IN-SITU STUDY OF THE CYCLIC DEFORMATION BEHAVIOUR OF THE MAGNESIUM

IN-SITU STUDY OF THE CYCLIC DEFORMATION BEHAVIOUR OF THE MAGNESIUM BASE WROUGHT ALLOY AZ31 BY MEANS OF

HIGH ENERGY SYNCHROTRON DIFFRACTION

Jens Gibmeier1*, Martin Götting2 and Berthold Scholtes2

1University of Karlsruhe, Inst. of Mat. Sci. and Eng. I, 76128 Karlsruhe (Germany) 2 University of Kassel, Inst. of Mat. Eng., 34125 Kassel (Germany)

ABSTRACT

With regard to the processing of structural lightweight components there exists an increasing demand for the application of magnesium base wrought alloys, which are highly textured due to the forming process. However, magnesium has a poor deformability at room temperature due to the hexagonal structure that limits its application considerably. Although the focus of recent research activities is on investigations of the texture evolution and the mechanical behaviour of magnesium base alloys during processing and in service, there still exists a lack of understanding of their mechanical-technological characteristics e.g. the knowledge about the deformability or the cyclic deformation behaviour with respect to the initial crystallographic texture. The deformation behaviour during cyclic loading of the highly textured hot rolled magnesium base wrought alloy AZ31 was investigated in-situ during elasto-plastic 4-point-bending using energy dispersive diffraction. Loading or residual stress distributions were determined for one load cycle including loading, load release and load reversion. The experiments were carried out at the energy dispersive diffraction beamline EDDI at Bessy II, Berlin. The results obtained for the multitude of reflexions being recorded simultaneously in one single diffraction spectrum clearly indicate the elastic isotropic behaviour of the textured alloy. For elasto-plastically bent bars a strong plastic anisotropy was observed leading to a distinct shift of the neutral fibre of the bars. Reverse loading causes a shift of the neutral fibre almost symmetrically in the opposite direction of the bar which can be attributed to the reversibility of twinning. Twinning and untwinning process can be clearly observed on basis of the diffraction results by local changes of the texture.

INTRODUCTION

The need for the conservative use of natural resources in order to reduce the CO2 emissions remarkably, enforces an increasing demand for lightweight applications. Mg-base alloys are very attractive for lightweight design e.g. for automotive or aircraft applications, justified by its low density, a sufficient strength and stiffness and its high potential for recycling [1]. According to the large numbers of publication on Mg-alloys within the last decades magnesium clearly experiences a renaissance with regard to the field of lightweight constructions. The major restriction for the prevalent application of magnesium wrought alloys for complex shaped structural components is the poor deformability of hexagonal materials at room tempera-ture. To overcome this severe limitation, process routes are studied using forming technologies applied at elevated temperature like e.g. conventional extrusion [2,3] or equal channel angular extrusion [4,5]. But the application of the structural components in service mostly at ambient temperature and the need to process complex shaped structures that can not be manufactured by a

* formerly at Hahn-Meitner-Institute Berlin, Structural Research Division, D-12489 Berlin, Germany

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warm forming process demand for a better understanding of the mechanical-technological characteristics of magnesium alloys at room temperature. Although a vast number of investigations on these topics have been carried out in recent years (see e.g. [6-9]) reliable material models are not available for the prediction of the processability or the mechanical behaviour of structural components wrought from magnesium base alloys. Due to the c/a-ratio < 3 , magnesium base alloys exhibit a limited number of glide systems at room temperature. Dislocation gliding is only possible on the {002}-basal planes in <110>-directions. At elevated temperatures further glide systems become activated permitting additional prismatic and pyramidal slip. The limited number of slip systems at ambient temperature in combination with the hindrance of transverse slip in the hexagonal system requires that twinning plays an essential role for plastic deformation of magnesium alloys. Twinning can occur for loading the hexagonal magnesium unit cells in compression parallel to the basal planes or in tension normal to the basal planes ({102}<101>-twinning) [1,10]. After twinning has occurred it has been shown by mechanical testing and complementary microscopic investigations that the twins can recover by reversing the loading direction (e.g. [11, 12]). During cyclic loading the reversibility of twinning is active for the first loading cycles. Apart from the asymmetric deformation behaviour of textured magnesium wrought alloys a strong Bauschinger effect was observed after unloading and changing of the loading direction from tension to compression and vice versa [12, 13]. Semi-finished parts of magnesium wrought alloys are predominantly highly textured; hence the dominant deformation mechanism will strongly depend on the crystallographic texture and the direction of deformation relative to the preferred orientation. In the present paper the deformation behaviour of the highly textured magnesium wrought alloy AZ31 was investigated by means of in-situ diffraction stress analysis during elasto-plastic 4-point bending. Energy dispersive diffraction using high energy synchrotron radiation was applied in order to obtain a deeper insight in the anisotropic mechanical behaviour of the highly textured magnesium base alloy during quasistatic loading. With this regard stress distribution for individual {hkl}-planes were determined for bending bars being subjected to purely elastic loading, elasto-plastic loading until total strain in the outer layer of the tensile loaded side of approximately 2% and after reversal of the load. Furthermore residual stress distributions after unloading of the elasto-plastically loaded samples were analysed. SAMPLE MATERIAL

The investigated wrought magnesium base alloy AZ31 was supplied as sheet material in a hot rolled state with dimension 1000 × 500 × 20 mm³. In the as received state the material was recrystallized and no further heat treatment was applied. The investigated alloy has a chemical composition with 3 wt.-% Al, 0.88 wt.-% Zn, 0.33 wt-% Mn, balanced by Mg. Texture measurements carried out on the as received sheet material using X-ray diffraction with CrKα -radiation have shown that the hexagonal unit cells are preferentially oriented with the basal planes parallel to the sheet plane due to the hot rolling process. Fig. 1 shows the incomplete pole figure (ψ ≤ 70°) of the {002} basal planes of the sheet material. More details about the characterization of the microstructure of the investigated alloy can be found e.g. in [11].


{002} – pole figure

3.603.202.802.402.001.601.200.800.40

7.206.806.406.005.605.204.804.404.00

pole density

3.603.202.802.402.001.601.200.800.40

7.206.806.406.005.605.204.804.404.00

pole density

direction 1(loading dir.)

direction 3

{002} – pole figure

3.603.202.802.402.001.601.200.800.40

7.206.806.406.005.605.204.804.404.00

pole density

3.603.202.802.402.001.601.200.800.40

7.206.806.406.005.605.204.804.404.00

pole density

direction 1(loading dir.)

direction 3

Figure 1: {002} basal pole figure (incomplete) measured by X-ray diffraction (CrKα-radiation) on the sheet middle plane

From the semi-finished sheet material bending bars of dimension 100 × 6 × 12 mm³ were cut out in such a way that the basal planes of the unit cells are oriented parallel to the considered load direction (3) and the neutral plane of the bending bars (1-2) was parallel to the sheet surface.

30 30 30

6

12

measured area

strain gage

unit cells are laying with the c-axis normal to the side face

basal planes are parallel to the loading direction

c

12

3

30 30 30

6

12

measured area

strain gage



c

12

3

(3)

FF1

23

12

3

ψ

ψ - rotation around (2)

30 30 30

6

12

me ured areaas

strain gage



c

12

3

30 30 30strain gage

6

12

me ured areaas



c

12

3

(3)

3

FF1

23

21

ψ

ψ - rotation around (2)

Figure 2: Dimension of the bending bars and predominant orientations of the magnesium unit

cells with respect to the loading direction, i.e. the longitudinal direction of the bars.

Figure 2 presents the geometry of the bending bars stating the loading situation as well as the predominant orientations of the hexagonal unit cells with respect to the sample coordinate system further referred to in the following. EXPERIMENTAL

Energy dispersive (ED) diffraction using high energy synchrotron radiation was applied in order to study the change in the inhomogeneous (residual) stress distributions of bending bars subjected to purely elastic as well as elasto-plastic 4-point-bending. The experiments were carried out at the EDDI-Beamline at Bessy II (Berlin) operated by the Hahn-Meitner-Institute Berlin using a white beam with photon energies of up to 150 KeV provided by a 7T-superconducting wiggler source. Basic information about the beamline layout, the experiment set-up at EDDI as well as typical measurement parameters are given in [14]. A deviant detail of the set-up used for the present approach is a sample-fixed primary aperture with an opening of 150 µm × 2 mm which was


additionally applied to the conventional primary aperture and the receiving double slit system. This sample-fixed aperture guarantees that always the same material volume was irradiated by the incoming beam for each considered sample tilt. The bending sample was installed on the five axis sample positioner with the side face towards the incident X-ray beam. Sin²ψ - measurements [15] were carried out by tilting the sample stepwise around the normal to the side surface (direction 2 in figure 2). 11 sample tilts between 0° ≤ ψ ≤ 90° were applied in equidistant steps in sin²ψ. Analyses of the bending stress distributions according to the sin²ψ -technique were carried out for 51 different coordinates of the bending height (3-direction). Measurements were carried out in transmission mode with a local resolution of 150 µm, which is the height of the sample-fixed primary slit with respect to the load situation. One main benefit of the chosen transmission set-up is the fact that elaborate sample preparation of the magnesium alloy in order to prevent effects of prior machining can be omitted since the gauge volume is always immersed in the sample volume. Furthermore 4-point-bending testing is a very useful experiment since various stress states covering the tensile to the compressive regime can be monitored within one single loading experiment. Within the investigations it was distinguished between the analysis of pure elastic loading states as well as bending stress distributions for elasto-plastically deformed bars loaded up to total strain in the outer layer of 2% on the tensile loaded side. In addition the reversibility of the twinning process has been investigated for reversely loaded samples likewise loaded up to total strain of 2% again for the outer layer of the tensile loaded side. For stress analysis using energy dispersive diffraction a 2θ-angle of 10° was chosen guaranteeing that a sufficient number of diffraction lines are recorded within one single spectrum, which can be separated excellently from each other. In total 10 different diffraction lines were evaluated i.e. the {100}, {002}, {101}, {102}, {110}, {103}, {200}, {112}, {201}, {004} (see also [16]).

Evaluation procedure According to Bragg’s law, the energy of the diffraction lines is related to the spacing of the corresponding {hkl} lattice planes according to

hklhklhkl d

constd

chE 1.1sin2

=⋅⋅

=θ

. (1)

Here Ehkl is the energy of the {hkl} reflection in keV, h is Planck’s constant, c is the velocity of light and dhkl is the lattice spacing of the {hkl}-planes in Å. The Lattice strain in a particular orientation ϕ,ψ with respect to the sample coordinate system can be given by

11 }{

}{0

}{0

}{}{ −=−= hkl

hkl

hkl

hklhkl

EE

dd

ϕψ

ϕψϕψε (2)

where characterizes the energy that corresponds to the strain free lattice spacing . Assuming that we have introduced plane bending in the 4-point bending experiment and friction effects from the bearings can be neglected, no shear stresses are introduced and the 1, 2 and 3 directions in fig. 2 coincide with the principal stress axes. Thus, according to the sin²ψ-method of X-ray stress analysis [15] the lattice strain for the measurements carried out in transmission geometry can be calculated by

}{0

hklE }{0

hkld

( )[ ] [ ]332211}{

133}{

212

3311}{

21}{

|0 22sin σσσσψσσε ψ ++++−=°

hklhklhklhkl sss (3)


in the azimuth ϕ = 0° that corresponds per definition with the longitudinal direction of the bar, which is the loading direction. The quantities and }{

1hkls }{

221 hkls are the diffraction elastic constants

(DEC). For stress evaluation the diffraction elastic constants for magnesium are taken from [17]. Accordingly, the sin²ψ - analyses carried out on the 4-point-bending bars provide the deviatoric stress component from the slope of the lattice strain vs. sin²ψ - plots. By the uniaxial loading within the bending experiment no stress component in the 3-direction of the samples should develop for the homogeneous magnesium alloy AZ31, hence exclusively the load stresses

are determined by diffraction measurements.

3311 σσ −

11σσ =load

RESULTS AND DISCUSSION

In spite of the strong texture of the investigated AZ31, for all orientations the diffraction information for the lattice planes and for the sample tilts considered here can be used to determine reliable stress quantities (see fig. 3) except for the basal planes {002} and {004}. This can be attributed to deviations from the ideal crystallographic texture guaranteeing that always a sufficient number of favourably oriented lattice planes exist.

-3 -2 -1 0 1 2 3

-100

-50

0

50

100 {200} {110}

Span

nung

[MPa

]

Koordinate der Biegehöhe [mm]

AZ31AZ31

stre

ss

Coord. of the bending height [mm]-3 -2 -1 0 1 2 3

-100

-50

0

50

100 {200} {110}

Span

nung

[MPa

]


AZ31AZ31

stre

ss

Coord. of the bending height [mm]

Figure 3: Loading stress distribution for the {200}-and the {110}-reflection of AZ31 after purely elastic 4-point-bending up to loading stresses of approx. 100 MPa in the outer layers.

For the basal plane the diffraction lines nearly vanish for some sample tilts. In addition the sin²ψ - plots were almost linear despite the pronounced texture. This statement can even be supported for the elasto-plastically bent bars. For the purely elastically loaded samples the loading stress distributions across the bending height for all lattice planes considered here were strictly linear and almost congruent as shown in fig. 3 exemplarily for the {200}- and the {110}-lattice planes. This is due to the fact that magnesium is nearly elastically isotropic having a stiffness reduction of only 9% for the [102]-lattice direction compared to the direction [001] [7]. Elasto-plastic 4-point bending up to total strains in the outer layer of 2% for the tensile loaded side results in a strongly asymmetric loading stress distribution with respect to the coordinate of the bending height, showing much higher stresses and a more pronounced hardening on the tensile loaded side compared to the compressive loaded side as shown in fig. 4 as an example for the {200}-diffraction line. By accompanying metallographic investigations it has been proved that extensive twinning can be observed during compressive loading [11,12]. The course of the integral width IB of the diffraction line clearly indicates a pronounced shift of the neutral fibre about 1 mm towards the tensile loaded side caused by the asymmetric mechanical behaviour of the textured AZ31.


-3 -2 -1 0 1 2 30,40

0,42

0,44

0,46

0,48

0,50{200}

IB [k

eV]


-0,03 -0,02 -0,01 0,00

-100

-50

0

True

Stre

ss [M

Pa]

True Strain

-200

-100

0

100

200 {200}

Spa

nnun

g [M

Pa]

clearclear shiftshift of of thethe neutral neutral fibrefibre

stre

ss

Coord. of the bending height

0,00 0,01 0,02 0,030

100

200

True

Stre

ss [M

Pa]

True Strain

Tension

CompressionTrue

Stre

ss [M

Pa]

Figure 4: Loading stress distribution for the {200}-reflection of AZ31 after elasto-plastic 4-point-

bending with 2% total strain in the outer layer of the tensile loaded side. For comparison the macroscopic stress-strain curves are shown (right hand side) (from [16]).

After load release characteristic bending residual stress distribution caused by the inhomogeneous plastic deformation during bending are determined. The residual stress distributions clearly reflect the asymmetric deformation behaviour. The shift of the neutral fibre is maintained, which results in an asymmetric residual stress distribution with respect to the centre layer. Furthermore a strong impact of the Bauschinger effect on the residual stress distributions can be observed. Knowledge about the residual stress distributions are of particular interest with respect to the spring back characteristic of AZ31 sheet materials and occurring distortions during metal forming. After load reversal a shift of the neutral fibre now about 1 mm towards the previous compressive loaded side was observed caused by the untwinning of the material (see also [16]). For further evaluation it was assumed that the total strains, which are controlled during the bending experiment via strain gauges applied on the outer layers of the bars (see fig. 2), are linear across the bending height and the detected shift of the neutral fibre was taken into account. Using that information the normalized integral intensities of the {002}- and the {200}-diffraction lines for measurements with the scattering vector pointing in load direction (1-direction, fig. 2) are plotted vs. the apparent plastic strain for the first bending state (left hand side) and after load reversal (right hand side). Since twinning results in a 86,4° reorientation of the basal poles from perpendicular to the loading axis to nearly parallel [18], the onset of twinning and the degree of twinning can easily be monitored by the intensity plots (fig. 5). Hence, the onset of twinning starts instantly with the onset of plastic deformation. According to the investigation of Brown et al. [18] who studied a similar material state the twinned volume fraction can be estimated by the slope of the {002} intensity curve. Using the relation given in [18] stating that the amount of twin fraction increase by a factor of 0,145 per unit plastic strain the twin fraction at a compressive strain of 3,4% should be about 50%. Corresponding to their findings the total twin fraction after saturation of twinning at about 8% plastic strain will be about 80%. The intensity curves presented on the right hand side of fig. 5 after load reversal emphasize that the twins recover


completely and twinning now occurs on the formerly tensile loaded side again under compressive loading. However, it appears that the onset of twinning starts slightly earlier, already in the vicinity of the neutral fibre on the tensile loaded side (fig. 5, right hand side).

2 1 0 -1 -2 -3

plastic strain [%]-3 -2 -1 0 1 2

0

20

40

60

80

100

norm

. int

egra

l int

ensi

ty [-

] {002} {200}

plastic strain [%]2 1 0 -1 -2 -3

plastic strain [%]-3 -2 -1 0 1 2

0

20

40

60

80

100

norm

. int

egra

l int

ensi

ty [-

] {002} {200}

plastic strain [%]

Figure 5: Normalized integral intensity of the diffraction lines vs. plastic strain for the basal {002} and the prisms plane {200} of AZ31 after elasto-plastic 4-point-bending with 2% total

strain in the outer layers. First bending state (left hand side), after load reversal (right hand side).

Fig. 6 shows the distributions of the loading stresses determined by means of ED diffraction of selected diffraction lines for the first loading state (left hand side) and after load reversal (right hand side).

2 1 0 -1 -2 -3 -4plastic strain [%]

-4 -3 -2 -1 0 1 2-200

-100

0

100

200

{100} {101} {102} {112} {201}

stre

ss [M

Pa]

plastic strain [%]2 1 0 -1 -2 -3 -4

plastic strain [%]-4 -3 -2 -1 0 1 2

-200

-100

0

100

200

{100} {101} {102} {112} {201}

stre

ss [M

Pa]

plastic strain [%]

Figure 6: Loading stress vs. plastic strain for selected {hkl}-planes of AZ31 after elasto-plastic 4-point-bending with 2% total strain in the outer layer of the tensile loaded side. First bending state (left hand side), after load reversal (right hand side).

The stress distributions point up the strong plastic anisotropy, which the textured AZ31 features. The application of the DEC calculated using the Kröner model, an approach which is justified by the results determined for purely elastic bending, results in heavily diverging stress quantities. Obviously the crystallites in the slightly stiffer directions (lattice planes {100}, {201}) take much higher load during uniaxial loading than for the elastically softer directions (i.e. the lattice planes {112}, {102} and {101}). The loading stresses taken by the individual lattice planes differ in the outer layers of the bars by a factor > 2. After load reversal a slight hardening can be observed for all lattice planes whilst the plastic anisotropy appears conserved.


CONCLUSIONS

Energy dispersive diffraction using high energy synchrotron radiation in transmission geometry was used for in-situ analysis of stress distributions and local crystallographic reorientations of elasto-plastically deformed hot rolled AZ31 subjected to 4-point-bending. The important findings can be summarized as follows: The analyses of purely elastically bent samples indicate the highly elastic isotropic behaviour of the textured magnesium alloy. For elasto-plastically bent bars a strong plastic anisotropy can be observed leading to a large shift of the neutral fibre of the bars towards the tensile loaded side. After reverse loading of the bars the reversibility of the twinning causes a shift of the neutral fibre almost symmetrically to the opposite direction. After release of the external load characteristic bending residual stress distributions have been determined indicating a strong effect of inelastic back strains (Bauschinger effect) on the determined residual stress distributions. The onset of twinning and the local untwining of the structure can easily be monitored by the change in the integral intensity of the diffraction lines. The onset of twinning comes along with the onset of plastic deformation. Obviously twinning of reversely loaded bars starts slightly earlier, i. e. already for small amounts of tensile loading. ACKNOWLEDGEMENTS

We thank Bessy for granting us beamtime at EDDI and the EDDI-team for their kind beamline support. Financial support by the German Science Foundation (DFG) is gratefully acknowledged. REFERENCES

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[3] D.-J. Yoon, K.-H. Na, C. Cho, Materials science forum, 2007 539-543, 1818-1823 [4] S.R. Agnew, D.W. Brown, C.N. Tome, Acta Materialia, 2006, 54, 4841–4852 [5] T. Mukai, M. Yamanoi, H. Watanabe, K. Higashi, Scipta Mat., 2001 45, 89-94 [6] X.Y. Lou , M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, Int. J. of Plast., 2007 23, 44-86 [7] M.R. Barnett, Mat. Sci. and Eng. A, 2007 464, 1-16 [8] S.R. Agnew, C.N. Tomé, D.W. Brown, T.M. Holden, S.C. Vogel, Scripta Mat., 2003 48,

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IN-SITU STUDY OF THE CYCLIC DEFORMATION BEHAVIOUR OF THE MAGNESIUM