Application of mixture rule to finite element analysis for forging of cast Mg–Zn–Y alloys with long period stacking ordered structure

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Abstract

To establish forging process for high strength Mg–Zn–Y alloys with a long period stacking ordered (LPSO) structure, the flow stresses of Mg–Zn–Y alloys with different volume fractions of LPSO phase were measured by the upsettability test. Since mixture rule for the flow stress was satisfied in Mg–Zn–Y two-phase (α-Mg and LPSO) alloys, the flow stresses of α-Mg and LPSO single phase alloys were estimated from the flow stresses of Mg–Zn–Y alloys with different volume fractions of LPSO phase. To examine the validity of the mixture rule, the finite element analysis for tensile test and forging of as-cast Mg–Zn–Y alloy was carried out using the estimated flow stresses of α-Mg and LPSO single phase alloys on the basis of mixture rule of the properties of Mg–Zn–Y alloy. The calculated load-stroke curves in tensile test and forging agreed well with the experimental ones, and the deformation behaviour of Mg–Zn–Y alloy was discussed.

Highlights

► Flow stresses of new Mg–Zn–Y alloys with a long period stacking ordered (LPSO) structure are measured. ► Mixture rule of flow stress of the Mg–Zn–Y alloys is discussed. ► Mixture rule of flow stress of the Mg–Zn–Y alloys is applied to finite element analysis for forging. ► The proposed method provides high accuracy calculation results. ► Deformation behaviour of the Mg–Zn–Y alloys is discussed from the results of the finite element analysis.

Introduction

Magnesium alloys are increasingly used in the automotive and electronics industries for lightweight structural and functional parts due to the low density and high specific strength. Mg–Zn–Y alloys which consist of a fine-grained α-Mg matrix and a long period stacking ordered (LPSO) structure exhibit excellent mechanical properties compared with conventional Mg alloys, for example, high strength above 600 MPa in Mg97Zn1Y2 (at.%) RS P/M (rapidly solidified powder metallurgy) [1], [2], [3], [4], [5]. Due to this, Mg–Zn–Y alloys are strongly desired to apply to the automotive parts and other structural parts, however, amount of investigations concerning the forming properties of these alloys, especially the forging properties (forgeability, flow stress), is still small [6], [7].

Some properties of Mg–Zn–Y two-phase (α-Mg and LPSO) alloys such as yield stress and hardness have been reported to satisfy with mixture rule [8], [9]. If the flow stress of Mg–Zn–Y alloys is satisfied with mixture rule, the flow stress of Mg–Zn–Y alloys with various compositions can be predicted without any experiment, and is available in the computational simulation such as finite element analysis for metal working processes because the flow stress is one of inevitable input data for the finite element analysis. Furthermore, Mg–Zn–Y alloy with optimum composition for forging process may be determined from the computational simulation applying of mixture rule, and a new method for alloy design may be established.

To clarify deformation mechanism of metals in metal working processes, inhomogeneity of metals has been considered as one of major solutions. Inhomogeneous deformation behaviour of Mg–Zn–Y alloys was experimentally observed by high precision markers [10]. In computational simulation technique, some methods for treatment of heterogeneity of material have been proposed to realize high-accuracy calculation as well as to clarify the deformation mechanism. To treat martensitic transformation induced by plastic deformation of 18-8 stainless steel, the flow stresses of austenite and martensite phases were considered in the finite element analysis of forging and deep drawing [11], [12]. In the finite element analysis of tensile deformation of aluminium alloy, anisotropy behaviour of the flow stress was considered for high-accuracy analysis [13]. The free surface roughening behaviour was also analyzed by the finite element simulation considering material inhomogeneity [14].

To establish forging process for Mg–Zn–Y alloys, the flow stresses of Mg–Zn–Y alloys with different volume fractions of LPSO phase were measured by the upsettability test in this study. The mixture rule for the flow stress of Mg–Zn–Y two-phase (α-Mg and LPSO) alloys was discussed and the flow stresses of α-Mg and LPSO single phase alloys were estimated from different composition alloys. The finite element analysis for forging of cast Mg97Zn1Y2 (at.%) alloy having 26 vol.% LPSO phase was carried out using the estimated flow stresses of α-Mg and LPSO single phase alloys. The deformation behaviour of the Mg alloy and the validity of the mixture rule on the finite element analysis were discussed.

Section snippets

Materials tested

The materials tested were as-cast Mg85Zn6Y9, Mg89Zn4Y7, Mg92Zn3Y5, Mg97Zn1Y2 and Mg99.2Zn0.2Y0.6 (at.%) alloys. The ingots were prepared by high-frequency induction melting in an Ar atmosphere followed by homogenizing at 773 K for 10 h. Fig. 1 shows the optical micrographs of as-cast Mg85Zn6Y9, Mg89Zn4Y7, Mg92Zn3Y5, Mg97Zn1Y2 and Mg99.2Zn0.2Y0.6 alloys. The volume fractions (ϕ) of the LPSO phase of Mg85Zn6Y9, Mg89Zn4Y7, Mg92Zn3Y5, Mg97Zn1Y2 and Mg99.2Zn0.2Y0.6 alloys are estimated ∼100, ∼86, ∼61,

Flow stress curve

Fig. 6 shows the isothermal flow stress curves of as-cast Mg–Zn–Y alloys having different volume fractions of LPSO phase, prior to the occurrence of a crack in the billet at various forging temperatures. The flow stress curves exhibited work hardening tendency at average equivalent strain lower than 0.45 irrespective of forging temperature. The flow stress mostly increased with increasing volume fraction of LPSO phase, however, the flow stresses at a temperature of 773 K were almost same values

Simulation method

To examine the validity of the mixture rule, the mixture rule was applied to the finite element analysis for forming of as-cast Mg–Zn–Y two-phase alloy. Experimental results and calculated ones employing different calculation methods were compared. One of the calculation methods was the conventional one and another method was a newly proposed one with consideration of the mixture rule.

In the conventional method, the properties of Mg–Zn–Y two-phase alloy such as the flow stress, density,

Application to finite element analysis of forging

The finite element analysis with applying the mixture rule was applied to warm forging of as-cast Mg97Zn1Y2 alloy (ϕ = 26%). The forging conditions were described in Section 2.4. Fig. 13 shows the finite element analysis model in forging. The two-dimensional axisymmetric analysis was conducted and the properties of α-Mg and LPSO phases were given to each element based on the volume fractions of α-Mg and LPSO phases. The initial size of each element was 200 μm × 200 μm. Heat transfer coefficients at

Conclusions

The flow stresses of as-cast Mg–Zn–Y alloys with different volume fractions of LPSO phase were measured by the upsettability test. The mixture rule for the flow stress of Mg–Zn–Y two-phase (α-Mg and LPSO) alloys was discussed and the finite element analyses of tensile test and forging of Mg–Zn–Y two-phase alloys was carried out with applying mixture rule. The following conclusions were obtained.

  • (1)

    Mixture rule for the flow stresses of Mg–Zn–Y two-phase (α-Mg and LPSO) alloys was approved in the

Acknowledgment

This work was supported by the Kumamoto Prefecture Collaboration of Regional Entities for the Advancement of Technological Excellence, Japan Science and Technology Agency (JST).

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