Abstract
The problem of a completely debonded short fiber (rigid line inclusion/anticrack) embedded in a 2D isotropic elastic soft matrix subjected to the remote loading condition is of fundamental interest. The current work investigates completely debonded anticrack embedded in a soft (isotropic) matrix using Kolosov Muskhelisvili's complex potential framework. Here two configurations are studied: debonded inclusion oriented (i) parallel and (ii) perpendicular to the loading direction. In particular, the potentials take the form of a non-homogeneous Riemann—Hilbert equation for the given problem. Upon solving analytical forms of potentials, the stress fields were obtained. The stress field for the fully debonded anticrack exhibited oscillatory singular behavior between r−3/4 and r−1/4 with the dependence on the oscillatory index ε and material constants. The correctness of the analytical solution was validated using numerical simulation and experiments based on the digital photoelasticity technique. The analytical results were in good agreement with the experimental and numerically obtained stress fields confirming the accuracy of it. The magnitude of singularity is quantified by defining a complex stress intensity factor at the tip of the discontinuity and compared with the experimentally estimated value. So far in the literature, no full-field analytical solution exists for the completely debonded rigid inclusion embedded in an isotropic soft matrix. The solution obtained in the present work is of fundamental importance in developing the constitutive properties of short fiber reinforced thermoplastic (SFRT) composites.
References
1.
Sato
, N.
, Kurauchi
, T.
, Sato
, S.
, and Kamigaito
, O.
, 1991
, “Microfailure Behaviour of Randomly Dispersed Short Fibre Reinforced Thermoplastic Composites Obtained by Direct SEM Observation
,” J. Mater. Sci.
, 26
(14), pp. 3891
–3898
. 2.
Hull
, D.
, and Clyne
, T.
, 1996
, An Introduction to Composite Materials
, 2nd ed., Cambridge University Press
, Cambridge
.3.
Andrianov
, I. V.
, Bolshakov
, V. I.
, Danishevs’kyy
, V. V.
, and Weichert
, D.
, 2007
, “Asymptotic Simulation of Imperfect Bonding in Periodic Fiber-Reinforced Composite Materials Under Axial Shear
,” Int. J. Mech. Sci.
, 49
(12), pp. 1344
–1354
. 4.
Fan
, M.
, Yi
, D. K.
, and Xiao
, Z. M.
, 2014
, “Elastic-Plastic Stress Investigation for an Arc-Shaped Interface Crack in Composite Material
,” Int. J. Mech. Sci.
, 83
, pp. 104
–111
. 5.
Arif
, M. F.
, Meraghni
, F.
, Chemisky
, Y.
, Despringre
, N.
, and Robert
, G.
, 2014
, “In Situ Damage Mechanisms Investigation of PA66/GF30 Composite: Effect of Relative Humidity
,” Compos. Part B
, 58
, pp. 487
–495
. 6.
Notta-Cuvier
, D.
, Lauro
, F.
, and Bennani
, B.
, 2015
, “Modelling of Progressive Fibre/Matrix Debonding in Short-Fibre Reinforced Composites Up To Failure
,” Int. J. Solids Struct.
, 66
, pp. 140
–150
. 7.
Hanhan
, I.
, and Sangid
, M. D.
, 2021
, “Damage Propagation in Short Fiber Thermoplastic Composites Analyzed Through Coupled 3D Experiments and Simulations
,” Compos. Part B
, 218
, p. 108931
. 8.
Agarwal
, B. D.
, Broutman
, L. J.
, and Chandrashekhar
, K.
, 2006
, Analysis and Performance of Fiber Composites
, 3rd ed., Wiley
, New York
.9.
Liu
, Y. J.
, Nishimura
, N.
, Otani
, Y.
, Takahashi
, T.
, Chen
, X. L.
, and Munakata
, H.
, 2005
, “A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model
,” ASME J. Appl. Mech.
, 72
(1), pp. 115
–128
. 10.
De
, S. K.
, and White
, J. R.
, 1996
, Short Fibre-Polymer Composites
, 1st ed., Woodhead Publication
, Cambridge
.11.
Fu
, S. Y.
, Hu
, X.
, and Yue
, C. Y.
, 1999
, “Effects of Fibre Length and Orientation Distributions on the Mechanical Properties of Short-Fibre-Reinforced Polymers—A Review
,” Mater. Sci. Res. Int.
, 5
(6Appendix
), pp. 74
–83
. 12.
Fu
, S. Y.
, Lauke
, B.
, and Mai
, Y. W.
, 2009
, Science and Engineering of Short Fibre Reinforced Polymers Composites
, 1st ed., Woodhead Publication
, Cambridge
.13.
Nguyen
, B. N.
, and Khaleel
, M. A.
, 2004
, “A Mechanistic Approach to Damage in Short-Fiber Composites Based on Micromechanical and Continuum Damage Mechanics Descriptions
,” Compos. Sci. Technol.
, 64
(5
), pp. 607
–617
. 14.
Tamboura
, S.
, Abdessalem
, A.
, Fitoussi
, J.
, Daly
, H. B.
, and Tcharkhtchi
, A.
, 2022
, “On the Mechanical Properties and Damage Mechanisms of Short Fibers Reinforced Composite Submitted to Hydrothermal Aging: Application to Sheet Molding Compound Composite
,” Eng. Fail. Anal.
, 131
, p. 105806
. 15.
Zhang
, L.
, Li
, Z.
, Zhang
, H.
, Liu
, Z.
, and Zhu
, P.
, 2022
, “Fatigue Failure Mechanism Analysis and Life Prediction of Short Fiber Reinforced Polymer Composites Under Tension-Tension Loading
,” Int. J. Fatigue
, 160
, p. 106880
. 16.
Wang
, S. S.
, and Chim
, E. S. M.
, 1983
, “Fatigue Damage and Degradation in Random Short-Fiber SMC Composite
,” J. Compos. Mater.
, 17
(2
), pp. 114
–134
. 17.
Noda
, K.
, Takahara
, A.
, and Kajiyama
, T.
, 2001
, “Fatigue Failure Mechanisms of Short Glass-Fiber Reinforced Nylon 66 Based on Nonlinear Dynamic Viscoelastic Measurement
,” Polymer
, 42
(13
), pp. 5803
–5811
. 18.
Huang
, H.
, and Talreja
, R.
, 2006
, “Numerical Simulation of Matrix Micro-cracking in Short Fiber Reinforced Polymer Composites: Initiation and Propagation
,” Compos. Sci. Technol.
, 66
(15
), pp. 2743
–2757
. 19.
Klimkeit
, B.
, Castagnet
, S.
, Nadot
, Y.
, Habib
, A.
, Benoit
, G.
, Bergamo
, S.
, Dumas
, C.
, and Achard
, S.
, 2011
, “Fatigue Damage Mechanisms in Short Fiber Reinforced PBT+PET GF30
,” Mater. Sci. Eng. A
, 528
(3
), pp. 1577
–1588
. 20.
Jendli
, Z.
, Fitoussi
, J.
, Meraghni
, F.
, and Baptiste
, D.
, 2005
, “Anisotropic Strain Rate Effects on the Fibre–Matrix Interface Decohesion in Sheet Moulding Compound Composites
,” Compos. Sci. Technol.
, 65
(3–4
), pp. 387
–393
. 21.
Shirinbayan
, M.
, Fitoussi
, J.
, Bocquet
, M.
, Meraghni
, F.
, Surowiec
, B.
, and Tcharkhtchi
, A.
, 2017
, “Multi-scale Experimental Investigation of the Viscous Nature of Damage in Advanced Sheet Molding Compound (A-SMC) Submitted to High Strain Rates
,” Compo. Part B
, 115
, pp. 3
–13
. 22.
Rolland
, H.
, Saintiera
, N.
, Raphael
, I.
, Lenoir
, N.
, King
, A.
, and Robert
, G.
, 2018
, “Fatigue Damage Mechanisms of Short Fiber Reinforced PA66 as Observed by In-Situ Synchrotron X-Ray Microtomography
,” Compos. Part B
, 143
, pp. 217
–229
. 23.
Dundurs
, J.
, and Markenscoff
, X.
, 1989
, “A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities
,” ASME J. Appl. Mech.
, 56
(3
), pp. 550
–555
. 24.
Hu
, K. X.
, and Chandra
, A.
, 1993
, “Interactions Among General Systems of Cracks and Anticracks: An Integral Equation Approach
,” ASME J. Appl. Mech.
, 60
(4
), pp. 920
–928
. 25.
Rolland
, H.
, Saintier
, N.
, and Robert
, G.
, 2016
, “Damage Mechanisms in Short Glass Fibre Reinforced Thermoplastic During In Situ Microtomography Tensile Tests
,” Compos. Part B
, 90
, pp. 365
–377
. 26.
Jobin
, T. M.
, Khaderi
, S. N.
, and Ramji
, M.
, 2022
, “A Photoelastic Investigation of Partially Debonded Rigid Line Inclusion
,” Int. J. Mech. Sci.
, 217
, p. 107003
. 27.
Kattis
, M.
, 1991
, “Thermal Stress Intensity Factors for a Partially Bonded Rigid Fiber Inclusion
,” Eng. Fract. Mech.
, 40
(1
), pp. 159
–165
. 28.
Wang
, Z.
, Zhang
, H. T.
, and Chou
, Y. T.
, 1985
, “Characteristics of the Elastic Field of a Rigid Line Inhomogeneity
,” ASME J. Appl. Mech.
, 52
(4
), pp. 818
–822
. 29.
Nuismer
, R. J.
, and Sendeckyj
, G. P.
, 1977
, “On the Changing Order of Singularity at a Crack Tip
,” ASME J. Appl. Mech.
, 44
(4
), pp. 625
–630
. 30.
Ballarini
, R.
, 1990
, “A Rigid Line Inclusion at a Bimaterial Interface
,” Eng. Fract. Mech.
, 37
(1
), pp. l
–5
. 31.
Symington
, M. F.
, 1987
, “Eigenvalues for Interface Cracks in Linear Elasticity
,” ASME J. Appl. Mech.
, 54
(4
), pp. 973
–974
. 32.
Hills
, D. A.
, and Barber
, J. R.
, 1993
, “Interface Cracks
,” Int. J. Mech. Sci.
, 3
(1
), pp. 27
–37
. 33.
Chang
, J.
, and Xu
, J. Q.
, 2007
, “The Singular Stress Field and Stress Intensity Factors of a Crack Terminating at a Bimaterial Interface
,” Int. J. Mech. Sci.
, 49
(7
), pp. 888
–897
. 34.
Cheng
, Z.
, Gao
, D.
, and Zhong
, Z.
, 2012
, “Interface Crack of Two Dissimilar Bonded Functionally Graded Strips With Arbitrary Distributed Properties Under Plane Deformations
,” Int. J. Mech. Sci.
, 54
(1
), pp. 287
–293
. 35.
Wang
, L.
, Bai
, R. X.
, and Chen
, H.
, 2013
, “Analytical Modeling of the Interface Crack Between a Piezoelectric Actuator and an Elastic Substrate Considering Shear Effects
,” Int. J. Mech. Sci.
, 66
, pp. 141
–148
. 36.
Shi
, P.
, and Zheng
, X.
, 2015
, “The Yoffe-Type Moving Tubular Interface Crack in a Hollow Composite Cylinder With Finite Length
,” Int. J. Mech. Sci.
, 98
, pp. 29
–38
. 37.
Bhat
, S.
, Nagesh
, S.
, Kambar
, M. M.
, and Ukadgaonker
, V. G.
, 2017
, “Strain Based Investigation of Mode I Crack Near Strong-Weak Interface in SSY Regime
,” Int. J. Mech. Sci.
, 123
, pp. 224
–237
. 38.
Itou
, S.
, 2017
, “Stresses Around a Moving Griffith Crack at an Interface Between a Non-homogeneous Bonding Layer and Two Dissimilar Orthotropic Half-Spaces
,” Int. J. Mech. Sci.
, 124
, pp. 122
–131
. 39.
England
, A. H.
, 1965
, “A Crack Between Dissimilar Media
,” ASME J. Appl. Mech.
, 32
(2
), pp. 400
–402
. 40.
Williams
, M. L.
, 1959
, “The Stresses Around a Fault or Crack in Dissimilar Media
,” Bull. Seismol. Soc. Am.
, 49
(2
), pp. 199
–204
. 41.
Atkinson
, C.
, 1977
, “On Stress Singularities and Interfaces in Linear Elastic Fracture Mechanics
,” Int. J. Fract.
, 13
(6
), pp. 807
–820
. 42.
Comninou
, M.
, 1978
, “The Interface Crack in a Shear Field
,” ASME J. Appl. Mech.
, 45
(2
), pp. 287
–290
. 43.
Rice
, J. R.
, 1988
, “Elastic Fracture Mechanics Concepts for Interfacial Cracks
,” ASME J. Appl. Mech.
, 55
(1
), pp. 98
–103
. 44.
Comninou
, M.
, 1990
, “An Overview of Interface Cracks
,” Eng. Fract. Mech.
, 37
(1
), pp. 197
–208
. 45.
Xu
, L.
, and Tippur
, H. V.
, 1995
, “Fracture Parameters for Interfacial Cracks: An Experimental Finite Element Study of Crack Tip Fields and Crack Initiation Toughness
,” Int. J. Fract.
, 71
(4
), pp. 345
–363
. 46.
Singh
, R. P.
, and Shukla
, A.
, 1996
, “Characterization of Isochromatic Fringe Patterns for a Dynamically Propagating Interface Crack
,” Int. J. Fract.
, 76
(4
), pp. 293
–310
. 47.
Soh
, A. K.
, 1999
, “An Improved Photoelastic Technique for Determining the Mixed-Mode Stress Intensity Factors for Interfacial Cracks in a Bi-material
,” Compos. Sci. Technol.
, 59
(7
), pp. 1033
–1039
. 48.
Marur
, P. R.
, and Tippur
, H. V.
, 1999
, “A Strain Gauge Method for Determination of Fracture Parameters in Bimaterial Systems
,” Eng. Fract. Mech.
, 64
(1
), pp. 87
–104
. 49.
Ravichandran
, M.
, and Ramesh
, K.
, 2004
, “Determination of Stress Intensity Factors for an Interfacial Crack in a Bi-material by Digital Photoelasticity
,” Appl. Mech. Mater.
, 1
, pp. 139
–146
. 50.
Ravichandran
, M.
, and Ramesh
, K.
, 2005
, “Evaluation of Stress Field Parameters for an Interface Crack in a Bimaterial by Digital Photoelasticity
,” J. Strain Anal. Eng. Des.
, 40
(4
), pp. 327
–344
. 51.
Desai
, C. K.
, Basu
, S.
, and Parameswaran
, V.
, 2012
, “Determination of Complex Stress Intensity Factor for a Crack in a Bimaterial Interface Using Digital Image Correlation
,” Opt. Lasers Eng.
, 50
(10
), pp. 1423
–1430
. 52.
Toya
, M.
, 1975
, “Debonding Along the Interface of an Elliptic Rigid Inclusion
,” Int. J. Fract.
, 11
(6
), pp. 989
–1002
. 53.
Chaudhuri
, R. A.
, 2006
, “Three-Dimensional Singular Stress Field Near a Partially Debonded Cylindrical Rigid Fiber
,” Compos. Struct.
, 72
(2
), pp. 141
–150
. 54.
Antipov
, Y.
, and Mkhitaryan
, S.
, 2017
, “A Crack Induced by a Thin Rigid Inclusion Partly Debonded From the Matrix
,” Q. J. Mech. Appl. Math.
, 70
, pp. 153
–185
. 55.
Prasad
, P. B. N.
, and Simha
, K. R. Y.
, 2003
, “Interface Crack Around Circular Inclusion: SIF, Kinking, Debonding Energetics
,” Eng. Fract. Mech.
, 70
(2
), pp. 285
–307
. 56.
Markenscoff
, X.
, and Ni
, L.
, 1996
, “The Debonded Interface Anticrack
,” ASME J. Appl. Mech.
, 63
(3
), pp. 621
–627
. 57.
Wang
, X.
, and Schiavone
, P.
, 2020
, “Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material
,” Q. J. Mech. Appl. Math.
, 73
(1
), pp. 76
–83
. 58.
Wang
, G.
, and Pindera
, M. J.
, 2016
, “Locally-Exact Homogenization Theory for Transversely Isotropic Unidirectional Composites
,” Mech. Res. Commun.
, 78
, pp. 2
–14
. 59.
Shu
, W.
, and Stanciulescu
, I.
, 2020
, “Multiscale Homogenization Method for the Prediction of Elastic Properties of Fiber-Reinforced Composites
,” Int. J. Solids Struct.
, 203
, pp. 249
–263
. 60.
Noselli
, G.
, Dal Corso
, F.
, and Bigoni
, D.
, 2010
, “The Stress Intensity Near a Stiffener Disclosed by Photoelasticity
,” Int. J. Fract.
, 166
(1–2
), pp. 91
–103
. 61.
Misseroni
, D.
, Dal Corso
, F.
, Shahzad
, S.
, and Bigoni
, D.
, 2014
, “Stress Concentration Near Stiff Inclusions: Validation of Rigid Inclusion Model and Boundary Layers by Means of Photoelasticity
,” Eng. Fract. Mech.
, 121
, pp. 87
–97
. 62.
Dal Corso
, F.
, Bigoni
, D.
, and Gei
, M.
, 2008
, “The Stress Concentration Near a Rigid Line Inclusion in a Prestressed, Elastic Material. Part I: Full-Field Solution and Asymptotics
,” J. Mech. Phys. Solids
, 56
(3
), pp. 815
–838
. 63.
Bigoni
, D.
, Dal Corso
, F.
, and Gei
, M.
, 2008
, “The Stress Concentration Near a Rigid Line Inclusion in a Prestressed, Elastic Material. Part II: Implications on Shear Band Nucleation, Growth and Energy Release Rate
,” J. Mech. Phys. Solids
, 56
(3
), pp. 839
–857
. 64.
Chen
, Q.
, Chatzigeorgiou
, G.
, and Meraghni
, F.
, 2021
, “Extended Mean-Field Homogenization of Viscoelastic-Viscoplastic Polymer Composites Undergoing Hybrid Progressive Degradation Induced by Interface Debonding and Matrix Ductile Damage
,” Int. J. Solids Struct.
, 210
, pp. 1
–17
. 65.
Marguères
, P.
, and Meraghni
, F.
, 2013
, “Damage Induced Anisotropy and Stiffness Reduction Evaluation in Composite Materials Using Ultrasonic Wave Transmission
,” Compos. Part A
, 45
, pp. 134
–144
. 66.
Chen
, Q.
, Chatzigeorgiou
, G.
, Robert
, G.
, and Meraghni
, F.
, 2022
, “Viscoelastic-Viscoplastic Homogenization of Short Glass-Fiber Reinforced Polyamide Composites (PA66/GF) With Progressive Interphase and Matrix Damage: New Developments and Experimental Validation
,” Mech. Mater.
, 164
, p. 104081
. 67.
Chen
, Q.
, Chatzigeorgiou
, G.
, Robert
, G.
, and Meraghni
, F.
, 2023
, “Combination of Mean-Field Micromechanics and Cycle Jump Technique for Cyclic Response of PA66/GF Composites With Viscoelastic–Viscoplastic and Damage Mechanisms
,” Acta Mech.
, 234
(4
), pp. 1
–20
. 68.
Pingle
, P.
, Sherwood
, J.
, and Gorbatikh
, L.
, 2008
, “Properties of Rigid-Line Inclusions as Building Blocks of Naturally Occurring Composites
,” Compos. Sci. Technol.
, 68
(10–11
), pp. 2267
–2272
. 69.
Gakhov
, F. D.
, 1966
, Boundary Value Problems
, 1st ed., Pergamon Press
, Oxford
.70.
England
, A. H.
, 1971
, Complex Variable Methods in Elasticity
, Wiley-Interscience
, New York
.71.
Lu
, J. K.
, 1995
, Complex Variable Method in Plane Elasticity
, World Scientific
, Singapore
.72.
Barber
, J. R.
, 2004
, Elasticity: Solid Mechanics and Its Applications
, 2nd ed., Kluwer Academic Publishers
, Dordrecht
.73.
Sadd
, M. H.
, 2014
, Elasticity: Theory, Applications, and Numerics
, Third ed., Elsevier Butterworth–Heinemann
, Oxford, UK
.74.
Muskhelishvili
, N. I.
, 1953
, Some Basic Problems of the Mathematical Theory of Elasticity
, Noordhoff
, Groningen
.75.
Ramesh
, K.
, 2000
, Digital Photoelasticity: Advanced Techniques and Applications
, Springer Verlag
, Berlin
.76.
Rice
, J. R.
, and Sih
, G. C.
, 1965
, “Plane Problems of Cracks in Dissimilar Media
,” ASME J. Appl. Mech.
, 32
(2
), pp. 418
–423
. 77.
Ramesh
, K.
, Yadav
, A. K.
, and Pankhawalla
, V. A.
, 1995
, “Plotting of Fringe Contours From Finite Element Results
,” Commun. Numer. Methods Eng.
, 11
(10
), pp. 839
–847
. Copyright © 2023 by ASME
You do not currently have access to this content.
