Abstract
A series of experiments has been conducted, utilizing sheet explosive opplied to clamped aluminum beams, with a neoprene buffer. As the load is monotonically increased, three damage modes are identified, which respecitively are major inelastic deformation, tearing at the extreme fiber, and transverse shear at the support.
Satisfactory correlation is reported for the extent of inelastic deformation using a lumped parameter, finite-difference code; thresholds for tearing and shear failure based on empirical criteria are presented. Using a Timoshenko beam theory, the shear threshold appears to be dependent on the section velocity, rather than upon the shear stress.
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Abbreviations
- c 2 :
-
propagation speed for shear waves (in./s)
- G :
-
shear modulus (ksi)
- h :
-
beam thickness (in.)
- H.E.:
-
high explosive (as abbreviation)
- I :
-
impulse intensity (ktaps)*
- I 0ε :
-
reference impulse, arbitrary strain, eq (1) (ktaps)†
- I 05 :
-
reference impulse, 5 percent strain, eq (1) (ktaps)†
- i :
-
subscript indicating material layer
- K ε :
-
defined by eq (3) (in./s)
- L :
-
beam length (in.)
- r :
-
radius of\(\sqrt {h^2 /12} (in.)\)
- \(\bar t\) :
-
time (s)
- t :
-
\({{\bar t} \mathord{\left/ {\vphantom {{\bar t} t}} \right. \kern-\nulldelimiterspace} t}_R \) (dimensionless)
- t R :
-
L/c 2 (s)
- \(\bar x\) :
-
distance along beam (in.)
- x :
-
\({{\bar x} \mathord{\left/ {\vphantom {{\bar x} L}} \right. \kern-\nulldelimiterspace} L}\) (dimensionless)
- \(\bar v_o \) :
-
initial average beam velocity (in./s)
- v o :
-
\({{\bar v_o } \mathord{\left/ {\vphantom {{\bar v_o } c}} \right. \kern-\nulldelimiterspace} c}_2 \) (dimensionless)
- Δ:
-
residual central deflection of beam (in.)
- ε:
-
strain (in./in.)
- λ:
-
slenderness ratio=L/r (dimensionless)
- μ:
-
defined by eq (3) (lbf-s2/in.3)
- ρ:
-
mass density (lbf-s2/in.4)
- σ:
-
uniaxial tensile stress (ksi)
- \(\bar \tau \) :
-
shear stress (ksi)
- τ:
-
\({{\bar \tau } \mathord{\left/ {\vphantom {{\bar \tau } G}} \right. \kern-\nulldelimiterspace} G}\) (dimensionless)
References
Costantino, C. J., “Two-Dimensional Wave Propagation through Non-Linear Media,”J. of Computational Phys.,4 (2),147–170 (Aug. 1969).
Symonds, P. S. andMentel, S., “Impulsive Loading of Plastic Beams with Axial Constraints,”J. of the Mech. and Phys. of Solids,6,186–202 (1958).
Florence, A. L. andFirth, R. D., “Rigid Plastic Beams under Uniformly Distributed Impulses,”J. of Appl. Mech.,32 (3),481–488 (Sept. 1965).
Humphreys, John S., “Plastic Deformation of Impulsively Loaded Straight Clamped Beams,”J. of Appl. Mech.,32 (1),7–10 (March 1965).
Lindholm, U. S. and Bessey, R. L., Elastic-viscoplastic Response of Clamped Beams under Uniformly Distributed Impulse, Southwest Research Inst. Tech. Report AFML-TR-68-396, San Antonio, TX (Jan. 1969).
Witmer, Emmett A., Balmer, Hans A., Leech, John W. andPian, T. H. H., “Large Dynamic Deformations of Beams, Rings, Plates and Shells,”AIAA J.,1 (8),1848–1857 (1963).
Balmer, Hans A., Improved Computer Programs DEPROSS 1, 2 and 3, M.I.T., Aeroelastic Structures Res. Lab. Tech. Report 128-3, Cambridge, MA (Aug. 1965).
Volterra, E. and Zachmanoglou, E. C., Dynamics of Vibrations, Charles E. Merrill, Columbus, OH, 528–529 (1965).
Prescott, J., “Elastic Waves and Vibrations of Thin Rods,”Phil. Mag.,33 (225),703–754 (Oct. 1942).
Leonard, R. W. and Budiansky, B., On Traveling Waves in Beams, NACA Tech. Note 2874, Washington, DC (1953).
Dengler, M. A. and Goland, M., “Transverse Impact of Long Beams, including Rotatory Inertia and Shear Effects,” Proc. First U. S. Nat. Cong. Appl. Mech. (Chicago, IL 1951), published by ASME, New York, 179–186 (1952).
Boley, B. A. andChao, C. C., “Some Solutions of the Timoshenko Beam Equations,”ASME Trans., J. of Appl. Mech.,77,579–586 (1955).
Zajac, E. E., Flexural Waves in Beams, PhD Thesis, Stanford Univ. (1954).
Plass, H. J., “Some Solutions for the Timoshenko Beam Equation for Short Pulse-Type Loading,”ASME Trans., J. of Appl. Mech.,80,379–384 (1958).
Chuo, P. S. and Mortimer, R., A Unified Approach to One-Dimensional Elastic Waves by the Method of Characteristics, Drexel Inst. of Technology Report 160-8, Philadelphia, PA (1966).
Jones, R. P. N., “Transient Flexural Stresses in an Infinite Beam,”Quart. J. of Mech. and Appl. Math.,8,373–384 (1955).
Meirovitch, L., Analytical Methods in Vibrations, MacMillan, London, 128–135 (1967).
Anderson, R. A., “Flexural Vibrations in Uniform Beams According to the Timoshenko Theory,”ASME Trans., J. of Appl. Mech.,75,504–511 (1953).
Thomson, W. T., Vibration Theory and Applications, Prentice-Hall, Englewood Cliffs, NJ, 307–309 (1965).
Garrelick, J., Analytical Investigation of Wave Propagation and Reflection in Timoshenko Beams, PhD Thesis, City College of New York (1969).
Bleich, H. H. and Shaw, R., Dominance of Shear Stresses in Early Stages of Impulsive Motion of Beams, Columbia Univ. Tech. Report 20 to ONR, Project NR 360.002 (Oct. 1957).
Karunes, B. andOnat, E. T., “On the Effect of Shear on Plastic Deformation of Beams under Transverse Impact Loading,”J. of Appl. Mech.,27 (1),107–109 (March 1960).
Sliter, G. et al, Warhead Optimization for the Structural Kill of Reentry Vehicles, Defense Atomic Supply Agency Tech. Report 2215, Washington, DC (July 1969).
Thurston, R. et al, Project Sunburst; Canned Ball; Volume II, Phase I; Experimental Results and Calculations, Los Alamos Tech. Report 4715, Los Alamos, NM (April 1972).
Clark, E. N. et al, Plastic Deformation of Structures, I: Beams, Air Force Flight Dynamics Lab. Tech. Report 64-64, Picatinny Arsenal, Dover, NJ (May 1965).
Seaman, L., SRI PUFF 3 Computer Code for Stress Wave Propagation, Tech. Report No. AFWL-TR-70-51, Air Force Weapons Lab., Kirtland AFB NM (Sept. 1970).
Flugge, W., Stresses in Shells, Springer-Verlag, Berlin, 219–233 (1960).
Forsberg, K., Review of Analytical Methods used to Determine the Modal Characteristics of Cylindrical Shells, NASA Admin. Report CR-613, Washington, DC (Sept. 1966).
Fisher, S. and Menkes, S. B., The Dynamic Response of Finite Elastic Cylinders, CUNY Tech. Report 68-15, City University of New York, 13–18 (Aug. 1968).
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Menkes, S.B., Opat, H.J. Broken beams. Experimental Mechanics 13, 480–486 (1973). https://doi.org/10.1007/BF02322734
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DOI: https://doi.org/10.1007/BF02322734