Experimental and theoretical investigation of the critical load of U-notched laminated composite specimens under in-plane shear loading

Document Type : Research Article

Authors

Faculty of New Science and Technologies, University of Tehran

Abstract

Numerous failure models for prediction of the load-carrying capacity of cracked and notched laminated composites have been of interest to researchers in the field of fracture mechanics. The cause of the importance of this subject was the extensive use of notched composite laminates in aerospace industries in the last decades. In this investigation, it was tried to predict the load-carrying capacity (critical failure load) of U-notched laminated composite specimens with various layup configurations under pure mode II loading (in-plane shear loading) conditions, by utilizing a simple and novel concept proposed recently by the authors. The new composed criteria have been proposed in the field of orthotropic fracture mechanics for the first time. For this aim, by using a newly proposed concept, namely the virtual isotropic material concept, and combining it with two well-known brittle fracture criteria in the field of linear elastic fracture mechanics, namely the maximum tangential stress and the mean stress criteria, the experimental results of the failure of the U-notched laminated semi-circular bend composite specimens under pure mode II loading condition, were theoretically predicted by using new last-ply-failure load curves. It was revealed that the experimental results are in good agreement with the theoretical predictions.

Keywords

Main Subjects


[1]
P. Beaumont, The failure of fiber composites: An overview, J Strain Anal, 24 (1989) 189-205.
[2]
M. Waddoups, J.R. Eisenman, B. Kaminski, Macroscopic fracture mechanics of advanced composite materials, J Compos Mater, 5 (1971) 446-451.
[3]
J. H. Zhao, X. F. Wang, L. R. Dhrani, Notch stress concentrations and failure characteristics in laminates with triple parallel notches, Compos Sci and Tech, 60 (2000) 2865-2872.
[4]
J. Awerbuch, H. Hahn, Crack-tip damage and fracture toughness of boron/aluminum composites, J Compos Mater, 13 (1979) 82-107.
[5]
J. Lee, C. Soutis, Measuring the notched compressive strength of composite laminates: Specimen size effects, Compos Sci and Tech, 68 (2008) 2359–2366.
[6]
V. Rizov, Mixed mode fracture study of polymer composites using single edge notched bend specimens, Comput Mater Sci, 77 (2013) 1-6.
[7]
L. Bokwon, V. Sankar, Lay-up independent fracture criterion for notched laminated composites, Compos Sci and Tech, 66 (2006) 2491-2499.
[8]
J. Whitney, R. Nuismer, Stress fracture criteria for laminated composites containing stress concentration, J Compos Mater, 8 (1974) 253-265.
[9]
S.C. Tan, Notched strength prediction and design of laminated composites under in-plane loadings, J Compos Mater, 21 (1987) 925-948.
[10]
S.C. Tan, Laminated composites containing an elliptical opening-II. experiment and model modification,  J Compos Mater, 21 (1987) 949-968.
[11]
R.B. Pipes, Wetherhold RC, Gillespie JW. Macroscopic fracture of fibrous composites, Mater Sci Eng, 45 (1980) 247-253.
[12]
J.K. Kim, D.S. Kim, N. Takeda, Notched strength and effective crack growth in woven fabric laminates, J Compos Mater, 29 (1995) 982-998.
[13]
J. Backlund, C.G. Aronsson, Tensile Fracture of Laminates with Holes and Cracks, J Compos Mater, 20 (1986) 259-285.
[14]
C.G. Aronsson, J. Backlund, Tensile fracture of laminates with cracks, J Compos Mater, 20 (1986) 287-307.
[15]
B.N. Nguyen, Three-dimensional modeling of damage in laminated composites containing a central hole, J Compos Mater, 31 (1997) 1672-1693.
[16]
G. Lawcock, L. Ye, Y. Mai, Progressive damage and residual strength of a carbon fiber reinforced metal laminate, J Compos Mater, 31 (1997) 762-787.
[17]
A. Afaghi-Khatibi, L. Ye, Y. Mai, An effective crack growth model for residual strength evaluation of composite laminates with circular holes, J Compos Mater, 30 (1996) 142-163.
[18]
N.K. Naik, P.S. Shembekar, M.K. Verma, On the influence of stacking sequence on the notch sensitivity of fabric laminates, J Compos Mater, 24 (1990) 838–52.
[19]
I. Eriksson, C.G. Aronsson, Strength of tensile loaded graphite/epoxy laminates containing cracks, open and filled holes, J Compos Mater, 24 (1990) 456-482.
[20]
C.J. Liu, A.H. Nijhof, L.J. Ernst, R. Marissen, A new ultimate strength model of notched composite laminates – including the effects of matrix failure. J Compos Mater, 44 (2010) 1335–49.
[21]
P. Ladeveze, A damage computational method for composite structures, Comput Struct, 44 (1992) 79-87.
[22]
B. Mohammadi, H. Hosseini-Toudeshky, M.H. Sadr-Lahidjani, Damage evolution of laminated composites using continuum damage mechanics incorporate with interface element, Key Eng Mater, 385 (2008) 277-280.
[23]
B. Mohammadi, H. Hosseini-Toudeshk, M.H. Sadr-Lahidjan, S. Aivazzadeh, Prediction of inelastic behavior of composite laminates using multi-surface continuum damage-plasticity, Adv Mater Res, 47 (2008) 773-776.
[24]
B. Mohammadi, A. Kazemi, R. Ghasemi, Damage analysis of holed composite laminates using continuum damage mechanics, (In Persian), Journal of Science and Technology of Composites, 2 (2015) 23-34.
[25]
L. Feng, X, Qian, Rapid S-N type life estimation for low sycle fatigue of high-strength steels at a low ambient temperature, Steel and Compos struct, 33 (2019) 777-792.
[26]
E. Satria, S.H. Kato, S.H. Nakasawa, Study on dynamic behavior of a new type of two-way single layer lattice dome with nodal eccentricity, Steel and Compos Struct, 8 (2008) 6-12.
[27]
F.J. Gómez, M. Elices, A. Valiente, Cracking in PMMA containing U‐shaped notches, Fatigue Fract Eng Mater Struct, 23 (2000) 795-803.
[28]
F.J. Gómez, M. Elices, A fracture criterion for sharp V-notched samples, Int J Fract, 123 (2003) 163-75.
[29]
F.J. Gómez, M. Elices, J. Planas, The cohesive crack concept: application to PMMA at -60 (deg.), Eng Fract Mech, 72 (2005) 1268-85.
[30]
Z. Yosibash, A. Bussiba, I. Gilad, Failure criteria for brittle elastic materials, Int J Fract, 125 (2004) 307-33.
[31]
F. Erdogan, G. Sih, On the crack extension in plates under plane loading and transverse shear, J Basic Eng Trans, 85 (1963) 528-534.
[32]
F. Berto, P. Lazzarin, F.J. Gomez, Elices M. Fracture assessment of U-notches under mixed mode loading: two procedures based on the equivalent local mode I concept, Int J Fract, 148 (2007) 415-433.
[33]
M.R. Ayatollahi, A.R. Torabi, A criterion for brittle fracture in U-notched components under mixed-mode loading, Eng Fract Mech, 76 (2009) 1883-96.
[34]
A.R. Torabi, Fracture assessment of U-notched graphite plates under tension, Int J Fract, 81 (2013) 285-292.
[35]
A.R. Torabi, M. Fakoor, E. Pirhadi, Tensile fracture in coarse-grained polycrystalline graphite weakened by a U-shaped notch, Eng Fract Mech, 111 (2013) 77-85.
[36]
A.R. Torabi, E. Pirhadi, Notch failure in laminated composites under opening mode, Compos Part B, 172, (2019) 61-75.
[37]
A.R. Torabi, E. Pirhadi, On the ability of fracture mechanics in predicting the last-ply-failure of blunt V-notch laminated composite specimens: A hard problem can be easily solved by conventional methods, Eng Fract Mech, 217 (2019) 106534.
[38]
A.R. Torabi, E. Pirhadi, Extension of the virtual isotropic material concept to mixed mode loading for predicting the last-ply-failure of U-notched glass/epoxy laminated composite specimens, Composite Part B, 176 (2019) 106537.
[39]
M.J. Laffan, S.T. Pinho, P. Robinson, L. Iannucci, Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction, Compos Sci and Tech, 70 (2010) 606–613.
[40]
J.H. Underwood, M.T. Kortschot, Notch-tip Damage and Translaminar Fracture Toughness Measurements from Carbon/Epoxy Laminates, US Army Armament Research, Development and EngineeringCentre, Technical Report ARCCB-TR-94010, (1994) 94010.
[41]
S.T. Pinho, P. Robinson, L. Iannucci, Fracture toughness of the tensile and compressive fibre failure modes in laminated composites, Compos Sci and Tech, 66 (2006) 2069–2079.
[42]
J.H. Underwood, M.T. Kortschot, W.R. Lloyd, H.L. Eidinoff, D.A. Wilson, N. Ashbaugh, Translaminar Fracture Toughness Test Methods and Results from Interlaboratory Tests of Carbon/epoxy Laminates, Fract Mech, 26 (1995) ASTM STP 1256.
[43]
Y.T. Yeow, D.H. Morris, H.F. Brinson, A correlative study between analysis and experiment on the fracture behavior of graphite/epoxy composites, J Test and Eval, 7 (1979) 117–125.
[44]
R. El-Hajjar, R. Haj-Ali, Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen, Eng Fract Mech, 72 (2005) 631–643.
[45]
C. Soutis, P.T. Curtis, N.A. Fleck, Compressive failure of notched carbon fibre composites, Proceedings of the Royal Society, 440  (1993) 241–256.
[46]
C.G. Sih, P.C. Paris, G.R. Irwin, On cracks in rectilinearly anisotropic bodies, International Journal of Fracture Mechanics, 1(3) (1965) 189–203.
[47]
Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials. Annual Book of ASTM Standard, D3039/D3039M.
[48]
Standard Test Method for Trans-laminar Fracture Toughness of Laminated Polymer Matrix Composite Materials. Annual Book of ASTM Standard, E1922-04.
[49]
R.O. Ritchie, J.F. Knott, J.R. Rice, On the relationship between critical stress and fracture toughness in mild steel, J Mech Phys Solids, 21 (1973) 395-410.
[50]
D. Taylor, Predicting the fracture strength of ceramic materials using the theory of critical distances, Eng Fract Mech, 71 (2004) 2407-2416.
[51]
K. Wieghard, U. Spalten, ZerreißenelastischerKorper Z. Math Phys 1907;55:60-103 Translated by Rossmanith HP, Fatigue Fract Eng Mater Struct, 18, (1995) 1371-1405.
[52]
M.R. Ayatollahi, A.R. Torabi, Brittle fracture in rounded-tip V-shaped notches, Mater Design, 31 (2010) 60-7.