a15-effect of strain ratio and strain rate on low cycle fatigue behavior of az31 wrought magnesium...

8/12/2019 A15-Effect of Strain Ratio and Strain Rate on Low Cycle Fatigue Behavior of AZ31 Wrought Magnesium Alloy

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Materials Science and Engineering A 517 (2009) 334343

Contents lists available atScienceDirect

Materials Science and Engineering A

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m s e a

Effect of strain ratio and strain rate on low cycle fatigue behavior of AZ31

wrought magnesium alloy

S. Begum a, D.L. Chen a,, S. Xu b, Alan A. Luo c

a Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canadab CANMET-Materials Technology Laboratory, Natural Resources Canada, 568 Booth Street, Ottawa, Ontario K1A 0G1, Canadac General Motors Research and Development Center, Warren, MI 48090, USA

a r t i c l e i n f o

Article history:Received 5 January 2009

Received in revised form 27 March 2009

Accepted 24 April 2009

Keywords:

Magnesium alloy

Cyclic deformation

Low cycle fatigue life

Strain ratio

Strain rate

a b s t r a c t

Magnesiumalloys are increasingly used in automotive and aerospace industriesfor weight reduction andfuel economyimprovement.Low cyclefatigue(LCF) behavior of these alloys is an importantconsideration

for the structural applications. The objective of the present investigation was to identify influences of

strainratio andstrain rate on cyclic deformation characteristicsand fatigue life of an AZ31 extrudedalloy.

As the strain ratio decreased, stronger cyclic hardening rate, more asymmetric hysteresis loop, smaller

stress amplitude, lower mean stress, and higher initial plastic strain amplitude were observed due to

increasing compressive stresses. This was considered to be associated with the twinning during cyclic

deformation in the compressive phase, and detwinning in the tensile phase. The residual twins acting as

barriers to dislocation slip and pile-up were considered to be the main cause for the occurrence of cyclic

hardening. Fatigue life increased with decreasing strain ratio and increasing strain rate. Fatigue crack

initiation occurred at the specimen surface due to the presence of larger grains near the surface, and

fatigue crack propagation was characterized by a mixture of striations and dimple-like ductile fracture

features.

2009 Elsevier B.V. All rights reserved.

1. Introduction

The increasing energy consumption and global climate change

have spurred research and development activities in lightweight

materials for transportation applications. Recently, potential appli-

cations of wrought magnesium alloys have attracted a great deal

of research interest in these alloys[15].Due to lightweight, high

strength-to-weight ratio and high specific stiffness, wrought mag-

nesium alloys are among the most promising structural materials.

However, wrought magnesium alloys with a hexagonal close-

packed (hcp) structure generally show a strong anisotropy or

tensioncompression asymmetry[6]. The limited number of slip

systems plays an important role in the orientation dependence of

the mechanical properties [7], which enhance the nucleation oftwins to assist the plastic deformation[8,9].For AZ31B alloy, an Al,

Zn rich magnesiumalloy with littlecontentof Fe,Ni, andCu, numer-

ous work has been done on the tensile and compressive properties

but only a limited amount of work has been reported on the cyclic

deformation behavior [1015]. A major concern while using this

alloy as structural components is the tensile and compressive yield

asymmetry. Monotonic tests are unable to envisage the effect of

Corresponding author. Tel.: +1 416 979 5000x6487; fax: +1 416 979 5265.

E-mail address:[email protected](D.L. Chen).

stress, strain, and deformation mode of the alloy subjected to alter-

nating stresses. In order to examine the combined effect of these

parameters it is essential to investigate the low cycle fatigue (LCF)

resistance. The objective of this paper is, therefore, to evaluate the

cyclic deformation behavior and fatigue fracture mode with par-

ticular emphasis on the effects of strain ratio and strain rate as no

such work on this alloy has been reported in the literature. The

cyclic stress response, change of mean stress, evolution of plastic

deformation, fatigue life, and failure characteristics are presented

in this paper.

2. Test material and experimental procedure

The AZ31 material used in the present investigation was in an

extruded form, with a nominal composition listed in Table 1.The

alloy was extruded at about 370 C with a plate thickness of 7 mm.

The plate contains two bars of about (30 mm25 mm) size along

theentire lengthof theplate. Duringthe manufacturing process the

applied extrusionspeed was 50.8 mm/s andthe extrusion ratiowas

6. After extrusion the alloy was air cooled.

Sub-sized fatigue samples of about 140mm in length were

machined in the extrusion direction. The samples had a gauge

lengthof 25mm anda widthof 6 mm(followingASTME8 standard).

The thickness of the samples was kept the same as the as-

received plate (7 mm). The specimens were ground progressively

0921-5093/$ see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2009.04.051
http://www.sciencedirect.com/science/journal/09215093http://www.elsevier.com/locate/mseamailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.msea.2009.04.051http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.msea.2009.04.051mailto:[email protected]://www.elsevier.com/locate/mseahttp://www.sciencedirect.com/science/journal/09215093


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S. Begum et al. / Materials Science and Engineering A 517 (2009) 334343 335

Table 1

Chemical composition (wt%) of the extruded AZ31 magnesium alloy used in the

present investigation.

Al Zn Mn Fe Ni Cu Mg

3.1 1.05 0.54 0.0035 0.0007 0.0008 Balance

along the loading direction with 1/0, 2/0, 3/0, 4/0 emery papers to

achieve a smooth and consistent surface.

For the strain controlled pullpush type fatigue tests the ASTM

standardE606 was followedas a guide.All thetests were performed

at room temperature using a computerized Instron 8801 fatigue

testing system via Fast Track Low Cycle Fatigue (LCF) program. To

study the effects of mean strain and mean stress on the LCF behav-

ior of AZ31 alloy, five different strain ratios, Rs = 0.5, 0, 0.5, 1,

and 2, were used at a given total strain amplitude of 0.4% and a

constant strainrate of 1102 s1. Different strainrates of 1103,

1102 and8102 s1 were further applied to evaluatethe effect

of strain rate on the fatigue life of the alloy. After fatigue tests scan-

ning electron microscope (SEM) was used to examine the fatigue

crack initiation sites and identify the mechanism of fatigue crack

propagation under the above applied conditions.

3. Results and discussion

3.1. Microstructure, texture and tensile properties

The microstructural characterization and tensile test results of

the extruded AZ31 magnesium alloy have been reported earlier

in[15]. Non-uniform grain sizes along the thickness of the spec-

imen were observed, with larger grains of an average size of about

150m appeared at both top and bottom surfaces of the speci-

men. Smaller grains with an average size of about 6 m appeared

in the middle of the specimen. Some Mn- and Al-containing par-

ticles were also observed [15]. The test material had an yield

strength of 201 MPa, ultimate tensile strength of 264MPa, and per-

cent elongation of 15.2% obtained at a strain rate of 1102 s1

[15]. The AZ31 extruded magnesium alloy was observed to con-tain a main texture of (1 12 4) 2 24 1, as shown inFig. 1,where

the pole figures were determined using an X-ray diffractome-

ter D8 DISCOVER with GADDS software. Due to the presence

of the crystallographic texture, the extruded magnesium alloy

exhibited a strong tensioncompression asymmetry in the longi-

tudinal/extrusion direction. As presented in[16],the compressive

yield strength was lower than a half of the tensile yield strength.

The strain life of this alloy fatigued at a fixed strain ratio (R =1)

and a constant strain rate of 1 102 s1 and the relevant fatigue

parameters have been reported in[15].

3.2. Effect of strain ratio

The strain ratio was defined as:

Rs =minmax

(1)

To reveal the potential effect of strain ratio on the fatigue char-

acteristics of AZ31 alloy, different strain ratios were applied while

Fig. 1. Pole figures of the extruded AZ31 magnesium alloy selected in the present

study. (a) 102, (b) 110, and (c) 103.

keeping other parameters unchanged. The obtained fatigue life is

given in Table 2. It is seen that the fatigue life increased with

decreasing strain ratio or mean strain under constant strain ampli-

tude and strain rate.

Evolution of stress amplitude during cyclic deformation is

shown inFig. 2.It is seen that the material exhibited higher cyclic

hardening at the lower (or more negative) strain ratio than at the

higher strain ratio, and at Rs = 0.5 the cyclic hardening becamemuch weaker and almost linear in the semi-log coordinate. The

stress amplitude also increased with increasing Rs value under

the same strain amplitude and strain rate. This was related to

the higher mean strain (Table 2), in agreement with the results

reported in[12]where the absolute value of high mean strain cor-

Table 2

Test parameters and fatigue life under different strain ratios at a strain amplitude of 0.4% and a strain rate of 1102 s1.

Strain ratio (Rs) Mean strain (mean ) (%) Maximum strain (max) (%) Minimum strain (min) ( %) Numbe r of cycles to f ailure (Nf)

0.5 1.2 1.6 0.8 3545

0 0.4 0.8 0 4090

0.5 0.133 0.533 0.267 4234

1 0 0.4 0.4 4294

2 0.133 0.267 0.533 7189


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336 S. Begum et al. / Materials Science and Engineering A 517 (2009) 334343

Fig. 2. Stress amplitude vs. the number of cycles for different strain ratios,Rs, at a

given strain amplitude of 0.4% and a constant strain rate of 1102 s1.

responded to the high stress amplitude. The evolution of cyclic

stress response during cyclic deformation was an important char-

acteristic in LCF process, and it was mainly governed by the cyclic

stability of the internal microstructural features related to disloca-

tion multiplication[1719].Furthermore, twins acting as barriers

to dislocation slip also facilitated the evolution of cyclic stress

[17,2025].

Fig. 3shows the variation of plastic strain amplitude with the

number of cycles for different applied strain ratios, Rs. It is seen

that at Rs = 0.5 and 0 there existed a sudden drop of the plastic

strain amplitude from the first cycle to the second cycle, and then

it remained almost constant until failure. As theRsdecreased from

0.5 to 0, the magnitude of the sudden change in the plastic strainamplitude decreased. Such an abrupt drop was again related to the

high positive mean strain (Table 2),which caused a large amount

of plastic deformation in the initial tensile phase of the first cycle,

as seen inFig. 4(a). At negative strain ratios the abrupt change was

Fig. 3. Plastic strain amplitude vs. the number of cycles for different strain ratios,

Rs, at a given strain amplitude of 0.4% and a constant strain rate of 1 102

s1

.

absent (Fig. 3) due to the absence of yielding in the tensile phase of

the first cycle (Fig. 4(a)). However, it is clearly seen fromFig. 4(a)

that the compressive yielding occurred much earlier than the ten-

sile yielding, i.e., the compressive yielding stress was only about

one third the tensile yielding stress, consistentwith the results from

the individual tensile and compressive tests [16]. The amountof the

compressive plastic deformation increased with decreasing strain

ratio. The asymmetry or skewness of the hysteresis loops could be

better seen from the second cycle (Fig. 4(b)), where the hysteresis

loop atRs =2 was most skewed, which became less skewed with

increasing strain ratio, and eventually it became almost symmetric

at Rs = 0.5. The reason for the asymmetry of hysteresis loops will be

discussed later. The shift of the hysteresis loops atRs = 0.5 and 0 in

Fig. 4(b) was due to the control of strain limits (i.e., the fixed val-

ues of the maximum strainmaxand minimum strain mingiven in

Table 2), which compelledthe occurrence of a large amountof plas-

tic deformation in the tensile phase of the first cycle (Fig. 4(a)). The

skewness of the hysteresis loops almost disappeared at the half-

life of the fatigue process (Fig. 4(c)). The changes in the hysteresis

loops correspondedto thechanges in theplasticstrain amplitude in

Fig. 3, where the plastic strain amplitude decreased with increasing

strain ratio and with increasing number of cycles. The plastic strain

amplitude became nearly constant after about 750cycles for allthe

strain ratios. The stronger decrease in the plastic strain amplitude atthe lower strain ratio inFig. 3reflected a stronger cyclic hardening

characteristic as shown inFig. 2.

The variation of the hysteresis loops with the strain ratio could

alsobe expressedas a minimum-to-maximum stress ratio,c/t,vs.

the strain ratio (Fig. 5),where the absolute values of the compres-

sive minimum stress c and the tensile maximum stress t were

used. The stress ratio at the first cycle decreased drastically with

increasing strain ratio, while the extent of change in the stress ratio

at the mid-life cycle became much smaller. It should be noted that

the change in the stress ratio inFig. 5indeed indicated the mean

stress relaxation or cycle-dependent relaxation[26].As expected,

the stress ratio between the first cycle and the mid-life cycle was

almost the same at Rs =1. However, the stress ratio at the mid-life

cycle became lower when the strain ratio was smaller than1, andhigher when the strain ratio was larger than 1.

The change in the strain ratioalso led to different mean stresses,

as shown in Fig. 6, where the mean stress was plotted as a

function of the ratio of the number of cycles to the fatigue life,

N/Nf, for different strain ratios. It is seen that the initial mean

stress decreased for Rs >1 and increased for Rs 1, and the

stabilization basically occurred after about 510% of fatigue life

for the applied strain ratios, except for the strain ratio of 0.5

where the mean stress decreased continuously. The unstability

in the mean stress at Rs = 0.5 might be related to the initial big

over-stretching (Fig. 4(a)), which also resulted in almost linear

and weaker cyclic hardening (Fig. 2).The nearly stable and posi-

tive/tensile mean stress over the majority of fatigue life decreased

from 50 to 25 MPa with decreasing strain ratio fromRs =0 toRs =2. This was in agreement with the results reported by Good-

enberger and Stephens [27] on AZ91E-T6 cast magnesium alloy.

The presence of tensile mean stresses was known to reduce fatigue

life, and the compressive mean stresses extended the fatigue life,

according to Morrow mean stress correction [7,26].Normally, for

materials exhibiting symmetric hysteresis loops the mean stress

would affect more the fatigue life of components in the high-

cycle regime since the large cyclic plastic strains in the low-cycle

regime would lead to the mean stress relaxation. However, for

the extruded AZ31 magnesium alloy tested at a given total strain

amplitude with different strain ratios, while the cyclic plastic strain

caused a certain extent of mean stress relaxation (Fig. 5), quite

big, and almost stable tensile mean stresses were indeed observed

to increase with increasing strain ratio (Fig. 6).Consequently, the


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Fig. 4. Hysteresis loops for different strain ratios,Rs, at a given strain amplitude of 0.4% and a constant strain rate of 1102 s1. (a) The first cycle, (b) the second cycle, and

(c) the mid-life cycle.

Fig.5. Stressratiosof thefirst cycle andthe mid-lifecycleas a functionof theapplied

strain ratio.

Fig.6. Meanstress vs.the ratio of thenumberof cyclesto thefatigue lifefor different

strain ratios.


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fatigue life increased as the strain ratio decreased, as shown in

Table 2.

Furthermore, the increase of fatigue life with decreasing strain

ratio was also associated with the lower cyclic stress amplitude

and stronger cyclic hardening characteristics at the lower strain

ratio (Fig. 2),in spite of the initial higher plastic strain amplitude

(Fig. 3).While the effect of cyclic stress amplitude on the fatigue

life was straightforward (i.e., the lower the stress amplitude, the

higher the fatigue life), the relationship between cyclic hardening

and fatigue life needs to be stated. Normally, materials with higher

monotonic strain hardening exponent exhibited cyclic hardening

and materials with larger values of cyclic strain hardeningexponent

had longer low cycle fatigue lives[7]. It has been reported that the

strain hardening exponent of solder affected the fatigue life under

temperature cycling as a result of thermal expansion mismatch,

representing a fatigue condition equivalent to the strain controlled

low cycle fatigue[7,28].A higher strain hardening exponent corre-

sponded to a lower cyclic strain range in the solder, thus increasing

the fatigue life [28]. Furthermore, the stronger cyclic strain harden-

ing corresponded to a longer fatigue initiation life in metal metrix

composites[29].These results reported in the literature corrobo-

rated the fact that the stronger cyclic hardening would promote a

longer low cycle fatigue life. The weaker and nearly linear cyclic

hardening (Fig. 2) and relatively high and unstable mean stress(Fig. 6)would be the main reasons for the short fatigue life of the

extruded AZ31 magnesium alloy tested atRs = 0.5.

The obvious asymmetry or skewness of the hysteresis loops

at lower strain ratios as shown inFig. 4needs to be addressed.

It is known that two characteristic deformation mechanisms

occurred during plastic deformation of magnesium at room tem-

perature: sliding and twinning[30,31].In the plastic deformation

of wrought magnesium alloys twinning played an important role

[6,810,13,14,17,3050]. This was mainlyattributedto theexistence

of strong crystallographic texture (Fig. 1). In a magnesium single

crystal basic mechanical twinning occurred when the basal plane

was in compression or the prism plane was in tension [30,31].

During compression the occurrence of twinning induced the com-

pressiveyield stress to be smaller thanthe tensile yieldstress.Cyclicdeformation behavior of common magnesium alloys at room tem-

perature was mostly dominated by the formation and change of

twins as well [10,14,15,18,30,32,33,44,48,4 9]. In the cyclic defor-

mation process twinning started in the compressive loading phase

and detwinning (or dissolution of twins) occurred in the tensile

loading phase [6,14,15,18,33,38,44,49,50]. A typical example on the

formation of twins near the fracture surface after cyclic defor-

mation is shown inFig. 7, where a large number of twins could

be seen in some larger grains. Due to the mechanical twinning

the extruded hexagonal close-packed magnesium alloy exhibited

tensioncompression yielding asymmetry (Fig. 4) and the mate-

rial deformed primarily by slip in one direction and by twinning

in the other [33,38]. This was due to the fact that the dominant

basal slip mode hadonly limited slip systems which could notmeetthe requirement of five independent slip systems based on the von

Mises criterion for an arbitrary homogeneous straining. In particu-

lar, the basal plane slip could not accommodate straining along the

c-axis. Besides the dislocation slip withc+ aBurgers vectors,being

a very hard deformation mechanism [44,51], twinning was consid-

ered to be the only active deformation mode that could provide

straining along the c-axis at room temperature[44]. In-situ neu-

tron diffraction during cyclic loading in tension and compression of

extruded bar revealedthat detwinningresultedin completetexture

reversal during initial cycles, but eventually fatigued resulting in

some residual twin component[33].The variation of cyclic hard-

ening characteristics in the AZ31 magnesium alloy with decreasing

strain ratio (Fig. 2)could be understood to be associated with the

formation of residual twins during cyclic deformation[1315].Wu

Fig. 7. Typical SEM micrographs showing the formation of twins near fracture sur-

face.(a) A lowermagnificationimage, (b) a magnifiedviewof areaB enclosed bythe

dashed line box, and (c) a magnified view of area C enclosed by the solid line box.

et al.[18] observed that in a wrought magnesiumalloy ZK60Aresid-

ual twins formed after the act of twinning and detwining in each

cycle, and with increasing number of cycles the volume fraction of

residual twins increased, leading to an increasing hardening rate.

As seen fromFig. 4, with decreasing strain ratio leading to more

asymmetric hysteresis loops, moretwins would be expectedto form

in the compressive phase due to the larger negative/compressive

stress, and subsequently more residual twins would also be likely

after the occurrence of detwining in the tensile phase, due to the

decreasing maximum tensile stress. Therefore, the stronger cyclic

hardening rate at the lower strain ratio (Fig. 2)was attributed to

the accumulation of more residual twins as cyclic deformation


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Table 3

Variation of fatigue lifetime with the strain rate applied at a strain ampli-

tude of 0.4% and a strain ratio of1.

Strain rate (s1) Number of cycles to failure (Nf)

1103 2467

1102 4294

8102 7268

proceeded, since theresidual twins would actas barriers to the dis-

location slip and pile-up. On the other hand, at the high strain ratio

ofRs = 0.5, as theintroduction of high mean strain (Table 2) resulted

in an insufficient compressive stress, the twinning was not antici-

pated, leading to the disappearance of skewness of the hysteresis

loop (Fig. 4) and the weaker and nearly linear cyclic hardening

(Fig. 2).

3.3. Effect of strain rate

Three different (low, middle, and high) strain rateswere applied

to examine the strain rate effect on the fatigue life of the extruded

AZ31 magnesium alloy. The test results obtained at the strain rates

applied are listed in Table 3. It is seen that a higher strain rate

corresponded to a longer fatigue life.Fig. 8shows the stress evolution during the strain controlled

low cycle fatigue tests where the stress amplitude vs. the number

of cycles was plotted for different strain rates. The stress ampli-

tude evolved under the applied high, middle, and low strain rates

was almost the same within the experimental error (with an ini-

tial stress amplitude of about 117123 MPa). It was, however, clear

that cyclic hardeningoccurredat allthe three strainrates. While the

cyclic hardeningrates werenearlythe same(i.e., almost parallel)for

the tests carried out at the strain rates of 1102 and 8102 s1,

the cyclic hardeningrate wassomewhatlower for the sample tested

at the low strain rate of 1 103 s1. This might be related to the

time dependence of cyclic deformation. As mentioned above, a cer-

tain degree of cycle-dependent stress relaxation occurred. If more

time in a cycle were given, corresponding to a lower strain rate,more cycle-dependent relaxation would be expected, giving rise to

a lower cyclic hardening rate.

Fig. 9 shows thevariation of theplasticstrain amplitudewith the

number of cycles at different strain rates. Similarly, the magnitude

Fig. 8. Stress amplitude vs. the number of cycles at a strain amplitude of 0.4% and

different strain rates.

Fig.9. Plastic strainamplitudevs.the number ofcycles ata strain amplitude of 0.4%

and different strain rates.

of the plastic strain amplitudes under the high, middle, and low

strain rates was roughly the same within the experimental error

(with an initial plastic strain amplitudes of about 0.090.1%). The

curves of the plastic strain amplitude vs. the number of cycles at

the strain rates of 1 102 and 8102 s1 were approximately

parallel with a slightly steeper slope, and the curve obtained at the

low strain rate of 1103 s1 was somewhat flatter. All of these

changes corresponded well to those in the stress amplitude at dif-

ferent strain rates shown inFig. 8.Therefore, the cyclic hardening

characteristics could be well represented by either the increase of

the cyclic stress amplitude (Fig. 8)or the decrease of the plastic

strain amplitude(Fig.9) with increasing numberof cycles in a strain

controlled low cycle fatigue test. This has been discussed in our

previous publications[1315].It is also seen from Fig. 9that theplastic strain amplitude first decreased and then suddenly changed

its direction from decrease to increase prior to failure. Such an

abrupt change has been found to represent the onset of fatigue

crack initiation [13]. It appeared that the fatigue crack initiation

stage before the turning point became shorter at the faster strain

rate. However, the process represented by an increase in the plas-

Fig.10. Meanstressvs. theratio ofthe numberof cyclesto thefatigue life ata strain

amplitude of 0.4% and different strain rates.


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tic strain amplitude after the turning point, corresponding to the

fatigue crack propagation stage prior to the final rapid failure [13],

lasted much longer with increasing strain rates from 1103 to

8102 s1 (theX-axis in Fig. 9 was in the log scale). Therefore, the

total fatigue life consisting of crack initiation life and propagation

life was mainly dependent on the crack propagation stage in the

varying strain-rate tests.

The variation in the strain rates also led to some changes in the

mean stress, as shown inFig. 10,where the mean stress was pre-

sentedasafunctionoftheratioofthenumberofcyclestothefatigue

life,N/Nf. It is seen that the initial mean stresses for all the three

strain rates were approximately the same, about 2530 MPa, but

they changed as cyclic deformation progressed. At the high strain

rate of8 102 s1, the mean stress increased rapidly within about

10% of the fatigue life, and then it remained basically constant. The

range within which themean stress increased becameabout20% of

the fatigue life at the intermediate strain rate of 1102 s1, while

themean stress increased slowly andcontinuously at thelow strain

rateof 1103 s1. Such changes gave rise to the largest difference

in the mean stresses occurring at the about 10% of the fatigue life,

after which the difference became gradually smaller although the

slightly higher mean stress arising from the higher strain rate could

still be seen.

3.4. Examination of fracture surfaces

Fig. 11shows an overall view of fracture surfaces of samples

fatigued at Rs =0.5, 0, 0.5, 1 and 2, respectively, containing

Fig. 11. Low magnification SEM images showing an overall view of fracture surfaces of specimens fatigued at a strain amplitude of 0.4% at a strain ratio of (a) 0.5, (b) 0, (c)

0.5, (d) 1, and (e) 2.


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Fig. 12. SEMmicrographsof fracture surfacesnearthe crack initiation of specimens fatigued at a strain amplitude of 0.4% at a strainratio of (a) 0.5, (b)0, (c)0.5, (d)1, and

(e) 2.

fatigue crack initiation, propagation, and final fast fracture regions.

It is seen that fatigue crack initiation basically occurred from the

specimen surface. In these low magnification images the river line

patterns were observed in all samples which were irregular and

broken and flowed along the crack propagation direction like a

wave form. The size of the crack propagation area varied largely

with the applied strain ratio; the lower the strain ratio, the largerthe propagation area. The sample tested at a strain ratio ofRs =2,

Fig. 11(e), exhibited the largest propagation area compared with

the samples tested at other strain ratios, due to the lowest max-

imum tensile stress (Fig. 4)and the smallest mean stress (Fig. 6).

This corresponded to the longest fatigue life compared to other

samples (Table 2). Fatigue crack propagation was dominated by the

stress intensity factor range, K, and only pulsating tension basi-

callydeterminedthe propagation rate [7]. AsseeninFig.2, thestress

amplitude atRs =2 test was the lowest of all the tests, which led

to a delayed crack initiation and a lower value of stress intensity

factor range for the crack propagation, thus increased the fatigue

life.

Fig. 12shows the images near the crack initiation sites of the

fatigued samples. Crack initiation with varying orientations in

different grains was observed. Crack growth was predominantly

transgranular or intercrystalline [52,53]. Such a cracking feature

varied with the applied strain ratio, with the highest percentage

occurred at Rs = 0.5sample compared to the other samples. The ini-

tial stage of crack growth in the hexagonal close-packed alloys like

Mg and Ti has been reported to exhibit striation-like features[52].

Indeed, fatigue crack propagation was mainly characterized by amixture of fatigue striations and dimple-like ductile fracture fea-

tures observed at higher magnifications as shown in Fig. 13(a)(d)

forRs = 0.5, 0, 1, and 2 tests. The striation spacing became larger

with increasing strain ratio. In addition, some secondary cracks

could also be seen. It is known that the occurrence of fatigue

striations was caused by a repeated plastic blunting-sharpening

process in face-centered cubic materials due to the slip of dislo-

cations in the plastic zone ahead of the fatigue crack tip [7,54].The

formation of the fatigue striations in the extruded hexagonal close-

packed magnesium alloy was anticipated to be associated with

twinning in the compressive phase and detwinning in the tensile

phase[6,1315,18,33,38,44,49,50]. Further studies on the forma-

tion mechanisms of the fatigue striations in magnesium alloys are

needed.


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Fig. 13. SEM micrographs of fracture surfaces in the fatigue crack propagation region of specimens fatigued at a strain amplitude of 0.4% at a strain ratio of (a) 0.5, (b) 0, (c)

1, and (d) 2.

4. Conclusions

1. Stronger cyclic strain hardening was observed to occur at the

lower strain ratio than at the higher strain ratio. This was related

to the formation of twins during cyclic deformation in the com-pressive phase, anddetwinning in thetensile phase.The residual

twins acting as barriers to dislocation slip and pile-up were the

main cause for the occurrence of cyclic hardening. The decrease

of cyclic hardening capacity at the higher strain ratio would be a

resultof fewertwins dueto a smaller or insufficient compressive

stress.

2. In the initial stage of cyclic deformation, the hysteresis loops

were more asymmetric or skewed with decreasing strain ratio

because of the presence of larger compressive stresses. The

skewness of hysteresis loops at the lower strain ratios basically

vanished at the half-life of fatigue process.

3. While the initial stress ratio decreased drastically with increas-

ing strain ratio, this decrease became modest at the half-life.

A certain extent of mean stress relaxation or cycle-dependentrelaxation was observed especially when the strainratiowas not

equal to 1 or the strain rate was low.

4. Fatigue life of the extruded AZ31 magnesium alloy increased

with decreasing strain ratio or mean strain and with increasing

strain rate, as a combined consequence of the cyclic hardening

rate, stress amplitude, plastic strain amplitude, and mean stress.

5. While fatigue crack initiation stage seemed to be shorter, the

crack propagation stage was observed to be much longer. Thus a

longer total fatigue life at the higher strain rate was obtained.

6. Fatigue crack initiated at the surface of the test samples due to

the presence of larger grains near the specimen surface. With

decreasingstrain ratio, the sizeof crack propagation areabecame

larger. Fatigue crack propagation was characterized by a mixture

of striations and dimple-like ductile fracture features.

Acknowledgements

The authors would like to thank the Natural Sciences and Engi-

neering Research Council of Canada (NSERC) and AUTO21 Network

of Centres of Excellence for providing financialsupport.This investi-gation involves part of CanadaChinaUSA Collaborative Research

Project on the Magnesium Front End Research and Development

(MFERD), and financial support from CANMET-MTL is acknowl-

edged.One ofthe authors (D.L.Chen)is also gratefulfor thefinancial

support bythe PremiersResearch Excellence Award(PREA),Canada

Foundation for Innovation (CFI), and Ryerson Research Chair (RRC)

program. Dr. K. Sadayappan, Dr. J. Lo, Dr. W. MacDonald and Dr. J.

Jackman are gratefully acknowledged for their support and con-

tinuous encouragement while performing this investigation. The

authors would also like to thank Dr. Xichen Sun of Chrylser for

providing the pole figures in this study, and Messrs. A. Machin,

Q. Li, J. Amankrah, D. Ostrom, and R. Churaman for easy access

to the laboratory facilities of Ryerson University and their assis-

tance in the experiments. The authors would also like to thankProf. S.D. Bhole, Prof. N. Atalla, Prof. S. Lambert, Prof. H. Jahed, Prof.

Y.S. Yang, Mr. R. Osborne, Dr. X.M. Su and Mr. L. Zhang for helpful

discussion.

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a15-effect of strain ratio and strain rate on low cycle fatigue behavior of az31 wrought magnesium...

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