Abstract
There is a significant breakthrough in use of composite materials in modern technology, construction, mechanical engineering and electronics in the past decade. Such popularity takes place due to ability to achieve required (electro-)mechanical properties of the composite. Analyzing stresses, strains and electric displacements in the elements of mechanical or electromechanical structures, the most important issue is to determine stress and electric displacement concentrations near the defects or cracks, which are characterized by intensity factors (IFs). Based on the experimental investigations, fracture of composites is found to be primary caused by the cracks located at the interface of the composite components.
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References
Muskhelishvili N (1977) Some basic problems of the mathematical theory of elasticity. Springer, Dordrecht
Panasyuk V (1968) Limit equilibrium of brittle bodies with cracks. Naukova Dumka, Kyiv (translation in English: Michigan information service, Detroit, 1971) (in Russian)
Parton V, Kudryavtsev B (1988) Electromagnetoelasticity. Gordon and Breach Science Publishers, New York
Cherepanov G (1979) Mechanics of brittle fracture. McGraw-Hill International Book Co., New York
Cruse T (1988) Boundary element analysis in computational fracture mechanics. Kluwer Academic Publishers, Dordrecht
Hahn H (1976) Bruchmechanik: Einführung in die theoretischen Grundlagen. Mechanik, Teubner-Studienbüche, Stuttgart
Sneddon L, Lowengrub M (1969) Crack problems in the classical theory of elasticity. Wiley, New York
Sih G (1973) Methods of analysis and solutions of crack problems. Mechanics of fracture, vol 1. Noordhoff International Publisher, Leyden
Kassir M, Sih G (1975) Three dimensional crack problems. Mechanics of fracture, vol 2. Noordhoff International Publisher, Leyden
Altenbach H, Altenbach J, Rikards R (1996) Einführung in die Mechanik der Laminatwerkstoffe. Deutscher Verlag für Grundstoffindustrie, Stuttgart
Qin Q (2001) Fracture mechanics of piezoelectric materials. WIT Press, Southampton and Boston
Kienzler R (1993) Konzepte der Bruchmechanik. Vieweg, Wiesbaden
Atluri S (1986) Computational methods in the mechanics of fracture. Elsevier Science Publisher, Noorth-Holland
Schwalbe K, Scheider I, Cornec A (2013) Guidelines for applying cohesive models to the damage behaviour of engineering materials. Springer, Heidelberg
Freund L (1990) Dynamic fracture mechanics. Cambridge University Press, Cambridge
Gdoutos E (1990) Fracture mechanics criteria and applications. Kluwer, Dordrecht, The Netherlands
Kanninen M, Popelar C (1985) Advanced fracture mechanics. Oxford University Press, New York
Tada H, Paris P, Irwin G (1985) The stress analysis of cracks handbook, 2nd edn. Paris Production Inc., St. Louis
Murakami Y (1987) Stress intensity factors handbook, vols 1–5. Pergamon Press, Oxford
Williams ML (1959) The stresses around a fault or cracks in dissimilar media. Bull Seism Soc America 49:199–204
Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32:418–423
England A (1965) A crack between dissimilar media. Trans ASME J Appl Mech 32:400–402
Erdogan F (1965) Stress distribution in bonded dissimilar materials with cracks. Trans ASME J Appl Mech 32(15):2027–2040
Mossakovsky V, Rybka M (1964) Generalization of the Griffith-Sneddon criterion for the case of a nonhomogeneous body. J Appl Math Mech 28(6):1277–1286
Nahta R, Moran B (1993) Domain integrals for axisymmetric interface crack problems. Int J Solids Struct 30:403–410
Martin-Moran C, Barber J, Comninou M (1983) The penny-shaped interface crack with heat flow. Part 1: perfect contact. J Appl Mech 50:29–36
Martin-Moran C, Barber J, Comninou M (1983) The penny-shaped interface crack with heat flow. Part 2: imperfect contact. J Appl Mech 50:770–776
Zhao M, Dang H, Fan C, Chen Z (2016) Analysis of an arbitrarily shaped interface cracks in a three-dimensional isotropic thermoelastic bi-material. Part 1: theoretical solution. Int J Solids Struct 97:168–181
Rice J (1988) Elastic fracture mechanics concept for interfacial cracks. J Appl Mech 55:98–103
Clements D (1971) A crack between dissimilar anisotropic media. Int J Engen Sci 9:257–265
Hwu C (1993) Fracture parameters for the orthotropic bimaterial interface cracks. Eng Fract Mech 45:89–97
Kattis M (1999) Nonplanar interfacial cracks in anisotropic bimaterials. Int J Fract 98:313–327
Quan W, Sun CT (1998) Methods for calculating stress intensity factors for interfacial cracks between two orthotropic solids. Int J Solids Struct 35:3317–3330
Ting TCT (1986) Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. Int J Solids Struct 22:965–983
Ting TCT (1990) Interface cracks in anisotropic bimaterial. J Mech Phys Solids 38:505–513
Ting TCT (2000) Recent developments in anisotropic elasticity. Int J Solids Struct 37:401–409
Comninou M (1977) The interface crack. J Appl Mech 44:631–636
Comninou M (1978) The interface crack in a shear field. ASME J Appl Mech 45:287–290
Dundurs J, Comninou M (1979) Some consequences of inequality conditions in contact and crack problems. J Elast 9:71–82
Comninou M, Dundurs J (1983) Partial closure of cracks at the interface between a layer and a hald-space. Eng Fract Mech 18:315–323
Ni L, Nemat-Nasser S (1991) Interface cracks in anisotropic dissimilar materials: an analytical solution. J Mech Phys Solids 39:113–144
Ni L, Nemat-Nasser S (1992) Interface cracks in anisotropic dissimilar materials: general case. Quaterly Appl Math 2:305–322
Huang Y, Wang W, Liu C, Rosakis A (1998) Intersonic crack growth in bimaterial interfaces: an investigation of crack face contact. J Mech Phys Solids 46:2233–2259
Simonov IV (1984) On the steady motion of a crack with slip and separation sections along the interface of two elastic materials. J Appl Math Mech 48(3):347–353. https://doi.org/10.1016/0021-8928(84)90144-8
Simonov I (1985) Brittle cleavage of a piecewise-homogeneous elastic medium. J Appl Math Mech 49(2):207–214
Simonov IV (1986) Crack at an interface in a uniform stress field. Mech Compos Mater 21:650–657. https://doi.org/10.1007/BF00605924
Beom H, Atluri S (1996) Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. Int J Fract 75:163–183
Atkinson C (1977) On stress singularities and interfaces in linear elastic fracture mechanics. Int J Fract 13:807–820
Atkinson C (1982) The interface crack with a contact zone (an analytical treatment). Int J Fract 18:161–177
Gautesen A, Dundurs J (1987) The interface crack in a tension field. J Appl Mech 54:93–98
Gautesen A, Dundurs J (1988) The interface crack under a combined loading. ASME J Appl Mech 55:580–586
Dundurs J, Gautesen A (1988) An opportunistic analysis of the interface crack. Int J Fract 36:151–159
Gautesen A (1992) The interface crack in a tension field: an eigenvalue problem for the gap. Int J Fract 55:261–271
Gautesen A (1993) The interface crack under a combined loading. Int J Fract 60:349–361
Loboda V (1993) The quasi-invariant in the theory of interface cracks. Eng Fract Mech 44:573–580
Kharun I, Loboda V (2003) A set of interface cracks with contact zones in combined tension-shear field. Acta Mechanica 166:43–56
Kharun I, Loboda V (2004) A thermoelastic problem for interface cracks with contact zones. Int J Solids Struct 41:159–175
Kharun I, Loboda V (2002) Interface cracks with contact zones in the field of concentrated forces and moments. Math Methods Phys-Mech Fields 45(2):103–113 (in Ukrainian)
Wang SS, Choi I (1983) The interface crack between dissimilar anisotropic composite materials. J Appl Mech 50:169–178
Qu J, Xue Y (1998) Three-dimensional interface cracks in anisotropic bimaterials: the non-oscillatory case. J Appl Mech 65:1048–1055
Nakhmein E, Nuller B (1976) A method for solving of contact periodic problems for the elastic strip and ring. USSR AS, MTT 40(3):53–61 (in Russian)
Nakhmein E, Nuller B (1986) Contact between an elastic half-plane and a partly separated stamp. J Appl Math Mech 50(4):507–515
Nakhmein E, Nuller B (1988) The pressure of a system of stamps on an elastic half-plane under general conditions of contact adhesion and slip. J Appl Math Mech 52(2):223–230
Nakhmein E, Nuller B (1992) Combined periodic boundary-value problems and their applications in the theory of elasticity. J Appl Math Mech 56:82–89
Herrmann K, Loboda V (1999) On interface crack models with contact zones situated in an anisotropic bimaterial. Arch Appl Mech 69:317–335
Herrmann K, Loboda V (2001) Contact zones models for an interface crack in a thermomechanically loaded anisotropic bimaterial. J Therm Stress 24:479–506
Kharun I, Loboda V (2004) A problem of thermoelasticity for a set of interface cracks with contact zones between dissimilar anisotropic materials. Mech Mater 7:585–600
Grinchenko V, Ulitko A, Shulga N (1989) Electroelasticity. In Mechanics of coupled fields in the elements of constructions, 5 vol, Naukova Dumka (in Russian)
Zhang T, Zhao M, Tong P (2002) Fracture of piezoelectric ceramics. Adv Appl Mech 38:147–289
Chen Y-H, Lu T (2003) Cracks and fracture in piezoelectrics. Adv Appl Mech 39:121–215
Zhang T, Gao C-F (2004) Fracture behaviors of piezoelectric materials. Theor Appl Fract Mech 41:339–379
Schneider G (2007) Influence of electric field and mechanical stresses on the fracture of ferroelectrics. Ann Rev Mater Res 37:491–538
Kudryavtsev B, Parton V, Rakitin V (1975) Fracture mechanics of piezoelectric materials. Rectilinear tunnel crack on the boundary with a conductor. J Appl Math Mech 39(1):136–146
Fil’shtinskii L, Fil’shtinskii M (1994) Green’s function for a composite piezoceramic plane with a crack between phases. J Appl Math Mech 58(2):355–362
Wang T, Han X (1999) Fracture mechanics of piezoelectric materials. Int J Fract 98:15–35
Gao C-F, Wang M (2000) Collinear permeable cracks between dissimilar piezoelectric materials. Int J Solids Struct 37:4969–4986
Beom H (2003) Permeable cracks between two dissimilar piezoelectric materials. Int J Solids Struct 40:6669–6679
Gao C-F, Hausler C, Balke H (2004) Periodic permeable interface cracks in pizoelectric materials. Int J Solids Struct 41:323–335
Zhou Z-G, Wang B (2006) Investigation of behavior of Mode-I interface crack in piezoelectric materials by using Schmidt method. Appl Math Mech 27:871–882
Deeg W (1980) The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD thesis, Stanford University
Sosa H (1991) Plane problems in piezoelectric media with defects. Int J Solids Struct 28:491–505
Suo Z, Kuo CM, Barnett DM, Willis JR (1992) Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40:739–765
Lekhnitsky S (1963) Theory of elasticity of an anisotropic elastic body. San Francisco: Holden-Day
Stroh AN (1962) Steady state problems in anisotropic elasticity. J Math Phys 41:77–103
Gao C-F, Fan W (1999) Exact solution for the plane problem in piezoelectric materials with an elliptic hole or a crack. Int J Solid Struct 36:2527–2540
Pak Y (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54:79–100
Ru CQ, Mao X, Epstein M (1998) Electric-field induced interfacial cracking in multilayer electrostrictive actuators. J Mech Phys Solids 46:1301–1318
Ru CQ (1999) Effect of electrical polarization saturation on stress intensity factors in a piezoelectric ceramic. Int J Solids Struct 36:869–883
Shen S, Nishioka T, Hu SL (2000) Crack propagation along the interface of piezoelectric bimaterial. Theor Appl Fract Mech 34:185–203
Wang XD (2000) Analysis of strip electric saturation model of crack problem in piezoelectric materials. Int J Solids Struct 37:6031–6049
Wang XD, Meguid SA (2000) On the electroelastic behaviour of a thin piezoelectric actuator attached to an infinite host structure. Int J Solids Struct 37:3231–3251
Hao T, Shen Z (1994) A new electric boundary condition of electric fracture mechanics and its application. Eng Fract Mech 47:793–802
Dunn M (1994) The effect of crack faces boundary conditions on the fracture mechanics of piezoelectric solids. Eng Fract Mech 48:25–39
McMeeking R (1999) Crack tip energy release rate for a piezoelectric compact tension specimen. Eng Fract Mech 64:217–244
Xu X, Rajapakse RKND (2001) On a plane crack in piezoelectric solids. Int J Solids Struct 38:7643–7658
Wang BL, May YW (2003) On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics. Int J Eng Sci 41:633–652
Gruebner O, Kamlah M, Munz D (2003) Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng Fract Mech 70:1399–1413
Govorukha V, Loboda V, Kamlah M (2006) On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound. Int J Solid Struct 43:1979–1990
Li Q, Chen Y (2008) Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. ASME J Appl Mech 75:1–13
Landis C (2004) Electrically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41:6291–6315
Li W, McMeeking R, Landis C (2008) On the crack face boundary conditions in electromechanical fracture and an experiment protocol for determining energy release rates. Eur J Mech A/Solids 27:285–301
Ricoeur A, Kuna M (2009) Electrostatic traction at dielectric interfaces and their implication for crack boundary conditions. Mech Res Commun 36:330–335
Qin Q, Mai Y-W (1999) A closed crack tip model for interface cracks in thermopiezoelectric materials. Int J Solids Struct 36:2463–2479
Herrmann K, Loboda V (2000) Fracture mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models. Arch Appl Mech 70:127–143
Herrmann K, Loboda V, Govorukha V (2001) On contact zone model for an interface crack with electrically insulated crack surfaces in a piezoelectric bimaterial. Int J Fract 111:203–227
Comninou M (1977) Interface crack with friction in the contact zone. J Appl Mech 44(4):780–781
Comninou M, Dundurs J (1980) Effect of friction on the interface crack loaded in shear. J Elast 10(2):203–212
Leguillon D (1999) Interface crack tip singularity with contact and friction. Comptes Rendus de l’Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy, vol 327, no 5, pp 437–442
Antipov Y (1995) An interface crack between elastic materials when there is dry friction. J Appl Math Mech 59(2):273–287
Ostrik V (2003) Friction contact of the edges of an interface crack under the conditions of tension and shear. Mater Sci 39(2):214–224
Sapsathiarn Y, Senjuntichai T, Rajapakse R (2012) Cylindrical interface cracks in 1-3 piezocomposites. Compos: Part B 43:2257–2264
Loboda V, Kharun I (2001) Plane problem of a crack on the interface of orthotropic plates with friction of crack lips. Mater Sci 37(5):735–745
Kaminsky A, Kipnis L, Kolmakova V (1995) Slip lines at the end of a cut at the interface of different media. Int Appl Mech 31(6):491–495
Kaminsky A, Kipnis L, Kolmakova V (1999) On the Dugdale model for a crack at the interface of different media. Int Appl Mech 35(1):58–63
Kaminsky A, Kipnis L, Dudik I (2004) Initial development of the prefracture zone near the tip of a crack reaching the interface between dissimilar media. Int Appl Mech 40(2):176–182
Kaminsky A, Dudik I, Kipnis L (2006) On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media. Int Appl Mech 42(2):136–144
Kaminsky A, Dudik I, Kipnis L (2007) Initial kinking of an interface crack between two elastic media. Int Appl Mech 43(10):1090–1099
Loboda V, Sheveleva A (2003) Determining prefracture zones at a crack tip between two elastic orthotropic bodies. Int Appl Mech 39(5):566–572
Sulim G, Grilitskii D, Belokur I (1977) Periodic problem for composite plane with cracks. Mater Sci 13(1):72–75
Nakhmein E, Nuller B, Ryvkin M (1982) Deformation of a composite elastic plane weakened by a periodic system of the arbitrarily loaded slits. J Appl Math Mech 45(6):821–826
Kudryavtsev B, Rakitin V (1976) Periodic set of cracks at the interface of piezoelectric and solid conductor. USSR Acad Sci Mech Solids 2:121–129 (in Russian)
Kaloerov S, Boronenko O (2006) Magnetoelastic problem for a body with periodic elastic inclusions. Int Appl Mech 42(9):989–996
Häusler C, Gao C-F, Balke H (2004) Collinear and periodic electrode-ceramic interfacial cracks in piezoelectric bimaterials. ASME J Appl Mech 71:486–492
Schmueser D, Comninou M (1979) The periodic array of interface cracks and their interaction. Int J Solids Struct 15:927–934
Ru C (2000) Electrode-ceramic interfacial cracks in piezoelectric multilayer materials. Trans ASME J Appl Mech 67:255–261
Liu M, Hsia K (2003) Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. J Mech Phys Solids 51:921–944
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Kozinov, S., Loboda, V. (2020). Literature Review on Cracks Located at the Interface of Dissimilar Materials (Interface Cracks). In: Fracture Mechanics of Electrically Passive and Active Composites with Periodic Cracking along the Interface. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-43138-9_1
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