Preparation of polymeric samples containing a

Polymer Testing 29 (2010) 494–502

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Polymer Testing journal homepage: www.elsevier.com/locate/polytest

Test Method

Preparation of polymeric samples containing a graduated modulus region and development of nanoindentation linescan techniques J.H. Gwynne a, *, M.L. Oyen b, R.E. Cameron a a b

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 January 2010 Accepted 22 February 2010

This work concerns the development of a technique for the nanoindentation of polymeric samples containing a graduated modulus region, and a method for the preparation of samples. The samples studied were prototype intervertebral disc prostheses, which were manufactured from polycarbonate urethanes using a single-step injection moulding procedure. Discs were sectioned, mounted and polished using a series of increasingly fine grades of silicon carbide paper. It was found that the smoothest samples exhibited a significant degree of polishing damage around the interface and that slightly rougher samples were in fact more uniform and more suitable for studying using nanoindentation. The variation of the measured Young’s modulus value with surface roughness was also investigated using calibration samples, and a nanoindentation linescan method was developed, which allows the variation in modulus across a polymeric sample to be investigated. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Polyurethane Nanoindentation Polishing Intervertebral disc prosthesis Graduated region

1. Introduction 1.1. Nanoindentation Nanoindentation, or depth-sensing indentation testing, is a technique used primarily to obtain values of the elastic modulus and hardness of materials, and involves bringing an indenter tip of known geometry into contact with a sample. The contact area is calculated by measuring the depth of penetration of the indenter tip into the sample surface and, since no residual plastic deformation is required for this calculation, nanoindentation can also be used on elastic or viscoelastic samples. The analysis of indentation data for elastic-plastic materials is routine, and is carried out using a method developed by Oliver and Pharr [1]. However, it has been found that this analysis method is unsuitable for viscoelastic or viscoelastic-plastic materials [2,3]. The Young’s modulus

* Corresponding author. Tel.: þ44 1223 762966; fax: þ44 1223 334567. E-mail address: [email protected] (J.H. Gwynne). 0142-9418/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2010.02.010

of a viscoelastic material is dependent on the strain rate, and as such, these materials have two limiting values of the modulus at short (E0) and long (EN) times. Although a detailed analysis method developed by Oyen [4] allows the calculation of both modulus values, a simple analysis method has been used in this work (described in Section 2.5.1), which has been found to give a good estimate of EN. 1.2. Sample preparation: mounting, grinding and polishing Nanoindentation is very sensitive to surface roughness since it can affect the depth of penetration of the indenter tip into the sample and, consequently, the calculated value of the contact area [5]. Any indentations carried out on, for example, scratches can give unreliable results and it is, therefore, common practice to polish samples prior to testing, although (as discussed below) this can be problematic in samples with varying moduli. The simplest method of sample preparation involves using a series of increasingly fine grades of abrasive paper (most commonly silicon carbide paper) in the same way as

J.H. Gwynne et al. / Polymer Testing 29 (2010) 494–502

for metallographic sample preparation. All mechanical grinding will result in some degree of damage to the surface of the sample, but each successive polishing stage should remove the damage introduced in the previous step, and the depth of the surface damage decreases as the abrasive paper becomes finer [6]. It is often assumed that the polishing procedure affects the surface of the specimen to a depth of about the same as the nominal grit size [5]. Samples are often mounted prior to grinding and polishing for a number of reasons, for example to make the samples easier to handle, or to prevent damage from occurring to the edge of the sample. However, care needs to be taken when mounting samples to ensure that the mounting material and the sample abrade at similar rates [7]. If the mounting material abrades more easily, the sample becomes higher than the surrounding material (known as positive relief) and the edges may be damaged. Conversely, if the mounting material abrades less easily, the sample surface becomes lower than the surrounding material (negative relief) and subsequent polishing becomes less effective. A similar effect can be seen in samples containing regions with different hardnesses and moduli (such as composite materials): the harder phase stands proud of the remaining surface, and the interface between the different regions may become rounded or damaged. A number of other defects and problems can arise during grinding and polishing of polymers, including melting of the sample surface, or grains of abrasive becoming imbedded in the surface, but these can usually be avoided by careful selection of grinding and polishing conditions [8]. Damage such as cracking can also be introduced at the earlier stage of specimen cutting, but this can be limited by carrying out the initial rough cutting at a distance from the region of interest and subsequently cutting more carefully. Variables influencing cutting quality when using a saw include the blade type and speed, the sample feed speed and the application of lubricant: one study has shown that for cutting unreinforced nylon better results are achieved using low blade and feed speeds [9]. It should be noted that another method commonly used to prepare thin flat slices of material is microtomy, which involves using steel or glass knives to cut specimens, typically to between about 1 and 40 mm thick. Ultramicrotomy involves using glass or diamond knives to produce even thinner slices (approximately 30–100 nm thick) [8]. However, these methods were unsuitable for the samples studied during this work, since the required nanoindentation depths were up to about 20 mm, which is a significant fraction of even the thickest achievable slice, and results would, therefore, be influenced by whatever substrate the samples were placed on. 1.3. Intervertebral discs prostheses and the CAdisc-L The degeneration of lumbar intervertebral discs is a major cause of lower back pain [10]. Spinal fusion is traditionally used to alleviate this pain, but this has limitations since it not only results in restricted motion and reduced spinal flexibility, but can also lead to abnormal stresses on adjacent discs, which may accelerate their degeneration. There have been many attempts to produce

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artificial intervertebral discs during the last fifty years, but very few of these have reached the stage of in vivo tests, and fewer still have been used in patients [11]. Most of the clinically available lumbar disc prostheses restore intervertebral height and maintain the flexibility of the spine, but do not preserve the compliance of a natural disc. They use hard, non-shock absorbing components which can transfer stresses to adjacent spinal levels in a similar way to fusion. A device that aims to overcome this problem is the CAdisc-L, designed by Ranier Technology Ltd., which is manufactured from viscoelastic polycarbonate urethanes using a novel injection moulding procedure. Polyurethanes are a family of polymers with a wide range of properties and applications, which are synthesised by the reaction between an isocyanate, a polyol and often a chain extender [12,13]. They have been used in a wide variety of biomedical applications, including: cardiac valves, wound dressing products, catheters, breast implants and components in replacement joints [14]. Polyurethanes typically undergo phase separation and often exist as a two-phase structure consisting of crystalline or amorphous hard segments within a matrix of soft segment material. The properties of the polyurethane are heavily dependent on the hard segment to soft segment ratio. The CAdisc-L is designed to mimic the structure of a natural disc and thereby allow the same degree of motion and axial compliance. It contains a lower modulus nucleus surrounded by a higher modulus annulus, separated by a graduated modulus region. This graduated region means that there is a smooth interface between the annulus and nucleus, which is likely to be beneficial to the lifetime and performance of the device, since a sharp interface between two different materials can be a potential long-term fatigue failure site due to the mismatch in mechanical properties. Schematic diagrams showing horizontal and vertical crosssections through the CAdisc-L are shown in Fig. 1. 1.4. Aims The objective of this work was to develop a nanoindentation method for the study of polymeric samples containing a graduated modulus region (in particular prototype CAdisc-L samples), and to establish a simple procedure for the preparation of samples. 2. Materials and methods 2.1. Materials The polyurethanes making up the annulus and nucleus materials are manufactured from the following chemical components: Annulus Nucleus End-plates

Graduated region

Fig. 1. Vertical (left) and horizontal (right) cross-sections through the CAdisc-L (width of prototype samples ¼ 3 cm).

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Methylene-bis-(4-cyclohexylisocyanate), or HMDI Polycarbonate diol Glycerol, which is trifunctional and acts as a crosslinking agent These are present in different relative proportions, which give the two materials different mechanical properties. The annulus material also contains a small quantity of butane diol (which acts as a chain extender). The proportion of glycerol and, therefore, the degree of crosslinking is higher in the annulus material than in the nucleus material. The polyurethanes are produced using a prepolymer method, in which each polyurethane is produced from two prepolymers, which are mixed just before injection into the disc mould. The pure annulus material is injected into the mould first, followed by the material making up the graduated region and, finally, the pure nucleus material. This is carried out in a continuous moulding process, and little curing takes place until after moulding is finished. The graduated region is manufactured using a series of moulding increments, the proportion of annulus material decreasing and the proportion of nucleus material increasing between successive increments. After injection of the polymers into the moulds, they are placed in a pressure pot (pressurised to 0.4 MPa, to prevent the formation of bubbles during curing) and put into an oven at 80 C overnight to complete the curing process. 2.2. Samples 1. Pure annulus (PUA) and pure nucleus (PUN) calibration samples, manufactured as 5 mm thick sheets. 2. Prototype CAdisc-L samples, with graduated regions ranging between 0 and 50% of the total disc volume. 3. An ‘‘insert moulded’’ sample: in this sample, the injection-moulded nucleus was allowed to cure fully before subsequent moulding of the surrounding annulus material in order to achieve as sharp an interface between these two regions as possible.

2.3. Mounting The resin used to mount the calibration and disc samples was ‘‘Epofix’’, manufactured by Struers, which is an epoxy resin formed by mixing a liquid resin material (containing bisphenol-A-epichlorhydrin) and a hardener (containing triethylenetetramine). Epofix cures at room temperature in 8–12 h. Sections (approximately 1.5 cm in width and length) were cut from the annulus and nucleus calibration samples using a scalpel. Disc samples were cut into quarters, as indicated in Fig. 2. Plastic moulds, consisting of a flat base and a cylindrical body (approximately 3 cm in diameter), were prepared by greasing their inner surfaces. The sample sections were placed flat onto the base of individual moulds (the cut lateral surface of the discs facing downwards) and Epofix mounting resin was prepared. This was poured into the moulds until they were almost filled (approximately 2.5 cm

Fig. 2. Disc sectioning.

in depth) in order to make resin pucks deep enough to be held in place in the nanoindenter sample holder. The temperature was monitored during curing: it was found that it did not exceed 27 C, which should have no effect on the polyurethanes. Once the resin had cured, the pucks were removed from the moulds and cleaned using detergent and ethanol to remove the grease from the surface. 2.4. Polishing The mounted samples were polished using a Struers Abramin automatic polishing machine consisting of a rotating polishing wheel and a smaller rotating sample holder, the centres of which are offset from each other. The sample holder can hold up to six samples: the resin pucks were inserted into holes, and screws were tightened to hold them in place. Whilst loading the samples, the holder was positioned on a stand that allowed the samples to protrude a consistent few millimetres from the under-side, ensuring the sample holder was balanced and that all the samples were evenly polished. A polishing speed of 150 revolutions per minute with a downwards force of 50 N was used and a continuous jet of cold water was applied as a lubricant. 2.4.1. Variation of measured modulus with surface roughness Before studying any disc samples, an experiment was carried out in order to provide an insight into the dependence of the measured Young’s modulus of the polyurethanes on the particle size of the abrasive paper used for polishing. Five mounted sections (approximately 1.5 cm square) of the annulus and nucleus calibration samples were polished to different degrees of smoothness using increasingly fine grades of silicon carbide paper ranging from P600 to P4000 (the ‘‘P’’ referring to the classification system used by the Federation of European Producers of Abrasives). The samples were polished in two batches, using a polishing regime designed to produce one annulus and one nucleus sample polished to each of five different surface finishes, whilst keeping the sample holder balanced during polishing. First, three PUA and three PUN samples were loaded into the holder as shown schematically in the left-hand image of Fig. 3, in which PUA samples have been labelled ‘‘A’’ and PUN

A1

A4

N3

A2

N2

A3 N1

A5

N5 N4

Fig. 3. First (left) and second (right) loading of PUA and PUN calibration samples into the automatic polishing machine.


2.5. Nanoindentation

Table 1 Polishing of 1st set of calibration samples. Sandpaper Designation

Polishing Time/min

P600 P800 P1200

3.0 3.5 4.0

Removal of A1 and N1 Removal of A2 and N2

samples have been labelled ‘‘N’’. All six samples were polished using P600 paper for 3 min. At the end of this time, samples A1 and N1 were removed from the sample holder and the remaining four samples were polished using P800 paper for 3.5 min. Samples A2 and N2 were then removed from the sample holder and the remaining two samples were polished using P1200 paper for 4 min. This is summarised in Table 1. The samples were loaded in this way such that pairs of samples directly opposite each other would be removed at the same time, in order to keep the sample holder balanced during the subsequent polishing. The remaining four samples (two PUA and two PUN) were loaded into the sample holder as indicated in the right-hand image of Fig. 3. All four samples were polished using P600 paper for 3 min, P800 paper for 3.5 min, P1200 paper for 4 min and P2500 paper for 4.5 min. Samples A4 and N4 were then removed from the sample holder and the remaining two samples were polished using P4000 paper for 5 min. This is summarised in Table 2. 2.4.2. Disc samples: polishing method 1 The disc samples were loaded into the sample holder such that the flat edge of the disc faced inwards towards the centre of the holder. This ensured that all discs were polished in the same direction and that the polishing direction was perpendicular to the lateral direction of interest, to try and minimise any polishing damage to the interfacial region between the annulus and nucleus regions. The samples were polished with papers from P600 to P4000 using the times shown in Table 2 (but without removing any samples between polishing steps). 2.4.3. Disc samples: polishing method 2 As will be seen in Section 3.2, the first polishing method resulted in generally smooth shiny surfaces, but a significant degree of polishing damage occurred at the interfacial region. In order to overcome this problem, the samples were first roughened using P600 sandpaper for 3 min to remove the damage caused by the initial polishing. They were then re-polished using the same regime as before, but the step using P4000 paper was omitted.

Nanoindentation tests were carried out using an MTS nanoindenter XP with a 500 mm radius spherical sapphire tip. Spherical tips are particularly effective for studying soft materials, and the use of a tip with a large radius meant that the sample surfaces did not need to be as highly polished as those required when smaller tips are used. The test method employed involved loading at a constant rate until a maximum load of 10 mN was reached and included a hold period of 10 s at this maximum load. Although the radius of the nanoindenter tip was 500 mm, the contact radius was calculated to be approximately 130 mm. This is slightly greater than the distance between indents (as described below), but indentation tests using a spherical tip on a viscoelastic material are non-destructive. This was confirmed by performing successive indents at the same location on some of the calibration samples: in all cases, the load-displacement curves lay directly on top of one another, indicating that choosing a distance between indents such that they overlapped would not affect the reliability of the results. 2.5.1. Data analysis methods The equation relating the load (P) and displacement (h) during the spherical indentation of an elastic medium is [15]:

h

3=2

1 n2 3 ¼ pffiffiffi P E 4 R

Polishing Time/min

P600 P800 P1200 P2500 P4000

3.0 3.5 4.0 4.5 5.0

(1)

where R is the radius of the indenter tip, E is the elastic modulus of the material and n is its Poisson’s ratio. A perfectly incompressible material has a Poisson’s ratio of exactly 0.5. Most materials have a Poisson’s ratio between 0 and 0.5 but it is found that rubbers have a value approaching 0.5. For the analysis carried out during this work, it has been assumed that the Poisson’s ratio of the polyurethanes is equal to 0.5. Schematic load-displacement curves for PUA and PUN are shown in Fig. 4. A simple estimate of the long-time Young’s modulus of the polyurethanes (which agrees well with the values calculated using the more detailed viscoelastic analysis developed by Oyen [4]) was obtained using

Table 2 Polishing of 2nd set of calibration samples. Sandpaper Designation

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Removal of A4 and N4 Fig. 4. Load-displacement curves for PUA and PUN.

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the point on the load-displacement curve at the end of the hold period, before the load was removed. The values of load (P) and displacement (h) at this point were substituted into equation (1), along with the values of the tip radius and Poisson’s ratio. 2.5.2. Calibration samples Three batches of nine indents in 3 3 arrays were carried out at random locations on the surfaces. A distance of 100 mm between indents in both the x- and the ydirections was used. 2.5.3. CAdisc-L linescans: first method The first linescan method used involved carrying out a series of 50–60 indents spaced 100 mm apart in a straight line from the pure annulus region, across the graduated region and into the pure nucleus region. This was performed laterally across the disc section, through the point at which the edge of the nucleus region extended furthest into the annulus, and was repeated twice, 100 mm to either side of the first linescan. This is illustrated schematically in Fig. 5, although it should be noted that the position and size of the indents are not shown to scale. This method produced three indents at the same distance from the edge of the disc and an average of the modulus values at these three points was calculated. 2.5.4. CAdisc-L linescans: second method As a result of a number problems associated with the first method (which will become evident in Section 3.4), it was necessary to refine the method used for carrying out linescans across the disc samples. Whereas the initial method involved performing three sets of 50–60 indents across the disc samples, the revised method instead involved carrying out 50–60 sets of three indents. A new surface find was executed for each batch of three indents, the tests within each batch being the same distance from the edge of the disc and spaced 100 mm apart. The sets of three were spaced 100 mm apart across the lateral direction of the disc and, therefore, this method resulted in indentation tests being performed at the same coordinates as the first method.

3. Results 3.1. Variation of measured modulus with surface roughness SEM images of the polished surfaces are shown in Fig. 6, and images of the as-cut unpolished surfaces have also been included for comparison. A marked difference is noticeable between the images, the sample surface becoming progressively smoother with finer grades of paper, as expected. The variation of the measured value of the Young’s Modulus after polishing to different surface finishes is shown in the top image of Fig. 7, and the variation in modulus with the average paper particle size (obtained from literature values [7,16]) is shown in the bottom image. 3.2. Polishing method 1 Although the calibration samples showed uniformly smooth surfaces after polishing using this method, the disc samples had smooth surfaces in the annulus and nucleus regions but exhibited a significant amount of polishing damage around the interface between the two, some of which was clearly visible to the naked eye. It was for this reason that the revised polishing method was developed. SEM images of the polishing damage in 20% and 30% graduated discs (in which the percentages refer to the percentage of the total disc volume that is incorporated into the graduated region) from a variety of locations around the interface and at various magnifications are shown in Fig. 8. 3.3. Polishing method 2 The samples polished using the second method were no longer visibly shiny, but there was now no noticeable polishing damage around the interface, as can be seen in the SEM images in Fig. 9. These show the same discs as Fig. 8, and in both cases, the interface between the annulus and nucleus regions passes roughly horizontally through the centre of the image. All the discs described in the following sections were polished using this method.

2.6. Scanning electron microscopy (SEM)

3.4. CAdisc-L linescans: first method

For all SEM work, samples were sputter coated with gold (using a current of 20 mA for 2 min) and examined using a JEOL 820 SEM.

The disadvantage of setting up the run of nanoindentation tests using the first method was that the surface find was carried out at the beginning of the batch of 50–60 indents and the software assumed that this value of the surface z-coordinate applied for all subsequent tests within the batch. Therefore, if the sample was held at a slight angle within the nanoindenter sample holder, if the surface height varied at all within the distance across which the linescan was carried out, or if the sample slipped even slightly within the sample holder during the series of tests, the surface find was no longer valid. An example of an unsuccessful linescan is shown in Fig. 10, in which the modulus values (relative to the value for pure PUA polished using P2500 paper) are plotted against the distance from the edge of the disc. This linescan is for a 0% graduated disc (in which the nucleus material

Fig. 5. Schematic diagram showing indent positions.


Fig. 6. Sample surfaces polished to different roughnesses.

499

500


was injected straight after the annulus material, meaning that the disc did not contain a graduated modulus region). The data obtained closer to the sample’s edge (corresponding to the annulus region) are as expected, with modulus values consistent with the modulus of the PUA calibration sample. However, where a fairly sharp decrease in modulus across the interface followed by a region of constant lower modulus would be expected, the data further into the linescan become meaningless, which is likely to be due to one of the reasons described above. 3.5. CAdisc-L linescans: second method

Fig. 7. Variation of measured modulus (relative to value for PUA polished using P2500 sandpaper) after polishing with different sandpapers (top) and dependence of measured modulus on sandpaper particle size (bottom). The actual values are of the order of a few MPa.

Although setting up linescans in this way proved to be much more time-consuming than using the initial method, the fact that new surface finds were carried out at each different distance from the edge of the disc meant that the problems associated with a variation in sample surface height were no longer an issue. Fig. 11 shows linescans for an insert moulded sample (top) and the same 0% graduated sample as shown in Fig. 10 (bottom). It can be seen that these exhibit the expected behaviour: a higher modulus for the annulus material, a decrease in modulus across the interface and a lower modulus for the nucleus region. It should be noted that the distances from the edges of the discs cannot be directly compared, because the insert moulded sample is a different size to the prototype CAdisc-L samples, since it was manufactured using a slightly different method. The vertical error bars (although so small that they are not easily seen on these graphs) represent the standard deviation of the

Fig. 8. Polishing damage on 20% graduated (a&b) and 30% graduated (c&d) discs.


501

Fig. 9. 20% (left) and 30% (right) graduated disc samples polished using the second polishing regime.

modulus values of the three indents within each batch, and the horizontal error bars represent the approximate contact radius of the nanoindenter tip. 4. Discussion 4.1. Variation of measured modulus with surface roughness It can be seen that the measured value of the Young’s modulus decreases and that the error in the measurement increases as the roughness of the surface finish increases. This can be explained by considering what happens when the indenter tip comes into contact with the sample surface, and is illustrated in Fig. 12. When the sample surface is very smooth (left-hand image), the spherical tip makes good contact with the surface. However, when the sample surface is very rough (right-hand image), the tip initially only makes contact with the tops of the asperities and the first part of the indent requires less force for a given displacement than when good contact is made. Therefore, for a given total applied force, a greater displacement will be achieved for a rough surface than a smooth surface, giving a lower calculated value of the Young’s modulus. The greater the surface roughness, the greater this effect will be and, hence, the lower the measured modulus.

polishing damage was observed at the interface between the annulus and nucleus materials, which would have had a significant effect on the success and reliability of nanoindentation results. The second polishing method overcame this problem and, although the samples were not as smooth, the surface roughness experiment showed that the surface finish was still suitable for nanoindentation: the measured modulus values of calibration samples polished using P2500 paper were not significantly different to those obtained for samples polished using P4000 paper, and the error in the modulus measurement was still acceptably small. 4.3. CAdisc-L linescans Although being more time-consuming to set up, linescans carried out using the second method proved to be

4.2. Polishing of discs Whilst polishing using the first method generally resulted in the smoothest surface finish, a substantial degree of

Fig. 10. Unsuccessful linescan.

Fig. 11. Linescans for insert moulded (top) and 0% graduated (bottom) samples.

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Acknowledgements

Fig. 12. Effect of surface roughness on an indentation test.

much more successful than those carried out using the first method. Regions of constant modulus were observed in the annulus and nucleus, as expected, with a change in modulus across the interface. The change was not quite as sharp in the 0% graduated sample as in the insert moulded sample, due to the difference in manufacturing methods: in the 0% graduated sample, some interdiffusion of the molecules can occur across the interface, since polymerisation only begins after the prepolymers are mixed just before injection into the mould. In contrast, the nucleus of the insert moulded sample is manufactured first and allowed to cure, before subsequent injection moulding of the annulus around it, meaning that there is no possibility for interdiffusion to occur. 5. Conclusions and summary During this work, it has been shown that polymeric samples containing a graduated modulus region can be prepared for nanoindentation using a simple polishing method, involving grinding using successively finer grades of silicon carbide paper. It was found that the smoothest surfaces actually suffered from a significant amount of polishing damage at the interface, and that samples polished to a slightly rougher finish were much more uniform and better suited to nanoindentation. A nanoindentation linescan method has also been developed, that allows the study of the variation in modulus across a graduated region.

The authors would like to acknowledge Dr Scott Johnson and Steven Scott at Ranier for guidance and help with sample manufacture respectively. Funding for this research was gratefully received from the EPSRC and Ranier Technology Ltd.

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