Capillary And Rotational Rheometry Engineering Essay

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In this project, through the combination capillary rheometry and rotational rheometry, the flow behaviour of PA12 in its virgin, used, sintered, heated and recycled states was established at temperatures ranging from 200 - 240 oC.

In the capillary rheometry, which focuses on medium to high shear rates, it was found that the used PA12 had a much higher viscocity than the virgin PA12 when at the same shear rate. It was also found that the PA12 that had been heated just below its melting temperature for three hours behaved almost identically to the used polymer. In addition, it was found that when the shear rate was increased and then decreased in the same run, the return viscosity from high to low was lower than when it was initially passed from low to high.

For the rotational rheoemeter, tests were carried out using a recycled samples, samples from the top of a sintered part and samples from the bottom of the sintered part. It was found that the sintered top and sintered bottom parts had similar flow properties, where the viscosity of the recycled powder was higher. Runs were also undertaken on the virgin bottom part using temperatures of 200, 220 and 240 oC. It was found that as the processing temperature increased, so did the viscosity of the sample.

Frequency and Amplitude sweeps were both used and it was concluded that the PA12, regardless of processing conditions, behaved as a viscoelastic fluid, which stayed in a linear viscoelastic state until a strain percentage of 16%.

Selective laser sintering is a process where a high power laser is used to fuse layers of small particles of plastic, metal, ceramic and glass into a three dimensional shape. Digital instructions on how to form the part are created via CAD software. Cross sections of this design are scanned and then fused by the laser onto the surface of the powder bed.

The surface is then subjected to a laser beam that selectively bonds and melts the powder to form a layer of the object. The plastic most often used in selective laser sintering is Nylon 12. The viscosity of the nylon at a specific shear rate depends on several variables, including whether the nylon is virgin or being re-used. This is predicted and explored using the Frenkel model, which explains how particles react when they are actually sintered.

The benefits of acquiring the perfect viscosity for the sintering process would result in a better quality of manufacture, leading to a product with better mechanical properties.

Another point of consideration is the age of the powder and the amount of thermal degradation is has undergone. If the polymer is held at a high temperature for long period of time, polymer degradation occurs which will reduce the molecular weight, adversely effecting the properties.

Literature Review


Rapid manufacturing is a fairly new extension of Rapid prototyping, in which a three dimensional object is produced by the stacking of two dimensional layers into the shape of a pre determined three dimensional model created by computer aided design software[2]. This experiment is concerned with the rapid manufacturing technique known as selective laser sintering, which has recently developed great interest in industry and research due to its ability to manufacture parts that were previously too difficult to produce without tooling. [1]

Selective laser sintering works by melting layers of powder into the shape of a three dimensional component with a computer controlled CO2 laser [3]. There are two major companies that specialize in the production of selective laser sintering equipment. These companies are the 3D systems corporation based in the USA and German based EOS GmbH. Together, these two companies hold a monopoly over the SLS market.


Fig 1

The above (fig 1) processing route is the one used by companies such as 3D systems and EOS [1,2]. The process works as follows: a shape is designed on CAD software and uploaded to the selective laser sintering system. The image is then cut horizontally into "slices", where each slice represents a layer of powder. A CO2 laser is then used to fuse the powder layers, progressively forming the shape of the desired solid object on a platform just below the base of the cylinder. If a high powered laser is used then the powdered is sintered better, up until a certain point where the powder is burnt [3]. The platform is then lowered by the height of the next layer and the next layer of powder is applied. This process is repeated until the entire model has been formed.

Materials for SLS

A large range of materials can be used for selective laser sintering. Papers have been published exploring the use of polymers, such as Nylon 12, ceramics and metals [2]. Polymer sintering is becoming more and more widely used in industry. This is due to the advantages that selective laser sintering possess over other forms of polymer forming, such as injection moulding [5].

Mechanisms for sintering polymers

Frenkel stated that surface stress could cause viscous flow in materials; and sintering of polymers can be explained by that phenomena. Polymer sintering can be given by the equation below [15]:

Where x is the neck radius, with , and being the particle radius, surface tension and viscosity respectively and is sintering time. By analysis of this above equation, it is clear that the main factors that determine the speed of sintering are particle size, surface tension and viscosity [15].

According to Frenkel, sintering takes place in two stages. In the first stage, the powder of the particles, which are sintered, begin to combine, allowing for the formation of pores [8]. This can be represented in the joining of two liquid drops. After a specific time, the two drops will touch each other along the circle of a radius Y(t)

Fig 2

In the above case, radius of the circle is Y=asinθ, where a is the spherical part of one of the drops. In the second, a process of pore over running takes place. This is when the huge concentration of point defect vacancies are decreasing due to diffusion.

Wang et al determined that a viscous flow mechanism was suitable for amorphous polymer sintering [9] and that the viscosity of the melt factored largely towards the overall quality of the sintered specimen. Pores can be formed between the layers of powder during SLS. These decrease the mechanical properties of the sintered part [5].

Polyamide 12


Nylon was created by Carothers in 1935 and was then made available to the general public by DuPont Corporation. Also known as polyamide, it is formed by combining molecules with an acid group on each end with molecules containing the amine group on each end. There are a wide range of Nylons available, but the most desirable and popular choice for selective laser sintering is Nylon 12, whose general reaction formula is shown below: [1,2].

There are two main synthesis routes to create polyamide 12 specifically. One of them is originated from 12-laurolactam, which is widely employed in Europe and USA. Another one used by Japanese is called 12-aminododecanoic acid route.

Physical properties

Polyamide 12 is a good engineering plastic for its general physical properties. It has a relatively low density compared to other commonly used materials.

Fig 4

Fig 3

As fig 3 shows, the polyamide 12 compares very favorably to other materials, being 2.5 times lighter than aluminum and boasting good thermal and electrical properties. Nylon 12 is tough, extremely flexible and possesses a very low level of water absorption. This is illustrated in the fig 4 above, showing that PA 12 absorbs much less water than Nylon 6 and Nylon 6,6, which are the other two Nylons commonly used in the engineering industry. Alongside this figure is a table summarising the physical properties of polyamide 12 [10].




Thermal Expansion



Thermal Conductivity



Specific Heat



Melting Temperature



Service Temperature









Breakdown Potential



Dielectric Loss Factor


Friction Coefficient





Water Absorption



Table 1

Mechanical properties




Young's Modulus



Shear Modulus



Tensile Strength






Bending Strength



Impact strength



Table 2

Upon inspection of table 2, it is clear that polyamide 12 possess several desirable qualities. These include high impact strength, bending strength and resistance to shrinkage at a wide range of temperatures. These qualities are desirable when considering that a snowboard could go from being quite cold due to the contact with the snow, to very warm in a short space of time due to friction with certain materials, such as rocks, on the ski slope.

Application of polyamide 12 in SLS

As mentioned previously, nylon 12 boasts good mechanical properties with low density, low water absorption and a good resistance to shrinkage. Studies have been carried out to show the processing affects on nylon 12, notably by Neil Hopkinson [1],[5],[6] who investigated how the degree of particle melt of Nylon 12 affected the mechanical properties of the sintered part. There is also work looking into how laser sintered nylon 12 coatings are bonded to carbon as coatings and how nylon 12 can be used as a polymer blend [3].


Fundamental theory for polymer melts

As shown by Hopkinson [1], the rheological properties of polymer melts play an important role in the completed part which has undergone selective laser sintering. The time the laser is in contact with the powder, and the power of the laser will determine the degree of particle melt. A greater amount of particle melt leads to better sintering [1].

For practical melt processing, such as selective laser sintering, the simple shear model represents a fairly accurate portrayal of the behavior of the melt when under said conditions [12]. Simple shear classifies fluids according to their viscous behavior, separating them into four models; Newtonian fluid (such as water), Bingham body (rigid at low stresses, viscous at high stresses), dilatant (viscosity increases with the rate of shear) and pseudo plastic (viscosity decrease with the rate of shear). Nylon 12 is typical of polymer melts in that is shows pseudo plastic behavior, with the viscosity decreasing with increasing shear rate [1].

Figure 5 shows the relationship between viscosity and shear rate for the three major types of fluid. These are known as the power law fluids. For these equations, the shear stress, Ï„, can be given be the following equation:

Where K is the flow consistency index, ∂u/∂y is the shear rate and n is the flow behavior index.

By using the above model, the effective viscosity as a function of shear rate can be found by the following equation:

The value of n determines the type of fluid. If n= 1 then the fluid is Newtonian, if n < 1 then its pseudo plastic, if n > 1 then the fluid is dilatant. Stress strain graphs for the fluids are shown below:

Fig 5

Fig 6

As well as the power law model, three others are less frequently used; the Polynomial, Ellis and Carreau.

Experimental methods

Figure 5 [15]To measure the flow properties (how viscous the material is under a certain shear), rheometers are used. There are two types of Rheometer. One is the rotational rheometer, which utilises a cone, plate and a concentric cylinder. The other group is called the capillary rheometer, which employs a ram extruder and melt flow indexer. Both of these instruments produce curves of viscosity against shear rate. The rotational rheometer specifies with low shear rate and the capillary rheometer works on the high shear rates.

Capillary rheometer

The capillary rheometer is the most common device for measuring viscosity. Either gravity, compressed gas or a piston is used to generate pressure onto the fluid in the reservoir. A capillary tube of known radius and length is connected to the bottom of the reservoir. The change in pressure and flow rate that occurs in this tube is used to determine the viscosity. A diagram is shown below:

Fig 7

For a capillary tube of length L and radius R, subject to force F, pressure P and flow rate Q, the following equations apply for Newtonian fluids [13]:

Shear stress inside the centre of the tube:

The velocity profile inside the tube: (at the wall r=R)

The shear rate is given by:

Where shear rate is for Newtonian fluids and apparent shear rate is for non Newtonian fluids.

The apparent viscosity can be found by dividing shear stress by shear rate, hence:

For non-Newtonian fluids, the following equation, known as the rabinowitch analysis is used:

To obtain the "true" shear rate, the flow rate must be plotted against the shear stress so the derivative can be calculated. For power law fluids, the slope is:

Unless the capillary tube is exceedingly long, then entrance pressure drop may affect the accuracy of the measurements. This can be corrected by using the Bagley correction, producing the true shear stress:

One problem encountered with capillary rheometers is the problem of die swell. This is due to the chains being straightened while in the die, while afterwards they revert back to their original shape once pressure has been relieved. The extent of the swelling is shown by the swell ratio.

Rotational Rheometer

The basic concept between rotational rheometry is that fluid is sheared between two surfaces; one or both is which is rotating. The advantage of this rheometer is that it can shear the sample for an unlimited period of time. They are also capable of creating normal stress tests that are capable of characterising the viscoelastic properties of the sample; useful as viscoelasticty has an unknown effect on sintered products.

Fig 8

There are two categories of rotational rheometers; stress controlled and rate controlled. In stress controlled, a constant force (torque) is applied to generate rotation, and the resulting speed is then determined, thus giving an indication of the viscosity. In rate controlled, a constant speed of rotation is maintained and the stress on the sample is determined using a stress sensitive device.

The above shows a type of rotational rheometer, known as the cone and plate rheometer. It has a radius of R with an angle θ between the cone and base plate. Polymer enters the gap between the cone and base plate and, as the cone rotates, is sheared. For a gap of height h at radius r, shear stress can be given by the shear rate [14]:

The shear stress, , is given by:

Where M is the total torque. By analysing x and x is can be concluded that the shear rate is constant. The flow curve of the polymer can be constructed from the stress and shear rate, which are both dependant on both the angular torque and total velocity.

Even by the rotational rheometers standards, the cone and plate is limited to a low shear stress measurement.

Fig 9

Another type of rotational rheometer is the concentric cylinder type, as shown above. The concentric cylinder works by two concentric cylinders shearing the polymer between them. The shear rate and stress can be given by:

Where is the angular velocity and is the torque per unit length of the cylinder. The shear rate is not constant in the concentric cylinder type, but approximate equations can be formed due to the gap being small.

The rotational rheometer focuses on the low shear conditions in comparison with the capillary rheometer that focuses on higher rates of shear.

Due to the rotational rheometer performing better at low shear rates and the capillary rheometer being better suited to higher rates of shear, the two can be used well in conjunction together to create a graph of viscosity against shear rate for a range of shear stresses.

Molecular weight

Solid state polymerisation

Solid state polymerization is a change in the molecular orientation due to overheating. When the polymer is heated to just below its melting point the polymer begins to separate via molecular scission and these molecules react with each other to change the properties of the polymer. Thermal degradation leads to a decrease in physical and optical properties, as well as an increase in molecular weight, embrittlement and cracking.

The process is split into three parts: initiation, propagation and termination. Initiation involves the loss of a hydrogen atom from the chain of the polymer due to the energy created from the heat. This leads to the creation of a highly unstable free radical polymer and a hydrogen atom with an unpaired electron. Propagation involves the free radical reacting with an oxygen molecule which then creates another hydrogen atom with an unpaired electron and the free radical is regenerated. Finally, termination occurs when free radicals combine to create inert products. [16]


Hydrolysis is a reaction with water. It is most likely to occur in the presence of strong acids and lower members of the Nylon family are less likely to be affected than the higher members. Therefore, hydrolysis is less likely to occur in Nylon 12 than a lower member, such as Nylon 6. When hydrolysis does occur, the molecular weight drops very quickly [17].

Fig 10


Nylons susceptibility to oxidation is increased as the temperature is increased. Sintering and the rheometers involve manipulating molten polymer, and these high temperatures can lead to oxidation. Oxidation causes the polymer chain to degrade into smaller pieces, and consequently the molecular weight decreases. However, excessive oxidation can result in cross linking to occur between the degraded polymer, subsequently causing the molecular weight to increase [18].

Complex Viscosity

Complex viscosity is a frequency dependant function that is determined during forced oscillation of shear stress. It is related to the shear modulus and represents the angle between elastic and shear stress. The complex viscosity function is equal to the difference between the dynamic and out of phase viscosity [19]

η* = complex viscosity

η' = dynamic viscosity

η'' = out-of-phase viscosity

Amplitude Sweep

In an amplitude sweep the amplitude of deformation is varied while the frequency is kept constant. The amplitude is the maximum of the oscillatory motion.

The results are displayed as a graph of the moduli η' and η'' against the deformation. The moduli in the linear - viscoelastic region at low level deformation characterises the structure in peace of the sample [20].

If the deformation is low then the values of η' and η'' are constant, meaning the structure of the sample is undisturbed. As the moduli start to decrease it means the structure is disturbed. The plateau value describes of η' in the linear-viscoelastic region describes the rigidity of the value at rest, where as the plateau value of η'' is a measure of the viscosity of the unsheared sample. If η' is larger than η'' then the sample behaves like a viscoelastic solid. If η'' is larger, then the sample behaves as a viscoelastic fluid. 

Frequency sweep

A frequency sweep consists of a test where the frequency is varied while the amplitude of the deformation, or the amplitude of the shear stress, is kept constant. η' and η'' are plotted against the frequency. The data at low frequencies describes the behaviour at low changes of stress, where as the behaviour at high stress is shown at the high frequencies [21].



In this project, five different kind of Nylon 12 were used. Information on these three is listed below:


Grade / Trade name


Melting Point (oC)


PA 12 Random Used




Fine powder

PA12 Virgin

PA 2200



Fine powder

PA 12 Virgin top




Fine powder

PA12 Virgin bottom




Fine powder

PA 12 Recycled




Fine powder

PA 12 Random Used: This powder has been put through the laser sintering machine and is the "left over" that was not sintered. However, it is not known how many runs through the powder has had, or whether the powder came from the top or bottom.

PA12 Virgin: Brand new powder, never before been used, straight from the manufacturer.

PA12 Virgin top: This is used powder with a known past history. It is the left over powder from the top of the sintered part. Due to it being on the top layer, it has been exposed to the heat for less time than the powder at the bottom.

PA Virgin bottom: The same as above, except the sintered part comes from the bottom, meaning it has been exposed to heat for longer.

PA Recycled: This is leftover powder from the middle of the first run, taken from between the top and bottom. It has been exposed to thermal degradation at a level between that of the top and bottom levels.

PA Heated: This is virgin PA12 that has been heated at 170 degrees for 3 hours.


Two rheometers were used to determine the flow behaviour of the PA samples. In addition to this, a compression moulding machine was used for sample preparation.


Model and Manufacturer


Capillary Rheometer

RH-7, Rosand

Measure flow behaviour at high shear rates.

Rotational Rheometer

ARES, TA Instruments

Measure flow behaviour at low shear rates.

Compression Moulding Machine


To prepare the disk samples for the rotational rheometer.


The overall process is shown below and details of each part are explained in the following parts.


The powders were dried before being run on the rheometers and compression moulding machine. The powder was placed on foil in an air dried over. The powder was heated for 1.5 hours at a temperature of 80 degrees. After the drying was complete, the powder was placed in an airtight plastic bag.

Compression Moulding

Compression moulding was used to prepare the powder so that it was compatible with the rotational rheometer. A square shaped mould was filled with powder and then clamped using two metal plates with two layers of plastic film between the powder and the plates. This was then inserted into the compression moulding machine once the temperature had reached 200 degrees. With a hold on pressure of 10 tonnes, the clamp was applied for 3 minutes, and then given 2 minutes for cool down. Disk shape samples, 25mm in diameter and 1mm thickness were then cut from the original mould.

Results and Discussion

Capillary Rheometer

Graph 1

The above graph shows the how the state of the powder, whether it be used, virgin or heated for 3 hours at 170 degrees C effects the shear flow.

For all of the capillary rheometer data, the Bagley correction was used to correct the shear stress. This is necessary due to the capillaries being relatively short, thus having an excess pressure drop at the capillary entry. This is shown by the equation [22]:

Where Pcap and P0 are the difference in pressure between the 16:1 die and 0 inch die respectively. With the shear stress corrected, an accurate value of the shear viscosity can be found, using the equation:

Graph 2

As shown in Zhongs previous work [15], it is again clear that at medium and high shear rate ranges (10 - 1000s-1), the flow behaviour of used PA 12 is very different to the flow behaviour of virgin PA12 at 200 degrees. From graph 1 we can see that for used PA 12, the shear viscosity decreases as the shear rate is increased, where as in comparison, the virgin PA 12 stays relatively constant. Interestingly, the behaviour of the heated powder closely resembles that of the used powder, suggesting that the conditions and amount of thermal degradation that the used powder underwent during the sintering process is equivalent to being held just below the melting temp (170 degrees) for a prolonged period of time. The shear viscosity of the used and heated PA12 was much higher than that of the virgin PA12; again an affirmation of Zhongs previous work. Once again the shear viscosity of the virgin powder dropped after the shear rate increases.

Knowledge of the power law constants of the different powders are invaluable to determine the flow behaviours of the polymers. To this end, a graph of log correct shear stress vs log shear rate on the straight parts was produced. The relationship between the graph and the power law constants is shown below [23]:

Where n and K are the power law constants. The graph is displayed below:

Graph 3

The equations of the lines came out as follows:

Virgin: y = 0.883x + 0.096

Used: y = 0.579x + 2.454

Heated: y = 0.711x + 1.987

These can be used, in conjunction with the above equation, to form the following value of tables:

PA 12 Used



PA 12 Virgin



PA 12 Heated



The value of the virgin was 0.833. This was the highest value of the three, meaning that the Virgin PA 12 behaved the most like a Newtonian fluid. The used PA 12 had a value of 0.579 and the heated PA 12 had a value of 0.711. This means that the used PA 12 behaved pseudo plastically. The heated PA 12 also did this, although not to the same extent as the Used PA 12. In comparison with Zhongs findings, [15], there are some discrepancies. Although the value for the used PA 12 was near identical, the value for the virgin PA 12 differed (0.883 to 1.026). This could possibly due to differences in the test sample, such as pores being present. This would account for the two values not being identical.

Graph 4

The above graph shows the effect that the size of the initial shear rate has on the viscosity. Used PA 12 was used for all three tests. The red line shows the slow to fast set up as used by Zhong, and the results are identical and to be expected. For the green fast to slow line, it isn't clear what is happening. Many of the first readings at the highest shear rates were unsuccessful, probably due to the warm up times of the rheometer not being sufficient to melt the polymer to the point where it could be extruded at such a high shear rate. Therefore it has been concluded that the fast to slow readings can be considered erroneous. The blue line shows the slow to fast to slow. To begin with, at the low shear rate the shear viscosity decreases as the rate of shear increases, as to be expected. This continues to the midpoint of the run, where the highest shear rate of 1000s-1 is reached. The shear rate then works back down to its original value of 20. The shear viscosity then increases as the shear rate decreases, but does not reach the same viscosity values that it had reached originally. This is strange because if anything, due to being held at a high temperature for longer, the shear viscosity would be expected to increase, as used does in relation to virgin polymer.

Graph 5

The above graph shows how the shear viscosity changes as the shear rate is increased from 10 - 1000, and then reduced back down to 10, for both used and virgin PA12. As the shear rate is increased, the viscosity of both the virgin and used decreases, as is expected and has been shown numerous times in previous tests. However, once the shear rate is then decreased from 1000 back down to 10, the shear viscosity increases at almost exactly the rate it decreases to a certain point. After this point, the shear viscosity continues to decrease past what it originally was, as shown by both lines above.

The anomaly confirms that the time spent in the rheometer has an effect. If this was not the case then the line would just work back on itself exactly. This is not the case meaning that some variable must be having an effect on the molecular weight as time in the rheoemeter increases.

This is unexpected, as the fact that the PA12 was exposed to heat for longer led to the assumption that solid state polymerisation took place, resulting in an increase in viscosity due to the increased molecular weight. However, it is clear that this is not the case; in fact the opposite has happened. Possible reasons for this happening could be that the polymer was not fully melted at the start of the process, and it wasn't until the shear rate was decreasing that the PA12 was fully molten, meaning the viscosity would be lower. However, the extrudate from the rheometer was fully molten from the very beginning, suggesting that the warm up time was sufficient to completely melt the PA12.

Another possibility is Hydrolysis. This is where the polymer chains come into contact with water, causing them to break down into smaller pieces. However, this is unlikely as both powders were dried out before use, and it seems unlikely than the powder would gain water after having been in the rheometer for an increased period of time.

An interesting point to note is that fact that the dip at the start of the virgin polymer repeats itself when the shear is reserved from fast to slow. As of yet it is unknown why this anomaly occurs.

Rotational Rheometer

Graph 6

The above graph shows the low shear strains vs viscosity created on the rotational rheometer at 200 degrees. The PA12 used was laser sintered plastic from the bottom of the laser sintered run, equivalent plastic from the top and the left over powder from the same run that wasn't sintered. This is known as "recycled".

Before seeing the results, it was predicted that the Virgin top would have the lowest viscosity, the Virgin bottom would have the highest viscosity and the Recycled would be in between the two. The reason for this prediction is that, as seen with the RH-7 results, the longer a specimen spends at an elevated temperature, the greater amount of solid state polymerisation will occur, resulting in increased molecular weight. This is believed to be why used PA12 has a higher viscosity than virgin PA12. Virgin bottom was anticipated to have the highest viscosity because, being placed down first, it would be exposed to heat much longer than the virgin top, which would only be exposed to the heat for a small amount of time at the end of the run. The recycled, which is a collection of all the powder from the top and bottom that wasn't sintered in the run, was predicted to be a mixture of the two.

The results show that the virgin top and virgin bottom have a similar viscosity throughout the entire run. Reasons for this could be that the virgin bottom isn't exposed to heat for as long as originally thought (once the laser has been and gone the sintered part could cool relatively quickly). However, a more likely explanation is that when the PA12 is sintered and melted, it undergoes a change on the molecular level which makes it impervious to condensation (thermal degradation). This would account for the virgin top and bottom having equivalent viscosity's and also explain why the recycled, which is still in the powder form, has a higher viscosity than the other two, as it is able to undergo solid state polymerisation.

Graph 7

The above graph shows strain rate vs viscosity for the virgin bottom sintered part at three different temperatures, 200, 220 and 240.

It was predicted that as the temperature increased, the viscosity would decrease, due to the extra heat breaking the bonds down. As shown by the graph, the opposite happened, with the virgin bottom 200 being the least viscous, and as the heat increases the viscosity actually increases.

The exact reason for this happening is unknown. What is known is that an increase in viscosity is associated with an increase in molecular weight. The only known reasons for this happening is due to the solid state sintering, or possibly excessive oxidation that has resulted in crossing linking, hence improved molecular weight.

Frequency Sweep

Graph 8

The above graph shows the out of phase viscosity of the laser sintered nylon 12's vs the frequency of rotation. The reason why this graph is presented is to highlight the difference, if any, that the actual sintering process and time exposed to heat has on the different types of viscosity (dynamic and out of phase viscosity).

As has been shown in the other graphs, the virgin top and virgin bottom have an almost identical viscosity, where as the un-sintered recycled powder does not. This further clarifies that the sintering of the polymer prevents the solid state polymerisation from occurring, which is why the virgin bottom's viscosity, and hence its molecular weight, does not exceed the virgin top, despite having been exposed to heat for longer.

Graph 9

This time, the above graph shows the dynamic viscosity of the same sintered parts with respect to the frequency. The graph is virtually identical to graph 8, meaning it is safe to assume that the process happening when in the rheometer acts equally on both the dynamic and complex areas of the viscosity.

It is evident that as the frequency of rotations increases, the viscosity also increases. This makes sense as the increased number of rotations means there is more resistance from the material.

Graph 10

The above graph shows how both the complex and imaginary viscosity's of the bottom sintered virgin differs at different temperatures when exposed to an increasing frequency of rotation.

Previously, when the viscosity was not broken down into its complex and imaginary parts, the opposite of what was expected occurred - as the temperature increased, the viscosity increased. This was attributed to an increase in molecular weight caused by solid state polymerisation or possibly oxidation.

For the sintered virgin bottom PA12 processed at 200, the η' viscosities behaved the way the combined viscosities did. The η' 200 started off with the lowest viscosity. The η' 220 had a viscosity only slightly higher than this, where as the η' 240 was considerably higher at the lower frequencies. As the high rotation speeds were reached, the viscosities got closer. Interestingly, the η' 200 finished with a higher viscosity than η' 220 and η'240. This could be due to the polymer not being as completely melted so that at the high frequencies of rotation, more resistance is encountered, meaning the viscosity is increased.

The behaviour of the η'' does not match that of the η'. The η'' 200 actually started at a viscosity higher than that of the η''220 which does not follow the trend set by all the other results, in which the lower temperature polymer always started at the bottom. The η'' 240 is higher than the other two at low frequencies of rotation, but once increased ends up about equal to η'' 220 and η'' 200. A possible reason for this could be that the higher temperature leads to a greater degree of melting and therefore a decreased amount of viscosity at the low frequencies. However, if then it should occur with the η'240, but it does not.

Amplitude Sweep

Graph 11

The above graph shows the amplitude sweep for the virgin bottom, virgin top and recycled samples.

For each of the three samples, it is evident that the η'' value is much higher their corresponding η' value. This means that regardless of the processing route, the samples all have the behaviour of a viscoelastic fluid.

All the samples stay in the linear viscoelastic region up until roughly the same point, a strain percentage of around 16%, so it is at this strain that the structure is disturbed.


The shear flow behaviour of PA12 in different states has been determined by two methods: capillary and rotational rheometry.

As originally shown by Zhong, it has been concluded that used PA12 has a much higher viscosity than virgin PA12. This is due to solid state polymerisation taking place which increases the molecular weight and hence the viscosity. Both the capillary and rotational rheometers produced results that ascertained this theory.

It was also apparent that the changing of shear rate mid test has an effect on the sample. Tests were completed with both virgin and used polymer where the shear rate started off low, was increased and then decreased again. The results showed that as the viscosity was decreased, the viscosity was less than what it was originally on both the used and virgin samples. The initial sharp incline in viscosity for the virgin PA12 when the shear rate was set from low to high was apparent also at the end of the high to low, meaning it cannot be attributed to the virgin polymer never having been melted.

Tests were also done to see if changing the temperature had any effect on the flow behaviour of a sintered part. Tests were done at 200, 220 and 240 degrees C and it was concluded that as the temperature increases the viscosity also increases, with the most notable increase being between 220 and 240 degrees c. This was concluded to be due to solid state polymerisation, excessive oxidation or an unknown process.

Another test looked at the difference between the viscosity of the virgin top, virgin bottom and recycled powder parts. It was shown that the recycled powder had a much higher shear rate than the virgin top and bottom sintering parts. From this it was concluded that the solid state polymerisation (or a process that has a similar effect in increasing the molecular weight) does not occur on a sintered part.

Tests were also done to investigate the complex and imaginary parts of the viscosity. It was concluded that all the samples, regardless of prior processing, had the behaviour of a viscoelastic fluid.

Future work

Future work recommended is concerned with investigating the results of this paper that don't have a concise explanation. This includes establishing why a dip is present at the low shear rates on the graph produced by the capillary rheometer for virgin PA12 when the shear rate is increased at the beginning of the run.

Another test that could be carried out involves investigating why, when the processing temperature is increased for the virgin bottom sintered part, the viscosity also increases. An investigation could be to see if the fact the part has been sintered has any effect on this behaviour.

Finally, an experiment could be conducted to see why, when moving from low to high to low shear rates, the viscosity decreases when moving back to low from high.

For SLS processing, an investigation into optimizing the most desirable mix between the virgin and used PA12 powder can be carried out with the results obtained in this project.