Research Papers

Effect of Curvature on Penetration Resistance of Polycarbonate Panels

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

Department of Biomedical Engineering and
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
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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Radin, J. , and Goldsmith, W. , 1988, “ Normal Projectile Penetration and Perforation of Layered Targets,” Int. J. Impact Eng., 7(2), pp. 229–259. [CrossRef]
Sands, J. , Patel, P. , Dehmer, P. , and Hsieh, A. , 2004, “ Protecting the Future Force: Transparent Materials Safeguard the Army's Vision,” AMPTIAC Q., 8, pp. 28–36.
Siviour, C. R. , Walley, S. M. , Proud, W. G. , and Field, J. E. , 2005, “ The High Strain Rate Compressive Behaviour of Polycarbonate and Polyvinylidene Difluoride,” Polymer, 46(26), pp. 12546–12555. [CrossRef]
Moy, P. , Weerasooriya, T. , Hsieh, A. , and Chen, W. , 2003, “ Strain Rate Response of a Polycarbonate Under Uniaxial Compression,” SEM Conference on Experimental Mechanics, T. Proulx , ed., Society for Experimental Mechanics, Bethel, CT, pp. 2–4. https://sem.org/wp-content/uploads/2015/12/sem.org-2003-SEM-Ann-Conf-s29p03-Strain-Rate-Response-Polycarbonate-Under-Uniaxial-Compression.pdf
Mulliken, A. D. , and Boyce, M. C. , 2006, “ Mechanics of the Rate-Dependent Elastic-Plastic Deformation of Glassy Polymers From Low to High Strain Rates,” Int. J. Solids Struct., 43(5), pp. 1331–1356. [CrossRef]
Mulliken, A. D. , 2006, Mechanics of Amorphous Polymers and Polymer Nanocomposites During High Rate Deformation, Massachusetts Institute of Technology, Cambridge, MA, p. 290.
Richeton, J. , Ahzi, S. , Daridon, L. , and Remond, Y. , 2005, “ A Formulation of the Cooperative Model for the Yield Stress of Amorphous Polymers for a Wide Range of Strain Rates and Temperatures,” Polymer, 46(16), pp. 6035–6043. [CrossRef]
Richeton, J. , Schlatter, G. , Vecchio, K. S. , Remond, Y. , and Ahzi, S. , 2005, “ A Unified Model for Stiffness Modulus of Amorphous Polymers Across Transition Temperatures and Strain Rates,” Polymer, 46(19), pp. 8194–8201. [CrossRef]
Richeton, J. , Ahzi, S. , Vecchio, K. S. , Jiang, F. C. , and Adharapurapu, R. R. , 2006, “ Influence of Temperature and Strain Rate on the Mechanical Behavior of Three Amorphous Polymers: Characterization and Modeling of the Compressive Yield Stress,” Int. J. Solids Struct., 43(7–8), pp. 2318–2335. [CrossRef]
Fleck, N. A. , Stronge, W. J. , and Liu, J. H. , 1990, “ High Strain-Rate Shear Response of Polycarbonate and Polymethyl Methacrylate,” Proc. R. Soc. London A, 429(1877), pp. 459–479. [CrossRef]
Ramakrishnan, K. R. , 2009, “ Low Velocity Impact Behaviour of Unreinforced Bi-Layer Plastic Laminates,” Australian Defence Force Academy, Canberra, Australia.
Rittel, D. , 2000, “ An Investigation of the Heat Generated During Cyclic Loading of Two Glassy Polymers—Part I: Experimental,” Mech. Mater., 32(3), pp. 131–147. [CrossRef]
Rittel, D. , and Rabin, Y. , 2000, “ An Investigation of the Heat Generated During Cyclic Loading of Two Glassy Polymers—Part II: Thermal Analysis,” Mech. Mater., 32(3), pp. 149–159. [CrossRef]
Rittel, D. , 1999, “ On the Conversion of Plastic Work to Heat During High Strain Rate Deformation of Glassy Polymers,” Mech. Mater., 31(2), pp. 131–139. [CrossRef]
Richeton, J. , Ahzi, S. , Vecchio, K. S. , Jiang, F. C. , and Makradi, A. , 2007, “ Modeling and Validation of the Large Deformation Inelastic Response of Amorphous Polymers Over a Wide Range of Temperatures and Strain Rates,” Int. J. Solids Struct., 44(24), pp. 7938–7954. [CrossRef]
Tervoort, T. , Smit, R. , Brekelmans, W. , and Govaert, L. E. , 1997, “ A Constitutive Equation for the Elasto-Viscoplastic Deformation of Glassy Polymers,” Mech. Time-Depend. Mater.,” 1(3), pp. 269–291. [CrossRef]
Boyce, M. C. , Parks, D. M. , and Argon, A. S. , 1988, “ Large Inelastic Deformation of Glassy-Polymers—1: Rate Dependent Constitutive Model,” Mech. Mater., 7(1), pp. 15–33. [CrossRef]
Varghese, A. G. , and Batra, R. C. , 2009, “ Constitutive Equations for Thermomechanical Deformations of Glassy Polymers,” Int. J. Solids Struct., 46(22–23), pp. 4079–4094. [CrossRef]
Varghese, A. G. , and Batra, R. C. , 2011, “ Strain Localization in Polycarbonates Deformed at High Strain Rates,” J. Polym. Eng., 31(6–7), pp. 495–519. [CrossRef]
Safari, K. H. , Zamani, J. , Ferreira, F. J. , and Guedes, R. M. , 2013, “ Constitutive Modeling of Polycarbonate During High Strain Rate Deformation,” Polym. Eng. Sci., 53(4), pp. 752–761. [CrossRef]
Chang, F. C. , and Chu, L. H. , 1992, “ Coexistence of Ductile, Semi-Ductile, and Brittle Fractures of Polycarbonate,” J. Appl. Polym. Sci., 44(9), pp. 1615–1623. [CrossRef]
Mills, N. , 1976, “ The Mechanism of Brittle Fracture in Notched Impact Tests on Polycarbonate,” J. Mater. Sci., 11(2), pp. 363–375. [CrossRef]
Fraser, R. , and Ward, I. , 1977, “ The Impact Fracture Behaviour of Notched Specimens of Polycarbonate,” J. Mater. Sci., 12(3), pp. 459–468. [CrossRef]
Allen, G. , Morley, D. , and Williams, T. , 1973, “ The Impact Strength of Polycarbonate,” J. Mater. Sci., 8(10), pp. 1449–1452. [CrossRef]
Rittel, D. , Levin, R. , and Maigre, H. , 1977, “ On Dynamic Crack Initiation in Polycarbonate Under Mixed-Mode Loading,” Mech. Res. Commun., 24(1), pp. 57–64. [CrossRef]
Plati, E. , and Williams, J. , 1975, “ Effect of Temperature on the Impact Fracture Toughness of Polymers,” Polymer, 16(12), pp. 915–920. [CrossRef]
Plati, E. , and Williams, J. , 1975, “ The Determination of the Fracture Parameters for Polymers in Impact,” Polym. Eng. Sci., 15(6), pp. 470–477. [CrossRef]
Adams, G. C. , Bender, R. G. , Crouch, B. A. , and Williams, J. G. , 1990, “ Impact Fracture-Toughness Tests on Polymers,” Polym. Eng. Sci., 30(4), pp. 241–248. [CrossRef]
Curran, D. R. , Shockey, D. A. , and Seaman, L. , 1973, “ Dynamic Fracture Criteria for a Polycarbonate,” J. Appl. Phys., 44(9), pp. 4025–4038. [CrossRef]
Rittel, D. , and Levin, R. , 1998, “ Mode-Mixity and Dynamic Failure Mode Transitions in Polycarbonate,” Mech. Mater., 30(3), pp. 197–216. [CrossRef]
Gunnarsson, C. A. , Weerasooriya, T. , and Moy, P. , 2011, “ Impact Response of PC/PMMA Composites,” Dynamic Behavior of Materials, Vol. 1, Springer, New York, pp. 195–209.
Kelly, P. M. , 2001, “ Lightweight Transparent Armour Systems for Combat Eyewear,” 19th International Symposium of Balllistics, Interlaken, Switzerland, pp. 7–11.
Dorogoy, A. , Rittel, D. , and Brill, A. , 2011, “ Experimentation and Modeling of Inclined Ballistic Impact in Thick Polycarbonate Plates,” Int. J. Impact Eng., 38(10), pp. 804–814. [CrossRef]
Shah, Q. H. , and Abakr, Y. A. , 2008, “ Effect of Distance From the Support on the Penetration Mechanism of Clamped Circular Polycarbonate Armor Plates,” Int. J. Impact Eng., 35(11), pp. 1244–1250. [CrossRef]
Shah, Q. H. , 2009, “ Impact Resistance of a Rectangular Polycarbonate Armor Plate Subjected to Single and Multiple Impacts,” Int. J. Impact Eng., 36(9), pp. 1128–1135. [CrossRef]
Livingstone, I. , Richards, M. , and Clegg, R. , 1999, “ Numerical and Experimental Investigation of Ballistic Performance of Transparent Armour Systems,” Lightweight Armour System Symposium (LASS), Shrivenham, UK.
Richards, M. , Clegg, R. , and Howlett, S. , 1999, “ Ballistic Performance Assessment of Glass Laminates Through Experimental and Numerical Investigation,” 18th International Symposium on Ballistics, pp. 1123–1130.
Hazell, P. J. , Roberson, C. J. , and Moutinho, M. , 2008, “ The Design of Mosaic Armour: The Influence of Tile Size on Ballistic Performance,” Mater. Design, 29(8), pp. 1497–1503. [CrossRef]
Antoine, G. , and Batra, R. , 2015, “ Low Velocity Impact of Flat and Doubly Curved Polycarbonate Panels,” ASME J. Appl. Mech., 82(4), p. 041003. [CrossRef]
Khalili, S. M. R. , Soroush, M. , Davar, A. , and Rahmani, O. , 2011, “ Finite Element Modeling of Low-Velocity Impact on Laminated Composite Plates and Cylindrical Shells,” Compos. Struct., 93(5), pp. 1363–1375. [CrossRef]
Gunnarsson, C. A. , Weerasooriya, T. , and Moy, P. , 2008, “ Measurement of Transient Full-Field, Out-of-Plane Back Surface Displacements of Polycarbonate During Impact,” 11th International Congress and Exposition on Experimental and Applied Mechanics, pp. 1403–1413.
Gunnarsson, C. A. , Ziemski, B. , Weerasooriya, T. , and Moy, P. , 2009, “ Deformation and Failure of Polycarbonate During Impact as a Function of Thickness,” International Congress and Exposition on Experimental Mechanics and Applied Mechanics, Society for Experimental Mechanics, Albuequerque, NM, June 1–4, Curran Assoc., Redhook, NY, pp. 1500–1511.
Batra, R. , and Peng, Z. , 1996, “ Development of Shear Bands During the Perforation of a Steel Plate,” Comput. Mech., 17(5), pp. 326–334. [CrossRef]
Batra, R. , and Chen, X. , 1994, “ Effect of Frictional Force and Nose Shape on Axisymmetric Deformations of a Thick Thermoviscoplastic Target,” Acta Mech., 106(1), pp. 87–105. [CrossRef]
Antoine, G. O. , and Batra, R. C. , 2015, “ Sensitivity Analysis of Low-Velocity Impact Response of Laminated Plates,” Int. J. Impact Eng., 78(4), pp. 64–80. [CrossRef]


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Fig. 1

Sketch of the impact problem studied

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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. 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. 4

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

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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. 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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