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On three-dimensional singular stress field at the front of a planar rigid inclusion (anticrack) in an orthorhombic mono-crystalline plate

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Abstract

A novel eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby–Stroh type affine transformation, is developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness anticrack reinforcing an infinite orthorhombic single crystal plate, of finite thickness and subjected to far-field mode I/II loadings. Anticrack-face boundary conditions and those that are prescribed on the top and bottom (free or fixed) surfaces of the plate are exactly satisfied. The present investigation considers six through-anticrack systems reinforcing orthorhombic single crystal plates. Explicit expressions for the singular stresses in the vicinity of the front of a through-thickness anticrack reinforcing an orthorhombic plate, subjected to far-field mode I/II loadings, are presented. Finally, hitherto largely unavailable results, pertaining to the through-thickness variations of stress singularity coefficients corresponding to symmetric and skew-symmetric sinusoidal loads that also satisfy the boundary conditions on the top and bottom surfaces of an orthorhombic mono-crystalline plate under investigation, bridge a longstanding gap in the stress singularity/fracture mechanics literature.

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References

  • Bednorz JG, Muller KA (1988) Perovskite-type oxides—the new approach to high-Tc superconductivity. Rev Mod Phys 60:585–600 (Nobel Lecture: 1988 The Nobel Foundation)

    Google Scholar 

  • Bigoni D, Dal Corso F, 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: 839–857

    Article  CAS  Google Scholar 

  • Carslaw HS (1930) Introduction to the theory of Fourier series and integrals, 3rd edn. Dover, New York

    Google Scholar 

  • Chaudhuri RA (2003a) Three-dimensional asymptotic stress field in the vicinity of the line of intersection of an inclusion and plate surface. Int J Fract 117: 207–233

    Article  Google Scholar 

  • Chaudhuri RA (2003b) Eigenfunction expansion solutions for three-dimensional rigid planar inclusion problem. Int J Fract 121: 95–110

    Article  Google Scholar 

  • Chaudhuri RA (2003c) Three-dimensional asymptotic stress field in the vicinity of the line of intersection of a circular cylindrical through/part-through open/rigidly plugged hole and a plate. Int J Fract 122: 65–88

    Article  Google Scholar 

  • Chaudhuri RA (2003d) Three-dimensional asymptotic stress field in the vicinity of the circumference of a penny shaped discontinuity. Int J Solids Struct 40: 3787–3805

    Article  Google Scholar 

  • Chaudhuri RA (2004a) An eigenfunction expansion solution for three-dimensional stress field in the vicinity of the circumferential line of intersection of a bimaterial interface and a hole. Int J Fract 129: 361–384

    Article  Google Scholar 

  • Chaudhuri RA (2004b) Three-dimensional asymptotic stress field in the vicinity of the circumferential tip of a fiber-matrix interfacial debond. Int J Eng Sci 42: 1707–1727

    Article  Google Scholar 

  • Chaudhuri RA (2006a) Three-dimensional asymptotic stress field in the vicinity of the circumference of a bimaterial penny shaped interface discontinuity. Int J Fract 141: 207–221

    Article  Google Scholar 

  • Chaudhuri RA (2006b) Three-dimensional singular stress field near a partially debonded cylindrical rigid fiber. Compos Struct 72: 141–150

    Article  Google Scholar 

  • Chaudhuri RA (2010a) Three-dimensional singular stress field at the front of a crack and lattice crack deviation in a cubic single crystal plate. Phil Mag 90: 2049–2113

    Article  CAS  Google Scholar 

  • Chaudhuri RA (2010b) On three-dimensional singular stress field at the front of a crack/anticrack in an orthotropic/orthorhombic plate subjected to far-field antiplane shear loading. Composite Structures 92, 1977-1984 (see also Erratum Composite Structures Compos Struct (2011) 93:1058)

  • Chaudhuri RA (2011) Three-dimensional singular stress field at the front of a crack weakening a unidirectional fiber reinforced composite plate. Compos Struct 93: 513– 527

    Article  Google Scholar 

  • Chaudhuri RA (2012) Three-dimensional singular stress/residual stress fields at crack/anticrack fronts in monoclinic plates under antiplane shear loading. Eng Fract Mech. doi:10.1016/j.engfracmech.2011.12.003

  • Chaudhuri RA, Balaraman K (2007) A novel method for fabrication of fiber reinforced plastic laminated plates. Compos Struct 77: 160–170

    Article  Google Scholar 

  • Chaudhuri RA, Chiu SHJ (2007) Three-dimensional asymptotic stress field at the front of an unsymmetric bimaterial wedge associated with matrix cracking or fiber break. Compos Struct 78: 254–263

    Article  Google Scholar 

  • Chaudhuri RA, Chiu SHJ (2009) Three-dimensional asymptotic stress field in the vicinity of an adhesively bonded scarf joint interface. Compos Struct 89: 475–483

    Article  Google Scholar 

  • Chaudhuri RA, Xie M (1998) Free-edge stress singularity in a bimaterial laminate. Compos Struct 40: 129–136

    Article  Google Scholar 

  • Chaudhuri RA, Xie M (2000a) A tale of two saints: St. Venant and “St. Nick”—does St. Venant’s principle apply to bimaterial straight edge and wedge singularity problems?. Compos Sci Tech 60: 2503–2515

    Article  Google Scholar 

  • Chaudhuri RA, Xie M (2000b) A novel eigenfunction expansion solution for three-dimensional crack problems. Compos Sci Tech 60: 2565–2580

    Article  Google Scholar 

  • Chaudhuri RA, Yoon J (2012) Three-dimensional asymptotic mode I/II stress fields at the front of interfacial crack/anticrack discontinuities in trimaterial bonded plates. Compos Struct 94: 351–362

    Article  Google Scholar 

  • Chaudhuri RA, Xie M, Garala HJ (1996) Stress singularity due to kink band weakening a unidirectional composite under compression. J Compos Mater 30: 672–691

    Article  CAS  Google Scholar 

  • Chaudhuri RA, Balaraman K, Kunukkasseril VX (2005) A combined theoretical and experimental investigation on free vibration of thin symmetrically laminated plates. Compos Struct 67: 85–97

    Article  Google Scholar 

  • Chaudhuri SN, Chaudhuri RA, Benner RE, Penugonda M (2006) Raman spectroscopy for characterization of interfacial debonds between carbon fibers and polymer matrices. Compos Struct 76: 375–387

    Article  Google Scholar 

  • Chiu JSH, Chaudhuri RA (2002) Three-dimensional asymptotic stress field at the front of an unsymmetric bimaterial pie-shaped wedge under antiplane shear loading. Compos Struct 58: 129–137

    Article  Google Scholar 

  • Chiu SHJ, Chaudhuri RA (2011) A three-dimensional eigenfunction expansion approach for singular stress field near an adhesively bonded scarf joint interface in a rigidly-encased plate. Engng Fracture Mech 78: 2220–2234

    Article  Google Scholar 

  • Cook RF, Dinger TR, Clarke DR (1987) Fracture toughness measurements of YBa2Cu3Ox single crystals. Appl Phys Lett 61: 454–456

    Article  Google Scholar 

  • Cotton FA, Wilkinson G (1980) Advanced inorganic chemistry, 4th edn. Wiley, New York

    Google Scholar 

  • Dal Corso F, Bigoni D (2009) The interactions between shear bands and rigid lamellar inclusions in a ductile metal matrix. Proc R Soc A 465: 143–163

    Article  Google Scholar 

  • Eshelby JD, Read WT, Shockley W (1953) Anisotropic elasticity with application to dislocation theory. Acta Metall 1: 251–259

    Article  Google Scholar 

  • Folias ES (1987) The 3D stress field at the intersection of a hole and a free surface. Int J Fract 35: 187–194

    Article  Google Scholar 

  • Folias ES (1989) On the stress singularities at the intersection of a cylindrical inclusion with the free surface of a plate. Int J Fract 39: 25–34

    Article  Google Scholar 

  • Folias ES (1989) On interlaminar stresses of a composite plate around the neighborhood of a hole. Int J Solids Struct 25: 1193–1200

    Article  Google Scholar 

  • Gladwell GML (1999) On inclusions at a bi-material elastic interface. J. Elast 54: 27–41

    Article  Google Scholar 

  • Gorbatikh L, Lomov SV, Verpoest I (2010) Original mechanism of failure initiation revealed through modelling of naturally occurring microstructures. J Mech Phys Solids 58: 735–750

    Article  Google Scholar 

  • Kaczynski A, Kozlowski W (2009) Thermal stresses in an elastic space with a perfectly rigid flat inclusion under perpendicular heat flow. Int J Solids Struct 46: 1772–1777

    Article  CAS  Google Scholar 

  • Kunukkasseril VX, Chaudhuri RA, Balaraman K (1975) A method to determine 18 rigidities of layered anisotropic plates. J Fibre Sci Tech 8: 303–318

    Article  Google Scholar 

  • Ledbetter H, Lei M (1991) Monocrystal elastic constants of orthotropic Y1Ba2Cu3O7: an estimate. J Mater Res 6: 2253–2255

    Article  CAS  Google Scholar 

  • Lei M, Sarrao JL, Visscher WM, Bell TM, Thompson JD, Migliori A (1993) Elastic constants of a monocrystal of superconducting YBa2Cu3O7-δ . Phys Rev B 47: 6154–6156

    Article  CAS  Google Scholar 

  • Li Q, Ting TCT (1989) Line inclusions in anisotropic elastic solids. ASME J Appl Mech 56: 556–563

    Article  Google Scholar 

  • Lin YY, Sung JC (1998) Stress singularities at the apex of a dissimilar anisotropic wedge. ASME J Appl Mech 65: 454–463

    Article  Google Scholar 

  • Newnham RE (1975) Structure-property relations. Springer, New York

    Google Scholar 

  • Noselli G, Dal Corso F, Bigoni D (2010) The stress intensity near a stiffener disclosed by photoelasticity. Int J Fract 166: 91–103

    Article  Google Scholar 

  • Qu J, Xue Y (1998) Three-dimensional interface cracks in anisotropic bimaterials: the non-oscillatory case. ASME J Appl Mech 65: 1048–1055

    Article  Google Scholar 

  • Reichardt W, Pintschovius L, Hennion B, Collin F (1988) Inelastic neutron scattering study of YBa2Cu3O7−x. Supercond Sci Tech 1: 173–176

    Article  CAS  Google Scholar 

  • Roa JJ, Capdevila XG, Martinez M, Espiell F, Segarra M (2007) Nanohardness and Young’s modulus of YBCO samples textured by Bridgman technique. Nanotechnology 18: 385701 (6pp)

    Article  Google Scholar 

  • Saint-Paul M, Henry JY (1989) Elastic anomalies in YBa 2 Cu 3 O 7-δ single crystals. Solid State Commun 72: 7685–7687

    Article  Google Scholar 

  • Selvadurai APS (2000) An inclusion at a bi-material elastic interface. J Eng Math 37: 155–170

    Article  Google Scholar 

  • Sih GC, Paris PC, Irwin GR (1965) On cracks in rectilinearly anisotropic solids. Int J Fract Mech 1: 189–203

    CAS  Google Scholar 

  • Shackelford JF (1996) Introduction to materials science for engineers, 4th edn. Prentice-Hall, Upper Saddle River

    Google Scholar 

  • Simmons G, Wang H (1971) Single crystal elastic constants and calculated aggregate properties: a handbook. MIT Press, Cambridge

    Google Scholar 

  • Sneddon I (1965) A note on the problem of the penny-shaped crack. Math Proc Camb Phil Soc 61: 609–611

    Article  Google Scholar 

  • Stenger F, Chaudhuri R, Chiu J (2000) Sinc solution of boundary integral form for two-dimensional bi-material elasticity problems. Compos Sci Tech 60: 2197–2211

    Article  Google Scholar 

  • Stroh AN (1958) Dislocations and cracks in anisotropic elasticity. Phil Mag 7: 625–646

    Article  Google Scholar 

  • Wilcox CH (1979) Uniqueness theorems for displacement fields with locally finite energy in linear elastostatics. J Elast 9: 221–243

    Article  Google Scholar 

  • Wikipedia (2010) http://en.wikipedia.org/wiki/Yttrium_barium_copper_oxide

  • Willis JR (1972) The penny shaped crack on an interface. Q J Mech Appl Math 25: 367–385

    Article  Google Scholar 

  • Xie M, Chaudhuri RA (1998) Three-dimensional stress singularity at a bimaterial interface crack front. Compos Struct 40: 137–147

    Article  CAS  Google Scholar 

  • Xie M, Chaudhuri RA (2001) Three-dimensional asymptotic stress field at the front of a bimaterial wedge of symmetric geometry under antiplane shear loading. Compos Struct 54: 509–514

    Article  Google Scholar 

  • Yoon J, Chaudhuri RA (2011) Three-dimensional asymptotic antiplane shear stress fields at the front of interfacial crack/anticrack type discontinuities in trimaterial bonded plates. Compos Struct 93: 1505–1515

    Article  Google Scholar 

  • Yoon J, Chaudhuri RA (2012) Three-dimensional asymptotic stress fields at the front of a trimaterial junction. Compos Struct 94: 337–350

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Utah, 122 S. Central Campus Dr., Room 304, Salt Lake City, UT, 84112-0560, USA

    Reaz A. Chaudhuri

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  1. Reaz A. Chaudhuri
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Correspondence to Reaz A. Chaudhuri.

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Chaudhuri, R.A. On three-dimensional singular stress field at the front of a planar rigid inclusion (anticrack) in an orthorhombic mono-crystalline plate. Int J Fract 174, 103–126 (2012). https://doi.org/10.1007/s10704-012-9679-1

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  • DOI: https://doi.org/10.1007/s10704-012-9679-1

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