Research progress of residual stress determination in magnesium alloys

Xiaomin Yuan,Jin Zhang,Yong Lian,Chang Du,Weisheng Xu,Yongle Zhao,Jiahao Mo

University of Science and Technology Beijing,30 Xueyuan Road,Haidian District,Beijing 100083,China

Abstract With the research development of the magnesium alloys,the deformation or stress corrosion induced by residual stress(RS)attracted extensive interests in industry and research efforts extensive.However,there are relatively few studies on the RS of magnesium alloys in the world.The generation cause of RS in magnesium alloys was analyzed at first Several methods of determinate the RS,including destructive methods(drilling hole,crack compliance,layer exfoliation etc.)and non-destructive methods(X-ray Diffraction,Neutron Diffraction,Short Wavelength X-ray Diffraction)were summarized.The factors that influenc the measuring accuracy of XRD method were emphasized.The research trends of RS in magnesium alloys were put forward.

Keywords:Residual stress;Magnesium alloys;Stress generation;Stress measurement.

1.Introduction

As lightweight structural materials,magnesium alloys have been widely used in aviation,automobile and electronics industry[1].The plastic processing methods of magnesium alloys are commonly used in extrusion,rolling and forging.Residual stress(RS)in the magnesium alloys would lead to distortional failure,deformation,stress-corrosion cracking,or fatigue of the workpiece which declines the production and increases costs[2,3].So that it is important to determinate RS in magnesium alloys.However,research on the RS mainly concentrated in the steel,aluminum alloys and other traditional metal materials.Due to magnesium alloys’crystal structure(HCP)and properties,it is difficul to determinate the RS accurately.In this review,the researches on RS in magnesium alloys were analyzed,and the development tendency of research about the RS in magnesium alloy was forecasted.

2.Residual stresses generation in magnesium alloys

RS are stresses that remain in a solid material after the original cause of the stresses has been removed.It can occur through a variety of mechanisms including inelastic(plastic)deformations,temperature gradients(during thermal cycle)or structural changes(phase transformation).

(1)Plastic deformation:During the process of plastic deformation,the material often has asymmetric shape,force states and inhomogeneous properties.Therefore,when processing is finished materials would rebound unevenly and generate RS[7].

(2)Temperature variation:The difference of temperature distribution in the process of heat treatment will make the volume of each part of the material change unevenly[8,9].Quenching would induce tensile RS in the central area,compressive stresses at the surface[10–12].As a lightweight structural material,magnesium alloy has some advantages in friction stir welding.However,due to the large temperature variation gradient between the base metal and welding area,the RS will be generated[13,14].

(3)Structure transformation:The Austenite and Martensite transformation in the steel would lead to the volume change.According the Mg-Al phase diagram[6],aluminum element content inα-phase is relatively low,it is not easy to crystallize plenty of dispersedβphase(Mg17Al12)so that the phase transformation only could generate fewer RS.

The distribution of RS in the welded joints is extremely uneven,such as the friction stir welding workpiece between the same kind of magnesium alloy[4],and hybrid laser-TIG welding workpiece between the magnesium alloy and steel[5],which would cause cracking and decrease the workpiece’s service life.Meanwhile,during the plastic deformation process,temperature variation and microstructure transformation could not be completely uniform,which would lead to the nonuniform distribution of RS.

It is very important to grasp the distribution of RS in the actual production process before eliminating or reducing stress which will lead to workpiece deformation or crack.However,with close-packed hexagonal structure,magnesium alloys are more likely to be anisotropic than the steel[15,16].Both the texture and large size of grain would make the residual stress determination more difficult.Thus,the methods to determine RS are necessary to be known.

3.The methods of determination residual stresses in magnesium alloys

There are several methods to determine the surface RS,such as X-ray diffraction(XRD)[17–19],drilling hole using strain gauge measuring[20–23],ultrasonic wave[24,25],hardness indentation[26–28]etc.As to the internal RS measuring,it is much more complicated and expensive.The destructive method of layer exfoliation and compensation is used traditionally.The non-destructive methods appeared in recent years using neutron diffraction,synchrotron radiation,short wave X-ray diffraction.

The several used methods in practice were introduced.

3.1.XRD method

The principle of X ray diffraction is based on the Bragg’s law formula and the elastic mechanics.It is considered that the lattice strain induced by RS can reflec macroscopic strain.RS is calculated by measuring the interplanar spacing which has the high accuracy.In recent years,Recently,a twodimensional(2D)X-ray detector has been readily available to allow the collection of the Debye–Scherrer ring(DSR)for the stress calculation.Compared to the traditional method called sin2ψ,this method could gain more information,and be more convenient[29–31].

The result of XRD method is the average value of many grains,thus it would be affected by material surface quality and diffraction planes[32].The common X-ray RS measurement was widely used.Because of the limited penetration ability of ordinary X ray,the condition ofσzzis usually satisfied Meanwhile,theψangle is define as the angle between the diffraction crystallographic planes’normal line and material surface normal line.If RS existed in the workpiece,the interplane spacing in the workpiece material will be changed.for the polycrystalline material,the change of the interplane spacing under different angles is different.Under the condition of continuous and isotropic material,it is necessary to test the linear relationship betweenεϕψandσϕ-sin2ψunder differentψangle,so as to realize the measurement of RS.For example,Kouadri and Barrallier[33]had done research on RS in laser welding of AZ91 magnesium alloy sheet measured by sin2ψmethod,and obtained the distribution of RS in the welding zone and the base metal.Outeiro et al.[34]acquired the distribution of RS in AZ31B magnesium alloy processed by cryogenic cooling,and the results showed that the RS is compressive in the surface layer(the distance beneath the surface is about 160 μm).

Fig 1.The residual stresses measured by neutron diffraction and contour method[38].

The RS was measured by using sin2ψmethod by X-ray mostly,its precondition is that the materials workpiece has isotropic properties[35–37].If they were processed by the plastic deformation,strong texture would occur,and sin2ψmethod would failure due to large deviating data from the actual situation seriously.

3.2.Short wavelength XRD method

The common method of X-ray diffraction has weak penetrating energy,only could obtain RS tens of microns beneath the surface.A short wavelength X-ray diffractometer(SWXRD)was developed by Southwest Technology and Engineering Research Institute,in which the target material is tungsten.Based on its strong penetrating energy,it can penetrate 40 mm Al alloys plate and 60 mm Mg alloys.Based on the Bragg’s law formula,when the RS existed in materials,the lattice space would change which leads to the migration of diffraction peak,and the stress free reference sample was made to acquire the original lattice space called d0,this method is called d0.To verify the accuracy of short wavelength X-ray diffractometer,Zhang et al.[38]gained the distribution of the RS in 7075 aluminum alloy plate by SWXRD and neutron diffraction at the same time.The results of the two methods showed good consistency which proved SWXRD is feasible and effective,the result was shown in Fig.1.

Measuring the internal RS in the magnesium alloys by SWXRD is currently under the research stage.Referring to the RS measurement in aluminum alloys,the principle of RS measurement in magnesium alloys is effective.The X-ray irradiated from the tungsten target could penetrate deeper in magnesium alloys than in aluminum alloys.The crystal structure of magnesium alloy has the crystal structure of close-packed hexagonal(hcp),which is different from that of the aluminum alloys(fcc),so it is necessary to study and get more data for fast measuring.

Fig 2.The residual stresses measured by neutron diffraction and contour method[19].

3.3.Neutron diffraction

For most materials,the penetration ability of neutral is obviously higher than the X-ray.We could carry out threedimensional,nondestructive and deep internal RS in the material by neutron diffraction.At present,the measurement of the internal RS of magnesium alloys is basically carried out by neutron diffraction.Woo et al.[4]in University of Tennessee measured the distribution of the internal RS in the FSW magnesium alloy sheets by neutron diffraction.The stresses by the two interplanar spacing((10-10)and(0002))and three directions(LD,TD and ND)was determinated.Fabre et al.in Ecole Nationale Supérieure d’Arts et Métiers[39]obtained the distribution of the internal RS in the laser welding sheets of the WE43,which has the tensile stress in the center layer.The results were shown in Fig.2.

3.4.The hole drilling method

The principle of hole drilling method is consistent with other destructive test method,and it is through removing part of the materials,causing the elastic deformation through the release of RS,then we could calculate the RS according to the deformation[40,41].The specifisteps are as follows:at first drilled a hole in the sample,then measured the hole diameter at the different test thickness in different circumferential angle,meanwhile,we should make out a cylinder that is the same with the reference hole at the same vertical direction by the EDM cutting,then measure the diameter of the reference hole at the same circumference angle and plate thickness,so that we could calculate the residual stresses fiel by using these radial strains in the vertical direction of the hole axis[35,36].The hole drilling method is rarely used to study the RS of magnesium alloys.Lehmann and Stockmann[42]at Chemnitz University of Technology measured the distribution of the RS along the thickness in the static aluminum/magnesium compound bars,and the results showed the good correlation with the computer numerical simulation.

3.5.Crack compliance method

The basic principle of the crack compliance method[43]is gradually increased the crack along the thickness direction into a depth to release the RS.While the crack is increasing,it is possible to measure the variation of strain,thus the result of RS would be calculated.Prime[44]in the Los Alamos National Laboratory used it to measure the RS before and after the stretching stress relieving method.

The above methods are widely used in the determination of RS in steel and aluminum at present,but rarely applied in the determination of RS in magnesium alloys.which needs plenty of researches to fin some suitable methods.Though the destructive testing method has low cost,the workpiece has to be destroyed and the implementation and calculation is more complex,which restricts its development.The specifiselection method needs to be analyzed in details according to the actual situation.

4.The factors affecting the accuracy of XRD stress measurement

At present,XRD stress measurement has been applied extensively.However,due to the various problems in the metal sheets,the RS measurement would be seriously error.The influenc factors of the accuracy of XRD stress measurement is as follows.

Stress free reference samples:when using SWXRD to measure the internal stresses in d0method,the stresses-free sample should be prepared to get the original interplanar spacing.There are three methods to prepare the stress-free sample:comb sample by high speed wire electrical-discharge machining,annealing and powdering.For magnesium alloys powder,exposing to the air would make it oxidize quickly,and the chemical composition of the powder would be changed,so it is not suitable to make standard sample,thus the comb cutting sample and annealing sample could be considered.The comb cutting stress-free sample is especially more suitable for being welding[45–47],because it could reflec the difference of interplanar spacing caused by microstructure and orientation in different parts.Due to the slit in the comb cutting sample,the diffraction volume could not be fille completely,which could cause the deviation of the geometric center in the actual diffraction gauge volume and the device diffraction volume.This deviation would make the migration of the diffraction peak which could influenc the accuracy.For the comb cutting stress-free sample of magnesium alloys sheets,the little size allowance is cut along the thickness direction(ND),which would lead to incomplete stress release.Meanwhile,it also could cause testing error in other direction.

For the annealing standard sample,there is no testing error caused by the complete diffraction volume of the sample,so it is more suitable to measure the magnesium alloy sheets.

①Grain size:the number of grains involved in the diffraction gauge volume will not only affect the size of the diffraction intensity,but also affect the statistical properties of the diffraction.If the number of grains in the diffraction gauge volume is less than 1000,the diffraction peak would be poor in quality,which makes it difficul to determine the peak of the diffraction spectrum.For the magnesium alloy rolling sheets,especially the sheets’rolling reduction is low,the grain is coarse.Xia et al.[48]in Hunan university prepared AZ31B magnesium alloy rolling sheets by differential speed rolling(the pass reduction is 5%,and total reduction is 35%).The grain size reached 30 μm,and it is too large to be involved enough in the gauge volume,which leads low measure accurate.

②Texture:the texture of material would affect the diffraction intensity and testing direction.In addition,the isotropic assumption could not be applied in the stress calculation while the strong texture exists.When testing the RS in the rolling direction of the magnesium alloy,if the texture intensity on both sides of the rolling direction is extremely strong,high quality diffraction spectrum cannot be obtained.To get accurate diffraction information,the testing direction should be in line with the rolling direction and the maximum of the pole density.For the wrought magnesium alloys,anisotropy of mechanical properties exists,which caused by texture during the plastic deformation processing[49].

③The inhomogeneous of chemical composition:the chemical elements in the alloys would influenc the inherent interplanar spacing and modulus of elasticity,and the slight variation would induce large deviation of the RS.Due to the low solubility,most of magnesium alloys are composed of two or three solid solution elements.Ganeshan et al.[50]at Pennsylvania State University calculated the influenc of the addition of alloying elements on the grain spacing and Young’s modulus through the firs principles.For example,adding 2.77at%aluminum elements could make the theoretical interplanar spacing of magnesium change from 3.195A to 3.183A,and adding about 2 at%Pb elements could decrease the young’s modulus of magnesium by 1 GPa.The effect of alloy chemical elements on the atomic interplanar spacing and the Young’s modulus is shown in the following Fig.3[30].Magnesium alloys sheets need to undergo a series of procedure,such as ingot casting and plastic deformation.These processes would inevitably cause uneven chemical composition of the alloy in the sheets,so that affected the accuracy of RS measurement.

Fig 3.Influenc of atomic radius of solute atom(X)on the lattice constant of Mg–2.77 at.%X solution[30].

5.The application of residual stresses determination in magnesium alloys

5.1.The determination of residual stresses in the welded magnesium alloys

The application of magnesium alloys welding technology is various,including friction stirring welding,laser welding and laser-TIG,which inevitably introduce RS.And the RS also could be generated by the uneven plastic deformation,volume change generated by phase transition or precipitation,and chemical effects[51,52].The RS in the welded workpiece would affect its fatigue strength,corrosion resistance and other properties,which could reduce the service life of the weldment.Zeng et al.[5]in University of Electronic Science and Technology of China obtained the RS distribution of the weldments of AZ31 and 304L steel by XRD and numerical simulation,the results were shown in Fig.4.Fabre et al.[39]in Arts et Métiers Paris Tech evaluated the RS state of WE43 magnesium alloy welded joint for the transversal direction by neutron diffraction.The result showed that tension stresses were found along welding joint.Lobanov[53]in E.O.Paton Electric Welding Institute of the NAS of Ukraine Obtained the distribution of RS in the argon arc welded ML10 magnesium alloys the hole drilling method.

5.2.The measurement of residual stresses in the surface treatment layer of magnesium alloys

In order to improve the service performance of magnesium alloys,some surface treatment,such as cold spraying and shot peening strengthening treatment[54,55],introduce compressive stress which could improve its fatigue resistance,wear resistance and corrosion resistance.Chen et al.[56]measured the distribution of residual stresses in the AZ91D magnesium alloy strengthen by shot peening through the numerical simulation and XRD measurement,both of the results showed the consistency,the RS in the surface layer increased firstl and then decreased while closing to the surface,the compressive stresses reached the peak at the distance beneath the surface to the 0.2 mm.Shayegan et al.[57]in University of Waterloo measured the RS of the AZ31B with cold sprayed by the aluminite powder in the surface layer.Through the XRD measurement,the surface RS was about-20 MPa,it also increased with the increase of the depth until to the-54 MPa,then gradually decrease until to 0 MPa beneath the surface of 400 μm.The shooting particle diameters’influenc to the residual stress was shown in Fig.5.

6.Development trend of research on residual stresses of magnesium alloys

6.1.Numerical simulation of residual stresses in magnesium alloys

In actual production,magnesium alloys need to be processed into various workpieces by means of casting,plastic deformation and welding.If we could get the distribution of RS in different processing technologies by numerical simulation,it would be very helpful for the optimization of processing.The simulation of RS is mainly based on the finit element numerical simulation.According to the theory of elasticplastic and heat conduction,a machining model is established,and the distribution of RS in the metal sheets could be obtained through computer calculations.Liao et al.[58]simulated the distribution of the RS in the extruded EW75 magnesium alloy in the as-quenched state,the results showed the RS on the surface is compressive and tensile in the center.

Fig 4.The distribution of residual stress on hybrid butt weld by simulation and determination(a:on middle cross-section and b:on the weld top surface)[5].

Fig 5.The distribution of residual stress in AZ31B sheet at the same particle velocity of 400 m/s with different particle diameters[57].

6.2.Formulation of relevant standards for determination residual stresses in magnesium alloys

At present,there have been few studies on RS in the magnesium alloys,only a few studies abroad are on measuring RS of magnesium alloy weldments.And the main references related with the neutron diffraction for the non-destructive internal RS measuring.However,the residual stress test of magnesium alloy mainly refers to the traditional method,but its accuracy still needs a lot of experiments to verify.Therefore,the formulation of RS test standard appears more urgent and crucial.

6.3.Fast detection of internal stress in magnesium alloys

The surface RS has been rapidly measured by using twodimensional detector,which could collect more diffraction information and improve measuring speed.It usually takes only a few minutes to obtain the data by the Debye-Scherer ring on the surface.The neutron diffraction and short wavelength XRD measurement take a lot of time,and the time of the preparation before the testing is long.For example,using the short wavelength XRD to measure the single internal point needs about 30 min.Short wavelength XRD is a way of collecting information through point scanning,so that its testing speed is low and only could collect little information.Referring to the fast detection of the surface RS,we could try to upgrade the detector to two-dimensional surface exploration,which helps to improve the accuracy and speed of test.

Acknowledgment

The work was supported by Ministry of Science and Technology of China(2016YFB0301105-2).