Mechanical behaviour and the evolution of the dislocation structure of 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 Meca ˆnica-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 (o pl /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: v[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:S0921-5093(02)00630-5
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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.
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
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.