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Study of the damage mechanisms in an OSPREY™ Al alloy-SiCp composite by scanning electron microscope in situ tensile tests
MATERIALS SCIENCE & ENGINEERING
A
Materials Science and Engineering A 196 (1995) 135-144
ELSEVIER
Study of the damage mechanisms in an OSPREY T M A1 alloy-SiCp composite by scanning electron microscope in situ tensile tests Eric Maire, Catherine Verdu, G6rard Lormand, Roger Foug~res GEMPPM, URA CNRS n ° 341, INSA-Lyon Bdt. 303, 20 avenue Albert Einstein, F-69621 Villeurbanne Cedex, France
Received 8 March 1994; in revised form 17 October 1994
Abstract Damage mechanisms in a 7049 A1 alloy + 15% SiCp metal matrix composite were studied qualitatively and quantitatively by in situ tensile tests in a scanning electron microscope with gold microgrids deposited onto the surface of the specimen. The first damage mechanisms were found to be rupture of the most elongated particles and, in smaller proportion, decohesion of the particle matrix interface. A high aspect ratio, large size and low local volume fraction of particles appeared to increase the cracking probability. An Eshelby iterative method modified to account for the elastoplastic behaviour of the matrix was used to calculate the stress field induced by the thermomechanical treatment and mechanical loading of the composite. Knowledge of the statistical characteristics of the damaged particles permitted estimation of the critical stress for the two observed damage initiation mechansims. In the case of particle cracking this stress depends on the particle size. Keywords: Damage; Aluminium alloys; SiCp composite; Tensile tests
1. Introduction During the last two decades, interest has been taken in metal matrix composites (MMCs) because their potential elastic properties (Young modulus and yield stress) are promising. The specific modulus of an aluminium alloy composite reinforced with 15 vol.% of SiC particles is close to 33.5 G P a c m 3 g 1, which can be compared with values of 26.8 for unreinforced alloy and 26 for steel [1]. This high value of specific modulus is due to the high stiffness of the reinforcing phase. The yield stress of the composite is also generally greater than that of the unreinforced alloy. This is partly due to load transfer from matrix to reinforcements, but also to microstructural changes in the matrix induced by the presence of the reinforcement (the particles affect the grain size, internal stresses, dislocation density and precipitate distribution). The counterpart of these high elastic properties is the loss in ductility and fracture toughness observed in all M M C systems. In situ tensile tests have been used successfully by several authors [2-6] to study the rupture of micro heterogeneous materials such as MMCs, and they give interesting explanations for the loss of ductility of such materials. The present paper sets out to describe failure Elsevier Science S.A. S S D I 0921-5093(94)09713-5
mechanisms of particulate M M C s obtained by the O S P R E Y T M route and to quantify the damage events using scanning electron microscope (SEM) in situ tensile tests. In addition experimental results are analysed by a model based on the Eshelby method [7].
2. Experimental conditions 2.1. Tensile conditions: s a m p l e s
In situ tensile tests were performed in a J E O L 840A type SEM. The tensile specimen is presented in Fig. 1. 30 mm
t - 7=h J>mm1,0= I
I
I
I
I
i t
1.2 mm
Fig. 1. Shape of the samples used for the SEM in situ tensile tests.
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E. Maire et al. / Materials Science and Engineering A 196 (1995) 135-144
In the middle of the sample, where the SEM observations are performed, it can be considered that the applied stress field is homogeneous and unidirectional. This homogeneity is particularly important because it allows us to analyse our observations quantitatively (no macroscopic stress concentration). In situ tests were carried out with a tensile loading device fixed on the goniometric stage of the SEM. This sensitive device has been designed to allow the observation area to be kept fixed during loading, the motion of the two grips being symmetrical. Gold microgrids were deposited onto a polished and etched surface of the specimen. These square gold microgrids are helpful for analysis of the plastic deformation modes of the matrix, measurement of the local plastic strains and detection of the first events in the damage mechanisms (examples of microgrids can be seen in Figs. 6-8). They are made of 0.17 I~m wide lines with a 2.25 lam pitch. These dimensions are suited to the size of the microstructure of the studied composites (particle diameter approximately 10 gm). Further details concerning the grid can be found in Refs. [4,8].
2.2. Experimental procedure The experimental procedure can be described as follows. Before loading, several specific observation zones are chosen within the useful part of the sample. Then the sample is loaded increasingly. During the tensile test, the loading is arrested in order to detect modifications induced by the damage in the chosen zones and eventually to select new interesting zones. The present work can be divided into two parts. Firstly, we determined the damage mechanism by observing several zones with different magnifications, using the microgrids for detection and measurement of the local deformations in the matrix. Secondly, we focused our study on the quantitative analysis of the damaging phenomena, observing a large surface (i.e. a large amount of particles) to obtain statistical values. The size of the efficient surface of the used sample was 2 x 5 mm 2. Fig. 2 shows the location of the 21 different zones that were chosen and observed during the tensile test and the position of the final rupture according to the x axis. The SEM magnification used was 750. This permitted good detection of damaging phenomena and meant that each zone observed was 160 x 125 lain2 in size. Thus the total size of the studied zones was 0.42 mm 2 (4% of the total surface). The total number of observable particles was close to 1300. The results of these two parts (qualitative and quantitative analyses) are presented in separate sections (3.1 and 3.2 respectively).
L
y
#
finalrupture
/
1/
D
E E~
#
1
2
3
x (.am)
Fig. 2. Location of the 21 observed zones and of the final rupture of the sample.
2.3. Material The studied material is a 7049 aluminium alloy reinforced with 15 vol.% SiC particles. It is obtained by the OSPREY T M route [1,9] then extruded and finally heat treated and slightly overaged. After extrusion the particles are aligned according to the extrusion axis (Fig. 3). This axis is also the tension axis during the tensile loading. The microstructure of the composite matrix was investigated by SEM and transmission electron microscope (TEM) observations. This allowed identification of the following intermetallic phases: r/ strengthening intragranular precipitation (MgZn2) corresponding to platelets (diameter 3 10 nm, thickness 1 nm); E dispersoids, i.e. Cr-rich intermetallics (rod-shape black phase, length 100nm); intergranular phase (q, Mg2Si, E disp e r s o i d s . . . ).
Fig. 3. Optical micrograph of the 7049-SIC composite showing the particle repartition.
E. Maire et al. / Materials Science and Engineering A196 (1995) 1.35 144
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Another problem could arise because the results are obtained from surface studies: in the vicinity of the surface, stress relaxation is easier, thus the stress level in each particle is reduced. After studies of broken samples Humphreys [2] mentions that in the bulk of the material, the number of damage initiation sites is different (more particles are broken or debonded), but the observed mechanisms are similar. The following results and discussion are presented according to the experimentally determined surface properties.
3. Results Fig. 4. Transmission electron micrograph showing the intermetallic phases and the PFZ at the SiC 7049 interface.
The grain size of these O S P R E Y T M composites is very small (3 [am). A classical precipitate-free zone (PFZ) of 4 0 n m size was observed at the grain boundaries. We also observed a PFZ and interfacial phases (r/ and E) at the SiC-matrix interface (Fig. 4). Using a computer controlled image analysis system, we characterized statistically the aspect ratio, the length and the surface fraction of the particles intersecting the polished surface (the definition of these parameters is given in the next section). The results are presented in Figs. 5(a), 5(b) and 5(c) respectively. These properties are largely scattered around the mean values which are mean length of 9.83 ~tm, mean aspect ratio of 1.93, and mean surface fraction of 15%.
2.4. Surface observations The particle size, the particle aspect ratio, and the local particle fraction are obtained by measurements of the cross-sections of particles: for example the length in the tensile axis, and the width perpendicular to this axis in the surface plane. The aspect ratio is the ratio of the length over the width of the particle and the surface fraction is, for a given area, the ratio of the total observable particle surface over the total surface of the area. These values are easy to determine, but are not completely representative of the bulk material properties. We have made the assumption that the particles are perfectly oriented by extrusion and that their bulk dimensions are homogeneously distributed. Under these assumptions, and as far as the volume fraction and aspect ratio of the SiC particles are concerned, the surface measurements give results close to the real intrinsic properties of the composite. As far as the dimensions are concerned, the surface measurements give smaller results than the real intrinsic properties, in the proportion of 2/~.
3.1. Qualitative analysis of the damage mechanisms An example of evolution of one of the selected zones during the test is given in Figs. 6-8. Each figure corresponds to a particular point of the stress-strain curve. Nothing was detected during the elastic loading and all the interesting phenomena described hereafter occurred in the plastic domain.
3. I. 1. Damage initiation The main damage initiation mechanism corresponds to fracture of the SiC particles (compare Figs. 6 and 7). Particle-matrix interface decohesions are also observed, but they occur less frequently, and generally at more important values of plastic strain. The first particle cracks (Fig. 7) are observed in the composite material for an average plastic strain of the sample ep=0.05% and an applied stress aa = 5 7 0 M P a (below the yield stress of the composite which is 0-o.2 = 600 MPa). For the two kinds of damage mechanism observed, the crack occurs most of the time along surfaces roughly perpendicular to the tension axis. This suggests that, when these damage mechanisms are dominant, the critical component of the stress tensor in SiC particles is the normal stress, hereafter noted 0-33.
3.1.2. Damage growth and fracture As the applied stress is increased, the number of damage sites increases. The width of the initial cracks also increases, so that their aspect becomes rectangular (compare Figs. 7 and 8). This can occur because the stress field in front of the crack tip is important. Therefore dislocations are emitted in directions inclined at an angle roughly equal to 45 ° to the crack plane, leading to very strong local shear deformation bands in the matrix (see Fig. 9). Owing to the stress concentration induced by the crack tip in these particles directions, these bands are intragranular. Using the deformation of the gold grids, we estimated the local strains around the particles before and
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E, Maire et al./ Materials Science aml Engineering A 196 (1995) 135 144
30 25
20
o~
M e a n v a l u e = 9.83 pm
18
Mean value = 1.93
920 particles
920 particles
20 ~- 15
~- 10 =
8
o
.~ 10
~ "
5
3
4
5
6 4
1
5
9 13 17 21 25 29 33 37 41 45
Length (um)
Aspect ratio
20 18
14 "G :E 12 8 ,,
4
Lo~I volume fm~ion (%)
Fig. 5. Histograms of (a) the aspect ratio, (b) the length and (c) the local surface fraction of the particles, determined experimentally by surface observations and image analysis.
after cracking. We have found that before and just after cracking (Figs. 6 and 7 respectively) the longitudinal deformation in the matrix near the particles is close to the macroscopic deformation of the sample (approximately 1.1%). This indicates that the plastic relaxation
Fig. 6. Initial state of the observed zone. The tensile axis is horizontal. Note the presence of the gold microgrid as a network of white lines.
of the local stresses is too weak to be measured in this state. As the applied stress is increased after the cracking, very strong shear deformations in the matrix close to the particle cracks lead to amplification of the longitudinal strain of the grid: approximately 5% in Fig. 8 and approximately 13% in Fig. 9 compared with 0.8%
Fig. 7. Particle cracking (same zone), a~,= 570 MPa, ep=0.05%. Note the deformation of the microgrid near the particle crack.
E. Maire et al.
,I Materials Science and Engineering A 196 (1995) 135 144
139
14
600
12
500
10
400
8
300 "B
g
200
4
100
2 0
0 0.2
0.4
0.6
0.8
Plastic strain (%)
Fig. 10. Cumulative fraction of damaged particles and interdamage distance vs. the plastic strain of the sample. Particle crackings occur first. Particle matrix decohesions occur at higher values of plastic strain. At rupture, the fraction of damaged particles is about 13% and the interdamage distance is about 100 gin. Fig. 8. Plastic deformation of the matrix in front of the crack tip, d,, = 600 MPa, Cp= 0.8%. Note the increase in width of the particle crack.
and 1.46 for the average macroscopic strains of the samples respectively. Post rupture observations permit us to show that in the present case, and away from the crack tips, the junction between the first cracks is rather intergranular. Crack propagation in the matrix is thus firstly intragranular (in front of the particle crack tip), and then intergranular. Fracture of the sample seems to occur when the number of particle c r a c k s - - a n d thus the interdamage distance reach critical values.
3.2. Quantitative analysis 3.2.1. Fraction of the damaged particles We have mentioned that as far as rupture is concerned, the important parameter seems to be the dis-
tance between the microcracks (propagation length). This parameter is dependent on the fraction of damaged particles. Fig. 10 shows the cumulated fraction Nr of damaged particles (Nr is the ratio of the total number of damaged particles to the total number of observed particles) vs. the macroscopic plastic strain of the sample. The first observed mechanism is particle cracking. Particle-matrix decohesions occur at a more important value of the plastic strain. Fig. 10 shows also the evolution of the mean distance between the microcracks calculated in the following way, D
d=--
where D is the mean interparticle distance: ( 7rL 3 ~1/3
O = t
L being the mean length (9.83 gm), s is the mean aspect ratio (1.93) and Vr the volume fraction (15%) of the observed particles (see Fig. 5) assumed to be arranged according to a simple cubic lattice. When the final rupture occurs, the total fraction of damaged particles is 13% of the total observed particles and the mean interdamage distance is about 100 ~tm. The final proportion of the two different mechanisms indicates that particle cracking dominant: particle cracking 9%, particle-matrix decohesion 4%.
3.2.2. Size of the damaged particles
Fig. 9. Deformation of the matrix in front of the particle crack tip. The gold microgrid can be used to estimate the value of local deformations. The macroscopic plastic deformation of the sample is c p - 1.46%.
Fig. 11 shows the mean length of the particles damaged during a loading step (from the previous arrest up to the next arrest) vs. the plastic strain of the sample. The length of damaged particles is widely distributed, but the mean value decreases with plastic strain and is also larger than the mean value of all the observed particles. This illustrates that the large particles are more likely to crack than the small particles.
E. Maire et al. / Materials Science and Engineering A196 (1995) 135 144
140
--0---PartiClecracking I I'-D- Particle/matH;-decohesionI
30
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:~ 25 z 20
,~=25 ~
~
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I
I
I
0.2
0.4
0.6
0.8
0.5
1
1.5
2
25
3
x (mm)
Plastic strain (%)
Fig. II. Mean length of the particles damaged during each step of loading as a function of plastic strain. The height of the segment is equal to the standard deviation.
Fig. 13. Fraction of damaged particles and local particle surface fraction vs. the x coordinate of the observed zones for different values of plastic strain. The final rupture occurs in a section in which the number of damaged particles is high, and their surface fraction low.
3.2.3• Aspect ratio of the damaged particles
are m a d e on d a m a g e g r o w t h and fracture.
Fig. 12 shows the mean aspect ratio of the particles damaged during a loading step vs. the plastic strain of the sample. Like the particle size, this parameter decreases with plastic strain. Its mean value is also larger than that of the whole observed particles. This is an experimental illustration that the elongated particles tend to crack more easily•
3.2.4• Damage localization in the sample For different values of plastic strain, Fig. 13 shows the evolution of the fraction of damaged particles in different sections of the sample vs. their position x along the sample length axis (see Fig. 2). Fig. 13 also permits us to visualize the experimentally determined local surface fraction of particles in each section. This surface fraction is the mean value of the nine measurements taken before the tensile test along the y axis of the sample and situated at the same x coordinate. We notice that the fracture occurs in a section corresponding to a position x where the number of damaged particles is high from the beginning of plastic deformation. 4. Discussion T h e m a i n p a r t o f t h e d i s c u s s i o n is d e v o t e d t o d a m a g e i n i t i a t i o n in c o m p o s i t e s . A f e w c o m p l e m e n t a r y r e m a r k s
4.5 4 .o
--o-- PedicJecracking -,o- Particle/matrix decohes on
4. I. D a m a g e initiation
Using a finite element method, Lay and Boivin [10] calculated that the presence of a PFZ around SiC particles leads to a slight reduction in the normal stress at the surface of the particle. Our experimental observations indicate that despite the presence of such a narrow PFZ (see Fig. 4), the main damage mechanism is still the rupture of SiC particles. Thus we have decided to neglect the PFZ effect in the following discussion, and in addition the metal-ceramic interface has been assumed to be perfect from a mechanical point of view. The value of the stress field within inclusions has a great influence on damage initiation. We briefly mention the main origins of this field in the case of MMCs: thermal incompatibilities arise during cooling of the sample owing to mismatch of the coefficients of thermal expansion between matrix and particle ( 0 ~ 7 0 4 9 - ~ S i C = 20 x 10 6 oc-1); elastic incompatibilities increase during loading owing to the mismatch of elastic properties (see Table 1); plastic incompatibilities arise because the matrix exhibits plastic deformations while the particles remain elastic. In order to explain in a theoretical way some of the experimental phenomena observed in the damage initiation domain, we used an Eshelby iterative model [11] which allows calculation of the internal stress field induced in the SiC particles by the incompatibilities mentioned above. In this model, particle reinforcements
3
2.5 2
Table 1 Thermoelastic constants used for the two constituents of the composite
Mean value for all the observed particles
1
0.5 0 0
I 0.2
J 0.4
I 0.6
I 0.8
I 1
plastic strain (%)
Fig. 12, Aspect ratio of the particles damaged during each step of loading as a function of the plastic strain. The height of the segment is equal to the standard deviation.
Material
E (GPa)
Poisson's ratio
~ (10 × 10 -6 °C I)
SiC 7049
403 ~ 72
0.2 0.33
3.5 23.5
a Measured using the nanoindentation technique.
E. Maire et al./ Materials Science and Engineering A 196 (1995) 135-144 Table 2 Variation in the secant modulus and Poisson's ratio of the elastoplastic matrix with plastic strain Plastic strain (%)
E secant (GPa)
v*
0 0.08 0.2 0.39 0.66 0.9
72 65.7 57.85 48.82 40.18 34.89
0.33 0.346 0.364 0.386 0.406 0.418
can be divided into several families, each being defined by values of different parameters corresponding to elastic properties, particle orientation in the applied stress field and aspect ratio. Compared with the initial presentation, we have introduced a modification in the model. It is an extension of calculation of the internal stresses to the non-linear case. This permits us to take the elastoplastic behaviour of the matrix into account. We replace the elastoplastic matrix by a virtual elastic material. The elastic properties of this material are given by the secant properties of the matrix under the considered loading. The initial elastic modulus and Poisson's ratio are replaced by the secant modulus and the instantaneous Poisson ratio corresponding to each plastic strain, which we have determined from the stress-strain tensile curve of the unreinforced alloy. These concepts were first introduced by Hill [12]. They were applied for example to the self-consistent scheme [13], to the three-phase model [14] and to the Tanaka and Mori model [15]. The secant values of the modulus and of the Poisson ratio are presented in Table 2. The instantaneous Poisson ratio is assumed to be a function of the ratio of the elastic and total deformations, calculated from equality of the variation in volume of the virtual elastic material and the real plastic matrix. The cracking of a given SiC particle occurs when the total loading (thermal, elastic and plastic) induces a critical stress field in this particle. A possible stress criterion could be based on an invariant of the stress tensor such as Tresca or Von Mises stresses. Nevertheless, the particle crack planes are observed to be perpendicular to the tensile axis. Moreover, the behaviour of the SiC particle is perfectly elastic whereas these criteria are well adapted to the description of the plastic behaviour. Thus, we chose to focus the analysis on the value of the normal stress which is calculated using the iterative Eshelby model. Typical thermomechanical properties of the two constituents are given in Table 1. The values of Young modulus of the SiC particles given in this table and used for the calculations were determined experimentally in our laboratory [16] by nanoindentation experiments [17,18]:
141
O0 o ©
0° o
.
} 0 f- {1} Fig. 14. Schematic representation of the model composite reinforced with several families of inclusions. In the Eshelby analysis, the particles are assumed to be ellipsoidal. The {1}, {2}, and {3} axes in the figure are the axes of the sample. The stress is applied according to the {3} axis.
The state of the sample held at the ageing temperature for a long time can be assumed to be a reference state in which the internal stresses in the whole body of the sample are completely relaxed. The temperature drop AT for thermal eigenstrain has been fixed at - 1 7 0 °C. This value corresponds to the difference between the ageing temperature and room temperature (no plastic relaxation). In order to represent accurately the studied composite material, we have defined different families which reproduce the distribution of the particle aspect ratio observed in the composite (see Fig. 5(a)). This distribution can be modelled by 21 families of particles. The aspect ratio and the partial volume fraction of each of the 21 families is determined from the histogram by the position and the height of the corresponding class. A schematic representation of the system is given in Fig. 14. Fig. 15 shows the normal stress component 033 vs. the applied stress o, calculated in four particular families of SiC particles (s = 0.25, 1, 2, and 6.25). The stress field in each family depends of course on the partial volume fraction and aspect ratio of the other families. The following remarks can be made. The curves become non-linear when plastic incompatibility begins to occur. The plastic incompatibility can become as important as thermal and elastic incom-
1500 i
N
z
t--u- s=l
~
0 ~---
-500
2" t
400
600
-1000 Applied stress (MPa) Fig. ]5. Normal stresses vs. the applied stress in four different families of SiC inclusions (s = 0.25, s = 1, s = 2 and s = 6.25). The composite is modelled according to the real distribution of the aspect ratios of the particles (Fig. 1 I, 21 families).
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E. Maire et al. / Materials Seienee and Engineering A 196 (1995) 135-144 1800
1800
1600
1600 •
~" 1400
g
1200 1000
c p-0.92%
~" 1400
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s p=0.66~. o
~
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~ -
~p~O~
~
~
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~
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zo
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o ¢p=0.92%
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Q ~p-O.39Y.
800 600 z
400
Pa~cle/matdx decoheslon
200-
200
0 I
I
I
I
I
I
50
100
150
200
250
300
Average surface (pm2)
Fig. 16. Particle cracking: rupture normal stress calculated in the particles with aspect ratio displayed in Fig. 12 as a function of their average surface. The corresponding plastic strain of the sample is also indicated. The normal stress required to break the small particles is more important.
patibilities when the plastic deformation ev reaches 0.2%, the value of p r o o f strain at which the conventional yield stress is defined. Before tensile loading of the composite (a, = 0), SiC particles exhibit a normal compression stress component, owing to the thermal incompatibility induced by cooling. As can be seen in Fig. 15, the longest particles (high aspect ratio) are the most compressed. Therefore at the beginning of tensile loading, the risk of damage is reduced in these particles. However, as the applied stress is increased, the normal stress ~r33 in the elongated particles increases more rapidly than in rather spherical particles. For an applied tensile stress c;, of 300 MPa, all the particles are submitted to a tensile stress according to the tensile axis. Then the situation is reversed: the normal stress within the elongated particles becomes higher than that within the other particles. As particle cracks have been observed at an applied stress of 570 MPa, it is clear from these theoretical considerations that the first broken particles are the most elongated particles. This is in good agreement with experimental observations.
4.2. Estimation of the rupture stress of the particles and of the ceramic-metal interfaces For particle cracking and particle-matrix decohesion respectively, Figs. 16 and 17 show the evolution of the critical values of the rupture normal stresses calculated in the damaged particles (i.e. having the aspect ratio given in Fig. 12) vs. their observed surface. We chose this surface parameter because it is representative of the size of the particles. There is a correlation between the stress we calculate and the experimental mean size of broken particles. Unfortunately, the kind of model we use cannot describe this effect: as a matter of fact the value of the stress field calculated from the Eshelby method does not depend on the size of the particles. The size effect may be explained by the fact that SiC
50
I 70
I 90
I 110
I 130 Average surface (pm2)
i 150
I 170
Fig. 17. Particle decohesion: rupture normal stress calculated in the particles with aspect ratio displayed in Fig. 12 as a function of their average surface. The corresponding plastic strain of the sample is also indicated. The normal stress required to debond the interface seems to be independent of the particle size.
particle cracking occurs probably at defects introduced during fabrication of these particles and that the large particles are likely to contain more defects than the small particles. This has been mentioned already in the literature [19] as a Weibull effect. This size influence appears to be weak in the case of the decohesion mechanism (see Fig. 17). The normal stress is calculated at the extreme poles of the particles, where the interface of the ellipsoidal particle is normal to the stress applied and also where the decohesions are observed experimentally. This indicates that this second kind of damage phenomenon seems to be independent of the size of the particle. Decohesion is controlled by the strength of the interface and is probably dependent on the level of plastic deformation in the matrix around the particle. Figs. 18 and 19 show (for particle cracking and particle-matrix decohesion respectively) the evolution of the rupture normal stress vs. the aspect ratio of the damaged particles. For a given damage mechanism, this value of stress should be an intrinsic constant of the material used for the reinforcement. We observe that the particle cracking, the stress that we calculate depends on the aspect ratio. This dependence should be linked to the size effect described above and, moreover, the large particles are likely to have a larger aspect ratio than the small particles. 1800 1600 1400 12oo 1000 "~ 800 600 Zo 400 2OO 0
t~ =0.66%
0 8p=0.2~,
Particlecracking
2.2
2.4
2.6
2.8
3
Aspect ratio
Fig. 18. Particle cracking: rupture normal stress calculated in the particles with mean aspect ratio displayed in Fig. 12 as a function of their aspect ratio. The corresponding plastic strain of the sample is also indicated.
E. Maire et al. / Materials Science and Engineering A 196 (1995) 135 1,14
1800 1600
_
1400
Cp=0.66% °
1200
C,o
lOOO
f;p=0.39 Y~
Ep=0,92%
800 600 z
particle/matrix
400
decohesion
200 0
I
1.9
21
i
i
2.3 2.5 Aspect ratio
I
I
2.7
2.9
Fig. 19. Particle matrix decohesion: rupture normal stress calculated in the particles with mean aspect ratio displayed in Fig. 12 as a function of their aspect ratio. The corresponding plastic strain of the sample is also indicated.
4.3. Rupture Fracture of the composite occurs by linking together of the microcracks in SiC particles by other cracks in the matrix. From a junction mechanism point of view, an important parameter is the distance between broken particles. This parameter decreases as the volume fraction of particles in the composite is increased, but it is also dependent on the local fraction of broken particles. We observe that rupture occurs in a section corresponding to a position x where this distance is a minimum (Fig. 20). The rupture resistance also depends on the way in which the junction in the matrix is produced. In our case, the junction mainly follows the grain boundaries. Owing to the small grain size in O S P R E Y T M composites, the junction distance is thus increased in these materials. This could have a beneficial effect on the ductility of these composites.
5. Conclusions Damage mechanisms in a 7049 aluminium alloySiCp composite were studied by means of SEM in situ tensile tests. Qualitatively, the different steps of the
143
fracture mechanism are the following: damage initiation occurs by cracking of SiC particles and decohesion of the aluminium-SiC interface according in a direction perpendicular to the tension axis. As the applied stress is increased the number of damage sites increases. So does the width of the first initiated cracks, inducing amplification of the local plastic deformation in the matrix. Fracture of the sample occurs by joining together the cracks in the SiC particles and by nucleation and growth of cracks in the matrix. These cracks are intergranular. Quantitative analysis of these phenomena has shown that the elongated and large particles tend to crack easily. Particle cracking occurs at the beginning of the plastic deformation. Decohesion occurs at larger values of the plastic strain. Fracture occurs in a section where the number of damaged particles is high, leading to a low value of interdamage distance. The stress field in the inclusions induced by the complex thermomechanical loading of the composite was calculated by an Eshelby iterative method modified to account for the elastoplastic behaviour of the matrix by using its secant modulus and instantaneous Poisson ratio in the elastic calculation. This has permitted us to explain some of the observations made during the tensile tests: the first cracks appear in the most elongated particles. This has also allowed us to predict the critical value of normal stress responsible for the occurrence of damage. For particle cracking, this predicted stress depends on the particle size.
Acknowledgements This work was financially supported by the Commission of the European Communities and all the partners of the European Brite contract "Low cost MMC made by Spray Deposition", which are fully acknowledged.
References 30
FINAL RUPTUR
150
A
----O-.-- Local Surface fraction ( % )
25
125
N D / N t (%) - o
20
Local inte~larrlage distance
lOO
,
15
E
7s
10~ o
5
50 0
1
2
3
X (mm)
Fig. 20. Mean local distance between the microcracks vs. the position in the sample. This distance is calculated with the mean local fraction of particles and the mean fraction of damaged particles just before
rupture (cp = 0.9%).
[ll T.C. Willis, J. White, R.M. Jordan and I.R. Hughes, Proc. Congress on P M Aerospace Materials, Lucerne, November 1987, 29-1. [2] F J . Humphreys, Proc. Congress EMAG MICRO 89, London, September 1989, p. 465. [3] A. Mocellin, R. Foug6res and P.F. Gobin, J. Mater. Sci., 28 (1993) 4855. [4] M.H. Ambroise, T. Bretheau and A. Zaoui, in G.J. Weng, M. Taya and H. Abe (eds.), Micromechanics and Homogeneity, New York, 1990, p. 41. [5] M. Manoharan and J.J. Lewandowski, Scr. Metall., 23 (1989) 1801. [6] C.S. Lee, Y.H. Kim, T. Lim and K.S. Han, Scr. Metall. Mater., 25 (1991) 613. [7] J.D. Eshelby, in I.N. Sneddon and R. Hill (eds.), Progress in Solid Mechanics, North-Holland, Amsterdam, 1961, p. 89.
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[8] A. Karimi, Mater. Sci. Eng., 63 (1984) 267. [9] A.R.E. Singer, Mater. Sci. Eng., A135 (1991) 13. [10] B. Lay and M. Boivin, in M.S.J. Hashmi (ed.), Proc. Int. Conf. on Advances in Materials and Processing AMPT'93, Dublin, 2 4 - 2 7 August 1993, p. 1149.
Technologies,
[11] R. Hamann, A. Mocellin, P.F. Gobin and R. Foug6res, Scr. Metall. Mater., 26 (1992) 963. [12] R. Hill, J. Mech. Phys. Solids, 13 (1965) 89. [13] M. Berveiller and A. Zaoui, J. Mech. Phys. Solids, 26(1979) 325.
[14] E. Herve and A. Zaoui, Eur. J. Mech., A, 9 (1990) 325. [15] N. Bourgeois, Ph.D. Thesis, Ecole Centrale Paris Chgttenay-Malabry, June 1994. [16] P. Lamagndre et al. to be published. [17] W.C. Oliver and G.M. Phar, J. Mater. Res., 7 (1992) 1565. [18] I.N. Sneddon, Int. J. Eng. Sci., 3 (1965) 47. [19] J. Llorca, A. Martin, J. Ruiz and M. Elices, Metall. Trans. A, 24 (1993) 1575.
A
Materials Science and Engineering A 196 (1995) 135-144
ELSEVIER
Study of the damage mechanisms in an OSPREY T M A1 alloy-SiCp composite by scanning electron microscope in situ tensile tests Eric Maire, Catherine Verdu, G6rard Lormand, Roger Foug~res GEMPPM, URA CNRS n ° 341, INSA-Lyon Bdt. 303, 20 avenue Albert Einstein, F-69621 Villeurbanne Cedex, France
Received 8 March 1994; in revised form 17 October 1994
Abstract Damage mechanisms in a 7049 A1 alloy + 15% SiCp metal matrix composite were studied qualitatively and quantitatively by in situ tensile tests in a scanning electron microscope with gold microgrids deposited onto the surface of the specimen. The first damage mechanisms were found to be rupture of the most elongated particles and, in smaller proportion, decohesion of the particle matrix interface. A high aspect ratio, large size and low local volume fraction of particles appeared to increase the cracking probability. An Eshelby iterative method modified to account for the elastoplastic behaviour of the matrix was used to calculate the stress field induced by the thermomechanical treatment and mechanical loading of the composite. Knowledge of the statistical characteristics of the damaged particles permitted estimation of the critical stress for the two observed damage initiation mechansims. In the case of particle cracking this stress depends on the particle size. Keywords: Damage; Aluminium alloys; SiCp composite; Tensile tests
1. Introduction During the last two decades, interest has been taken in metal matrix composites (MMCs) because their potential elastic properties (Young modulus and yield stress) are promising. The specific modulus of an aluminium alloy composite reinforced with 15 vol.% of SiC particles is close to 33.5 G P a c m 3 g 1, which can be compared with values of 26.8 for unreinforced alloy and 26 for steel [1]. This high value of specific modulus is due to the high stiffness of the reinforcing phase. The yield stress of the composite is also generally greater than that of the unreinforced alloy. This is partly due to load transfer from matrix to reinforcements, but also to microstructural changes in the matrix induced by the presence of the reinforcement (the particles affect the grain size, internal stresses, dislocation density and precipitate distribution). The counterpart of these high elastic properties is the loss in ductility and fracture toughness observed in all M M C systems. In situ tensile tests have been used successfully by several authors [2-6] to study the rupture of micro heterogeneous materials such as MMCs, and they give interesting explanations for the loss of ductility of such materials. The present paper sets out to describe failure Elsevier Science S.A. S S D I 0921-5093(94)09713-5
mechanisms of particulate M M C s obtained by the O S P R E Y T M route and to quantify the damage events using scanning electron microscope (SEM) in situ tensile tests. In addition experimental results are analysed by a model based on the Eshelby method [7].
2. Experimental conditions 2.1. Tensile conditions: s a m p l e s
In situ tensile tests were performed in a J E O L 840A type SEM. The tensile specimen is presented in Fig. 1. 30 mm
t - 7=h J>mm1,0= I
I
I
I
I
i t
1.2 mm
Fig. 1. Shape of the samples used for the SEM in situ tensile tests.
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E. Maire et al. / Materials Science and Engineering A 196 (1995) 135-144
In the middle of the sample, where the SEM observations are performed, it can be considered that the applied stress field is homogeneous and unidirectional. This homogeneity is particularly important because it allows us to analyse our observations quantitatively (no macroscopic stress concentration). In situ tests were carried out with a tensile loading device fixed on the goniometric stage of the SEM. This sensitive device has been designed to allow the observation area to be kept fixed during loading, the motion of the two grips being symmetrical. Gold microgrids were deposited onto a polished and etched surface of the specimen. These square gold microgrids are helpful for analysis of the plastic deformation modes of the matrix, measurement of the local plastic strains and detection of the first events in the damage mechanisms (examples of microgrids can be seen in Figs. 6-8). They are made of 0.17 I~m wide lines with a 2.25 lam pitch. These dimensions are suited to the size of the microstructure of the studied composites (particle diameter approximately 10 gm). Further details concerning the grid can be found in Refs. [4,8].
2.2. Experimental procedure The experimental procedure can be described as follows. Before loading, several specific observation zones are chosen within the useful part of the sample. Then the sample is loaded increasingly. During the tensile test, the loading is arrested in order to detect modifications induced by the damage in the chosen zones and eventually to select new interesting zones. The present work can be divided into two parts. Firstly, we determined the damage mechanism by observing several zones with different magnifications, using the microgrids for detection and measurement of the local deformations in the matrix. Secondly, we focused our study on the quantitative analysis of the damaging phenomena, observing a large surface (i.e. a large amount of particles) to obtain statistical values. The size of the efficient surface of the used sample was 2 x 5 mm 2. Fig. 2 shows the location of the 21 different zones that were chosen and observed during the tensile test and the position of the final rupture according to the x axis. The SEM magnification used was 750. This permitted good detection of damaging phenomena and meant that each zone observed was 160 x 125 lain2 in size. Thus the total size of the studied zones was 0.42 mm 2 (4% of the total surface). The total number of observable particles was close to 1300. The results of these two parts (qualitative and quantitative analyses) are presented in separate sections (3.1 and 3.2 respectively).
L
y
#
finalrupture
/
1/
D
E E~
#
1
2
3
x (.am)
Fig. 2. Location of the 21 observed zones and of the final rupture of the sample.
2.3. Material The studied material is a 7049 aluminium alloy reinforced with 15 vol.% SiC particles. It is obtained by the OSPREY T M route [1,9] then extruded and finally heat treated and slightly overaged. After extrusion the particles are aligned according to the extrusion axis (Fig. 3). This axis is also the tension axis during the tensile loading. The microstructure of the composite matrix was investigated by SEM and transmission electron microscope (TEM) observations. This allowed identification of the following intermetallic phases: r/ strengthening intragranular precipitation (MgZn2) corresponding to platelets (diameter 3 10 nm, thickness 1 nm); E dispersoids, i.e. Cr-rich intermetallics (rod-shape black phase, length 100nm); intergranular phase (q, Mg2Si, E disp e r s o i d s . . . ).
Fig. 3. Optical micrograph of the 7049-SIC composite showing the particle repartition.
E. Maire et al. / Materials Science and Engineering A196 (1995) 1.35 144
137
Another problem could arise because the results are obtained from surface studies: in the vicinity of the surface, stress relaxation is easier, thus the stress level in each particle is reduced. After studies of broken samples Humphreys [2] mentions that in the bulk of the material, the number of damage initiation sites is different (more particles are broken or debonded), but the observed mechanisms are similar. The following results and discussion are presented according to the experimentally determined surface properties.
3. Results Fig. 4. Transmission electron micrograph showing the intermetallic phases and the PFZ at the SiC 7049 interface.
The grain size of these O S P R E Y T M composites is very small (3 [am). A classical precipitate-free zone (PFZ) of 4 0 n m size was observed at the grain boundaries. We also observed a PFZ and interfacial phases (r/ and E) at the SiC-matrix interface (Fig. 4). Using a computer controlled image analysis system, we characterized statistically the aspect ratio, the length and the surface fraction of the particles intersecting the polished surface (the definition of these parameters is given in the next section). The results are presented in Figs. 5(a), 5(b) and 5(c) respectively. These properties are largely scattered around the mean values which are mean length of 9.83 ~tm, mean aspect ratio of 1.93, and mean surface fraction of 15%.
2.4. Surface observations The particle size, the particle aspect ratio, and the local particle fraction are obtained by measurements of the cross-sections of particles: for example the length in the tensile axis, and the width perpendicular to this axis in the surface plane. The aspect ratio is the ratio of the length over the width of the particle and the surface fraction is, for a given area, the ratio of the total observable particle surface over the total surface of the area. These values are easy to determine, but are not completely representative of the bulk material properties. We have made the assumption that the particles are perfectly oriented by extrusion and that their bulk dimensions are homogeneously distributed. Under these assumptions, and as far as the volume fraction and aspect ratio of the SiC particles are concerned, the surface measurements give results close to the real intrinsic properties of the composite. As far as the dimensions are concerned, the surface measurements give smaller results than the real intrinsic properties, in the proportion of 2/~.
3.1. Qualitative analysis of the damage mechanisms An example of evolution of one of the selected zones during the test is given in Figs. 6-8. Each figure corresponds to a particular point of the stress-strain curve. Nothing was detected during the elastic loading and all the interesting phenomena described hereafter occurred in the plastic domain.
3. I. 1. Damage initiation The main damage initiation mechanism corresponds to fracture of the SiC particles (compare Figs. 6 and 7). Particle-matrix interface decohesions are also observed, but they occur less frequently, and generally at more important values of plastic strain. The first particle cracks (Fig. 7) are observed in the composite material for an average plastic strain of the sample ep=0.05% and an applied stress aa = 5 7 0 M P a (below the yield stress of the composite which is 0-o.2 = 600 MPa). For the two kinds of damage mechanism observed, the crack occurs most of the time along surfaces roughly perpendicular to the tension axis. This suggests that, when these damage mechanisms are dominant, the critical component of the stress tensor in SiC particles is the normal stress, hereafter noted 0-33.
3.1.2. Damage growth and fracture As the applied stress is increased, the number of damage sites increases. The width of the initial cracks also increases, so that their aspect becomes rectangular (compare Figs. 7 and 8). This can occur because the stress field in front of the crack tip is important. Therefore dislocations are emitted in directions inclined at an angle roughly equal to 45 ° to the crack plane, leading to very strong local shear deformation bands in the matrix (see Fig. 9). Owing to the stress concentration induced by the crack tip in these particles directions, these bands are intragranular. Using the deformation of the gold grids, we estimated the local strains around the particles before and
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E, Maire et al./ Materials Science aml Engineering A 196 (1995) 135 144
30 25
20
o~
M e a n v a l u e = 9.83 pm
18
Mean value = 1.93
920 particles
920 particles
20 ~- 15
~- 10 =
8
o
.~ 10
~ "
5
3
4
5
6 4
1
5
9 13 17 21 25 29 33 37 41 45
Length (um)
Aspect ratio
20 18
14 "G :E 12 8 ,,
4
Lo~I volume fm~ion (%)
Fig. 5. Histograms of (a) the aspect ratio, (b) the length and (c) the local surface fraction of the particles, determined experimentally by surface observations and image analysis.
after cracking. We have found that before and just after cracking (Figs. 6 and 7 respectively) the longitudinal deformation in the matrix near the particles is close to the macroscopic deformation of the sample (approximately 1.1%). This indicates that the plastic relaxation
Fig. 6. Initial state of the observed zone. The tensile axis is horizontal. Note the presence of the gold microgrid as a network of white lines.
of the local stresses is too weak to be measured in this state. As the applied stress is increased after the cracking, very strong shear deformations in the matrix close to the particle cracks lead to amplification of the longitudinal strain of the grid: approximately 5% in Fig. 8 and approximately 13% in Fig. 9 compared with 0.8%
Fig. 7. Particle cracking (same zone), a~,= 570 MPa, ep=0.05%. Note the deformation of the microgrid near the particle crack.
E. Maire et al.
,I Materials Science and Engineering A 196 (1995) 135 144
139
14
600
12
500
10
400
8
300 "B
g
200
4
100
2 0
0 0.2
0.4
0.6
0.8
Plastic strain (%)
Fig. 10. Cumulative fraction of damaged particles and interdamage distance vs. the plastic strain of the sample. Particle crackings occur first. Particle matrix decohesions occur at higher values of plastic strain. At rupture, the fraction of damaged particles is about 13% and the interdamage distance is about 100 gin. Fig. 8. Plastic deformation of the matrix in front of the crack tip, d,, = 600 MPa, Cp= 0.8%. Note the increase in width of the particle crack.
and 1.46 for the average macroscopic strains of the samples respectively. Post rupture observations permit us to show that in the present case, and away from the crack tips, the junction between the first cracks is rather intergranular. Crack propagation in the matrix is thus firstly intragranular (in front of the particle crack tip), and then intergranular. Fracture of the sample seems to occur when the number of particle c r a c k s - - a n d thus the interdamage distance reach critical values.
3.2. Quantitative analysis 3.2.1. Fraction of the damaged particles We have mentioned that as far as rupture is concerned, the important parameter seems to be the dis-
tance between the microcracks (propagation length). This parameter is dependent on the fraction of damaged particles. Fig. 10 shows the cumulated fraction Nr of damaged particles (Nr is the ratio of the total number of damaged particles to the total number of observed particles) vs. the macroscopic plastic strain of the sample. The first observed mechanism is particle cracking. Particle-matrix decohesions occur at a more important value of the plastic strain. Fig. 10 shows also the evolution of the mean distance between the microcracks calculated in the following way, D
d=--
where D is the mean interparticle distance: ( 7rL 3 ~1/3
O = t
L being the mean length (9.83 gm), s is the mean aspect ratio (1.93) and Vr the volume fraction (15%) of the observed particles (see Fig. 5) assumed to be arranged according to a simple cubic lattice. When the final rupture occurs, the total fraction of damaged particles is 13% of the total observed particles and the mean interdamage distance is about 100 ~tm. The final proportion of the two different mechanisms indicates that particle cracking dominant: particle cracking 9%, particle-matrix decohesion 4%.
3.2.2. Size of the damaged particles
Fig. 9. Deformation of the matrix in front of the particle crack tip. The gold microgrid can be used to estimate the value of local deformations. The macroscopic plastic deformation of the sample is c p - 1.46%.
Fig. 11 shows the mean length of the particles damaged during a loading step (from the previous arrest up to the next arrest) vs. the plastic strain of the sample. The length of damaged particles is widely distributed, but the mean value decreases with plastic strain and is also larger than the mean value of all the observed particles. This illustrates that the large particles are more likely to crack than the small particles.
E. Maire et al. / Materials Science and Engineering A196 (1995) 135 144
140
--0---PartiClecracking I I'-D- Particle/matH;-decohesionI
30
o~ 30
:~ 25 z 20
,~=25 ~
~
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~ 15
~ lo.
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5.
0
I
I
I
I
0.2
0.4
0.6
0.8
0.5
1
1.5
2
25
3
x (mm)
Plastic strain (%)
Fig. II. Mean length of the particles damaged during each step of loading as a function of plastic strain. The height of the segment is equal to the standard deviation.
Fig. 13. Fraction of damaged particles and local particle surface fraction vs. the x coordinate of the observed zones for different values of plastic strain. The final rupture occurs in a section in which the number of damaged particles is high, and their surface fraction low.
3.2.3• Aspect ratio of the damaged particles
are m a d e on d a m a g e g r o w t h and fracture.
Fig. 12 shows the mean aspect ratio of the particles damaged during a loading step vs. the plastic strain of the sample. Like the particle size, this parameter decreases with plastic strain. Its mean value is also larger than that of the whole observed particles. This is an experimental illustration that the elongated particles tend to crack more easily•
3.2.4• Damage localization in the sample For different values of plastic strain, Fig. 13 shows the evolution of the fraction of damaged particles in different sections of the sample vs. their position x along the sample length axis (see Fig. 2). Fig. 13 also permits us to visualize the experimentally determined local surface fraction of particles in each section. This surface fraction is the mean value of the nine measurements taken before the tensile test along the y axis of the sample and situated at the same x coordinate. We notice that the fracture occurs in a section corresponding to a position x where the number of damaged particles is high from the beginning of plastic deformation. 4. Discussion T h e m a i n p a r t o f t h e d i s c u s s i o n is d e v o t e d t o d a m a g e i n i t i a t i o n in c o m p o s i t e s . A f e w c o m p l e m e n t a r y r e m a r k s
4.5 4 .o
--o-- PedicJecracking -,o- Particle/matrix decohes on
4. I. D a m a g e initiation
Using a finite element method, Lay and Boivin [10] calculated that the presence of a PFZ around SiC particles leads to a slight reduction in the normal stress at the surface of the particle. Our experimental observations indicate that despite the presence of such a narrow PFZ (see Fig. 4), the main damage mechanism is still the rupture of SiC particles. Thus we have decided to neglect the PFZ effect in the following discussion, and in addition the metal-ceramic interface has been assumed to be perfect from a mechanical point of view. The value of the stress field within inclusions has a great influence on damage initiation. We briefly mention the main origins of this field in the case of MMCs: thermal incompatibilities arise during cooling of the sample owing to mismatch of the coefficients of thermal expansion between matrix and particle ( 0 ~ 7 0 4 9 - ~ S i C = 20 x 10 6 oc-1); elastic incompatibilities increase during loading owing to the mismatch of elastic properties (see Table 1); plastic incompatibilities arise because the matrix exhibits plastic deformations while the particles remain elastic. In order to explain in a theoretical way some of the experimental phenomena observed in the damage initiation domain, we used an Eshelby iterative model [11] which allows calculation of the internal stress field induced in the SiC particles by the incompatibilities mentioned above. In this model, particle reinforcements
3
2.5 2
Table 1 Thermoelastic constants used for the two constituents of the composite
Mean value for all the observed particles
1
0.5 0 0
I 0.2
J 0.4
I 0.6
I 0.8
I 1
plastic strain (%)
Fig. 12, Aspect ratio of the particles damaged during each step of loading as a function of the plastic strain. The height of the segment is equal to the standard deviation.
Material
E (GPa)
Poisson's ratio
~ (10 × 10 -6 °C I)
SiC 7049
403 ~ 72
0.2 0.33
3.5 23.5
a Measured using the nanoindentation technique.
E. Maire et al./ Materials Science and Engineering A 196 (1995) 135-144 Table 2 Variation in the secant modulus and Poisson's ratio of the elastoplastic matrix with plastic strain Plastic strain (%)
E secant (GPa)
v*
0 0.08 0.2 0.39 0.66 0.9
72 65.7 57.85 48.82 40.18 34.89
0.33 0.346 0.364 0.386 0.406 0.418
can be divided into several families, each being defined by values of different parameters corresponding to elastic properties, particle orientation in the applied stress field and aspect ratio. Compared with the initial presentation, we have introduced a modification in the model. It is an extension of calculation of the internal stresses to the non-linear case. This permits us to take the elastoplastic behaviour of the matrix into account. We replace the elastoplastic matrix by a virtual elastic material. The elastic properties of this material are given by the secant properties of the matrix under the considered loading. The initial elastic modulus and Poisson's ratio are replaced by the secant modulus and the instantaneous Poisson ratio corresponding to each plastic strain, which we have determined from the stress-strain tensile curve of the unreinforced alloy. These concepts were first introduced by Hill [12]. They were applied for example to the self-consistent scheme [13], to the three-phase model [14] and to the Tanaka and Mori model [15]. The secant values of the modulus and of the Poisson ratio are presented in Table 2. The instantaneous Poisson ratio is assumed to be a function of the ratio of the elastic and total deformations, calculated from equality of the variation in volume of the virtual elastic material and the real plastic matrix. The cracking of a given SiC particle occurs when the total loading (thermal, elastic and plastic) induces a critical stress field in this particle. A possible stress criterion could be based on an invariant of the stress tensor such as Tresca or Von Mises stresses. Nevertheless, the particle crack planes are observed to be perpendicular to the tensile axis. Moreover, the behaviour of the SiC particle is perfectly elastic whereas these criteria are well adapted to the description of the plastic behaviour. Thus, we chose to focus the analysis on the value of the normal stress which is calculated using the iterative Eshelby model. Typical thermomechanical properties of the two constituents are given in Table 1. The values of Young modulus of the SiC particles given in this table and used for the calculations were determined experimentally in our laboratory [16] by nanoindentation experiments [17,18]:
141
O0 o ©
0° o
.
} 0 f- {1} Fig. 14. Schematic representation of the model composite reinforced with several families of inclusions. In the Eshelby analysis, the particles are assumed to be ellipsoidal. The {1}, {2}, and {3} axes in the figure are the axes of the sample. The stress is applied according to the {3} axis.
The state of the sample held at the ageing temperature for a long time can be assumed to be a reference state in which the internal stresses in the whole body of the sample are completely relaxed. The temperature drop AT for thermal eigenstrain has been fixed at - 1 7 0 °C. This value corresponds to the difference between the ageing temperature and room temperature (no plastic relaxation). In order to represent accurately the studied composite material, we have defined different families which reproduce the distribution of the particle aspect ratio observed in the composite (see Fig. 5(a)). This distribution can be modelled by 21 families of particles. The aspect ratio and the partial volume fraction of each of the 21 families is determined from the histogram by the position and the height of the corresponding class. A schematic representation of the system is given in Fig. 14. Fig. 15 shows the normal stress component 033 vs. the applied stress o, calculated in four particular families of SiC particles (s = 0.25, 1, 2, and 6.25). The stress field in each family depends of course on the partial volume fraction and aspect ratio of the other families. The following remarks can be made. The curves become non-linear when plastic incompatibility begins to occur. The plastic incompatibility can become as important as thermal and elastic incom-
1500 i
N
z
t--u- s=l
~
0 ~---
-500
2" t
400
600
-1000 Applied stress (MPa) Fig. ]5. Normal stresses vs. the applied stress in four different families of SiC inclusions (s = 0.25, s = 1, s = 2 and s = 6.25). The composite is modelled according to the real distribution of the aspect ratios of the particles (Fig. 1 I, 21 families).
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E. Maire et al. / Materials Seienee and Engineering A 196 (1995) 135-144 1800
1800
1600
1600 •
~" 1400
g
1200 1000
c p-0.92%
~" 1400
PaRticle cracking
s p=0.66~. o
~
12001000
~ -
~p~O~
~
~
%
~
800.
zo
400-
o ¢p=0.92%
cp,-0.66% o
Q ~p-O.39Y.
800 600 z
400
Pa~cle/matdx decoheslon
200-
200
0 I
I
I
I
I
I
50
100
150
200
250
300
Average surface (pm2)
Fig. 16. Particle cracking: rupture normal stress calculated in the particles with aspect ratio displayed in Fig. 12 as a function of their average surface. The corresponding plastic strain of the sample is also indicated. The normal stress required to break the small particles is more important.
patibilities when the plastic deformation ev reaches 0.2%, the value of p r o o f strain at which the conventional yield stress is defined. Before tensile loading of the composite (a, = 0), SiC particles exhibit a normal compression stress component, owing to the thermal incompatibility induced by cooling. As can be seen in Fig. 15, the longest particles (high aspect ratio) are the most compressed. Therefore at the beginning of tensile loading, the risk of damage is reduced in these particles. However, as the applied stress is increased, the normal stress ~r33 in the elongated particles increases more rapidly than in rather spherical particles. For an applied tensile stress c;, of 300 MPa, all the particles are submitted to a tensile stress according to the tensile axis. Then the situation is reversed: the normal stress within the elongated particles becomes higher than that within the other particles. As particle cracks have been observed at an applied stress of 570 MPa, it is clear from these theoretical considerations that the first broken particles are the most elongated particles. This is in good agreement with experimental observations.
4.2. Estimation of the rupture stress of the particles and of the ceramic-metal interfaces For particle cracking and particle-matrix decohesion respectively, Figs. 16 and 17 show the evolution of the critical values of the rupture normal stresses calculated in the damaged particles (i.e. having the aspect ratio given in Fig. 12) vs. their observed surface. We chose this surface parameter because it is representative of the size of the particles. There is a correlation between the stress we calculate and the experimental mean size of broken particles. Unfortunately, the kind of model we use cannot describe this effect: as a matter of fact the value of the stress field calculated from the Eshelby method does not depend on the size of the particles. The size effect may be explained by the fact that SiC
50
I 70
I 90
I 110
I 130 Average surface (pm2)
i 150
I 170
Fig. 17. Particle decohesion: rupture normal stress calculated in the particles with aspect ratio displayed in Fig. 12 as a function of their average surface. The corresponding plastic strain of the sample is also indicated. The normal stress required to debond the interface seems to be independent of the particle size.
particle cracking occurs probably at defects introduced during fabrication of these particles and that the large particles are likely to contain more defects than the small particles. This has been mentioned already in the literature [19] as a Weibull effect. This size influence appears to be weak in the case of the decohesion mechanism (see Fig. 17). The normal stress is calculated at the extreme poles of the particles, where the interface of the ellipsoidal particle is normal to the stress applied and also where the decohesions are observed experimentally. This indicates that this second kind of damage phenomenon seems to be independent of the size of the particle. Decohesion is controlled by the strength of the interface and is probably dependent on the level of plastic deformation in the matrix around the particle. Figs. 18 and 19 show (for particle cracking and particle-matrix decohesion respectively) the evolution of the rupture normal stress vs. the aspect ratio of the damaged particles. For a given damage mechanism, this value of stress should be an intrinsic constant of the material used for the reinforcement. We observe that the particle cracking, the stress that we calculate depends on the aspect ratio. This dependence should be linked to the size effect described above and, moreover, the large particles are likely to have a larger aspect ratio than the small particles. 1800 1600 1400 12oo 1000 "~ 800 600 Zo 400 2OO 0
t~ =0.66%
0 8p=0.2~,
Particlecracking
2.2
2.4
2.6
2.8
3
Aspect ratio
Fig. 18. Particle cracking: rupture normal stress calculated in the particles with mean aspect ratio displayed in Fig. 12 as a function of their aspect ratio. The corresponding plastic strain of the sample is also indicated.
E. Maire et al. / Materials Science and Engineering A 196 (1995) 135 1,14
1800 1600
_
1400
Cp=0.66% °
1200
C,o
lOOO
f;p=0.39 Y~
Ep=0,92%
800 600 z
particle/matrix
400
decohesion
200 0
I
1.9
21
i
i
2.3 2.5 Aspect ratio
I
I
2.7
2.9
Fig. 19. Particle matrix decohesion: rupture normal stress calculated in the particles with mean aspect ratio displayed in Fig. 12 as a function of their aspect ratio. The corresponding plastic strain of the sample is also indicated.
4.3. Rupture Fracture of the composite occurs by linking together of the microcracks in SiC particles by other cracks in the matrix. From a junction mechanism point of view, an important parameter is the distance between broken particles. This parameter decreases as the volume fraction of particles in the composite is increased, but it is also dependent on the local fraction of broken particles. We observe that rupture occurs in a section corresponding to a position x where this distance is a minimum (Fig. 20). The rupture resistance also depends on the way in which the junction in the matrix is produced. In our case, the junction mainly follows the grain boundaries. Owing to the small grain size in O S P R E Y T M composites, the junction distance is thus increased in these materials. This could have a beneficial effect on the ductility of these composites.
5. Conclusions Damage mechanisms in a 7049 aluminium alloySiCp composite were studied by means of SEM in situ tensile tests. Qualitatively, the different steps of the
143
fracture mechanism are the following: damage initiation occurs by cracking of SiC particles and decohesion of the aluminium-SiC interface according in a direction perpendicular to the tension axis. As the applied stress is increased the number of damage sites increases. So does the width of the first initiated cracks, inducing amplification of the local plastic deformation in the matrix. Fracture of the sample occurs by joining together the cracks in the SiC particles and by nucleation and growth of cracks in the matrix. These cracks are intergranular. Quantitative analysis of these phenomena has shown that the elongated and large particles tend to crack easily. Particle cracking occurs at the beginning of the plastic deformation. Decohesion occurs at larger values of the plastic strain. Fracture occurs in a section where the number of damaged particles is high, leading to a low value of interdamage distance. The stress field in the inclusions induced by the complex thermomechanical loading of the composite was calculated by an Eshelby iterative method modified to account for the elastoplastic behaviour of the matrix by using its secant modulus and instantaneous Poisson ratio in the elastic calculation. This has permitted us to explain some of the observations made during the tensile tests: the first cracks appear in the most elongated particles. This has also allowed us to predict the critical value of normal stress responsible for the occurrence of damage. For particle cracking, this predicted stress depends on the particle size.
Acknowledgements This work was financially supported by the Commission of the European Communities and all the partners of the European Brite contract "Low cost MMC made by Spray Deposition", which are fully acknowledged.
References 30
FINAL RUPTUR
150
A
----O-.-- Local Surface fraction ( % )
25
125
N D / N t (%) - o
20
Local inte~larrlage distance
lOO
,
15
E
7s
10~ o
5
50 0
1
2
3
X (mm)
Fig. 20. Mean local distance between the microcracks vs. the position in the sample. This distance is calculated with the mean local fraction of particles and the mean fraction of damaged particles just before
rupture (cp = 0.9%).
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