×

Analytical investigation of nonlinear interlaminar fracture in trilayered polymer composite beam under mode II crack loading conditions using the \(J\)-integral approach. (English) Zbl 1293.74378

Summary: The present study is concerned with a nonlinear fracture analysis of trilayered beam built up by two unidirectional fiber-reinforced polymer composites. It is assumed that two interlaminar cracks exist between the layers. A tensile force applied to the middle layer generates pure mode II crack loading conditions. The \(J\)-integral approach is used to investigate the nonlinear fracture behavior of the beam. The elastic-linearly hardening model is applied to describe the mechanical behavior of the two composites. Sixth expressions for \(J\)-integral are derived using a beam theory model. These expressions correspond to the characteristic magnitudes of the external force. The validity of the formulae obtained is proved by comparison with the \(J\)-integral solution in the case of linear-elastic behavior of the composite materials. A numerical example is presented in order to demonstrate the ability of the expressions obtained for the analysis of nonlinear fracture in polymer composites.

MSC:

74R10 Brittle fracture
74E30 Composite and mixture properties
74B05 Classical linear elasticity
74B20 Nonlinear elasticity
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Robinson, P.; Song, D. Q., A modified DCB specimen for mode I testing of multidirectional laminates, J. Compos. Mater., 26, 1554-1577, (1992)
[2] Davies, P.; Sims, G. D.; Blackman, B. R.K.; etal., Comparison of test configurations for determination of mode II interlaminar fracture toughness results from international collaborative test program, Plastics, 28, 432-437, (1999)
[3] Junti, M.; Asp, L. E.; Olsson, R., Assessment of evaluation methods for the mixed-mode bending test, J. Compos. Technol. Res., 21, 37-48, (1999)
[4] Davies, P.; Blackman, B. R.K.; Brunner, A. J., Standard test methods for delamination resistance of composite materials: current status, Appl. Compos. Mater., 5, 345-364, (1999)
[5] Tay, T. E.; Williams, J. F.; Jones, R., Characterization of pure and mixed mode fracture in composite laminates, Theor. Appl. Fract. Mech., 7, 115-123, (1987)
[6] Brunner, A. J., Experimental aspects of mode I and mode II fracture toughness testing of fiber-reinforced polymer-matrix composites, Comput. Methods Appl. Mech. Eng., 185, 161-172, (2000) · Zbl 0945.74505
[7] Reeder, J. R.; Crews, J. H., The mixed-mode bending method for delamination testing, AIAA J., 28, 1270-1276, (1990)
[8] Reeder, J. R.; Crew, J. H., Redesign of the mixed-mode bending delamination test to reduce non-linear effects, J. Compos. Technol. Res., 14, 12-19, (1992)
[9] Reeder, J.R.: A bilinear failure criterion for mixed-mode delamination. In: Camponeschi, E.T. Jr. (ed.) Composite Materials Testing and Design, ASTM STP 1206, vol. 11, pp. 303-322 (1993)
[10] Lee, S. M., An edge crack torsion method for mode III delamination fracture testing, J. Compos. Technol. Res., 15, 193-201, (1993)
[11] Li, J., Wang, Y.: Analysis of mode III delamination fracture testing using a mid-plane edge crack torsion specimen. In: Deo, R.B., Saff, C.R. (eds.) Composite Materials: Testing and Design, ASTM STP 1274, vol. 12, pp. 166-181 (1996)
[12] Li, J., O’Brien, T.K.: Characterizing fatigue delamination onset under mode III loading for laminated composites. In: 11th Tech. Conf. of Am. Soc. for Composites, Atlanta, GA, Technomic Publ., Lancaster, PA, pp. 419-427 (1996)
[13] Becht, G.; Gillespie, J. W., Design and analysis of the crack rail shear specimen for mode III interlaminar fracture, Compos. Sci. Technol., 31, 143-157, (1988)
[14] Donaldson, S. L., Mode III interlaminar fracture characterization of composite materials, Compos. Sci. Technol., 32, 225-249, (1988)
[15] Chen, H.; Wang, L.; Karihaloo, B. L.; Williams, F. W., Fracture analysis of multi-material system with an interface crack, Comput. Mater. Sci., 12, 1-8, (1998)
[16] Wang, J.; Karihaloo, B. L., Optimum in situ strength design of composite laminates. Part I: in situ strength parameters, J. Compos. Mater., 30, 1314-1337, (1996)
[17] Wang, J.; Karihaloo, B. L., Optimum in situ strength design of composite laminates. Part II: optimum design, J. Compos. Mater., 30, 1338-1358, (1996)
[18] Szekrenyes, A., Prestressed fracture specimen for delamination testing of composites, Int. J. Fract., 139, 213-237, (2006)
[19] Szekrenyes, A., Improved analysis of unidirectional composite delamination specimens, Mech. Mater., 39, 953-974, (2007)
[20] Szekrenyes, A.; Uj, J., Comparison of some improved solutions of mixed-mode composite delamination coupons, Compos. Struct., 72, 321-329, (2006)
[21] Johannesson, T., Blickstadt, M.: Fractography and fracture criteria of the delamination process. In: Johnson, W.S. (ed.) Delamination and Debonding of Materials, ASTM STP 876, pp. 411-423 (1985)
[22] Hahn, H. T., A mixed-mode fracture criterion for composite materials, Compos. Technol. Rev., 5, 26-29, (1983)
[23] Richard, H.A.: Safety estimation for construction units with cracks under complex loading. Structural failure product liability and technical insurance. In: Rossmanith, H.P. (ed.) Proceeding of 2nd International Conference on July 1-3, Vienna, Austria, Geneva: Inderscience, pp. 423-437 (1986)
[24] Carlsson, L. A.; Gillespie, J. W.; Trethewey, B. R., Mode II interlaminar fracture of graphite/epoxy and graphite/PEEK, J. Reinf. Plast. Compos., 5, 170-187, (1986)
[25] Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, 379-386, (1968)
[26] Muskhelishvili N.: Some Basic Problems in the Mathematical Theory of Elasticity. Nauka, Moscow (1966) · Zbl 0151.36201
[27] Broek D.: Elementary Engineering Fracture Mechanics. Springer, Berlin (1986)
[28] Ewalds H.L., Wanhill R.J.H.: Fracture Mechanics. Hodder Headline PLC, London (1984)
[29] Chakrabarty J.: Theory of Plasticity. Elsevier Butterworth-Heinemann, Oxford (2006)
[30] Lubliner J.: Plasticity Theory. University of California, Berkeley (2006)
[31] Ilyushin A.A.: Plasticity. OGIZ, Moscow (1948)
[32] Bezuhov N.I.: Theory of Elasticity and Plasticity. GITTL, Moscow (1953)
[33] Hoff N.J.: The Analysis of Structures. Wiley, New York (1956) · Zbl 0071.23806
[34] Nadai F.: Theory of Flow and Fracture of Solids. McGraw-Hill, New York (1963)
[35] Seely F.B., Smith J.O.: Advanced Mechanics of Materials. Wiley, New York (1967)
[36] Washizu K.: Variational Methods in Elasticity and Plasticity. Pergamon Press, Oxford (1974) · Zbl 0164.26001
[37] Composite Materials Handbook, Volume 2: Polymer Matrix Composites Material Properties. Department of Defense, USA, 17 June (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.