Deslocamento Subestruturas Celulas de Deslocações
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Transcript of Deslocamento Subestruturas Celulas de Deslocações
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: [email protected] (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
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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.
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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).
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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.
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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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