Quantifying the Degree-of-Sinter in Ferrous P/M Materials
Thomas F. Murphy
Scientist, Laboratory Services
Hoeganaes Corporation
1001 Taylors Lane
Cinnaminson, NJ 08077
USA
Improvements in the physical and mechanical properties of pressed and sintered ferrous
materials are made during the sintering process. Particle bonding and alloying by diffusion
occur during sintering with property enhancements resulting as the sintering time is
increased. The effects of sintering are visible as changes in microstructural features, such as
particle boundaries and pore edges. Some of the improvements in sintering appear as a loss
in particle boundaries, smoother pore edges, and a lessening in the number of angular features
between particles. The appearance of these features and characteristics, in conjunction with
their frequency of occurrence, is often referred to as degree-of-sinter. Quantification of the
degree-of-sinter can be performed on properly prepared metallographic specimens using
well-understood stereological practices. Three test methods will be discussed as techniques
for quantifying and separating materials sintered to varying degrees. Additionally, images of
an iron-copper-carbon premix, sintered at varying times, will be used to illustrate these
microstructural changes.
Introduction: A successful sintering operation is an essential process in the manufacture of
high quality powder metallurgy parts. The combination of an elevated temperature and a
protective furnace atmosphere cause particles in intimate contact to form metallurgical bonds
and leads to alloying of the matrix material by diffusion of the elemental additives. Visually,
the effectiveness of sintering is characterized by changes in the appearance of the
microstructure as a disappearance of particle boundaries, a smoothing of the sharp features
along pore edges, and a lessening in the pore perimeters. These result in a reduction of the
particle-to-particle and pore surface-to-material volume ratios. It is through the evaluation of
these characteristics that an objective estimate of the degree-of-sinter can be made.
Historically, an evaluation of this type was performed on a subjective basis and relied heavily
on the experience and skill of an operator to assess materials and determine where and when
differences existed. The basis for many of these tests was the accurate counting of particle
boundaries and angular pores on a properly prepared metallographic specimen. Problems
were seen when trying to correlate the test results with physical or mechanical properties and
in trying to coordinate results within multiple testing facilities. Results were often inadequate
because they were limited to comparative terms, such as good, fair, poor, etc.
An illustration of the progress of sintering can be seen in Figures 1 through 4 using an
atomized iron mixed with 2 w/o Cu and 0.6 w/o graphite, compacted, and sintered in a pusher
furnace at 1120 °C for various times. In this experiment, the time in the hot zone varied
between 1 and 50 minutes in 5-minute intervals. Consequently, the samples with residence
times in the hot zone of 10 minutes or less did not reach the sintering temperature.
Figure 1. Sample sintered for 1
minute in the hot zone. Particle
boundaries and unmelted Cu
particles are evident. Graphite has
not diffused into the iron particles.
(original magnification 200x)
Figure 2. Sample sintered for 5
minutes. Copper particles remain
unmelted, however much of the
graphite has diffused into the iron
particles.
(original magnification 200x)
Figure 3. A higher magnification
image showing the microstructure
after 15 minutes in the hot zone.
The copper has melted and traveled
along the particle boundaries, pore
edges, and grain boundaries. Some
of the Cu remains in the boundary
regions due to insufficient time for
diffusion. The composition is
pearlite, ferrite, and free Cu in the
particle boundaries. Remnants of
the particle boundaries can be seen
at the particle edges.
(original magnification 1000x)
Figure 4. Image showing the
microstructure after 20 minutes in
the hot zone. Particle boundaries
have disappeared and no evidence
of unmelted Cu remains.
(original magnification 1000x)
Specimens from this series of sintered samples, in addition to iron + carbon samples, were
used as the subjects for the degree-of-sinter study. Two stereological test methods and one
fractal-like technique were used to explore the microstructural changes caused by varying the
total time in the hot zone while keeping the sintering temperature constant.
Test Methods: The simplest, and most commonly used technique for evaluating the surfaceto-volume ratio of boundary surfaces incorporates the application of an array of parallel,
straight-line probes onto a live image or photomicrograph.1,2 In practice, the line probes are
overlaid on the image and a counter is incremented as a line crosses a pore edge. Each
crossing event, known as a ‘point’, is accumulated and the calibrated total line length
determined. The average number of points/unit line length is calculated and used to
determine the surface-to-volume ratio (SV) of the metal/pore composite. The formula used in
the calculation is shown below as Equation 1 where the surface-to-volume ratio of the
composite is equal to twice the average number of points per unit line length (PL):
SV = 2PL
a
(1)
b
Figure 5a shows a polished and unetched surface of a well-sintered material with the array of
parallel line sample probes. The ends of the coincident line segments shown within the pores
in Figure 5b represent individual ‘points’ in each field.
When using this test technique, the features of interest within the sample must be isotropic,
uniform, and random (IUR) in distribution. This presents problems with most powder
metallurgy materials due to the methods used for part compaction. The pressing operation
places directionality in the pore structure and forces the person performing the test to either
remove orthogonal sections from the test material or find an alternative testing procedure, one
that accounts for the presence of anisotropy into the sampling.
This problem is addressed by fixing both the orientation of the removed sample and the type
of probe used to sample the prepared surface. A horizontal plane perpendicular to the plane
of orientation is removed for testing rather than to a plane of random orientation. This is
referred to as a vertical section. Straight-line probes are replaced by cycloid shaped probes
arranged in four orientations. The cycloid shaped curves have been shown to randomly
sample oriented structures when properly applied to the directionality within the sample.3,4 A
cycloid test curve is shown in Figure 6.
The cycloid shape is defined by the following equations, 2 and 3, where 0 ≤ Θ < π:
x = Θ – sinΘ
y = 1 – cosΘ
(2)
(3)
Figure 6. The cycloid test curve,
where the length of the curve is
twice the height.
Four orientations of the cycloids are arranged uniformly as an overlay and used as the test
probe. The testing is similar to that describe previously with the straight-line probes.
Counting of the crossing points is performed the same as are making the calculations. A
convenient arrangement of the cycloid orientations is a sine-like wave overlay as shown in
Figure 7. This connected pattern can be repeated to multiple ‘waves’ to uniformly cover the
image as is shown in Figure 8. Manually following the wave may be more convenient for
some operators as opposed to counting many separated cycloid segments.
Figure 7. Sine-like
wave composed of the
four cycloid
orientations.
Figure 8. Multiple
wave array of
cycloids overlaid on
an as-polished field.
Counts of points are
made as the wave
crosses the pore
edges.
Using the image in Figure 8 as an example, the surface-to-volume ratio was calculated in a
similar manner as with the straight-line probes. The formula for determining the surface-tovolume ratio remains the same as shown in Equation 1, SV = 2PL. Incrementally increased
counts for P are also the same, at locations where the curve crosses the pore edge, and the
total line length is measured or calculated from the number of cycloid segments.
The surface-to-volume ratio of the particle boundaries within the metallic phase can be
determined using either the straight line or cycloid overlays. Directional problems caused by
orientation effects still exist if the materials are pressed, but counts using the cycloid arrays
are valid. The difference in counting boundaries vs. pore edges is that one count is made as
the line crosses a particle boundary rather than two or more counts being made at each pore
(multiple crossings at each pore). Calculations are the same as previously shown.
Another method used for comparing the smoothness of pore edges and the presence of
particle boundaries is a fractal-like technique known as the Box Counting Dimension.5 With
this method, grids of various size boxes are overlaid on live images or photomicrographs.
Pore edges or particle boundaries are extracted from the image and the grid boxes containing
segments of the edges or boundaries are counted. As the grid size becomes smaller, the
number of boxes counted increases due to the increased resolution. At the conclusion of the
counting, a log-log plot is made of the total number of counts vs. the box sizes. The slope of
the linear plot multiplied by –1 is determined to be the box counting dimension.
Figure 9. Surface of an as polished pressed
and sintered material. Most of the particle
boundaries have been sintered. The features
of interest are the pore edges. The rectangle
defined with the blue edges contains features
for illustrating the effect of change in box
size.
Figure 10. Left image with grid overlay. Right image shows colored boxes containing pore
edges.
Figure 11. Same image as used in Figure 10 with a smaller grid overlay. Colored boxes in
right image contain pore edges.
The overlaid grids containing progressively smaller boxes continues using a minimum of four
grid sizes. The graph is then plotted and the slope calculated. The irregularity of materials
sintered to different degrees should become apparent by the difference in the number of
boxes counted as the grid size changes. In some cases, the combination of image
magnification, coupled with the box size variation may give a more acceptable separation of
materials sintered to varying degrees.
Conclusions: Test techniques exist to aid the researcher in quantifying and/or separating
materials sintered to differing degrees. Utilizing the inherent variations in both prior particle
boundary and pore surface irregularity, the stereological test methods provide calculated
quantities through the use manual or automated procedures. The box counting dimension can
also aid the researcher in determining differences in the effectiveness of sintering through
careful design of the test magnification and grid sizes.
References:
1. Underwood, E.E., Surface Area and Length in Volume, Quantitative Microscopy,
Editors: R.T. DeHoff and F.N. Rhines, 1968, McGraw-Hill, Inc., New York, NY, pp.
78-127.
2. Russ, J.C., DeHoff, R.T., Practical Stereology, 2nd Edition, 1999, Plenum Press, New
York, NY, pp. 49-62.
3. Baddeley, A.J., Gundersen, H.J.G., Cruz-Orive, L.M., Estimation of Surface Area
from Vertical Sections, Journal of Microscopy, Vol. 142 Pt. 3, June 1986, pp. 259276.
4. Gundersen, H.J.G., et.al., Some New, Simple and Efficient Stereological Methods and
Their Use in Pathological Research and Diagnosis, APMIS, Vol. 96, 1988, pp. 379394.
5. H.-O, Peitgen, H. Jurgens, D.Saupe, Fractals for the Classroom, Part One,
Introduction to Fractals and Chaos, Springer-Verlag, New York, NY, pp. 240-244