Abstract
An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined.
It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.
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Abbreviations
- 2h :
-
plate thickness, in.
- R :
-
radius of the unclamped part of the plate, in.
- r,z :
-
cylindrical coordinates
- σ r , σφ :
-
radial and tangential principal stresses, lb-in−2
- ∈ r , ∈φ :
-
radial and tangential principal strains
- M r,M ϕ :
-
radial and tangential bending moments, lb-in.
- И r , Иφ :
-
radial and tangential curvatures
- E :
-
Young's elastic modulus, lb-in−2
- E sec :
-
secant modulus, lb-in−2
- σYD :
-
uniaxial dynamic yield stress, lb-in−2
- σY S :
-
uniaxial static yield stress, lb-in−2
- t :
-
time, sec
- T :
-
duration of the stress pulse, sec
- P *,p * :
-
force and stress due to the stress pulse, lb and lb-in−2
- P, p :
-
actual force and stress acting on the plate due to the pulse, lb and lb-in−2
- P o :
-
limit load or static collapse load, lb
- ρ:
-
dimensionless radial coordinate
- ω(r,t):
-
deflection of the plate, in
- δ:
-
central deflection of the plate, in
- a :
-
radius of the loading area, in
- v(r,t) :
-
velocity of plate middle surface, in.-sec−1
- V :
-
impact velocity, in.-sec−1
- ν:
-
Poisson's ratio
- D :
-
flexural rigidity
- γ:
-
Euler's constant=0.577
- μp :
-
specific density of plate material, lb-in−3
- μb :
-
specific density of bar material, lb-in−3
- β:
-
coupling paramter
- τ:
-
material relaxation time, sec
- A :
-
area of shock bar,P=p/A, in2
- W :
-
work done on the plate, in.-lb
- E o :
-
kinetic energy of the impact bar
- L 1 :
-
length of impact bar, in
- c :
-
longitudinal wave velocity, in.-sec−1
- ψ, λ:
-
eigen function and eigen value
- D v :
-
visco-plastic flexural rigidity
References
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Wilshaw, T.R., Kelley, J.M. Response of circular clamped plates to square-wave stress pulses. Experimental Mechanics 8, 450–458 (1968). https://doi.org/10.1007/BF02327409
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DOI: https://doi.org/10.1007/BF02327409