Mechanisms of dynamic fragmentation: Factors governing fragment size

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

doi:10.1016/0167-6636(85)90028-6

Cited by 69 publications

(63 citation statements)

References 6 publications

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“…The fragmentation of materials under high rate expansion has been treated extensively by Grady and co-workers [50][51][52][53][54]. The theoretical prediction of fragment size S when solid spall is dominated by flow stress is given by the Grady-Kipp (G-K) theory for ductile materials.…”

Section: Fragment Size Modelingmentioning

confidence: 99%

Laser shock-induced spalling and fragmentation in vanadium

et al. 2010

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Section: Fragment Size Modelingmentioning

confidence: 99%

Laser shock-induced spalling and fragmentation in vanadium

et al. 2010

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“…The critical question is: given a material and loading rate, what will be the fragment size distribution? Assuming that the local kinetic energy is responsible for creating new surfaces, Grady (1982) and Grady and Kipp (1985) predicted that the (average) fragment size decrease with increasing strainrate and material brittleness. Glenn and Chudnovsky (1986) introduced a correction term into Grady's theory that accounts for the stored elastic energy before failure, and predicted a quasistatic average fragment size that is independent of strain-rate.…”

Section: Introductionmentioning

confidence: 99%

Effects of material properties on the fragmentation of brittle materials

2006

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We present a fundamental investigation of the influence of material and structural parameters on the mechanics of fragmentation of brittle materials. First, we conduct a theoretical analysis (similar to Drugan's single wave problem, Drugan, W..) and obtain closed form solutions for a problem coupling stress wave propagation and single cohesive crack growth. Expressions for a characteristic fragment size s 0 and a characteristic strain-rateε 0 are given. Next, we use a numerical approach to analyze a realistic fragmentation process that involves multiple crack interactions. The average fragment size s is calculated for a wide variety of strain-ratesε and a broad range of material parameters. Finally, we derive an empirical function that relates the normalized fragment size s/s 0 to the normalized strain-rateε/ε 0 and that fits all of the numerical results with a single master curve.

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“…Several researchers have suggested seeding material properties with variability in numerical simulations to capture such effects (e.g. [42][43][44]). For this example, the initial yield stress is perturbed.…”

Section: Example: Fragmenting Ringmentioning

confidence: 99%

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

Bishop

Strack

2011

Numerical Meth Engineering

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SUMMARYA novel method is presented for assessing the convergence of a sequence of statistical distributions generated by direct Monte Carlo sampling. The primary application is to assess the mesh or grid convergence, and possibly divergence, of stochastic outputs from non-linear continuum systems. Example systems include those from fluid or solid mechanics, particularly those with instabilities and sensitive dependence on initial conditions or system parameters. The convergence assessment is based on demonstrating empirically that a sequence of cumulative distribution functions converges in the L ∞ norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov-Smirnov statistic. The statistical method is independent of the underlying distributions.The statistical method is demonstrated using two examples: (1) the logistic map in the chaotic regime, and (2) a fragmenting ductile ring modeled with an explicit-dynamics finite element code. In the fragmenting ring example the convergence of the distribution describing neck spacing is investigated. The initial yield strength is treated as a random field. Two different random fields are considered, one with spatial correlation and the other without. Both cases converged, albeit to different distributions. The case with spatial correlation exhibited a significantly higher convergence rate compared with the one without spatial correlation.

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Mechanisms of dynamic fragmentation: Factors governing fragment size

Cited by 69 publications

References 6 publications

Laser shock-induced spalling and fragmentation in vanadium

Laser shock-induced spalling and fragmentation in vanadium

Effects of material properties on the fragmentation of brittle materials

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

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