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Research Papers

Effect of Curvature on Penetration Resistance of Polycarbonate Panels

[+] Author and Article Information
G. O. Antoine

Department of Biomedical Engineering and
Mechanics,
M/C 0219,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: antoineg@vt.edu

R. C. Batra

Fellow ASME
Department of Biomedical Engineering and
Mechanics,
M/C 0219,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: rbatra@vt.edu

1Corresponding author.

Manuscript received May 31, 2016; final manuscript received August 22, 2016; published online September 13, 2016. Assoc. Editor: Weinong Chen.

J. Appl. Mech 83(12), 121002 (Sep 13, 2016) (12 pages) Paper No: JAM-16-1274; doi: 10.1115/1.4034520 History: Received May 31, 2016; Revised August 22, 2016

Three-dimensional transient deformations of clamped flat and doubly curved polycarbonate (PC) panels impacted by a rigid smooth hemispherical-nosed circular cylinder have been numerically studied by the finite-element (FE) method to delineate effects of the panel radius of curvature to its thickness ratio on their penetration resistance. The PC is modeled as thermoelastoviscoplastic with the effective plastic strain rate depending upon the hydrostatic pressure. The effective plastic strain of 3.0 at failure is ascertained by matching for one set of flat panels the computed and the experimental minimum perforation speeds. It is found that a negative curvature (i.e., the center of curvature toward the impactor) of a panel degrades its penetration performance, and the positive curvature enhances it especially for thin panels with thickness/radius of curvature of 0.01. However, the benefit is less evident for panels with the panel thickness/radius of curvature of 0.04 or more. For positively curved thin panels, an elastic hinge forms around the central impacted area during an early stage of deformations, and subsequent deformations occur within this region. No such hinge is observed for flat plates, negatively curved panels of all the thicknesses, and positively curved thick panels. Furthermore, the maximum effective stress induced in regions surrounding the impacted area is less for positively curved panels than that for flat panels. The dominant failure mechanism is found to be the deletion of failed elements due to the effective plastic strain in them exceeding 3.0 rather than due to plug formation. For an example problem, the dependence of the effective plastic strain rate upon the hydrostatic pressure and the consideration of the Coulomb friction at the contact surfaces exhibited minimal effects on the penetration characteristics. This information should be useful for designers of impact-resistant transparent armor, such as an airplane canopy, automobile windshield, and goggles.

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Figures

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Fig. 1

Sketch of the impact problem studied

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Fig. 4

Deformed shapes and plastic strain distributions in 4.45-mm thick panels for 72 m/s impact speed

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Fig. 2

Time histories of the impactor KE and of the plate internal, kinetic, and erosion energies for the impact of the 5.85-mm thick flat PC plate at 100 m/s. KE, kinetic energy; IE, internal (elastic + plastic) energy; and EE, eroded energy.

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Fig. 5

Time histories of the internal, the kinetic, and the eroded energies of the 4.45-mm thick panels for 72 m/s impact velocity

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Fig. 6

Time histories of the effective stress at the centers of the plate top, the mid, and the bottom faces of the panels with h = 4.45 mm and different curvatures (impact speed = 72 m/s)

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Fig. 7

Time histories of the effective stress at the center of the 12.32-mm thick plate's top, mid, and bottom faces and different curvatures for the impact speed of 115 m/s

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Fig. 8

Average axial stress and average axial stretch for the 4.45-mm thick panels and 72 m/s impact velocity as a function of the initial arc length (measured from the panel center)

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Fig. 3

Contact force as a function of time for 4.45-mm thick positively curved PC panels with R = 127 mm impacted at 72 m/s with different values of the friction coefficient

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Fig. 9

Average axial stress and the difference between the axial stress on the top and on the bottom surfaces of the (a) 3 mm, (b) 4.45 mm, (c) 5.85 mm, (d) 9.27 mm, and (e) 12.32 mm thick panels as a function of the initial arc length measured from the panel centroid. For each panel thickness, the impact velocity equals the V50 of the flat plate, i.e., 62.5, 72, 80, 100, 100, and 115 m/s, respectively, for (a)–(e).

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Fig. 10

Normalized impactor energy for perforation as a function of the panel curvature

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Fig. 11

For an impact speed of 72 m/s, the deformed shape in the 4.45-mm thick positively curved panel (R = 127 mm) at t = 1.6 ms (a) and (b), in the flat plate at t = 1 ms (c), and of positively curved 12.32-mm thick panel at t = 0.4 ms (d). There is no hinge formed in both the flat plate and the positively curved thick panel.

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Fig. 12

Time history of the effective strain at the hinge in the 4.45-mm thick positively curved panel (R = 127 mm) impacted at 72 m/s

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Fig. 13

Deformed shapes and plastic strain distributions in the 4.45-mm thick flat and positively curve panels (R = 127 mm) for 72 m/s impact speed with and without considering the effect of the pressure on the plastic multiplier in the PC constitutive relation. For each plot, the left part is obtained with pressure coefficients αpα=0.128 and αpβ=0.254, and the right part with αpα=αpβ=0.

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