Skip to main content

Crack Initiation and Propagation in Laminated Composite Materials

  • Living reference work entry
  • First Online:
Handbook of Nonlocal Continuum Mechanics for Materials and Structures
  • 271 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • A. Berezovski, G.A. Maugin, On the propagation velocity of a straight brittle crack. Int. J. Fract. 143, 135–142 (2007)

    Article  MATH  Google Scholar 

  • P.A.D. Bois, S. Kolling, W. Fassnacht, Modelling of safety glass for crash simulation. Comput. Mater. Sci. 28, 675–683 (2003)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • S.K. Dwivedi, H.D. Espinosa, Modeling dynamic crack propagation in fiber reinforced composites including frictional effects ☆. Mech. Mater. 35, 481–509 (2003)

    Article  Google Scholar 

  • F. Zhigang and Z. Jianping, On the viscoelastic finite element method, Shanghai J. Mech. 16(1), 20–26 (1995)

    Google Scholar 

  • 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

    MATH  Google Scholar 

  • P. Forquin, F. Hild, A probabilistic damage model of the dynamic fragmentation process in brittle materials. Adv. Appl. Mech. 44, 1–72 (2010)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • J.A. Hauch, M.P. Marder, Energy balance in dynamic fracture, investigated by a potential drop technique. Int. J. Fract. 90, 133–151 (2010)

    Article  Google Scholar 

  • J. Lambros, A.J. Rosakis, Dynamic crack initiation and growth in thick unidirectional graphite/epoxy plates. Compos. Sci. Technol. 57, 55–65 (1997)

    Article  Google Scholar 

  • B. Lawn, R. Wilshaw, Review: indentation fracture: principles and applications. J. Mater. Sci. 10, 1049–1081 (1975)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • B.B. Mandelbrot, Fractal geometry of nature. WH Freeman and Company (1983)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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

    MATH  Google Scholar 

  • J.H. Nielsen, J.F. Olesen, H. Stang, The fracture process of tempered soda-lime-silica glass. Exp. Mech. 49, 855–870 (2009)

    Article  Google Scholar 

  • H. Park, W.W. Chen, Experimental investigation on dynamic crack propagating perpendicularly through interface in glass. J Appl. Mech-t ASME 78(5) (2011)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • E. Sharon, J. Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 397, 333–335 (1999)

    Article  Google Scholar 

  • E. Sharon, G. Cohen, J. Fineberg, Crack front waves and the dynamics of a rapidly moving crack. Phys. Rev. Lett. 88, 47–103 (2002)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • J.H. Song, H. Wang, T. Belytschko, A comparative study on finite element methods for dynamic fracture. Comput. Mech. 42, 239–250 (2008)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • S.R. Swanson, L.W. Christensen, A constitutive formulation for high-elongation propellants. J. Spacecr. Rocket. 20, 559–566 (2015)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • N. Vandenberghe, R. Vermorel, E. Villermaux, Star-shaped crack pattern of broken windows. Phys. Rev. Lett. 110, 285–291 (2013)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jun Xu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics