Critical mechanical properties and FEA simulation for crashworthiness assessment of a coarse-grained cast AM50 alloy

S.Xu*,C.H.M.Simha,M.Gesing,J.Liang,J.Lo

CanmetMATERIALS,Natural Resources Canada,183 Longwood Rd S,Hamilton,Ontario L8P 0A5,Canada

Critical mechanical properties and FEA simulation for crashworthiness assessment of a coarse-grained cast AM50 alloy

S.Xu*,C.H.M.Simha,M.Gesing,J.Liang,J.Lo

CanmetMATERIALS,Natural Resources Canada,183 Longwood Rd S,Hamilton,Ontario L8P 0A5,Canada

A coarse-grainedAM50 alloy was used as a model alloy for investigation of constitutive behaviour,Charpy toughness and effect of stress state on deformation and failure of cast Mg alloys.The results provide critical mechanical properties of a cast AM50 alloy for crashworthiness assessment and development of fnite element simulation techniques.For cast Mg alloys,the effect of strain rate and temperature is larger on tensile strength than on compressive strength because twinning is more extensive in compression than in tension.The effect of strain rate on compressive strength is negligible because twinning activity of the cast Mg alloy is dominant.The load vs.defection of Charpy specimens were measured for modelling,and the effect of loading rate and temperature on load of Charpy specimens is very small because part of the specimen is in compression.The equivalent strain to fracture of the cylindrical round notched tension specimen decreases with increasing stress triaxiality;though for the fat-grooved plane strain specimen,the equivalent fracture strain remains constant over the range of stress triaxiality investigated.Because the two different specimen geometries give rise to different Lode angle values,the test results show that the Lode angle parameter is an important parameter for deformation and fracture of Mg alloys.Finite element simulations of loading of the cylindrical notched-tension and Charpy specimens were carried out using a Lode-angle dependent von Mises model,and were found to provide a reasonable description of the load–displacement curves measured in the tests.For the fat-grooved plane strain specimens,the computations under-predicted the force–displacement response measured.

Effect of strain rate and temperature;Tensile and compressive;Crash;Simulation;AM50

1.Introduction

Magnesium alloys have received special attention in transportation applications since the mid-1990s mainly due to their low density,which has great potential for weight reduction in the transportation industry.To expand the applications of Mg alloys to automotive and rail crash-related applications,assessment of critical mechanical properties and simulation of deformation and fracture behaviours of Mg alloys are essential.In the recent MFERD project[1],tensile and compressive properties for crashworthiness assessment were characterized for fve commercial cast and wrought Mg alloys[2].However, compressive tests were only performed in limited conditions for die casting alloys[3];Charpy and fracture tests were only performed on large extrusions[4].The reason for this is that typical cast Mg alloys for automotive applications are produced using a high pressure die casting(HPDC)process,and the HPDC castings generally have a thin gauge section.For thin gauge castings,tensile tests can be performed conveniently, however,due to problems with specimen preparation and testing(for thin sections),compression,Charpy,and fracture tests are diffcult to conduct,especially when testing a range of strain-rates and temperatures.

In this work,a squeeze cast AM50 alloy was employed as a model alloy for the investigation of constitutive behaviour,fracture and the effect of stress state on deformation and failure of cast Mg alloys.A variety of mechanical and fracture test specimen types can be prepared from the centre of squeeze cast discs,which are porosity-free and have relatively uniform microstructure.The results provide critical mechanical properties of a cast AM50 alloy for crashworthiness assessment,and load cases for fnite element simulation.Finite element simulations using theAbaqus fnite element software in conjunction with a user-developed subroutine that consisted of a Lode-angle dependent von Mises model was employed to model thedeformation response.Computational results are compared with the experimentally measured force–displacement curves.

Fig.1.Macrograph of the squeeze cast disc(the thickness is 15 mm).

2.Material and experimental procedures

2.1.Material

The AM50 alloy was manufactured by a squeeze casting process into 90 mm diameter discs 15 mm thick at CanmetMATERIALS.Fig.1 shows a micrograph of the crosssection of a disc.In the centre of the discs,grains are mostly equiaxial and exhibit sizes of up to～2.4 mm.A micrograph in the centre of a disc is shown in Fig.2.The etchant used for solidifcation structure was acetic glycol(20 mL acetic acid, 1 mL HNO3,60 mL ethylene glycol,20 mL water)for 15–20 s. The nominal compositions(measured in weight percent)of the AM50 alloy are 5%Al,0.4%Mn and 95.6%Mg.

All mechanical and fracture specimens were machined from the centre part of discs and were cut from the plane of the discs.2.2.Tensile and compressive

The tensile specimens were round tensile dog bones with a gauge length of 25.4 mm and diameter of 6.34 mm.The cylindrical compression specimens were 19.1 mm in height and 6.35 mm in diameter.

Fig.2.Microstructure in the middle thickness region.

Tensile and compression tests were conducted using a servohydraulic universal test machine equipped with an environmental chamber for achieving test temperature between 100°C and?142°C.The strain rates used were between 0.00075 s?1and 9 s?1.In compressive tests,Tefon sheet was used as lubricant and applied to the contact surfaces to reduce friction.

2.3.Charpy testing

Standard un-notched and V-notched Charpy specimens (10×10×55 mm)were machined according to ASTM E23 [5].V-notches were machined in through-thickness direction. Un-notched Charpy bars were tested in the same position as the V-notched specimens.Charpy specimens were tested at impact rate(5.1 m/s)in an instrumented Charpy machine and at slow rate using a three-point bend fxture in a servo-hydraulic universal test machine.

2.4.Round notched tensile(NT)and fat-grooved plane strain testing

Notched tension specimens are often used to study the effects of constraint(e.g.,stress triaxiality)on deformation and failure.Round notched tensile specimens used are shown in Fig.3 including standard tensile specimen geometry.Notch radius(R)of the NT specimens was 1.5 mm,3 mm and 6 mm.

Flat-grooved plane strain specimens were prepared and the geometry is shown in Fig.4.Notch radius(R)included 6.35 mm,10 mm,25.4 mm and 63.5 mm.

Notched tensile tests were performed under a loading rate of 1.125 mm/min at 23°C.

The two different specimen geometries give rise to different Lode angle values,and thus the test results show the effect of Lode angle on deformation and fracture of the cast Mg alloy.

3.Results and discussions

A variety of mechanical and fracture tests were performed to compare the effects of strain rate and temperature on fow strength,to assess Charpy and fracture toughness properties and to investigate effects of stress-state on deformation and fracture properties.

3.1.Effects of strain rate and temperature on tensile and compressive strength

Effects of strain rate and temperature(thermal effects)on fow and fracture properties are essential to crashworthiness assessment and simulation.In the MFERD project,effects of strain rate on fow strengths of HPDC AM50 and AM60 alloys were determined[2,3].A HPDC AM60B alloy exhibits less than 20% positive strain rate dependence in tension but approximately only 10%in compression from a quasi-static rate of 0.00075–10 s?1strain rate[3].It is of interest to know if the lower strain-rate dependence in compression than in tension is the case for other cast Mg alloys.

Examples of tensile and compressive true stress vs.strain curves are shown in Figs.5–8.The effect of strain rate and temperature on tensile fow strength is observable;though on compressive fow strength,the effect is much smaller or negligible.The tensile curves showed approximately power-law shape,which is typical dislocation dominant deformation,while the compressive curve exhibited typical tensile twinningdominant deformation(e.g.,Ref.[2]).

Table 1Tensile properties of a squeeze cast AM50 at quasi-static rate.*

Tensile and compressive properties at quasi-static rate and at 100°C and 23°C are listed in Tables 1 and 2,respectively.The fow stress(σ)of a Mg alloy can be written,as the sum of two components,a thermal component,σthermal(related to shortrange obstacles),and an athermal component,σathermal(related to long-range obstacles)[2,6].The quasi-static fow strengths of Mg alloys at 100°C are taken as the athermal strengths and the strength increases at lower temperature and/or higher strain rate are considered as thermal strengths[2,6],i.e.,

Fig.3.Round notched tensile specimens.

The effect of strain rate and temperature is a thermal effect and can be described by a rate parameter(R),i.e., R =A +B? T ?ln(5. 3× 107ε˙),where A and B are constants,T is temperature in Kelvin andε˙is strain rate in s?1[2,6].The yield strengths vs.rate parameter of the squeeze castAM50 are plotted in Fig.9including the ftting constants.There is a thermal effect in tension but negligible in compression.Tounderstand the difference between thermal effects of tension and compression,it is important to recognize that twinning is another deformation mechanism in addition to dislocation slip, and that the critical stress of twinning is athermal(i.e.,not sensitive to strain rate and temperature).Twinning is more extensive in compression than in tension of Mg alloys(i.e., dislocation slip is a more signifcant fraction mode of deformation in tension)[7],and this is the case for the AM50 alloy. Metallographic examination on interrupted tensile and compressive tests at a strain of～1.5%showed much more twinning activities in the compressive specimen than in the tensile specimen(Figs.10 and 11).The negligible strain rate sensitivity in compression for this coarse-grained AM50 alloy is due to the dominant twinning deformation mechanism.

Table 2Compressive yield strength of a squeeze cast AM50 at quasi-static rate.*

Fig.4.Flat-grooved plane strain specimen geometry.

Fig.5.Tensile true stress–strain curves at 23°C,showing effect of strain rate.

Fig.6.Tensile true stress–strain curves at quasi-static rate,showing effect of temperature.

Fig.7.Compressive true stress–strain curves at 23°C,showing effect of strain rate.

Fig.8.Select compressive true stress–strain curves showing effect of strainrate and temperature.

Fig.9.Effect of strain rate and temperature on yield strength of the squeeze cast AM50.

The effect of strain rate and temperature on yield strength of HPDC AM50[2]shows larger thermal stress than on that of squeeze castAM50(Fig.12).The effect of strain rate decreaseswith increasing grain size due to twinning tendency in coarsegrained alloys,and is also reported in literature(e.g.,Ref.[8]).

Fig.10.Metallographs of AM50 in tension to a strain of 1.5%.

Fig.11.Metallograph of AM50 in compression to a strain of 1.5%.

3.2.Charpy tests

Standard Charpy testing employed a three-point bend type specimen and the specimen experiences both tensile and compressive stresses simultaneously.The load vs.defection curves of Charpy tests may be used as load cases for fnite element simulations of Mg alloys because effects of notch,loading rate, and stress state may be included in the Charpy results.Figs.13 and 14 show typical load vs.defection curves of the AM50 alloy.The effect of loading rate and temperature on the force–displacement curve is very small because part of the specimen is in compression,though the effect of temperature on fracture and maximum load is evident,i.e.,the higher the temperature, the larger the defection(or the higher the maximum load) because the fracture was attained later and the alloy was strainhardened further(Fig.13).For the Charpy V-notch specimen, the effect of loading rate on the load vs.defection curve is negligible,however,the un-notched specimen showed larger maximum defection at a quasi-static rate than in impact loading(Fig.14).

Fig.12.Effect of strain rate and temperature on yield strength of the squeeze cast AM50 and HPDC AM50.

Fig.13.Charpy load vs.defection curve;effect of temperature.

Charpy absorbed energy(CVN)increased with increasing temperature,especially for un-notched specimens(Fig.15). This shows that the un-notched Charpy specimen is better than theV-notched specimen to detect rate and temperature sensitivity.The ratios of CVN of V-notched to un-notched specimens are 0.26–0.30 for impact tests.

3.3.Round notched tensile(NT)and fat-grooved plane strain tests

The stress state of material can infuence deformation,ductility and fracture behaviours.It is well known that stress triaxiality can reduce ductile fracture strain of a material[9,10] because it accelerates the void growth process.Recently, another stress state parameter,the Lode angle,has been applied to analyze deformation and fracture of materials under different loading conditions(e.g.,Refs.[11–13]).In this work,bothround notched tension specimens and fat-grooved tension specimens as employed in Ref.[11]were used to investigate the effects of stress triaxiality and the Lode angle on deformation and fracture of the Mg alloyAM50 and to provide load cases of complex stress state for FE modelling.

Fig.14.Charpy load vs.defection curve;effect of notch and loading rate.

Fig.15.Effect of notch and temperature on Charpy absorbed energy.

At the centre of the necked cross section of a round notched tensile specimen(see Fig.3),which is the fracture initiation site,the Bridgman formula of the stress triaxiality parameter is

where R is the local radius of a neck in the round bar specimen and r is the radius of the notched section.The fracture strain can be approximately calculated as where r0is the original radius and rfis the radius at fracture of the tension specimen.

For the fat-grooved plane strain specimens shown in Fig.4, the thickness of the specimen at the groove is 2a0(fxed at 6.36 mm in this work),and radius of the groove is R.The stress triaxiality(η)of the fat-grooved specimen is given as

The equivalent strain to fracture of a fat-grooved plane strain specimen can be approximated as where a0is the initial half thickness and afis the half fracture ligament thickness of the specimen.The Lode angle parameter of cylindrical notched tension specimen corresponds to the axisymmetric compression,while the Lode angle parameter of the fat-grooved specimen corresponds to plain strain or generalized shear loading conditions[11].

Fig.16.Load vs.radial displacement of round notched tension specimens.

The load vs.displacement curves of round NT and fatgrooved plane specimens are shown in Figs.16 and 17,respectively.These are useful load cases for fnite element simulation of deformation and fracture of Mg alloys because they involve different stress triaxiality and Lode angle parameters.

The round NT tensile specimens cover initial stress triaxiality from approximately 0.5 to 0.8 according to Eq.2.For the fat-grooved specimens,the initial stress triaxiality ranges between 0.61 and 0.84.The tensile strength of the AM50 alloy increases with increasing stress triaxiality as shown in Fig.18 for both NT and fat-grooved specimens.The equivalent strain to fracture of the NT specimen decreases with increasing stress triaxiality(Fig.19),which is in agreement of common observations of metals and alloys;although the effect is smaller in the Mg alloy than in steels[11].At the same time,for the fatgrooved specimen,the equivalent fracture strain remains constant over the range of stress triaxiality investigated,which shows the Lode angle parameter as an important parameter for simulation of deformation and fracture of Mg alloys.Note that the ductile failure strain was found to correlate well with stresstriaxiality for steels as tested using the NT and fat-grooved specimens(e.g.,Ref.[14]).

Fig.17.Examples of load vs.notch displacement of fat-grooved specimens.

Fig.18.Average tensile strength vs.initial triaxiality parameter.

4.FEA deformation simulation

Finite element computations of the loading of the notched, and Charpy specimens were carried out using theAbaqus fnite element software.A user-defned subroutine based on a Lode angle dependent von Mises model from Ref.[13]was employed to describe the constitutive response of the AM50 alloy.In this model,the behaviour of the fow stress in a standard von Mises plasticity model was modifed and a Lode angle dependence was introduced.In the Lode-angle dependent von Mises model, the fow surface is given as:

where F represents the yield surface,is the von Mises effective stress and the surfaces of isotropic hardening,σ(k)is the yield and fow strengths in the yield and fow surfaces for isotropic hardening yields(k=1,2,3,etc.indicating increment point)and θ′is an angle related to Lode angle θ as is given below, θ′=±30°for the principle stress axes and θ′=0°for an angle with 30°to the principle stress axes.

Fig.19.Average equivalent failure strain vs.initial triaxiality parameter.

This Lode angle dependent von Mises model achieved better simulation results than the conventional von Mises model in modelling the effect of notch,and obtained good agreement with the load–radial displacement response measured in the test.In the current work,the Lode-angle dependent von Mises model is further evaluated by employing the previously developed subroutine to model the notched and the Charpy specimen.The present model does not include damage and failure; consequently,the behaviour beyond maximum load in the experiment is not captured by the simulations.

Exploiting symmetry,one-eighth models comprising eightnoded continuum elements with reduced integration were used to mesh the spatial domain of the notched-tension tests.Threedimensional models were constructed for the Charpy simulations.An implicit solver was used to integrate the equilibrium equations.The measured tensile properties were used for simplicity because tensile and compressive at room temperature and quasi-static rate are similar for the casting AM50.In all of the simulations for the notched-tension specimens,the load and radial displacement was monitored.

Results of the computations for the cylindrical NT specimens are presented in Figs.20 and 21.

Results of the computations for the fat-grooved plane strain notched-tension test are presented in Figs.22 and 23.The computational results show that as the notch radius is increased, the loads predicted by the computations are lower than the loads measured in the experiment.The source of this underprediction could be due to the approximations that were invoked in the implementation of the subroutine[13],or due to the inclusion of the Lode-angle dependence in the fow behaviour.This shows the challenge of numerical simulation of Mg alloys.

Fig.20.FE simulation of load vs.radial displacement of cylindrical notchedtension test with notch radius of 1.5 mm.

Fig.21.FE simulation of load vs.radial displacement of cylindrical notchedtension test with notch radius of 6 mm.

Fig.22.FE simulation of load vs.radial displacement of fat-grooved plane strain tension test with notch radius of 6.35 mm.

Fig.23.FE simulation of load vs.radial displacement of fat-grooved plane strain tension test with notch radius of 63.5 mm.

Fig.24.FE simulation of load vs.displacement of un-notched Charpy bar.

In modelling Charpy testing,the geometries of impact tup and support anvils are consistent with ASTM E23-07.Results of the three-dimensional simulations of the statically loaded un-notched Charpy bar and the notched bar are shown in Figs.24 and 25.Here,the load versus displacement curves from the computations are compared with the experimental curves. The computation captures the load–displacement reasonably well in both un-notched and V-notched Charpy specimens.The“bump”in the static Charpy curves occurs at the point when the material in contact with the anvils yields.On-going work is under way to investigate how to improve the Lode angle dependent von Mises model and to incorporate damage model to simulate Mg deformation and fracture for crash design.

5.Conclusions

A variety of mechanical and fracture test specimen types were prepared from the centre of squeeze cast AM50 discs, which are relatively porosity-free.The results provide criticalmechanical properties of a castAM50 alloy for crashworthiness assessment and load cases for development of fnite element simulation.Some conclusions are summarized below.

Fig.25.FE simulation of load vs.displacement of a CharpyV-notch specimen.

?For cast Mg alloys,the effect of strain rate and temperature is larger on tensile strength than on compressive strength because twinning is more extensive in compression than in tension.The effect of strain rate on compressive strength is negligible in this coarse-grained alloy because twinning activity is dominant.

?The effect of loading rate and temperature on load of Charpy specimens is very small because part of the specimen is in compression.The fracture ductility of a Charpy specimen is enhanced by an increase in temperature.

?The tensile strengths of both NT and fat-grooved specimens increase with increasing stress triaxiality.The equivalent strain to fracture of the NT specimen decreases with increasing stress triaxiality;though for the fat-grooved specimen, the equivalent fracture strain remains constant over the range of stress triaxiality investigated,which shows the Lode angle parameter as an important parameter for simulation of deformation and fracture of Mg alloys.

?Finite element simulations,employing a Lode-angle dependent yield function developed earlier,were used to simulate loading of the notched-tension and Charpy specimens.In the cases of cylindrical notched tension and Charpy specimens, the model provided a reasonable account of the experimental results.In contrast,in the fat-grooved plane strain tension plane strain specimens the model under predicted the experimental results.

Acknowledgements

This study is part of CanmetMATERIALS(CMAT)projects funded by the Magnesium Front End R&D(MFERD)program provided by Natural Resources Canada through the Program of Energy Research and Development and Transport Canada.We would like to thank Mr.Raul Santos(CMAT)for manufacturing and providing the AM50 alloy,and Ms.Renata Zavadil for metallographic examination.We also would like to thank Dr. M.S.Kozdras,Program Manager of Advanced Materials for Transportation,for his assistance in preparing the project proposal,guidance in performing the work and useful review of the manuscript.

[1]A.A.Luo,E.Nyberg,K.Sadayappan,W.Shi,in:M.O.Pekguleryuz,N.R. Neelameggham,R.S.Beals,E.A.Nyberg(Eds.),Magnesium Technology Symposium 2008,The Minerals,Metals&Materials Society,2008,pp. 3–10.

[2]S.Xu,W.R.Tyson,R.Eagleson,R.Zavadil,Z.Liu,P.-L.Mao,et al.,J. Magnes.Alloys 1(2013)275–282.

[3]D.A.Wagner,S.D.Logan,K.Wang,T.Skszek.FEA predictions and test results from magnesium beams in bending and axial compression.SAE Technical Paper,SAE 2010-01-0405.2010.

[4]S.Xu,W.R.Tyson,G.Shen,R.Eagleson,A.Balmy.Uniaxial deformation,charpy and fracture toughness testing ofextruded magnesium alloyAM30.SAETechnical Paper,SAE 2010-01-0406.2010.

[5]ASTM International,ASTM E23-07a,Standard Test Methods for Notched Bar Impact Testing of Metallic Materials,ASTM International, West Conshohocken,PA,USA,2010.

[6]S.Xu,W.R.Tyson,R.Bouchard,V.Y.Gertsman,J.Mater.Eng.Perform. 18(2009)1091–1101.

[7]S.Xu,V.Y.Gertsman,J.Li,J.P.Thomson,M.Sahoo,Can.Metall.Q.44 (2)(2005)155–165.

[8]H.J.Choi,Y.Kim,J.H.Shin,D.H.Bae,Mater.Sci.Eng.A 527A(2010) 1565–1570.

[9]J.R.Rice,D.M.Tracy,J.Mech.Phys.Solids 17(1969)201–217.

[10]C.Yan,W.Ma,V.Burg,Y.-W.Mai,M.G.D.Geers,Key Eng.Mater.312 (2006)59–64.

[11]Y.Bai,X.Teng,T.Wierzbicki,J.Eng.Mater.Technol.131(2009) 021002-1–021002-10.

[12]H.A.Taiebat,J.P.Carter,Comput.Geotech.35(2008)500–503.

[13]G.Shen,S.Xu,J.Liang,J.Sollen,SAE Int.J.Mater.Manuf.7(3)(2014) 609–615,doi:10.4271/2014-01-1013.

[14]J.W.Hancock,D.K.Brown,J.Mech.Phys.Solids 31(1)(1983)1–24.

Received 5 May 2015;accepted 30 June 2015 Available online 28 September 2015

*Corresponding author.CanmetMATERIALS,Natural Resources Canada, 183 Longwood Rd S,Hamilton,Ontario L8P 0A5,Canada.Tel.:+905 645 0815;fax:+1 613 9928735.

E-mail address:sxu@nrcan.gc.ca(S.Xu).

http://dx.doi.org/10.1016/j.jma.2015.06.001

2213-9567/Crown Copyright?2015 Production and hosting by Elsevier B.V.on behalf of Chongqing University.All rights reserved.

Crown Copyright?2015 Production and hosting by Elsevier B.V.on behalf of Chongqing University.All rights reserved.