Skip to main content
SpringerLink
Log in

Progressive Failure Analysis of Multi-Directional Composite Laminates Based on the Strain-Rate-Dependent Northwestern Failure Theory

  • Conference paper
  • First Online:
Mechanics of Composite and Multi-functional Materials, Volume 6

Abstract

The failure progression of a fiber-reinforced toughened-matrix composite (IM7/8552) was experimentally characterized at quasi-static (10−4 s−1) strain rate using crossply and quasi-isotropic laminate specimens. A progressive failure framework was proposed to benchmark the initiation and progression of damage within composite laminates based on the matrix-dominated failure modes. The Northwestern Failure Theory (NU Theory) was used to provide a set of physics-based failure criteria for predicting the matrix-dominated failure of embedded plies using the lamina-based transverse tension, transverse compression, and shear failure strengths. The NU Theory was used to predict the first-ply-failure (FPF) of embedded plies in [0/904]s and [02/452/−452/902]s laminates for the embedded 90° and 45° plies. The Northwestern Criteria were found to provide superior prediction of the matrix-dominated embedded ply failure for all evaluated cases compared to the classical approaches. The results indicate the potential to use the Northwestern Criteria to provide the predictive baseline for damage propagation in composite laminates based on experimentally identified damage response on a length scale-relevant basis.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Daniel, I.M., Ishai, O.: Engineering Mechanics of Composite Materials. Oxford University Press, Oxford (2006)

    Google Scholar 

  2. Reifsnider, K.L., Masters, J.E.: An investigation of cumulative damage development in quasi-isotropic graphite/epoxy laminates. In: Damage in Composite Materials ASTM STP 775, pp. 40–62. American Society for Testing and Materials, West Conshohocken (1982)

    Google Scholar 

  3. Henaff-Gardin, C., Lafarie-Frenot, M.C.: The use of a characteristic damage variable in the study of transverse cracking development under fatigue loading in cross-ply laminates. Int. J. Fatigue. 24(2–4), 389–395 (2002)

    Article  MATH  Google Scholar 

  4. Kashtalyan, M., Soutis, C.: Stiffness degradation in cross-ply laminates damaged by transverse cracking and splitting. Compos. A: Appl. Sci. Manuf. 31(4), 335–351 (2000)

    Article  Google Scholar 

  5. Lee, J.-W., Daniel, I.M.: Progressive transverse cracking of crossply composite laminates. J. Compos. Mater. 24, 1225–1243 (1990)

    Article  Google Scholar 

  6. Li, C., Ellyin, F., Wharmby, A.: On matrix crack saturation in composite laminates. Compos. Part B Eng. 34(5), 473–480 (2003)

    Article  Google Scholar 

  7. Li, S., Jiang, C., Han, S.: Modeling of the characteristics of fiber-reinforced composite materials damaged by matrix-cracking. Compos. Sci. Technol. 43(2), 185–195 (1992)

    Article  Google Scholar 

  8. Reifsnider, K.L., Highsmith, A.L.: Stiffness reduction mechanisms in composite laminates. In: Damage in Composite Materials ASTM STP 775, pp. 103–117. American Society for Testing Materials, West Conshohocken (1982)

    Google Scholar 

  9. Tagarielli, V.L., Minisgallo, G., McMillan, A.J., Petrinic, N.: The response of a multi-directional composite laminate to through-thickness loading. Compos. Sci. Technol. 70(13), 1950–1957 (2010)

    Article  Google Scholar 

  10. Chou, P.C., Wang, A.S.D.: A stochastic model for the growth of matrix cracks in composite laminates. J. Compos. Mater. 18, 239–254 (1984)

    Article  Google Scholar 

  11. Chou, T.W., Fukunaga, H.: Probabilistic failure strength analysis of graphite/epoxy cross-ply laminates. J. Compos. Mater. 18, 339–356 (1984)

    Article  Google Scholar 

  12. Gamby, D., Rebière, J.L.: A two-dimensional analysis of multiple matrix cracking in a laminated composite close to its characteristic damage state. Compos. Struct. 25(1–4), 325–337 (1993)

    Article  Google Scholar 

  13. Huang, Z.Q., Nie, G.H., Chan, C.K.: An exact solution for stresses in cracked composite laminates and evaluation of the characteristic damage state. Compos. Part B Eng. 42(5), 1008–1014 (2011)

    Article  Google Scholar 

  14. Joffe, R., Varna, J.: Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90° layers. Compos. Sci. Technol. 59(11), 1641–1652 (1999)

    Article  Google Scholar 

  15. Vaughan, T.J., McCarthy, C.T.: Micromechanical modelling of the transverse damage behaviour in fibre reinforced composites. Compos. Sci. Technol. 71, 388–396 (2011)

    Article  Google Scholar 

  16. Daniel, I.M., Lee, J.-W.: Damage development in composite laminates under monotonic loading. J. Compos. Technol. Res. 12(2), 98–102 (1990)

    Article  Google Scholar 

  17. Karthikeyan, K., Russell, B.P., Fleck, N.A., Wadley, H.N.G., Deshpande, V.S.: The effect of shear strength on the ballistic response of laminated composite plates. Eur. J. Mech. A. Solids. 42(0), 35–53 (2013)

    Article  Google Scholar 

  18. Pandya, K.S., Dharmane, L., Pothnis, J.R., Ravikumar, G., Naik, N.K.: Stress wave attenuation in composites during ballistic impact. Polym. Test. 31(2), 261–266 (2012)

    Article  Google Scholar 

  19. Gower, H.L., Cronin, D.S., Plumtree, A.: Ballistic impact response of laminated composite panels. Int. J. Impact Eng. 35(9), 1000–1008 (2008)

    Article  Google Scholar 

  20. Mohan, S., Velu, S.: Ballistic impact behaviour of unidirectional fibre reinforced composites. Int. J. Impact Eng. 63(0), 164–176 (2014)

    Article  Google Scholar 

  21. Morye, S.S., Hine, P.J., Duckett, R.A., Carr, D.J., Ward, I.M.: Modelling of the energy absorption by polymer composites upon ballistic impact. Compos. Sci. Technol. 60(14), 2631–2642 (2000)

    Article  Google Scholar 

  22. Naik, N.K., Doshi, A.V.: Ballistic impact behaviour of thick composites: Parametric studies. Compos. Struct. 82(3), 447–464 (2008)

    Article  Google Scholar 

  23. Naik, N.K., Shrirao, P.: Composite structures under ballistic impact. Compos. Struct. 66(1–4), 579–590 (2004)

    Article  Google Scholar 

  24. Sevkat, E., Liaw, B., Delale, F., Raju, B.B.: A combined experimental and numerical approach to study ballistic impact response of S2-glass fiber/toughened epoxy composite beams. Compos. Sci. Technol. 69(7–8), 965–982 (2009)

    Article  Google Scholar 

  25. Shaktivesh, N.N.S., Sesha Kumar, C.V., Naik, N.K.: Ballistic impact performance of composite targets. Mater. Des. 51(0), 833–846 (2013)

    Article  Google Scholar 

  26. Halabe, U.B.: 18 – Non-destructive evaluation (NDE) of composites: Techniques for civil structures. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 483–517e. Woodhead Publishing (2013)

    Google Scholar 

  27. Karbhari, V.M.: 1 – Introduction: The future of non-destructive evaluation (NDE) and structural health monitoring (SHM). In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 3–11. Woodhead Publishing (2013)

    Google Scholar 

  28. Chang, R.R.: Experimental and theoretical analyses of first-ply failure of laminated composite pressure vessels. Compos. Struct. 49(2), 237–243 (2000)

    Article  MathSciNet  Google Scholar 

  29. Huang, J.Q.: 2 – Non-destructive evaluation (NDE) of composites: Acoustic emission (AE). In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 12–32. Woodhead Publishing (2013)

    Google Scholar 

  30. Kim, R.J.-Y., Choi, N.-S., Ferracane, J., Lee, I.-B.: Acoustic emission analysis of the effect of simulated pulpal pressure and cavity type on the tooth–composite interfacial de-bonding. Dent. Mater. 30, 876 (2014). (0)

    Article  Google Scholar 

  31. Maimı´, P., Camanho, P.P., Mayugo, J.A., Turon, A.: Matrix cracking and delamination in laminated composites. Part I: Ply constitutive law, first ply failure and onset of delamination. Mech. Mater. 43(4), 169–185 (2011)

    Article  Google Scholar 

  32. Njuhovic, E., Bräu, M., Wolff-Fabris, F., Starzynski, K., Altstädt, V.: Identification of interface failure mechanisms of metallized glass fibre reinforced composites using acoustic emission analysis. Compos. Part B Eng. 66, 443. (0)

    Google Scholar 

  33. Romanowicz, M.: Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics. Int. J. Solids Struct. 51(13), 2549–2556 (2014)

    Article  Google Scholar 

  34. Roozen, N.B., Tazelaar, K., Koussios, S., Beukers, A.: A new method to measure critical strain in composite materials – Combining the Euler–Fresnel spiral with acoustic emission to assess crack positions. Compos. Sci. Technol. 100(0), 228–236 (2014)

    Article  Google Scholar 

  35. Satish Kumar, Y.V., Srivastava, A.: First ply failure analysis of laminated stiffened plates. Compos. Struct. 60(3), 307–315 (2003)

    Article  Google Scholar 

  36. Woo, S.-C., Kim, T.-W.: High-strain-rate impact in Kevlar-woven composites and fracture analysis using acoustic emission. Compos. Part B Eng. 60(0), 125–136 (2014)

    Article  Google Scholar 

  37. Tittmann, B.R., Miyasaka, C., Guers, M., Kasano, H., Morita, H.: 16 – Non-destructive evaluation (NDE) of aerospace composites: Acoustic microscopy. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 423–49e. Woodhead Publishing (2013)

    Google Scholar 

  38. Avdelidis, N.P., Gan, T.H.: 24 – Non-destructive evaluation (NDE) of Composites: Infrared (IR) thermography of wind turbine blades. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 634–50e. Woodhead Publishing (2013)

    Google Scholar 

  39. Ley, O., Godinez, V.: 12 – Non-destructive evaluation (NDE) of aerospace composites: Application of infrared (IR) thermography. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 309–36e. Woodhead Publishing (2013)

    Google Scholar 

  40. Shirazi, A., Karbhari, V.M.: 19 – Non-destructive evaluation (NDE) of composites: Application of thermography for defect detection in rehabilitated structures. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, p. 515–541. Woodhead Publishing, 2013

    Google Scholar 

  41. Suratkar, A., Sajjadi, A.Y., Mitra, K.: 25 – Non-destructive evaluation (NDE) of composites for marine structures: Detecting flaws using infrared thermography (IRT). In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 649–68e. Woodhead Publishing (2013)

    Google Scholar 

  42. Feng, M.Q., Roqueta, G., Jofre, L.: 22 – Non-destructive evaluation (NDE) of composites: Microwave techniques. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 574–616. Woodhead Publishing (2013)

    Google Scholar 

  43. Hsu, D.K.: 15 – Non-destructive evaluation (NDE) of aerospace composites: Ultrasonic techniques. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 397–422. Woodhead Publishing (2013)

    Google Scholar 

  44. Dong, Y.: 23 – Non-destructive evaluation (NDE) of composites: Using fiber optic sensors. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 617–633. Woodhead Publishing (2013)

    Google Scholar 

  45. Schaefer, J.D., Lee, J., Liguore, S.L., Richardson, T.D.: (2015, October 26–29). High Fidelity Test Database for Validation of Progressive Failure Analysis Methods. Composites and Advanced Materials Expo, Dallas, TX, USA

    Google Scholar 

  46. Francis, D.: 4 – Non-destructive evaluation (NDE) of composites: Introduction to shearography. In: Karbhari, V.M. (ed.) Non-Destructive Evaluation (NDE) of Polymer Matrix Composites, pp. 56–83. Woodhead Publishing (2013)

    Google Scholar 

  47. Schaefer, J.D., Justusson, B.P., Liguore, S.L., A comparison of emerging in-situ inspection techniques for validation of composite PDA methods, Society for the Advancement of Material and Process Engineering, Long Beach, CA, 23–26 May 2016

    Google Scholar 

  48. Daniel, I.M., Cho, J.-M., Werner, B.T., Fenner, J.S.: Characterization and constitutive modeling of composite materials under static and dynamic loading. AIAA J. 49(8), 1658–1664 (2011. 2011/08/01)

    Article  Google Scholar 

  49. Hart-Smith, L.J.: The role of biaxial stresses in discriminating between meaningful and illusory composite failure theories. Compos. Struct. 25(1–4), 3–20 (1993)

    Article  Google Scholar 

  50. Hart-Smith, L.J.: A re-examination of the analysis of in-plane matrix failures in fibrous composite laminates. Compos. Sci. Technol. 56(2), 107–121 (1996)

    Article  Google Scholar 

  51. Hart-Smith, L.J.: Predictions of a generalized maximum-shear-stress failure criterion for certain fibrous composite laminates. Compos. Sci. Technol. 58(7), 1179–1208 (1998)

    Article  Google Scholar 

  52. Hart-Smith, L.J.: Comparison between theories and test data concerning the strength of various fibre–polymer composites. Compos. Sci. Technol. 62(12–13), 1591–1618 (2002)

    Article  Google Scholar 

  53. Deng, S., Li, X., Lin, H., Weitsman, Y.J.: The non-linear response of quasi-isotropic composite laminates. Compos. Sci. Technol. 64(10–11), 1577–1585 (2004)

    Article  Google Scholar 

  54. Cândido, G.M., Costa, M.L., Rezende, M.C., Almeida, S.F.M.: Hygrothermal effects on quasi-isotropic carbon epoxy laminates with machined and molded edges. Compos. Part B Eng. 39(3), 490–496 (2008)

    Article  Google Scholar 

  55. Ogi, K., Kim, H.S., Maruyama, T., Takao, Y.: The influence of hygrothermal conditions on the damage processes in quasi-isotropic carbon/epoxy laminates. Compos. Sci. Technol. 59(16), 2375–2382 (1999)

    Article  Google Scholar 

  56. Tong, J., Guild, F.J., Ogin, S.L., Smith, P.A.: On matrix crack growth in quasi-isotropic laminates—I. Experimental investigation. Compos. Sci. Technol. 57(11), 1527–1535 (1997)

    Article  Google Scholar 

  57. Tong, J., Guild, F.J., Ogin, S.L., Smith, P.A.: On matrix crack growth in quasi-isotropic laminates—II. Finite element analysis. Compos. Sci. Technol. 57(11), 1537–1545 (1997)

    Article  Google Scholar 

  58. Swanson, S.R., Trask, B.C.: Strength of quasi-isotropic laminates under off-axis loading. Compos. Sci. Technol. 34(1), 19–34 (1989)

    Article  Google Scholar 

  59. Hallett, S.R., Jiang, W.-G., Khan, B., Wisnom, M.R.: Modelling the interaction between matrix cracks and delamination damage in scaled quasi-isotropic specimens. Compos. Sci. Technol. 68(1), 80–89 (2008)

    Article  Google Scholar 

  60. Chen, J.-F., Morozov, E.V., Shankar, K.: Simulating progressive failure of composite laminates including in-ply and delamination damage effects. Compos. A: Appl. Sci. Manuf. 61(0), 185–200 (2014)

    Article  Google Scholar 

  61. Herakovich, C.T.: Failure modes and damage accumulation in laminated composites with free edges. Compos. Sci. Technol. 36(2), 105–119 (1989)

    Article  Google Scholar 

  62. Zhou, G., Sim, L.M., Brewster, P.A., Giles, A.R.: Through-the-thickness mechanical properties of smart quasi-isotropic carbon/epoxy laminates. Compos. A: Appl. Sci. Manuf. 35(7–8), 797–815 (2004)

    Article  Google Scholar 

  63. Paradies, R.: Designing quasi-isotropic laminates with respect to bending. Compos. Sci. Technol. 56(4), 461–472 (1996)

    Article  Google Scholar 

  64. Edgren, F., Asp, L.E., Joffe, R.: Failure of NCF composites subjected to combined compression and shear loading. Compos. Sci. Technol. 66(15), 2865–2877 (2006)

    Article  Google Scholar 

  65. Esrail, F., Kassapoglou, C.: An efficient approach to determine compression after impact strength of quasi-isotropic composite laminates. Compos. Sci. Technol. 98(0), 28–35 (2014)

    Article  Google Scholar 

  66. Garg, A.C.: The fracture mechanics of some graphite fibre-reinforced epoxy laminates, part 1: Quasi-isotropic laminates. Composites. 17(2), 141–149 (1986)

    Article  Google Scholar 

  67. Guedes, R.M., de Moura, M.F.S.F., Ferreira, F.J.: Failure analysis of quasi-isotropic CFRP laminates under high strain rate compression loading. Compos. Struct. 84(4), 362–368 (2008)

    Article  Google Scholar 

  68. Kaddour, A.S., Hinton, M.J., Soden, P.D.: A comparison of the predictive capabilities of current failure theories for composite laminates: Additional contributions. Compos. Sci. Technol. 64(3–4), 449–476 (2004)

    Article  Google Scholar 

  69. Park, I.K., Park, K.J., Kim, S.J.: Rate-dependent damage model for polymeric composites under in-plane shear dynamic loading. Comput. Mater. Sci. 96, 506. (0)

    Google Scholar 

  70. Schultheisz, C.R., Waas, A.M.: Compressive failure of composites, part I: Testing and micromechanical theories. Prog. Aerosp. Sci. 32(1), 1–42 (1996)

    Article  Google Scholar 

  71. Soden, P.D., Hinton, M.J., Kaddour, A.S.: A comparison of the predictive capabilities of current failure theories for composite laminates. Compos. Sci. Technol. 58(7), 1225–1254 (1998)

    Article  Google Scholar 

  72. Sun, C.T., Tao, J.: Prediction of failure envelopes and stress/strain behaviour of composite laminates. Compos. Sci. Technol. 58(7), 1125–1136 (1998)

    Article  Google Scholar 

  73. Wolfe, W.E., Butalia, T.S.: A strain-energy based failure criterion for non-linear analysis of composite laminates subjected to biaxial loading. Compos. Sci. Technol. 58(7), 1107–1124 (1998)

    Article  Google Scholar 

  74. Zubillaga, L., Turon, A., Maimí, P., Costa, J., Mahdi, S., Linde, P.: An energy based failure criterion for matrix crack induced delamination in laminated composite structures. Compos. Struct. 112(0), 339–344 (2014)

    Article  Google Scholar 

  75. Welsh, J.S., Mayes, J.S., Biskner, A.C.: 2-D biaxial testing and failure predictions of IM7/977-2 carbon/epoxy quasi-isotropic laminates. Compos. Struct. 75(1–4), 60–66 (2006)

    Article  Google Scholar 

  76. Tay, T.E., Lim, E.H.: Analysis of stiffness loss in cross-ply composite laminates. Compos. Struct. 25(1–4), 419–425 (1993)

    Article  Google Scholar 

  77. Bogetti, T.A., Hoppel, C.P.R., Harik, V.M., Newill, J.F., Burns, B.P.: Predicting the nonlinear response and progressive failure of composite laminates. Compos. Sci. Technol. 64(3–4), 329–342 (2004)

    Article  Google Scholar 

  78. Whitney, J.M.: On the ‘ply discount method’ for determining effective thermo-elastic constants of laminates containing transverse cracks. Compos. A: Appl. Sci. Manuf. 36(10), 1347–1354 (2005)

    Article  Google Scholar 

  79. Sun, C.T., Tao, J., Kaddour, A.S.: The prediction of failure envelopes and stress/strain behavior of composite laminates: Comparison with experimental results. Compos. Sci. Technol. 62(12–13), 1673–1682 (2002)

    Article  Google Scholar 

  80. Daniel, I.M., Schaefer, J.D., Werner, B.: Yield criteria for matrix and composite materials under static and dynamic loading, 20th international conference on composite materials, 19–24 July 2015

    Google Scholar 

  81. Schaefer, J.D., Daniel, I.M.: Strain-Rate-Dependent Yield Criteria for Composite Laminates, Fracture, Fatigue, Failure, and Damage Evolution, vol. 8, pp. 197–208. Springer International Publishing (2016)

    Google Scholar 

  82. Schaefer, J.D., Daniel, I.M.: Characterization and modeling of progressive damage of angle-ply composite laminates under varying strain rate loading, 31st ASC technical conference and ASTM D30 meeting 2016

    Google Scholar 

  83. Schaefer, J.D., Werner, B.T., Daniel, I.M.: Strain-rate-dependent failure of a toughened matrix composite. Exp. Mech. 54(6), 1111–1120 (2014)

    Article  Google Scholar 

  84. Schaefer, J.D. Justusson, B.P., Liguore, S.L., Renieri, G.D.: Assessment of predictive capabilities of progressive damage analysis methods using high fidelity experiments for validation, Society for the advancement of material and process engineering, Long Beach, 23–26 May 2016

    Google Scholar 

  85. Razi, H., Schaefer, J.D., Wanthal, S.: Rapid integration of new analysis methods in production, 31st ASC technical conference and ASTM D30 meeting 2016

    Google Scholar 

Download references

Acknowledgement

Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Author information

Authors and Affiliations

  1. The Boeing Company, 6300 James S McDonnell Blvd, Berkeley, MO, 63134, USA

    Joseph D. Schaefer

  2. Sandia National Laboratories, 7011 East Avenue, Livermore, CA, 94550, USA

    Brian T. Werner

  3. Northwestern University, 2137 Tech Drive, Evanston, IL, 60208-3020, USA

    Isaac M. Daniel

Authors
  1. Joseph D. Schaefer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brian T. Werner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Isaac M. Daniel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph D. Schaefer .

Editor information

Editors and Affiliations

  1. Dow Chemical Company, Freeport, Texas, USA

    Piyush R Thakre

  2. School of Mechanical and Aerospace Engineering, Helmerich Advanced Technology Research Center, Oklahoma State University, Tulsa, Oklahoma, USA

    Raman Singh

  3. U.S. Army Research Laboratory, Aberdeen, Maryland, USA

    Geoff Slipher

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Schaefer, J.D., Werner, B.T., Daniel, I.M. (2018). Progressive Failure Analysis of Multi-Directional Composite Laminates Based on the Strain-Rate-Dependent Northwestern Failure Theory. In: Thakre, P., Singh, R., Slipher, G. (eds) Mechanics of Composite and Multi-functional Materials, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-63408-1_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-63408-1_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63407-4

  • Online ISBN: 978-3-319-63408-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation