On the rule of mixtures for bimetal composites without bonding

Bo Feng,Xiowei Feng,Chngjin Yn,Yunchng Xin,?,Hiyn Wng,Jun Wng,Kihong Zheng

a Guangdong Institute of Materials and Processing,Guangdong Academy of Sciences,Guangzhou 510650,China

b International Joint Laboratory for Light Alloys,College of Materials Science and Engineering,Chongqing University,Chongqing 400030,China

Received 30 September 2019;received in revised form 17 November 2019;accepted 24 November 2019 Available online 5 August 2020

Abstract In the present study,three types of bimetal composites,Al 6082 sleeve/Al 6082 core,Mg AZ31 sleeve/Mg AZ31 core and Al 6082 sleeve/Mg AZ31 core,were fabricated by drilling and assembling.The rule of mixtures(ROM)for the flow curves and yield strengths during compressive test were addressed.Our results show that the ROM can predict well the experimental flow curves and yield strengths of bimetal composites without bonding,irrespectively of the different strain hardening behavior between the two components.

Keywords:Magnesium alloys;Aluminum alloys;Composites;Mechanical behavior.

1.Introduction

Bimetal composites that combine the advantages of two different metals are effective to tailor mechanical properties such as strength,plasticity,abrasion resistance and impact performance[1–4].For instance,compared to Mg AZ31 rod,a Mg AZ31/Al 7050 composite rod exhibits a higher yield tensile strength(about 345MPa)and compressive yield strength(about 270MPa)without obvious compromise in density(a density of 2.1g/cm3)[5].Another typical example is Cu/Al composite,which can offer lighter weight and lower cost when compared to copper alloy with equivalent properties[4].Various bimetal composites were successfully fabricated by roll bonding[6,7],explosive bonding[8,9],co-extrusion[3,10,11]and cold drawing[12].Among those bimetal composites,Mg/Al composites have spawn much interest in field of light-weight saving industries.

For hybrid metal composites,the relationship between the mechanical behavior of a composite and its constituents is an important issue.A deep understanding about this relationship contributes to predicting the mechanical performance of composites.The rule of mixtures(ROM)has been reported to work well for the strength of bimetal composites with layer thickness or filamentary diameter in millimeter scale[13–17].It should be pointed out that,in previous publications,the strengths of each constituent for the ROM predictions were not measured on samples directly cut from the composite,but from monolithic constituent products that were fabricated using the same process as the composite.This may generate an inaccuracy to some extent.

Recently,Feng et al.found that interface characteristic and strain hardening behavior of two components affected the applicability of ROM[18,19].When the two components have a similar work hardening behavior,the ROM for flow curves is applicable irrespective of the interface characteristic.When there is a large mismatch in strain hardening,the efficiency of ROM is highly dependent on the thickness of diffusion layer.The experimental flow curve would largely deviate from the ROM calculation with a much thick diffusion layer(about 200–300μm)[19].In previous publications,it should be pointed out that the interface of bimetal composites had a good metallurgical bonding.A good bonding in the interface can effectively transfer the load during tension or compression process[20,21].In contrast,a severely cracked interface could be detrimental to the load transfer during loading of bimetal composites[19].Therefore,the bonding condition between the two components plays an important role in the mechanical behavior of bimetal composites.However,an unbonded layer exists in the interface of bimetal composites combined by mechanical process(such as drilling and fitting).Up to now,there is not a systematical study on the mechanical behavior of bimetal composite without bonding.Whether the ROM works or not for the yield strength and flow curve has not been reported.

Fig.1.Schematic diagrams showing the preparation of specimens for compression tests.

In the present study,three types of bimetal composites,Al 6082 sleeve/Al 6082 core,Mg AZ31 sleeve/Mg AZ31 core and Al 6082 sleeve/Mg AZ31 core,were fabricated by drilling and assembling.The ROM for the flow curves and yield strengths during compressive test were systematically studied,with the aim to disclose how the strain hardening behavior of two components affects the applicability of ROM for bimetal composites without bonding.In order to obtain the accurate mechanical properties of each component for the ROM calculations,the flow curves of each component were tested.This study provides new insights on the mechanical behavior of bimetal composites.

2.Materials and methods

2.1.Fabrication of bimetal specimens

Al 6082 and Mg AZ31 in as-cast and homogenized condition were used for the preparation of bimetal specimens.Al 6082 and Mg AZ31 billets were machined into cylinders with a diameter 80mm.The two billets were extruded at 400°C using an extrusion ratio 25:1 and an extrusion rate of 1m/min.The extruded Al 6082 rod was immediately quenched into water after exiting the die followed by aging at 175°C for 11h.The final extruded rods have a diameter of 16mm.As seen in Fig.1,three types of bimetal specimens(the designated Al/Al,Al/Mg and Mg/Mg)were prepared by drilling and assembling.The extruded Al and Mg rods were machined into hollow tubes with an outer diameter 8mm and an inner diameter 4mm.Al and Mg rods with a diameter 4mm were cut,polished and fitted into the Al and Mg hollow tubes.

2.2.Compressive mechanical tests

Bimetal specimens with a diameter of 8mm and a height of 12mm were cut and used for compression tests.The volume fraction of core Al or Mg in those bimetal specimens was about 25%.The hollow tube and the core specimens were also cut and used for compressive mechanical properties measurement.Compression tests along the extrusion direction(ED)at room temperature were performed on a Shimadzu mechanical testing machine using a strain rate of 10?3s?1.Each mechanical test was repeated three times.

2.3.Examination of microstructure and texture

Electron backscattered diffraction(EBSD)measurements using a step size of 1.5μm were performed on a FEI Nova 400 SEM equipped with a HKL Channel 5 system.The specimens for EBSD mapping were carefully ground with a series of SiC sand papers followed by electrochemical polishing(AC2 electrolyte for Mg alloy and perchloric acid solution for Al alloy(1ml perchloric acid+9ml ethanol))at 20V.Twinning behavior in Mg constituent during compression along the ED was also studied by EBSD on a cross section in the middle.To acquire a statistical and reproducible results about the texture and twin fraction,two EBSD maps of 350μm×350μm were recorded.The step size for EBSD mapping was 0.5μm.The twin fraction was measured as the area fraction of twins in EBSD maps.All EBSD data were analyzed using the Channel 5 software.The interface of bimetal specimens after 2% and 7% compression were examined by SEM(TESCAN VEGA 3).

Fig.2.The experimental true stress-strain curves(solid lines)and the ROM predicted ones(dash lines)under compression along the ED:(a)Al/Al,(b)Al/Mg,(c)Mg/Mg.Pre.and Exp.refer to the ROM predicted flow curves and the experimental ones,respectively.(For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

Table 1Compressive yield strength(CYS)and ultimate compressive strength(UCS)of the bimetal composites and their constituents under compression along the ED.

3.Results

3.1.Mechanical behavior

True stress-strain curves of Al/Al,Al rod and Al hollow tube under compression along the ED are shown in Fig.2a.The curve of composite as well as its components has a similar concave-down shape,which is the typical feature of a slip predominant deformation.Obviously,the curve predicted by the ROM(the dash lines)is close to the experimental one.As seen in Fig.2b,although the compressive flow curve of Al constituent shows a concave-down shape,that of Al/Mg composite exhibits a sigmoidal shape(the typical feature of{102}twinning predominant deformation),similar to that of Mg constituent.However,the experimental compressive curve is also quite close to the ROM predictions.For Mg/Mg composite shown in Fig.2c,the compressive curve of composite as well as its constituents shows a sigmoidal shape.Clearly,the experimental compressive curve is in good agreement with the ROM prediction,irrespective of the strain hardening behavior between the two components.

The compressive yield strength(CYS),ultimate compressive strength(UCS)extracted from those stress-strain curves are listed in Table 1.The deviations of experimental CYS from the ROM predictions in this study together with those in previous publications are analyzed in Fig.3.Clearly,there is a much lower deviation in this study.

Strain hardening behaviors of bimetal specimens and their constituents under compression along the ED were analyzed in Fig.4.The strain hardening rate was calculated by differentiation of the true stress-strain curves.It can be seen that Al/Al composite and Al constitutes have a continuously decreasing strain hardening rate(Fig.4a),while the hardening curves of Mg constituents contain three distinct stages:a fast drop in hardening rate(Stage 1),a quick increasing(Stage 2)and a fast drop again(Stage 3)(Fig.4c).This three stages is extensively reported in strain hardening curve of Mg alloys predominantly deformed by{102}twinning[22–24].Obviously,as seen in Fig.4b and c,this hardening peak also appears in curves of Al/Mg and Mg/Mg specimens.

3.2.Microstructure and texture

Microstructure and texture of the extruded Al rod were examined using EBSD with the relevant results shown in Fig.5.The examined sample exhibits a recrystallized microstructure.The Al rod has a typical double fiber texture,with100and111parallel to the ED.Microstructure and texture of the extruded Mg rod were presented in Fig.6.The extruded Mg rod has a bimodal grain structure containing much finer grain(about 10μm)and coarse grain(about 100μm).As shown in Fig.6,the Mg rod exhibits a typical texture of extruded rod,a sharp fiber with c-axis largely normal to the ED and a preferred distribution of prismatic plane(<100>//ED or<110>//ED).

Fig.3.Deviations of the experimental yield strengths from the ROM predictions as a function of fraction of strong constituent(a)and strength ratio of two constituents(b).(For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

Fig.4.Strain hardening rate as a function of strain under compression along the ED:(a)Al/Al,(b)Al/Mg,(c)Mg/Mg.

Fig.5.Inverse pole figure map and pole figure of Al 6082 rod.ED and RD refer to the extrusion direction and radial direction,respectively.

Fig.6.Inverse pole figure map and pole figure of Mg AZ31 rod.ED and RD refer to the extrusion direction and radial direction,respectively.

Fig.7.Cross-sectional SEM micrographs of the 2%compressed bimetal samples along the ED:(a)Al/Al(low magnification)and(d)Al/Al(high magnification),(b)Al/Mg(low magnification)and(e)Al/Mg(high magnification),(c)Mg/Mg(low magnification)and(f)Mg/Mg(high magnification).

Debonding or cracking at the interface is an important issue during loading of bimetal composites.Here,microstructure near the interface of the 2% and 7% compressed bimetal samples were examined by SEM in the middle of the crosssection.As seen in Fig.7,a severely cracked or unbonded layer takes place at the interface of the 2% compressed samples.Obviously,more cracked or unbonded layer occurs at the interface of the 7% compressed bimetal samples(Fig.8).The layer with a thickness of 20–80μm is clearly discerned at the interface of the compressed bimetal samples.Several other regions were also examined and similar results were observed.

Microstructure of Al and Mg constituents in the 2% compressed Al/Mg sample are given in Figs.9 and 10,respectively.Al constituent exhibits a recrystallized microstructure.The examined Al sample has a typical double fiber texture,with100and111parallel to the ED.A large number of{102}twins(the red lamellae)are identified in the Mg sample.Contraction twins({101}and{103})or double twins({101}-{102}and{103}-{102})are hardly detected.Those{102}twins tend to preferentially appear and grow in big grains.The area fractions of{102}twins are about 20%.

Fig.8.Cross-sectional SEM micrographs of the 7%compressed bimetal samples along the ED:(a)Al/Al(low magnification)and(d)Al/Al(high magnification),(b)Al/Mg(low magnification)and(e)Al/Mg(high magnification),(c)Mg/Mg(low magnification)and(f)Mg/Mg(high magnification).

Fig.9.Inverse pole figure map and pole figure of Al 6082 sleeve in the 2% compressed Al/Mg sample.ED and RD refer to the extrusion direction and radial direction,respectively.

4.Discussion

Much effort has been made to build the strength relationship between the composite and its constituents.The ROM shown in Eq.(1),has been applied to both continuous filamentary composites and sandwich sheet materials[14,16,25,26]:

Fig.10.Inverse pole figure map and boundary misorientation map of Mg AZ31 core in the 2% compressed Al/Mg sample.TB represents twin boundary.ED and RD refer to the extrusion direction and radial direction,respectively.

Here,σcis strength of composite,σ1(σ2)andV1(V2)are the strength and volume fraction of each constituent,respectively.For a bimetal composite with layer thickness or filamentary diameter down to a nanometer length scale,the strength of composite can be significantly in excess of values predicted by the ROM[12,27].When dimensions of the constituent are in nano length scale,there are a large number of interfaces between different constituents.Those interfaces can act as effective barriers to dislocation gliding,and make it difficult for dislocations in either phase to across the interface boundary,which increases the strength of composite[12,27–29].

For the hybrid metal composites with layer thickness or filamentary diameter in millimeter length scale,it is extensively reported that the ROM works well to predict the strength of composites[11,13,14,16,25,26].In previous publications,the strengths of each constituent for the ROM predictions were not measured on samples directly cut from the composite,but from monolithic constituent products that were fabricated using the same process as the composite.In this study,the strengths for components rod and hollow tube were directly measured from the specimens cut from the extruded rod.As seen in Fig.3,the results demonstrate that the way to measure the mechanical properties of each constituent also affects the deviation from the ROM.In the present study,our results also confirm that this way to measure the mechanical properties of each constituent provides a lower deviation from the ROM predictions.Recently,Feng et al.found that the interface characteristic and the strain hardening behavior of two components affected the applicability of ROM[18].When the two components have a similar work hardening behavior,the ROM for flow curves is applicable.When there is a large mismatch in strain hardening,the efficiency of ROM is highly dependent on the thickness of diffusion layer.The experimental flow curve would largely deviate from the ROM calculation with a much thick diffusion layer(about 200–300μm)[19].

In previous publications,it should be pointed out that the interface of bimetal composites had a good metallurgical bonding.A good bonding between the two components can effectively transfer the load during tension or compression process[20,21].In this study,an unbonded layer exists in the interface of bimetal composites combined by drilling and assembling.As seen in Figs.7 and 8,even although a severely cracked or unbonded layer takes place at the interface during compression of bimetal composite,the ROM works well.In this case,it is suspected that the cracked or unbonded interface can also effectively transfer the load during compression process.To confirm this speculation,the strain hardening behavior of Al and Mg constituents in Al/Mg composite during compression is analyzed in detail in Fig.11.There is a large gap in the work hardening rate difference between position 2 and 5.In the ROM predictions,the stress increment of bimetal composite by strain hardening is a compound result of the hardening of each constituent.When the two constituents have a quite different work hardening rate,there exists a large gap in stress increment between the two constituents with increasing the same strain.To accommodate this different hardening in the two constituents,an effective load transfer between the two constituents is required.In this study,the work hardening between different positions during compression of Al/Mg is also analyzed in Table 2.Obviously,the hardening of composite is close to that of the ROM prediction.Therefore,the results strongly support the speculation.

Recently,it has been reported that a much thick reaction layer(about 200–300μm)was detrimental to the strength of Mg/Al rod owing to its susceptibility to crack during compression[19].A severely cracked thick interface cannot effectively transfer the load and the experimental flow curve would largely deviate from the ROM calculation[18].In this work,the ROM is applicable for the experimental compressive curves and yield strengths of bimetal composites without bonding,irrespectively of the different strain hardening behavior between the two components.It should be pointed out that although the cracked or unbonded layer is clearly discerned at the interface during compression process(Fig.7 and 8),the interface can still effectively transfer the load and the strength of bimetal composites do not decrease significantly.

Fig.11.Strain hardening behavior of Al sleeve,Mg core and Al/Mg composite during compression along the ED.Pre.and Exp.refer to the ROM predicted flow curves and the experimental ones,respectively.The WHD refers to the work hardening rate difference between Mg core and Al sleeve.(For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

Table 2Work hardening of the composite,Mg core and Al sleeve between different positions in Fig.11 during compression along the ED of Al/Mg.

In this study,an effective load transfer for bimetal composites is most probably dependent on mechanical interlock between the two constituents,which eventually results in the experimental compressive strengths are in good agreement with the ROM predictions.

5.Conclusions

In the present study,three types of bimetal composites,Al 6082 sleeve/Al 6082 core,Mg AZ31 sleeve/Mg AZ31 core and Al 6082 sleeve/Mg AZ31 core,were fabricated by drilling and assembling.The rule of mixtures(ROM)for the flow curves and yield strengths during compressive tests were systematically studied,with the aim to disclose how the strain hardening behavior of two components affects the applicability of ROM for bimetal composites without bonding.Our results show that the ROM is applicable for the experimental flow curves and yield strengths of bimetal composites without bonding,irrespectively of the different strain hardening behavior between the two components.

Acknowledgement

This study is supported by Guangdong Academy of Science Fund(2020GDASYL-20200101001,2018GDASCX-0967,2019GDASYL-0302017 and 2019GDASYL-0502009),National Natural Science Foundation of China(51905111),Guangdong Science and Technology Project(2018dr005)and Guangzhou Science and Technology Project(201704030094).