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Year 1 5 1 1 17 Show more Language English 24 Italian 1 Undetermined 1. Displaying Editions 1 - 10 out of Print book.
Plastics by N J Mills;. Laser compression with ultrafast spectroscopy as a diagnostic has also probed structural stretching and relaxation processes with polymers subject to femptosecond loads [ 39 , 40 , 41 , 42 ]. The constants c 0 and S are generally determined by experiment.
Dr Mike Jenkins
In materials that change phase, there is generally a transition state and linear behaviour in regimes either side of the transformation state. In this case S is fit to collected data either side of this point and generally takes different values either side of the transformation state see [ 53 ] for example. Unlike in simple metals, a bulk sound speed, c 0 , calculated from ultrasonic measurements of c L and c s does not correspond to the intercept of the plot of Eq.
Secondly in the low pressure below the GPa transition the curve in many polymers has a non-linear form and may be fitted with a polynomial to represent the data. Shock data on PTFE obtained from various commercial and pedigree sources has shown there to be no significant effect of controlled production and purity at least within the experimental scatter Fig.
However, this low-pressure region contains the phase transformation from phase II to phase III which occurs at 0. For many commercially available polymers and specially produced plastics, a linear response is observed above a particle velocity of ca. The intercept on the shock velocity axis c 0 is less than the ambient longitudinal sound speed c L as noted previously. There have also been recovery experiments that show details of changes in crystallinity in the low pressure region [ 45 ].
Here changes in mechanical response are most closely linked to changes in the percentage of crystallinity and crystalline domain size [ 46 ]. Nevertheless Carter and Marsh showed that the low-pressure data can be approximated assuming only a two-dimensional force field is present between chains in a shocked thermoplastic [ 13 ]. In crossing the WSL boundary a shift in behaviour and properties is found and the resulting microstructures may be expected to have markedly different properties to those of the parent polymer.
In summary, low pressure shock behaviour is akin to densification of a porous medium whilst the high pressure transition accesses fully dense behaviour with an overdriven strong shock regime in plastics familiar in other classes of material where the response is homogeneous. The non-invasive measurement of in-material states of stress and strain within loaded targets is a paradigm that has yet to be fully achieved yet the shear strength within compressed materials represents an integrated history of microstructural evolution within the loaded targets e.
To do this requires sensors to measure these changes during the compression impulse. Mounting these sensors within polymers is simple and reproducible since the material is an insulator and the mounting epoxies are matched to the target.
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In recent times, great advances have been made using manganin sensors to achieve this goal [ 59 , 60 , 61 , 62 , 63 , 64 , 65 ]. To appreciate the technique requires a brief digression into stress states behind a shock front when the material has been shocked to a state of macroscopic uniaxial strain. Further details of the flow at low stresses must be taken into account so that a staged refinement of the analysis used to deconvolve the change in resistance back to stress can be used over the range of stresses up to the weak shock limit where homogeneous and hydrodynamic behaviours ensue [ 66 , 67 , 68 , 69 , 70 ].
In what follows the evolution of the shear stress during impact in a range of polymers is determined in the lower pressure regime with embedded gauges. Response of the thermoset epoxy. Two stress levels 3. Impact on polycarbonate at two stress levels ca. In both cases the longitudinal stress induced was 1. To allow details of the history to be observed more easily, the symmetrical impact stress has been multiplied by a factor of 1. Lateral and longitudinal stress are dashed and shear stress histories are solid curves [ 81 ].
The region near the impact face sees an unsteady response for a period of a microsecond or so before the lateral stress equilibrates Fig. In the bulk of the material Fig. Furthermore the shear resistance rises more rapidly at higher stress as the impulse compresses microstructure to achieve high density. The flow near an impact surface in the weak shock regime is only one-dimensional at the macroscale and then only when flyer and target are of the same material so that flow is symmetric. Brittle materials attain an inelastic state by microfracture driven from the impact face; such a zone also exists in metals but now stress state equilibration by slip is much faster.
Indeed there is always such a region where materials of differing impedance interact, in which surface lateral strain must exist and in which assumptions of one-dimensional behaviour breakdown. This region is of greater extent in polymers than is the case for metals and brittle solids as can be seen above. Nevertheless there are features of the behaviour that are due to this asymmetry in the flow in both the other classes of materials.
In metals this is seen in variation of microhardness in material in the hundreds of microns near the impact face, whilst in brittle ceramics, fracture waves are initiated when the impact is asymmetric that are not present in the symmetric case [ 71 , 72 ]. In polymers the surface zone is of a different nature since in this case the response is dominated by densification of the initial open structure; by Van de Waals forces in thermoplastics or compressing cross-linking bonds in thermosets.
This densification zone defines the response of plastics to dynamic loads above the yield stress and the shock regime exemplifies this behaviour well as these histories show. The strength of polymers is controlled by electronic and steric interactions, which in combination act to define response during dynamic loading. However, in all the cases investigated here, polymers show increasing shear strength with pressure consistent with static measurements [ 73 ].
Material strength data has been collected in a series of tests corresponding to different loaded volumes and as the pulse duration is reduced, the strength increases. This data is collected here to suggest that strength measured approaches the theoretical strength at the pressure where the change in shock behaviour is observed.
The shaded region times shorter than ca. The strain-rate associated with a test may be transformed into its components in order to recover the loading time and spatial zone accessed within the material. The strain at failure may be determined from the yield stress through the modulus. This is then used along with the tabulated strain rate to calculate a characteristic equilibration time for the process at the scale at which the test is conducted. In addition, tests on small volumes of material or with short pulses can be added to the data to review the strengths deduced in these experiments.
Such a process has been conducted on the data from Fig. The logarithm of strength is plotted against the logarithm of the time duration of loading and data for plate impact ca. The impulse sweeps a volume and a characteristic swept length scale can be calculated via the wave speed for the material. Since the scale is logarithmic and the wave speed of polymers slow ca. The laser shock pulse is probing distances of order a few monomer units within the polymer and records deduce values for the strength that approach the theoretical strength for the material.
Clearly these data are exceeded at the highest pressures since the modulus itself is rapidly changing during compression and plate impact strengths included here at two nominal low pressures are around this limit for both the polymers considered. Finally a theoretical strength is included at a nominal 0.
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Whilst the laser measurement does not reach this value it is close to it indicating that such tests may be used to directly probe the ultimate strengths of condensed phase materials. The shaded region separates a microscale from a mesoscale response and potentially two different classes of mechanism in each case.
Thus intermediate strain rate and shock data probe different bonding and strength properties with a polymer. Further the boundary between these regions separates ordered from disordered regions within the microstructure.
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Advances in new tools and diagnostics have illuminated their response dramatically and this is favoured since they have low density and can be easily penetrated by X-ray and particle sources to image deformation in real time under load [ 84 , 85 ]. Their response to a dynamic impulse shows behaviour of a different nature to that of metals and ceramics which are close-packed at the bond 0. The micromechanics of the response of polymers to weak shock can be described in terms of the packing of the polymer chains at distances of five to ten times these dimensions. While the response of fully dense metals or ceramics in the weak shock regime is dominated in the first moments of load by the creation of localised regions to accommodate macroscopic strain, polymers respond by compressing against the weaker inter-chain Van der Waals forces or the lower density of cross-links [ 53 , 70 ].
Microscale packing dominates behaviour and with approximately inverse square dependence on chain separation response is sensitive to conformation once compression begins [ 31 , 86 , 87 ]. Strength increasing behind the shock results from the closer proximity of the molecular components with strong attractive bonding and greater steric entanglement that resists further strain as time develops [ 73 ].
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