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The introduction of reinforcement in a Metal Matrix causes micro-stresses which may prove to be very detrimental for the life of the component. Submitting the components to annealing thermal treatments introduces thermal mismatch stresses. They are generated during cooling due to the difference between the thermal expansion coefficient of the two phases. Finite Element Analysis has been performed to study this effect and the results have been experimentally validated by X-ray diffraction, SEM investigation and EDAX on an AA2009 + 25% SiCp extruded shaft for helicopters, simplified as a thin extruded tube.
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Advanced Composites Letters, Vol.14, No.4, 2005 123
FINITE ELEMENT SIMULATION AND EXPERIMENTAL DETERMINATION
OF RESIDUAL STRESSES AFTER EXTRUSION PROCESS IN METAL MATRIX
COMPOSITES
G.Albertini1,2, E.Girardin1,2, A.Giuliani1,2, D.E.Ilie3, B.P.ODonnell3, J.P.McGarry3 and P.E.McHugh3
1 Univ.Politecnica delle Marche, Dipartimento di Fisica e Ingegneria dei Materiali e del Territorio, Via Brecce
Bianche, 60131 Ancona, Italy
2 Istituto Nazionale per la Fisica della Materia (INFM), Ancona Unit, Via Brecce Bianche, 60131 Ancona, Italy
3 Micromechanics Research Unit, Department of Mechanical Engineering, National University of Ireland, Galway,
Ireland
(Received 4/05; accepted 10/05)
ABSTRACT
The introduction of reinforcement in a Metal Matrix causes micro-stresses which may prove to be very detrimental
for the life of the component. Submitting the components to annealing thermal treatments introduces thermal
mismatch stresses. They are generated during cooling due to the difference between the thermal expansion
coefficient of the two phases. Finite Element Analysis has been performed to study this effect and the results
have been experimentally validated by X-ray diffraction, SEM investigation and EDAX on an AA2009 + 25%
SiCp extruded shaft for helicopters, simplified as a thin extruded tube.
1. INTRODUCTION
Since the 1980s, the automotive and aeronautical
industries of Europe, Japan and United States, have
shown the feasibility of using particulate reinforced
MMC structural components such as brake disks,
connecting rods or engine blocks in cars, blade
sleeves, tail rotor spider plates, shafts in helicopters
and floor struts and stringers in aircraft. The
methodology developed provided optimised forming
parameters to produce MMC components free of
defects such as porosity, microstructural
heterogeneity, with minimised internal residual
stresses, with mechanical properties tailored to the
in-service loading conditions. In all application areas
where they can be used as structural components,
Metal Matrix Composites are of great interest. In fact,
an added ceramic reinforcement, having stiffness
higher than the metal matrix but similar density,
increases the specific stiffness of the material. Weight
saving and increased mechanical properties are thus
obtained in components made of aluminium or steel
if composite materials are used in their place. Such
potential applications made MMC strongly
widespread in the aerospace and automotive
industries. In fact a weight reduction enhances the
fuel efficiency.
On the other hand, introducing reinforcement usually
causes micro-stresses, which proved to be very
detrimental for the component life. Also submitting
the components to annealing thermal treatments will
introduce thermal mismatch stresses. They are
generated at cooling, due to the difference between
the thermal expansion coefficients of the two phases.
In order to study residual stress effects, an AA2009
+ 25 % SiCp MMC was considered. This material is
used in aerospace applications; in particular as an
extruded tube for helicopters. In the present study a
simplified form was considered: a thin (1.65 mm
thickness) extruded tube. The material was analysed
experimentally using X-ray diffraction, scanning
electron microscopy (SEM) and EDAX techniques.
In addition, a micromechanical Finite Element
Analysis (FEA) was performed to explore whether
predictive models can be reliably used to quantify
internal micro-stresses.
2. MATERIALS AND METHODS
A thin AA2009 + 25 vol. % SiCp tube for aeronautical
purposes was studied: it is a component of a helicopter
intermediate drive shaft.
The composition of the AA2009 aluminium alloy is
given in Table 1.
The components manufacture has been carried out
by a specialist of profile extrusion. A Ø 83 mm thin
tube was realized. The extrusion was made in two
steps:
1. Extrusion of billet (Ø 355 mm) to a Ø 170 mm
bar;
G.Albertini, E.Girardin, A.Giuliani, D.E.Ilie, B.P.ODonnell, J.P.McGarry and P.E.McHugh
124 Advanced Composites Letters, Vol.14, No.4, 2005
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Table 1. Chemical composition of the AA2009 aluminium alloy.
2. Tube direct extrusion 83 mm, thickness
1.65mm).
A tube of 6 m long was extruded and then treated in
T4 conditions (4h at 498° C, followed by water
quenching and natural aging).
In order to analyse the residual micro-stresses due to
the introduction of reinforcement in the AA2009
matrix and to evaluate thermal mismatch stresses
generated during cooling of the T4 heat treatment,
Finite Element Analysis (FEA) has been performed.
The results have been experimentally validated by
X-ray diffraction, SEM investigation and EDAX.
A RU300 Rigaku Denki x-ray source equipped with
a conventional vertical diffractometer and a Ni
filtered Cu-ka line (wavelength l= 0.154 nm) was
used for the purposes of phase recognition (at
Università Politecnica delle Marche). Residual stress
analysis was performed at the X1 diffractometer of
the Technician University of Berlin (D). The slits
defined a gauge surface of 1x3.14 mm2 . Not filtered
CuKa radiation was used and thus both the CuKa1
(l1 = 0,154061 nm) and CuKa2 (l2 = 0,154178 nm)
wavelengths were used.
A Scanning Electron Microscope Philips XL20
equipped with an EDAX microanalysis device was
also used (at Università Politecnica delle Marche).
3. FINITE ELEMENTS ANALYSIS
MMCs have been the subject of intense analytical
and experimental investigation, to characterise and
understand their mechanical properties and
performance. This is true for MMCs with various
types of reinforcement structures such as particulate,
filaments and continuous fibre reinforcements.
Computational micromechanics has proven very
useful for analysing and predicting both the micro-
scale and macro-scale mechanical performance of
these materials [1, 2]. Computational micromechanics
was used here to explicitly represent the material
microstructure in a FE model. Due to the fact that
the complete analysis of an MMC microstructure, in
which the matrix and reinforcement are represented
separately, with realistic reinforcement geometries
and distribution, is still beyond reasonable
computational capabilities, many micromechanical
descriptions of composites are based on periodic unit
cell approaches. Excellent reviews of investigations
into these aspects of MMCs can be found in Bohm
[3] and Llorca[4].
In the periodic unit cell approach, the microstructure
is divided into periodically repeating unit cells in two
or three dimensions, to which the investigation may
be limited without greatly reducing its generality. The
periodic unit cell methodology has been used very
successfully to study the monotonic tensile loading
behaviour of materials, based on models with
idealised and regular microstructural geometries [1,
2].
In the present study a two dimensional unit cell
approach was taken. The accuracy of two dimensional
models in such situations has been demonstrated in
[2].
The unit cell geometry and the FE mesh were
generated in Patran® using four noded generalised
plane strain elements (Fig. 1).Appropriate elastic
properties for the SiC and elasticplastic properties
for the AA2009 matrix were used. The plastic material
properties of the matrix were reflexive of those of
AA2009 at typical extrusion temperatures (circa
350OC). The SiC particles were assumed to be bonded
to the matrix. To enforce the periodicity of the unit
cell the north and south boundaries had their
displacements coupled, as had the west and east
boundaries of the unit cell. Loading of the model was
simulated by tensile displacements in the vertical
direction (Fig. 2). ABAQUS® was used to perform
the FE simulations. A plot of the maximum tensile
principal residual stress in the material, after a large
strain (50%) and unloading, is shown in Fig. 2.
Evident in the plot is the high local level of maximum
principal stress in some of the particles and in the
separating matrix material, for high macroscopic
strains, strains that are reflexive of those experienced
during extrusion. The average minimum stress in the
particles varies between 160 MPa and 120 MPa;
the average maximum stress in the matrix is between
76 and 160 MPa. These values correlate well with
the experimentally measured values shown in the
Finite Element Simulation and Experimental Determination of Residual Stresses After Extrusion Process in Metal
Matrix Composites
Advanced Composites Letters, Vol.14, No.4, 2005 125
Fig.1: Periodic unit cell
Fig. 2: Contour plot of maximum principal stress in MPa
Fig. 3 reports the obtained diffraction profile. The main
precipitate obtained is Mg2Si, which was assumed to
nucleate during the thermal treatment. Their presence
is generally beneficial because Mg2Si precipitate acts
as a barrier to the dislocations motion. In any case if
the load transfer is excessive, it can lead to the particles
failure.
In order to validate the results obtained by the x-ray
diffraction, the scanning electron microscopy was
used. The samples were cut so that two surfaces with
different orientation with respect to the sample could
be examined: one perpendicular and one parallel to
the extrusion direction. The latter was along a radial
direction of the tube. The analysis were performed
in backscattering mode.
The different atomic numbers allowed discriminating
AA2009 matrix from SiC reinforcement. The
differently coloured areas colour in Fig. 4 corresponds
to SiC particles (Black) and matrix (Grey).
following Table 4.
4. MICROSTRUCTURAL INVESTIGATION
The microstructure of the tube has been investigated
by non-destructive dye penetrating inspection. No
defects such as cracks have been detected.
Further investigation of the microstructure of the
extruded sample was performed. In fact, the optimal
production process minimizes the residual stress from
mechanical or thermal processing and improves the
material strength. Fine dispersions or precipitate phases
can increase the yield strength of the material by
forming a barrier to the dislocation motion. The x-
ray diffraction was used first to detect the precipitate.
The size of the SiC particles is about 6 mm. They are
homogeneously distributed in the samples both in the
extrusion direction and through the tube thickness.
No clustering effect of relevant importance is
observed. EDAX microanalysis was also performed
in different zones of the sample and the following
results were obtained:
1. Wt % values for the alloy elements found in the
matrix are those foreseen in literature for the AA2009
(inside the experimental error), except the Si
percentages that are higher than what foreseen
(probably due to contribution from SiC particles, not
well discriminated from the matrix).
2. Al residues are found in the reinforcement: also
this fact can be attributed to a non perfect
discrimination between matrix and SiC particles.
3. The most interesting result is obtained at the
interface between matrix and reinforcement, where
percentages of Mg, Cu or Si are detected not higher
than those normally obtained in the AA2009 matrix.
This observation can lead to the conclusion that
Mg2Si precipitates (previously detected by x-ray
diffraction) are homogeneously distributed in the
matrix and not located at the interface as it happens
in the case of other composites precipitates [5 ,6].
5. RESIDUAL STRESS ANALYSIS
Residual stress analysis has been performed using x-
ray diffraction in order to validate the simulation
results. The difference in the thermal and elastic
properties of the matrix and the reinforcement, as
G.Albertini, E.Girardin, A.Giuliani, D.E.Ilie, B.P.ODonnell, J.P.McGarry and P.E.McHugh
126 Advanced Composites Letters, Vol.14, No.4, 2005
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Fig. 4. a. SEM magnificated image of an area through the thickness of the tube, b. SEM magnificated image
of an area along the extrusion direction.
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Table 2: Thermal expansion coefficient, Young Modulus and Poisson ratio of the Aluminium matrix and of SiC
reinforcement.
Finite Element Simulation and Experimental Determination of Residual Stresses After Extrusion Process in Metal
Matrix Composites
Advanced Composites Letters, Vol.14, No.4, 2005 127
shown in Table 2, are expected to induce residual
stresses both of thermal and of mechanical nature.
5.1. Experimental conditions
X-ray measurements were performed in the inner and
outer part of the AA2009 + 25 vol. % SiCp tube. The
lay-out of the measurements is shown in Fig. 5: the
axial (Fig. 5a) and hoop (Fig. 5b) directions of the
strain were investigated.
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direction.
The considered crystallographic planes are reported
in Table 3.
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Table 3: Interplanar distance of the considered planes in
Aluminium matrix and in SiC reinforcement.
The gauge region was at the surface of the wall,
localized as in the Fig.5. Measurements were
performed in two corresponding points on the inner
and outer surface of the cut tube. The high absorption
of x-ray beams in the material ensures that only the
surface region is investigated. Thus the radial stress
can be assumed as vanishing.
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5.2. Results
The measured data were analysed through the method
explained in [5 ] obtaining the experimental total
stresses shown in Table 4.
For both phases, the errors are not higher than ± 50
MPa. The model developed in [7] was used in order
to split macro and microstresses (Table 5).
Measurements on Al phase (axial direction) were also
performed on outer surface of the not-cut tube in order
to check if new residual stresses are introduced when
the tube is cut (with the aim of measuring the inner
surface too). No appreciable difference was detected.
6. CONCLUSIONS
We observed a good particles distribution by SEM.
No defects such as cracks have been detected. Mg2Si
precipitates (detected by x-ray diffraction) are
homogeneously distributed in the matrix: their
presence is generally beneficial because this
precipitate acts as a barrier to the dislocations motion.
In any case if the load transfer is excessive, it can
lead to the particles failure.
The aluminium matrix has a larger coefficient of
thermal expansion (CTE) than the reinforcement,
while the reinforcement is stiffer than the matrix. This
leads to two effects:
- upon cooling, tensile stresses are generated
G.Albertini, E.Girardin, A.Giuliani, D.E.Ilie, B.P.ODonnell, J.P.McGarry and P.E.McHugh
128 Advanced Composites Letters, Vol.14, No.4, 2005
in the matrix and compressive stresses in the
reinforcement. These are the thermal mismatch
microstresses, expected to be isotropic,
- then under any applied or residual load, the
stress is composed of a macrostress, which varies over
a spatial range of many grains and is the same in
each phase of the composite, and of an elastic
mismatch microstress which represents the transfer
of load to the stiffer phase.
We studied the inner and outer part of the tube. No
difference has been noticed between them. We
observed quite low macrostresses, as expected due
to the T4 thermal treatment. However, relatively high
thermal microstresses have been detected, in
particular in the SiC reinforcement.
It is clear that there is good agreement between the
experimental results for residual stresses (Table 4)
and the FE model predictions. In particular the
predicted average minimum stress in the particles and
the average maximum stress in the matrix are in the
same order of magnitude as that measured
experimentally for the hoop direction, at both inner
and outer points of the tube. This demonstrates the
usefulness of the finite element models in obtaining
an understanding of the micro-scale mechanical
behaviour of the material during processing. Going
further, the model shows that very high peak tensile
residual stress values are present at certain points in
the microstructure, in particular in the matrix
separating clustered particles. This would indicate a
high risk of material rupture during processing of this
type. However as mentioned above, no micro-scale
damage was observed for this material. In light of
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Table 5: Separation of macroscopic, elastic mismatch and thermal expansion misfit stresses.
the model predictions this would indicate very good
bonding between particles and matrix and the absence
of flaws in the material prior to extrusion.
ACKNOWLEDGEMENTS
The measurements at the TU  Berlin were performed
in the frame of the EU project Human Capital
Mobility  Access to large scale facilities, which is
gratefully acknowledged.
This investigation is a follow up of the EU project
COFCOM (No. BE-97 4568).
References:
1. M.S. Bruzzi, P.E. McHugh, F. ORourke, T. Linder,
Intern. J. of Plasticity, 17 (2001), 565  599.
2. M.S. Bruzzi, P.E. McHugh, J. of Engin. Mater. and
Tech., 127 (2005), 106  118
3. Böhm, H.J., Introduction to Continuum Mechanics,
Course Notes for CISM Course on Mechanics of
Microstructured Materials, 2003, Udine, Italy
4. Llorca, J., Deformation and Damage in Particle
Reinforced Composites: Experiments and Models,
Course Notes for CISM Course on Mechanics of
Microstructured Materials, 2003, Udine, Italy
5. Giuliani, PhD Thesis, Politechnical University of
Marche, A.Y. 2001-2002, Ancona (Italy).
6. G. Albertini, A.A. Forn, E.Girardin, A. Giuliani,
A. Manescu, S. Sereni, Comparative analysis of the
presence, displacement and role of precipitates in Al-
based Matrix Composites, submitted to Materials
Science & Engineering A
7. E. Fitzpatrick, M. T. Hutchings, P. J. Withers, Acta
mater., 45/12 (1997), 4867  4876.
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Article
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The objective of this work was to use micromechanical finite element models to simulate the static mechanical behavior of a metal matrix composite: a cast Al 359 alloy reinforced with 20% SiC particles, at two different temperatures: room temperature and 150°C. In the simulations, periodic unit cell models incorporating the explicit representation of the matrix, reinforcing particles and precipitated primary silicon crystals in both 2D and 3D were used. Micromechanical models with both idealized and realistic reinforcing particle geometries and distributions were generated. The realistic particle geometries and distri-butions were inferred from experimental SEM micrographs. The pattern and intensity of the plastic deformation within the matrix was studied and the macroscale behavior of the composite was inferred from average stress and strain values. In order to include the effects of residual stresses due to the processing of the material, a quenching simulation was performed, prior to mechanical loading, and its effects on the macroscopic and microscopic behavior of the MMC was assessed. The effects of introducing the damage mechanisms of ductile void growth and brittle failure of the reinforcing particles was also investigated. The results of the simulations were compared with experimental results for the MMC in terms of macroscopic tensile stress–strain curves and conclusions were drawn.
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The optimization of the mechanical properties of composites requires a detailed simulation of the complex deformation and failure mechanisms which arise in these heterogeneous microstructures upon loading. It has been shown that damage in the form of particle fracture, interface decohesion or ductile matrix failure controls many important mechanical properties, and this has led to the development of micromechancial models which include damage. This article reviews the current progress in this area within the framework of the two leading simulation approaches: the homogeneization techniques and the finite element analysis of three-dimensional multiparticle unit cells. Although the simulation tools presented are general, they are focused on analysing the behavior of metal- or polymer-matrix composites reinforced with stiff and brittle ceramic particles.
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We discuss basic issues in continuum mechanical modeling of microstructured materials, and present a number of physically based modeling approaches. Among them are mean field and bounding methods as well as unit cell and embedding models. In addition, important aspects of multi-scale modeling are addressed, and a short introduction to the treatment of damage on the constituent level within micromechanical models is given.
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Neutron diffraction measurements of the strain profile in a quenched plate of an aluminium-dash;silicon carbide particle-reinforced metal matrix composite are reported. The results have been used to evaluate the efficacy of an analysis technique which allows distinction of the stiffness mismatch and shape misfit stresses between the matrix and reinforcement, as well as between these and any macrostress present. The analysis is presented for measurements made on a metal matrix composite plate which, as a consequence of quenching from elevated temperature, shows large variations in residual stress as a function of position through the plate thickness. The measurements illustrate the additional insight which can be obtained through the separation of the elastic mismatch and thermal misfit stresses. The stress components thus obtained show good agreement with calculated long-range residual and mismatch stresses.
Article
The objective of this study was to use micromechanical finite element models to simulate both the static and cyclic mechanical behaviour of a metal matrix composite: a forged Al 2124 alloy reinforced with 17% SiC particles, at two different temperatures: room temperature and 150°C. In the simulations, periodic unit cell models incorporating the explicit representation of the matrix and the reinforcing particles in both 2D and 3D, were used. Micromechanical models with both idealised and realistic reinforcing particle shapes and distributions were generated. The realistic particle shapes and distributions were inferred from experimental SEM micrographs. The pattern and intensity of the plastic deformation within the matrix was studied and the macroscale behaviour of the composite was inferred from average stress and strain values. In order to include the effects of residual stresses due to the processing of the material, a quenching simulation was performed, prior to the mechanical loading, and its effects on the macroscopic tensile behaviour of the MMC was assessed. The effects of removing the periodicity constraint on the models by using a cell embedding technique was investigated. In order to try and model the deformation behaviour of the matrix more accurately, crystal plasticity models, which included the explicit representation of individual grains were examined for different matrix grain morphologies. The results of the simulations were compared with experimental results for the MMC in terms of macroscopic tensile stress–strain curves. Finally, the effects of different matrix strain hardening models were examined in order to investigate the cyclic behaviour of the MMC.
Comparative analysis of the presence, displacement and role of precipitates in Albased Matrix Composites
  • G Albertini
  • A A Forn
  • E Girardin
  • A Giuliani
  • A Manescu
  • S Sereni
G. Albertini, A.A. Forn, E.Girardin, A. Giuliani, A. Manescu, S. Sereni, Comparative analysis of the presence, displacement and role of precipitates in Albased Matrix Composites, submitted to Materials Science & Engineering A
  • M S Bruzzi
  • P E Mchugh
M.S. Bruzzi, P.E. McHugh, J. of Engin. Mater. and Tech., 127 (2005), 106 118
  • M S Bruzzi
  • P E Mchugh
  • F Orourke
  • T Linder
M.S. Bruzzi, P.E. McHugh, F. ORourke, T. Linder, Intern. J. of Plasticity, 17 (2001), 565 599.
  • E Fitzpatrick
  • M T Hutchings
  • P J Withers
E. Fitzpatrick, M. T. Hutchings, P. J. Withers, Acta mater., 45/12 (1997), 4867 4876.