruded (2) states. In the recrystallized state, several stages of deformation can be distinguished: transitional stage (T), stage III, stage IV, stage V, and stage VII (according to the classification used in [74,75]).

Although a decrease of θ is observed at the transitional stage T, the shape of the curve is not parabolic (Figure 6). Stage II with a constant θ is suppressed, and it is immediately followed by stage III up to ε_true~0.03, at which θ decreases and the dependence σ = f(ε) becomes parabolic. The next stage IV (0.03 < ε_true < 0.1) is almost linear. At a short parabolic stage V (0.1 < ε_true < 0.105), the strain hardening coefficient drops sharply to almost zero. Finally, at the final stage, stage VII (0.105 < ε_true < 0.115), a sharp drop of θ to (−6) GPa is observed, and the alloy is destroyed.

A similar trend may be observed on the temperature curve ΔT(ε_true) in Figure 8. In their case, for the Mg-2.9Y-1.3Nd alloy in the recrystallized state, there is an extended part of the curve (up to ε_true~0.03, corresponds to the stage III on the deformation curves) on which the temperature decreases by about 0.5 °C and becomes negative. This is due to the well-known thermoelastic effect [76].

At the next stage, stage IV (0.03 < ε_true < 0.1) the temperature increases by about 2.5 °C, followed by a very short stage V (0.1 < ε_true < 0.105). Finally, at the final stage, stage VII (0.105 < ε_true < 0.115), there is a sharp jump by 10 °C followed by the destruction of the alloy.

On the curves σ_true(ε_true) and θ(ε_true) for the Mg-2.9Y-1.3Nd alloy in the extruded state, the following deformation stages can be isolated: transitional stage (T) with θ increasing to ε_true < 0.002, parabolic stage III with decreasing θ (0.01 < ε_true < 0.04), linear stage IV with almost constant θ (0.04 < ε_true < 0.19), parabolic stage V with decreasing θ (0.19 < ε_true < 0.2), and stage VII with negative θ (0.2 < ε_true < 0.225).

On the curves depicting the temperature for the Mg-2.9Y-1.3Nd alloy in the extruded state, the part corresponding to a negative temperature (stage III on the deformation curves) increases to ε_true~0.04. Then, at stages IV and V (0.04 < ε_true < 0.2), an increase in ΔT by about 5 °C is observed. In contrast to what has been noted in the recrystallized state, before the destruction of the extruded Mg-2.9Y-1.3Nd alloy, at stage VII there is no sharp increase in temperature; ΔT increases only by about 2 °C. The strain hardening coefficient decreases by 2.5 and reaches a value (−1.5) GPa.

Figure 9 shows a series of frames from thermal films for the Mg-2.9Y-1.3Nd alloy in the recrystallized (a) and the extruded (b) states. The shape of the IR thermograms indicates that during the deformation of the recrystallized sample, the plastic deformation bands, which are sources of heat release, are less pronounced, and a thermal effect manifests itself insignificantly until the destruction of the sample (Figure 9a). Just before the destruction, one observes a small area of localized deformation whose appearance determines the locations of the defects. Then, in this region, two deformation bands, directed at an angle of 45°, intersect, a sharp jump of temperature is observed, and the instantaneous destruction of the sample occurs.

In an extruded sample with deformations above ε_true = 0.085, plastic deformation bands can be observed whose direction corresponds to the highest shear stresses. In the deformation lines, the alloy is in a plastically activated state, while other regions of the alloy operate in the elastic deformation area. As the flow stress increases, the width of the deformation bands increases, and this is accompanied by a gradual increase of temperature and by the generation of the deformation centers, which increase in size, unite, and develop in the form of a main line.

Further deformation, maximum temperature increase, and destruction of the alloy occur in this region, in which the main line is generated without the formation of a ‘neck’ (Figure 9b).

In Figure 10 the energy parameters, namely the specific work of plastic deformation Ap, the amount of released heat Q, and absorbed energy during plastic deformation Es, are plotted as functions of the true strain released during deformation for the Mg-2.9Y-1.3Nd alloy in the recrystallized (a) and the extruded (b) states.

The limiting values of the specific work of plastic deformation were 20 MJ/m³ and 45 MJ/m³ for the Mg-2.9Y-1.3Nd alloy in the recrystallized and extruded states, respectively.

From the dependences shown in the figure, one can conclude that for the Mg-2.9Y-1.3Nd alloy samples, in both the extruded and the recrystallized states, the amount of heat released during deformation is different in different areas. At the initial stage, up to ε_true~0.03, almost 100% of the work of plastic deformation is converted into internal energy. This indicates the ability of the alloy to effectively use the structural energy absorption channel at the initial stage of deformation, regardless of its structural state, and this is associated with dispersion strengthening by intermetallic particles.

Then, the dependences of the released and the absorbed energy in the recrystallized and extruded states behave linearly. For the samples in the recrystallized state, the amount of the heat released due to the thermoplastic effect comprises 60% of the work of plastic deformation, and comprises to 12 MJ/m³, whereas the specific energy absorbed by the alloy is about 40% of the work of plastic deformation and is equal to 8 MJ/m³. In this case, for the alloy in the recrystallized state, before fracture, a sharp temperature jump of 10 °C occurs, and the strain hardening coefficient becomes negative, amounting to (−6) GPa, indicating a local softening of the alloy.

At the same time, the amount of heat released due to the thermoplastic effect in the extruded state is about 35% of the work of plastic deformation (15 MJ/m³), and the remaining 65% of the energy (30 MJ/m³) is absorbed by the alloy. This points to the fact that the magnesium alloy in the extruded state dissipates energy twice as efficiently as it does in the recrystallized state.

Obviously, the amount of released heat depends on the structural and phase state as well as on the thermophysical properties of the materials. Previously, it was shown that the amount of heat released from the total strain energy for coarse-grained (CG) titanium was 50% [77], for annealed stainless steel 60–70% [78,79], and for copper 80–90% [80].

The formation of the UFG state also has a strong effect on energy dissipation. In [77], it was shown that substructural hardening in UFG pure titanium under SPD leads to changes in deformation, thermal behavior, and energy accumulation and dissipation during deformation. At the initial stage, up to ε_true~0.04, almost the whole energy of plastic deformation is stored by the material. In the next stages, the amount of released heat increases and reaches 70% just before destruction, whereas the energy stored by the material comprises 30% of the work of plastic deformation. The dispersion strengthening by the ω-phase particles and the α-phase formation in the UFG Ti-45Nb alloy reduce the influence of the UFG structure on the deformation and on thermal behavior, especially at the initial stage of deformation. At this stage, up to ε_true~0.05, almost the total energy of plastic deformation is stored by Ti-45Nb in both the CG and the UFG states. In the next stages, the amount of released heat increases and reaches 40% and 70% just before destruction, whereas the amounts of energy absorbed by the material are 60% and 30% of the work of plastic deformation, respectively, for the Ti-45Nb alloy in the CG and UFG states.

Moreover, our data are in good agreement with the results of [47], where the simulation of energy accumulation, and its dissipation during plastic deformation, was performed. It was shown in [47] that the UFG state of metals contributes to the accumulation of the energy of plastic deformation at the initial stage of deformation. At the same time, dispersion strengthening and the presence of strengthening particles in alloys weaken the effect of substructural hardening during the formation of the UFG structure, as has been demonstrated by the results of the present work.

Thus, SPD by extrusion of the magnesium alloy Mg-2.9Y-1.3Nd leads to formation of a bimodal structure consisting of grains with an average size of 15 μm and ultrafine-grained grains (less than 1 μm in size) with a volume fraction of up to 50 %, as well as fine particles of the second phases Mg₂₄Y₅ and equilibrium β-phase and metastable β1-and β′-phases and texture formation. It provides a significant increase of mechanical properties and affects the deformation behavior and regularities of energy accumulation and dissipation during tension.

4. Conclusions

A comprehensive analysis of the microstructure and deformation, as well as the corresponding temperature dependences, demonstrate the significant influence of the extrusion on the regularities of energy accumulation and dissipation during plastic deformation of the Mg-2.9Y-1.3Nd alloy.

It is shown that the use of SPD by the extrusion method in the magnesium alloy Mg-2.9Y-1.3Nd promotes the formation of the UFG state (the fraction of UFG grains is 50% of the volume), as well as the occurrence of fine particles of the second phases of Mg₂₄Y₅ and equilibrium β-phase, metastable β1- and β′-phases, and the formation of texture.

It was found that the refinement of the SPD structure by extrusion of Mg-2.9Y-1.3Nd leads to an increase in the yield strength, increase in the tensile strength by 1.5 times, and increase in the ductility by 1.8 times due to substructural strengthening, redistribution of the phase composition, and texture formation.

It was revealed that SPD leads to the redistribution of thermal energy over the sample during deformation, does not cause a sharp increase in temperature, and reduces the strain hardening coefficient by a factor of 2.5. The magnesium alloy in the extruded state dissipates energy twice as efficiently as it does in the recrystallized state.