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Finite-Layer Method: Exact Numerical and Analytical Calculations of the Energy Release Rate for Unidirectional Composite Specimens in Double-Cantilever Beam and End-Notched Flexure Tests

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Mechanics of Composite Materials Aims and scope

Based on the finite-layer method, a method for evaluating the stress-strain state and energy release rate for specimens with delaminations in double-cantilever beam and end-notched flexure tests is proposed. Exact numerical solutions of boundary-value problems for the “stiff” systems of differential equations describing deformations of test specimens are obtained. The distributions of forces, moments, displacements, and rotations in the specimens and the distributions of normal and tangential stresses on their midline are presented. New closed-form expressions for these functions and for compliance of the specimens are developed. Calculation results for the energy release rate obtained by a numerical differentiation and from analytical relations are presented. Two new techniques for estimating the energy release rate are proposed: (1) using the calculated values of peak stress and jumps of displacements at the tip of delamination; (2) by evaluation of indeterminacy at the tip of delamination with the use of stresses and derivatives of stresses and displacements. The effect of the transverse shear and Poisson ratio on the results is estimated. A comparison of the numerical and analytical solutions obtained with known results and the ASTM standard is presented.

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References

  1. A. M. Timonin, “Finite-layer method: a unified approach to a numerical analysis of interlaminar stresses, large deflections, and delamination stability of composites. Part 1. Linear behavior,” Mech. Compos. Mater., 49, No. 3, 231-244 (2013).

    Article  Google Scholar 

  2. A. M. Timonin, “Finite-layer method: a unified approach to a numerical analysis of interlaminar stresses, large deflections, and delamination stability of composites. Part 2. Nonlinear behavior,” Mech. Compos. Mater., 49, No. 4, 369-380 (2013).

    Article  Google Scholar 

  3. A. M. Timonin, “Finite-layer method: a unified approach to a numerical analysis of interlaminar stresses, large deflections, and delamination stability of composites. Part 3. Stability,” Mech. Compos. Mater., 50, No. 2, 187-196 (2014).

    Article  Google Scholar 

  4. A. M. Timonin, “Finite-layer method: bending and twisting of laminated plates with delaminationS,” Mech. Compos. Mater., 52, No. 1, 55-72 (2016).

    Article  Google Scholar 

  5. S. K. Godunov, “About the numerical solution of boundary value problems for the systems of linear ordinary differential equations,” Uspekhi Matematicheskikh Nauk (Russian Mathematical Surveys), 16, No. 3, 171−174 (1961).

    Google Scholar 

  6. J. M. Grigorenko, Isotropic and Anisotropic Layered Shells of Revolution of Variable Rigidity, Kiev: Naukova Dumka (1973).

    Google Scholar 

  7. A. V. Karmishin, V. A. Ljaskovets, V. I.Mjachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures, Moscow: Mashinostroenie (1975)

  8. D. F. Adams, L. A. Carlsson, and R. B. Pipes, Experimental Characterization of Advanced Composite Materials, N. Y.: CRC Press, (2003).

    Google Scholar 

  9. F. Ozdil and L. A. Carlsson, “Beam analysis of angle-ply laminate DCB specimens,” Compos. Sci. Technol., 59, No. 2, 305-315 (1999).

    Article  Google Scholar 

  10. J. D. Gunderson, J. F.Brueck, and A. J. Paris, “Alternative test method for interlaminar fracture toughness of composites,” Int. J. of Fracture, 143, No. 3, 273-276. (2007).

  11. E. Zile and V. Tamuzs, “Mode II delamination of a unidirectional carbon fiber/epoxy composite in four-point bend end-notched flexure tests,” Mech. Compos. Mater., 41, No. 5, 383-390 (2005).

    Article  Google Scholar 

  12. ASTM D6671/D6671M-06, “Standard Test Method for Mixed Mode I − Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites,” West Conshohocken, Pennsylvania: American Society for Testing and Materials (2006).

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Authors and Affiliations

  1. Centre Composite, Riga, LV-1073, Latvia

    A. M. Timonin

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  1. A. M. Timonin
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Correspondence to A. M. Timonin.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 52, No. 4, pp. 665-690, July-August, 2016.

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Timonin, A.M. Finite-Layer Method: Exact Numerical and Analytical Calculations of the Energy Release Rate for Unidirectional Composite Specimens in Double-Cantilever Beam and End-Notched Flexure Tests. Mech Compos Mater 52, 469–488 (2016). https://doi.org/10.1007/s11029-016-9598-8

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  • DOI: https://doi.org/10.1007/s11029-016-9598-8

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