Experimental Study of Fracture Behavior of Magnesium

Single Crystals

V. Kaushika, R. Narasimhana,, R.K. Mishrab

aDepartment of Mechanical Engineering, Indian Institute of Science,Bangalore 560012, India. Tel: +91-80-22932959

bGeneral Motors Corporation, 30500 Mound Rd., Warren, MI 48090, USA

Abstract

In this work, the fracture behavior of magnesium single crystals is stud-

ied by conducting experiments with notched three point bend specimens of

three crystallographic orientations. In the first and second orientations, the

c-axis is along the normal to the flat surface of the notch, while in the third

it is aligned with the notch front. For all the orientations, in-situ electron

back scattered diffraction observations made around the notch root show pro-

fuse tensile twinning of {1012}-type. Further, in the first two orientationsbasal and prismatic slip traces are identified from optical metallography. The

width of the most prominent twin saturates at around 120 - 150 m, while

twins continue to nucleate farther away to accommodate plastic deformation.

In all the orientations, crack initiation occurs before the attainment of peak

load and the crack grows stably along twin-matrix interface before deflect-

ing at twin-twin intersections. Results show that profuse tensile twinning

is an important energy dissipating mechanism that enhances the fracture

Corresponding author.Email address: narasi@mecheng.iisc.ernet.in (R. Narasimhan )

Preprint submitted to Materials Science and Engineering: A November 30, 2013

toughness.

Keywords: Magnesium single crystals; Fracture behavior; Tensile twinning;

Fracture toughness; crack deflection; EBSD

1. INTRODUCTION

Magnesium alloys are well known for their mechanical properties such as

high specific strength at room temperature and low density as compared to

the commonly used aluminum alloys, making them prospective candidates for

applications in aerospace and automobile industries. However, poor corrosion

resistance and low fracture toughness (Yan et al., 2004) impedes their usage.

Most research pertaining to mechanical behavior of magnesium has focused

on understanding tension/compression asymmetry (Barnett, 2007; Knezevic

et al., 2010), stress-strain response (Wonsiewicz, 1966; Kelley and Hosford,

1968; Fernandez et al., 2011) and texture changes (Brown et al., 2005; Graff

et al., 2007). By contrast, few studies have been devoted to investigating the

fracture response of Mg.

Deformation twinning is particularly important in crystals of lower sym-

metry (e.g, HCP metals), where the Von Mises criterion for general defor-

mation may not be satisfied due to the absence of five independent slip sys-

tems. Kelley and Hosford (1968), and Wonsiewicz (1966) investigated the

formation of different types of twins along with slip activities by conducting

channel die compression experiments on magnesium single crystals corre-

sponding to various orientations. They concluded that extension of c-axis

is predominantly accommodated by {1012} tensile twins (TTs), owing totheir low critical resolved shear stress (CRSS), while contraction of c-axis

2

is accommodated through pyramidal< a + c > slip along with {1011} con-traction twins (CTs). This claim was further substantiated by Yoo (1981)

who indicated that only {1012} tensile twin-type and {1011}, {1013} con-traction twin-types are active in Mg. Recent experimental work has focused

on polycrystalline magnesium alloys owing to their application in structural

components. Studies by Barnett (2007) on alloy AZ31 have indicated that

extensive tensile twinning may enhance ductility of the alloy. Further, ex-

perimental observations by Knezevic et al. (2010) on AZ31 have shown that

formation of CTs cause strain hardening while TTs are found to contribute

very little to strain hardening. Also, they reiterate that extensive formation

of TTs enhances ductility.

In magnesium alloys the fracture toughness can be as low as 7-20 MPa

m

(Yan et al., 2004; Somekawa and Mukai, 2006) which will impede their ap-

plication as structural components. Therefore, the operative fracture mech-

anisms and crack growth resistance of magnesium alloys need to be carefully

investigated. To understand whether cleavage of basal {0001} plane (Schmid,1931) and prismatic {1010} plane (Schiebold and Siebel, 1931) is observedin magnesium, Reed-Hill and Robertson (1957) performed tension experi-

ments on Mg single crystals with loading axis on the basal plane. These

experiments showed parting along {3034} habit plane unlike the commonlyobserved basal cleavage in HCP metals. Further, they noted that for the

crystal orientations considered in their work, the fracture mechanism is un-

affected by the presence of {1012} twins. From their channel die experiments,Kelley and Hosford (1968) reported reduced ductility in Mg single crystals

oriented for compression along c-axis and attributed it to the formation of

3

{1011} twins.Yan et al. (2004) noted that there is a transition in fracture mechanism

from brittle to ductile with decrease in constraint level in AM60 Mg alloy.

Similar transition was observed by Mukai et al. (2001) in AZ31 Mg alloy

with refinement in grain structure. Somekawa et al. (2009) and Somekawa

et al. (2010) conducted fracture experiments on coarse-grained (grain size of

50 m) and fine-grained (grain size of 5 m) AZ31 Mg alloy, respectively.

They noted that in the fine-grained alloy, sub-grain structures form near

the crack tip promoting blunting and ductile fracture occurs by void growth

and coalescence. On the other hand, the formation of TTs near the crack

tip in the coarse-grained alloy causes premature crack growth along the twin-

matrix interface leading to slightly lower fracture toughness. Somekawa et al.

(2009) attributed the reason for crack growth along the twin-matrix inter-

face to dislocation pile up at the twin boundary and incompatibility in the

strains at the interface. By contrast, experiments by Yu et al. (2012) on Mg

single crystals indicated that nanotwins formed near the crack tip to shield

it and promote crack blunting. Similar observations of crack blunting due to

formation of tensile twins were made by Govila (1970) in Be single crystals.

In order to obtain a clear understanding of the fracture behavior of Mg,

a systematic study of interaction of tensile twins with a notch or crack tip

under mode I loading needs to be conducted. Also, the dependence of lattice

orientation with respect to the notch surface or crack plane on twin evolu-

tion and fracture resistance should be examined. These issues may be better

studied using Mg single crystal fracture specimens rather than with a poly-

crystalline Mg alloy. Such a study will allow for tracking the evolution of

4

individual twins, their interaction with neighboring twins of the same and

different variants and also with a notch tip. To this end, systematic fracture

experiments using pre-notched three point bend specimens of Mg single crys-

tals are conducted within a scanning electron microscope (SEM). Specimens

having three different crystallographic orientations are considered. In two of

the orientations, the normal to the flat surfaces of the notch coincides with

the c-axis, whereas in the third the notch front is aligned along the c-axis.

In-situ observations on the evolution of twins near the notch are made us-

ing electron backscattered diffraction (EBSD). Also, optical metallography

is performed on the unloaded specimens to examine the slip and twin traces

and the crack path. Fractographic observations are conducted to understand

the operative fracture mechanism. The results show that in all orientations

studied, profuse TT formation occurs ahead of the notch tip and contributes

to toughening. However, crack growth occurs along boundary of a promi-

nent twin and gets deflected at twin-twin intersections. In a follow-up work

(Kaushik et al., 2013), finite element simulations are conducted to provide

further insights on the mechanics of fracture of Mg single crystals.

2. Experimental Procedure

2.1. Specimen details

The experiments are conducted using edge-notched three point bend

(TPB) specimens as shown in Fig. ??. Three orientations are chosen in

this study. In the first and second orientations, referred to in the sequel as

orientations A and B, the normal to the flat surface of the notch (X2 axis)

is aligned along [0001]. In orientation A, the notch front (X3 axis) is along

5

[1210] direction and the crack growth direction (X1 axis) is along [1010]. In

orientation B, the above mentioned notch front and crack growth directions

are interchanged. Orientation C mimics the basal-textured magnesium al-

loys with the c-axis along X3, while [1210] and [1010] are along X2 and X1,

respectively. The dimensions of the tested specimens pertaining to the three

orientations are summarized in Table 1.

2.2. Specimen preparation and test set-up

The specimens are cut using electric discharge machining (EDM) from

short cylinders of Mg single crystals, grown from seed crystals. A notch of

radius ro = 200 m is machined using EDM up to the center of each specimen

along the width. The specimens are chemically polished with 83% ethanol,

10% HCL, and 7% HNO3, followed by etching and electropolishing. After

preparing the specimens, EBSD scans in the form of inverse pole figures

(IPF) and image quality (IQ) maps are obtained to check the correctness of

the initial lattice orientation.

The experiments are carried out in LEO-1550 SEM so that it is possible

to make detailed in-situ observations of crack initiation and growth. It is

coupled with EBSD hardware to obtain scans at intermediate loading stages.

This hardware, obtained from EDAX, USA, has a resolution of up to 1 m

supplemented with high speed cameras to expedite the data acquisition. The

SEM is also fitted with a miniature three point bend (TPB) stage procured

from DEBAN, UK, to conduct the fracture tests. The TPB stage is mounted

in the SEM such that it is tilted at an angle of 700 with respect to the horizon-

tal plane. This angle is optimum for acquiring good quality EBSD patterns.

It is ensured that the load on the specimen remains at zero before conducting

6

the experiment. The load cell of the TPB stage has a maximum capacity of

200 0.2 N. A lead-screw attached to the loading pin, threaded clockwise atone end and anti-clockwise at the other imparts displacement to the loading

pin at a rate between 0.1 mm/min to 1.5 mm/min. For the present exper-

iments, a displacement rate of 0.1 mm/min is used. The test is interrupted

at different stages to capture EBSD data and SEM images in the loaded con-

dition. It has been noticed that slip traces on single crystal specimens can

be better visualized using an optical microscope (Patil et al., 2009; Biswas

et al., 2013). Hence, in some cases the specimen is unloaded and taken out

in order to observe it using an optical microscope. The optical images are

taken using Zeiss Axio Vert.A1 microscope. The surface profilometry was

conducted using a Vecco profilometer.

3. Results and discussion

3.1. Load versus displacement curves

The recorded load (P) versus load point displacement () curves are

shown in Fig. ??(a) for all three orientations. The P- curves for all three

orientations show a bilinear behavior until peak load is reached. Thus, for

the sake of illustration, the curve for orientation B has been divided into

parts HI and IJ in Fig. ??(a). The part HI of the curve with a steep slope

depicts an overall elastic response, while IJ with a reduced slope indicates

elastic-plastic behavior. Numerous serrations are observed in the elastic-

plastic regime (part IJ) of the load-displacement curve. In order to visualize

the serrations better, a magnified view of a region between points E ( =

0.2 mm) and F ( = 0.3 mm) of the P- curve for orientation B is shown

7

in Fig. ??(b). The load drops, giving rise to a saw-tooth like appearance,

are found to correspond with the nucleation of twins which result in sudden

increments in tensile strain (Reed-Hill, 1972).

From in-situ observations in the SEM, the crack initiation stage is noted

and indicated by o on the P- curves (refer Fig. ??(a)). Also, the peak

load is marked by . In all cases, the crack initiates before the peak loadis attained and grows in a slow, stable manner. On comparing the three

orientations, it can be seen that orientation C hardens the most (has the

largest slope of P- curve in the inelastic regime) and attains the highest

peak load, while orientations A and B have similar (but lower) hardening

rates.

3.2. Twin nucleation and growth at the notch root

EBSD data was acquired at different stages of loading and post-processed

to obtain IPF and IQ maps of the scanned surface. Fig. ??(a) represents the

IPF of the as-polished specimen, for orientation A. In the IPF, the lattice

vector parallel to specimen surface normal at any point on the surface char-

acterizes the orientation of that point which is displayed within a standard

triangle in the stereographic projection using a color code. The region F

indicated in the IPF shown in Fig. ??(a) corresponds to unindexed data.

Surface damage during polishing may be responsible for giving rise to the

unindexed data. However, other than this small region, the rest of the sur-

face in Fig. ??(a) is free of residual strains.

Fig. ??(b)-(d) correspond to IQ maps of orientation A at different stages

of deformation. The OIM software identifies the different twin types by color-

ing the twin boundary with a specific color. For example, TT is identified by

8

red color in the IQ maps (refer Fig. ??(b)-(d)). It can be observed from the

above figures that wedge-shaped twins labeled as W and V have nucleated at

the notch root and grown in the region ahead of it. It appears that twin W

is the prominent one (as can be seen from the greater width and length) and

is the first to nucleate at the notch root. The width of this twin is measured

using the image processing software Image-J and is plotted against load P

using a solid curve in Fig. ?? along with similar variation for orientation B

to be discussed subsequently. From the curve it can be seen that up to P

= 2.5 N the twin width increases slowly (since the specimen is experiencing

predominantly elastic deformation). Beyond this load level, an accelerated

growth of the twin width is observed up to P = 5 N followed by a phase

where the twin width saturates at a value of about 120 m. The last phase

coincides with nucleation of twins farther away from the notch root (refer

Fig. ??(d)). It can be concluded that once the growth of the initially formed

twin near the notch root tends towards saturation, new twins nucleate farther

away rapidly to accommodate plastic deformation.

Twin growth occurs due to motion of the twinning dislocations into the

matrix (Christian and Mahajan, 1995). At early stages of deformation this

dislocation motion takes place with fewer obstacles and interactions and

hence, requires lower stresses. At later stages, due to greater dislocation

interactions, higher stresses are required to cause dislocation motion. These

dislocation interactions and the consequent hardening resist twin growth,

promoting the tendency for the twin width to saturate. Also, the twins that

nucleate early grow with less hindrance as compared to the ones that nucleate

later.

9

The notation used for the various tensile twin variants is indicated in

Table 2. Further, the table summarizes the angle made by each twin variant

with the notch line for orientations A, B and C which are denoted by a,

b and c, respectively. Here, positive is measured in the counterclockwise

sense with respect to the notch line (i.e., X1 axis). The twin traces observed

in the IPF/IQ maps are identified by comparing the angles made by them

with the X1 axis against the values indicated in this table. In this manner,

the twin variants seen in Fig. ?? for orientation A (as well as for other

orientations to be discussed below) are summarized in Table 3. For example,

the twin trace labeled as W in Fig. ?? corresponds to variant TT1 or TT2.

Fig. ??(a) shows the IPF of the as-polished specimen for orientation B. It

can be seen from the figure that unlike orientation A, the as-polished surface

of this specimen has twins induced during polishing. These twins are labeled

as E and F and will be referred to in the sequel as polishing twins. The

lattice orientation inside these twins is represented by HCP unit cells along

with that of the matrix which is marked by G. It can be seen that, the

lattice has rotated by 86 degrees inside the twinned region with respect to

the matrix. Fig. ??(b)-(d) show the IPF maps of orientation B at various

load levels. Polishing twin E acts as an obstacle for nucleation and growth

of twins in the region above the notch line and, hence, predominant twin

activity takes place only below the notch line.

In general, twin growth can occur by lengthening and widening of an in-

dividual twin or through coalescence with adjacent twins of the same variant

(Ostrikov, 2012). The growth of twin F occurs by the second mechanism as

seen in Fig. ??(b)-(d) where twin M nucleates at the notch root and coalesces

10

with twin F. Twin trace X also grows through twin-twin coalescence. The

lengthwise extension of twin L is obstructed by twin F and it grows only

through widening. This obstruction takes place due to twin boundary inco-

herency and geometric incompatibility (Christian and Mahajan, 1995; Os-

trikov, 2012). Similarly, lengthwise extension of twin X is hindered by twin

Y as seen in Fig. ??(c) and ??(d). On the upper half above the notch line,

the growth of twin U is deterred by the polishing twin E and a secondary

twin T forms inside the latter as shown in Fig. ??(b). These intersecting

twins do not cross each other.

The width of twin F which appears to have grown to the maximum extent

is plotted against the load P in Fig. ??. The twin widening trend in this case

is similar to that exhibited by the prominent twin in orientation A. Thus,

there is an initial slow growth phase when the specimen experiences predom-

inantly elastic deformation, followed by rapid widening and saturation at a

value of about 140 m.

In Fig. ??, EBSD maps for orientation C are presented corresponding

to different load levels. Fig. ??(a) represents the IPF of the as-polished

specimen. In Fig. ??(b)-(d), IPF maps around the notch root with increase

in load are shown. On examining Fig. ??(b) and (c), it can be observed

that unlike in orientations A and B, TTs nucleate away from the notch

root (especially close to the load application zone) and extend towards the

notch with increase in load level (see for example, TTs marked as K and

N). As before, the TT variant to which these twins correspond is identified

and indicated in Table 3. The HCP unit cell is shown in Fig. ??(c) inside

twinned regions K and N as well as in the matrix (marked as O). With further

11

increase in load to a level of 9.6 N, faint trace of twin Z which belongs to

a different variant as compared to K and N forms as seen from Fig. ??(d).

Thus, from Table 3 it can be noted that three types of twin traces form due

to deformation around the notch root in orientation C. This is in contrast

to orientations A and B where only two types of twin traces occur during

deformation (apart from the pre-existing polishing twins).

Fig. ??(d) shows that except for a small region R about 150 m in size

surrounding the notch root profuse tensile twinning has taken place ahead

of the notch. It is well known that TTs can lead to c-axis extension. Since,

c-axis is aligned parallel to specimen thickness for this orientation, this ob-

servation implies that predominant region ahead of the notch experiences

out-of-plane bulging which will be confirmed later from surface profile maps.

This is contrary to known behavior exhibited by isotropic plastic solids which

show out-of-plane contraction on the free surface (Narasimhan and Rosakis,

1990). In region R, no TT traces are observed which suggests that there

is no c-axis extension in this region. High resolution EBSD images did not

show any CT activity as well in region R. In order to ascertain if dislocation

activity (especially on pyramidal< a+ c > system which can cause out-of-

plane contraction) occurs close to the notch root, a TEM study needs to be

performed. This study, however, has not been conducted in the present work.

3.3. Observations of slip and twin traces from optical metallographs

Optical microscopy is used to observe slip traces on the specimen surface

which are otherwise difficult to perceive from in-situ SEM images. An optical

metallograph of a fractured specimen corresponding to orientation A is shown

in Fig. ??(a). The slip traces are classified as S1 and S2 corresponding to basal

12

and prismatic slip systems, respectively. From Fig. ??(a), S1 slip traces can

be noticed at the notch flanks and beyond the extended crack tip, whereas

the region around the extended crack shows S2 slip traces. Also, faint twin

traces belonging to two variants can be perceived in Fig. ??(a). On closely

examining Fig. ??(a), slip traces inside a twinned region (secondary slip

traces) can be observed. Thus, it can be seen that RQ representing slip trace

S1 in the matrix region is deflected by 860 in the twinned region (see trace

QP).

Since the flat surface of the notch coincides with basal plane in both

orientations A and B, the slip activities are found to be identical as can

be seen from Fig. ??(b). Thus, S1 slip traces are observed along the notch

flanks while S2 slip traces are noticed in the region ahead of the notch where

crack extension has occurred. Also, secondary slip traces (i.e., within twins)

are observed in the magnified region of the fractured sample corresponding

to orientation B in Fig. ??(c). Thus, in this figure, HI and JK are S1 slip

traces in the untwinned region, whereas IJ is the deflected slip trace inside

the twinned region by 860.

3.4. Twin volume fraction development through the thickness

As seen in Sec. 3.2, the IPF and IQ maps show profuse tensile twin-

ning around the notch root for all three orientations studied in this work.

Twinning is a three-dimensional phenomenon, whereas the twin traces ob-

served on the free surface are intersections of the twin boundaries with the

surface. Hence, in order to get a perspective of the 3D nature of the twin

boundaries, EBSD data for orientation A was obtained at the quarter-plane

and mid-plane of the specimen in addition to the free surface. To this end,

13

the unloaded specimen was chemically polished and etched (so that external

straining of the crystal is prevented) to reduce the thickness up to the desired

plane (quarter-plane and mid-plane) and subjected to EBSD analysis. The

IQ plots taken around the notch root for orientation A at the free surface,

quarter-plane and mid-plane after unloading the specimen from a load of 5.8

N are shown in the Fig. ??(a)-(c). On examining these figures, it may be

seen that the development of twin traces in all three planes is similar. In

fact, many twins can be seen to extend completely through the specimen

thickness (see for example, the twin marked as W).

The average twin volume fraction (fatt) is quantified at the three planes

indicated above in order to understand its through-thickness variation. For

this purpose, a planar region PQRS is chosen as shown in Fig. ??(a)-(c).

The area enclosed in this region is first calculated precisely using Image-J

software. Next, the area enclosed by each individual twin is determined by

constructing a polygon along its periphery and calculating the area enclosed

by it. The average twin volume fraction fatt considering a thin slice of material

can then be defined as the ratio of the total area enclosed by all the twins

in the planar region PQRS to the area of this region. By employing this

procedure, the average twin volume fraction at the free surface, quarter-

plane and mid-plane are evaluated to be 0.24, 0.27 and 0.25, respectively.

Thus, it can be concluded that in orientation A twin volume fraction does

not vary much through the thickness.

In Fig. ??(d) and (e), IQ plots for orientation C at the free surface and

mid-plane obtained after unloading the specimen from a load of 18.3 N are

shown. On comparing Fig. ??(d) and (e), it may be seen that there is a

14

strong 3D character to the development of TTs near the notch root in this

case. Thus, there is more profuse distribution of twin traces in the mid-plane

as compared to the free surface. Indeed, many of the twin traces seen at

the mid-plane cannot be observed on the specimen free surface. Further, the

twins appear wider (i.e., they have grown or coalesced more with adjacent

twins) in the mid-plane than on the free surface. However, three TT variants

can be noticed on both the surfaces (as opposed to two in case of orientation

A). Also, the twin traces do not extend up to the notch root in both the

mid-plane and free surface. In other words, in a small neighborhood of the

notch root, no TTs are observed, which is in contrast to orientation A.

As before, the average twin volume fraction within the rectangular region

PQRS marked in Fig. ??(d) and (e) is determined using image processing. It

is found that the average twin volume fraction fatt at the mid-plane is 0.89 and

is greater than that at the free surface which is 0.78. Therefore, orientation

C, unlike orientation A, shows considerable through thickness variation of

twin volume fraction.

3.5. Energy release rate J and average twin volume fraction fatt versus load

The energy release rate J was computed from the load-displacement

curves presented in Fig. ??(a) using the deep crack formula given by Rice

et al. (1973). This can be written as:

J =A

Bb, (1)

where is a shape factor, b is the uncracked ligament length (W -a), B is

the specimen thickness and A is area under the P- curve. The shape factor

15

is generally taken to be 2 for deeply cracked bend specimens in isotropic

plastic solids (see Rice et al., 1973). However, in the context of Mg single

crystals it is calibrated to be 1.65 by comparing with J computed using the

domain integral method from finite element analysis results (Kaushik et al.,

2013).

The energy release rate J determined by the above procedure is plotted

against load P for all the three orientations in Fig. ??(a) up to crack initiation

stage, which is marked on each of the curves by o. The J values at crack

initiation are 12.21, 4.5 and 10 N/mm for orientations A, B and C, respec-

tively. The notched fracture toughness value Jc of orientation A is slightly

higher than orientation C but it is more than twice that of orientation B.

Although crack initiation load Pc of configuration C is much more than that

of A (refer Fig. ??(a)), it does not reflect in the notched fracture toughness

value. This is because the total work done (comprising predominantly of

plastic dissipation) up to load Pc is greater for orientation A as compared to

the other two orientations.

As in Sec. 3.4, average twin volume fraction fatt is computed over a rect-

angular region surrounding the notch root from the IPF or IQ maps on

the specimen free surface which were presented earlier (see, for example,

Fig. ??(a)). The evolution histories of fatt are plotted against load P for

all the three orientations in Fig. ??(b). This figure indicates that the twin

growth rates for orientation A and B are similar in the early stages although

for the latter fatt starts evolving from a non-zero initial value due to presence

of polishing twins. However, fatt in this case saturates at a value of about 0.2

as load increases while that for orientation A continues to enhance steeply.

16

Also, although the width of the prominent twin close to the notch root in

orientation A and B saturates at a low load level (refer Fig. ??), the twin

volume fraction around the notch continues to increase as an outcome of

progressive nucleation of twins farther away. In contrast to orientations A

and B, twin volume fraction evolves gradually with load for orientation C.

The trends exhibited by the energy release rate J versus load P for the

three orientations in Fig. ??(a) corroborate well with the evolution histories

of average twin volume fraction around the notch root shown in Fig. ??(b).

This confirms that energy dissipation in all three orientations occurs predom-

inantly due to tensile twins. Thus, the fast twin volume fraction evolution

exhibited by orientation A leads to rapid dissipation in the inelastic zone

and high toughness. Also, the lowest Jc displayed by orientation B despite

its similarity with orientation A may be attributed to saturation in average

twin volume fraction. This has occurred due to presence of pre-existing pol-

ishing twins which have impeded the nucleation and growth of deformation

twins around the notch root.

3.6. Extended crack trajectories

On referring to Fig. ??(a), it can be seen that the crack grows in an in-

clined manner before deflecting instead of following a straight path typically

observed in isotropic plastic solids subjected to mode I loading. Also, it can

be noted from Fig. ??(a) that the crack extends initially along a twin bound-

ary MN which is parallel to twin W (refer Fig. ??). When it encounters a

twin-twin intersection point N, it is deflected along line NO (which is parallel

to twin V indicated in Fig. ??). Fig. ??(a) shows a SEM image of specimen

corresponding to the same orientation, where the crack growth segment MN

17

is seen to be parallel to the twin trace BC. It is noticed that further crack

growth seems to occur along two different twins nucleating at the extended

crack tip O. This suggests that twin formation during crack growth may also

dictate the crack growth direction.

Similar observations can be made in the specimen corresponding to ori-

entation B from Fig. ??(c). The extended crack MN grows into a twin or

along a twin boundary and gets deflected at the intersection point N of two

twins belonging to different variants. The deflected crack NO grows along the

twin-matrix boundary. Thus, it can be concluded that twin-matrix interface

is the preferred crack growth path due to strain incompatibility and high

stress concentrations (Somekawa et al., 2009). Indeed, it has been observed

in Fe-Si single crystals (Berry, 1959 and Hull, 1960) that slip steps formed

at the twin-matrix interface due to dislocation dissociation into partials pro-

duces a line of weakness that increases the stress concentration. The scanning

electron micrograph shown in Fig. ??(b) confirms deflection of crack path (as

segments MN-NO) for the specimen pertaining to orientation B. The crack

also forks at point N. Thus, a faint trace of a micro-crack NP which extends

along MN but has arrested subsequently can be perceived. This suggests

that at the intersection point N of two twins, deflection of the crack is fa-

vored from an energetic standpoint (i.e, it possibly results in higher energy

release rate). The above issue will be addressed in a follow-up work from

finite element simulations incorporating discrete twins near the notch root

(Kaushik, et.al., 2013).

18

3.7. Fracture surface morphology

Fractography is performed in order to understand the underlying fracture

mechanism. The specimens were broken manually in liquid nitrogen so that

the fracture surface features remain preserved. Fig. ??(a) shows the SEM

fractograph of the specimen corresponding to orientation B, where the region

above the red line denotes the fracture surface formed due to deformation of

the specimen during three point bend loading. A high magnification image

of zone A indicated in the Fig. ??(a) is displayed in Fig. ??(b). This figure

shows that the fracture surface slants towards the free surface starting from

the ridge denoted as PQ. This suggests that the fracture surface does not

necessarily conform to the boundary of a twin at the notch root as implied

above on the basis of the optical image taken on the free surface (Fig. ??(c)).

Instead, it possibly cuts into the twinned region in the specimen interior.

On either side of the ridge PQ, one observes slanted surfaces which con-

tain elongated parallel stripes (see, for example, those marked by RS and

TU). These stripes correspond to the intersection of parallel twins (belong-

ing to a variant different from the one along which the crack has extended)

with the fracture surface (see Fig. ??(b)). The surfaces of the stripes are

relatively smooth implying that they have been sheared as the crack prop-

agates. However, some dimples may be seen inside the stripes which have

been shown encircled in Fig. ??(b). These dimples possibly arise due to dis-

location activity in the twinned region and the matrix. The vertical stripes

below the red line in Fig. ??(a) have formed when the specimen was broken

open manually.

19

3.8. Surface profilometry

As mentioned in Sec. 3.2, tensile twinning ahead of the notch in the case

of orientation C suggests occurrence of out-of-plane bulging. In order to

confirm this hypothesis, surface profilometry scans are carried out for this

case up to a distance of 200 m, 350 m, 550 m and 850 m, in front of the

notch root which are shown in Fig. ??(a)-(d). In each of the above figures, 2D

contour maps of the surface as well as variations of the surface profile along

horizontal lines XY are displayed. In the contour maps, the blue and green

regions experience out-of-plane contraction whereas the yellow and red zones

show out-of-plane bulging. On examining Fig. ??(a), it can be seen that close

to the notch root there is out-of-plane contraction which is also confirmed

from the line plot of the surface profile taken along XY. At a distance of

110 m from the notch root (refer Fig. ??(b)), it can be seen that the data

along XY can be divided into 3 regions. Regions P and R correspond to

out-of-plane bulging, whereas region Q pertains to out-of-plane contraction.

Fig. ??(c) and (d) represent surface profiles farther away from the notch and

show that there is out-of-plane bulging with almost no region of contraction.

It should also be noted that out-of-plane extension increases with distance

from the notch root (i.e., as the load application zone is approached).

The out-of-plane bulging at large distances ahead of the notch root which

give rise to tensile twinning as seen in Fig. ??(b) - (d) can be rationalized

as follows. The uncracked ligament ahead of the notch tip is subjected to

bending and hence comprises of zones experiencing tensile and compressive

normal stress 22 which are separated by a plastic hinge point. This point is

found to be close to the notch tip (Kaushik et.al., 2013). Thus, the normal

20

stress on the plane ahead of the notch tip is tensile very close to the notch

root (region R in Fig. ??(d)) and farther away, it becomes compressive. This

compressive normal stress on the ligament, coupled with the compressive

contact stress field close to the loading pin at the edge of the specimen causes

out-of-plane extension due to plastic incompressibility. The numerical results

of Kaushik et.al.(2013) also corroborate with the difference in twin activity

between the mid-plane and free surface for this orientation (Fig.8(d),(e)).

4. Summary and Conclusions

In this work, experiments have been conducted using notched three point

bend specimens to study the mode I fracture response of magnesium single

crystals. Three crystallographic orientations referred to as A, B and C were

chosen for this study. The main observations / conclusions from the work

are summarized below.

The load-displacement curves for the three orientations show that thehardening rates corresponding to orientation A and B (wherein the c-

axis is perpendicular to the flat surfaces of the notch) are similar, while

that of orientation C (in which c-axis is parallel to the notch front) is

significantly higher.

Optical metallographs corresponding to orientations A and B revealbasal and prismatic slip traces. The metallographs also show deflec-

tion of basal slip traces by about 860 inside the twinned region (i.e.,

secondary slip).

21

Profuse tensile twinning is observed in all the orientations. In orien-tations A and B, TT formation commences from the notch root and

spreads outwards, whereas in orientation C, TTs are observed to nu-

cleate near the loading edge and grow towards the notch root but they

do not extend up to it. This behavior has relevance to polycrystalline

Mg alloys that have a basal texture. Indeed, in a rolled Mg alloy AZ31

which has a basal texture profuse TT formation ahead of a crack tip

which leads to strong changes in texture has been recently observed

(Prasad et al., 2013).

The surface profile scans for orientation C show out-of-plane bulgingof the specimen ahead of the notch tip except very close to it. Here,

surface profiles show that there is some contraction. Thus, the TTs

accommodate extension along the c-axis (i.e., thickness direction).

The width of the most prominent twin near the notch root in orien-tations A and B is found to evolve rapidly at small load levels, but

saturates at around 120-150 m, while twins continue to nucleate far-

ther away to accommodate plastic deformation.

The evolution of average twin volume fraction fatt taken over a rectan-gular region around the notch root on the specimen free surface with

respect to load corresponding to all three orientations corroborate well

with similar histories of the energy release rate J. It is found that

orientation A has the highest notched fracture toughness followed by

orientation C. The low fracture toughness of orientation B can be at-

tributed to the tendency of fatt to saturate at small loads owing to the

22

presence of polishing twins which impede the growth of new twins for

this case.

Crack initiation occurs just before attainment of the peak load and itgrows stably along the twin-matrix interface before deflecting at twin-

twin intersections. The fractographs show some penetration of the

crack into the twin and traces of other tensile twin variants intersecting

the fracture surface.

The present study has shown that profuse tensile twinning can cause en-hancement in fracture toughness through large plastic dissipation. On

the other hand, if only a few prominent tensile twins form near a notch

root (as in the case of orientation B), large plastic strain may accumu-

late at the twin-matrix interface leading to premature crack initiation

and low toughness. Thus, this work suggests that an important way

of enhancing the toughness of Mg alloys is to ensure that homogenous

TT nucleation occurs easily so that plastic dissipation gets distributed

over many twins rather than being restricted to a few prominent ones.

Some of the experimental observations such as the occurrence of profuse

tensile twinning in orientation C which causes out-of-plane extension and

deflection of the crack at twin intersections require further analysis. Hence,

to gain additional insights on the mechanics of fracture, finite element sim-

ulations using crystal plasticity theory will be reported in a follow-up work

(Kaushik et.al., 2013). This will enable understanding the 3D nature of

plastic slip, twin volume fraction and stress distribution.

23

Acknowledgement

The authors gratefully acknowledge General Motors Research and Devel-

opment Centre, Warren, Michigan, USA, for financial support through the

sponsored project GM/IISC/SID/PC20037. The authors are thankful to Mr.

Robert Kubic Jr. for his valuable assistance in the experimental work. The

authors are also thankful to Dr. Michael J. Lukitsch for his help in obtaining

the surface profilometry scans.

24

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28

Table 1: Various dimensions of the specimens (see Fig. ??) pertaining to the three orien-

tation considered in the study.

Orientation 2r0 W a L Thickness t

(m) (mm) (mm) (mm) (mm)

A 400 4.0 2.0 12.0 1.63

B 400 4.0 2.2 12.0 1.50

C 400 4.0 2.0 12.0 1.70

Table 2: Nomenclature used for representing the six tensile twin variants of a HCP crystal

and the angles a, b, c made by traces with the notch line for orientation A, B and C.

Variant Twin Plane Twinning shear Direction a b c

TT1 (1012) [1011] 43.2 0.0 90.0

TT2 (1012) [1011] 43.2 0.0 90.0

TT3 (1102) [1101] 25.1 39.0 30.0TT4 (1102) [1101] 25.1 39.0 30.0TT5 (0112) [0111] 25.1 39.0 30.0TT6 (0112) [0111] 25.1 39.0 30.0

29

Table 3: Summary of the observed twin traces of orientations A, B and C which are

identified using the nomenclature given in Table 2

Orientation Twin trace Corresponding TT variant

A W TT1 / TT2

V TT3 / TT5

B E TT1 / TT2

F TT3 / TT6

X TT3 / TT6

M TT3 / TT6

Y TT4 / TT5

L TT4 / TT5

U TT4 / TT5

C K TT4 / TT6

N TT3 / TT5

Z TT1 / TT2

30

x1

x2

BA

p

p

a0 b

h

31