Creep of a Die-Cast Mg–5Al–2Ca Alloy: An Overview

Abstract

A comprehensive research program on the creep of a die-cast Mg–5Al–2Ca (mass%) alloy, which has been conducted in the last two decades by our group, is overviewed. The obtained results are summarized into the following categories: microstructure and creep strength, creep parameters, dislocation analysis, and life assessment. The creep strength of the alloy is predominantly ascribed to the interconnected skeleton of C36–(Mg,Al)₂Ca phase, while the fine C15–Al₂Ca precipitates have limited effects on creep strength. The change in creep parameters, n and Q_c, results from the decreased creep strength driven by the divorce of the interconnected skeleton of C36 phase during creep. At stress levels below the yield stress, the dislocation climb in the primary α-Mg grains is inferred as the rate-controlling process for the alloy. Mostly ⟨a⟩ type dislocations are introduced within the primary α-Mg grains during die-casting, and the dislocation segments are mainly located on the basal plane. The basal segments of dislocations bow out and glide on the basal planes under stress, and the jogs follow the basal segments with the help of climb during creep. The minimum creep rate and creep rupture life follow the phenomenological Monkman–Grant relationship for the alloy. When the Larson–Miller constant is set at 20, the value of Larson–Miller parameter is uniquely described by the logarithm of the applied stress.

Fig. 1 FE-SEM image of the die-cast AX52 alloy (reproduced from Ref. 39)).

1. Introduction

Magnesium alloys have gained much interest as lightweight structural materials in automotive and aerospace industries to achieve high fuel efficiency and worldwide environmental protection.^1,2) The development of heat-resistant magnesium alloys can achieve further weight reduction in a transport equipment, which promotes the widespread use of magnesium alloys.³⁾ Pure magnesium has low strength at elevated temperatures,^4,5) and the secondary elements in magnesium show limited solubility.⁶⁾ The high-temperature strength of heat-resistant magnesium alloys can be enhanced using intermetallic phases and composites with high thermal stability.^7–9)

Ca addition to Mg–Al alloys can considerably enhance creep strength,^10–13) because it promotes the formation of harder Laves phases with higher thermal stability while suppressing the formation of β-Mg₁₇Al₁₂ phase with low thermal stability.¹⁴⁾ A Mg–Al–Ca ternary system, which exhibits excellent non-flammability, is a promising alloy system for developing cost-effective heat-resistant magnesium alloys.^15,16) Basic knowledge concerning liquid projection¹⁷⁾ and phase diagram^18–21) has been extensively investigated for the Mg–Al–Ca ternary system in the last 20 years to achieve widespread use of Mg–Al–Ca alloys in high-temperature components.

Heat-resistant magnesium alloys are mostly used in as-cast condition, and the casting condition plays a crucial role in determining the resulting properties. The creep properties have been researched for Mg–Al–Ca alloys produced by die-casting,^22–30) squeeze-casting,^31,32) thixomolding,^32,33) and other methods.^{25,27,28,34,35)} Zhu et al. investigated the creep properties of Mg–Al–Ca alloy MRI153 produced by die-casting, squeeze-casting, and ingot-casting.²⁵⁾ They reported that the squeeze-cast material exhibited the best creep resistance, while the die-cast material exhibited the worst creep resistance; the ingot-cast material exhibited intermediate creep resistance. Saddock et al. reported that the creep resistance of Mg–Al–Ca alloy AXJ530 produced by die-casting was higher compared to that of the alloy produced by permanent mold casting.²⁷⁾ Mondal et al. reported that Mg–Al–Ca alloy MRI230D developed by high-pressure die-casting exhibited superior creep resistance than the alloy developed by ingot-casting.²⁸⁾

High pressure die-casting is the most common method of casting magnesium alloys because of its cost effectiveness, short cycle time, etc.³⁶⁾ In 2001, we began a comprehensive research program on the high-temperature creep of Mg–Al–Ca alloys produced by die-casting, focusing on the alloy composition of Mg–5Al–2Ca (in mass%) (hereafter referred to as AX52) and the creep temperature of 423–498 K. The present paper overviews the creep properties of the die-cast AX52 alloy on the basis of our previous work. The contents of this paper are as follows: microstructure and creep strength (section 2), creep parameters (section 3), dislocation analysis (section 4), and life assessment (section 5). Three kinds of AX52 die-cast alloy specimens; heat A, B, and C, were used in this program and their composition is listed in Table 1. A heat means a series of die-cast plates with the identical alloy composition. Several tens of die-cast plates were produced in each heat in this research. The creep tests shown in section 2 were carried out by using heat A, while the experimental results shown in sections 3, 4, and 5 are provided by using heat B. The microstructure observation using field-emission scanning electron microscopy (FE-SEM) in section 2 involved the use of heat C.

Table 1 Alloy composition of AX52 used in the research program (in mass%).

2. Microstructure and Creep Strength

Mg–Al–Ca alloys consist of a dual-phase microstructure: a soft α-Mg matrix reinforced with hard intermetallic Laves phases in the form of an interconnected network. These alloys comprise three types of Laves phases: C15–Al₂Ca, C36–(Mg,Al)₂Ca, and C14–Mg₂Ca, which form during solidification due to eutectic reactions.¹⁷⁾ The type of Laves phase formed in the microstructure during casting depends predominantly on the [Ca]/[Al] ratio.^37,38) In this section, the correlation between microstructure and creep strength is presented for the die-cast AX52 alloy.

2.1 C36–(Mg,Al)₂Ca phase

The microstructure of the die-cast AX52 alloy consists of the primary α-Mg grains and interconnected skeleton of C36–(Mg,Al)₂Ca phase. The FE-SEM image of the as-die-cast alloy specimen (heat C) is shown in Fig. 1.³⁹⁾ The interconnected skeleton^38,40) of C36 phase covers the α-Mg grains, which are about 5 µm in size. The interconnected skeleton is thermally stable in morphology at temperatures below 500 K, while the morphology of skeleton is evidently unstable at temperatures above 573 K.⁴¹⁾ Suzuki et al. reported that the C36 phase transforms to the C15 phase by the aging treatment at 573 K, which is geometrically possible by a shear mechanism involving synchro-Shockley dislocations.⁴²⁾ In addition, the morphology of C36 phase changes to a discrete plate shape during aging at 573 K and finally becomes a coarsened spherical particle.¹⁷⁾ Such a microstructure evolution results in the divorce of interconnected skeleton, which covers the primary α-Mg grains.

Fig. 1

FE-SEM image of the die-cast AX52 alloy (reproduced from Ref. 39)).

2.2 C15–Al₂Ca phase

When the die-cast AX52 alloy is subjected to the aging treatments at temperatures of 473–573 K, a fine C15–Al₂Ca phase precipitates along the basal plane within the primary α-Mg grains. The TEM image within the primary α-Mg grains of the alloy (heat A) aged at 523 K for 30 h, corresponding to the early stage of the over-aged condition, is shown in Fig. 2.⁴³⁾ The C15 precipitates are most clearly observable at the incident beam direction of $\textbf{B} = [11\bar{2}0]$ and the reciprocal lattice vector of g = 0002.^44–46) Numerous C15 precipitates, measuring approximately 20 nm in length, are uniformly distributed along the (0001) basal plane of the primary α-Mg grains. The strain contrast associated with the individual precipitate is also clearly visible, which indicates the coherent precipitation of the C15 phase with respect to the α-Mg matrix. Kashiwase et al. reported that C15 precipitates have a hexagonal plate-like morphology; their planar surface is parallel to the (0001) basal plane, while the sides of the hexagonal plate are parallel to the $\{ 11\bar{2}0\} $ second columnar plane of the α-Mg matrix.⁴⁷⁾ When the alloy was aged at 523 K for 100 h, the Al₂Ca precipitate showed a thickness, equal to six layers of the (111)_C15 plane composed of Ca atoms, of approximately 1.5 nm.

Fig. 2

TEM BFI within the α-Mg grain of the die-cast AX52 alloy aged at 523 K for 30 h (reproduced from Ref. 43)).

2.3 Creep strength

The creep strength of the die-cast AX52 alloy is predominantly ascribed to the interconnected skeleton of C36–(Mg,Al)₂Ca phase, while the fine C15–Al₂Ca precipitates have limited effect on creep strength. The interconnected skeleton of C36 phase decreases the creep rate by a factor of 330 for the alloy (heat A). As shown in Fig. 3, the creep rate is plotted against time in double logarithmic coordinates for the as-die-cast and homogenized (750 K/1 h/WQ) AX52 alloy specimens. Here, the creep rate was obtained from the creep curve by differentiating the creep strain with respect to time, and the creep tests were carried out at 448 K under a stress of 70 MPa.³⁹⁾ Note that the interconnected skeleton of C36 phase is fully divorced by the homogenization treatment, while the average diameter of the α-Mg grains remains unchanged at about 5 µm. The creep rate for the as-die-cast specimen decreases by more than four orders of magnitude in the transient region, and the minimum creep rate is 1.5 × 10⁻⁹ s⁻¹. Meanwhile, for the homogenized specimen, the decrease in creep rate in the transient region is less emphasized, and the minimum creep rate is 5.0 × 10⁻⁷ s⁻¹.

Fig. 3

Creep rate vs. time in a log–log diagram at 448 K under a stress of 70 MPa for the AX52 alloy: as-die-cast (open) and homogenized at 750 K for 1 h (solid) (reproduced from Ref. 39)).

In the case of die-cast AX52 alloy, the precipitation of the fine C15 phase within the primary α-Mg grains decreases the creep rate by a factor of ∼2. Yamashita et al. evaluated the effect of fine C15 precipitates on creep resistance for AX52 alloy specimens by carrying out the creep tests at 448 K for homogenized (750 K/1 h/WQ) and aged specimens (heat A). They reported that the peak-age heat treatment at 523 K for 10 h improved the creep resistance of the homogenized material by a factor of 2.6.³⁹⁾ Suzuki et al. evaluated the creep resistance at 448 K for as-die-cast and aged Mg–Al–Ca AXJ530 alloys and reported that the peak-age heat treatment at 523 K for 1 h improved the creep resistance of the as-die-cast material by a factor of 1.5–2.⁴⁴⁾

3. Creep Parameters

If the dislocation creep is operative in the die-cast Mg–Al–Ca alloys, the creep rate strongly depends on both the applied stress and temperature.^48–51) In this section, the creep parameters, such as the stress exponent of minimum creep rate, n, and activation energy for creep, Q_c, are characterized for the die-cast AX52 alloy at temperatures of 423–498 K. Here, the interconnected skeleton of C36 phase is thermally stable, while the precipitation of C15 phase is negligible. All the creep tests were performed up to rupture to explicitly determine the secondary creep rates and obtain the creep parameters with sufficient accuracy.

3.1 n value

The value of n increases at the yield stress, and it lowers at higher temperatures from 16 at 423 K to 9 at 498 K at stress levels below the yield stress for the die-cast AX52 alloy. Minimum creep rates for the alloy (heat B) are summarized as a function of stress in Fig. 4.²⁴⁾ At each temperature, two distinct creep regimes, i.e., low and high stress-exponent regimes, were observed. The critical stress of both regimes becomes less emphasized when the temperature is increased from 423 K to 498 K. The critical stress at each temperature corresponds to the yield stress for the alloy. The increase in the n value at the yield stress of the die-cast AX52 alloy is probably due to the introduction of many dislocations by the stress application of creep tests above the yield stress. The introduced dislocations increase the creep deformation and result in higher creep rates.

Fig. 4

Plots of minimum creep rate vs. stress for the die-cast AX52 alloy at temperatures between 423 and 498 K (reproduced from Ref. 24)).

3.2 Q_c value

The value of Q_c decreases with increasing applied stress typically below the yield stress from 231 kJ/mol at 50 MPa to 164 kJ/mol at 110 MPa for the die-cast AX52 alloy. The activation energy for creep, Q_c, determined from the Arrhenius plots of minimum creep rate against the reciprocal absolute temperature for the alloy (heat B) is shown as a function of stress in Fig. 5.²⁴⁾ Q_c is negatively related to stresses below the yield stress. On the contrary, Q_c shows negligible dependence on stress, being about 250 kJ/mol in the stresses above the yield stress, while the number of the data is quite limited. In general, the Q_c in magnesium alloys shows a decreasing trend with the increase in applied stress below the yield stress and is detected experimentally in the creep of pure magnesium^4,52) and magnesium alloys.^53,54)

Fig. 5

Activation energy for creep as a function of stress for the die-cast AX52 alloy (reproduced from Ref. 24)).

3.3 Change in creep parameters

The change in creep parameters, n and Q_c, results from the decreased creep strength driven by the divorce of the interconnected skeleton of C36–(Mg,Al)₂Ca phase during creep for the die-cast AX52 alloy. The microstructure of the alloy evolves during high-temperature creep. As a typical example, the FE-SEM image of the alloy (heat B) creep-ruptured at 473 K and 80 MPa is shown in Fig. 6.²⁴⁾ The C36 phase covering the primary α-Mg grains partly divorces during creep, while the average diameter of the α-Mg grains remains unchanged at about 5 µm. Thus, the divorce of the interconnected skeleton of C36 phase characterizes the microstructure change of the alloy during creep. In addition, isolated but well-defined sub-boundaries were observed after 238 h creep test at 473 K and 60 MPa in the alloy specimen (heat B), as shown in Fig. 7.⁵⁵⁾ The sub-boundaries generally connect with the dendrite boundaries free from the C36 phase, suggesting that the divorce of C36 interconnected skeleton promotes the recovery of dislocations in α-Mg grains during creep. In contrast, isolated dislocations are concentrated in the vicinity of C36 skeleton, which is indicative that the skeleton prevents the recovery of dislocations introduced in the α-Mg grains.

Fig. 6

FE-SEM image of the die-cast AX52 alloy creep-ruptured at 473 K under a stress of 80 MPa. The time to creep rupture is 59 h. The C36–(Mg,Al)₂Ca phase partly divorces during creep as indicated by arrowheads (reproduced from Ref. 24)).

Fig. 7

A sub-boundary developed after 238 h of the creep test at 473 K and 60 MPa in the die-cast AX52 alloy, taken with $\textbf{B} = [1\bar{2}1\bar{3}]$, $\textbf{g} = 1\bar{1}01$ (reproduced from Ref. 55)). A sub-boundary is indicated by a black arrowhead, and the divorced C36 skeleton is denoted by a red parenthesis. Isolated dislocations are concentrated in the vicinity of C36 skeleton (yellow arrowheads).

The minimum creep rates for the AX52 alloy are schematically illustrated against stress and 1/T in Fig. 8(a) and (b), respectively.²⁴⁾ The shaded area in Fig. 8(a) indicates the decreased creep strength driven by the divorce of the interconnected skeleton of C36 phase. Larger values of n are obtained in the case where the C36 phase hardly divorces during creep. However, long-term exposure at higher temperatures causes microstructure change that decreases the creep strength, which results in the negative dependence of n on temperature. The apparent activation energy for the alloy must include the thermally activated component and the decreased creep strength by the microstructure change during creep. In the stresses below the yield stress, the decreased creep strength becomes less pronounced at higher stresses, resulting in the negative dependence of Q_c on stress.

Fig. 8

Correlation between minimum creep rate and stress for the die-cast AX52 alloy at temperatures between 423 and 498 K (a). The creep rates without the decreased creep strength attributed to the collapse of the interconnected skeleton of C36 phase, which covers the primary α-Mg grains, are estimated at 448, 473, and 498 K by thin lines. The estimated values of the creep rate at 90 and 120 MPa are plotted against the reciprocal absolute temperature in (b) (reproduced from Ref. 24)).

The creep rates without the decreased creep strength by the microstructural change during creep estimated at 90 and 120 MPa were plotted against 1/T in Fig. 8(b). As shown in the figure, the stress of 90 MPa is located in the stresses below the yield stress at all temperatures, while the stress of 120 MPa is located above the yield stress at temperatures higher than 430 K. Our results showed that the Q_c value of the alloy without the decreased creep strength by the microstructures change is 143 kJ/mol at 90 MPa, which is the same as that for the inter-diffusion in the Mg–Al solid solution alloys (143 kJ/mol)⁵⁶⁾ and similar to that for the lattice self-diffusion of magnesium (136 kJ/mol).^57,58)

3.4 Creep mechanism

Dislocation climb in the primary α-Mg grains is inferred as the rate-controlling process for the die-cast AX52 alloy at stress levels below the yield stress. First, in the case of the climb-controlled dislocation creep, the normal transient creep is detected in the alloy (Fig. 3), whereas the inverse transient creep occurs in the creep controlled by the viscous glide of dislocations.⁵⁰⁾ Second, the activation of dislocation-climb mechanism for the alloy is indicated by the well-defined sub-boundary (Fig. 7). Third, the Q_c value of the alloy without the decreased creep strength by the microstructure change during creep is evaluated to be 143 kJ/mol at stress levels below the yield stress (Fig. 8(b)). This value is close to that for the lattice self-diffusion of magnesium. Zubair et al.³⁸⁾ summarized the creep parameters (n and Q_c) for the die-cast Mg–Al–Ca alloys reported by Luo et al.,²²⁾ Nakaura et al.,²³⁾ and Saddock et al.²⁷⁾ Their results suggest that the grain-boundary sliding is operative at low temperatures below 423 K, while the dislocation climb creep takes control at high temperatures above 423 K for the alloys.

4. Dislocation Analysis

This section describes creep deformation mechanisms for the die-cast Mg–Al–Ca alloys by identifying the dislocation arrangement after creep and analyzing the creep behavior. The AX52 alloys as-die-cast form and after creep deformation are analyzed using TEM to clarify the motion of individual dislocations during creep deformation. In addition, a model on dislocation motion during creep for the alloy is proposed to account for the observed creep behavior.

4.1 Dislocation analysis of as-die-cast alloy specimen

Dislocations are introduced within the primary α-Mg grains during die-casting for the AX52 alloy; the dislocations are mostly ⟨a⟩ type and dislocation segments are mainly located on the basal plane. The bright-field image taken with $\textbf{B} = [2\bar{1}\bar{1}0]$ for the as-die-cast alloy specimen (heat B) is shown in Fig. 9.⁵⁵⁾ The line directions of the straight dislocations are parallel to the trace of the basal planes, and those of the curved dislocations extend from the trace. This indicates that both basal and non-basal segments are included in the dislocations introduced within the primary α-Mg grains in the die-casting process. A series of two-beam conditions with an incident beam direction of $\textbf{B} = [2\bar{1}\bar{1}0]$ was used to characterize the dislocations detected in the alloy specimen by Nomoto et al.^45,46) Based on the observations under three kinds of two-beam conditions g = 0002, $01\bar{1}0$, and $01\bar{1}1$, the introduced dislocations are mostly ⟨a⟩ type according to the g · b invisibility criterion. TerBush et al. studied the dislocation substructures of crept Mg–Al–Ca die-cast alloys: AXJ530, MRI153M, and MRI230D and reported that ⟨a⟩ dislocations were majorly detected in the primary α-Mg grains for the alloys.⁵⁹⁾ These dislocations were observed on both basal and non-basal planes.

Fig. 9

Dislocation substructure of the as-die-cast AX52 alloy, taken with $\textbf{B} = [2\bar{1}\bar{1}0]$, g = 0002 (reproduced from Ref. 55)).

4.2 Dislocation motion during creep

The basal segments of dislocations bow out and glide on the basal planes under stress, and the jogs follow the basal segments with the help of climb during creep for the die-cast AX52 alloy. The TEM bright-field image of the alloy specimen (heat B) creep-interrupted at 238 h of the creep test at 473 K and 60 MPa, taken with $\textbf{B} = [01\bar{1}0]$ and $\textbf{g} = \bar{2}110$, is shown in Fig. 10.⁵⁵⁾ Dislocations tend to be aligned parallel to the basal plane of the α-Mg phase. The non-basal segments of dislocations develop into a tapered shape in some cases, while smoother curvature remains unchanged during creep in other cases.

Fig. 10

Dislocation substructure developed after 238 h of the creep test at 473 K and 60 MPa in the die-cast AX52 alloy, taken with $\textbf{B} = [01\bar{1}0]$, $\textbf{g} = \bar{2}110$ (reproduced from Ref. 55)).

The schematic illustrations showing the dislocation motion during creep for the die-cast AX52 alloy are summarized in Fig. 11.⁵⁵⁾ Most of the dislocations are ⟨a⟩ dislocations and are introduced within the primary α-Mg grain interior in the die-casting process, which consists of both basal and non-basal segments (Fig. 11(a)). The non-basal segments of dislocations have a smoother curvature in as-die-cast state and exhibit steps parallel to the basal plane during high-temperature exposure (Fig. 11(b)). The basal segments of dislocations easily glide on the basal planes during the stress application of creep tests and bow out under the influence of a stress (Fig. 11(c)). The jogs follow the basal segments with the help of climb during creep but may not be glissile on their crystallographic planes (Fig. 11(d)). When the sample shown in Fig. 11(d) is tilted to the basal planes parallel to the incident electron beam, such as $\textbf{B} = [01\bar{1}0]$ and $[1\bar{2}10]$, the dislocation may take a tapered shape with a composite line consisting of both basal and non-basal segments, as shown in Fig. 11(e). The dislocations with a composite line as illustrated in Fig. 11(e) were detected for the die-cast Mg–Al–Ca alloy AXJ530 crept at 448 K in the detailed TEM observation using the weak-beam dark field imaging technique with $\textbf{B} = [1\bar{2}10]$, which is reported by Suzuki et al.⁴⁴⁾ The dislocation steps illustrated in Fig. 11(b) cannot be generated when the initial non-basal segments are perpendicular to the basal plane. In this case, the smoother curvature of non-basal segments remains during creep deformation (Fig. 11(f)).

Fig. 11

Schematic illustrations showing the dislocation motion during creep for the die-cast AX52 alloy. Dislocations, which are introduced in the die-casting process, consist of both the basal and non-basal segments (a). The non-basal segments exhibit steps parallel to the basal plane during high-temperature exposure (b). The basal segments of dislocations easily glide on the basal planes (c), and the jogs follow the basal segments with the help of climb (d). A dislocation takes a composite line when the sample is tilted to the basal planes parallel to the incident electron beam (e) (reproduced from Ref. 55)). A smoother curvature of non-basal segments remains during creep, when the non-basal segments are located on the columnar plane (f).

4.3 Dislocation motion and creep rate

The easy glide of the basal segments of dislocations introduced in the die-casting process controls the creep rates immediately after the stress application of creep tests for AX52 alloy. According to the model on dislocation motion during creep for the alloy presented in the above section, the creep deformation immediately after the stress application of creep tests would be ascribed to the glide of the basal segments of dislocations generated in the die-casting process rather than the climb of jogs, as illustrated in Fig. 11(c). The well-known Orowan equation can be used to describe the plastic strain rate of crystalline solids:⁶⁰⁾   

\begin{equation} \dot{\varepsilon} = \rho_{\text{m}}b v^{*} \end{equation} (1)

where $\dot{\varepsilon }$ is the creep rate, ρ_m is the density of mobile dislocations, b is the length of the Burgers vector, and v^* is the dislocation glide velocity in the field of local obstacles. Dislocations with the density in the order of 10¹³ m⁻² are introduced within the primary α-Mg grains during die-casting in the case of AX52 alloy (heat B).⁵⁵⁾ At the stress application of creep test, the value of ρ_m in eq. (1), i.e., the density of the basal segments of dislocations, does not depend on applied stress at stress levels below the yield stress. Since the value of b in eq. (1) is the material constant and the mean glide velocity of dislocations (v^*) is proportional to the applied stress,^61,62) the stress exponent of creep rates is expected to be unity immediately after the stress application of creep tests. At three seconds after the stress application for the die-cast AX52 alloy, the creep rates at 473 K under stresses between 15 MPa and 70 MPa fall on a straight line with a slope of 1.2.⁵⁵⁾ The creep rates immediately after the stress application of creep tests are controlled by the easy glide of the basal segments of dislocations introduced in the die-casting process, while the creep mechanism for the alloy is deduced as dislocation climb. The easy glide of the basal segments can also degrade bolt-load retention in the automotive applications for the die-cast Mg–Al–Ca alloys.

5. Life Assessment

In order to ensure the reliability and safety of high working-temperature components, it is essential to accurately assess the long-term creep rupture life. The Monkman–Grant relationship describes the creep rupture of metallic materials under uniaxial tension.⁵¹⁾ Specifically, Monkman and Grant showed that the overall creep rupture life t_rup in long-term tensile creep tests is inversely proportional to the power function of the minimum creep rate $\dot{\varepsilon }_{\text{min}}$, i.e.,   

\begin{equation} t_{\text{rup}} = C_{0}/\dot{\varepsilon}_{\min}{}^{m} \end{equation} (2)

where m and C₀ are constants, and their values depend on the material and/or creep testing temperature.⁶³⁾ In addition, the creep rupture life of heat-resistant metallic materials is usually predicted using the Larson–Miller parameter (LMP), which is described by the following equation:⁶⁴⁾   

\begin{equation} \mathrm{LMP} = T [\log t_{\text{rup}} + C_{\text{LM}}] \end{equation} (3)

where T is the creep testing temperature, and C_LM is the Larson–Miller constant. The value of C_LM is determined phenomenologically, as the LMP is uniquely described by the logarithm of the applied stress. This technique is also used to predict the creep rupture life of heat-resistant materials, and the value of C_LM is approximately 20.^65,66) In this section, the applicability of the Monkman–Grant relationship and LMP is verified for the die-cast AX52 alloy.

5.1 Monkman–Grant relationship

The minimum creep rate and creep rupture life follow the phenomenological Monkman–Grant relationship for the die-cast AX52 alloy. The correlation between the minimum creep rate and rupture life for the alloy (heat B) is shown in Fig. 12.⁶⁷⁾ This figure does not present the two-stage relationship detected in Fig. 4. All the data points toward the 28 different creep conditions fall on a single line with a slope of −1, regardless of the creep testing temperature and stress regime. This result indicates that the Monkman–Grant relationship is observed in the creep rupture of the alloy in the rupture life range from a few minutes to ten thousand hours. The exponent m in eq. (2) for this data is unity, and the constant C₀ is evaluated as 2.0 × 10⁻². The similar shapes of the creep curves for the alloy, which were independent of the creep testing condition, may result in the value m = 1 for the exponent m. Note that the Monkman–Grant relationship is confirmed for the squeeze-cast Mg–Al–Ca alloy MRI153 by Zhu et al.³¹⁾

Fig. 12

Minimum creep rate vs. creep rupture life obtained at temperatures between 423 and 498 K for the die-cast AX52 alloy (reproduced from Ref. 67)).

5.2 Larson–Miller parameter

The value of Larson–Miller parameter is uniquely described by the logarithm of the applied stress when the Larson–Miller constant is set at 20 for the die-cast AX52 alloy. In Fig. 13, the logarithm of the applied stress is plotted as a function of the LMP for the alloy (heat B), where the Larson–Miller constant is chosen as 20.⁶⁷⁾ As shown in the figure, all data points fall on a single line, regardless of the creep testing temperature. In other words, when the Larson–Miller constant is 20, the logarithm of the applied stress for the alloy can be used to describe the value of the LMP, regardless of the creep testing temperature. Therefore, the LMP with C_LM = 20 can be an efficient design parameter to accurately predict the long-term creep rupture life of the alloy. It is noteworthy that a linear relationship is obtained for both low and high stress-exponent regimes when the applied stress is plotted against the LMP in a double-linear coordinate for the die-cast AX52 alloy.⁶⁷⁾

Fig. 13

Larson–Miller parameter vs. stress obtained at temperatures between 423 and 498 K for the die-cast AX52 alloy; the Larson–Miller constant was set at 20 (reproduced from Ref. 67)).

6. Summary

This paper overviews a comprehensive research program on the creep of a die-cast Mg–5Al–2Ca (mass%) alloy, which has been conducted in the last two decades by our group. The obtained results are summarized into the following categories: microstructure and creep strength, creep parameters, dislocation analysis, and life assessment. The final conclusions of each category are listed as follows:

1. (1)    The microstructure consists of the primary α-Mg grains and interconnected skeleton of C36–(Mg,Al)₂Ca phase. A fine C15–Al₂Ca phase precipitates along the basal plane within the primary α-Mg grains when the alloy is subjected to the aging treatment at temperatures of 473–573 K. The creep strength of the alloy is predominantly ascribed to the interconnected skeleton of C36 phase, while the fine C15 precipitates have limited effects on creep strength.
2. (2)    The value of n increases at the yield stress, and it lowers at higher temperatures at stress levels below the yield stress. The value of Q_c decreases with increasing applied stress typically below the yield stress. The change in creep parameters, n and Q_c, results from the decreased creep strength driven by the divorce of the interconnected skeleton of C36 phase during creep. Dislocation climb in the primary α-Mg grains is inferred as the rate-controlling process for the alloy at stress levels below the yield stress.
3. (3)    During die-casting, mostly ⟨a⟩ type dislocations are introduced within the primary α-Mg grains, and the dislocation segments are mainly located on the basal plane. Under stress, the basal segments of dislocations bow out and glide on the basal planes, and the jogs follow the basal segments with the help of climb during creep. The creep rates immediately after the stress application of creep tests are controlled by the easy glide of the basal segments of dislocations introduced in the die-casting process.
4. (4)    The minimum creep rate and creep rupture life follow the phenomenological Monkman–Grant relationship. When the Larson–Miller constant is set at 20, the value of Larson–Miller parameter is uniquely described by the logarithm of the applied stress.

Acknowledgments

The author would like to thank Professor Tatsuo Sato (Tokyo Institute of Technology), Professor Masahiko Morinaga (Nagoya University), and Professor Yoshinori Murata (Nagoya University) for their fruitful discussion. The author acknowledges Mitsubishi Aluminum Co. for providing die-cast alloy specimens. This work was supported by JSPS KAKENHI Grant Number JP22K04735. The author also appreciates the support of the Light Metal Education Foundation.

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