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Mechanics Based Modeling of Composite and Sandwich Structures in the Naval Environment: Elastic Behavior, Fracture and Damage Evolution

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Advances in Thick Section Composite and Sandwich Structures

Abstract

The chapter summarizes selected work by the author and her collaborators on mechanics based modeling of composite and sandwich materials and structures for marine applications. Models and results are presented on various aspects of the mechanical response of these systems. Closed form solutions for elastic response and wave propagation and dispersion of layered plates subject to thermo-mechanical loadings, also in the presence of interfacial damage and imperfections, are derived using the theory of elasticity, matrix methods and a multiscale homogenization technique. Interface fracture mechanics solutions are derived, which are useful for the characterization of the fracture properties of sandwich composites, and account for the effects of shear on energy release rate and mode mixity. Evolution and interaction of damage mechanisms in sandwich beams with compressive yielding cores subject to time-dependent loading are investigated and energy barriers to the propagation of face-sheet delaminations identified. A multiscale modeling strategy for mode II dominant delamination fracture of laminated and sandwich beams is presented which does not require a through-thickness discretization of the problem and captures, using the same kinematic variables of a classical equivalent single-layer theory, local and global effects caused by the layered architecture and the interaction of the delaminations.

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References

  1. Massabò R (2017) Propagation of Rayleigh-lamb waves in multilayered plates through a multiscale structural model. Int J Solids Struct 124:108–124. https://doi.org/10.1016/j.ijsolstr.2017.06.020

    Article  Google Scholar 

  2. Massabò R (2017) Cut-off frequencies and correction factors of equivalent single layer theories. Procedia Eng 199:1466–1471. https://doi.org/10.1016/j.proeng.2017.09.406

    Article  Google Scholar 

  3. Massabó R (2018) Wave propagation and dynamic correction factors for composite structures In: Gopalkrishnan, S., Rajapakse Y, editor. Blast mitigation strategies in marine composite sandwich structures Springer, ISBN 9789811071706; p. 191–208

    Google Scholar 

  4. Massabò R, Campi F (2014) An efficient approach for multilayered beams and wide plates with imperfect interfaces and delaminations. Compos Struct 116:311–324. https://doi.org/10.1016/j.compstruct.2014.04.009

    Article  Google Scholar 

  5. Darban H, Massabò R (2018) Thermo-elastic solutions for multilayered wide plates and beams with interfacial imperfections through the transfer matrix method. Meccanica 53:553–571. https://doi.org/10.1007/s11012-017-0657-6

    Article  Google Scholar 

  6. Darban H, Massabò R (2017) 2D thermo-elastic solutions for laminates and sandwiches with interlayer delaminations and imperfect thermal contact. In: Lo Presto V, Langella A, Abrate S (eds) Dynamic response failure composite materials structures. Elsevier Inc., pp 3–46. https://doi.org/10.1016/B978-0-08-100887-4.00001-9

    Chapter  Google Scholar 

  7. Darban H (2018) Multiscale modeling of delamination fracture in multilayered structures. Ph.D. Thesis, University of Genova

    Google Scholar 

  8. Barbieri L, Massabò R, Berggreen C (2018) The effects of shear and near tip deformations on interface fracture of symmetric sandwich beams. Eng Fract Mech 201:1–24. https://doi.org/10.1016/j.engfracmech.2018.06.039

    Article  Google Scholar 

  9. Østergaard RC, Sørensen BF (2007) Interface crack in sandwich specimen. Int J Fract 143:301–316. https://doi.org/10.1007/s10704-007-9059-4

    Article  Google Scholar 

  10. Suo Z, Hutchinson JW (1990) Interface crack between two elastic layers. Int J Fract 43:1–18. https://doi.org/10.1007/BF00018123

    Article  Google Scholar 

  11. Andrews MG, Massabò R (2007) The effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers. Eng Fract Mech 74:2700–2720. https://doi.org/10.1016/j.engfracmech.2007.01.013

    Article  Google Scholar 

  12. Li S, Wang J, Thouless MD (2004) The effects of shear on delamination in layered materials. J Mech Phys Solids 52:193–214. https://doi.org/10.1016/S0022-5096(03)00070-X

    Article  Google Scholar 

  13. Kardomateas GA, Berggreen C, Carlsson LA Energy-release rate and mode Mixity of face/Core Debonds in Sandwich beams. AIAA J 51(2913):885–892. https://doi.org/10.2514/1.J051765

    Article  Google Scholar 

  14. Massabò R, Cavicchi A (2012) Interaction effects of multiple damage mechanisms in composite sandwich beams subject to time dependent loading. Int J Solids Struct 49:720–738. https://doi.org/10.1016/j.ijsolstr.2011.11.012

    Article  Google Scholar 

  15. Campi F, Massabò R (2011) An analytical assessment of the influence of skin imperfections on the indentation collapse mechanism in composite sandwich beams. Compos Struct 94:299–311. https://doi.org/10.1016/j.compstruct.2011.05.006

    Article  Google Scholar 

  16. Daniel IM (2010) Impact response and damage tolerance of composite sandwich structures. Proceedings of the ICSS-9, Pasadena. 1–10

    Google Scholar 

  17. Massabò R, Darban H (2019) Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach. Eng Fract Mech 213:280–301. https://doi.org/10.1016/j.engfracmech.2019.03.002

    Article  Google Scholar 

  18. Massabò R (2014) Influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach. Frattura ed Integrità Strutturale 8:230–240. https://doi.org/10.3221/IGF-ESIS.29.20

    Article  Google Scholar 

  19. Massabò R, Campi F (2015) Assessment and correction of theories for multilayered plates with imperfect interfaces. Meccanica 50:1045–1071. https://doi.org/10.1007/s11012-014-9994-x

    Article  Google Scholar 

  20. Pelassa M, Massabò R (2015) Explicit solutions for multi-layered wide plates and beams with perfect and imperfect bonding and delaminations under thermo-mechanical loading. Meccanica 50:2497–2524. https://doi.org/10.1007/s11012-015-0147-7

    Article  Google Scholar 

  21. Jones JP (1964) Wave propagation in a two-layered medium. J Appl Mech Trans 31:213–222. https://doi.org/10.1115/1.3629589

    Article  Google Scholar 

  22. Yang PC, Norris CH, Stavsky Y (1966) Elastic wave propagation in heterogeneous plates. Int J Solids Struct 2:665–684. https://doi.org/10.1016/0020-7683(66)90045-X

    Article  Google Scholar 

  23. Thomson WT (1950) Transmission of elastic waves through a stratified solid medium. J Appl Phys 21:89–93. https://doi.org/10.1063/1.1699629

    Article  Google Scholar 

  24. Liu L, Bhattacharya K (2009) Wave propagation in a sandwich structure. Int J Solids Struct 46:3290–3300. https://doi.org/10.1016/j.ijsolstr.2009.04.023

    Article  Google Scholar 

  25. Whitney JM, Sun CT (1973) A higher order theory for extensional motion of laminated composites. J Sound Vib 30:85–97. https://doi.org/10.1016/S0022-460X(73)80052-5

    Article  Google Scholar 

  26. di Sciuva M (1986) Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model. J Sound Vib 105:425–442. https://doi.org/10.1016/0022-460X(86)90169-0

    Article  Google Scholar 

  27. Chen WQ, Cai JB, Ye GR (2003) Exact solutions of cross-ply laminates with bonding imperfections. AIAA J 41:2244–2250. https://doi.org/10.2514/2.6817

    Article  Google Scholar 

  28. Fan J, Ye J (1990) An exact solution for the statics and dynamics of laminated thick plates with orthotropic layers. Int J Solids Struct 26:655–662. https://doi.org/10.1016/0020-7683(90)90036-U

    Article  Google Scholar 

  29. Qian H, Zhou D, Liu W, Fang H (2014) 3-D elasticity solutions of simply supported laminated rectangular plates in uniform temperature field. J Therm Stresses 37:661–677. https://doi.org/10.1080/01495739.2014.885329

    Article  Google Scholar 

  30. Qian H, Zhou D, Liu WQ, Fang H, Lu WD (2015) 3-D elasticity solutions of layered rectangular plates subjected to thermo-loads. J Therm Stresses 38:377–398. https://doi.org/10.1080/01495739.2014.985570

    Article  Google Scholar 

  31. Williams TO, Addessio FL (1997) A general theory for laminated plates with delaminations. Int J Solids Struct 34:2003–2024. https://doi.org/10.1016/S0020-7683(96)00131-X

    Article  Google Scholar 

  32. Andrews MG, Massabò R (2008) Delamination in flat sheet geometries with material imperfections and thickness variations. Compos Part B Eng 39:139–150. https://doi.org/10.1016/j.compositesb.2007.02.017

    Article  Google Scholar 

  33. Andrews MG, Massabò R, Cox BN (2006) Elastic interaction of multiple delaminations in plates subject to cylindrical bending. Int J Solids Struct 43:855–886. https://doi.org/10.1016/j.ijsolstr.2005.04.025

    Article  Google Scholar 

  34. Brandinelli L, Massabò R (2006) Mode II weight functions for isotropic and orthotropic double cantilever beams. Int J Fract 139:1–25

    Article  Google Scholar 

  35. Ustinov K (2015) On separation of a layer from the half-plane: elastic fixation conditions for a plate equivalent to the layer. Mech Solids 50:62–80. https://doi.org/10.3103/S0025654415010070

    Article  Google Scholar 

  36. Berggreen C, Simonsen BC, Borum KK (2007) Experimental and numerical study of interface crack propagation in foam-cored sandwich beams. J Compos Mater 41:493–520. https://doi.org/10.1177/0021998306065285

    Article  CAS  Google Scholar 

  37. Rice JR (1988) Elastic fracture mechanics concepts for interfacial cracks. J Appl Mech 55:98–103. https://doi.org/10.1115/1.3173668

    Article  Google Scholar 

  38. Thouless MD (2018) Shear forces, root rotations, phase angles and delamination of layered materials. Eng Fract Mech 191:153–167. https://doi.org/10.1016/j.engfracmech.2018.01.033

    Article  Google Scholar 

  39. Abrate S (1997) Localized impact on Sandwich structures with laminated facings. Appl Mech Rev 50:69. https://doi.org/10.1115/1.3101689

    Article  Google Scholar 

  40. Shenhar Y, Frostig Y, Altus E (1996) Stresses and failure patterns in the bending of sandwich beams with transversely flexible cores and laminated composite skins. Compos Struct 35:143–152. https://doi.org/10.1016/0263-8223(96)00016-5

    Article  Google Scholar 

  41. Shipsha A, Zenkert D (2005) Compression-after-impact strength of sandwich panels with core crushing damage. Appl Compos Mater 12:149–164. https://doi.org/10.1007/s10443-005-1119-1

    Article  Google Scholar 

  42. Steeves CA, Fleck NA (2004) Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part I: analytical models and minimum weight design. Int J Mech Sci 46:561–583. https://doi.org/10.1016/j.ijmecsci.2004.04.003

    Article  Google Scholar 

  43. Wu CL, Sun CT (1996) Low velocity impact damage in composite sandwich beams. Compos Struct 34:21–27. https://doi.org/10.1016/0263-8223(95)00127-1

    Article  Google Scholar 

  44. Jackson M, Shukla A (2011) Performance of sandwich composites subjected to sequential impact and air blast loading. Compos Part B Eng 42:155–166. https://doi.org/10.1016/j.compositesb.2010.09.005

    Article  CAS  Google Scholar 

  45. Schubel PM, Luo JJ, Daniel IM (2004) Low velocity impact behavior of composite sandwich panels. Compos Part A Appl Sci Manuf 2005. https://doi.org/10.1016/j.compositesa.11.014

  46. Andrews MG, Massabò R, Cavicchi A, Cox BN (2009) Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending. Int J Solids Struct 46:1815–1833. https://doi.org/10.1016/j.ijsolstr.2008.11.027

    Article  CAS  Google Scholar 

  47. Brandinelli L, Massabò R (2003) Free vibrations of delaminated beam-type structures with crack bridging. Compos Struct 61:129–142. https://doi.org/10.1016/S0263-8223(03)00035-7

    Article  Google Scholar 

  48. Lundsgaard-Larsen C, Massabò R, Cox BN (2009) The design of dynamic tests to infer rate dependence in large-scale crack bridging. Soc Exp Mech – SEM Annu Conf Expo Exp Appl Mech 1:2009

    Google Scholar 

  49. Sridhar N, Massabò R, Cox BN, Beyerlein IJ (2002) Delamination dynamics in through-thickness reinforced laminates with application to DCB specimen. Int J Fract 118:119–144. https://doi.org/10.1023/A:1022884410968

    Article  Google Scholar 

  50. Allix O, Ladevèze P (1992) Interlaminar interface modelling for the prediction of delamination. Compos Struct 22:235–242. https://doi.org/10.1016/0263-8223(92)90060-P

    Article  Google Scholar 

  51. Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736. https://doi.org/10.1002/nme.93

    Article  Google Scholar 

  52. Turon A, Camanho PP, Costa J, Renart J (2010) Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: definition of interlaminar strengths and elastic stiffness. Compos Struct 92:1857–1864. https://doi.org/10.1016/j.compstruct.2010.01.012

    Article  Google Scholar 

  53. Lundsgaard-Larsen C, Massabò R, Cox BN (2012) On acquiring data for large-scale crack bridging at high strain rates. J Compos Mater 46:949–971. https://doi.org/10.1177/0021998311413622

    Article  CAS  Google Scholar 

  54. Bruno D, Greco F (2001) Mixed mode delamination in plates: a refined approach. Int J Solids Struct 38:9149–9177. https://doi.org/10.1016/S0020-7683(01)00179-2

    Article  Google Scholar 

  55. Barbero EJ, Reddy JN (1991) Modeling of delamination in composite laminates using a layer-wise plate theory. Int J Solids Struct 28:373–388. https://doi.org/10.1016/0020-7683(91)90200-Y

    Article  Google Scholar 

  56. Rybicki EF, Kanninen MF (1997) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 9:931–938. https://doi.org/10.1016/0013-7944(77)90013-3

    Article  Google Scholar 

  57. Darban H, Massabò R (2017) A multiscale structural model for cohesive delamination of multilayered beams, AIMETA 2017 – Proceedings of the 23rd conference of the Italian association of theoretical and applied mechanics, 2, pp. 1785–1792

    Google Scholar 

  58. Icardi U, Zardo G (2005) C0plate element for delamination damage analysis, based on a zig-Zag model and strain energy updating. Int J Impact Eng 31:579–606. https://doi.org/10.1016/j.ijimpeng.2004.02.002

    Article  Google Scholar 

  59. Groh RMJ, Tessler A (2017) Computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations. Comput Methods Appl Mech Eng 320:369–395. https://doi.org/10.1016/j.cma.2017.03.035

    Article  Google Scholar 

  60. Eijo A, Oñate E, Oller S (2014) Delamination in laminated plates using the 4-noded quadrilateral QLRZ plate element based on the refined zigzag theory. Compos Struct 108:456–471. https://doi.org/10.1016/j.compstruct.2013.09.052

    Article  Google Scholar 

  61. Eijo A, Oñate E, Oller S (2013) A numerical model of delamination in composite laminated beams using the LRZ beam element based on the refined zigzag theory. Compos Struct 104:270–280. https://doi.org/10.1016/j.compstruct.2013.04.035

    Article  Google Scholar 

  62. Groh RMJ, Weaver PM, Tessler A (2015) Application of the refined zigzag theory to the modeling of delaminations in laminated composites. https://doi.org/10.13140/RG.2.1.3147.0804

  63. Averill RC (1994) Static and dynamic response of moderately thick laminated beams with damage. Compos Eng 4:381–395. https://doi.org/10.1016/S0961-9526(09)80013-0

    Article  Google Scholar 

  64. Madhukar MS, Drzal LT (1992) Fiber-Matrix adhesion and its effect on composite mechanical properties: IV. Mode I and mode II fracture toughness of graphite/epoxy composites. J Compos Mater 26:936–968. https://doi.org/10.1177/002199839202600701

    Article  CAS  Google Scholar 

  65. Massabò R, Barbieri L, Berggreen C (2017) Energy release rate and mode mixity of face/core debonds in sandwich beams, AIMETA 2017 – Proceedings of the 23rd conference of the Italian association of theoretical and applied mechanics, 2, pp. 1913–1919

    Google Scholar 

  66. Massabò R, Ustinov K, Barbieri L, Berggreen C (2019) Fracture mechanics solutions for interfacial cracks between compressible thin layers and substrates, Coatings, 9(3), art. no. 152., https://doi.org/10.3390/coatings9030152

    Article  Google Scholar 

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Acknowledgments

The support by the U.S. Navy, Office of Naval Research, ONR, grant N00014-17-1-2914 and the useful discussions and suggestions of the program manager Dr. Y.D.S. Rajapakse are gratefully acknowledged.

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Correspondence to Roberta Massabò .

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Massabò, R. (2020). Mechanics Based Modeling of Composite and Sandwich Structures in the Naval Environment: Elastic Behavior, Fracture and Damage Evolution. In: Lee, S. (eds) Advances in Thick Section Composite and Sandwich Structures. Springer, Cham. https://doi.org/10.1007/978-3-030-31065-3_12

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