Analytical Study of Elastic-Plastic Fracture in the Crack-Lap Shear Multilayered Beam Configuration

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Abstract

This paper reports an analytical study of delamination fracture in the Crack-Lap Shear (CLS) multilayered beam configuration with taking into account the material non-linearity. A delamination crack was located arbitrary along the beam height. It was assumed that the CLS mechanical response can be described by using a power-law stress-strain relation. It should be mentioned that each layer may have different material constants in the stress-strain relation. Besides, the thickness of each layer may be different. The classical beam theory was applied in the present study. The non-linear fracture behaviour was analyzed by the J-integral. Analytical solutions of the J-integral were obtained for homogeneous as well as for multilayered CLS beams. In order to verify the solutions obtained, analyses of the strain energy release rate were developed with considering material non-linearity. Material properties and crack location effects on the non-linear fracture behaviour were investigated. The analysis revealed that the J-integral value increases when the material non-linearity is taken into account. It was found also that the J-integral value decreases with increasing the lower crack arm thickness. The approach developed here is very convenient for parametric fracture analyses. The solutions derived can be used for optimization of the CLS multilayered beams with respect to their fracture performance.

[1] Davidson, B. D., V. Sundararaman. A Single-Leg Bending Test for Interfacial Fracture Toughness Determination. Int. J. Fract., 78 (1996), 193-210.

[2] Narin, J. A. Energy Release Rate Analysis of Adhesive and Laminate Double Cantilever Beam Specimens Emphasizing the Effect of Residual Stresses. Int. J. Adh. Adhes., 20 (1999), 59-70.

[3] Yeung, D. T. S., D. C. C. Lam, M. M. F. Yuen. Specimen Design for Mixed Mode Interfacial Fracture Properties Measurement in Electronic Packages. J. Electr. Packag., 122 (2000), 67-72.

[4] Szekrenyes, A., W. M. Vicente. Interlaminar Fracture Analysis in the GII-GIII Plane Using Prestressed Transparent Composite Beams. Composites Part A: Appl. Sci. Manuf., 43 (2012), 95-103.

[5] Szekrenyes, A. Fracture Analysis in the Modified Split-Cantilever Beam Using the Classical Theories of Strength of Materials. J. Phys.: Conference Series, 240 (2010), 012030.

[6] Guadette, F. G., A. E. Giannapoulos, S. Suresh. Interfacial Cracks in Layered Materials Subjected to a Uniform Temperature Change. Int. J. Fract., 28 (2001), 5620-5629.

[7] Jiao, J., G. K. Gurumurthy, E. J. Kramer, Y. Sha, C. Y. Hui, P. Borgesen. Measurement of Interfacial Fracture Toughness Under Combined Mechanical and Thermal Stress. J. Electron Packag., 120 (1998), 325-349.

[8] Markov, I., D. Dinev. Theoretical and Experimental Investigation of a Beam Strengthened by Bonded Composite Strip. Reports of International Scientific Conference VSU’2005, 2005.

[9] Yokozeki, T., T. Ogasawara, T. Aoki. Correction Method for Evaluation of Interfacial Fracture Toughness of DCB, ENF and MMB Specimens with Residual Thermal Stresses. Compos. Sci. Technol., 68 (2008), 760-767.

[10] Hsuesh, C. H., W. H. Tuan, W. C. J. Wei. Analyses of Steady-State Interface Fracture of Elastic Multilayered Beams Under Four-Point Bending. Scripta Mater., 60 (2009), 721-724.

[11] Her, S-C., W-B. Su. Interfacial Fracture Toughness of Multilayered Composite Structures. Strength of Materials, 47 (2015) No. 1; DOI:10.1007/s11223-015-9646-y.

[12] Rice, J. R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. J. Appl. Mech., 35 (1968), 379-386.

[13] Cherepanov, G. Brittle Materials Fracture Mechanics. Nauka, M., 1974.

[14] Broek, D. Elementary Engineering Fracture Mechanics. Springer, 1986.

[15] Hoff, N. J. The Analysis of Structures. John Wiley&Sons, New York, 1956.

[16] NADAI, A. Theory of Flow and Fracture of Solids, 2. McGraw-Hill, New York, 1963.

[17] Seely, F. B., J. O. Smith. Advanced Mechanics of Materials, JohnWiley&Sons, New York, 1967.

[18] Washizu, K. Variational Methods in Elasticity and Plastici, Pergamon press, Oxford, 1974.

[19] Hutchinson, J. W., Z. Suo. Mixed Mode Cracking in Layered Materials. Adv. Appl. Mech., 64 (1992), 804-810.

Journal of Theoretical and Applied Mechanics

The Journal of Institute of Mechanics of Bulgarian Academy of Sciences

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CiteScore 2017: 1.14

SCImago Journal Rank (SJR) 2017: 0.217
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