Close Range Explosive Loading on Steel Column in the Framework of Anisotropic Viscoplasticity
Abstract
1. Introduction
2. Constitutive Assumptions
2.1. Introductory Remarks
2.2. Description of the Surrounding Air and the Condensed Charge
2.3. Behavior of the Steel Column
- (i)
- Existence of the free energy function . Formally, we apply the following form (cf. [53] for extensive discussion on such an assumption):
- (ii)
- The axiom of objectivity (spatial covariance). The material model should be invariant with respect to any superposed motion (diffeomorphism).
- (iii)
- The axiom of the entropy production. For every regular process the constitutive functions should satisfy the second law of thermodynamics.
- (iv)
- The evolution equation for the internal state variable vector should be of the form:
- (i)
- the field equations:
- (ii)
- the boundary conditions:
- (a)
- displacement is prescribed on a part of and tractions are prescribed on a part of , where and ,
- (b)
- heat flux is prescribed on , and
- (iii)
- the initial conditions are given for each particle at ,
- The elastic range is isotropic and independent of microdamage state, thus (for more general setup cf. [24]):
- The thermal expansion is isotropic, thus:
- The rate dependence of fracture porosity has the form [24]:
- The normalised directions of viscoplastic flow, under the above assumptions, are defined as:
- The microdamage mechanism assumes the growth term only ( while nucleation is replaced by the initial microdamage distribution assumption), therefore taking the additional assumptions [16,62]: (i) Velocity of the microdamage growth is coaxial with the principal directions of the stress state, and (ii) only positive (tension) principal stresses induces the growth of the microdamage, one has:
- The tensor is a symmetric part of the fourth order unity tensor [16]:
- Lastly, for temperature evolution, the following relation is considered:
3. Numerical Prediction of Blast Effect on Steel Column
3.1. Introductory Remarks
- After the ignition moment in the centre of the explosive, the combustion wave goes through the charge domain, and then releases a high amount of kinetic and thermal energies;
- the transition phase generates a high pressure wave on the charge and ambient boundaries; and
- finally, the pressure reaches the obstacle boundaries and induces the thermomechanical process within its bounds, which is of strong wave character.
3.2. Steel Column Modeling Assumptions
3.3. Results
- High quality of the numerical results symmetry is observed,
- equivalent plastic strains are locally as high as ca. in the strain localization zones,
- the temperature in the strain localization zones is as high as ca. 800 C,
- the evolution of the porosity is restricted to the zones of high plastic strains,
- thermal stresses can be locally as high as 2000 MPa or more,
- the displacement field is localised in the zone of the evolving flying fragment, whereas in the remaining part for ms reaches ca. m,
- the strain hardening causes the Huber–Mises–Hencky stresses to be as high as ca. 900 MPa, and
- air pressure is highly scattered in the fluid domain and reaches locally 150 MPa (161 MPa according to the standards cf. [20]).
4. Experimental Validation
- High-speed camera Phantom v711 with mobile stand,
- Bosch GLM 80 Professional Laser Rangefinder, and
- ICP Free-field Blast Pressure “Pencil” Probe.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Jones–Wilkins–Lee (JWL) Properties for TNT Explosive | ||
---|---|---|
A | Pa | |
B | Pa | |
- | ||
- | ||
- | ||
6930 | ||
1630 | ||
0 | Pa·s | |
Ideal gas (IG) properties for Ambient Air | ||
R | 287 | |
101,325 | ||
0 | ||
Pa·s |
Material Parameters for S355 Steel | |||
---|---|---|---|
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Sielicki, P.W.; Sumelka, W.; Łodygowski, T. Close Range Explosive Loading on Steel Column in the Framework of Anisotropic Viscoplasticity. Metals 2019, 9, 454. https://doi.org/10.3390/met9040454
Sielicki PW, Sumelka W, Łodygowski T. Close Range Explosive Loading on Steel Column in the Framework of Anisotropic Viscoplasticity. Metals. 2019; 9(4):454. https://doi.org/10.3390/met9040454
Chicago/Turabian StyleSielicki, Piotr Witold, Wojciech Sumelka, and Tomasz Łodygowski. 2019. "Close Range Explosive Loading on Steel Column in the Framework of Anisotropic Viscoplasticity" Metals 9, no. 4: 454. https://doi.org/10.3390/met9040454
APA StyleSielicki, P. W., Sumelka, W., & Łodygowski, T. (2019). Close Range Explosive Loading on Steel Column in the Framework of Anisotropic Viscoplasticity. Metals, 9(4), 454. https://doi.org/10.3390/met9040454