EFFECT OF DENSITY ON THE MICROSTRUCTURE AND MECHANICAL BEHAVIOR
OF POWDER METALLURGY FE-MO-NI STEELS
N. Chawla and X. Deng
Mechanical Behavior of Materials Facility
Arizona State University
P.O. Box 876006
Tempe, AZ 85287-6006
M. Marucci and K.S. Narasimhan
Hoeganaes Corporation
Cinnaminson, NJ 08077
ABSTRACT
The microstructure and mechanical properties of Fe-0.85Mo-Ni powder metallurgy (P/M) steels
were investigated as a function of sintered density. A quantitative analysis of microstructure was
correlated with tensile and fatigue behavior to understand the influence of pore size, shape, and
distribution on mechanical behavior. Tensile strength, Young’s modulus, strain-to-failure, and
fatigue strength all increased with a decrease in porosity. The decrease in Young’s modulus with
increasing porosity was predicted by analytical modeling. Two-dimensional microstructurebased finite element modeling showed that the enhanced tensile and fatigue behavior of the
denser steels could be attributed to smaller, more homogeneous, and more spherical porosity
which resulted in more homogeneous deformation and decreased strain localization in the
material. The implications of pore size, morphology, and distribution on the mechanical behavior
and fracture of P/M steels is discussed.
INTRODUCTION
Ferrous powder metallurgy (P/M) components are typically characterized by residual porosity
after sintering, which is quite detrimental to the mechanical properties of these materials [1-7].
The nature of the porosity is controlled by several processing variables such as green density,
sintering temperature and time, alloying additions, and particle size of the initial powders [1]. In
particular, the fraction, size, distribution, and morphology of the porosity have a profound impact
on mechanical behavior [2-7].With an increase in porosity fraction (> 5%), the porosity tends to
be interconnected in nature, as opposed to the situation where pores are isolated (< 5%) [1].
Under monotonic tensile loading, porosity reduces the effective load bearing cross-sectional area
and acts as a stress concentration site for strain localization and damage, decreasing both strength
and ductility [2]. Interconnected porosity causes an increase in the localization of strain in the
relatively small sintered regions between particles, while isolated porosity results in more
homogeneous deformation. Thus, for a given amount of porosity, interconnected porosity
reduces macroscopic ductility [2]. The distribution of pores may also be inhomogeneous,
because of the broad distribution of particle sizes in the sintered powder mixture, resulting in
“pore clusters” where strain localization may also take place [8].
Porosity also significantly affects fatigue behavior, although the role of porosity in fatigue is
somewhat different than that in tension. In many investigations [2-6, 9-11], crack initiation was
reported at pores or pore clusters located at or near the specimen surface. Holmes and Queeney
[9] proposed that the relatively high stress concentration at pores, particularly surface pores, is
responsible for localized slip leading to crack initiation. Christian and German [10] showed that
total porosity, pore size, pore shape, and pore spacing are important factors that control the
fatigue behavior of P/M materials. In general, more irregular pores will have a higher stress
concentration than perfectly round pores [1]. Pores have also been proposed to act as linkage
sites for crack propagation through interpore ligaments [2, 6]. Polasik et al. [6] showed that small
cracks nucleate from the pores during fatigue and coalesce to form a large crack that leads to
fatigue fracture. Crack propagation was observed to be quite torturous in nature, due to the
heterogeneous nature of P/M microstructures. Crack arrest and crack deflection mechanisms
were attributed to microstructural barriers such as particle boundaries, fine pearlite, and/or
nickel-rich regions.
While the general effects of porosity on tensile and fatigue behavior of P/M steels have been
reported, a comprehensive and quantitative understanding of the effect of porosity on the
mechanical behavior of P/M steels is still needed. In this study, we have systematically examined
the effect of porosity on the tensile and fatigue behavior of a Fe-0.85Mo-Ni steel at three
densities: 7.0 g/cm3, 7.4 g/cm3, and 7.5 g/cm3. Quantitative analysis of the microstructure was
performed to determine pore size distribution and pore shape. The tensile behavior of the alloys
was examined, showing an increasing Young’s modulus and tensile strength with increasing
density. Analytical and microstructure-based numerical models were used to predict the Young’s
modulus and overall monotonic stress-strain behavior as a function of density, respectively. The
stress versus cycles (S-N) fatigue behavior of the alloys was also examined, which showed that
decreasing porosity significantly increased the fatigue life of the alloys. Finally, fractographic
analysis was carried out to correlate the observed tensile and fatigue behavior with the
underlying fracture mechanisms.
MATERIALS AND EXPERIMANTAL PROCEDURE
Powder mixtures of Fe-0.85Mo pre-alloy powder, 2 wt.% Ni, and 0.6 wt.% graphite were
blended and binder-treated using a proprietary process developed by Hoeganaes Corporation [12,
13]. Powders were compacted into rectangular blanks, and sintered at 1120ºC for 30 minutes in a
90% N2-10% H2 atmosphere. Conventional compaction and sintering were used to obtain
sintered densities of 7.0 g/cm3 and 7.4 g/cm3, while a double-press, double sinter approach
enabled achieving the highest density of 7.5 g/cm3. Following sintering, the sintered density of
the alloys was measured using Archimedes and image analysis techniques.
The fraction of porosity and pore shape were measured using conventional image analysis
techniques. Pore shape was qualitatively characterized using a shape form factor, F:
F=
4πA
P2
[1]
where A is the measured pore area and P is the measured pore perimeter. For the shape form
factor, a value of “1” denotes a perfectly round pore, and values that approach zero correspond to
increasingly irregular pores. Analysis of pores approximately larger than 75 µm2 was conducted
from image analysis of optical micrographs, while pores approximately less than 75 µm2 were
analyzed by scanning electron microscopy (SEM).
Tensile and fatigue testing was conducted on uniform diameter cylindrical specimens machined
from the sintered rectangular blanks. The specimens had a diameter of 5 mm and a gage length
of 15 mm [6]. All testing was conducted on a servohydraulic frame. Tensile tests were conducted
in strain control at a constant strain rate of 10-3/s. Fatigue specimens were hand polished to a 1
µm finish, prior to testing. Fatigue testing was conducted in load control, R-ratio (σmin/σmax) of –
1, and a frequency of 40 Hz (40 cycles per second).
RESULTS AND DISCUSSION
Microstructure Characterization
The sintered density, measured by Archimedes technique, and porosity, calculated from sintered
density and measured by image analysis, are shown in Table 1. The porosity measured by image
analysis yielded values ranging from around 12% for 7.0 g/cm3 to 2.6% for 7.5 g/cm3. These
values were similar to the porosity values computed from the sintered density of the alloys,
although at the lower densities (7.0 g/cm3 and 7.4 g/cm3), the porosity measured from image
analysis was slightly higher than that from Archimedes technique. This can be attributed to the
fact that only open porosity is considered in the latter technique, so the contribution from closed
porosity is not accounted for. Optical micrographs revealed significantly different
microstructures for all three alloys, particularly in terms of pore size, morphology, and
distribution, Fig. 1. The pores at the lowest density appeared to be much larger and more
irregular than pores in the other two alloys. Pores at the lowest density also appeared to be more
clustered and segregated along the interstices between particles.
Table 1. Sintered density and porosity in Fe-Mo-Ni alloys
Sintered Density
(g/cm3)
6.98
7.43
7.53
Porosity from
sintered density
(%)
10.3
4.5
3.2
Porosity from
image analysis
(%)
12.1 ± 0.8
5.9 ± 0.6
2.6 ± 0.2
(b)
(a)
(c)
Figure 1. Microstructure of P/M steels at
three densities: 7.0 g/cm3, 7.4 g/cm3, and
7.5 g/cm3. Note the higher fraction of
porosity, as well as larger, more irregular
pores at the lowest density.
Pore size distribution of large pores (> 75 µm2), shown in Figure 2(a), revealed that the alloy at
7.0 g/cm3 had the highest density of larger pores, while the highest density alloy, 7.5 g/cm3,
Figure 2(b), had a much smaller average pore size and narrow size distribution. At smaller pore
100
7.0 g/cm3
80
7.4 g/cm3
4
3
7.0 g/cm
3.5
7.4 g/cm
3
Frequency (%)
40
Frequency (%)
Frequency (%)
3
60
7.5 g/cm3
80
3
7.5 g/cm
2.5
2
1.5
1
60
40
0.5
0
20
300
375
450
525
600
675
750
825
900
975
2
Pore Size (µm )
0
75 150 225 300 375 450 525 600 675 750 825 900 975
2
Pore Size (µm )
20
0
1
15
30
45
2
Pore size (µm )
60
75
(b)
(a)
2
Figure 2. Pore size distribution for all alloys: (a) pores larger than 75 µm and (b) pores smaller than
75 µm2. As expected, a higher density of larger pores was observed at 7.0 g/cm3, while a higher
density of smaller pores was observed at 7.5 g/cm3.
size (< 75 µm2), as expected, a higher density of smaller pores was observed in the alloy with 7.5
g/cm3 density. Pore shape analysis of larger pores (> 75 µm2), indicated that all three alloys had
approximately the same pore shape factor distribution, Fig. 3(a), although increasing density
resulted in a somewhat narrower pore shape distribution. Interestingly, smaller pores (< 75 µm2)
had a much more spherical shape and are likely a direct result of sintering, Fig 3(b). A direct
comparison of pore shape versus pore size shows, indeed, that with increasing pore size the pores
become increasingly irregular in shape, Fig. 3(c).
25
30
7.5 g/cm
(a)
3
7.4 g/cm
20
3
7.5 g/cm
3
25
(b)
7.0 g/cm
3
20
15
7.0 g/cm
7.4 g/cm
3
3
15
10
10
5
0
5
0
0
0.2
0.4
0.6
0.8
1
0
0.2
2
Pore Shape Factor (F=4πA/P )
0.4
0.6
0.8
Pore Shape Factor, F
7.0 g/cm 3
200
Figure 3. Pore shape factor of all three
alloys: (a) pores smaller than 75 µm2, (b)
pores larger than 75 µm2, (c) direct
comparison of pore shape versus pore
size. Increasing pores size results in an
increase in irregularity of pore shape.
1
7.4 g/cm 3
150
100
50
(c)
0
0
0.2
0.4
0.6
Pore shape factor, F
irregular
0.8
1
spherical
Tensile Behavior
The monotonic behavior of the alloys was clearly influenced by the fraction of porosity and the
pore morphology. Increasing density resulted in increased Young’s modulus, proportional limit
stress (taken as the onset of yielding in the material, as measured by a 2% deviation from the
linear elastic portion of the stress-strain curve), tensile strength, and strain-to-failure, Table 2.
Figure 4 shows a comparison of representative stress-strain curves for each alloy. Note that even
a moderate amount of porosity (~10-12%) is sufficient in inducing a significant decrease in
strength and strain-to-failure relative to the close to fully-dense material (7.5 g/cm3).
Table 2. Tensile behavior of Fe-Mo-Ni steels.
Density
(g/cm3)
7.0
7.4
7.5
Young’s
Modulus
(GPa)
138.6 ± 1.2
171.6 ± 0.8
182.6 ± 1.9
It is well known that porosity
decreases the Young’s modulus of
a material [1]. Here we use the
approach of Ramakrishnan and
Arunachalam (R-A) [14], who
model a single spherical pore
surrounded by a spherical matrix
shell. The R-A model also
considers the intensification of
pressure on the pore surface due to
interaction of pores in the material.
The Young’s modulus of a
material, E, with a given fraction of
porosity, p, is given by [14]:
 (1 − p )2 
E = Eo 

1 + κ E p 
Proportional
Limit Stress
(MPa)
160.0 ± 19.4
189.0 ± 8.1
196.4 ± 9.3
Ultimate Tensile
Strength
(MPa)
570.6 ± 8.1
745.2 ± 24.0
784.4 ± 16.3
Strain-toFailure
(%)
2.1 ± 0.1
4.6 ± 0.4
6.5 ± 0.7
800
7.5 g/cm
7.4 g/cm
700
3
3
600
7.0 g/cm
3
500
400
300
200
100
Fe-Mo-Ni-C
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Strain (mm/mm)
Figure 4. Effect of density on tensile behavior of the P/M
steels. A marked decrease in strength and ductility in the
7.0 g/cm3 alloy is observed, relative to the close to fullydense material, 7.5 g/cm3.
where E0 is the Young’s modulus
of the fully-dense steel (taken by
extrapolating the experimental data to zero porosity, which yielded a value of approximately 201
GPa), and κE is a constant in terms of the Poisson’s ratio of the fully-dense material, νo:
κ E = 2 − 3ν o
For a fully-dense steel the Poisson’s ratio is approximately 0.3. A comparison of the
experimental data and the R-A prediction is shown in Figure 5. The R-A predicts the
experimental data very well, for the range of porosity examined here. The relatively good
agreement between experiment and theory, based on a simple spherical pore geometry, indicates
that the elastic properties of these materials do not appear to be significantly influenced by the
shape and morphology of the porosity microstructure. This is supported by the analysis of
Ramakrishnan and Arunachalam [14], who compared the bulk modulus of porous materials with
spherical versus angular pore geometry by FEM. For the range of porosities studied here (<
10%), they observed that the decrease in modulus for angular pores versus spherical pores is less
than 5%.
The increase in proportional
limit stress and ultimate tensile
strength with an increase in
density can be explained by
modeling the damage evolution
in the microstructure of each of
the three alloys. The
microstructures in Figure 1
were used as a basis for FEM
analysis of uniaxial loading.
The analysis was twodimensional (2D) under plane
strain condition. It should be
noted that the 2D analysis
effectively treats the pores as
holes in the microstructure. This
model is quite different from
the pores in actuality, which are
three-dimensional (3D) and
surrounded by matrix material.
Nevertheless, the 2D analysis
presented here shows a qualitative
perspective of the effects of pore
microstructure on localized plastic
strain initiation and evolution
around the pores. 3D
microstructure-based visualization
and FEM analysis, through the use
of serial sectioning techniques, are
currently underway to obtain a
more quantitative description of
the plastic strain evolution in
porous materials [15].
250
Experiment
R-A Model
200
150
100
50
Fe-Mo-Ni-C
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Fraction of Porosity
Figure 5. Young’s modulus of P/M steels versus porosity. The
R-A model predicts the experimental data very well.
1
Steel Matrix
0.8
3% Porosity
4% Porosity
0.6
10% Porosity
0.4
0.2
The macroscopic stress-strain
0
0
0.002
0.004
0.006
0.008
0.01
behavior predicted by the model is
Strain
shown in Figure 6. The stressFigure 6. Modeled stress-strain behavior by 2D FEM
strain input for the fully dense
analysis. A sharp decrease in strength is observed at 10%
steel (extrapolated from the
porosity, commensurate with the experimental data.
experimental stress-strain behavior
at the three different densities), is
also shown. Note that even a slight decrease in porosity (4-10%) results in a significant decrease
in strength of the steel, as was observed experimentally. The reason for this can be gleaned from
the equivalent plastic strain evolution in each of the three microstructures, shown in Figure 7. A
large amount of strain localization takes place in the sintered regions between pores. In
particular, networks of pores are quite effective in localizing the strains in the steel ligaments
between the pores. Thus, a very small section of the microstructure is actually being plastically
deformed, so that a large portion of the materials is largely undeformed. The modeling results are
confirmed by experimental observations that porosity causes deformation to be localized and
inhomogeneous [16-18]. The strain intensification in the sintered ligaments between pores, likely
serve as areas for crack initiation. Once the onset of crack initiation takes place, the large pores
will be linked, and the effect load-bearing area of the materials locally will decrease very
quickly, resulting in fracture of the material. An increase in porosity decreases the overall
sintered ligament fraction and spacing between pores, thus accelerating the intensification of
strain in the matrix material. Our modeling also shows that plastic strain intensification begins at
the tips of the irregular pores in the microstructure. Vedula and Heckel [16] compared the
damage mechanisms between round and angular pores in materials with identical pore fraction
and observed that highly localized slip bands formed at the sharp tips of angular pores, producing
uneven distribution of strain around angular pores. This resulted in highly localized and
inhomogeneous plastic deformation compared to the deformation around round pores which was
much more homogeneous.
(a)
Figure 7. Effective plastic strain
contours in modeled
microstructures: (a) 7.0 g/cm3,
(b) 7.4 g/cm3, and (c) 7.5 g/cm3.
Larger and interconnected pores
cause strain intensification, while
smaller, more homogeneously
distributed pores contribute to
more homogeneous deformation.
(b)
(c)
The distribution of the pores is also important, since it has been shown that plasticity may initiate
at pore clusters because of the higher localized stress intensity associated with these defects [2, 6,
19]. The plastic strain distribution in the modeled microstructure for the densest steel, 7.5 g/cm3,
shows that when the pores are much smaller and more homogeneously distributed, the plastic
strain distribution is more uniform and the deformation is more uniformly distributed throughout
the material. We are now able to explain why only a slight increase in density from 7.43 g/cm3 to
7.53 g/cm3 resulted in a significant increase in strain-to-failure, although the strength of the
material increased only slightly. This may be attributed to a narrower and more homogeneous
distribution of pores in the 7.5 g/cm3 alloy versus 7.4 g/cm3, although the total amount of
porosity in the latter alloy was not significantly higher. Thus, while the strength of the material is
controlled by the fraction of pores, macroscopic ductility is also influenced by the size
distribution and degree of clustering of the pores, since the sintered ligaments of the steel control
fracture of the material. An equally important result of the model is that, even in the highest
density material, a large amount of strain intensification takes place at as ingle pore cluster in the
microstructure, Fig. 7. Thus, even when the overall amount of porosity is relatively low (4-5%),
strain intensification may take place around pore clusters. It follows that the homogeneity and
distribution of the porosity is as important as the fraction of porosity in controlling the evolution
of plastic strain, and thus, the onset of crack initiation.
Fractography of tensile fracture surfaces provided further insight into the role of porosity in
fracture of these materials. At the lowest density, fracture took place primarily by localized void
nucleation and growth in sintered necks of the material, Fig. 8(a). At higher densities, however,
the fracture morphology was more characteristic of that of fully-dense materials, with a
combination of ductile rupture as well as brittle fracture from fully dense pearlitic grains, Fig.
8(b).
10 µm
(a)
(b)
Figure 8. Tensile fracture in (a) 7.0 g/cm3 alloy and (b) 7.5 g/cm3 alloy. Localized void growth is
observed at the lower density, while a combination of void growth and brittle cleavage fracture is
observed at higher density.
Fatigue Behavior
Perhaps the most significant influence of porosity was in fatigue behavior, Fig. 9. Stress versus
cycle curves revealed that the 7.0 g/cm3 alloy had significantly lower fatigue endurance limit
than the other two alloys. It is well known that single large pores or clusters of pores act as stress
concentration sites for fatigue crack initiation [2-6, 8-10]. As in the case of tensile loading, pores
with a more irregular shape will have a higher stress concentration and are more probably sites
for crack initiation. Thus, the higher observed fatigue strength with increasing density can be
400
attributed to a higher density of
isolated porosity, more rounded
pores, and a lower degree of pore
clustering.
Fe-Mo-Ni-C
350
300
7.5 g/cm 3
250
3
7.4 g/cm
Fatigue fractography provided
additional insight into the
200
influence of microstructure on
3
7.0 g/cm
fatigue damage. Figure 10 shows
150
the fatigue fracture surface of the
3
7.0 g/cm alloy. The fracture
surface characteristics are
100
103
104
105
106
107
108
somewhat similar to that observed
Cycles to Failure, Nf
under tensile loading, showing
localized dimple rupture, and
Figure 9. Stress versus cycles (S-N) fatigue behavior of P/M
evidence of void nucleation and
steels as a function of density. Increasing density significantly
coalescence in the sintered necks
increases fatigue life.
bonding the particles. A large
number of spherical submicron MnS particles were also observed, although the influence of MnS
inclusions on fatigue crack nucleation and/or propagation is unclear. It would be appear that the
effect of the inclusions would be negligible when the pore size is much larger than the inclusion
size, since the pores acts as the weakest links for crack initiation in the material. Localized
fatigue striations were also apparent, although the propensity of these increased with an increase
in density. Figure 11 shows a region of localized fatigue striation in an alloy with density of 7.4
g/cm3. Localized striations have also been observed by Polasik et al. [6] and have been
hypothesized to form in areas of the microstructure that are favorably orientation to the loading
axis.
10 µm
1 µm
Figure 10. Fatigue fracture surface of 7.0 g/cm3 alloy: (a) low magnification and (b) high magnification
inset of (a), showing localized void growth at MnS particles.
(a)
(b)
Figure 11. Fatigue fracture surface of 7.5 g/cm3 alloy: (a) low magnification and (b) high magnification
inset of (a) showing localized fatigue striations.
In general, the fatigue strength of P/M materials is correlated to the ultimate tensile strength, by
computing the fatigue ratio (σfat/σuts), in order to obtain some estimate of the fatigue strength
relative to the monotonic strength. In P/M materials the fatigue ratio is typically between 0.30.4, which is much lower than that reported for conventional wrought steels, 0.4-0.5 [1]. The
lower fatigue in P/M materials can be attributed to the presence of porosity. Nevertheless,
correlating fatigue strength to the ultimate tensile strength may not be the best approach, since
the ultimate tensile strength is really a measure of large-scale macroscopic damage that takes
place at relatively large applied stress or plastic strain. Fatigue damage, on the other hand, is
more complex, and typically takes place at much lower applied stress by localized plasticity at
defects in the material. Thus, a more appropriate measure of fatigue strength may be the
proportional limit stress or the Young’s modulus of the porous material. The proportional limit
stress is a measure of the onset of plasticity during monotonic loading. Thus, while the onset of
plasticity under monotonic conditions is certainly not equivalent to cyclic plasticity, it may be a
better measure of the fatigue strength, since the onset of plasticity is related to the onset of
damage in the material. Young’s modulus may also be a good measure of the fatigue strength in
heterogeneous materials, such as porous materials, since for a given stress, an increase in
Young’s modulus will result in a lower applied strain to the material. A lower macroscopic
applied strain will result in a lower degree of strain localization, which should decrease fatigue
damage and increase fatigue life. In particle reinforced metal matrix composites, for example, an
increase in the volume fraction of high stiffness reinforcement particles results in an increase in
fatigue strength [20]. Lewandowski et al. [21] showed that the higher fatigue resistance could be
attributed to the increase in Young’s modulus brought about by the increase in reinforcement
volume fraction. Similarly, in porous materials, an increase in Young’s modulus can be
correlated to an increase in load bearing area and a decrease in the localization of strain.
Figure 12 shows a plot of proportional limit stress and Young’s modulus versus fatigue strength.
While there is no exact correlation between σpl and E with σfat, there is certainly a good
correlation between these parameters. It should be noted that the lower proportional limit stress
5. CONCLUSIONS
Proportional limit stress (MPa)
210
210
200
200
190
190
Proportional limit
stress
180
180
Young's modulus
170
170
160
160
150
150
140
140
130
140
160
180
200
220
240
260
130
280
Fatigue strength (MPa)
In this study the effect of
Figure 12. Correlation between fatigue strength and: (a)
porosity on the mechanical
proportional limit stress and (b)Young’s modulus.
behavior of sintered steels was
systematically studied. The following conclusions can be made based on the results of this study:
•
Increasing sintered density resulted in lower pore fraction, smaller average pore size, and
more spherical pore shape. Increase pore size was directly correlated with an increase in the
irregularity of pore shape.
•
Tensile strength increased with an increase in sintered density. Microstructure-based FEM
modeling showed that larger, irregular, and highly clustered pores contribute to significant
strain localization which results in premature failure at lower densities. At higher densities,
the pores were more spherical and more homogeneously distributed, resulting in a more
homogeneous distribution of plastic strain over a larger fraction of material.
•
Fatigue strength also increased with an increase in sintered density. Here, the increase in
fatigue strength may be attributed to smaller overall pore size and a lower degree of pore
clustering, which acts a stress concentration for fatigue crack initiation.
•
Direct correlations exist between fatigue strength and the following two quantities:
Proportional limit stress and Young’s modulus. These correlations may be more effective
than fatigue strength to tensile strength, since the latter quantity is a measure of large-scale
plasticity and damage that takes place at much higher stresses than high cycle fatigue
stresses.
ACKNOWLEDGMENTS
The authors acknowledge Hoeganaes Corp. for financial support to conduct this research and D.
Babic for experimental assistance with this work.
Young’s modulus (GPa)
relative to fatigue strength may
be attributed to our definition of
fatigue strength as fatigue runout
at 107 cycles. Recent work has
shown that fatigue failures can
take place at longer fatigue lives
than 107 cycles [22]. Thus, at
very long fatigue lives it is
possible that the fatigue strength
may approach the proportional
limit stress.
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