Strain Rate Effects in the Mechanical Properties of Polymer Foams

Transcription

1 Strain Rate Effects in the Mechanical Properties of Polymer Foams I J P T Serials Publications Strain Rate Effects in the Mechanical Properties of Polymer Foams M. Z. Hassan 1 and W. J. Cantwell 2 1 Universiti Teknologi Malaysia, Jalan Semarak Kuala Lumpur, Malaysia 2 Department of Engineering, University of Liverpool, Liverpool, L69 3GH, United Kingdom A series of compression, single edge notch bend and shear tests have been carried out on a range of crosslinked PVC, linewar PVC and PET polymer foams in order to investigate the influence of strain rate on their mechanical properties. The tests in compression have highlighted the rate-sensitivity of the plastic collapse strenss of the foams, with some values increasing by over one hundred percent in passing from quasi-static to dynamic rates of loading. Tests have shown that the rate-sensitivity of the foam increases with foam density, an effect that has been observed by other researchers. Mode I tests using the single edge notch bend geometry have shown that the crosslinked PVC foams, as well as the PET foams, fail in a brittle manner at low and high rates of loading. In contrast, the linear PVC foams fail in a ductile mode, highlighting their excellent energy-absorbing characteristics. A test technique has been developed to characterise the Mode II (shear properties of the foams). Here, it has been shown that the Mode II shear toughnesses of the crosslinked PVC foams were up to thirty-five times greater than their corresponding Mode I values. In contrast, the Mode II enhancement effect was less in the linear PVC and PET foams. The final part of this study investigated strain rate effects in the indentation response of sandwich structures based on a range of polymer foams. Here, it is shown that the indentation stiffness is directly related to the plastic collapse strength of the foam, with the quasi-static and dynamic values falling on a single trace. INTRODUCTION As a result of their lightness and general versatility, polymer foams are finding widespread use in a range of high-performance, lightweight sandwich structures. Currently, a number of different polymer foams are being used in engineering design, ranging from crosslinked PVC foams, for use in applications such as cockpit doors, cryogenic tanks and helicopter rotor blades to PET systems that are ideally suited for shear webs, shells and nacelles in wind turbine construction. As a result of their widespread use, much attention has focussed on characterising the fracture properties of polymer foams under different loading conditions [1-4]. Given that many foam-based sandwich structures are subjected to dynamic loading conditions, such as those associated with impact or blast loading, there is a pressing need to understand how these materials behave at high rates of strain. Subhash et al. [5] investigated the quasi-static and high strain rate compressive response of epoxy-based structural foam specimens using a servohydraulic test machine and a split Hopkinson pressure bar. They found that the * Corresponding author: ??? failure strength of the foams increased with strain rate, whereas the strain to failure decreased. In addition, the authors noted that the rate-sensitivity increased with increasing foam density. Song and co-workers [6] tested a syntactic epoxy foam at low and high strain rates and found that the compressive strength of the foam increased with strain rate up to a transition strain rate between 550 and 1030/s. Above this threshold, strain-rate induced damage resulted in a reduction in the strength of the foam. Based on these findings, the authors developed a constitutive model incorporating strain-rate and damage effects, which showed good agreement with the experimental data. Ouellet et al. [7] conducted compression tests on a range of polystyrene, polyethylene and polyurethane foams at strain rates up to 2500/s and showed that the rate-sensitivity of the foams increased at strain rates above 1000/s. The fracture toughness characteristics of polymer foams has not received a great deal of attention in the published literature. In an early study, McIntyre and Anderton [8] conducted single edge notch bend (SENB) tests on a rigid polyurethane foam with densities in the range 32 to 360 kg/m 3. They showed that the fracture toughness of the foams increased International Journal of Polymers and Technologies 3(1) January-June

2 M. Z. Hassan and W. J. Cantwell continuously with foam density, approaching a value of approximately 250 J/m 2 for the highest density system. The aim of this research study was to investigate strain rate effects in a wide range of mechanical properties of polymer foams. Initial attention focuses on the compression response. This is subsequently extended to consider the Mode I and Mode II fracture response of the foams. Finally, the work is completed by considering the indentation behaviour of sandwich structures based on a range of foams. EXPERIMENTAL PROCEDURE Nine foams were investigated in this study, details of which are given in Table 1. Five of the foams were based on a crosslinked PVC polymer, two on a linear PVC system and two on PET. All of the foams were supplied in the form of 20 mm thick sheets. Table 1 Summary of the Mechanical Properties of the Nine Foams Tested in this Study Foam Type Nominal Plastic Mode I Mode II Density Collapse Work of Work of (kg/m 3 ) Strength Fracture Fracture (MPa) (kj/m 2 ) (kj/m 2 ) Crosslinked PVC Crosslinked PVC Crosslinked PVC Crosslinked PVC Crosslinked PVC Linear PVC Linear PVC PET PET Initial attention focused on determining the influence of strain rate on the compression properties of the nine types of polymer foam. Quasi-static tests were undertaken on foam blocks with dimensions of 25 x 25 x 20mm on an Instron 4505 universal test machine at 10 mm/minute. The tests were stopped when the foams reached the densification stage in the stress-stress curve. The dynamic compressive properties of the foams were evaluated using a dropweight impact tower. A 50 mm diameter steel plate was fitted to the impact carriage to load the foams, which themselves were supported on the solid steel base of the impact rig. Masses of approximately 6 kg were dropped from heights of up to 1.2 metres to load the aforementioned blocks in compression. The force during the test was recorded using a piezoelectric load cell and the displacement using a high-speed video camera. The output from the load cell and camera were combined to yield stress-strain traces. The fracture properties of the foams under Mode I loading were evaluated through a series of single edge notch bend (SENB) tests on samples with length, depth and thickness dimensions of 150, 30 and 20 mm respectively, Figure 1a. A notch with a length of approximately 10 mm was introduced half way along the length of the sample. The notch was sharpened using a blade prior to testing. Quasi-static tests were conducted on the above-mentioned Instron testing machine using simple supports positioned 120 mm apart. Impact tests were conducted by placing the test samples on the same supports as were used for quasistatic testing and impacting the sample using the instrumented carriage. A 10 mm diameter loading bar was located on the nose of the carriage in order to apply a line load to the samples. As before, the load and displacement were recorded using a piezoelectric load cell and a high speed video camera respectively. The toughnesses of the various foams were characterised by determining the Work of Fracture, w f. from the area under the loaddisplacement trace and the area of the fractured ligament. This approach was used because some of the foams failed in a brittle manner, whereas other failed in a highly ductile mode. The determination of the work of fracture was found to offer the most appropriate procedure for comparing the foams. The fracture properties of the foams in Mode II (shear) were determined using a purpose-built rig in which notched specimens, with dimensions 80, 30, 20 mm, were clamped at one end and loaded in a shearing mode by a steel traverse, Figure 1b. The notch length was 10 mm. The action of the verticallymoving traverse sheared the sample along a plane immediately parallel to the clamping fixture. As before, the work of fracture was determined from the area under the load-displacement trace and the area of the fractured ligament. Unfortunately, it was not possible to conduct these tests at high rates of loading. In the final part of this study, indentation tests were conducted on sandwich structures based on 0.5 mm thick woven glass fibre reinforced polyamide 6,6 skins with a nominal fibre weight fraction of 55%. The composite skins were bonded to the core materials using a two part epoxy paste and cured under pressure for twelve hours at room temperature. Here a wider range of foams were used, details of which are given elsewhere [9]. The quasi-static indentation response of the sandwich structures was investigated 28 International Journal of Polymers and Technologies 3(1) January-June 2011

3 Strain Rate Effects in the Mechanical Properties of Polymer Foams on an Instron 4045 universal test machine. Tests were undertaken at a crosshead displacement rate of 1 mm/minute using a 10 mm diameter hemispherical indentor. Low velocity impact tests were conducted using the previously-discussed instrumented impact tower. During impact, the panels were fully supported on a steel base and impacted by the 10 mm diameter hemispherical steel indentor. RESULTS AND DISCUSSION Figure 2 shows typical stress-strain curves following quasi-static compression tests on two crosslinked PVC foams and the two linear PVC foams. All of the traces exhibit a similar appearance with the load increasing to a maximum value (termed the plastic collapse stress of the foam) before stabilising at an approximately constant value. Continued loading resulted in densification of the foam, leading to a final increase in the measured load. Clearly, increasing the density of the foam serves to increase its load-bearing Figure 2: Typical Stress-strain Traces Following Quasi-static Compression Tests on the 60 and 100 kg/m 3 Crosslinked PVC Foams and the 90 and 140 kg/m 3 linear PVC Foams Figure 1: Single Edge Notch Bend (SENB) Geometry for Measuring the Work of Fracture in Mode I Schematic of the Test Fixture for Determining the Work of Fracture in Shear capacity, with the 100 kg/m 3 crosslinked foam and the 140 kg/m 3 foam offering higher values of plastic collapse stress than their lower density counterparts. Figure 3 presents the corresponding loaddisplacement traces following tests at impact rates of loading. Here, a distinct oscillatory response is in evidence, most particularly in the higher density foams. This type of dynamic behaviour is likely to be associated with ringing in the load-cell following impact on the rigid foams. In these tests, it proved more difficult to establish the plastic collapse stress, since the maximum value has been accentuated by the dynamic effects in the testing apparatus. Instead, an average plateau value was used in order to characterise the compressive behaviour of the foams. A comparison of Figures 2 and 3 indicates that the International Journal of Polymers and Technologies 3(1) January-June

4 M. Z. Hassan and W. J. Cantwell dynamically-loaded samples exhibited a greater resistance to compression, reflecting the strain-rate sensitivity of these polymer foams. The compressive response of the nine foams tested here are summarised in the form of a bar chart in Figure 4, where a number of important observations can be made. Firstly, as previously mentioned, the compression strength increases with foam density. This is clear in the data for the crosslinked PVC foams, where an increase in the nominal density from 60 to 200 kg/m 3 resulted in a five fold increase in plastic collapse stress. The linear PVC foams offer lower strength values than their crosslinked counterparts, a clear reflection of the effect of introducing crosslinks into the polymer foam. The PET foams appear to exhibit compression properties that lie between those of the linear and crosslinked PVC foams. The bar chart also highlights the strain-rate sensitivity of the various types of foam, with all systems exhibiting an increase Figure 3: Typical Stress-strain Traces Following Dynamic Compression Tests on the 60 and 100 kg/m 3 Crosslinked PVC Foams and the 90 and 140 kg/m 3 linear PVC Foams Figure 4: Summary of the Quasi-static and Dynamic Plastic Collapse Strengths of the Foams in compression properties at higher rates. A cursory examination of the data indicates that the strain rate sensitivity increases with foam density, with the dynamic compression strength of the highest density foam being more than double that of its quasi-static value. This observation agrees with the findings of previous researchers who have established that ratesensitivity in closely linked to foam density [5,6]. This evidence suggests that it is very important to use the dynamic properties of a foam when attempting to model the impact or blast resistance of sandwich structures. The Mode I fracture properties of the foams were characterised through a series of single edge notch bend tests at quasi-static and dynamic rates of loading. Figure 5 shows typical load-displacement traces for two crosslinked PVC foams and the two PET foams following SENB tests at quasi-static rates. An examination of the figure indicates that both crosslinked PVC foams failed in a relatively brittle manner with the load increasing to a peak value, before dropping sharply as the crack propagates upwards through the polymer. The saw tooth appearance in the traces is associated with the crack arresting before subsequently propagating in an unstable manner. In contrast, the PET foams exhibited a mixed failure mode, with the load-increasing in a highly non-linear fashion before unstable crack propagation at the maximum load. The dynamic loaddisplacement traces for the crosslinked PVC foams were similar in appearance to the quasi-static curves, again highlighting a relatively brittle mode of failure. Interestingly, the PET foams failed in a more distinct brittle mode at higher rates of loading, with the 30 International Journal of Polymers and Technologies 3(1) January-June 2011

5 Strain Rate Effects in the Mechanical Properties of Polymer Foams Figure 6: Summary of the Quasi-static and Dynamic Values of the Work of Fracture of the Foams. The Value for the 90 kg/ m 3 Linear PVC foam has been Omitted for Clarity Figure 5: Typical load-displacement Traces Following Mode I SENB Tests on the Crosslinked PVC Foams and the PET Foams maximum loads and displacements being significantly lower that those measured quasistatically. Figure 6 summarises the Mode I work of fracture data for the nine foams at the two extremes of loading condition. It should be noted that the data for the 140 kg/m 3 linear PVC foam has not been included, since its high value of 12,150 J/m 2 distorts the figure. An examination of the figure highlights the impressive toughness characteristics of the linear PVC and PET foams. Indeed the value in excess of 12 kj/m 2 for the higher density linear PVC foam highlights the extraordinary toughness of this foam. The figure also illustrates a rate-sensitivity in all of the foams, with the dynamic values of the work of fracture tending to be lower than the quasi-static values. The rate-sensitivity is most pronounced in the PET foams, where the dynamic values are significantly lower than those measured at 10 mm/ minute. It is also evident that the linear PVC foams suffer a reduction in toughness at higher rates, although this is not as significant as that observed in the PET foams. Once again, this evidence suggests that when analysing structures based on polymer foams it is important to use the appropriate fracture data. The fracture properties of the foams in Mode II were characterised using the specially-developed test fixture shown in Figure 1b. Typcal load-dispalcement traces following Mode II tests on two crosslinked PVC foams and the two PET foams are shown in Figure 7. All four traces exhibit a similar appearance, with the load-increasing in a non-linear fashion to the peak load followed by unstable crack propagation. The non-linearity in the initial portions of the loaddisplacement traces is associated with plastic deformation directly under the steel loading traverse. In all cases, crack propagation occurred in a stick-slip mode, involving relatively small periods of unstable crack propagation. As before, increasing the foam density serves to increase the maximum load registered during the test. Once again, the work of fracture was determined from the area under the loaddisplacement trace and the area of the fractured ligament. Figure 8 summarises the Mode II fracture data, where the work of fracture in shear is plotted against foam density. A cursory examination of the figure indicates that the toughness values in shear are significantly higher than in Mode I. It is interesting to note that there is roughly a linear relationship between the shear toughness and density for the five crosslinked PVC foams. Perhaps surprisingly, the toughnesses of the linear PVC foams are similar to International Journal of Polymers and Technologies 3(1) January-June

6 M. Z. Hassan and W. J. Cantwell Figure 7: Typical Load-displacement Traces Following Mode II Shear Tests on the Crosslinked PVC Foams and the PET Foams those of its crosslinked counterpart, contradicting the observations in Mode I. The PET foams offer the lowest shear toughness for a given density, although these values still remain impressive. The relationship between the Mode I and Mode II toughness characteristics of the foams are assessed in Figure 9. As previously stated, the Mode II toughnesses are significantly greater than their corresponding Mode I values. This is most pronounced in the crosslinked PVC foams, where the Mode II values are approximately thirty times greater than the Mode I values. This Mode II enhancement is much lower in the linear PVC, where the Mode II values are only two to three times greater than the Mode I data. The final part of this research study focused on investigating the influence of loading rate on the indentation response of sandwich structures based on glass fibre reinforced polyamide skins. Figure 10 shows typical load-indentation plots following tests on structures based on the 130 kg/m 3 crosslinked PVC foam and the 90 kg/m 3 linear PVC foam. All traces are relatively linear over the range of indentation depths considered. It is clear that the slope of the traces increases with loading rate, again highlighting the rate-sensitivity of the foams. The load-indentation behaviour of the foams was subsequently characterised by applying a Meyer indentation law of the form: P = Ca n Where C and n are indentation constants and a?is the indentation depth. Investigations showed that the value of n was approximately unity for most of the polymeric foams, suggesting an approximate linear relationship between the force and indentation. In contrast, the value of C, reflecting the effective slope Figure 8: The Variation of the Mode II Work of Fracture with Foam Density Figure 9: The Variation of the Mode II Work of Fracture with the Mode I Work of Fracture 32 International Journal of Polymers and Technologies 3(1) January-June 2011

7 Strain Rate Effects in the Mechanical Properties of Polymer Foams Figure 11: The Variation of the Contact Stiffness C with Plastic Collapse Stress Figure 10: Typical Load-indentation Traces Following Tests on Sandwich Structures Based on 90 kg/m 3 linear PVC foam and the 130 kg/m 3 Crosslinked PVC foam at Quasi-static and Impact Rates of Loading of the trace, was found to be highly dependent on the foam type as is apparent in Figure 10. From the figure, it is clear that the value of C increases with strain rate, probably reflecting the rate-sensitivity of the foam core directly under the indentor. This was investigated further by plotting the value of C against the plastic collapse stress and these results are shown in Figure 11. Here, it is evident that the indentation constant C exhibits a clear dependency on the plastic collapse stress. Included in the figure are values corresponding to the impact indentation tests on the foams. It is clear that the dynamic data and quasistatic data fall on the one curve, highlighting the clear link between these two parameters. CONCLUSIONS A series of mechanical tests have been undertaken on a range of polymer foams in order to investigate how polymer type, foam density and loading rate influence the properties of these lightweight systems. Compression tests have shown that the plastic collapse strength is very sensitive to both foam density and strain rate, tending to increase with increases in both of these parameters. Indeed, the strain-rate sensitivity has been shown to increase with foam density, an effect that has been observed by previous workers. Mode I fracture tests using the single edge notch bend specimen geometry have shown that the work of fracture increases with foam density and decreases with strain rate. In these tests, the linear PVC foams offered extremely high values of toughness, clearly out-performing their crosslinked PVC and PET counterparts. Evidently, loading at a higher strain rate reduces local plasticity at the crack tip, leading to a lower toughness. A simple geometry has been developed to measure the work of fracture properties of the foams under Mode II (shear) loading. As before, the work of fracture increased with foam density, with the PVC foams offering higher values than their PET counterparts. Here, the values of the work of fracture in shear were significantly higher than those in tension, this being most pronounced in the crosslinked PVC systems where the Mode II values were up to forty times greater than the corresponding Mode I data. Finally, a series of indentation tests has shown that the indentation stiffness of a sandwich structure is directly linked to the plastic collapse stress of the foam core. International Journal of Polymers and Technologies 3(1) January-June

8 M. Z. Hassan and W. J. Cantwell ACKNOWLEDGEMENTS The authors would like to thank the Universiti Teknologi Malaysia and the Malaysian Government for supporting this work. REFERENCES [1] V. C. Shunmugasamy, N. Gupta, N. Q. Nguyen and P. G. Coelho, Strain Rate Dependence of Damage Evolution in Syntactic foams, Materials Science and Engineering A 527, 2010, [2] J. D. Mcrae, H. E. Naguib Mechanical and N. Atalla, Acoustic Performance of Compression-Molded Open-Cell Polypropylene Foams, Journal of Applied Polymer Science, 116, 2010, [3] M. A. Hazizan and W. J. Cantwell, The Low Velocity Impact Response of Foam-based Sandwich Structures, Composites Part B: Engineering, 33, 2002, [4] F. Ramsteiner, S. Forster, Testing the Deformation Behaviour of Polymer Foams, Polymer Testing 20, 2001, [5] G. Subhash, Q. Liu and X-L. Gao, Quasistatic and High Strain Rate Uniaxial Compressive Response of Polymeric Structural Foams, Int. J. of Impact Engineering, 31, 2006, [6] B. Song and W. Chen, Dynamic Compressive Response and Failure Behavior of an Epoxy Syntactic Foam, Journal of Composite Materials 38, 2004, [7] S. Ouellet, D. Cronin and M. Worswick, Compressive Response of Polymeric Foams under Quasi-static, Medium and High Strain Rate Conditions, Polymer Testing 25, 2006, [8] A. McIntyre and G. E. Anderton, Fracture Properties of a Rigid Polyurethane Foam over a Range of Densities, Polymer, 20, 1979, [9] M. Z. Hassan and W. J. Cantwell, The Indentation Behaviour of Foam based Sandwich Structures, to be published in the Journal of Composite Materials. 34 International Journal of Polymers and Technologies 3(1) January-June 2011