Abstract
PVB laminated glass is a kind of typical laminated composite material and its crack characteristics are of great interest to vehicle manufacturers, safety engineers, and accident investigators. Because crack morphology on laminated windshield contains important information on energy mitigation, pedestrian protection, and accident reconstruction. In this chapter, we investigated the propagation characteristics for both radial and circular cracks in PVB laminated glasses by theoretical constitutive equations analysis, numerical simulation, experiments, and tests of impact. A damage-modified nonlinear viscoelastic constitutive relations model of PVB laminated glass were developed and implemented into FEA software to simulate the pedestrian head impact with vehicle windshield. Results showed that shear stress, compressive stress, and tensile stress were main causes of plastic deformation, radial cracks, and circumferential cracks for the laminated glass subject to impactor. In addition, the extended finite element method (XFEM) was adopted to study the multiple crack propagation in brittle plates. The effects of various impact conditions and sensitivity to initial flaw were discussed. For experiment analysis, crack branching was investigated and an explicit expression describing the crack velocity and number of crack branching is proposed under quasi-static Split Hopkinson Pressure Bar (SHPB) compression experiments. And the radial crack propagation behavior of PVB laminated glass subjected to dynamic out of - plane loading was investigated. The steady-state cracking speed of PVB laminated glass was lower pure glass, and it increased with higher impactor speed and mass. The supported glass layer would always initiate before the loaded layer and the final morphologies of radial cracks on both sides are completely overlapped. Two different mechanisms of crack propagation on different glass layers explained the phenomenon above. Then further parametric dynamic experiments study on two dominant factors, i.e., impact velocity and PVB thickness are investigated: Firstly, a semiphysical model describing the relationship between the maximum cracking velocity and influential factors was established; Then the Weibull statistical model was suggested considering various factors to describe the macroscopic crack pattern in this chapter; Finally, the relation between radial crack velocity and crack numbers on the backing glass layer and the relation between the crack length and the capability of energy absorption on the impacted glass layer were proposed.
Similar content being viewed by others
References
A. Berezovski, G.A. Maugin, On the propagation velocity of a straight brittle crack. Int. J. Fract. 143, 135–142 (2007)
P.A.D. Bois, S. Kolling, W. Fassnacht, Modelling of safety glass for crash simulation. Comput. Mater. Sci. 28, 675–683 (2003)
E. Bouchaud, J.P. Bouchaud, J.P.S.G. Lapasset, The statistics of crack branching during fast crack propagation. Fractals-Compl. Geom. Patterns Scaling Nat. Soc. 1, 1051–1058 (2012)
J. Chen, J. Xu, X. Yao, B. Liu, X. Xu, Y. Zhang, Y. Li, Experimental investigation on the radial and circular crack propagation of PVB laminated glass subject to dynamic out-of-plane loading. Eng. Fract. Mech. 112–113, 26–40 (2013)
B.E. Clements, J.N. Johnson, R.S. Hixson, Stress waves in composite materials. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdisc. Top. 54, 6876–6888 (1996)
N.P. Daphalapurkar, H. Lu, D. Coker, R. Komanduri, Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method. Int. J. Fract. 143, 79–102 (2007)
S.K. Dwivedi, H.D. Espinosa, Modeling dynamic crack propagation in fiber reinforced composites including frictional effects ☆. Mech. Mater. 35, 481–509 (2003)
F. Zhigang and Z. Jianping, On the viscoelastic finite element method, Shanghai J. Mech. 16(1), 20–26 (1995)
U. Fischer, K. Washizu, Variational Methods in Elasticity & Plasticity, 3rd edn. (Pergamon Press, Oxford/New York, 1982.) XV, 630 S., £ 40.00. US $ 100.00. ISBN 0 08 026723 8, Zamm Journal of Applied Mathematics & Mechanics Zeitschrift Für Angewandte Mathematik Und Mechanik, 64 (1984) 70–71
P. Forquin, F. Hild, A probabilistic damage model of the dynamic fragmentation process in brittle materials. Adv. Appl. Mech. 44, 1–72 (2010)
D. Grégoire, H. Maigre, A. Combescure, New experimental and numerical techniques to study the arrest and the restart of a crack under impact in transparent materials. Int. J. Solids Struct. 46, 3480–3491 (2009)
J.A. Hauch, M.P. Marder, Energy balance in dynamic fracture, investigated by a potential drop technique. Int. J. Fract. 90, 133–151 (2010)
J. Lambros, A.J. Rosakis, Dynamic crack initiation and growth in thick unidirectional graphite/epoxy plates. Compos. Sci. Technol. 57, 55–65 (1997)
B. Lawn, R. Wilshaw, Review: indentation fracture: principles and applications. J. Mater. Sci. 10, 1049–1081 (1975)
J.W. Lee, I.K. Lloyd, H. Chai, Y.G. Jung, B.R. Lawn, Arrest, deflection, penetration and reinitiation of cracks in brittle layers across adhesive interlayers. Acta Mater. 55, 5859–5866 (2007)
W. Lili, Z. Xixiong, S. Shaoqiu, G. Su, and B. Hesheng, An impact dynamics investigation on some problems in bird strike on windshields of high speed aircrafts. Acta Aeromauticaet Astronautica Sinica, 12(2), B27–B33 (1991)
B.B. Mandelbrot, Fractal geometry of nature. WH Freeman and Company (1983)
M.A. Martínez, I.S. Chocron, J. Rodríguez, V.S. Gálvez, L.A. Sastre, Confined compression of elastic adhesives at high rates of strain. Int. J. Adhes. Adhes. 18, 375–383 (1998)
B. Michel, L.B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, Cambridge, 1990.) XVII, 563 pp., L 40.00 H/b. ISBN 0-521-30330-3 (Cambridge Monographs on Mechanics and Applied Mathematics), Zeitschrift Angewandte Mathematik Und Mechanik, 72 (1992) 383–384
J.H. Nielsen, J.F. Olesen, H. Stang, The fracture process of tempered soda-lime-silica glass. Exp. Mech. 49, 855–870 (2009)
H. Park, W.W. Chen, Experimental investigation on dynamic crack propagating perpendicularly through interface in glass. J Appl. Mech-t ASME 78(5) (2011)
K. Ravi-Chandar, W.G. Knauss, An experimental investigation into dynamic fracture: IV. On the interaction of stress waves with propagating cracks. Int. J. Fract. 26, 189–200 (1984)
E. Sharon, J. Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 397, 333–335 (1999)
E. Sharon, G. Cohen, J. Fineberg, Crack front waves and the dynamics of a rapidly moving crack. Phys. Rev. Lett. 88, 47–103 (2002)
Y.P. Shen, Y.H. Chen, Y.F. Pen, The finite element method of viscoelastic large deformation plane problem with Kirchhoff stress tensors-green strain tensors constitutive relation. Acta Mech. Solida Sin. 87–91 (1987)
R.P. Singh, V. Parameswaran, An experimental investigation of dynamic crack propagation in a brittle material reinforced with a ductile layer. Opt. Lasers Eng. 40, 289–306 (2003)
J.H. Song, H. Wang, T. Belytschko, A comparative study on finite element methods for dynamic fracture. Comput. Mech. 42, 239–250 (2008)
M.G. Stout, D.A. Koss, C. Liu, J. Idasetima, Damage development in carbon/epoxy laminates under quasi-static and dynamic loading. Compos. Sci. Technol. 59, 2339–2350 (1999)
X. Sun, M.A. Khaleel, X. Sun, M.A. Khaleel, Effects of different design parameters on stone-impact resistance of automotive windshields. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219, 1059–1067 (2005)
X. Sun, W. Liu, W. Chen, D. Templeton, Modeling and characterization of dynamic failure of borosilicate glass under compression/shear loading ☆. Int. J. Impact Eng. 36, 226–234 (2009)
S.R. Swanson, L.W. Christensen, A constitutive formulation for high-elongation propellants. J. Spacecr. Rocket. 20, 559–566 (2015)
A. Thom, Experimental and modeling studies of stress wave propagation in multilayer composite materials: low modulus interlayer effects. J. Compos. Mater. 39, 981–1005 (2005)
M. Timmel, S. Kolling, P. Osterrieder, P.A.D. Bois, A finite element model for impact simulation with laminated glass. Int. J. Impact Eng. 34, 1465–1478 (2007)
N. Vandenberghe, R. Vermorel, E. Villermaux, Star-shaped crack pattern of broken windows. Phys. Rev. Lett. 110, 285–291 (2013)
H.W. Wang, Z.J. Lai, X.U. Sun, D.J. Ming-Qiao, S.Q. Huang, Shi, Dynamic deformation and fracture of polymers taking account of damage evolution. J Ningbo University, 16(4), 373–381 (2003)
L.L. Wang, X.L. Dong, Z.J. Sun, Dynamic constitutive behavior of materials at high strain rate taking account of damage evolution. Explosion Shock Waves 26, 193–198 (2006)
X. Wang, Z. Feng, F. Wang, Z. Yue, Dynamic response analysis of bird strike on aircraft windshield based on damage-modified nonlinear viscoelastic constitutive relation. Chinese J. Aeronaut. 20, 511–517 (2007)
J. Xu, Y. Li, Model of vehicle velocity calculation in vehicle-pedestrian accident based on deflection of windshield. J. Mech. Eng. 45, 210–215 (2009)
J. Xu, Y. Li, G. Lu, W. Zhou, Reconstruction model of vehicle impact speed in pedestrian–vehicle accident. Int. J. Impact Eng. 36, 783–788 (2009)
J. Xu, Y. Li, X. Chen, Y. Yan, D. Ge, M. Zhu, B. Liu, Characteristics of windshield cracking upon low-speed impact: numerical simulation based on the extended finite element method. Comput. Mater. Sci. 48, 582–588 (2010)
J. Xu, Y. Li, B. Liu, M. Zhu, D. Ge, Experimental study on mechanical behavior of PVB laminated glass under quasi-static and dynamic loadings. Compos. Part B 42, 302–308 (2011a)
J. Xu, Y.B. Li, X. Chen, D.Y. Ge, B.H. Liu, M.Y. Zhu, T.H. Park, Automotive windshield – pedestrian head impact: energy absorption capability of interlayer material. Int. J. Automot. Technol. 12, 687–695 (2011b)
J. Xu, Y. Sun, B. Liu, M. Zhu, X. Yao, Y. Yan, Y. Li, X. Chen, Experimental and macroscopic investigation of dynamic crack patterns in PVB laminated glass sheets subject to light-weight impact. Eng. Fail. Anal. 18, 1605–1612 (2011c)
J. Xu, Y. Li, X. Chen, D. Ge, B. Liu, M. Zhu, T.H. Park, Automotive windshield – pedestrian head impact: energy absorption capability of interlayer material. Int. J. Automot. Technol. 12, 687–695 (2011d)
X.X. Zhang, R.C. Yu, G. Ruiz, M. Tarifa, M.A. Camara, Effect of loading rate on crack velocities in HSC. Int. J. Impact Eng. 37, 359–370 (2010)
S. Zhao, L.R. Dharani, X. Liang, L. Chai, S.D. Barbat, Crack initiation in laminated automotive glazing subjected to simulated head impact. Int. J. Crashworthiness 10, 229–236 (2005)
S.M. Zhao, L.R. Dharani, L. Chai, S.D. Barbat, Analysis of damage in laminated automotive glazing subjected to simulated head impact. Eng. Fail. Anal. 13, 582–597 (2006a)
S. Zhao, L.R. Dharani, L. Chai, S.D. Barbat, Dynamic response of laminated automotive glazing impacted by spherical featureless headform. Int. J. Crashworthiness 11, 105–114 (2006b)
F. Zhou, L. Wang, S. Hu, A damage-modified nonlinear VISCO-elastic constitutive relation and failure criterion of PMMA at high strain-rates. Combust. Explosion Shock Waves 12, 333–342 (1992)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this entry
Cite this entry
Xu, J., Zheng, Y. (2016). Crack Initiation and Propagation in Laminated Composite Materials. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_24-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-22977-5_24-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22977-5
Online ISBN: 978-3-319-22977-5
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering