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Accelerated testing of creep in polymeric materials using nanoindentation
Polymer Testing 30 (2011) 366–371
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test Method
Accelerated testing of creep in polymeric materials using nanoindentation A.S. Maxwell*, M.A. Monclus, N.M. Jennett, G. Dean National Physical Laboratory, Materials Division, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 December 2010 Accepted 4 February 2011
Creep properties of polymers are conventionally obtained from tensile creep tests but, due to the different processing conditions used in their manufacture, the microstructure and properties of the specimens used in this type of test are often different to those found in actual components. This is particularly likely for micromouldings in which extreme processing conditions are experienced in their manufacture. Nanoindentation test procedures have, therefore, been developed to obtain creep properties directly from injection moulded components. This paper shows how creep data can be obtained from indentation experiments and how these tests can be accelerated by performing short-term indentation tests at elevated temperatures to predict long-term creep at ambient temperature. This technique can significantly reduce the length of time required to conduct indentation creep tests, allowing the creep properties of a polymer moulding to be mapped in less than a fifth of the time. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.
Keywords: Accelerated testing Nanoindentation Creep Elastic modulus Crystallinity
1. Introduction With ever expanding developments in miniaturised devices using polymeric micromouldings there is an everincreasing demand for new tools to characterise the mechanical properties of such products. Creep is one of the most important of these properties, because the timedependent deformation of a material needs to be included in modelling if accurate predictions are to be made of product performance and, thus, reliable product design. Conventional creep test methods involve subjecting a bulk test specimen to a constant tensile load and measuring the deformation of the specimen as a function of time. The problem with this method is that the processing conditions used to manufacture the specimen can be
* Corresponding author. Tel.: þ44 (0) 20 8943 6454. E-mail addresses: [email protected] (A.S. Maxwell), miguel. [email protected] (M.A. Monclus), [email protected] (N.M. Jennett), [email protected] (G. Dean).
significantly different to those used to produce actual products; the levels of residual stress and crystallinity present in a specimen can be considerably different to those found in actual products, leading to significantly different creep properties. Nanoindentation is one of the most promising techniques for measuring the mechanical properties of products [1], as the tests are conducted on actual components with little or no need for specimen preparation. With nanoindentation of plastics, mechanical properties are determined by measuring the displacement that occurs when small loads (mN) are applied to the surface of the specimen using a diamond-tipped indenter. The region of the specimen covered by the indenter tip during a test is small, typically 1 mm–10 mm in diameter, allowing mechanical properties to be measured precisely in an extremely small region of the specimen. This technique also allows the mechanical properties to be mapped, for example across cross-sections of specimens, enabling local variation in the mechanical properties to be revealed with high spatial resolution. This is particularly important when examining
0142-9418/$ – see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2011.02.002
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371
polymeric mouldings, whose mechanical properties can vary significantly across the moulding due to processing. The measurement of creep properties using nanoindentation is not, however, a simple task and a consensus on the most suitable method of measuring creep in viscoelastic materials has not yet been established [2–10]. The most commonly used technique for calculating the creep compliance J(t) is to measure the depth (h) the indenter penetrates the surface of the material when a constant load (P) is applied. This technique gives good results provided that the deformation remains linear viscoelastic [6]. Techniques have been proposed to extract creep data from non-linear viscoelastic indents using multi-parameter models to fit the experimental force-displacement curves either iteratively [11] or by inverse modelling [6]. Although it has been suggested that using low forces can result in larger uncertainties in the creep compliance [6], the simplest approach is to avoid non-linear viscoelastic behaviour by performing shallow indents to limit the maximum strain level imposed on the polymer [7]. In this paper we demonstrate that accurate creep data can be obtained from shallow indent experiments and examine methods by which the acquisition of creep data can be accelerated. The effect that the geometry of the indenter tip has on the results is considered by comparing the results obtained from nanoindentation with conventional tensile creep data. This offers the possibility of obtaining improved accuracy for the creep data. Methods for accelerating the acquisition of creep data by testing at elevated temperatures to predict longterm creep properties have been examined. The accuracy of this technique has been validated by mapping the creep properties of a commercially produced polymeric moulding using an accelerated method and comparing the results with those obtained during long-term tests at ambient temperature. 2. Materials 2.1. Tensile test specimens The polyoxymethylene material (POM) studied here was supplied by Du Pont (under the trade name Delrin 1260 NC010) in the form of compression moulded plates 160 mm square and 3 mm thick. The processing conditions used were selected to ensure that isotropic, homogenous material was obtained. All tensile creep tests were carried out on specimens of essentially the same age (in excess of 2 years old) so that changes in the relaxation behaviour caused by physical ageing were considered to be negligible.
2.2. Injection moulded specimens In the second part of the study actual components were used; these were cable ties consisting of a single-gated injection moulding of Delrin (Fig. 1). The region of the moulding examined was 10 mm from the gate in a section of the moulding 5 mm wide by 3 mm thick.
367
Fig. 1. Cable ties examined using depth-sensing indentation.
3. Experimental 3.1. Elevated temperature nanoindentation testing Creep compliance and modulus values were determined using a NanoTest instrumented indentation platform (Micro Materials Ltd.), details of which are reported in previous papers [7,12]. For high temperature testing, the nanoindenter was fitted with a hot-stage, shown schematically in Fig. 2a. This consisted of thermally controlled wire-wound heaters that were fitted to both the Berkovich diamond indenter and to the specimen holder. This enabled the instrument to be operated at temperatures up to 500 C (Fig. 2b). Separate heating and active temperature control of both the indenter and specimen ensured that minimum heat flow occurred during the indentation process. A thermal shield placed between the pendulum and the stage protected the capacitance displacement transducers from convection currents or other thermal instabilities. Once thermal equilibrium was achieved, the active temperature controller maintained stability with a small power input, which limited thermal drift. This enabled long-duration tests, such as indentation creep tests, to be performed at elevated temperatures. Indentation creep tests were conducted on the bulk POM specimens; a 30 mN force was applied at a constant loading rate over 1 s, the maximum force P0 was then held for 500 s before unloading at 6 mN/s. Three indentation runs were performed over a range of four temperatures; room temperature (23 C), 40 C, 50 C and 60 C. The automated surface-mapping feature of the NanoTest system was used to produce 16 16 indentation maps (Fig. 3) at temperatures of 23 C and 50 C on the injection moulded POM specimens, with a 110 mm separation between indents. These indentation maps were performed on the same cross-section of POM moulding (5 mm wide and 3 mm thick), extending from the core to the surface of the moulding. Values of indentation modulus, Er, were calculated from the unloading slope dP/dh evaluated at maximum force (P0) and the indenter area function Ac(hc), obtained by indentation into a certified reference fused silica specimen (NPL Datasure) according to standard procedures in ISO14577 2002 [13]. The creep compliance J (t) was calculated from the depth indentation data (h(t)) using the following expression:
JðtÞ ¼
4h2 ðtÞ pð1 nÞP0 tana
(1)
where a is the angle between the indenter and the specimen surface (for a Berkovich equivalent cone indenter
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A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371
Fig. 2. (a) Nanoindentation apparatus with hot-stage and temperature control used for creep compliance experiments. (b) Schematic of NanoTest hot stage showing separate tip and sample heaters.
a ¼ 19.7 ) and n is Poisson’s ratio. It is, however, well known that no indenter is perfectly sharp or even of a perfect angle at the very tip. Normalisation was, therefore, used to eliminate the effects of variation in the geometry of the indenter from the results. Normalisation was achieved by dividing the creep compliance at time t by the initial compliance immediately after the constant load was applied (t0), using the following expression:
JðtÞ ¼ Jðt0 Þ
2 hðtÞ hðt0 Þ
(2)
clamped in a fixed position and the other attached to a dead weight loading system. Creep displacement was measured using a pair of extensometers attached to opposite faces of the specimen; the gauge length of each extensometer was 25 mm. Averaging the extensometer readings eliminated the influence of any specimen bending on the strain measurement. Normalised creep compliance was calculated in the same way as in the indentation experiments by dividing the creep compliance at time t by the initial compliance immediately after the full force had been applied. 3.3. Crystallinity measurements
3.2. Uniaxial tensile creep tests Uniaxial tensile creep tests were performed on rectangular specimens of the bulk POM (10 mm 3 mm 160 mm). Each sample was clamped into a creep machine with one end
The crystallinity of the injection moulded specimens was measured using differential scanning calorimetry, DSC, (TA Instruments) at two positions; one at the centre of each moulding, and the other close to the surface. DSC specimens weighing between 5 mg and 10 mg were sealed into aluminium pans and heated at a rate of 10 C min1 over the temperature range between 20 C and 150 C. Data were analysed using the TA software and the system calibrated using an indium standard. The enthalpy of fusion DHmelt in J/g was used to calculate the crystallinity of the specimens according to equation (3) and assuming that the enthalpy of fusion of a 100% crystalline sample of POM to be 390 Jg1 [14].
cystallinity ð%Þ ¼
DHmelt
390
100
(3)
4. Results and discussion 4.1. Analysis of indentation creep data
Fig. 3. Microscope image of 16 16 indentation maps taken at room temperature (———) and 50 C (d).
Normalised creep compliances for the compression moulded POM specimens (Fig. 4) were determined from the indentation data using equation (2). Normalising the
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371
369
1.40
Normalised compliance
1.35 1.30 1.25 o
Tensile 23 C
1.20
o
Indentation 23 C
1.15
Tensile 40 C
1.10
Indentation 40 C
o
o
o
Tensile 50 C
1.05
o
Indentation 50 C o
Tensile 60 C
1.00
o
Indentation 60 C
0.95 0
100
200
300
400
500
Time (seconds) Fig. 4. Comparison of normalised creep compliances from depth-sensing indentation and tensile creep experiments.
compliance data eliminated most of the uncertainties associated with the geometry [15] of the indenter, reducing the uncertainties by approximately a half. In comparing these results with those obtained using conventional tensile creep tests, it can be seen that there is good agreement across a wide range of different temperatures and times. 4.2. Accelerating creep tests One of the main problems with measuring creep using indentation is the length of time required to conduct the tests, which is a particular problem when a multiple array of different indentations are required to map the creep properties across a surface. A commonly used method to accelerate conventional tensile creep tests is to conduct the tests for shorter periods of time at elevated temperatures and to extrapolate the results back to normal service conditions. One method of achieving this is to use an Arrhenius relationship [16]; this gives a relationship between the activation energy f, absolute temperature T and the relaxation time s:
s ¼ Aef=RT
4.3. Mapping creep in mouldings The accelerated test procedure was validated by mapping the creep properties through a cross-section of an actual injection moulded product using accelerated testing at 50 C and comparing the results with those obtained at room temperature (23 C). Using the Arrhenius relationship, it was predicted that creep properties obtained after 40 s at 50 C should be equivalent to those obtained after
4.8
(4)
t JðtÞ ¼ JðiÞ þ JðcÞ 1 exp
s
(5)
where J(t) is the creep compliance at time t, J(i) is the instantaneous creep compliance, J(c) is the creep compliance coefficient and s is the relaxation time. Rearranging the Arrhenius equation, it can be seen that the relationship between lns and 1/T should be linear if the Arrhenius relationship holds:
(6)
4.7
Log relaxation time (seconds)
where A is a constant and R is the universal gas constant (8.314 J mol1). The time-dependent property used to examine the creep behaviour was the relaxation time, s, determined using the following spring and dashpot model [17]:
f 1 þ lnA lnðsÞ ¼ R T
Plotting lns against 1/T (Fig. 5), it can be seen that a good linear fit is obtained for both the indentation creep and the tensile creep data, indicating that the Arrhenius relationship can be used to describe accelerated indentation creep tests. An example of data shifted by the Arrhenius expression can be seen in Fig. 6, where creep data obtained at 50 C have been shifted to longer times corresponding to a temperature of 23 C, and are in good agreement with experimental data obtained at 23 C.
4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9
Indentation creep data Uniaxial tensile creep data
3.8 3.7 0.0027
0.0028
0.0029
0.0030
0.0031
0.0032
0.0033
0.0034
0.0035
-1
1/T Temperature (K ) Fig. 5. Arrhenius plot of lns versus 1/T for indentation and tensile creep data, where s is the relaxation time obtained from a spring and dashpot model. The linear relationship indicates that the indentation creep behaviour obeys the Arrhenius relationship.
370
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371 1.30
Surface of moulding 1500 1400 1300
1.28 1.26
1.22 1.20 1.18 1.16 1.14 1.12
o
Creep at 23 C
1.10
o
Creep at 50 C 1.08
1200 1100
Surface of moulding
Normalised compliance
1.24
1000 900 800 700 600 500
o
Creep at 50 C shifted using Arrhenius
1.06
Log time (seconds)
X-direction (µm)
Fig. 6. Log time shift of normalised creep compliance data obtained at 50 C to times that are equivalent to tests conducted at 23 C using Arrhenius relationship.
200 s at room temperature. The creep properties obtained under these two sets of conditions are shown in Figs. 7 and 8, respectively. The core of the moulding is in the bottom right hand corner of the diagram, with the mould surfaces on the top and the left hand side of the diagram. Similar trends were obtained from both the room temperature and the accelerated tests, with the normalised creep compliance in both tests varying from 1.15 to 1.25. In both cases the lowest normalised creep compliance was obtained in the region of the core of the moulding, with higher normalised compliances obtained towards the surfaces (Figs. 7 and 8). The reproducibility of the creep compliance values was determined by conducting ten repeat indentation tests in a region close to the centre of the moulding. This gave a value (0.03) for the standard deviation of the normalised creep compliance. This demonstrates that this measurement method is highly reproducible and also that the observed variation in the
100
300
500
700
8
900
6
1100
4
1300
2
1500
1.04 0
Y-direction (µm)
400
1.225-1.25
300 200
1.2-1.225
100
1.15-1.175
1.175-1.2
Core of moulding
Fig. 8. Normalised creep compliance from a cross-section of injection moulded POM, measured using a constant load of 30 mN for 40 s at 50 C.
normalised creep compliance across the moulding is significant. The accuracy of modulus values determined by the standard quasi-static analysis of the unloading curves is well-known to be questionable for viscoelastic materials. However, the use of a long hold at maximum force and rapid unloading can give a reasonable semi-quantitative estimate for the spatial variation of elastic modulus [5]. Modulus values obtained using the same indentation data revealed that the modulus of the polymer was also higher towards the centre of the moulding and lower at the surface (Fig. 9). Such variations in the creep compliance and modulus of the moulding can be the result of variations in the crystallinity of the polymer; it is well known [18] that the crystallinity of injection moulded polymers can be significantly higher at the centre of a moulding than close to the walls. This is due to the polymer cooling more slowly at the centre of the moulding than at the walls, leading to increased crystallinity at the centre. The consequence of this increase in crystallinity is that the modulus increases
Surface of moulding
Surface of moulding
1500 1400 1300 1200 1100 1000 900 800 Y direction (µm) 700 600
100
300
500
700
900
1100
1300
1500
500 400 300 200 100
1.225-1.25 1.2-1.225 1.175-1.2 1.15-1.175
Core of moulding
X direction (µm) Fig. 7. Normalised creep compliance from a cross-section of injection moulded POM, measured using a constant load of 30 mN for 200 s at 23 C.
Fig. 9. Young’s modulus of injection-moulded POM clip obtained from nanoindentation unloading curves at 23 C.
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371 Table 1 Percentage crystallinity obtained by DSC at different positions within an injection-moulded POM clip. Position of specimen in moulding
Crystallinity (%)
Core Skin
41 28
and, due to the crystallinity reducing the mobility of the polymer chains, the creep compliance decreases towards the centre of the moulding [19]. To verify the prediction that the degree of crystallinity varies across the moulding, DSC has been used to determine the crystallinity of the polymer (Table 1). The results confirm that the crystallinity of the polymer at the core of the moulding was significantly greater than that at the surface. These variations in the microstructure and properties within commercially produced injection mouldings are not unexpected. However, it is only with techniques such as nanoindentation that these variations can be detected with micron-scale resolution. 5. Conclusions Test procedures have been developed using nanoindentation to obtain creep properties from actual injection moulded components. This was achieved by applying a constant load to the intender tip on the surface of the moulding and measuring its displacement over time. By normalising the data to reduce uncertainties resulting from the geometry of the indenter tip, an extremely good fit was obtained between creep data obtained using this technique and that obtained from conventional tensile creep tests. A procedure was then developed to accelerate the acquisition of creep data by conducting tests at elevated temperatures for shorter periods of time, using an Arrhenius equation to predict the long-term creep properties at room temperature. An extremely good fit of data to the Arrhenius expression was obtained for Delrin over a wide range of temperatures and times. The accelerated creep test was validated by measuring the creep properties over a cross-section of a commercially injection moulded specimen at temperatures of 23 C and 50 C, and comparing the creep results after shifting the 50 C results to an effective temperature of 23 C. The data obtained by indentation mapping the crosssection of the moulding revealed that the normalised creep compliance was higher at the edges of the specimen than it was at the centre. Likewise, indentation modulus values obtained from the same data revealed that the modulus was lower at the edges than in the centre of the specimen. The most likely explanation for this is that polymer at the edges of the specimen had less time to crystallise due to rapid cooling at the surface than it did at the centre of the
371
moulding, leading to lower crystallinity at the edges of the specimen [18]. This was confirmed using differential scanning calorimetry. Acknowledgements This work was carried out as part of the UK Government Department of Business Industry and Skills (DBIS), National Measurement System (NMS), Programme for Innovation Research and Development 2008–10. References [1] A. Flores, F. Ania, F.J. Balta-Calleja, From the glassy state to ordered polymer structures: a microhardness study, Polymer 50 (2009) 729–746. [2] H. Lu, B. Wang, J. Ma, G. Huang, H. Viswanathan, Measurement of creep compliance of solid polymers by nanoindentation, Mechanics of Time-dependent Materials 7 (2003) 189–207. [3] M.V.R. Kumar, R. Narasimhan, Analysis of spherical indentation of linear viscoelastic materials, Current Science 87 (2004) 1088–1095. [4] L. Cheng, X. Xia, L.E. Scriven, Spherical-tip indentation of viscoelastic material, Mechanics of Materials 37 (2005) 213–226. [5] M. Vandamme, F.J. Ulm, Viscoelastic solutions for conical indentation, International Journal of Solids and Structures 43 (2006) 3142–3165. [6] R. Seltzer, Y.-W. Mai, Depth sensing indentation of linear viscoelastic-plastic solids: a simple method to determine creep compliance, Engineer Fracture Mechanics 75 (2008) 4852–4862. [7] C.A. Tweedie, K.J. Van Vliet, Contact creep compliance of viscoelastic materials via nanoindentation, International Journal of Materials Research 21 (2006) 1576–1589. [8] M.L. Oyen, Analytical techniques for indentation of viscoelastic materials, Philosophical Magazine 86 (2006) 5625–5641. [9] M.L. Oyen, Relating viscoelastic nanoindentation creep and load relaxation experiments, International Journal of Materials Research 99 (2008) 823–828. [10] M.L. Oyen, A.J. Bushby, Viscoelastic effects in small-scale indentation of biological materials, International Journal of Surface Science and Engineering 1 (2007) 180–197. [11] T.C. Ovaert, B.R. Kim, J. Wang, Multiparameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modelling, Progress in Organic Coatings 47 (2003) 312–323. [12] B.D. Beake, J.F. Smith, High-temperature nanoindentation testing of fused silica and other materials, Philosophical Magazine A 82 (2002) 2179–2186. [13] ISO 14577, Metallic Materials - Instrumented Indentation Test for Hardness and Materials Parameters Part 1: Test Method (2002). [14] T. Jaruga, E. Bociaga, Crystallinity of parts from multicavity injection mould, Archives of Materials Science and Engineering 30 (2008) 53–56. [15] K. Herrmann, N.M. Jennett, W. Wegener, J. Meneve, K. Hasche, R. Seemann, Progress in determination of the area function of indenters used for nanoindentation, Thin Solid Films 377-378 (2000) 394–400. [16] I.M. Ward, J. Sweeney, An Introduction to the Mechanical Properties of Solid Polymers. John Wiley and Sons, 2004. [17] W.H. Li, S. Keesam, C.G. Lee, B.C. Wei, T.H. Zhang, Y.Z. He, The characterisation of creep and time-dependent properties of bulk metallic glasses using nanoindentation, Materials Science and Engineering, A 478 (2008) 371–375. [18] H.F. Giles, J.R. Wagner, E.M. Mount, Extrusion: The Definitive Processing Guide and Handbook Volume 1 pg 181. Plastic Design Library, 2005. [19] K. Banik, G. Mennig, Influence of injection molding process on the creep behaviour of semicrystalline PBT during aging below its glass transition temperature, Mechanics of Time-dependent Materials 9 (2006) 247–257.
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test Method
Accelerated testing of creep in polymeric materials using nanoindentation A.S. Maxwell*, M.A. Monclus, N.M. Jennett, G. Dean National Physical Laboratory, Materials Division, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 December 2010 Accepted 4 February 2011
Creep properties of polymers are conventionally obtained from tensile creep tests but, due to the different processing conditions used in their manufacture, the microstructure and properties of the specimens used in this type of test are often different to those found in actual components. This is particularly likely for micromouldings in which extreme processing conditions are experienced in their manufacture. Nanoindentation test procedures have, therefore, been developed to obtain creep properties directly from injection moulded components. This paper shows how creep data can be obtained from indentation experiments and how these tests can be accelerated by performing short-term indentation tests at elevated temperatures to predict long-term creep at ambient temperature. This technique can significantly reduce the length of time required to conduct indentation creep tests, allowing the creep properties of a polymer moulding to be mapped in less than a fifth of the time. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.
Keywords: Accelerated testing Nanoindentation Creep Elastic modulus Crystallinity
1. Introduction With ever expanding developments in miniaturised devices using polymeric micromouldings there is an everincreasing demand for new tools to characterise the mechanical properties of such products. Creep is one of the most important of these properties, because the timedependent deformation of a material needs to be included in modelling if accurate predictions are to be made of product performance and, thus, reliable product design. Conventional creep test methods involve subjecting a bulk test specimen to a constant tensile load and measuring the deformation of the specimen as a function of time. The problem with this method is that the processing conditions used to manufacture the specimen can be
* Corresponding author. Tel.: þ44 (0) 20 8943 6454. E-mail addresses: [email protected] (A.S. Maxwell), miguel. [email protected] (M.A. Monclus), [email protected] (N.M. Jennett), [email protected] (G. Dean).
significantly different to those used to produce actual products; the levels of residual stress and crystallinity present in a specimen can be considerably different to those found in actual products, leading to significantly different creep properties. Nanoindentation is one of the most promising techniques for measuring the mechanical properties of products [1], as the tests are conducted on actual components with little or no need for specimen preparation. With nanoindentation of plastics, mechanical properties are determined by measuring the displacement that occurs when small loads (mN) are applied to the surface of the specimen using a diamond-tipped indenter. The region of the specimen covered by the indenter tip during a test is small, typically 1 mm–10 mm in diameter, allowing mechanical properties to be measured precisely in an extremely small region of the specimen. This technique also allows the mechanical properties to be mapped, for example across cross-sections of specimens, enabling local variation in the mechanical properties to be revealed with high spatial resolution. This is particularly important when examining
0142-9418/$ – see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2011.02.002
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371
polymeric mouldings, whose mechanical properties can vary significantly across the moulding due to processing. The measurement of creep properties using nanoindentation is not, however, a simple task and a consensus on the most suitable method of measuring creep in viscoelastic materials has not yet been established [2–10]. The most commonly used technique for calculating the creep compliance J(t) is to measure the depth (h) the indenter penetrates the surface of the material when a constant load (P) is applied. This technique gives good results provided that the deformation remains linear viscoelastic [6]. Techniques have been proposed to extract creep data from non-linear viscoelastic indents using multi-parameter models to fit the experimental force-displacement curves either iteratively [11] or by inverse modelling [6]. Although it has been suggested that using low forces can result in larger uncertainties in the creep compliance [6], the simplest approach is to avoid non-linear viscoelastic behaviour by performing shallow indents to limit the maximum strain level imposed on the polymer [7]. In this paper we demonstrate that accurate creep data can be obtained from shallow indent experiments and examine methods by which the acquisition of creep data can be accelerated. The effect that the geometry of the indenter tip has on the results is considered by comparing the results obtained from nanoindentation with conventional tensile creep data. This offers the possibility of obtaining improved accuracy for the creep data. Methods for accelerating the acquisition of creep data by testing at elevated temperatures to predict longterm creep properties have been examined. The accuracy of this technique has been validated by mapping the creep properties of a commercially produced polymeric moulding using an accelerated method and comparing the results with those obtained during long-term tests at ambient temperature. 2. Materials 2.1. Tensile test specimens The polyoxymethylene material (POM) studied here was supplied by Du Pont (under the trade name Delrin 1260 NC010) in the form of compression moulded plates 160 mm square and 3 mm thick. The processing conditions used were selected to ensure that isotropic, homogenous material was obtained. All tensile creep tests were carried out on specimens of essentially the same age (in excess of 2 years old) so that changes in the relaxation behaviour caused by physical ageing were considered to be negligible.
2.2. Injection moulded specimens In the second part of the study actual components were used; these were cable ties consisting of a single-gated injection moulding of Delrin (Fig. 1). The region of the moulding examined was 10 mm from the gate in a section of the moulding 5 mm wide by 3 mm thick.
367
Fig. 1. Cable ties examined using depth-sensing indentation.
3. Experimental 3.1. Elevated temperature nanoindentation testing Creep compliance and modulus values were determined using a NanoTest instrumented indentation platform (Micro Materials Ltd.), details of which are reported in previous papers [7,12]. For high temperature testing, the nanoindenter was fitted with a hot-stage, shown schematically in Fig. 2a. This consisted of thermally controlled wire-wound heaters that were fitted to both the Berkovich diamond indenter and to the specimen holder. This enabled the instrument to be operated at temperatures up to 500 C (Fig. 2b). Separate heating and active temperature control of both the indenter and specimen ensured that minimum heat flow occurred during the indentation process. A thermal shield placed between the pendulum and the stage protected the capacitance displacement transducers from convection currents or other thermal instabilities. Once thermal equilibrium was achieved, the active temperature controller maintained stability with a small power input, which limited thermal drift. This enabled long-duration tests, such as indentation creep tests, to be performed at elevated temperatures. Indentation creep tests were conducted on the bulk POM specimens; a 30 mN force was applied at a constant loading rate over 1 s, the maximum force P0 was then held for 500 s before unloading at 6 mN/s. Three indentation runs were performed over a range of four temperatures; room temperature (23 C), 40 C, 50 C and 60 C. The automated surface-mapping feature of the NanoTest system was used to produce 16 16 indentation maps (Fig. 3) at temperatures of 23 C and 50 C on the injection moulded POM specimens, with a 110 mm separation between indents. These indentation maps were performed on the same cross-section of POM moulding (5 mm wide and 3 mm thick), extending from the core to the surface of the moulding. Values of indentation modulus, Er, were calculated from the unloading slope dP/dh evaluated at maximum force (P0) and the indenter area function Ac(hc), obtained by indentation into a certified reference fused silica specimen (NPL Datasure) according to standard procedures in ISO14577 2002 [13]. The creep compliance J (t) was calculated from the depth indentation data (h(t)) using the following expression:
JðtÞ ¼
4h2 ðtÞ pð1 nÞP0 tana
(1)
where a is the angle between the indenter and the specimen surface (for a Berkovich equivalent cone indenter
368
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371
Fig. 2. (a) Nanoindentation apparatus with hot-stage and temperature control used for creep compliance experiments. (b) Schematic of NanoTest hot stage showing separate tip and sample heaters.
a ¼ 19.7 ) and n is Poisson’s ratio. It is, however, well known that no indenter is perfectly sharp or even of a perfect angle at the very tip. Normalisation was, therefore, used to eliminate the effects of variation in the geometry of the indenter from the results. Normalisation was achieved by dividing the creep compliance at time t by the initial compliance immediately after the constant load was applied (t0), using the following expression:
JðtÞ ¼ Jðt0 Þ
2 hðtÞ hðt0 Þ
(2)
clamped in a fixed position and the other attached to a dead weight loading system. Creep displacement was measured using a pair of extensometers attached to opposite faces of the specimen; the gauge length of each extensometer was 25 mm. Averaging the extensometer readings eliminated the influence of any specimen bending on the strain measurement. Normalised creep compliance was calculated in the same way as in the indentation experiments by dividing the creep compliance at time t by the initial compliance immediately after the full force had been applied. 3.3. Crystallinity measurements
3.2. Uniaxial tensile creep tests Uniaxial tensile creep tests were performed on rectangular specimens of the bulk POM (10 mm 3 mm 160 mm). Each sample was clamped into a creep machine with one end
The crystallinity of the injection moulded specimens was measured using differential scanning calorimetry, DSC, (TA Instruments) at two positions; one at the centre of each moulding, and the other close to the surface. DSC specimens weighing between 5 mg and 10 mg were sealed into aluminium pans and heated at a rate of 10 C min1 over the temperature range between 20 C and 150 C. Data were analysed using the TA software and the system calibrated using an indium standard. The enthalpy of fusion DHmelt in J/g was used to calculate the crystallinity of the specimens according to equation (3) and assuming that the enthalpy of fusion of a 100% crystalline sample of POM to be 390 Jg1 [14].
cystallinity ð%Þ ¼
DHmelt
390
100
(3)
4. Results and discussion 4.1. Analysis of indentation creep data
Fig. 3. Microscope image of 16 16 indentation maps taken at room temperature (———) and 50 C (d).
Normalised creep compliances for the compression moulded POM specimens (Fig. 4) were determined from the indentation data using equation (2). Normalising the
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369
1.40
Normalised compliance
1.35 1.30 1.25 o
Tensile 23 C
1.20
o
Indentation 23 C
1.15
Tensile 40 C
1.10
Indentation 40 C
o
o
o
Tensile 50 C
1.05
o
Indentation 50 C o
Tensile 60 C
1.00
o
Indentation 60 C
0.95 0
100
200
300
400
500
Time (seconds) Fig. 4. Comparison of normalised creep compliances from depth-sensing indentation and tensile creep experiments.
compliance data eliminated most of the uncertainties associated with the geometry [15] of the indenter, reducing the uncertainties by approximately a half. In comparing these results with those obtained using conventional tensile creep tests, it can be seen that there is good agreement across a wide range of different temperatures and times. 4.2. Accelerating creep tests One of the main problems with measuring creep using indentation is the length of time required to conduct the tests, which is a particular problem when a multiple array of different indentations are required to map the creep properties across a surface. A commonly used method to accelerate conventional tensile creep tests is to conduct the tests for shorter periods of time at elevated temperatures and to extrapolate the results back to normal service conditions. One method of achieving this is to use an Arrhenius relationship [16]; this gives a relationship between the activation energy f, absolute temperature T and the relaxation time s:
s ¼ Aef=RT
4.3. Mapping creep in mouldings The accelerated test procedure was validated by mapping the creep properties through a cross-section of an actual injection moulded product using accelerated testing at 50 C and comparing the results with those obtained at room temperature (23 C). Using the Arrhenius relationship, it was predicted that creep properties obtained after 40 s at 50 C should be equivalent to those obtained after
4.8
(4)
t JðtÞ ¼ JðiÞ þ JðcÞ 1 exp
s
(5)
where J(t) is the creep compliance at time t, J(i) is the instantaneous creep compliance, J(c) is the creep compliance coefficient and s is the relaxation time. Rearranging the Arrhenius equation, it can be seen that the relationship between lns and 1/T should be linear if the Arrhenius relationship holds:
(6)
4.7
Log relaxation time (seconds)
where A is a constant and R is the universal gas constant (8.314 J mol1). The time-dependent property used to examine the creep behaviour was the relaxation time, s, determined using the following spring and dashpot model [17]:
f 1 þ lnA lnðsÞ ¼ R T
Plotting lns against 1/T (Fig. 5), it can be seen that a good linear fit is obtained for both the indentation creep and the tensile creep data, indicating that the Arrhenius relationship can be used to describe accelerated indentation creep tests. An example of data shifted by the Arrhenius expression can be seen in Fig. 6, where creep data obtained at 50 C have been shifted to longer times corresponding to a temperature of 23 C, and are in good agreement with experimental data obtained at 23 C.
4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9
Indentation creep data Uniaxial tensile creep data
3.8 3.7 0.0027
0.0028
0.0029
0.0030
0.0031
0.0032
0.0033
0.0034
0.0035
-1
1/T Temperature (K ) Fig. 5. Arrhenius plot of lns versus 1/T for indentation and tensile creep data, where s is the relaxation time obtained from a spring and dashpot model. The linear relationship indicates that the indentation creep behaviour obeys the Arrhenius relationship.
370
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371 1.30
Surface of moulding 1500 1400 1300
1.28 1.26
1.22 1.20 1.18 1.16 1.14 1.12
o
Creep at 23 C
1.10
o
Creep at 50 C 1.08
1200 1100
Surface of moulding
Normalised compliance
1.24
1000 900 800 700 600 500
o
Creep at 50 C shifted using Arrhenius
1.06
Log time (seconds)
X-direction (µm)
Fig. 6. Log time shift of normalised creep compliance data obtained at 50 C to times that are equivalent to tests conducted at 23 C using Arrhenius relationship.
200 s at room temperature. The creep properties obtained under these two sets of conditions are shown in Figs. 7 and 8, respectively. The core of the moulding is in the bottom right hand corner of the diagram, with the mould surfaces on the top and the left hand side of the diagram. Similar trends were obtained from both the room temperature and the accelerated tests, with the normalised creep compliance in both tests varying from 1.15 to 1.25. In both cases the lowest normalised creep compliance was obtained in the region of the core of the moulding, with higher normalised compliances obtained towards the surfaces (Figs. 7 and 8). The reproducibility of the creep compliance values was determined by conducting ten repeat indentation tests in a region close to the centre of the moulding. This gave a value (0.03) for the standard deviation of the normalised creep compliance. This demonstrates that this measurement method is highly reproducible and also that the observed variation in the
100
300
500
700
8
900
6
1100
4
1300
2
1500
1.04 0
Y-direction (µm)
400
1.225-1.25
300 200
1.2-1.225
100
1.15-1.175
1.175-1.2
Core of moulding
Fig. 8. Normalised creep compliance from a cross-section of injection moulded POM, measured using a constant load of 30 mN for 40 s at 50 C.
normalised creep compliance across the moulding is significant. The accuracy of modulus values determined by the standard quasi-static analysis of the unloading curves is well-known to be questionable for viscoelastic materials. However, the use of a long hold at maximum force and rapid unloading can give a reasonable semi-quantitative estimate for the spatial variation of elastic modulus [5]. Modulus values obtained using the same indentation data revealed that the modulus of the polymer was also higher towards the centre of the moulding and lower at the surface (Fig. 9). Such variations in the creep compliance and modulus of the moulding can be the result of variations in the crystallinity of the polymer; it is well known [18] that the crystallinity of injection moulded polymers can be significantly higher at the centre of a moulding than close to the walls. This is due to the polymer cooling more slowly at the centre of the moulding than at the walls, leading to increased crystallinity at the centre. The consequence of this increase in crystallinity is that the modulus increases
Surface of moulding
Surface of moulding
1500 1400 1300 1200 1100 1000 900 800 Y direction (µm) 700 600
100
300
500
700
900
1100
1300
1500
500 400 300 200 100
1.225-1.25 1.2-1.225 1.175-1.2 1.15-1.175
Core of moulding
X direction (µm) Fig. 7. Normalised creep compliance from a cross-section of injection moulded POM, measured using a constant load of 30 mN for 200 s at 23 C.
Fig. 9. Young’s modulus of injection-moulded POM clip obtained from nanoindentation unloading curves at 23 C.
A.S. Maxwell et al. / Polymer Testing 30 (2011) 366–371 Table 1 Percentage crystallinity obtained by DSC at different positions within an injection-moulded POM clip. Position of specimen in moulding
Crystallinity (%)
Core Skin
41 28
and, due to the crystallinity reducing the mobility of the polymer chains, the creep compliance decreases towards the centre of the moulding [19]. To verify the prediction that the degree of crystallinity varies across the moulding, DSC has been used to determine the crystallinity of the polymer (Table 1). The results confirm that the crystallinity of the polymer at the core of the moulding was significantly greater than that at the surface. These variations in the microstructure and properties within commercially produced injection mouldings are not unexpected. However, it is only with techniques such as nanoindentation that these variations can be detected with micron-scale resolution. 5. Conclusions Test procedures have been developed using nanoindentation to obtain creep properties from actual injection moulded components. This was achieved by applying a constant load to the intender tip on the surface of the moulding and measuring its displacement over time. By normalising the data to reduce uncertainties resulting from the geometry of the indenter tip, an extremely good fit was obtained between creep data obtained using this technique and that obtained from conventional tensile creep tests. A procedure was then developed to accelerate the acquisition of creep data by conducting tests at elevated temperatures for shorter periods of time, using an Arrhenius equation to predict the long-term creep properties at room temperature. An extremely good fit of data to the Arrhenius expression was obtained for Delrin over a wide range of temperatures and times. The accelerated creep test was validated by measuring the creep properties over a cross-section of a commercially injection moulded specimen at temperatures of 23 C and 50 C, and comparing the creep results after shifting the 50 C results to an effective temperature of 23 C. The data obtained by indentation mapping the crosssection of the moulding revealed that the normalised creep compliance was higher at the edges of the specimen than it was at the centre. Likewise, indentation modulus values obtained from the same data revealed that the modulus was lower at the edges than in the centre of the specimen. The most likely explanation for this is that polymer at the edges of the specimen had less time to crystallise due to rapid cooling at the surface than it did at the centre of the
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moulding, leading to lower crystallinity at the edges of the specimen [18]. This was confirmed using differential scanning calorimetry. Acknowledgements This work was carried out as part of the UK Government Department of Business Industry and Skills (DBIS), National Measurement System (NMS), Programme for Innovation Research and Development 2008–10. References [1] A. Flores, F. Ania, F.J. Balta-Calleja, From the glassy state to ordered polymer structures: a microhardness study, Polymer 50 (2009) 729–746. [2] H. Lu, B. Wang, J. Ma, G. Huang, H. Viswanathan, Measurement of creep compliance of solid polymers by nanoindentation, Mechanics of Time-dependent Materials 7 (2003) 189–207. [3] M.V.R. Kumar, R. Narasimhan, Analysis of spherical indentation of linear viscoelastic materials, Current Science 87 (2004) 1088–1095. [4] L. Cheng, X. Xia, L.E. Scriven, Spherical-tip indentation of viscoelastic material, Mechanics of Materials 37 (2005) 213–226. [5] M. Vandamme, F.J. Ulm, Viscoelastic solutions for conical indentation, International Journal of Solids and Structures 43 (2006) 3142–3165. [6] R. Seltzer, Y.-W. Mai, Depth sensing indentation of linear viscoelastic-plastic solids: a simple method to determine creep compliance, Engineer Fracture Mechanics 75 (2008) 4852–4862. [7] C.A. Tweedie, K.J. Van Vliet, Contact creep compliance of viscoelastic materials via nanoindentation, International Journal of Materials Research 21 (2006) 1576–1589. [8] M.L. Oyen, Analytical techniques for indentation of viscoelastic materials, Philosophical Magazine 86 (2006) 5625–5641. [9] M.L. Oyen, Relating viscoelastic nanoindentation creep and load relaxation experiments, International Journal of Materials Research 99 (2008) 823–828. [10] M.L. Oyen, A.J. Bushby, Viscoelastic effects in small-scale indentation of biological materials, International Journal of Surface Science and Engineering 1 (2007) 180–197. [11] T.C. Ovaert, B.R. Kim, J. Wang, Multiparameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modelling, Progress in Organic Coatings 47 (2003) 312–323. [12] B.D. Beake, J.F. Smith, High-temperature nanoindentation testing of fused silica and other materials, Philosophical Magazine A 82 (2002) 2179–2186. [13] ISO 14577, Metallic Materials - Instrumented Indentation Test for Hardness and Materials Parameters Part 1: Test Method (2002). [14] T. Jaruga, E. Bociaga, Crystallinity of parts from multicavity injection mould, Archives of Materials Science and Engineering 30 (2008) 53–56. [15] K. Herrmann, N.M. Jennett, W. Wegener, J. Meneve, K. Hasche, R. Seemann, Progress in determination of the area function of indenters used for nanoindentation, Thin Solid Films 377-378 (2000) 394–400. [16] I.M. Ward, J. Sweeney, An Introduction to the Mechanical Properties of Solid Polymers. John Wiley and Sons, 2004. [17] W.H. Li, S. Keesam, C.G. Lee, B.C. Wei, T.H. Zhang, Y.Z. He, The characterisation of creep and time-dependent properties of bulk metallic glasses using nanoindentation, Materials Science and Engineering, A 478 (2008) 371–375. [18] H.F. Giles, J.R. Wagner, E.M. Mount, Extrusion: The Definitive Processing Guide and Handbook Volume 1 pg 181. Plastic Design Library, 2005. [19] K. Banik, G. Mennig, Influence of injection molding process on the creep behaviour of semicrystalline PBT during aging below its glass transition temperature, Mechanics of Time-dependent Materials 9 (2006) 247–257.