Mechanical behaviour and the evolution of the dislocation structureof copper polycrystal deformed under fatigue�/tension and tension�/

fatigue sequential strain paths

W.P. Jia a,b, J.V. Fernandes a,*a Departmento de Engenharia Mecanica-FCTUC, Polo 2, Universidade de Coimbra, CEMUC, Pinhal de Marrocos, P-3030-201 Coimbra, Portugal

b State Key Laboratory for Corrosion and Protection of Metals, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s

Republic of China

Received 27 February 2002; received in revised form 16 September 2002

Abstract

Two sequences of tension�/fatigue and fatigue�/tension tests were performed on copper polycrystal sheet, with a mean grain size of

32 mm. For the angle between the two successive loading directions, two typical values (0 and 458) have been chosen. The effect of

strain path change on subsequent initial work hardening rate and saturation stress in tension�/fatigue, as well as the effect of strain

path change on subsequent yield and flow behaviour in fatigue�/tension have been investigated. The strain rate for the tension tests

was 5�/10�3 s�1, while the fatigue tests were performed under constant plastic strain amplitude control with different values of

amplitudes (opl�/6�/10�4, 1.5�/10�3, 3�/10�3). Slip morphology and dislocation microstructure were observed by optical and

transmission electron microscopy (TEM) after mechanical tests. Under these conditions, in the case of fatigue�/tension, it was found

that fatigues prestraining influences the subsequent yield and flow behaviour in tension. However, the subsequent mechanical

behaviour of samples seems only to be affected by the magnitude of strain path change (namely, the angle between the two

successive loading directions), and not by the value of the plastic strain amplitude of the preceding fatigue tests. In the case of

tension�/fatigue, the strain amount of preloading in tension obviously affects the initial cyclic hardening rate, while it has almost no

effect on the saturation stress of subsequent fatigue tests, irrespective of the value of the angle between the two successive loading

directions. The occurrence of microbands in the saturation fatigue dislocation structures of samples prestrained in tension implies

that fatigue is a more effective loading mode than tension, in causing intense glide on the activated slip systems. The correlation

between mechanical properties and microstructural observations is discussed.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Polycrystal; Strain path change; Tension; Fatigue; Dislocation structure

1. Introduction

In recent decades, much research has been done on

the mechanical behaviour and the substructural changes

in metal polycrystals (especially copper, a typical

material, which shows wavy slip characteristics) strained

under plastic deformation with strain path change [1�/6].

It was found that the mechanical behaviour during

subsequent loading appears to be only slightly affected

by the type of initial loading mode. It is mainly

dependent on the magnitude of the strain path change,

for example, a parameter a , defined by the cosine of the

angles between the two vectors that represent the

successive strain tensors, has been proposed [7]. In

most cases, the yield stress upon reloading (back

extrapolated stress) is larger than the stress reached at

a given equivalent strain for the same material deformed

along the same load path without preloading. The

subsequent strain hardening exhibits a transient stage

with lower values just after the reloading yield stress.Microscopic substructures developed during se-

quences of double loading are not only affected by the

sequential strain mode and the magnitude of the strain

path change, but are also affected by the grain sizes [2].

* Corresponding author. Tel.: �/351-239-790-716; fax: �/351-239-

790-701

E-mail address: valdemar.fernandes@dem.uc.pt (J.V. Fernandes).

Materials Science and Engineering A348 (2003) 133�/144

www.elsevier.com/locate/msea

0921-5093/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 6 3 0 - 5

In large grain size (for example 250 mm) specimens,

microbands appear inside many grains just after yield-

ing, these microbands are aligned with the trace of {111}

planes, corresponding to the principal active slip planesin tension. In smaller grain size specimens (20 mm, for

example), by contrast, no trace of localised deforma-

tions was noted, the dislocation structure evolves in a

more or less continuous manner by a partial dissolution

of the prestrain substructure. The different microstruc-

tural behaviours can be interpreted on the basis of strain

accommodation principles. In large grain size speci-

mens, the strain accommodation between adjacentgrains is constricted in the vicinity of grain boundaries

and grain boundary triple junctions. Thus, most of the

volume of grain behaves like a single crystal, which is

the reason why the strain distribution is not homo-

genous at the level of the grain size. Smaller grains are

mainly influenced by their surroundings, three or more

non-coplanar systems can be equivalently activated, so

that their behaviour agrees with the Taylor approach tomultiple slip [8], a more homogenous intragranular

deformation is observed in this case.

The mechanical behaviour and the microstructural

development of cyclically deformed copper polycrystals

have also been studied in considerable detail and many

results have been obtained [9�/12]. The Taylor and Sachs

factors, as well as the exponent law can be applied for

the cyclic stress strain (CSS) curves depending on theloading condition as well as on the grain size. No

plateau region occurred, which is a common phenom-

enon in the CSS response of single crystals oriented for

single slip and some special double and multiple slip

[13]. The dislocation patterns are mainly cell and parallel

wall structures, due to the activation of multiple slip

systems to meet the need for strain compatibilities in the

vicinity of grain boundaries. Persistent Slip Bands(PSBs), which prevail in cyclically deformed monocrys-

tals, can also be found in some grains because of the

different strain values accommodated by different

grains. Nevertheless, the PSB ladder structure does not

lead to the occurrence of a plateau region in the CSS

curves, as in single crystals, in which PSBs and the

presence of a plateau have a one-to-one correlation as

indicated in Winter’s double phase model [14].While it is easy to imagine that sequential loading

interfered with cyclic loading, which is highly relevant to

technical application, as far as the authors know, until

now, little work has been done on polycrystalline

materials deformed under strain path change, with

fatigue as one of the loading modes [15]. The loading

modes for strain path changes are mainly rolling,

shearing and tension. This paper concentrate on study-ing the macroscopic properties and the microstructural

development of copper polycrystals with a relatively

small grain size (32 mm) deformed in sequential strain

paths of fatigue�/tension and tension�/fatigue. The

following will be emphasised in the paper, the effects

of preloading in tension on the initial cyclic hardening

behaviours and CSS response of subsequent fatigue; the

effects of preloading in fatigue on the yield stress andflow behaviour of subsequent tension; the evolution of

the dislocation microstructures after reloading.

2. Experimental procedures

The experiments were performed on oxygen-free high

conductivity (OFHC) copper with a purity of 99.995%.

The previously cold-rolled copper sheet, with a thicknessof 10 mm (for this thickness, the phenomena of buckling

of test specimens under the compression half cycle of

fatigue loading can be effectively avoided even when the

applied plastic strain amplitude reached 3�/10�3) was

annealed for 1 h 30 min at 500 8C in a 10�6 mbar

vacuum in order to obtain an equiaxed grain structure

with a mean grain size of 32 mm.

For the mechanical tests, two different kinds ofsequential loading paths were employed, i.e. fatigue�/

tension and tension�/fatigue, and two angle values

(namely F�/0 and 458, F is the angle between two

successive loading directions) were chosen in each case.

Test specimens for prestraining were cut along the

transverse direction (normal to the rolling direction of

the sheet), when F�/08, and 458 inclined to the

transverse direction, when F�/458. The specimens forsubsequent reloading were cut out of the central region

of the as-prestrained specimens with the loading direc-

tion axis always parallel to the transverse direction for

all F values, in order to make sure that the subsequent

mechanical curves of different cases can be compared in

the absence of the texture effects. Thus, two different

types of dimensions for the specimens to be prestrained

were necessary, 60 mm in gauge length and 50�/10 mmin the cross section of the gauge part for F�/458; 60 mm

in gauge length and 12.5�/10 mm in the cross section of

the gauge part for F�/08. The tension tests were

conducted on an Instron machine at room temperature.

An extensometer with a gauge length of 50 mm was

attached to the specimen when testing. The strain rate

for the tension tests was 5�/10�3 s�1 and signals from

load and extension were recorded and analysed by amicrocomputer interfaced with the tensile machine.

Cyclic symmetrical pull push fatigue tests (stress ratio

R�/�/1) were conducted under constant plastic strain

amplitude on an Instron servohydraulic fatigue testing

machine at room temperature. A triangular waveform

signal with a frequency of 0.5 Hz was used. All the

fatigue tests were continued until the specimens were

saturated.In the sequential paths of fatigue�/tension, for the

preloading in fatigue, three plastic strain amplitudes opl

were applied: 6�/10�4, 1.5�/10�3, 3�/10�3. The

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144134

subsequent tension tests were performed until 5% and

rupture, respectively, in each prestrained condition and

the effect of strain path change on subsequent yield and

flow behaviour of samples was investigated. In the caseof tension�/fatigue sequential paths, for preloading in

tension, tests were performed up to strains of 2, 5 and

10%, for each condition. The subsequent fatigue tests

were performed under three different constant plastic

strain amplitudes: 6�/10�4, 1.5�/10�3, 3�/10�3. The

effect of strain path change on initial cyclic hardening

rate and CSS response was investigated. For the purpose

of comparison, the monotonic tests of tension andfatigue without preloading were also studied.

After the mechanical tests, optical and transmission

electron microscopy (TEM) were used to clarify the

change of slip morphology and dislocation substructures

during the second strain path. Specimens for optical

microscopy were prepared by electropolishing in a

solution containing 250 ml orthophosphoric acid, 250

ml ethanol, 500 ml distilled water and 3 g urea, using acurrent density of 0.6 A cm�2. This was done just before

the mechanical tests to obtain a mirror-like surface for

surface morphology observation. Thin foils for TEM

observation were taken from the middle part of the

gauge length of the specimens with the observation

plane always normal to the loading direction. Thin slices

were mechanically ground on both surfaces and then

electropolished using a double-jet thinner. A dilutesolution of orthophosphoric acid (2:1) at room tem-

perature under 10 V tension was used. TEM observa-

tions were performed in JEOL100S microscope

operation at 100 kV.

3. Results

As a reference and to make a comparison withsequential loading cases, one single strain path of

tension or fatigue tests of the copper polycrystal

employed in the present study without preloading was

performed. True stress�/true strain curves of samples

with the loading axis along transverse direction were

obtained and can be seen in Fig. 8. The initial cyclic

hardening curves of samples fatigued at three applied

constant plastic strain amplitudes without preloading intension are shown in Fig. 1. According to Liu’s theory

for polycrystals [9,10] and Winter’s two phase model for

single crystals [14], the three strain amplitudes chosen in

the present study, 6�/10�4, 1.5�/10�3, 3�/10�3,

correspond to the three different typical regions (i.e.

region A, vein-bundle structure; region B, PSB ladder

embedded in matrix vein structure; region C, cell or

parallel wall structure) of fatigue behaviours of copperpolycrystals.

The saturation dislocation structures of samples

fatigued at different applied plastic strain amplitudes

without preloading are shown in Fig. 2. For the fine-

grain-sized (32 mm) copper polycrystal employed in this

study, it can easily be seen that at the lower strain

amplitude (6�/10�4), the dislocation arrangement is

mainly a vein-bundle structure, as single dislocation

lines exist here and there in the channels between

dislocation bundles. No dense dislocation tangles can

be detected. At intermediate strain amplitude (1.5�/

10�3), elongated cell structures as well as parallel wall

structures are formed. In fact, this structure is not well

developed and can be considered a transition state

between vein structure and well developed closed cell

structure. At higher strain amplitude (3�/10�3), a dense

dislocation cell structure with decreased cell size and a

thickness of cell walls which is comparable to that found

at intermediate strain prevails in most of the grains.In the case of monotonic tension strain loading,

dislocation patterns after different strains are shown in

Fig. 3. Under the given condition (observation planes

are always normal to the loading direction), the

dislocation microstructure consists of a loose, rather

equiaxed and disorganised cell structure even when the

sample has been strained to rupture. At the larger

strains, the cell size decreases and the dislocation densityin the interior of cells and the cell walls increases.

3.1. Effect of tension prestraining on subsequent fatigue

behaviour

3.1.1. Mechanical behaviour

Detailed test parameters and results of tension and

fatigue are listed in Table 1. The cyclic hardening curves

of prestrained samples are shown in Fig. 4. The

following three prominent features can be easily sum-

marised:

i) The tensile prestrain (2, 5 or 10%) has obviouseffects on the initial cyclic hardening rate u0.2

(u0.2�/Ds /Do , when Do�/0.2, the cumulative plastic

strain o�/4Nopl), while it has almost no effects on

Fig. 1. Cyclic hardening curves for three applied constant plastic

strain amplitudes of annealed samples.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144 135

the saturation stress ssat of subsequent fatigue

behaviour.

ii) When the strain of preloading in tension increases,

u0.2 of subsequent fatigue behaviours of samples

decreases drastically. This is caused by the higher

stress, which occurs instantaneously after reloading,

when larger strains are applied in tension.

iii) The difference between the results of the two groups

of tests, F�/0 and 458, where F is the angle between

the two sequential loading directions, is mainly

reflected by the stress at the beginning of reloading

and not by ssat at the end of the fatigue tests. At the

beginning of the second strain path, reloading stress

amplitudes of samples where F�/08 are obviously

lower than those of the samples where F�/458 when

fatigued under the same plastic strain amplitude.

Fig. 2. Saturation dislocation structures of annealed samples fatigued

at various plastic strain amplitudes, (a) opl�/6.0�/10�4; (b) opl�/

1.5�/10�3; (c) opl�/3.0�/10�3.

Fig. 3. Dislocation structures of annealed samples deformed in tension

to different strains, (a) 0.02; (b) 0.05; (c) up to rupture (around 0.40).

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144136

3.1.2. Dislocation microstructures

3.1.2.1. F�/08. The TEM observation allows us to say

that for small tensile prestrains (less than or equal to

0.05), the preloading history has almost no effect on the

saturation dislocation microstructures formed in the

subsequent fatigue process (see Fig. 5). The loose cell

structures formed at small tensile prestrains werecompletely destroyed by the subsequent cyclic loading.

In this case, the cumulative plastic strain of the second

loading path is 4�/7, while the total strain in the first

tensile path is only 0.02�/0.05. This is certainly the main

cause of the disappearance of the not very well-devel-

oped cell structure formed in the tensile prestraining.

However, at relatively high tensile prestrain (0.10), the

dislocation cell structure formed in tension is retained insome grains throughout the fatigue loading. Thus, the

cell structure formed in the prestraining process can also

be found after fatigue at low strain amplitude (see Fig.

6), while in the annealed sample, only the vein structure

can be detected at low strain amplitude (see Fig. 2(a)).

3.1.2.2. F�/458. A parameter a has been proposed to

measure the magnitude of the strain path change in the

earlier work of Schmitt et al. [7], a is the cosine of the

angle between the two strain vectors representing the

prestrain and the subsequent strain in the deformationspace. When a �/0, which corresponds to F around 508in tension�/tension sequential loading, the greatest effect

of the strain path change is observed, and the maximum

of the relative reloading stress is attained. In the present

study, fatigue is axial tension and compression, so we

can choose F�/458 to obtain a considerable effect on

strain path change.

The saturation dislocation microstructures after se-quential tension�/fatigue strain paths are shown in Fig.

7. Unlike the case of 08, dislocation cell structures can be

found in some grains even at low plastic strain

amplitude (opl�/6�/10�4) after small tensile prestrain

(0.02). It is worth mentioning here that, in the sample

prestrained to a tensile strain of 0.02 and fatigued

subsequently at opl�/1.5�/10�3, microbands embedded

in cell structure were detected in some grains (see Fig.7(b)). These microbands are along {111} slip plane

traces as reported in previous papers [2,3]. Although

microbands were also detected under some other con-

ditions, the most dominant dislocation structures in

most samples are cell structures and parallel wall

structures.

3.2. Effect of fatigue prestraining on subsequent tension

deformation behaviour

3.2.1. Mechanical behaviour

Test parameters and results are described in Table 2.True stress�/true strain curves are shown in Fig. 8. Two

main results are obtained as follows:

i) At the same magnitude of strain path change

(represented here by F ), the preloading strain

Table 1

Effects of tensile prestraining on the initial cyclic hardening coefficient u0.2 and axial saturation stress ssat of subsequent fatigue behaviours of copper

polycrystal samples

a (8) op sp (MPa) opl u0.2 (MPa) ssat (MPa)

�/ �/ �/ 6.0�10�4 195.4 100.8

�/ �/ �/ 1.5�10�3 264.4 126.2

�/ �/ �/ 3.0�10�3 305.9 146.4

0 0.02 79.5 6.0�10�4 89.0 98.2

0 0.05 117.5 6.0�10�4 42.2 98.8

0 0.10 190.8 6.0�10�4 15.9 111.7

0 0.02 78.1 1.5�10�3 89.8 126.7

0 0.05 129.4 1.5�10�3 28.7 127.0

0 0.10 166.8 1.5�10�3 �23.1 125.5

0 0.02 70.1 3.0�10�3 129.5 140.6

0 0.05 117.4 3.0�10�3 74.9 137.7

0 0.10 177.9 3.0�10�3 �10.0 142.7

45 0.02 68.3 6.0�10�4 14.4 91.8

45 0.05 126.1 6.0�10�4 �30.2 116.4

45 0.10 183.5 6.0�10�4 �46.0 116.6

45 0.02 73.4 1.5�10�3 �28.0 119.8

45 0.05 119.6 1.5�10�3 �22.8 120.1

45 0.10 178.5 1.5�10�3 �21.7 119.2

45 0.02 71.9 3.0�10�3 28.5 148.6

45 0.05 121.4 3.0�10�3 9.3 150.8

45 0.10 179.8 3.0�10�3 �96.5 157.8

a , Angle between two sequential loading directions; op, amount of strain at preloading in tension; sp, axial stress at the end of tension prestraining

tests; opl, axial plastic strain amplitude of subsequent fatigue; u0.2, cyclic initial hardening coefficient; ssat, axial saturation stress.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144 137

amplitude in fatigue has almost no effect on the

subsequent yield and flow behaviour, irrespective of

the plastic strain amplitude during the first fatigue

loading path.

ii) Fatigue prestraining increases the yield stress of

tensile behaviour noticeably. Moreover, the yield

stress of subsequent tensile tests is much higher for

458 than for 08.

3.2.2. Surface morphology

Surface morphology examination was conducted and

the surface slip lines of samples fatigued at a plastic

strain amplitude of 3�/10�3 with and without subse-

quent straining in tension are shown in Fig. 9 as an

example. At this high fatigue amplitude, two or more

families of slip lines can be found in most grains (Fig.

9(a)). It is worth noting here that in the case of

sequential loading, bending of the slip lines is apparent

(Fig. 9(b)). This may be connected with the rotation in

some regions and/or with roughness development.

3.2.3. Dislocation microstructural observation

3.2.3.1. F�/08. TEM observations after mechanical

tests were conducted and the dislocation patterns at

two tensile strains (0.05 and rupture (around 0.4)) after

preloading in fatigue are shown in Fig. 10. When the

tensile strain of subsequent loading is 0.05, generally

speaking, the dislocation structures formed in the first

strain path of fatigue were retained. However, many

isolated dislocation lines are found between the walls

of dislocation cells or veins. When the subsequent

tension tests were done until rupture, the dislocation

structures are almost the same as that of annealed

samples after tensile straining until rupture without

preloading.

3.2.3.2. F�/458. The dislocation patterns in this case

are shown in Fig. 11. Almost no difference can be

detected between the two cases when F�/0 and 458.

Fig. 4. Comparison between cyclic hardening curves of samples prestrained to different strain values.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144138

4. Discussion

4.1. Influence of the magnitude of strain path change on

subsequent macro- and micro-behaviours

For a given prestrain mode and amount, the subse-

quent deformation behaviour of samples is mainly a

function of the magnitude of the strain path change,

which is determined by the angle between the loading

directions of sequential straining paths as well as by the

two loading modes. A parameter a , defined as the cosine

of the angle between the two strain vectors representing

the prestrain and the subsequent strain in the deforma-

tion space, has been proposed by Schmitt et al. as an

effective measure of the magnitude of the strain path

change [7]. For the sequential strain paths of tension�/

fatigue and fatigue�/tension employed in the present

study, two values of the angle between the sequential

loading directions, 0 and 458, were chosen as corre-

sponding to the smallest and largest magnitude of the

strain path change, respectively.

In tension�/fatigue sequential strain paths, almost no

difference was found in saturation stress ssat between

the two cases when F�/0 and 458. This can be partly

related to the relatively small tensile prestrain (less than

or equal to 10%) as well as the weak evolution of texture

during tensile prestrain. However, the transient stage at

the beginning of the reloading strain path depends

closely on the magnitude of the strain path change: the

axial stress during the transient where F�/458 is

obviously higher than where F�/08 (see Fig. 4 (c and

d)); and the initial cyclic hardening rate where F�/458 is

lower than where F�/08. In fact, when F�/458, most of

the slip systems activated in fatigue are inactive during

prestraining, so fewer mobile dislocations are available

compared with the case of F�/08, where most of the

active slip systems during the two strain paths are the

same. Moreover, when F�/08, because the same active

slip systems operate, the dynamic recovery effect is

obvious under the reverse straining of fatigue. These are

the two main causes accounting for the higher axial

stress during the transient stage where F�/458 com-

pared with when F�/08.Another interesting phenomenon worth noting here is

that, fatigue saturation dislocation arrangements with

Fig. 5. Saturation dislocation structures of samples fatigued after

small tensile prestrain at various plastic strain amplitudes, (a) opl�/

6.0�/10�4 after 2% tension; (b) opl�/1.5�/10�3 after 2% tension; (c)

opl�/3.0�/10�3 after 5% tension.

Fig. 6. Saturation dislocation structures of sample fatigued at opl�/

6.0�/10�4 after 10% tensile prestraining.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144 139

or without preloading in tension are different and the

magnitude of the strain path change also affects the

arrangements of dislocations significantly. However, at

the same reloading fatigue plastic strain amplitude, the

different dislocation arrangements lead to identical

stress amplitudes. Similar findings were reported earlier

in the literature [15,16].

In fatigue�/tension sequential strain paths, the rela-

tively high macroscopic reloading yield stress in the case

of F�/458 is due to the latent hardening effect of slip

systems activated in the first strain path on the new

Fig. 7. Saturation dislocation structures of samples fatigued after

tensile prestrain at various plastic strain amplitudes with large

magnitude of strain path change (i.e. F�/458), (a) opl�/6.0�/10�4

after 2% tension; (b) opl�/3.0�/10�3 after 2% tension; (c) opl�/3.0�/

10�3 after 5% tension.

Table 2

Effects of fatigue prestraining on the subsequent tensile deformation

behaviours of copper polycrystal samples

a (8) opl syield (Mpa) smax (MPa)

�/ �/ 20.0 329.0

0 6.0�10�4 145.0 321.1

0 1.5�10�3 135.0 310.8

0 3.0�10�3 154.0 319.2

45 6.0�10�4 178.9 336.6

45 1.5�10�3 182.0 313.5

45 3.0�10�3 206.0 306.5

a , Angle between two sequential loading directions; opl, axial plastic

strain amplitude of preceding fatigue.

Fig. 8. True stress�/true strain curves of samples after fatigue

prestraining at various strain amplitudes of, (a) F�/08; (b) F�/458.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144140

active slip systems. Moreover, it was found that for each

angle between the two successive loading paths, the

subsequent tension yield and flow behaviours are quitesimilar, independent of the plastic strain amplitude of

the first fatigue loading. This can be explained by the

following two reasons, (a) the saturation stress of fatigue

behaviour is smaller than the reloading yield stress; (b)

the tensile strain part of each fatigue loading cycle (opl�/

0.0006�/0.003) is negligible compared with the strain of

the following tensile loading. As the reloading strain

increases, the dislocation arrangements evolve continu-ously to the structures of tensile-strained samples with-

out preloading, resulting in the identical maximum

stress of samples with different preloading fatigue strain

amplitude or without preloading.

4.2. Comparison between the loading modes of fatigue

and tension during two sequential strain paths

The phenomenon by which changes are induced in the

properties of materials due to the repeated application

of stresses or strains is commonly referred to by the term

fatigue [18]. Cyclic deformation behaviour of materialsunder symmetrical tension�/compression strain is of

great importance in the study of saturation dislocation

structures and fatigue crack initiation. In fact, for

copper crystals, even under the fully reversed (i.e. equal

tension�/compression) fatigue loading condition, be-

cause of the wavy slip characteristics, it is easy for

dislocations to change from one slip plane to another on

closely neighbouring parallel slip planes, when moving

during one loading cycle. Thus it is not difficult to

understand that the slip is not completely reversible.

However, generally speaking, this slip irreversibility is

small, it almost does not cause any rotation of the slip

system with respect to the loading direction. This can be

easily seen in Fig. 9. The surface slip lines of the

specimen fatigued without subsequent tensile loading

are straight, while many of the slip lines of the specimen

that was fatigued and then tensile-loaded are bent,

indicating the rotation of the slip system with respect

to the loading direction.

In an earlier paper [3], Fernandes et al. observed the

disappearance of microbands at the stage of reloading

after tension, when the subsequent loading mode is also

in tension, the axis at 548 to the previous tensile axis,

and the strain over 0.06. This phenomenon was attrib-

uted to the rapid grain rotation caused by the simple

shearing associated with the activity of the microbands.

In tension�/shear sequential loading, evolution of the

microbands is quite different. Microbands are super-

imposed on the previous substructure up to a relatively

Fig. 9. Slip morphology of samples after, (a) fatigue straining at opl�/3.0�/10�3 up to stress saturation; (b) successive loading of fatigue at opl�/

3.0�/10�3 up to saturation and then 5% tension.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144 141

high equivalent strain amount (around 0.35) [3]. They

suggest that a necessary condition for microband

development, during the reloading of a prestrained

sample, is the occurrence of intense glide on one slip

system that was inactive during the prestrain. The

condition for persistence of microbands during reload-

ing up to a large deformation is that grain rotation

caused by the subsequent loading is weak, and thus an

intense activity on one slip plane is compatible with the

applied stress strain state.

Fig. 10. Dislocation structures after tensile deformation upon fatigue prestraining, F�/08, (a) 5% tension after opl�/6.0�/10�4; (b) 5% tension after

opl�/1.5�/10�3; (c) 10% tension after opl�/3.0�/10�3; (d) tension until rupture after opl�/3.0�/10�3.

Fig. 11. Dislocation patterns in tensile-deformed specimens after fatigue prestraining, F�/458, (a) 5% tension after opl�/1.5�/10�3; (b) tension until

rupture after opl�/1.5�/10�3.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144142

In fact, microstructural modifications during complex

strain paths depend mainly on the material, grain size,

and type of path change [1�/3,17]. In the present study,

two cases of sequential strain paths have been employed,

i.e. tension�/fatigue and fatigue�/tension. (a) In the first

case, under the conditions of tension (2%)*/fatigue

(opl�/1.5�/10�3), F�/458, sets of parallel microbands

have been detected in some grains, see Fig. 9(b).

Moreover, under the conditions of tension (5%)*/

fatigue (opl�/3.0�/10�3), with a relatively large subse-

quent strain amplitude, isolated microbands can also be

detected in some grains, see Fig. 12. It should be noted

that the grain size used here (32 mm) is small, compared

with that of the earlier papers [1�/5]. For this grain size,

a few grains were observed with microbands only when

the prestrain amount was large (30 or 50%) and the

second tension test was done until rupture occurred.

This was attributed to the high shear component, which

developed during necking of a tension specimen. (b) In

the second case, no microbands were detected even when

F�/458, and the strain amount of the second tension

strain path (2 and 5%) was less than 6%, which is the

value favouring the occurrence of microbands, as

mentioned in the literature [3]. Thus, from the discussion

above, we can conclude that fatigue is a more effective

loading mode than tension in causing intense glide on

the activated slip system. This is partly the result of the

repeated straining in the fatigue loading procedure,

leading to relatively large cumulative strain when the

axial stress of the specimens reaches saturation; the

weakness of rotation of grains caused by symmetrical

pull�/push fatigue loading; and also the higher disloca-

tion density obtained in cyclic deformation which leads

to a more pronounced latent hardening, i.e. favouring

single slip.

5. Conclusions

The following conclusions can be drawn from the

results and discussion above.

5.1. Tension�/fatigue sequential loading

(a) The amount of tension prestrain has obvious

effects on the initial cyclic hardening rate, while it has

almost no effect on the saturation stress of subsequent

fatigue behaviour. With increasing tensile prestrain,

initial cyclic hardening rate u0.2 of subsequent fatigue

behaviours of samples decreases drastically. The differ-

ence between the two groups of tests, i.e. F�/0 and 458,F being the angle between the two sequential loadingdirections, is mainly reflected by the stress at the

beginning of reloading and not by ssat at the end of

the fatigue tests. At the beginning of the second strain

path, the reloading stress amplitudes of samples where

F�/08 are obviously lower than those of the samples

where F�/458, when fatigued at the same plastic strain

amplitude.

(b) TEM observation of subsequent fatigue saturationdislocations implies that, at small tensile prestrain (less

than or equal to 0.05), the loose cell structure formed in

tension is completely destroyed while at relatively high

tensile prestrain (0.10), the dislocation cell structure

formed in tension remains in some grains throughout

the fatigue loading. For F�/458, microbands embedded

in cell structures were detected in some grains. However,

the most prevailing dislocation structures in mostsamples are cell and parallel wall structures.

(c) For the present small grain size and for large

subsequent fatigue plastic strain amplitude, the appear-

ance of microbands shows that fatigue is a more

effective loading mode than tension in causing intense

glide on the activated slip systems.

5.2. Fatigue�/tension sequential loading

(a) Fatigue prestraining increases the reloading yieldstress of subsequent tension markedly. Moreover, the

yield stress of subsequent tensile stress�/strain curves is

higher when F�/458 (�/200 MPa) than when F�/08(�/150 MPa).

(b) The dislocation structures formed in the first

strain path are retained when the second tensile strain

amount is not very large. However, many isolated

dislocation lines are found between the walls of disloca-tion cells or veins. At a large enough strain in tension,

the dislocation structures become typical of this strain

path. Almost no difference can be detected between F�/

0 and 458.Fig. 12. Saturation dislocation patterns after 5% tensile prestraining

where F�/458 and subsequent to fatigue at opl�/3.0�/10�3.

W.P. Jia, J.V. Fernandes / Materials Science and Engineering A348 (2003) 133�/144 143

Acknowledgements

This work was financially supported by a grant for

scientific research from the Portuguese Science andTechnology Foundation. This support is gratefully

acknowledged. Dr W.P. Jia expresses his heartfelt

thanks to Professor J.V. Fernandes for his invitation

to work as a postdoctoral fellow at CEMUC, Centro de

Engenharia Mecanica da Universidade de Coimbra

(Mechanical Engineering Research Centre, Coimbra

University), Portugal, as well as for his warm-hearted

advice on this paper and living in Portugal. The authorswould also like to acknowledge Professor J.A.M.

Ferreira of ICEMS for permission to use mechanical

testing equipment and Dr Vasco Bairos of the Faculty of

Medicine of the University of Coimbra for use of the

TEM.

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