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2012-03-14

Failure Mechanisms and Texture Evolution of Wrought AZ31B Failure Mechanisms and Texture Evolution of Wrought AZ31B

Magnesium at Temperatures Ranging from 25 C to 125 C Magnesium at Temperatures Ranging from 25 C to 125 C

Jonathan Michael Scott Brigham Young University - Provo

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Failure Mechanisms and Texture Evolution of Wrought AZ31B

Magnesium at Temperatures Ranging from 25 C to 125 C

Jonathan Scott

A thesis submitted to the faculty of Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

David T. Fullwood, Chair Mike P. Miles Eric R. Homer

Department of Mechanical Engineering

Brigham Young University

April 2012

Copyright © 2012 Jonathan Scott

All Rights Reserved

ABSTRACT

Failure Mechanisms and Texture Evolution of Wrought AZ31B

Magnesium at Temperatures Ranging from 25 C to 125 C

Jonathan Scott Department of Mechanical Engineering, BYU

Master of Science

Failure mechanisms were studied in wrought AZ31B magnesium alloy under different strain paths and various temperatures. Optical micrographs were used to observe the formation of shear bands and regions of high twin density in samples strained under uniaxial, biaxial and plane strain conditions. Interrupted testing at 4% effective strain increments until failure was used to observe the evolution of the microstructure. Results showed that shear bands with a high percentage of twinned grains appeared early in the samples strained under biaxial or plane strain tension. These bands are similar to the failure region in uniaxial tension specimens. A forming limit diagram for AZ31B was developed from the strain data, showing that plane strain and biaxial tension had very similar limit strains, in contrast to materials like steel or aluminum alloys which typically have greater ductility in biaxial tension compared to plane strain tension.

When the experiments are repeated at elevated forming temperatures of 75 C and 125 C there is no observable shear band formation. The forming limit diagrams for each temperature were created and showed a marked increase in biaxial tension formability, compared to plane strain tension. Optical microscopy showed no sign of any compression twins and very few tensile twins in samples strained in biaxial or plane strain tension, up to 12% effective strain. The lack of compression twins at these strain levels shows that the effect of temperature on critical resolved shear stress for <c+a> slip is greater than previously expected.

Keywords: Jonathan Scott, optical microscopy, CRSS, shear band, compression twin

ACKNOWLEDGEMENTS

I would like to thank Dr. Raj Mishra for all the support throughout this research. His

input was vital in understanding the microstructure evolution. Thank you to General Motors as

well, who supplied all the materials as well as provided me with an internship opportunity.

Thanks to Ali Khosravani who helped me with most of my research. I would have been lost on

the SEM without him. Thanks, last of all, to my wife for all her support while her husband was

spending nights with microscopes and polishing tables.

This material is based upon work supported by the National Science Foundation under

Grant No. 0928923. Any opinions, findings, and conclusions or recommendations expressed in

this material are those of the author and do not necessarily reflect the views of the National

Science Foundation.

v

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................................ vi

1 Development of Shear Bands with High Twin Density in Wrought Magnesium AZ31B Sheet at Room Temperature.......................................................................................................... 1

1.1 Introduction ........................................................................................................................... 1

1.2 Experimental Procedure ........................................................................................................ 3

1.3 Results .................................................................................................................................. 6

1.4 Discussion of Results .......................................................................................................... 15

1.5 Conclusions ......................................................................................................................... 17

2 Formability and Failure Mechanisms of Wrought AZ31B Magnesium at Slightly Elevated Temperature .................................................................................................................. 19

2.1 Introduction ........................................................................................................................ 19

2.2 Experimental Procedure ...................................................................................................... 22

2.3 Results ................................................................................................................................. 24

2.4 Discussion of Results .......................................................................................................... 32

2.5 Conclusion ........................................................................................................................... 35

REFERENCES ....................................................................................................................................... 37

vi

LIST OF FIGURES

Figure 1-1: AZ31B specimen pulled to 19% uniaxial tensile strain along the RD. A high density of compression twins is seen in the area around the crack tip. ........................6

Figure 1-2: SEM image showing compression twins in the necked failure region of a uniaxial strained specimen. ...........................................................................................7

Figure 1-3: SEM image showing compression twins 2mm from the necked failure region of a uniaxial strained specimen. ...........................................................................................8

Figure 1-4: IPF + IQ image of a compression twin with accompanying grain boundary misorientation graph. ....................................................................................................9

Figure 1-5: Shear band in a 7% strain uniaxial specimen composed of a single line of tension twins. .............................................................................................................................9

Figure 1-6: Tension twin boundaries, shown in red, from a shear band in a uniaxial tension specimen strained to 7%. ............................................................................................10

Figure 1-7: Shear band forming on TD plane, in specimen stretched to 4% effective strain along the RD in plane strain. Dotted white line added for easy identification. .........11

Figure 1-8: Multiple shear bands forming on TD plane in specimen stretched to 8% effective strain along the RD in plane strain. Dotted white lines are added parallel to shear bands for ease of identification. ..................................................................................12

Figure 1-9: Image of the ND plane on a sample pulled in biaxial tension to 8% strain, showing three shear bands, with a high density of compression twins in each band. ............................................................................................................................13

Figure 1-10: Image taken from the same area as Figure 6 at greater magnification, showing compression twins within a shear band. .....................................................................14

Figure 1-11: Forming limit diagram for 2 mm thick alloy AZ31B at room temperature. .............15

vii

Figure 2-1: Strain history for a point undergoing plane strain .......................................................25

Figure 2-2: Strain history for a point undergoing biaxial strain. ...................................................26

Figure 2-3: Microstructure near the center of a biaxial sample strained to 12% at 75 C. .............27

Figure 2-4: Microstructure near the edge of a biaxial sample strained to 12% at 75 C. ................28

Figure 2-5: Microstructure near the edge of a plane strain sample strained to 5%at 75 C. The twins shown appear to be the stunted beginnings of a shear band that never fully developed. ...................................................................................................................29

Figure 2-6: Forming Limit Diagram for AZ31B at 75 C ...............................................................30

Figure 2-7: Microstructure at the edge of a plane strain sample strained to 5% at 125 C. ............31

Figure 2-8: Forming Limit Diagram for AZ31B at 125 C. ............................................................32

Figure 2-9: Forming limit diagram comparison of AZ31B at 25, 75 and 125 C. ..........................34

1

1 DEVELOPMENT OF SHEAR BANDS WITH HIGH TWIN DENSITY IN WROUGHT MAGNESIUM AZ31B SHEET AT ROOM TEMPERATURE

1.1 Introduction

Over the last 10 years magnesium consumption has increased 20% [1-2]. This is due to

the fact that magnesium has many mechanical properties that are desirable in structural parts

such as high specific strength, high fracture toughness, good electromagnetic shielding, good

heat transfer characteristics, recyclability and vibration and noise damping, among others [3].

However, magnesium has poor formability at room temperature and this has limited its use for

applications where complex shapes need to be formed.

The poor formability of magnesium at room temperature has been attributed to the lack of

slip systems in the HCP crystal structure [4–7]. Additionally, in a rolled AZ31B sheet there is a

strong basal texture present with no easy slip planes to accommodate strain of the c-axis at room

temperature [6, 8, 9]. The typical approach to overcoming the low formability of AZ31B is to

form the material at elevated temperatures, usually 250 °C or higher [10, 11]. Forming at these

high temperatures is expensive and difficult to implement in a high-volume production

environment. It is therefore important to study the formability of wrought magnesium at room

temperature in order to understand the failure initiation mechanisms that precede fracture. If an

understanding of failure mechanisms can be gained, then it is possible that the starting

microstructure or the forming path can be manipulated in order to increase formability.

2

Previous studies on formability and failure mechanisms have been performed on samples

that undergo either compression or uniaxial tensile strains, where measurements were taken in a

highly deformed or necked region. Although compression is vital to the sheet rolling process

and uniaxial tension is a good t ool in understanding material behavior, neither strain path is

crucial in the part forming process. Complex strain paths, on the other hand, are vital in the

sheet forming and stamping processes and ultimately control the geometry of any parts made

from AZ31B magnesium. It has been shown that the majority of part failures during forming or

stamping occur in plane strain regions [12]. Since prior work on c rack nucleation and failure

initiation has depended primarily on uniaxial tension specimens with strains well above 10%, the

present study focused on failure mechanisms for biaxial and plane strain tension, with

comparisons to uniaxial tension.

The primary mechanism for both through-thickness deformation and failure in AZ31B in

samples strained by either compression or uniaxial tension, is thought to be {101�1} compression

twinning [4, 13]. The strong basal texture in AZ31B means that any in-plane tensile deformation

of wrought sheet causes compression of the c-axis, which is accommodated by compression

twinning. At high strains, compression twins also act as a major contributing factor in fracture

initiation [14–16]. T here have been observations linking crack nucleation with {101�1}

compression twins. Cracks are seen near and parallel to compression twins in extruded AZ31B

and ZK60 bar as well as rolled AZ31B when pulled in tension [15, 17–19].

One study measured a steady decrease in the number of {101�2} tension twins as strain, or

cold work reduction, increased [20]. This reduction of twins was attributed to the fact that the

measurements excluded shear-banded regions of the microstructure. The same study showed a

steady increase in shear banded area with increasing strain. B ecause of limitations of EBSD

3

microscopy, the study could not identify microstructures inside the shear bands and therefore the

relationship between twin fraction and shear band area had to be implied rather explicitly

measured.

A study by Kang et al. [21] showed that for tensile strains above 10% in rolled AZ31B

formations of compression twins that quickly clustered into shear bands were observed. There

was a strong correlation between the formation of compression twin shear bands and the onset of

diffuse necking.

To investigate the relationship between the strain path and the failure initiation

mechanisms, twin formations during uniaxial, biaxial and plane strain conditions in annealed

AZ31B were studied. Samples were strained at increments of 4% until failure. Microstructure

evolution was evaluated using optical microscopy. A forming limit diagram (FLD) for AZ31B

at room temperature was constructed to give a complete picture of formability under the three

strain paths.

1.2 Experimental Procedure

The material investigated was composed of 2.05 mm thick sheets of cold rolled AZ31B

magnesium with 3% Al and 1% Zn by weight alloying elements. The average linear intercept

grain size in 10µm. All samples were annealed at 350 °C for a minimum of 15 minutes and then

air-cooled outside the oven. Specimens were rough cut using a water-jet before annealing.

Samples for microscopy were cut from the strained specimens using wire electrical discharge

machining (EDM).

Tension specimens were prepared from the annealed sheets using the ASTM E8 standard

[22], with one exception, and pulled at a constant crosshead speed of 16 mm/min. The other

4

tensile specimen was prepared with a variable width gauge section similar to samples prepared

by Kank et al. [21]. The sample was 30mm long and tapered so that the center of the sample was

3mm wide, increasing to a width of 5mm at the ends of the gauge length.

Biaxial and plane strain specimens were strained using the limiting dome height (LDH)

tooling, with a standard 100 mm diameter punch and punch speed of 38 mm/min. Plane strain

was achieved by using the LDH tooling with a 100 mm wide specimen, which was determined

by experimenting with specimens of various widths until plane strain tension was achieved in the

area between the top of the dome and the clamped region of the sheet. Clamping dies were

modified for magnesium sheet by using three small lock beads instead of one large lock bead, as

it typical for steel or aluminum. The die changes were made in order to avoid fractures in the

clamped area and are described in greater detail in [19].

Strain was measured by coating the surface of each sample with a white paint. B lack

paint was then applied in a speckle pattern for use with a digital image correlation (DIC) system

for strain measurement. A Trilion DIC [23] system was used to map the strain during the

stretching experiments. For tensile specimens a facet size of 15 pixels was used. For biaxial and

plane strain specimens the smallest facet size that would not produce gaps in the data was used

and ranged from 29 to 21 pixels. Variation was caused by the uneven size distribution within the

black speckled pattern.

Biaxial and plane strain samples were lubricated by placing a thin layer of boron nitride

paste on the surface of the sample in contact with the punch. Biaxial strain measurements were

taken from the surface of the dome, in the pole area. Plane strain measurements were taken from

the area of the sheet that was determined, experimentally, to be in plane strain, using surface

5

strain measurements, and was located approximately midway between the dome peak and the

clamp.

Optical micrographs were taken in order to observe a much larger area than can be seen

using EBSD. Samples were chemically etched with a solution of 100 ml ethanol, 10 ml water, 5

ml acetic acid and 6 g picric acid.

For convenience RD, TD and ND refer to rolling direction, transverse direction and

normal direction respectively. A plane identified as the RD plane is one whose normal is along

the rolling direction.

Effective strain (𝜖𝑒𝑓𝑓) was calculated using the following equation:

𝜖𝑒𝑓𝑓 = �23

(𝜀12 + 𝜀22 + 𝜀32) (1-1)

where 𝜀1 is the measured strain in the major axis, 𝜀2 is the measured or calculated strain in the

minor axis and 𝜀3 is the measured or calculated strain through the thickness of the sheet. The

following results were used for each strain case:

𝜀𝑢𝑛𝑖𝑎𝑥𝑖𝑎𝑙 ≈ 𝜀1 (1-2)

𝜀𝑏𝑖𝑎𝑥𝑖𝑎𝑙 = 2 ∗ 𝜀1 (1-3)

𝜀𝑝𝑙𝑎𝑛𝑒 = 2√3∗ 𝜀1 (1-4)

6

1.3 Results

Uniaxial tension specimens behaved as previously reported [4] and demonstrated limited

{101�1} compression twinning until the onset of necking, which happens suddenly before failure.

After failure the region in the necked area of the specimen was examined. There was a high

density of compression twins in the area near the crack tip, as shown in figure 1-1. Individual

shear bands were difficult to see because of the large number of twins present.

Figure 1-1: AZ31B specimen pulled to 19% uniaxial tensile strain along the RD. A high density of compression twins is seen in the area around the crack tip.

Using a Scanning Electron Microscope (SEM), a higher magnification image was taken

from a uniaxial sample at the failure site as shown in figure 1-2. The areas with compression

twins are circled in red. When a similar image is taken 2mm farther away from the failure site a

sharp decrease in compression twin activity can be seen as shown in figure 1-3. Again,

RD

TD

7

compression twins are highlighted with red circles. Images taken at 4mm or farther from the

fracture site show little to no compression twins.

Figure 1-2: SEM image showing compression twins in the necked failure region of a uniaxial strained specimen.

These features were inspected with Transmission Electron Microscopy (TEM). A sample

was cut from a region of the material that contained features that are consistent with compression

twins, that is thin straight twins with multiple twins in a single grain. TEBSD analysis with a

step size of 10nm verified that the features were indeed compression twins with a misorientation

angle of 56.8° as shown in figure 1-4.

8

At lower strains of less than 10% shear bands were observed with optical microscopy.

Figure 1-5 shows a shear band that formed in a variable width uniaxial specimen, similar to the

ones used by Kang [21]. The area shown is in the 7% strain region. EBSD analysis showed that

the twins in the shear band were tension twins, as seen in figure 1-6.

Figure 1-3: SEM image showing compression twins 2mm from the necked failure region of a uniaxial strained specimen.

9

Figure 1-4: IPF + IQ image of a compression twin with accompanying grain boundary misorientation graph.

Figure 1-5: Shear band in a 7% strain uniaxial specimen composed of a single line of tension twins.

10

When specimens were stretched in plane strain tension, shear bands formed at much

lower strain levels than in the uniaxial tension case. Figure 1-7 shows a shear band containing

compression twins in a specimen stretched to 4% effective strain. At 8% effective strain, which

is essentially the limit strain for this material in plane strain tension, numerous shear bands have

formed, as can be seen in figure 1-8.

For specimens strained in biaxial tension similar results were seen. At 4% effective

strain shear bands began to form and then became increasingly easy to identify at higher strains.

Figure 1-9 shows three parallel shear bands on the ND surface from a sample stretched to 8%

effective strain. F igure 1-10 is a magnified image of one of the shear bands showing that the

band is indeed populated by a large number of compression twins.

Based on uniaxial tension, plane strain, and biaxial tension testing experiments a forming

limit diagram (FLD) was constructed for AZ31B, as shown in figure 1-11.

Figure 1-6: Tension twin boundaries, shown in red, from a shear band in a uniaxial tension specimen strained to 7%.

11

Figure 1-7: Shear band forming on TD plane, in specimen stretched to 4% effective strain along the RD in plane strain. Dotted white line added for easy identification.

12

Figure 1-8: Multiple shear bands forming on TD plane in specimen stretched to 8% effective strain along the RD in plane strain. Dotted white lines are added parallel to shear bands for ease of identification.

13

Figure 1-9: Image of the ND plane on a sample pulled in biaxial tension to 8% strain, showing three shear bands, with a high density of compression twins in each band.

14

Figure 1-10: Image taken from the same area as Figure 6 at greater magnification, showing compression twins within a shear band.

15

Figure 1-11: Forming limit diagram for 2 mm thick alloy AZ31B at room temperature.

1.4 Discussion of Results

A study conducted by Barnett [20] established an inverse relationship between the

number of twins and the area of shear bands in compressed AZ31B; however, EBSD methods

did not allow for observing the microstructure of the shear bands. T he optical micrographs

shown in figures 1-9 and 1-10 show that shear bands in biaxial and plane strain tension

specimens are populated by compression twins. The study conducted by Kang [21] showed that

the onset of shear bands with a high density of compression twins in uniaxial samples

0

5

10

15

20

25

30

-20 -15 -10 -5 0 5 10

% m

ajor

Str

ain

% minor Strain

Forming Limit Diagram

Parrallel to RD

Perpendicular to RD

Bi-axial

16

immediately precedes diffuse necking and failure. The work by Barnett and Kang and Figures

1-1 through 1-3 show that compression twins appear in large quantities only in the necked region

of uniaxially strained samples where the local strain is very high. The shear bands observed in

biaxial and plane strain specimens are similar to those seen in uniaxial specimens near a failure,

but occur at much lower effective strains.

Kang [21] also observed that specimen thinning occurred very little before failure,

because of the difficulty of c-axis compression in AZ31B. The formation of compression twin

shear bands directly correlates to the reduction of thickness and onset of necking. D uring

uniform straining of a uniaxial tension specimen the strain in the minor direction allows for

strain to occur without an immediate need for c-axis compression. However, in biaxial and plane

strain specimens thinning cannot be delayed because of the imposed strains in the plane of the

sheet. Therefore, the reduction in sheet thickness is accommodated by e arly formation of

compression twin shear bands, compared to uniaxial tension. It is reasonable to conclude that the

relatively low limit strains observed for biaxial and plane strain tension experiments were caused

by early development of shear bands composed of compression twins, compared to the uniaxial

tension case.

The room temperature FLD for AZ31B is not typical for ductile metals because the limit

strain for biaxial tension is about the same as it is for plane strain tension. Typically for

aluminum or steel alloys the biaxial limit strain is significantly greater than it is for plane strain

[24-25]. Similar results to those reported here for AZ31B were reported in another study by

Chino [26], except that the limit strains in both biaxial and plane strain tension were 2% lower

than those measured in the present study. This discrepancy is possibly caused by a combination

of small punch radius and large grid pattern used by Chino.

17

1.5 Conclusions

The microstructure of magnesium alloy AZ31B was examined by optical microscopy for

specimens strained in uniaxial, biaxial and plane strain tension, and the following conclusions

were reached:

(1) Shear bands with a high concentration of compression twins begin to appear at about

4% effective strain in biaxial and plane strain tension specimens.

(2) These shear bands are similar to the shear bands that occur in tensile specimens near a

fracture. Their early appearance contributes to lower limit strains in the biaxial and

plane strain tension specimens.

(3) The measured FLD for alloy AZ31B shows an inverse relationship between shear

band formation and formability. Shear band formation is similar in the plane strain

and biaxial tension cases, and both of these exhibit similar levels of formability. This

behavior is in contrast with other ductile metals, which typically show greater levels

of formability in biaxial tension compared to plane strain tension.

19

2 FORMABILITY AND FAILURE MECHANISMS OF WROUGHT AZ31B MAGNESIUM AT SLIGHTLY ELEVATED TEMPERATURE

2.1 Introduction

Magnesium alloys are gaining popularity in the automotive manufacturing world as a

structural material and as an alternative to steel and aluminum. Over the last 10 years this

increased interest has translated into 20% increase in magnesium consumption [1-2]. Magnesium

is favored due to the fact that it has many mechanical properties that are desirable in structural

parts such as high specific strength, high fracture toughness, good e lectromagnetic shielding,

heat shedding characteristics, recyclability, and vibration and noise damping, among others [3].

However, magnesium’s greatest drawback is its poor formability at room temperature and this

has limited its use for applications where complex shapes need to be formed. The present study

focuses on expanding the usefulness of AZ31B by investigating the relationship between failure

mechanisms and forming temperature for biaxial and plane strain tension, with comparisons to

uniaxial tension.

The poor formability of magnesium at room temperature has been attributed to the HCP

crystal structure and lack of active slip systems [4–7]. A ccording to Taylor, a crystalline

material needs at least 5 independent active slip systems in order to deform into an arbitrary

shape. Metals with a BCC or FCC crystal structure have 6 or 8 independent slip planes due to

their symmetry. Steel, aluminum and copper are examples of these. AZ31B has 5 independent

20

slip systems. If it didn’t it would be as brittle as ceramics. However, the critical resolve shear

stress (CRSS) of these slip systems differs greatly and not all slip systems are active all the time.

AZ31B has a strong basal texture aligning the c-axis of the HCP crystals with the sheet

normal. This texture can be as high as 20x random [26]. Slip in the basal plane is the easiest slip

system to activate with a CRSS of 1 MPa at room temperature in a single crystal [27]. Models

predict that the CRSS for polycrystalline AZ31B is about 10 MPa. The basal plane contains two

independent slip systems, both of which accommodate slip only in the <a> direction. Prismatic

slip allows for a third independent slip system with a component of slip on the basal plane but it

also has a CRSS that is 55Mpa or higher at room temperature. Any thinning of the sheet requires

slip with <c+a> components. The prismatic and pyramidal slip systems each have a slip plane

with <c+a> components, but the CRSS is reported to be as high as 100 Mpa [28].

Measurements of the CRSS of compression twinning have been inconclusive [15, 29-31].

It has been shown that <c+a> slip and compression twinning are competitive modes of c-axis

compression, but the estimates for compression twin CRSS vary greatly, ranging from 25 MPa to

well over 100 MPa [15, 29–31]. According to Ono [32], the primary mechanism for through-

thickness deformation is <c+a> slip which can account for 40% of the total dislocations at room

temperature. H owever, many researchers have observed significant compression twinning

whenever c-axis compression is present [4, 13].

At high strains, compression twins also act as a major contributing factor in fracture

initiation[14–16]. T here have been observations linking crack nucleation with compression

twins. Cracks are seen near and parallel to compression twins in extruded AZ31B and ZK60 bar

as well as rolled AZ31B when pulled in tension [15, 17, 18, 33].

21

Effectively identifying compression twins is rather difficult due to the nature of the twin.

Compression twins are much thinner than tension twins, often reaching only 1µm in width.

Compression twins also do not grow in width as tension twins do when strain is increased.

Multiple parallel twins can also appear in a single grain. Because the surface of the twin is so

small, EBSD data from these areas is often interpreted as noise. With a fine enough scan many

researchers have been able to identify compression twins and verify that the optical features

coincide with compression twin boundaries [15, 20]. O ther researchers have simply

characterized compression twins based on their optical properties [34].

The usual approach to overcoming the low formability of AZ31B is to form the material

at an elevated temperature, typically 250 C or higher [10–12]. When the temperature increases

there is a g reater availability of energy and slip planes activate at lower strains, effectively

increasing the formability of the material. Forming at these high temperatures is expensive and

difficult to implement in a high-volume production environment. It i s therefore important to

study the formability of wrought magnesium near room temperature in order to understand the

failure initiation mechanisms that precede fracture. More importantly, since the majority of part

failures during forming or stamping occur in plane-strain tension [35], focus will be given to

complex strain paths like biaxial and plane strain tension. If an understanding of failure

mechanisms can be gained, then it is possible that the starting microstructure or the forming path

can be manipulated in order to increase formability with limited increase in forming temperature.

To understand the relationship between forming temperature and failure initiation

mechanisms, samples will be deformed at 2% surface strain increments until failure for both 75C

and 125 C . O ptical microscopy will be used to observe large areas of the microstructure.

Forming Limit Diagrams (FLD’s) will also be constructed from the data.

22

2.2 Experimental Procedure

2.05 mm thick sheets of cold rolled magnesium with 3% Al and 1% Zn by w eight

alloying elements (AZ31B) were annealed at 350 C for a minimum of 15 minutes and then air-

cooled outside the oven. Specimens were rough cut using a water-jet before annealing.

Tension specimens were then prepared from the annealed sheets using the ASTM E8 standard

[22, 24]. A gage length of 4 inches was chosen so the heater attached to the Instron would heat

the entire gage length evenly. Tension samples were pulled at a constant crosshead speed of 16

mm/min.

Biaxial and plane strain specimens were strained using the limiting dome height (LDH)

tooling, with a standard 100 mm diameter punch and punch speed of 38 mm/min. Plane strain

was achieved by using the LDH tooling with a 88 mm wide specimen, which was determined by

experimenting with specimens of various widths until plane strain tension was achieved in the

area between the top of the dome and the clamped region of the sheet. Clamping dies were

modified for magnesium sheet by using three small lock beads instead of one large lock bead, as

it typical for steel or aluminum. The die changes were made in order to avoid fractures in the

clamped area and are described in greater detail in the work by Miles [19].

Strain was measured by coating the surface of each sample with a white paint. B lack

paint was then applied in a speckle pattern for use with a digital image correlation (DIC) system

for strain measurement. A Trilion DIC [25] system was used to map the strain during the

stretching experiments. For tensile samples a facet size of 15 pixels was used. For biaxial and

plane strain samples the smallest facet size that would not produce gaps in the data was used and

23

ranged from 29 t o 21 p ixels. Variation was caused by the uneven size distribution within the

black speckled pattern.

Biaxial and plane strain samples were lubricated by placing a thin layer of boron nitride

paste on the surface of the sample in contact with the punch. Biaxial strain measurements were

taken from the surface of the dome, in the pole area. Plane strain measurements were taken from

the area of the sheet that was determined experimentally to be in plane strain, approximately

midway between the dome peak and the clamp.

Tension samples were heated through radiation by placing heating coils on both sides of

the tension sample while it is clamped in the Instron. The coils were maintained at a constant

percentage of their heating capacity until a steady state temperature was achieved. At 75 C there

was a variation of 1 C along the gage length. At 125 C there was a variation of 4 C along the

gage length.

Bi-axial and plane strain samples were heated by conduction with belt heaters attached to

the forming die. Two thermocouples were welded to a sample to measure the temperature, one

at the center of the sample and the other approximately two inches away near the clamp. Again

the heaters were maintained at a specific power level until a steady state temperature was

achieved. At 75 C there was a variation of 1 C within the forming area and at 125 C there was a

variation of 5 C.

Samples for microscopy were cut from the strained specimens using wire electrical

discharge machining (EDM). Cut samples were mounted in a two part epoxy. EBSD samples

had nickel nano-strands added to the epoxy for additional conductivity.

Samples were polished using a series of fine grit sandpapers. Once cleaned, the samples

were exposed only to distilled water for all subsequent polishing steps. O il based

24

monocrystaline diamond suspensions of decreasing size ending with 1 µm diamonds were used

next followed by OP-S colloidal silica.

Optical micrographs were taken in order to observe a much larger area than can be seen

using EBSD. After polishing, samples were chemically etched with a solution of 100 ml ethanol,

10 ml water, 5 ml acetic acid and 6 g picric acid.

For convenience RD, TD and ND refer to rolling direction, transverse direction and

normal direction respectively. A plane identified as the RD plane is one whose normal is along

the rolling direction.

2.3 Results

DIC was used to verify that the stain conditions stated were indeed achieved. Figure 2-1

shows the strain history at a point assumed to be in plane strain. The specimen was deformed at

75 C to failure. As you can see there was very little strain in the minor direction throughout the

deformation. Likewise, when the strain history is seen for a biaxially strained specimen at 75 C,

as shown in figure 2-2, you c an see that the point of interest demonstrated biaxial strain

throughout the experiment.

When a biaxial sample strained to 12% effective strain at 75 C is viewed under an optical

microscope we see a distinct absence of shear band formations as shown in figures 2-3 and 2-4.

In room temperature samples strained to 4% shear bands formed near the edge and propagated

inward with twins occupying almost the entire edge. With 3 times more strain we would expect

25

Figure 2-1: Strain history for a point undergoing plane strain.

to see at least as much twinning and shear band formation. However, all twin formation appears

to be very limited. Tension twins formed throughout the material but at a much lower frequency

and never in groups or shear bands.

26

In plane strain samples strained to 5% at 75 C we see similar results as shown in figures

2-3 and 2-4. In figure 2-5 we see a much stronger concentration of twins and they almost appear

to be forming a shear band. However, there is no continuity between the twins except proximity.

Outside the image there are no more twins. This group of twins appears to be forming the

earliest stages of a shear band that never fully developed. Images elsewhere in the sample also

show no indication of shear band formation.

Figure 2-2: Strain history for a point undergoing biaxial strain

27

Figure 2-3: Microstructure near the center of a biaxial sample strained to 12% at 75 C

An FLD for AZ31B at 75 C is constructed from the forming data and is presented in

figure 2-6. T he FLD departs from the unusual FLD shape as t he biaxial strain increases

significantly. The limit strain in plane strain tension also increases, but to a much lower degree.

As can be expected, samples strained at 125 C showed no shear band formation. Figure

2-7 shows the greatest concentration of twins that could be found on any sample strained at 125

C. The FLD shown in figure 2-8 shows that formability has continued to increase in a manner

similar to the 75 C results.

28

Figure 2-4: Mirostructure near the edge of a biaxial sample strained to 12% at 75 C

29

Figure 2-5: Microstructure near the edge of a plane strain sample strained to 5%at 75 C. The twins shown appear to be the stunted beginnings of a shear band that never fully developed

30

Figure 2-6: Forming Limit Diagram for AZ31B at 75 C

0

5

10

15

20

25

30

35

40

-30.00 -25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00

Maj

or S

trai

n

Minor Strain

FLD for 75 C

31

Figure 2-7: Microstructure at the edge of a plane strain sample strained to 5% at 125 C.

32

Figure 2-8: Forming Limit Diagram for AZ31B at 125 C

2.4 Discussion of Results

The dominant failure mechanism in AZ31B for samples strained in tension or

compression at room temperature is thought to be void nucleation near compression twins [4,

13]. When the material starts to thin, which is late in the evolution of the microstructure, the

compression of the c-axis causes compression twin nucleation and eventually void nucleation.

When forming tests are conducted at 75 C we see st artling differences. T here is no

evidence of shear band formation or compression twin nucleation. Tension twins form

throughout the material but at a relatively low density and never in groups or bands. This

apparent lack of compression twins prior to failure may be justified by Agnew [36] when he

proposed that the ratio between the CRSS for <a> and <c+a> slip in AZ31B could be as small as

0

5

10

15

20

25

30

35

40

45

-40 -30 -20 -10 0 10 20

Maj

or S

trai

n

Minor Strain

FLD for 125 C

33

2-2.5. This countered his own earlier results which asserted that the value of the CRSS for non-

basal slip was significantly higher.

In a study conducted by Chapuis and Driver [31], a single crystal of AZ31B was

preferentially aligned for <c+a> slip and then strained. T he crystal twinned instead, forming

compression twins until the sample was heated to over 200 C. T he activation energy of the

compression twin was over 100 MPa. Further study by the same researchers estimated the CRSS

for <c+a> slip at 20 MPa. In addition, they showed a strong inverse correlation to the forming

temperature and the CRSS of compression twinning and <c+a> slip [30], both of which

decreased at roughly the same rate.

There is no disputing the fact that there is some <c+a> slip at room temperature [32], but

compression twinning was seen to be the primary means of c-axis compression when thinning

was imposed during biaxial and plane strain forming experiments. However, at even modestly

elevated temperatures of 75C and 125C, compression twinning ceases to be the dominant

mechanism of c-axis compression and instead it is reasonable to assume (based on a l ack of

compression twinning and shear band development) that <c+a> slip becomes dominant, thus

increasing the forming limits of AZ31B significantly, compared to that seen at room

temperature. The CRSS for <c+a> slip reaches a t hreshold, below which the local stresses at

each grain is relieved by <c+a> slip and never builds high enough for compression twinning.

The change in biaxial formability when forming temperature is increased by 50 C is

surprising. Figure 2-9 shows the results of all three forming limit diagrams for comparison.

During biaxial forming, the strain of the sheet thickness must accommodate for stretching of the

plate in both directions. This increase in formability is likely due to the decrease in local stress

in biaxial samples

34

The basal texture of AZ31B causes the c-axis to be parallel to the sheet normal, but it has

no effect on the orientation of the grain around that axis. Grains have a random rotation around

the sheet normal. To an individual grain, this makes little difference. Slip directions can rotate

only 30 de grees from the global strain before they start becoming redundant. O n a

polycrystalline scale, however, this means that the second independent <a> slip component of

each grain is plus or minus 30 from parallel to the global strain, increasing the CRSS for that slip

system. With every grain stressed in the same direction, polycrystalline deformation become

more difficult. Local strains in a biaxial sample relieve stress in every direction. B ut local

strains in plane strain samples can only relieve stress transverse to the major strain axis. Because

the global strain in the minor direction for a plane strain sample has to be zero, any strain along

Figure 2-9: Forming limit diagram comparison of AZ31B at 25, 75 and 125 C

35

the major strain axis increases the local stress on the neighboring grains. This stress increases

until a grain deforms in the transverse direction, relieving the built up stress. This stress

concentration is a likely site for void nucleation, which would cause premature fracture.

Disrupting the texture of AZ31B has little effect. In fact, Delvalle [37] determined that

the optimal forming criterion for AZ31B is basal texture with 10 µm grain size, which was the

microstructure of every sample used in this study. If a high forming temperature is undesirable,

then the most effective way to increase the formability of wrought AZ31B magnesium is to

increase the forming temperature by 50 C and design a forming process that avoids plane strain

while emphasizing biaxial and uniaxial tensile strains.

2.5 Conclusion

Forming AZ31B at elevated temperatures has led to the following conclusions:

1) Compression twins were not visible in samples strained in biaxial and plane

strain.

2) The temperature dependence of the CRSS for <c+a> slip and compression

twinning is roughly the same. However, the decrease in CRSS for <c+a> slip

reaches a threshold where compression twinning is no l onger needed for c-

axis compression, even near the limit strains of the material.

3) With compression twinning no longer present the failure initiation mechanism

is no longer tied to void nucleation along compression twins. A t higher

strains the local stress states in plane strain tension specimens cannot be

relieved as easily as in biaxial tension specimens, resulting in relatively

greater forming limits for biaxial tension.

37

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