Spherical Waves and Cylindrical Waves

Yang, Liming; Feng-hua, Zhou; Wang, Lili

doi:10.1016/b978-008044494-9/50008-1

Cited by 27 publications

(55 citation statements)

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“…One other important quantity is the tangent of the transverse wave angle, which from Equations (8), (14) and (19) can be written as…”

Section: Strain Immediately Following Impactmentioning

confidence: 99%

“…Various methods have been used to determine Young's modulus and sometimes the strength of such materials at high strain rates. Lim et al [13] used a miniature Kolsky bar, and others have used a split Hopkinson bar, as discussed by Wang [14], who points out that the results take considerable experimental sophistication to interpret. The method we use involves 'yarn shooting experiments' whereby a single yarn, under a prescribed level of initial tension, is subjected to transverse impact by a projectile.…”

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confidence: 99%

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Modeling and Experiments on Ballistic Impact into UHMWPE Yarns Using Flat and Saddle-Nosed Projectiles

Phoenix

Heisserer

Werff

et al. 2017

Fibers

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Abstract:Yarn shooting experiments were conducted to determine the ballistically-relevant, Young's modulus and tensile strength of ultra-high molecular weight polyethylene (UHMWPE) fiber. Target specimens were Dyneema ® SK76 yarns (1760 dtex), twisted to 40 turns/m, and initially tensioned to stresses ranging from 29 to 2200 MPa. Yarns were impacted, transversely, by two types of cylindrical steel projectiles at velocities ranging from 150 to 555 m/s: (i) a reverse-fired, fragment simulating projectile (FSP) where the flat rear face impacted the yarn rather than the beveled nose; and (ii) a 'saddle-nosed projectile' having a specially contoured nose imparting circular curvature in the region of impact, but opposite curvature transversely to prevent yarn slippage off the nose. Experimental data consisted of sequential photographic images of the progress of the triangular transverse wave, as well as tensile wave speed measured using spaced, piezo-electric sensors. Yarn Young's modulus, calculated from the tensile wave-speed, varied from 133 GPa at minimal initial tension to 208 GPa at the highest initial tensions. However, varying projectile impact velocity, and thus, the strain jump on impact, had negligible effect on the modulus. Contrary to predictions from the classical Cole-Smith model for 1D yarn impact, the critical velocity for yarn failure differed significantly for the two projectile types, being 18% lower for the flat-faced, reversed FSP projectile compared to the saddle-nosed projectile, which converts to an apparent 25% difference in yarn strength. To explain this difference, a wave-propagation model was developed that incorporates tension wave collision under blunt impact by a flat-faced projectile, in contrast to outward wave propagation in the classical model. Agreement between experiment and model predictions was outstanding across a wide range of initial yarn tensions. However, plots of calculated failure stress versus yarn pre-tension stress resulted in apparent yarn strengths much lower than 3.4 GPa from quasi-static tension tests, although a plot of critical velocity versus initial tension did project to 3.4 GPa at zero velocity. This strength reduction (occurring also in aramid fibers) suggested that transverse fiber distortion and yarn compaction from a compressive shock wave under the projectile results in fiber-on-fiber interference in the emerging transverse wave front, causing a gradient in fiber tensile strains with depth, and strain concentration in fibers nearest the projectile face. A model was developed to illustrate the phenomenon.

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“…One other important quantity is the tangent of the transverse wave angle, which from Equations (8), (14) and (19) can be written as…”

Section: Strain Immediately Following Impactmentioning

confidence: 99%

mentioning

confidence: 99%

Modeling and Experiments on Ballistic Impact into UHMWPE Yarns Using Flat and Saddle-Nosed Projectiles

Phoenix

Heisserer

Werff

et al. 2017

Fibers

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show abstract

“…25 Moreover, the wave speed of the STF, C 2 , will be calculated according to the PDV results. A characteristic analysis 26 was used to analyze the dynamic response of the STF with the first velocity peak value.…”

mentioning

confidence: 99%

Dynamic response of shear thickening fluid under laser induced shock

Zhong

Yin

et al. 2015

Applied Physics Letters

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“…However, it is not a shock phenomenon since the tangential modulus of the tensile stress-strain curve decreases continuously with the strain, and eventually, the deformation is dominated by the softening mechanism due to the formation of single fracture process zone [17]. The shock phenomenon in dynamic compression is caused by the localised dynamic densification of the collapsed cells leading to the overall increase of compressive stress and shock discontinuity [18]. Another observation from Fig.…”

Section: Stress-strain Relationshipmentioning

confidence: 87%

Strain-rate sensitivity of foam materials: A numerical study using 3D image-based finite element model

Sun

Withers

2015

EPJ Web of Conferences

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Abstract. Realistic simulations are increasingly demanded to clarify the dynamic behaviour of foam materials, because, on one hand, the significant variability (e.g. 20% scatter band) of foam properties and the lack of reliable dynamic test methods for foams bring particular difficulty to accurately evaluate the strain-rate sensitivity in experiments; while on the other hand numerical models based on idealised cell structures (e.g. Kelvin and Voronoi) may not be sufficiently representative to capture the actual structural effect. To overcome these limitations, the strain-rate sensitivity of the compressive and tensile properties of closed-cell aluminium Alporas foam is investigated in this study by means of meso-scale realistic finite element (FE) simulations. The FE modelling method based on X-ray computed tomography (CT) image is introduced first, as well as its applications to foam materials. Then the compression and tension of Alporas foam at a wide variety of applied nominal strain-rates are simulated using FE model constructed from the actual cell geometry obtained from the CT image. The stain-rate sensitivity of compressive strength (collapse stress) and tensile strength (0.2% offset yield point) are evaluated when considering different cell-wall material properties. The numerical results show that the rate dependence of cell-wall material is the main cause of the strain-rate hardening of the compressive and tensile strengths at low and intermediate strain-rates. When the strain-rate is sufficiently high, shock compression is initiated, which significantly enhances the stress at the loading end and has complicated effect on the stress at the supporting end. The plastic tensile wave effect is evident at high strain-rates, but shock tension cannot develop in Alporas foam due to the softening associated with single fracture process zone occurring in tensile response. In all cases the micro inertia of individual cell walls subjected to localised deformation is found to have negligible effect on the macro strain-rate sensitivity of Alporas foam.

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Spherical Waves and Cylindrical Waves

Cited by 27 publications

References 0 publications

Modeling and Experiments on Ballistic Impact into UHMWPE Yarns Using Flat and Saddle-Nosed Projectiles

Modeling and Experiments on Ballistic Impact into UHMWPE Yarns Using Flat and Saddle-Nosed Projectiles

Dynamic response of shear thickening fluid under laser induced shock

Strain-rate sensitivity of foam materials: A numerical study using 3D image-based finite element model

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