Residual stress evolution with compressive plastic deformation in
6061Al-15 vol.% SiCw composites as studied by neutron diffraction
R.Fernández a,1, G.Bruno b,c, G.González-Doncel a,*
a
Dept. of Physical Metallurgy, Centro Nacional de Investigaciones Metalúrgicas (CENIM), C.S.I.C.,
Av. de Gregorio del Amo 8, E-28040 Madrid, Spain
b
Institut Laue-Langevin, ILL, Rue Jules Horowitz, BP 156F-38042 Grenoble Cedex 9, France
c
Manchester Materials Science Centre, Grosvenor str., Manchester M1 7HS, UK.
Keywords: Metal Matrix Composites, Residual Stress, Neutron Diffraction, Plastic Deformation.
Abstract
The evolution of the residual stress (RS) with compressive plastic deformation of several
discontinuously reinforced 6061Al-15 vol.% SiCw metal-matrix composites (MMCs) has been
investigated. The composites were obtained by a powder metallurgical route and heat treated to a
fully hardened, T6, condition. The RS was determined from neutron diffraction. The results show
that deformation relaxes the hydrostatic component of the macroscopic RS (M-RS) progressively
until a minimum is reached, around 2-5% plastic strain. Similarly, the hydrostatic component of the
microscopic RS (m-RS) relaxes rapidly with deformation. Relaxation continues with further strain
and at ≈15% this m-RS component disappears. The deviatoric components of both the M-RS and the
m-RS, however, remain unaltered with increasing plastic strain. The increase of the full width at the
half maximum (FWHM) of the Al diffraction peaks with strain reveals the increased lattice
distortion and microscopic RS gradient around the reinforcing particles. The linear correlation found
between the FWHM of the two phases suggests also the activation of a lattice distortion transfer
mechanism from the Al phase to the SiC phase.
1, Present address: Thin Film R&D Dept. INDO, SA, 08902 L'Hospitalet de Llobregat,
Barcelona, SPAIN
* Corresponding author. E-mail address, ggd@cenim.csic.es
Tel.: +34 915538900; fax: +34 915347425.
1
1. Introduction
Discontinuously reinforced metal-matrix composites (MMCs), in particular aluminum alloys
reinforced by silicon carbide, have better mechanical properties than the corresponding metallic
matrices [1, 2]. Among the factors responsible for this improvement, the residual stress (RS) arising
from several sources plays a crucial role. Of particular importance is the microscopic RS originated
on the different thermal expansion of the matrix and the reinforcement. This stress account, for
example, for the strength differential effect observed between uniaxial tensile and compressive test
[3,4]. Despite the well-known correlation between RS and the mechanical behavior, it is not yet well
understood how this stress evolves with plastic deformation and how it can affect service life
performance of structural components [5]. Some few studies analyzing the influence of plastic
deformation on the RS state in MMCs have been conducted [5-8]. Following the separation of the
RS into macroscopic and microscopic RS (M-RS and m-RS) and the separation of the m-RS into an
elastic mismatch term and a thermo-plastic contribution (misfit stress) [6], it has been shown that a
small amount of plastic deformation (≈1%) is sufficient to reduce the misfit stress and that thermal
and plastic stresses are of the same nature [7]. The deformation processes employed in these studies
center mostly on bending tests. The effect of plasticity has been also studied at the front of crack
front of notched samples and in the vicinity of a cold expanded hole [9] with the aim of
understanding the effect of changes in the misfit stress on the fatigue crack propagation in MMCs
[8]. Whereas the conclusions resulting from these studies are relevant, they do not analyze the effect
of accumulative (increasing) plasticity on the RS of these materials.
The purpose of this research is, therefore, to study the evolution of the RS state in 6061Al-15 vol.%
SiCw composites with accumulative compressive plastic deformation and to understand the
mechanisms that govern RS relaxation.
2. Materials and experiment
The materials studied were three 6061Al-15 vol.% SiCw composites, labeled C38, C45 and E219,
and the unreinforced 6061Al alloy, labeled E220, prepared by powder metallurgy (PM) involving
hot extrusion [10-12]. Letters C and E of material’s code denote conical and flat extrusion dies,
respectively. This characteristic of materials preparation did not affect the RS state of the composites
[13]. The evolution of RS with deformation was studied in a T6 condition obtained after solution
treatment at ≈520ºC followed by water quenching and annealing at 146ºC (see [10-12] for details).
The microstructure was studied by scanning electron and optical microscopy (SEM and OM) and the
texture of the Al and SiC phases by X-ray diffraction. The detailed analysis of this study is reported
elsewhere [11]; only a brief description will be given here.
2
The RS was studied by neutron diffraction (ND) using the REST diffractometer at Studsvik Neutron
Research Laboratory, Sweden. The neutron wavelength was 1.7 Å. Appropriate slits were selected to
produce a gauge volume of 3x3x3 mm3. Because of the cylindrical symmetry of the extrusion
process, the principal directions were assumed to be the axial (extrusion axis), the radial, and the
hoop, mutually perpendicular. Samples of 13 mm length and 6.5 mm diameter (with the sample axis
parallel to the extrusion direction), also suitable for compression tests, were used. Reference samples
for the aluminum phase included the 6061Al alloy and 6061Al powder. The same heat treatment
given to the alloy was given to the powder to achieve also the T6 condition. Loose SiC powder was
measured as reference of this phase.
Samples for ND measurements underwent ex-situ compression tests. These tests were conducted up
to different strain levels in a conventional screw driven testing machine at a strain rate of 10 -4 s-1.
Particular interest was focused on the initial regions of plastic deformation, where a rapid hardening
rate is observed [4]. Determination of RS at high plastic strain values, however, was also conducted
in two of the composites under study. Specifically, strain values were selected around 1, 2, 5, and
15% compressive deformation.
3. Residual stress determination
The diffraction peaks were fitted with simple Gaussian functions. The sin2 method (with  the
angle between the sample axis direction and the scattering vector, Q), using the  geometry (the
sample is tilted within the scattering plane), was utilized. The lattice parameter of the 311 planes of
both the Al and SiC phases was determined [14] by applying Bragg equation. Then, the lattice
strains at different tilt angles, from =0º (axial direction, parallel to the extrusion axis) to =±90º
(radial direction) could be calculated (see [4, 12] for more details). The axial and radial RS
components could been finally obtained from the residual strain data using the generalized Hooke´s
law, which for the case of cylindrical symmetry it reads:
 ax 
E
1  2 1   
 rad   hoop 
 1    ax  2 rad 
(1a)
  rad   ax 
(1b)
E
1  2 1   
where E and  are the Young modulus and Poisson ratio, respectively. The radial and hoop terms of
the strain and stress tensors coincide because the measurements have been performed at the center of
the samples. An analysis of the full width at the half maximum (FWHM) of both the Al and SiC
peaks (FWHMAl and FWHMSiC, respectively) was also conducted. The calculation of the RS from
3
equations (1a) and (1b) was done using plane-specific diffraction elastic constants as evaluated by
means of a Kröner model [15]:
E311-Al = 69 GPa ; 311-Al = 0.35
E311-SiC = 387 GPa ; 311-SiC = 0.19
These elastic constants are very similar to macroscopic values for both Al and SiC.
Errors have been calculated according to error propagation formulae [16].
4. Results
The microstructure, the texture, and the initial residual stress of the materials are described in
previous works [4, 11, 12]. In summary, the extrusion process of the Al/SiC powder blends leads to
a <111>+<100> fiber texture (with the fiber axis parallel to the extrusion axis) of the 6061Al matrix,
typical in extruded aluminum alloys [11, 17], and to a slight trend of the short SiC fibers to be
aligned with the extrusion axis. Figure 1 describes, through inverse pole figures of the extrusion axis
direction, the texture of: a) the unreinforced alloy, b) the aluminum matrix of the composite E219,
and c) the SiC whiskers of this composite. As can be seen, the composite matrix and the alloy
develop similar texture components. The texture is more accentuated in the alloy than in the
composites. All composites have, roughly, a similar microstructure and texture.
The initial total RS state of the materials in the T6 condition is fully described in Table 1 of [12]. It
is very similar in all composites. In summary, the RS is tensile in the matrix and compressive in the
reinforcement, and accounts for the presence of m-RS with length-scale of the order of the SiC interparticle distance [18]. This m-RS term is caused by the different coefficient of thermal expansion,
CTE, of aluminum and of silicon carbide [19]. Also, the absolute total axial RS (at =0º) is higher
than the radial one (at =±90º): i.e., a deviatoric RS state is developed.
Although smaller than in the composites, also a tensile RS with a deviatoric character builds up in
the 6061Al alloy [12]. This RS is macroscopic and is raised during the high temperature gradient
brought about by the quenching prior to the annealing for the T6 condition. A tensile M-RS resulting
from material’s quenching has been obtained in several investigations [20-22].
To separate m- and M-RS terms appropriate stress equilibrium condition has been applied [7],
Al
SiC
 Mac,i  (1  f r ) Tot,
i  f r Tot,i
(2)
Phase
Phase
where,  Tot,
i   Mac,i   mic, i , sub-indexes Tot, Mac, and mic refer to total, macroscopic, and
microscopic RS, respectively, sub-index i refers to, axial and radial (hoop) component, and fr is the
volume fraction of the reinforcement. The bars stand for the fact that average stress values over the
gauge volume are determined. This is a large region if compared to the microstructural scale of these
4
composites. The magnitude of the hydrostatic and deviatoric stress terms could be readily calculated
using hd = (ax+2rad)/3 (with rad=hoop≠ax) and d =ax-rad.
As it has been already summarized in previous works [4,12], the M-RS in the undeformed condition
is mostly hydrostatic, and higher in the alloy than in the composites in agreement with the higher
CTE of the former [23]. A certain deviatoric character is present because of sample shape: the
temperature gradient along the axial and the radial directions are different. The m-RS is tensile in the
matrix and compressive in the reinforcement, and is also strongly hydrostatic because the SiC is
mostly randomly oriented. The deviatoric term is due to the population of short SiC fibers aligned
with the extrusion axis (≈ 30%, [12]). The m-RS.
The compressive tests revealed the improved mechanical response of the composites in the T6
condition in comparison to that of the alloy, Fig. 2. The pronounced strain hardening rate of the
composites in the early stages of deformation, up to 0.05 strain, accounts for a rapid multiplication
rate of geometrically necessary dislocations (GNDs). This is not observed in the E220 alloy in which
the dislocation-precipitate interaction (cutting mechanism) should predominate, leading to a limited
strain hardening rate. At high values of strain, the composites and the alloy behave similarly. This is
because the multiplication of statistical dislocations dominates the hardening process similarly in the
alloy and the composites [24]. The slight differences in the stress-strain curves of the composites is
attributed to the differences in the orientation/distribution and to the inter-particle spacing of the SiC.
The evolution of the M-RS and m-RS components with compressive plastic deformation is shown in
Figs. 3 and 4, respectively. A rapid drop of the hydrostatic M-RS occurs with small plastic strain in
all materials investigated, Fig. 3. Relaxation of RS with plastic deformation is consistent with
previous investigation on the effect of plasticity on the RS state of MMCs [7]. The M-RS reaches a
minimum around 2-5% of deformation. However, it increases again with further plasticity. A RS
value close to that in the undeformed condition is reached at 15% of deformation in composites C38
and C45. On the other hand, the deviatoric term remains essentially constant in the complete range
of deformation.
Similarly to the M-RS, the axial and radial components of the m-RS evolve in parallel, such that the
deviatoric term remains constant with plastic deformation, Fig. 4. This result is consistent with the
observation that the stress-strain curves in tension and compression run nearly parallel, separated by
a certain stress value: i.e., the strength differential effect SDE [4]. The hydrostatic m-RS relaxes
progressively with plastic pre-deformation. Relaxation occurs rapidly during the initial stages of
plastic deformation, <2%, and slowly at high levels of strain.
5
The radial component of the m-RS reverts its sign (becomes compressive in the matrix and tensile in
the reinforcement) at about 2% of plastic deformation, Fig. 4. Sign reversal of the m-RS with strain
has been reported in a cold expanded hole (expanded 4% by a split sleeve technique) at a distance up
to some 5 mm from the edge of the hole in a 2124Al-17 vol.% SiCp plate [9]. Since deformation was
imposed by the split-sleeve technique (it depends on the distance from the edge of the hole and on
the strain hardening behavior of the material), it is not evident from [9] the amount of plastic
deformation needed to achieve sign reversal of the RS. The present work indicates that sign reversal
occurs with only ≈ 2% strain. This effect has been attributed to a mechanism of load transfer from
the matrix to the reinforcement [9, 25].
Although the instrumental contribution could not be separated in the analysis of the FWHM, it can
be assumed to be the same at the diffraction angles for the Al and SiC phases (they are relatively
near). Therefore, a deconvolution of the different sources of peak broadening was not needed. In this
way, the variation of the FWHM can be attributed only to microstructural changes with plastic prestrain (lattice micro-strains or type-III RS, m-RS-III [17]). The evolution of FWHMAl and FWHMSiC
with plastic strain is summarized in the plots of Fig. 5. As can be seen, the FWHM increases with
increasing plastic deformation in all materials. The increase of FWHMAl is more evident than that of
FWHMSiC.
5. Discussion
Once the different components of the RS are known, it is worth comparing the evolution of the
hydrostatic and devatoic M-RS and m-RS of the composites with accumulative plastic strain. This is
shown in the plots of Figs. 6a) and 6b) for the C38, and C45 composites, respectively.
The hydrostatic m-RS decreases monotonically towards total relaxation. On the other hand, the
hydrostatic M-RS term first decreases rapidly, but surprisingly it increases with further deformation
after some 2-5% plastic strain. Upon homogeneous deformation in compression, the misfit between
internal and external regions should be “washed out” and the M-RS should go to zero. The increase
in M-RS must, therefore, be attributed to some kind of non-homogeneous deformation occurring
during composite deformation at large strains. In fact, barreling was observed in the highly deformed
samples. This leads to a higher plastic deformation in the center of the sample than in regions close
to the platens. This plasticity gradient may have helped to the re-generation of the M-RS when large
plastic deformation accumulated.
The relaxation of the hydrostatic m-RS agrees with previous experimental work which have shown
that plasticity reduces the misfit between the matrix and the reinforcement and, hence, the m-RS [57, 26-28]. It is interesting to note that this is also valid for non-homogeneous deformation (large
6
level of plastic compression) because the length scale of variation of m-RS and M-RS are very
different. It is worth mentioning that simple mechanistic models on the influence of plastic
deformation on the residual stress state of MMCs predicts that uniaxial tensile plastic flow would
generate a m-RS which would be compressive in the aluminum matrix in the axial direction (and
tensile in the radial one). On the other hand, the opposite would be expected after uniaxial
compressive plastic flow [5, 6]. Previous experiments have shown results in full agreement with our
observations. Further work is, therefore, needed to understand in detail the specific micromechanisms that lead to the relief of the m-RS with plasticity.
The deviatoric component of both the M-RS and m-RS seems to stay constant within the error bar.
In particular, the m-RS behavior reveals the strong influence of the non isotropic nature of materials
microstructure. This RS is associated to the microstructural parameters linked to the reinforcing SiC
(orientation and distribution) and to the texture of the matrix material, whereas the M-RS is mostly
associated to sample geometry. The fact that the m-RS turns totally deviatoric with compressive
plastic deformation accounts for the relevance of the activity of geometrically necessary
dislocations, GNDs. GNDs are particularly active at the ends of the short SiC whiskers [29]. Since a
part of the reinforcement population is aligned with the extrusion axis, the symmetry of the GNDs
distribution after deformation should be similar and the axial m-RS state should remain with strain.
The direct connection of the increasing FWHM with plastic deformation becomes evident from the
plot of Fig. 7. In this plot, the compressive stress-strain curve of the composite C38 and the FWHM
of the two phases at the different levels of plastic strain are shown. The data have been normalized
between 0 and 1 to render all variables dimensionless according to,
Υ n   
Υ    Υ min
Υ max  Υ min
where Yn() and Y() denote the normalized and measured value (flow stress and FWHM) as a
function of the true plastic strain, , and sub-indexes min, and max denote minimum and maximum
values, respectively. The rate at which the FWHMAl increases with plastic strain follows very closely
the rate at which the flow stress increases with strain (hardening rate). This result is in good
agreement with several investigations [30] and reveals the increasing lattice distortion due to the
increasing dislocation density, , with plastic deformation.
Specifically, the edge character of the dislocations generates a “pressure”, P, at a given distance (x,y)
of the dislocation core (in a coordinate system in which the dislocation lies along the z axis and x,y
denote the distance from the slip plane and the distance in the sip plane, respectively) given by,
7
P
E bedge
6  1   
y
x  y2
(3)
2
where bedge is the edge component of the Burgers vector [31]. Hence, the corresponding m-RS-III is
compressive above the dislocation slip plane (in the region where the extra plane is located) and
tensile below it. The net effect results in broadening of the diffraction peaks. Peak width increases
with increasing , Fig. 7, and, according to equation (3), is proportional to E/(1-).
A change of the RS distribution around the SiC reinforcement with plastic deformation, as calculated
by Dutta et al. [25] by means of finite element models (FEM), can also result in broadening of the
diffraction peaks. Regions of compressive and tensile hydrostatic stress alternate around the fibres
and their tips, thus creating a highly inhomogeneous RS field and broadening of the diffraction
peaks. Other microstructural factors, such as grain size variations, could also affect peak broadening,
but these factors do not change significantly with plastic pre-strain and, therefore, do not contribute
to the increase of the FWHM.
Broadening of the Al diffraction peaks is, hence, due to the increasing lattice distortion and to the
increasing m-RS gradient around the SiC particles, both caused by dislocation multiplication.
However, since the SiC reinforcement does not deform during testing, the origin of the FWHM SiC
increase must be different. The fact that the normalized FWHMSiC and FWHMAl broaden at a similar
rate, Fig. 7, suggests a linear correlation between FWHMAl and FWHMSiC for the different
composites and at the different levels of plastic strain. This dependence is shown in the plot of Fig. 8
in which the average slope is Δ FWHMAl/Δ FWHMAl=6.32, which correlates reasonably well with
the ratio, [E311-SiC(1-ν311-Al)]/[E311-SiC(1-ν311-SiC)]=4.5.
This good correlation and, yet, the samall mismatch suggest that the increase in FWHMSiC is also
due to an increasing distortion of the SiC lattice and to m-RS gradient in the particles induced by
those of the Al phase. In other words, the increasing distortion and m-RS gradient of the Al lattice is
transmitted to the SiC in a similar manner as an external load is transferred to the particles (as
predicted by Shear-Lag or Eshelby type mechanisms). This would explain the inequality, Δ
FWHMAl/Δ FWHMAl > [E311-SiC(1-ν311-Al)]/[ E311-SiC(1-ν311-SiC)]. Additional contributions could be
as follows:
(i) The occurrence of local damage at Al-SiC interface during straining which lead to local
debonding or decohesion at the Al-SiC interface or to SiCw breakup [see for example, ref. 32] and,
hence, to local m-RS-III relaxation of the SiCw particles (but not of the Al phase).
(ii) Dislocation rearrangement in low energy configurations, leading to sub-grain or domain
formation, as observed in Al-SiC system by transmission electron microscopy after small plastic
8
strain [33]. In this case, peak broadening in the Al phase would occur not only by dislocation
accumulation, but also by sub-grain or domain formation, according to the Scherrer’s formula.
These two additional sources of of peak broadening are believed to be minor in our case because no
debonding was observed, and the (sub)grain size stays constant
6. Conclusions
The evolution of the macroscopic and microscopic residual stress, M-RS and m-RS, in powder
metallurgy 6061Al-15 vol.% SiCw composites with increasing compressive plastic deformation has
been studied. Neutron diffraction has been used for this investigation. The following are the main
conclusions that can be drawn from this investigation.
(i) A strongly hydrostatic RS state has been observed in these composites in the T6 condition. The
small deviatoric component is attributed to the alignment of part of the short SiCw reinforcement
with the extrusion axis direction (m-RS) and to the cylindrical sample shape (M-RS). The M-RS
is generated during quenching prior to annealing (at 146ºC) to achieve the peak aged (T6)
condition. This stress is present in the composites and in the unreinforced alloy and is lower in
the composites because of their lower CTE.
(ii) M-RS and m-RS relax with compressive plastic deformation. A rapid relaxation occurs in the
very early stage of deformation (<1% strain). In the composites an increase of the M-RS is
observed at high plastic deformation. This is attributed to non uniform deformation (barreling)
during compressive testing. The deviatoric component remains constant with deformation, even
at the high level (≈ 15%) of plastic deformation.
(iii) The axial deviatoric component of the m-RS is not affected by plastic deformation; Instead, the
hydrostatic m-RS relaxes. This implies that GNDs regenerate not only with heat treatments but
also with plastic deformation (shape misfit). Nonetheless, this is unexpected for compressive
deformation and further work is needed to fully understand the detailed micro-mechanisms of
plastic deformation which lead to the relaxation of the m-RS.
(iv) The FWHM of both Al and SiC phases increases with plastic deformation. A proportionality
between the FWHMAl and the FWHMSiC is found. The slope of the straight line correlates well
with the ratio of the term (1-)/E of the SiC and Al phase. This suggest that plasticity in the
matrix phase causes increasing lattice distortion (RS of type III) in both phases. The increased
inhomogenity of the m-RS also influences broadening of the diffraction peaks.
Acknowledgements
Projects MAT 01-2085 from MCYT and 07N-0066-98 from CAM, Spain, and support from NFL
(Studsvik) under contract nº N01 HPRI-CT-1999-00061 in the frame of ARI Program. Help from
9
Mihail Butman, who performed the compression tests, and from R. Lin Peng and Bertil Trostell (†),
technical responsible of the REST diffractometer, NFL, Studsvik, is gratefully acknowledge.
References
[1] T.Christman, A.Needleman, S.Suresh, Acta Metall. 37 (1989) 3029-3050.
[2] V.C.Nardone, J.R.Strife: Metall Trans. 18A (1987) 109-114.
[3] T.W. Clyne and P.J.Withers: An introduction to metal matrix composites, Cambridge Univ.
Press, UK, 1993, pp.77-78.
[4] R. Fernandez, G. Bruno, G. Gonzalez-Doncel, Acta Mater. 52 (2004) 5471-5483.
[5] R.Levi-Tuviana, A.Baczmanski, A.Lodini, Mater. Sci. Eng. A341 (2003) 74-86.
[6] M.E.Fitzpatrick, P.J.Withers, A.Baczmanski, M.T.Hutchings, R.Levy, M.Ceretti, A.Lodini, Acta
Mater. 50 (2002) 1031-1040.
[7] M.E.Fitzpatrick, M.Dutta, L.Edwards, Mater. Sci. Technol. 14 (1998) 980-986.
[8] M.E.Fitzpatrick, M.T.Hutchings, P.S.Withers, Acta Mater. 47 (1999) 585-593.
[9] M.E. Fitzpatrick, in: Proc. 5th Int. Conf. on “Residual stresses”, University of Linköping,
Sweden, June 1997, vol 2. T. Ericsson, M. Odén, and A. Andersen eds. Linköping. pp. 886-891.
[10] A.Borrego, J.Ibañez, V.López, M.Lieblich, G.González-Doncel, Scripta Mater. 34 (1996) 471478.
[11] A.Borrego, R.Fernández, M.C.Cristina, J.Ibañez, G.González-Doncel, Comp. Sci. Technol. 62
(2002) 731-742.
[12] G.Bruno, R. Fernández, G.González-Doncel, Mater. Sci. Eng. A382 (2004) 188-197.
[13] R. Fernández, Ph.D. Thesis, Universidad Complutense de Madrid, 2003.
[14] VAMAS TWA 20 standard, ISO/TTA 3, 2001.
[15] E.Kröner, Z.f.Phys. 151 (1958) 504-518.
[16] J.R. Taylor, 1982, An Introduction to Error Analysis: The Study of Uncertainties in Physical
Measurements, University Science Books, New York.
[17] C.J.McHargue, L.K.Jetter, J.C.Ogle, Trans. Met. Soc. AIME, 215 (1959) 831-837.
[18] L.Pintschovius, in: M.T.Hutchings, A.D.Krawitz (Eds.), Proceedings of the NATO Advanced
Research Workshop on Measurements of Residual and Applied Stress Using Neutron
Diffraction, Kluwer Academic Publishers, Dordrecht, 1992, pp.115-130.
[19] H.M.Ledbetter, M.W.Austin, Mater. Sci. Eng. 89 (1987) 53-61.
[20] K.Maeda, K.Wakashima, M.Ono, Scripta Mater. 36 (1997) 335-340.
[21] M.E.Fitzpatrick, M.T.Hutchings, P.S.Withers, Acta Mater. 45 (1997) 4867-4876.
[22] S.Sen, B.Aksakal, A.Ozel, Int. Journal of Mech. Sci. 42 (2000) 2013-2029.
10
[23] M.F.Ashby, Acta Metall. Mater. 41 (1993) 1313-1335.
[24] A. Borrego, Ph.D. Thesis, Universidad Complutense de Madrid, 2004.
[25] I.Dutta, J.D.Sims, D.M.Seigenthaler, Acta Metall. Mater. 41 (1993) 885-908.
[26] I.Dutta, G.Bruno, L.Edwards, M.E.Fitzpatrick, Acta Mater. 52 (2004) 3881-3888.
[27] G.L.Povirk, A.Needleman, S.R.Nutt, Mater. Sci. Eng. A123 (1991) 31-38.
[28] G.Bruno, M.Ceretti, E.Girardin, A.Giuliani, A.Manescu, Scripta Mater. 51 (2004) 999-1004.
[29] D.C.Dunand, A.Mortensen, Acta Metall. Mater. 39 (1991) 127-139.
[30] A.L.Ortiz, L.Shaw, Acta Mater. 52 (2004) 2185-2197.
[31] D.Hull, D.J.Bacon, in: Introduction to Dislocations, 1984, Pergamon Press, Oxford. p. 78.
[32] B.Y.Zong, C.W.Lawrence, B.Derby, Scripta Mater. 37 (1997) 1045-1052.
[33] C.Y. Barlow, in: MMCs, 12th Risø Int. Symp. on Materials Science: Processing, Microstructure
and Properties. N.Hansen, D.Juul Jensen, T. Lefferes, H.Lilholt, T. Lorentzen, A.S. Pedersen
O.B. Pedersen, and B. Ralph, eds. Risø. Sept. 1991, p. 1-15.
11
Figure Captions
Figure 1.- Inverse pole figures of the extrusion axis showing the texture of the unreinforced alloy
and of both phases (Al and SiC) of one of the composites (E219). The <111>+<100> fiber texture of
the unreinforced alloy is stronger than that of the Al phase of the composite.The SiC tends to be
aligned with the extrusion axis.
Figure 2.- True stress-true strain compressive curves of the unreinforced alloy (E220) and of the
three composites (C38, C45, E219). The better behavior of the composites than that of the
unreinforced alloy is apparent.
Figure 3. Macroscopic RS of each composite and of the unreinforced alloy. The axial, radial,
deviatoric and hydrostatic stress components are represented as a function of compressive pre-strain.
Figure 4. Evolution of the axial, radial, deviatoric and hydrostatic components of the m-RS in both
phases of the three composite materials with compressive pre-strain.
Figure 5. Evolution of the FWHMAl and FWHMSiC with plastic deformation.
Figure 6. Evolution of the deviatoric (axial) and hydrostatic components of the macroscopic residual
stress in the unreinforced alloy and in the composites C38 and C45 with compressive pre-strain.
Figure 7.- Evolution of the normalized compressive flow stress and FWHM of the Al and SiC phases
(composite C38) with plastic pre-strain. The good correlation between the increasing flow stress
with strain (hardening rate) and the increase of the FWHMAl and FWHMSiC is evident.
Figure 8.- Correlation between FWHMAl, and FWHMSiC at the different levels of increasing plastic
deformation for all the three composites investigated. A linear correlation is obtained for all data.
12
E220
Max.=21.8
E219-Al
Max.=12.8
E219-SiC
Max.=4.6
Figure 1.- Inverse pole figures of the extrusion axis showing the texture of the unreinforced alloy
and of both phases (Al and SiC) of one of the composites (E219). The <111>+<100> fiber texture of
the unreinforced alloy is stronger than that of the Al phase of the composite.The SiC tends to be
aligned with the extrusion axis.
13
Figure 2.- True stress-true strain compressive curves of the unreinforced alloy (E220) and of the
three composites (C38, C45, E219). The better behavior of the composites than that of the
unreinforced alloy is apparent.
14
140
E220
120
Residual stress (MPa)
Residual stress (MPa)
140
Axial
100
Radial
80
60
40
Deviatoric
20
Hydrostatic
0
-1
0
1
2
C38
120
100
Radial
60
40
20
Deviatoric
0
3
0
5
10
15
20
Plastic strain (%)
140
C45
Axial
120
Hydrostatic
100
Radial
80
60
40
Deviatoric
20
0
5
10
15
Residual stress (MPa)
140
Residual stress (MPa)
Hydrostatic
80
Plastic strain (%)
0
Axial
E219
120
100
60
Radial
Hydrostatic
40
20
0
-1
20
Axial
80
Deviatoric
0
1
2
3
Plastic strain (%)
Plastic strain (%)
Figure 3. Macroscopic RS of each composite and of the unreinforced alloy. The axial, radial,
deviatoric and hydrostatic stress components are represented as a function of compressive pre-strain.
15
100
Axial
C38 (Al)
Residual stress (MPa)
Residual stress (MPa)
80
60
40
Deviatoric
20
Hydrostatic
0
Radial
Radial
0
-100
Deviatoric
-200
-300
-400
-500
0
5
10
15
Hydrostatic
20
Axial
0
80
10
15
20
100
Axial
C45 (Al)
Residual stress (MPa)
Residual stress (MPa)
5
Plastic strain (%)
Plastic strain (%)
60
40
Deviatoric
20
Hydrostatic
0
Radial
0
5
10
15
Radial
0
Deviatoric
-200
-300
-400
Axial
C45 (SiC)
-500
20
Hydrostatic
-100
0
5
10
15
20
Plastic strain (%)
Plastic strain (%)
80
100
Axial
60
E219 (Al)
Residual stress (MPa)
Residual Stress (MPa)
C38 (SiC)
Hydrostatic
40
20
Deviatoric
0
Radial
-1
0
1
2
Radial
0
-100
Hydrostatic
-200
-300
-400
Axial
-500
-1
3
Deviatoric
E219 (SiC)
0
1
2
3
Plastic strain (%)
Plastic strain (%)
Figure 4. Evolution of the axial, radial, deviatoric, and hydrostatic components of the microscopic
RS in both phases of the three composite materials with compressive pre-strain.
16
0.8
6061Al phase
FWHM
0.7
0.6
E220
C38
C45
E219
0.5
0.4
0.3
0
2
4
6
8
10
12
14
16
14
16
Plastic strain (%)
0.48
SiC phase
FWHM
0.46
0.44
0.42
C38
C45
E219
0.4
0.38
0
2
4
6
8
10
12
Plastic strain (%)
Figure 5. Evolution of the FWHMAl and FWHMSiC with plastic deformation.
17
120
Residual stress (MPa)
C38
100
80
Macro-RS, Hydr.
60
40
Macro-RS, Dev.
20
micro-RS, Dev.
0
micro-RS, Hydr.
0
5
10
15
20
Plastic strain (%)
Residual Stress (MPa)
120
C45
100
Macro-RS, Hydr.
80
60
40
Macro-RS, Dev.
20
micro-RS, Dev.
0
micro-RS, Hydr.
0
5
10
15
20
Plastic strain (%)
Figure 6. Evolution of the deviatoric (axial) and hydrostatic components of the macroscopic residual
stress in the unreinforced alloy and in the composites C38 and C45 with compressive pre-strain.
18
Normalized stress&FWHM
1.0
0.8
0.6
0.4
FWHM
0.2
FWHM
Al
SiC
0
C38
0
0.04
0.08
0.12
0.16
true plastic strain
Figure 7.- Normalized compressive flow stress and FWHM of the Al and SiC phases (composite
C38) as a function of plastic pre-strain. The good correlation between the increasing flow stress with
strain (hardening rate) and the increase of the FWHMAl and FWHMSiC is evident.
19
0.8
C38
C45
0.7
15%
FWHM
Al
E219
5%
0.6
6.32
2%
0.5
Y = M0 + M1*X
-2.1476
M0
6.324
M1
0.93336
R
1%
0%
0.4
0.6
0.5
0.4
FWHM
SiC
Figure 8.- Correlation between FWHMAl, and FWHMSiC at the different levels of increasing plastic
deformation for all the three composites investigated. A linear correlation is obtained for all data.
20