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Abstract

Shrinkage during the sintering of powder compacts depends on numerous parameters, including green body characteristics such as particle size and green density. These parameters are also decisive for the initial microstructure and its evolution during sintering. In this study, a novel experimental setup is used to quantify the time-dependent microstructural evolution in water-atomised Astaloy 85Mo powder. Green bodies with different particle sizes and density levels were polished on the top surface and then subjected to an interrupted sintering procedure in a quenching dilatometer. Intermediate examinations of the microstructure by scanning electron microscopy revealed the pore morphology and the thermally etched austenite grain size. It was found that pore rounding relies solely on the local curvature only, whereas neck growth is in good agreement with analytical models. An increase in diffusivity was found on the macroscale and on the microscale due to the pre-deformation of the particles.

Keywords

water-atomised iron powder sintering kinetics surface diffusion neck growth grain growth thermal etching anisotropy

Introduction

The conventional manufacturing process in powder metallurgy (PM) consists of the compaction of powder and its subsequent consolidation during the sintering. The latter induces diffusion processes within the powder compact. Depending on the sintering temperature, lattice diffusion, grain boundary diffusion, surface diffusion and evaporation and condensation contribute to different extent to the formation of sintering necks and the rounding of pores. While surface diffusion, which is identified as a major mechanism in the sintering of ferrous compounds, does not cause a dimensional change on the macroscale, lattice diffusion and grain boundary diffusion induce a mass flow that decreases the component’s dimensions and subsequently increases the bulk density.¹ The diffusion processes are driven by a gradient of the vacancy concentration in the particles. The local vacancy concentration underneath a surface can be described by its curvature, assuming a linear proportionality between the curvature and the vacancy concentration.¹ Consequently, the mass flow along a surface can be directly related to the gradient of curvature. The progress of sintering can be described by the sinter neck ratio, relating the size $x$ of the connection between two particles to their diameter $D$ , assuming spherical powder particles. Herring proposed a relation between the particle size and the neck ratio, which is described in a scaling law²:

\frac{t_{2}}{t_{1}} = {(\frac{D_{2}}{D_{1}})}^{m}

(1)

D_{1}

and

D_{2}

are arbitrary particle diameters, whereas

t_{1}

and

t_{2}

describe the time that is necessary to achieve the same sintering progress with the different particles. The constant

m

depends on the diffusion mechanism.

This concept has been expanded by analytical descriptions of the time-dependent evolution of the neck ratio proposed by Exner.³ Considering surface diffusion as the predominant mechanism for neck formation, neck growth can be described as

\frac{x}{D} (t) = {[\frac{23 \cdot γ \cdot D_{S} \cdot δ \cdot Ω}{R \cdot T} \cdot {(\frac{D}{2})}^{- m} \cdot t]}^{1 / n}

(2)

where

γ

is the surface energy,

D_{S}

is the surface diffusion coefficient,

δ

is the surface thickness,

Ω

is the molar volume,

R

is the gas constant, and

T

is the temperature. The exponent

n

is an empirical constant that depends on the respective diffusion mechanism.

Neck growth equations, such as in equation (2), were derived for different materials in the middle of the last century, using either wire compacts or spherical powders, which were cut and polished after a varying sintering time.^4–7 Kingery and Berg⁸ utilised a microstage furnace to directly observe and quantify the neck growth kinetics between loosely spilled spherical powder particles. These studies relied on the assumption of perfectly spherical particles and little information was gathered on iron powder, whereas Eisen⁹ investigated the microstructural evolution of different iron powders in a powder compact. A hot stage scanning electron microscopy (SEM) was used to observe identical microstructural regions at different time steps to identify the influence of the compaction pressure, the powder morphology and the atmosphere on the sintering process in a qualitative manner. Schoeler¹⁰ conducted quasi-in-situ sintering experiments with ferrous compacts alloyed with different molybdenum contents in a dilatometer to observe the microstructural evolution at different temperatures. Molinari et al.¹¹ measured the neck curvature and neck size of water-atomised and cold isostatically pressed iron powder after 30 min of pre-sintering at lower temperatures based on SEM images. Few investigations were carried out on the grain growth of PM steels during sintering. The effect of the porosity and particle size on the austenite grain growth kinetics of sinter-hardened Fe–Mo–Cr compacts was reported by Dlapka,¹² whereas the independence of austenite grain size of the porosity was shown for Astaloy 85Mo.¹³

Simulation methods, such as phase-field,¹⁴ Monte-Carlo¹⁵ or level-set¹⁶ allow the evaluation of the microstructural evolution during sintering from a numerical perspective. The validation of published investigations is mostly based on the comparison to analytical findings, such as equation (2).¹⁷ Moreover, these methods have rarely been applied to real microstructures yet.

Regarding the evolution during sintering on a macroscale, numerous investigations on the influence of parameters, such as particle size, have been published^18–20 and analytical equations for the axial shrinkage were derived.^8,11 In most studies, an anisotropic shrinkage behaviour has been reported that is ascribed to different root causes in literature.^20–26 Among those, a currently widely held theory includes the contribution of dislocations to the sintering process. Compaction is generally accompanied by a work hardening of the powder particles. Wendel et al.¹⁸ used electron backscattered diffraction (EBSD) to estimate an increase of dislocation density in powder particles of a green body due to the compaction. Similar measurements revealed an anisotropic distribution of the dislocation density with more pronounced accumulations of dislocations in areas perpendicular to the direction of compaction.²⁷ An elevated dislocation density may contribute to an increase of the effective diffusivity and subsequently to a higher shrinkage in axial direction.^28,11

Although most phenomena of sintering are understood, none of the investigations fully evaluated the interdependence of the evolution of microscopic and macroscopic characteristics, such as neck growth and shrinkage. To the authors’ knowledge, no quantitative description of neck growth and the evolution of the pore morphology of water-atomised iron-based powder has been reported yet. Thus, a new experimental setup is proposed that enables the derivation of correlations between process parameters and the evolution of the green body during sintering on different length scales. The experiment includes the metallographic preparation of powder compacts and quasi-in-situ sintering experiments in a quenching dilatometer with intermediate SEM investigations of predefined areas to quantify pore rounding and neck growth by tracking the evolution of specific pores and particles. Simultaneously, the austenite grain growth is measured. The results are related to macroscopic findings gathered by dilatometry and the variation of the green density as well as the powder particle size. Hereby, the sintering kinetics are both investigated on a macroscale and a microscale. Based on the findings and the SEM images of this work, investigations on the numerical simulations of sintering on a mesoscale will be conducted in future work.

Materials and methods

In this study, water-atomised Astaloy 85Mo powder was used. Prior to compaction, the powder was separated into two groups. The first half of the powder was sieved into three fractions, whereas the second half was subjected to a simple milling process in order to modify the particle shape and artificially increase the dislocation density. Powder and ceramic milling balls were filled in a jar that was then rotated for approximately 24 h. Afterwards, the powder particles revealed a significantly deformed shape.

The particle size distribution of each powder fraction was measured by laser diffraction technique using a Horiba LA-950. The results are listed in Table 1 and correspond well to the SEM images of the powder particles, as depicted in Figure 1. Contrary to the untreated particles, the deformed powder reveals a rather smooth surface and appears flatter and less isotropic. As stated in the literature, ball milling can increase the oxygen content of powder particles.²⁹ Hence, the oxygen contents of both the deformed and the undeformed powder were measured by hot-gas-extraction technique, using a Bruker Galileo G8. The deformed powder revealed an oxygen content of 0.34 wt-%, whereas 0.16 wt-% was measured for the other powders.

Figure 1.

SEM images of powder particles: (a) ‘coarse’; (b) ‘medium’; (c) ‘fine’; and (d) ‘deformed’.

Table 1.

Particle sizes of the different powders measured by laser diffraction.

	Particle size ( $μ m$ )
Variant	$D_{10}$	$D_{50}$	$D_{90}$
‘Coarse’ (C)	64	141	230
‘Middle’ (M)	51	83	140
‘Fine’ (F)	25	38	58
‘Deformed’ (D)	33	86	220

Each fraction of the undeformed powder was then mixed with 0.25 wt-% carbon and 0.6 wt-% wax. In order to compensate for the higher amount of oxides in the deformed powder, 0.55 wt-% carbon was added to the deformed powder. Subsequently, the powder was compacted into cylindrical specimens with an approximate height of 10 mm and a diameter of 9.5 mm using a floating die. For each powder fraction, green parts were produced with a target density of 6.7, 6.9 and 7.1 ${g cm}^{- 3}$ , which leads to 12 different variants, consisting of four different powders and three different densities. These are referred to using the labels from Table 2.

Table 2.

Overview over the different variants.

	Green density ( $g c m^{- 3}$ )
Variant	$6.7$	$6.9$	$7.1$
‘Coarse’ (C)	C67	C69	C71
‘Middle’ (M)	M67	M69	M71
‘Fine’ (F)	F67	F69	F71
‘Deformed’ (D)	D67	D69	D71

For each specimen, the density was measured geometrically, assuming a perfectly shaped cylinder.

In order to extract the wax, a debinding step followed. The specimens were placed in a belt furnace and continuously heated up to a temperature of 600 $\circ$ C in a nitrogen atmosphere, which helped to avoid additional oxidation. The debinding was accompanied by a slight increase in dimensions, leading to a decrease in density. Thus, the true densities differed from the target values.

For each variant, one sample was embedded in a hot resin to be metallographically prepared on the top faces. The surfaces were ground and polished in several steps, which were regularly interrupted to perform an etching to remove fragments within the porosity and reveal hidden pores. Nitric acid with a concentration of 3% was chosen as an etchant. The etching required caution to avoid artificially enhanced porosity. After a short exposure to the etchant, the latter was first roughly removed with isopropanol, while the remaining etchant was then extracted in a vacuum bell jar. No ultrasonic cleaning was carried out, as this would probably have damaged the polished surface. Visual inspections were then carried out using light optical microscopy at 1000 $\times$ magnification to ensure that the measures carried out have not caused any rounding of the edges of individual pores. Depending on the green strength of the specimens, a soluble glue was optionally added to the surfaces to prevent outbreaks of powder particles. The glue could be fully removed using acetone. However, these measures could not prevent an artificial increase of local density by squeezing particles into large pores, which had been removed by polishing before. In two final steps, diamond and alumina suspension with respective particle sizes of 0.25 $μ$ m and 60 nm were used successively to finish the surface polishing. The samples were released from the resin that they had been mounted in and investigated by SEM with a Jeol JSM 6400, using secondary electron (SE) images at a maximum magnification of 1000. For each specimen, six different areas of the polished surfaces were documented at different magnifications. The position of each area was precisely recorded. Following this, quasi-in-situ sintering experiments were conducted in a quenching dilatometer DIL 805 A/D/T from TA Instruments with a vacuum furnace. The specimens are subjected to an alternating heat treatment by being inductively heated up to a temperature of 1120 $\circ$ C, which is held for a varying time and then being cooled with a moderate cooling rate of 200 K min⁻¹ to a temperature of 700 $\circ$ C. Helium was added afterwards to keep the cooling rate constant. After each cycle, the specimens were investigated by SEM in order to evaluate the sintering progress as well as the grain growth at the predefined regions of interest (ROIs). The isothermal sintering was first carried out for 3 min, and subsequently, 9 and 36 min, which adds up to a cumulative sintering time of 48 min. The heating rate is chosen to be 40 K min⁻¹ in the first step, whereas heating is accelerated in the other steps to 100 K min⁻¹ to reduce the further sintering during the heating stage. The procedure is summarised in Figure 2.

Figure 2.

Temperature profile of the quasi-in-situ experiments.

The moderate heating rate in the first step ensures a sufficient time for the carbothermal reduction that is necessary to reduce the surface oxides that are to be expected in water-atomised powders. It is reported that an increase in the heating rate might lead to the enclosure of oxides, which in turn decreases the diffusivity.³⁰

The microstructural evolution was evaluated by investigating the change of local curvature, neck growth and grain growth. The local curvature $κ$ was determined with the open-source software Fiji.³¹ The images are first binarised by selecting a suitable threshold value so that pores remain black while powder particles appear white. Subsequently, the contours of individual pores were approximated with B-Splines using the Fiji plugin ‘Kappa’, which directly provides information on the maximum curvature within each contour. The latter corresponds to the inverse value of the radius of an osculating circle that locally approximates the shape of the contour at a given position.

For each pore, an ROI was defined that revealed a similar morphology concerning the gradient of curvature along the surface as the driving force of sintering. The evolution of the respective pore was tracked by repeating this procedure after every sintering step. For each sample, five pores were evaluated.

Neck growth was investigated by comparing images of the same ROIs after different time steps and identifying particles between which a connection was formed during sintering. The minimum distance between the outlines of each neck was taken as the neck size, which was then related to the respective particle size.

The experimental setup enabled the identification of former austenite grains due to the thermal etching effect that was caused on the polished surfaces. The austenite grain size was measured by evaluating the SEM images with the line intercept method. For each variant, three micrographs were investigated at a magnification of 500 and 1000 after each sintering step. As the intensity of the etching effect varied significantly from experiment to experiment, some specimens could not be evaluated at the same ROI after each step. In this case, which applied for M69 and C67, different areas were investigated, whereas the number of micrographs is increased to five or six to account for the variation of grain size distribution. The results were then fitted for each powder variant using the equation:

G^{3} (t) = G_{0}^{3} + K \cdot t

(3)

with

G

as the grain size after time

t

G_{0}

as the initial grain size and

K

as a factor indicating the grain mobility. The grain growth exponent is taken as 3, as suggested by German.³²

In order to monitor the effect of the alternating sintering process on the sintering kinetics, identical samples were sintered continuously for 48 min. The length change in axial direction was recorded during each sintering experiment, whereas radial length changes were measured discretely after each sintering step by means of a micrometer. These samples were used to evaluate the sintering process on the macroscale, whereas the firstly described samples were used to evaluate the microstructural evolution. The successful reduction of the surface oxides was indirectly proven by measuring the carbon content of the powder, the green bodies and the sintered samples after 48 min of continuous sintering. The measurements were carried out with a LECO-800 using a hot-gas-extraction technique. Each powder variant revealed a carbon content of 0.1 to 0.12 wt-% after sintering, whereas 0.26 to 0.29 wt-% were measured after debinding. This indicates a carbon loss of about 0.16 wt-%, which corresponds to the oxygen content of the powder mixtures.

Results

The local curvature $κ$ is the smallest microstructural descriptor that was investigated. Figure 3 shows the evolution of a single pore in sample M67. In addition, the measured maximum curvatures of the contour at the upper left and at the lower side are listed. Before sintering, the pore reveals sharp edges and highly curved surfaces. After 3 min, the sharp edges have been transformed into curved surfaces, whose curvature is steadily decreased in the course of the next two sintering steps with 9 and 36 min, as shown by the displayed curvatures in Figure 3.

Figure 3.

Evolution of a pore in sample M67 during sintering at 1120 $\circ$ C: (a) 0 min; (b) 3 min; (c) 12 min and (d) 48 min.

Figure 4 shows the evolution of a more complex pore morphology that was found in specimen C71. Comparing the first two images, a significant decrease of curvature within 3 min can be noticed, whereas the morphology changed only slightly afterwards. The upper side of the pore reveals a highly curved section at the beginning that is almost completely convex. During sintering, the pore was rapidly transformed into a concave shape, whose curvature decreased steadily until the end of the experiment. This induced a widening of the pore, which is accompanied by a pore coalescence, as highlighted in Figure 4(d).

Figure 4.

Evolution of a pore in sample C71 during sintering at 1120 $\circ$ C: (a) 0 min; (b) 3 min; (c) 12 min; and (d) 48 min.

These qualitative observations are quantified in Figure 5, which summarises the evolution of the maximum curvature within 40 ROIs, as in Figure 3. As the results do not reveal any significant difference between the different variants and the dependency of surface diffusion on the local curvature is well known, each figure displays the evolution of the local curvature starting from a different range of initial curvatures instead. Each figure contains a comparison between convex (negative) and concave (positive) pores.

Figure 5.

Evolution of local curvature: (a) $κ (0 \min) < 4 μ m^{- 1}$ ; (b) $4 μ m^{- 1} < κ (0 \min) < 7 μ m^{- 1}$ ; and (c) $κ (0 \min) > 7 μ m^{- 1}$ .

The figures clearly show that the evolution of the local curvature $κ$ is strongly dependent on the initial curvatures. Figure 5(a) indicates a moderate decrease of curvature, whereas higher initial values provoke a much more pronounced evolution, as shown in Figure 5(b) and (c). Moreover, the scatter of the data gathered after 3 min of sintering is increased with increasing initial curvature. However, the curvature tends to a value between 0.5 and 1 for longer sintering time, revealing no dependency on the initial condition. Comparing the evolution of negative and positive curvatures, no difference can be noticed.

During sintering, necks were formed between the powder particles. For each sample, nine sinter necks were randomly selected after the first sinter step and compared with the corresponding sintering necks after 12 and 48 min of cumulative sintering time. Each variant shows an increase in the neck size ratio with increasing sintering time. The averaged results of all measurements are depicted in Figure 6. While samples made of coarser powder reveal just a moderate growth rate, fine powder leads to a pronounced neck growth. Contrary to this observation, the deformed variant distinguishes itself by a significant neck growth. A comparison between the different green densities suggests that it does not have any impact on neck growth. Figure 6 also displays the results of an optimisation of the parameters of equation (2) with $m = 4.063$ , $n = 5.606$ and the pre-factor as $1.06 \cdot 10^{- 26}$ , which was applied to all data points of variants F, M and C. The standard deviations of the measurements of each sintering step and density variant vary from 0.01 to 0.04 for coarse powder to 0.05 to 0.08 for fine powder, while variants M and D reveal similar deviations in the range of 0.03 to 0.04.

Figure 6.

Neck growth depending on particle size and time: (a) green density 6.7 $g c m^{- 3}$ ; (b) green density 6.9 $g c m^{- 3}$ ; and (c) green density 7.1 $g c m^{- 3}$ .

An example of neck growth is given in Figure 7. Two sinter necks can be noticed in Figure 7(b). The left one does not reveal any growth kinetics, whereas the second neck has slightly increased during the following sintering steps. Comparing Figure 7(c) and (d), it is to be remarked that two pores emerged during the process, which indicates the presence of pores right beyond the surface.

Figure 7.

Neck growth in sample F67 during sintering at 1120 $\circ$ C: (a) 0 min; (b) 3 min; (c) 12 min; and (d) 48 min.

A further example to emphasise the extent of neck growth is given in Figure 8. The interface between single particles was fully transformed into sinter necks. It is to be noticed that these grain boundaries mostly coincide with the former interfaces. Additionally, a pronounced pore rounding can be observed. The small pore on the lower left side stands out by its convexity, which caused diffusion to a similar extent as in Figure 4.

Figure 8.

Neck growth, pore rounding and grain growth in sample M71 during sintering at 1120 $\circ$ C. The arrows mark positions of former interfaces that were transformed into grain boundaries: (a) 0 min and (b) 48 min.

As outlined in the previous section, the density at the polished surfaces had presumably increased. This can be confirmed by considering the average greyscale values which are associated with each image at a magnification of 200 after it has been binarised. Taking the greyscale value as an equivalent of the relative density within the respective area, the variation of the relative density between the different density levels of each powder variant is negligibly small. However, a small variation can be found between the different powder variants. According to the image analysis, fine and deformed specimens reveal the highest relative densities of 98 to 99%. The middle and the coarse powder show densities of 95% and 94%, respectively. This may contradict the visual impression conveyed by the depicted examples. It should be noted, however, that the ROIs selected for the assessment of curvature and neck growth represent small regions whose relative density is not representative of the particular area in which they are located. This observation needs to be taken into account once a rather macroscopical descriptor of the microstructure is considered, such as the grain size.

For the evaluation of the grain size, the averaged value of all density levels is taken for each time step, considering the influence of the particle size only, which is due to the artificial decrease of porosity. For each powder fraction, a minimum of 650 intercepts were evaluated for the last time step, while 1100 up to 3100 intercepts were considered for the first time step. This variation between the different powder fractions is attributed to the variation of grain size with particle size and the decreasing number of grains with increasing sintering time. The obtained evolution of grain size is depicted in Figure 9(a), showing both the averaged measured results and the respective fitted curve according to equation (3). The standard deviation, which is not depicted for a more comprehensible visual appearance, ranges from $1.9 μ$ m for fine powder to $6.0 μ$ m for coarse powder. The grain growth velocity appears to increase with the particle size, whereas the deformed powder reveals the most pronounced grain growth despite its comparatively small particle size. In Figure 9(b) and (c), the fit parameters are displayed as a function of the $D_{50}$ value of each powder. The initial grain size after 0 min of isothermal sintering varies in the range of 13.6 to 16.6 $μ m$ , tending to increase linearly with the particle size. A similar relation is revealed by the factor $K$ . Neglecting the results for variant D, a linear relationship can be assumed. It can be noticed that the zero of this linear function is nearly equivalent to the $G_{0}$ values.

Figure 9.

Grain growth during isothermal sintering: (a) grain growth; (b) grain growth velocity; and (c) initial grain size.

For each variant, length changes were continuously recorded. Figure 10 displays the significant difference between the specimens made of conventional powder and the deformed powder for all three densities. During heating, all specimens experienced a similar amount of thermal expansion. Once the austenitisation temperature was reached, the transformation strain was overlaid with an additional strain component that is the more pronounced the finer the particles are and increases also with the green density, which is depicted in Figure 11. However, the deformed specimens reveal the highest deviation of the expected linear elongation due to thermal expansion. While Figure 11(a) shows a period of about 4 min of an almost stagnant length change for D67, Figure 11(b) and (c) even show shrinkage during heating. This effect can be noticed less pronounced for the fine powder, whereas variants M and C reveal only a slight deviation for the highest densities. Considering the slope of the curve at the beginning of isothermal sintering in Figure 10 the deformed powder again stands out by a more pronounced shrinkage. Even after 48 min of sintering, a much higher shrinkage rate can be observed, which increases with the green density. The literature offers different mathematical descriptions of isothermal shrinkage. Among those, the power law proposed by Exner³ is chosen to represent the results for axial shrinkage:

ε_{x} = a \cdot t^{b}

(4)

As this investigation focuses on the kinetics of sintering, the differential length change is evaluated. The first derivative in a logarithmic scaling is given as:

\log (\dot{ε_{x}}) = \log (a b) + (b - 1) \cdot \log (t)

(5)

The initial velocity is characterised by

| a \cdot b |

, whereas

b - 1

represents the slope of the curve and therefore the deceleration of the process. Figure 12(b) shows that – apart from the coarse variant – the initial differential length change generally increases with increasing density. Most significant is the slope which is revealed by the deformed variant. Contrarily, Figure 12(c) shows an increase of deceleration with increasing density for any conventionally made specimens, whereas sintering activity is reduced much less for the deformed powder, which is well reflected by the curves in Figure 12(a).

Figure 10.

Axial length change during the experiments: (a) green density 6.7 $g c m^{- 3}$ ; (b) green density 6.9 $g c m^{- 3}$ ; (c) and green density 7.1 $g c m^{- 3}$ .

Figure 11.

Axial length change in the region of the $α$ – $γ$ transformation: (a) green density 6.7 $g c m^{- 3}$ ; (b) green density 6.9 $g c m^{- 3}$ ; and (c) green density 7.1 $g c m^{- 3}$ .

Figure 12.

Evaluation of isothermal shrinkage: (a) green density 6.9 $g c m^{- 3}$ ; (b) initial shrinkage velocity; and (c) deceleration of shrinkage.

The relative axial length $ε_{x}$ change after each step can be related to the respective relative radial dimensional change $ε_{r}$ , which is expressed by the anisotropy factor $R_{A}$ with

R_{A} = \frac{ε_{x}}{ε_{r}}

(6)

Figure 13 displays the impact of the particle size and the green density on the anisotropic length change. Again, the values tend to increase with decreasing particle size. The deformed powder leads to the highest values. A comparison of the three diagrams evokes the impression that the curves are shifted upwards with increasing green density. This is most pronounced regarding coarser powders.

Figure 13.

Influence of density and particle size on anisotropy: (a) green density 6.7 $g c m^{- 3}$ ; (b) green density 6.9 $g c m^{- 3}$ ; and (c) green density 7.1 $g c m^{- 3}$ .

In order to relate these results to the assumptions stated at the beginning, the orientation of powder particles in a cross-section parallel to the direction of compaction is evaluated. As Figure 14 clearly indicates, the deformed particles are elongated and orientated perpendicular to the direction of compaction. This tendency cannot be found in any other sample made of conventional powder.

Figure 14.

Microstructure of a green sample D71. The vertical axis corresponds to the direction of compaction.

Discussion

The independence of the evolution of local curvatures from the particle size and the green density confirms the general assumption that sintering is mainly driven by the gradient of local curvatures. As similar pores were evaluated, each pore has a similar initial condition which causes a nearly invariant initial mass flow that is presumably mainly initiated by surface diffusion. The slight differences that can be observed between the curves are attributed to the influence of the curvature in the third dimension, which cannot be investigated using SEM images.

Considering the neck formation during sintering, the neck growth rate steadily decreases, which can be attributed to the evolution of local curvatures that have been discussed before. The dependence on time and particle size that is observed reflects the mathematical descriptions that were derived for spherical powders quite well. Firstly, Herring’s law in equation (1) can be applied to compare the results for variants F and M. The ratio between the particle sizes is close to 2. Taking $m$ as 4,¹ the same neck ratio should be achieved for variant M as for variant F if the sintering time is increased by a factor of 16. Comparing the results of variant F after 3 min and variant M after 48 min, only a small difference can be noticed. Secondly, the pre-factors and exponents for equation (2) correspond to the recommendations of Exner and German, proposing $m = 4$ ¹ and $n$ between 3 and 7³ for pure surface diffusion. Assuming $γ$ as 1.59 $J m^{- 2}$ and $D_{S} \cdot δ$ as $5.99 \cdot 10^{- 19}$ $m^{3} s^{- 1}$ ,³³ a pre-factor of $1.344 \cdot 10^{- 26}$ can be derived, which corresponds to the experimental findings. This shows that the kinetic laws, which are applicable to spherical powder, are valid for water-atomised powder as well, excluding variant D. The latter has a particle size that is comparable to variant M. However, it reveals a more pronounced neck growth within the first 12 min of sintering. The slope between the second and the third sintering step is comparable to that of variant M. This deviation is probably due to additional active diffusion mechanisms, such as lattice diffusion. It is reported that an increase of the dislocation density can increase the effective volume diffusivity,^28,11 which contributes to the neck formation in a similar manner as surface diffusion, once the diffusion coefficient is sufficiently high.

It was observed that there is a noteworthy relationship between the particle size and grain growth which is linear, while the initial austenite grain size was found to be nearly constant for all particle sizes. Consequently, the number of austenite grains within a powder particle increases proportionally to the particle size. As the powder particles can be considered fully dense, grain growth within the particles is hardly impeded, which explains the observed linear increase of the grain growth velocity. Even though an influence of the relative density could not be investigated due to the disadvantages of the experimental setup, the assumption can be made that there is a negligibly small impact by the density at a temperature of 1120 $\circ$ C. As already mentioned, the derived relationship states that the grain growth factor $K$ becomes zero at a particle size of 19.5 $μ m$ , which is slightly higher than the initial grain size in the particles. Inversely this means that grain growth is only possible if the grain size is smaller than the particle size. This holds true as long as grain growth beyond the sinter necks is suppressed, which is the case for initial stage sintering. Initial stage sintering is characterised by a maximum sinter neck ratio of 0.3,¹ which is not exceeded in the experiments. A similar observation was stated by Dlapka, who also investigated the effect of the particle size, the temperature and the sintering time on austenite grain size.¹² Variant D needs to be excluded again from this observation, as the grain growth is much more pronounced. This effect can be partly explained by the course of the sintering necks in Figure 6(a), which was found to be higher than expected for the particle size. The wider the sinter neck, the lower the energetic barrier for grain boundaries to overcome a sinter neck.

The effect of the deformation of the powder is even more pronounced when the dilatometric results are compared. It was shown that the deformed powder leads to a much faster, higher and more anisotropic shrinkage than it can be observed otherwise, which reflects the microscopic findings, as the macroscopic shrinkage is strongly related to neck formation induced by diffusion through the particle volume. The investigation of the elongation during heating indicates that sintering starts in variant D at much lower temperatures, which could also be provoked in variant F, once higher green densities were considered. The latter suggests a dependency on the compaction pressure. Both the cold working of powder D as well as the increase of compaction pressure are related to a higher dislocation density within the powder particles.^34,28 Presumably, this provokes also a higher isothermal shrinkage as well as a higher initial shrinkage velocity, which could be additionally attributed to an increase of contact areas between the powder particles with an increase in compaction pressure. Molinari et al.¹¹ related the extent of isothermal shrinkage to an effective volume diffusion coefficient that was described as a function of dislocation density. Accordingly, the pre-factor $a$ in equation (4) was given as:

a = {(\frac{2 D_{V} γ Ω}{R T D^{3}})}^{b}

(7)

with

D_{V}

as the volume diffusion coefficient and

D

as the mean particle size. Applying this to the results of this work, an average increase of diffusivity by pre-deformation by a factor of 18.7 can be found, which confirms the assumptions made to explain the deviation of the neck growth kinetics. The differences in Figure 12(b) and (c) can be explained based on the assumption that the dislocation density and the induced pipe diffusion effect are rapidly reduced at the beginning of the isothermal sintering,¹¹ which leads to a higher initial shrinkage rate and a more pronounced deceleration. This applies to variants F and M, which reveal an increase of shrinkage during heating and an increase of the initial shrinkage velocity as well as a more pronounced deceleration with an increase in density. Variant D is subjected to an almost density- independent deceleration, which is presumably attributed to an anisotropic microstructure that is depicted in Figure 12(c). This suggests a negligible sensitivity of pre-deformed powder to the compaction pressure. Contrarily variant C reveals an almost inverse behaviour, indicating no dependency on a dislocation pipe diffusion effect that was induced by compaction. In a similar investigation it was observed that with a decrease in the particle size, an increase of shrinkage in the ferrite region is to be expected, whereas isothermal shrinkage simultaneously decreases.¹⁸ This effect was reported as even more pronounced for higher compaction pressures and lower heating rates, leading to a maximum fraction of 83% of shrinkage beyond the phase transformation. Inversely that led to a slightly higher isothermal shrinkage for coarser powder under the same process conditions. As a root cause, a dependency of the dislocation density on the particle size was stated, as the deformed volume fraction steadily decreases with increasing particle size. This is corroborated once comparing the course of the anisotropy factor, which decreases noticeably during sintering for higher densities, whereas it is nearly constant over all three experiments for the smallest density. The values gathered after the first sintering step show the only significant dependency on the green density whereas the other values remain almost constant. This is presumably caused by the dislocation pipe diffusion effect, which is increased by the compaction pressure and is rapidly reduced during sintering, as already observed before. As proven by EBSD measurements, dislocations are unevenly distributed in a powder compact and show an orientation related to the direction of compaction.²⁷ This suggests that dislocations increase the axial length change, whereas the radial shrinkage is less affected, leading to a higher anisotropy. However, a contribution of an anisotropic orientation of contact surfaces must not be neglected.^25,35,36 The differences that can be noticed between the results of all variants after the last sinter step are most likely attributed to the microstructural orientation. Assuming a proportional increase of anisotropy with the green density,³⁷ the vertical shift of the data points in Figure 13 can be explained.

Conclusion

A new experimental setup was used to characterise and quantify the microstructural and macroscopic evolution of PM steels during sintering. It was found that neither green density nor the particle size affected the surface diffusion, whereas the neck growth varies with particle size. This indicates the validity of the classical two-sphere sinter model and the associated analytical descriptions for water-atomised powders.

Thermal etching was used to quantify the austenite grain growth and to derive a linear relationship between grain mobility and the powder particle size that corresponds well with the physical boundary conditions of this mechanism that grain growth is limited by the particle interfaces.

On the macroscale, a relationship between green density and differential length change was derived. The results based on deformed powder as well as the quantification of anisotropy indicate an increase of diffusivity that can be attributed to the dislocation pipe diffusion effect. This is well reflected in an increase in neck growth kinetics. Further work is required to investigate the effect of cold deformation of the powder on the sintering process.

Footnotes

Acknowledgements

This work has been carried out within the Cluster of Excellence ‘Internet of Production’ (IoP) at RWTH Aachen University. GKN Powder Metallurgy GmbH is acknowledged for debinding the specimens.

Declaration of conflicting interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Supported by the German Research Foundation DFG (Project-ID: 390621612) within the Cluster of Excellence ‘Internet of Production’ (IoP).

Notes on contributors

Oliver Schenk received his master’s degree in mechanical engineering at Wuppertal University in 2020 and works on simulation of powder metallurgical manufacturing processes in the Institute for Materials Applications in Mechanical Engineering (IWM) at RWTH Aachen University. His research interests include the numerical simulation of sintering processes on the mesoscale as well as the macroscale.

Yuanbin Deng received his master’s degree in materials engineering at RWTH Aachen University in 2015 and works on simulation of powder metallurgical manufacturing processes in the IWM at RWTH Aachen University. He is currently the head of the Process Simulation group in the Powder Technology department of IWM. His research interests centre around the macroscopic modelling and simulation of sintering and hot isostatic pressing process, geometry optimisation for near net shape manufacturing.

Anke Kaletsch is head of the division Powder Technology at the IWM at RWTH Aachen University. Besides, she is the deputy head of the Institute of Applied Powder Metallurgy and Ceramics (IAPK), which is an associated institute of RWTH Aachen University. Anke Kaletsch studied Mechanical Engineering in Aachen and received her doctoral degree from RWTH Aachen University in 2016. At IWM and IAPK, she coordinates research activities and projects in the field of powder metallurgy and ceramics. The main research areas in her department are additive manufacturing, hot isostatic pressing and sinter simulation for various production processes.

Christoph Broeckmann worked with the Institute of Materials Science at Bochum until 2000 after finishing his studies in Mechanical Engineering at Ruhr-University Bochum, Germany, in 1990. He got his PhD in 1994 on a thesis on the fracture of carbide-rich steels. As a senior scientist, he established a research group on creep-related problems at Bochum University. In 2000, Christoph Broeckmann got his lecture qualification (habilitation) based on a work on the creep of particle-reinforced materials. In 2000, he moved to the machine factory Köppern GmbH & Co. KG in Hattingen where he first was responsible for material and design-related research and development. Since 2003, he became managing director of ‘Köppern Entwicklungs GmbH’ a subsidiary dedicated to the development, production and delivery of large, powder metallurgically produced wear parts. He joined RWTH Aachen University as a professor in 2008. Since 2009, he has been head of the Institute for Materials Application in Mechanical Engineering.

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Multiscale investigation of sintering kinetics of Astaloy 85Mo

Abstract

Keywords

Introduction

Materials and methods

Results

Discussion

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interest

Funding

Notes on contributors

References