Geometric statistics and dynamic fragmentation

Grady, D. E.; Kipp, M.E.

doi:10.1063/1.336139

Cited by 288 publications

(172 citation statements)

References 23 publications

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“…Exponential type forms for fragmenting metals are generally considered to arise from uncorrelated nucleation of failure points or cracks governed by Poisson statistics. The distributions of Grady and Kipp 5,6 and Mott and Linfoot 7 are widely used for high strain-rate fragmentation processes in which there is a characteristic length or mass scale.…”

Section: Introductionmentioning

confidence: 99%

Impact fragmentation of aluminum reactive materials

Hooper

2012

Journal of Applied Physics

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We report the fragmentation of brittle, granular aluminum spheres following high velocity impact (0.5-2.0 km/s) on thin steel plates. These spheres, machined from isostatically pressed aluminum powder, represent a prototypical metallic reactive material. The fragments generated by the impacts are collected in a soft-catch apparatus and analyzed down to a length scale of 44 lm. With increasing velocity, there is a transition from an exponential Poisson-process fragment distribution with a characteristic length scale to a power-law behavior indicative of scale-invariance. A normalized power-law distribution with a finite size cutoff is introduced and used to analyze the number and mass distributions of the recovered fragments. At high impact velocities, the power-law behavior dominates the distribution and the power-law exponent is identical to the universal value for brittle fragmentation discussed in recent works. The length scale at which the power-law behavior decays is consistent with the idea that the length of side microbranches or damage zones from primary cracks is governing this cutoff. The transition in fragment distribution at high strain-rates also implies a significant increase in small fragments that can rapidly combust in an ambient atmosphere.

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Section: Introductionmentioning

confidence: 99%

Impact fragmentation of aluminum reactive materials

Hooper

2012

Journal of Applied Physics

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“…47 The fragments (clusters) follow the Poisson distribution if the occurrence of a fragment is random. The probability of finding a fragment of length between l and l + dl is found to be…”

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confidence: 99%

Coulomb-driven cluster-glass behavior in Mn-intercalated Ti1+yS2

et al. 2012

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“…Because solid fragmen- tation typically results in a broad distribution of fragment sizes, with breaks occurring at apparently random locations, a statistical approach is usually taken [14,15]. The breakup of a rod under impact is known to give rise to broad distributions of fragment sizes [16,17], with a highly skewed shape and a long tail, a phenomenology also encountered in other contexts, including liquid sprays [18].…”

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confidence: 99%

Dynamic Buckling and Fragmentation in Brittle Rods

et al. 2005

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We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength λ for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials, buckling leads to the fragmentation of the rod. Measured fragment length distributions show two clear peaks near λ/2 and λ/4. The non-monotonic nature of the distributions reflect the influence of the deterministic buckling process on the more random fragmentation processes.Long, thin supports are ubiquitous in natural and engineered load bearing structures, from spider legs to the steel struts of a skyscraper [1,2]. A single rod will buckle if too much force is applied along its axis, which can lead to the catastrophic failure of the structure. The buckling instability is seen at all sizes, from pole vaulting [3] to protein microtubules confined in vesicles [4] and carbon nanotube atomic force microscope probes [5]. While the classic Euler buckling of a rod is due to a static axial load [6], a different physical process occurs when the stress is applied suddenly, as during impact [7,8,9]. In this Letter, we show that this "dynamic buckling" [10] obeys a simple scaling law, which we derive by combining the approach of Saint-Venant with the classical theory of elastic rods [6,7]. For brittle rods, buckling often leads to breaking, for which we find the distribution of fragment lengths displays a unique non-monotonic shape reflecting the primary buckling instability.The process of dynamic buckling and subsequent fragmentation is illustrated in Fig. 1, in which a falling weight strikes an upright brittle rod (dry pasta). Within a fraction of a millisecond after impact, a sinusoidal perturbation appears (Fig. 1b), much different than the halfwavelength seen in Euler buckling. A few tenths of a millisecond later, the pasta has buckled appreciably and begins to shatter (Fig. 1c). This imparts angular momentum of alternating signs to the fragments, which rotate and scatter (Fig. 1d-f).Our experimental setup consists of a simple metal holder for the rod, and a pneumatic cannon in which a pressure reservoir at 60 psi delivers an impulse to a steel cylindrical projectile (1.46 cm diameter, 24.9 or 10.0 g) held at the end of a 1.5 m acrylic tube with two magnets. The holder rests on a steel plate in a sandbox which serves as a shock absorber to stop the projectile. The buckling and fragmentation dynamics were imaged by a high speed digital video camera (Phantom v5.0), capable of capturing up to 62,000 frames per second. The speed of the projectile was also measured just before impact using the video system. The materials used included dry pasta (ρ = 1.5 g/cm 3 , d = 1.1 mm and 1.9 mm) [11], borosilicate glass (ρ = 2.4 g/cm 3 , d = 2.0 mm), type 303 stainless steel (ρ = 7.9 g/cm 3 , d = 1.6 mm), and teflon (PTFE) (ρ = 2.2 g/cm 3 , d = 2.0...

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Geometric statistics and dynamic fragmentation

Cited by 288 publications

References 23 publications

Impact fragmentation of aluminum reactive materials

Impact fragmentation of aluminum reactive materials

Coulomb-driven cluster-glass behavior in Mn-intercalated Ti1+yS2

Dynamic Buckling and Fragmentation in Brittle Rods

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