July 18, 2008
On the Influence of Chain Morphology on the Shock Response of Three Thermoplastics
By Bourne, N K Millett, J C F
It is increasingly important to understand the dynamic response of polymers and polymer composites as their engineering application increases. This work aims to investigate the effects of additions to thermoplastic carbon chains on the response of the resulting polymer at the continuum scale. Polyethylene, polyvinyldichloride, and polymethylmethacrylate are shocked, and their equation of state and strength properties is presented. An explanation is sought for the greater hardening observed in polymethylmethacrylate by looking at tacticity and electronic attractive forces, as well as entanglement of chains as a result of the large pendent side group. It is concluded that this entanglement has the greatest effect upon the observed strengthening in these thermoplastics. DOI: 10.1007/s11661- 007-9371-7
(c) The Minerals, Metals & Materials Society and ASM International 2007
POLYMERS and composites (with polymers as their matrix) are of great importance in a range of engineering applications. It is thus a pressing need to understand their mechanical response. Whereas there have been great developments in applying microstructural understanding to the continuum response of metals, such advances have been less apparent in polymers and composites containing them. This is partly due to the paucity of data collected in the shock regime. Early static work at high pressure was augmented by shock studies by Carter and Marsh and Champion, but this is nevertheless a field with relatively few published studies.[1-5]
It is the aim of this work to understand the effect of microstructural order upon the dynamic response of polymeric materials. These materials do not have the microstructure to couple with the traditional techniques used in metals and crystals to understand their response at the smallest scales. Polymers may be ordered into two broad groups: those that consist of chains packed in an ordered or amorphous manner (thermoplastics) and those having a three-dimensional network (thermosets or rubbers). Thermoplastics may have some cross-linking, but in the study presented here, the three materials do not.
The three compared are polyethylene (PE), the simplest hydrocarbon, with hydrogen atoms substituted onto a simple carbon backbone; polyvinylchloride (PVC), which has a chlorine atom substituted onto every other carbon; and polymethylmethacrylate (PMMA). Polyethylene is a commodity thermoplastic extensively used in consumer products. It is classified into at least nine different categories based primarily on its density, molecular weight, and branching. The current work focuses on high density polyethylene with a density of 950 kg m~3. It has a low degree of branching and thus greater intermolecular forces and tensile strength. The second material is PVC, which represents halogenation of the chain with a chlorine atom substituted onto every other carbon atom. Other work has studied the effect of fluorination of the chain.l?] Polyvinylchloride is an industrially important polymer that finds widespread application in the building industry. These two polymers are semicrystalline, comprising crystalline domains exhibiting a high degree of order both along the polymer backbone and between the polymer chains. These domains are surrounded by an amorphous fill. An overview of the molecular microstructures is shown in Figure 1.
Polymethylmethacrylate consists of much larger side groups on the carbon chain. Every other carbon has a methyl and an acrylate group, which result from the polymerization of methylmethacrylate. The pendent methyl (CH3) groups prevents the polymer chains from packing closely in a crystalline fashion and from rotating freely around the carbon-carbon bonds. It is thus the only one of the three to be entirely amorphous. As a result, PMMA is a transparent and rigid plastic. Because it retains these properties over years of exposure to ultraviolet radiation and weather, PMMA is an ideal substitute for glass. In the cases of PVC and PMMA, the tacticity of the chains becomes an issue. The preferential distribution of groups on either side of the backbone will allow differing interactions. In particular, polar bonding will become possible. Because these are commercial materials, all the chains are believed to be atactic.
Carter and Marsh examined the high stress Hugoniot of a range of polymers from a minimum particle velocity of approximately 0.7 mm [mu]s^sup -1^.E4] Many of these polymers show a change in the shock vs particle velocity (U^sub S^-u^sub p^) curve at high pressures, in the case of PVC at approximately 22.3 GPa. They suggested that this was due to a structural change where the bonds within the polymer chain breakdown and reform as a three-dimensional tetragonal network. The response of high-density polyethylene to shock has been characterized in some detail in order to provide a baseline on which to compare the effect of further microstructural variations.[8,9] At lower pressures, Mori and Nagayama presented results that suggested that the U^sub s^-u^sub p^ relation in PVC showed nonlinear behavior, with a decrease in slope at a particle velocity of approximately 0.15 mm [mu]s^sup -1^. Although the shock response of polymers has not been extensively investigated, PMMA has been looked at by several workers because of its use as a window.[10,15] The most notable and detailed study pertaining to this work is that by Barker and Hollenbach in their investigation of transparent materials for windows for VISAR. Other work has dealt with the shock velocity and strength issues in this material, as cited previously.
In the current investigation, the effect of increasing the size of pendent side groups over addition of an electronegative atom upon the shock behavior of the polymers is presented. This extends the work of a series of previous studies focused on individual hydrocarbon and fluorocarbon polymers.[18,16-23] It has been noted that the work to date has focused on the higher velocity regime, and so this work is concerned with lower particle velocities up to 1 km s^sup -1^.
The materials chosen were selected from targets fabricated for experiments from stock and were stored in that manner for a series of experimental programs. Given the size of these campaigns, they represent several batches from the same supplier. These materials will be termed commercial off the shelf in what follows to differentiate their properties from the other, carefully pedigreed material reported previously The properties of the materials are tabulated in Table I . The polyethylene is high density but is termed PE in what follows. Note the values of the shock constants C^sub 0^ and S are derived in the work described subsequently.
Plate impact experiments were performed using a 5-m long, 50-mm bore single stage gas gun. The shock stress, shock velocity, and particle velocity relations were determined to deduce the equation of state. Target assemblies were made by fixing a manganin stress gage (MicroMeasurements type LMSS-025CH-048, MicroMeasurements, Rayleigh, NC) between 5- or 6-mm plates of the polymers with a low viscosity epoxy adhesive. A second gage (the 0-mm position) was supported on the front with a 1-mm plate of either durai (aluminum alloy 6082-T6) or copper, which was matched to the material of the flyer plate. In this way, both shock stress (from the amplitude of the signal) and shock velocity through the known spacings of the gages in terms of position within the target assembly and time could be determined. Gage calibrations were according to Rosenberg et al. The shocks were induced by impact of 5-mm durai or copper flyer plates impacted in the velocity range up to approximately 1000 m s^sup -1^. The velocities of the impacting plates were measured by the shorting of sequentially mounted pairs of pins to an accuracy of 0.5 pet. The particle velocity in the material flow behind the shock front (u^sub p^) was determined from the known response of the flyer plate materials, the measured impact velocity, and the longitudinal stresses from the gages using impedance matching techniques. A second set of experiments measured the lateral component of stress (sigma^sub y^) and, from that, the shear strength behind the shock front (2tau) through the relation
In this case, manganin gages of a different type (MicroMeasurements J2M-SS-580SF-025) were introduced into sectioned 10-mm plates of the polymers, 4 mm from the impact face. The targets were reassembled using a low viscosity adhesive and held in a special jig for a minimum of 12 hours. Afterward, the impact face was lapped flat to no greater than five optical fringes from a monochromatic light source, across 50 mm. Lateral stresses were determined from the work of Rosenberg and Partom, using a modified analysis that does not require knowledge of the longitudinal stress. Finally, the particular gage used has a different response to the more familiar grid gages at low stresses, which was accounted for in the conversion from voltage to stress.1281 Specimen alignment was controlled by an accurately machined end piece to the gun barrel. A schematic of specimen configurations and gage placements are presented in Figure 2. The acoustic properties of each polymer were measured using quartz transducers in longitudinal and shear orientation at 5 MHz, using a Panametrics PR5077 pulse receiver. IV. RESULTS AND DISCUSSION
Figure 3 shows typical longitudinal gage traces for the three materials. The data are recorded in a series of experiments and show similar features across the three. The shot conditions for the data are as follows. In the case of PE, a 5-mm copper flyer plate was launched, traveling at 98 m s^sup -1^, while a 5-mm aluminum alloy (6082-T6) plate traveled at 438 m s^sup -1^. The traces for PMMA were due to 10-mm aluminum alloy and 3-mm copper flyers traveling at 207 and 194 m s^sup -1^. Finally, those for PVC were the result of 5- mm aluminum alloy flyers traveling at 320 and 426 m s^sup -1^ and a 5-mm copper flyer traveling at 595 m s^sup -1^. All seven impacts show common features. In all cases, there is some electrical noise, which may be due to the piezoelectric response in the materials. This manifests itself in ringing at the peak and a dip at the start of each pulse. The rise in each case is fast and without any features indicating an elastic limit with wave separation. This is discussed subsequently. Finally, the histories are flat topped showing no indication that the waves are unsteady.
Figure 4 shows the Hugoniot curves for the three materials. In the particle velocity range chosen, there are data from Anderson, Carter and Marsh, Marsh,[26) and Millett and Bourne.181 Note that in the latter data, longitudinal stress values were measured using suitable sensors. In the case of the first works, free surface velocities are recorded and converted back to hydrodynamic pressure, P. It has been shown thai the pedigree of the material is not critical for equation of state response. The error bars for each point are less than the size of the symbol in each case. Thus, the nature of the mesoscale microstructure, and the spherulite size and amorphous packing, has little effect on the states achieved. It is therefore clear that first-order equation of state predictions can be made with limited attention to polymer pedigree. It does however remain critical when addressing the effects of shock prestraining, damage and fracture, and quasi- static and intermediate strain-rate deformation response.[21-23,30- 32]
The three materials order as follows. The PVC (with the highest density) lies uppermost, and PE (with the lowest) is at the base. The PMMA lies between the two. This reflects the ordering of the density among the three materials. The separation of the Hugoniot and the hydrostat is an indication of the strength of the materials, because in an elastic-perfectly plastic material, the longitudinal stress, sigma^sub x^, is related to the pressure, P, and the strength, tau; thus,
These relative orderings will be returned to subsequently in comparison with more direct measurements of strength.
Figure 5 shows the shock wave velocity as a function of the resulting particle velocity in the flow. The PE and PVC all show linear fits to these curves at higher particle speeds. The PMMA has a nonlinear region described by Barker and Hollenbach and not further here. While the materials all show linear fits to these curves at higher particle speeds, it has been shown that these thermoplastics show some curvature at lower shock speeds at velocities less than approximately 0.2 mm [mu]s^sup -1^. This is seen in Table I, which indicates that the elastic wave speed is always less than the zero particle velocity value of the bulk sound speed (c^sub 0^). This is true for all three of the materials considered here, although this is, of course, an extrapolation of the measured large u^sub p^ behavior. In the case of PE and PVC, this is believed to be due to the composite nature of the microstructure, where the sound speed in one of the phases drops into the elastic range while the amorphous surrounding remains hydrodynamic. The square of the elastic wave speed in elastic plastic solids is (K + 4/3 [mu])/rho, whereas that of the bulk sound speed is K/rho. The value of c^sub 0^ obtained is fit to data in excess of the elastic limit, and yet c^sub 0^ is greater than c^sub L^, which is generally not observed in other classes of materials. This has the result that the elastic and plastic waves do not separate in these polymers, as is observed in metals or brittle materials.
The PE lies at the highest shock speeds, followed by PMMA and PVC at the base. The curves for PE and PVC have similar slope, with that for PE slightly greater, and PMMA has a nonlinear form lying between the two. The plot shows that the slope of the fit for PE is greater than those of the others. The value of S has been correlated with the first pressure derivative of the bulk modulus. This indicates the polyethylene matrix to be more compressible than the other two, which is reasonable given the larger atoms in PVC and the pendent side groups in PMMA.
The equation of state of the three materials reflects the average bulk properties of the material and is not sensitive to details of crystallinity and its length scales, or to stereoisomerizism in the macromolecules. Both PMMA and PVC are below their glass transition temperature so that resistance to compression can only result from electronic interactions between the packed polymer chains. In PMMA, the size of the side groups prevents crystallinity, but the amorphous network results in Van de Waals interactions giving rise to the observed nonlinear U^sub s^-u^sub p^ behavior.
Figure 6 presents lateral stress histories for the three polymers taken at gage locations 2 mm from the impact face. These represent typical traces taken from the large number of shots undergone in the programs run. In all cases, the traces rise to a peak and then decay over the period observed. There is no structure observed in the rise of the pulse. This can be seen on each of the histories presented. The shot conditions for the data in Figure 6 are as follows for the three materials. In the case of PE, copper flyer plates were launched traveling at 500 and 943 m s^sup -1^ respectively. The traces for PMMA were aluminum alloy (6082-T6) flyers traveling at 346 and 1116 m s^sup -1^, and those for PVC, the same alloy flyers traveling at 444 and 946 m s^sup -1^. The PVC material gave the noisiest traces and this presumably indicates electrical activity, which is picked up by the gages acting as aerials.
The lateral stress, in the case of the highest amplitude PVC history reproduced here, rises to a value of approximately 4 GPa before relaxing over the next few microseconds to a value of approximately 3 GPa. This reducing lateral stress must be contrasted with the longitudinal component (recorded for equation of state determination) that remains constant over the same period described previously. Thus, the strength of the polymer is increasing through the pulse, indicative of time-dependent processes occurring within the microstructure. This effect is mirrored in the PMMA and PE traces. This drop in lateral stress and corresponding increase in strength (from Eq. [I]) means that in order to rank each impact, a characteristic value of the strength measured must be arrived at by quoting a value corresponding to that at the beginning of the pulse before strengthening has occurred. The reader should note that the strengths are thus minimum values that occur before the microstructure develops, as described previously.
Figure 7 shows the behavior of the calculated strength as a function of the increasing impact stress. The histories are reduced, knowing the initial value of the lateral and the measured longitudinal stresses to give a value of twice the shear strength for each impact stress.
All three materials show a hardening behavior with impact stress. With its simple carbon backbone, polyethylene shows the least increase in strength for the three materials considered here. The others rank with the size of the addition to the chain. The PMMA shows the largest strength gain with increasing impact stress. The observed hardening is among the highest observed by the present program over a wide range of polymers. As has been found elsewhere, all three of these materials collapse to zero strength at higher stress values.
The three materials considered here are all thermoplastics with two microstructural features of note that relate to the observed strength of the materials. In the case of PVC, the electronegative chlorine addition allows electrostatic attractive forces between the chains. The material nevertheless has a crystalline phase, which will have different moduli and density to its amorphous counterpart. Thus, longer timescale interactions can result, affecting the kinetics of propagation within the material. As has been mentioned previously, there is a higher value of S for PE. This has been related to dK/dP, which reflects hydrodynamic effects, and Van de Waals forces are least for PE. Iso- and syndiotactic chains in PVC and PMMA would increase these forces further. It is PVC that shows the smallest S, which reflects the greater magnitude of potential electrostatic repulsion for that material.
The polyethylene chains can exhibit Van de Waals bonding, which increases the strength of the material as the confining pressure forces chains together, and this is equally true for PVC. However, the larger chlorine atom and its increased electronegativity allow polar attractions to increase the bond strength in these materials.
In PMMA, the attractive forces will include hydrogen bonding as the chains come closer, but also the size of the attached group increases the entanglement of the polymer chains. Further, the size of the side groups ensures that the material has no crystalline phase, and so the effects of crystallinity, observed in PE and PVC, are not present. Nevertheless, the size of the side chain is sufficient to cause hardening of the material, as observed in Figure 7. This work has indicated the dominant effect of steric hindrance and entanglement in controlling polymer strength in the shock regime. V. CONCLUSIONS
Three thermoplastics have been investigated to observe shock effects across a range of techniques probing equation of state and strength. The PVC shows differences in behavior to PE due to the presence of the electronegative chlorine atom. The PMMA, as a completely amorphous polymer, exhibits increased strength due to the size of its attached side group. In both cases, the shock loading allows one to probe the details of the response of the microstructure of the material and connect polymer microstructure to observed continuum response.
The forces acting between polymer chains control the equation of state. Van de Waals forces bond chains in all three materials. However, the possibility exists for electrostatic attractive forces in PVC and hydrogen bonding in PMMA to supplement these effects. These forces are all pressure dependent, and, in the low impact velocity regime, these effects can be observed for all three materials.
The strength of the material is additionally controlled by entanglement of the chains, and PMMA, with an amorphous microstructure, shows the largest strength increase due to this effect. Other thermoplastics with side groups have been investigated, but PMMA shows the greatest strength increase over the hydrocarbon PE. The strength increase in PVC due to polar interactions may be contrasted with the steric effects in PMMA, and it appears that the latter has the greatest effect. These qualitative conclusions will be tested using molecular dynamics simulation in future work.
We thank Matt Eatwell and Ivan Knapp, Cranfield University, for performing parts of the work done in that facility.
(c) British Crown Copyright 2007/MOD
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N.K. BOURNE, Professor and Distinguished Scientist, and J.C.F. MILLETT, Senior Scientist, are with AWE, Aldermaston, Reading, RG7 4PR, Berkshire, United Kingdom. Contact e-mail: neil.bourne@ mac.com
This article is based on a presentation made in the symposium entitled "Dynamic Behavior of Materials," which occurred during the TMS Annual Meeting and Exhibition, February 25-March 1, 2007 in Orlando, Florida, under the auspices of The Minerals, Metals and Materials Society, TMS Structural Materials Division, and TMS/ASM Mechanical Behavior of Materials Committee.
Article published online December 19, 2007
Copyright Minerals, Metals & Materials Society Feb 2008
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