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Broken beams

Tearing and shear failures in explosively loaded clamped beams

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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)

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Authors and Affiliations

  1. Mechanical Engineering, The City College of New York, 10031, N. Y.

    S. B. Menkes (Professor)

  2. Picatinny Arsenal, NDED, TASB, 07801, Dover, N. J.

    H. J. Opat (Senior Research Physicist)

Authors
  1. S. B. Menkes
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  2. H. J. Opat
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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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