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Dynamic buckling and fragmentation in brittle rods.
J R Gladden1, N Z Handzy, A Belmonte
1W. G. Pritchard Laboratories, Department of Mathematics, Penn State University, University Park, Pennsylvania 16802, USA.
Physical Review Letters
|February 9, 2005
Summary
Projectile impact causes slender rods to buckle and fragment. We identified a preferred buckling wavelength and scaling law, observing distinct fragment patterns in brittle materials.
Area of Science:
- Solid Mechanics
- Materials Science
- Impact Dynamics
Background:
- Slender rods are susceptible to buckling under axial load.
- Projectile impact introduces complex dynamic forces.
- Understanding fragmentation is crucial for material failure analysis.
Purpose of the Study:
- To investigate the dynamic buckling and fragmentation of slender rods under axial projectile impact.
- To derive and experimentally verify a preferred buckling wavelength and scaling law.
- To analyze fragment length distributions in brittle materials.
Main Methods:
- Experimental impact tests on rods of various materials (Teflon, pasta, glass, steel).
- Application of Saint-Venant and elastic beam theory to model buckling.
- Analysis of fragment length distributions using statistical methods.
Main Results:
- A preferred buckling wavelength (lambda) was derived and experimentally confirmed.
- A scaling law for buckling instability was verified across different materials.
- Fragment length distributions in brittle materials exhibited two peaks near lambda/2 and lambda/4.
Conclusions:
- The study successfully links elastic beam theory to dynamic buckling phenomena.
- Buckling instability is a deterministic precursor to fragmentation in brittle rods.
- Fragment patterns provide insights into the interplay between deterministic and stochastic failure processes.