Abstract
The second chapter presents analysis of stress fields in elastic plane with a semi-infinite notch under conditions of plane stress state or plane strain state. Well-known boundary value problem solutions for eigenvalues of a wedge in the plane elasticity theory are considered at first. Then the same solutions are constructed for the semi-infinite rounded V-shaped notch. Based on these solutions, the relationship between stress concentration factor and stress intensity factor in elastic bodies with rounded or sharp V-shaped notches had been established.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akin, J.E.: The generation of elements with singularities. Int. J. Numer. Methods Eng. 10, 1249–1259 (1976)
Aleksandrov, A.Y., Zinov’ev, B.M., Kurshin, L.M.: One numerical method of solving problems of elasticity with allowance for singularities of the stresses state near corner points and lines. Mech. Solids 15(3), 39–49 (1980)
Aleksanyan, R.K.: On a class of solutions of the equations of the plane theory of elasticity of an anisotropic body. Rep. Acad. Sci. Armen. SSR 61(4), 219–224 (1975)
Aleksanyan, R.K., Gevorkyan, S.H.: On the first fundamental problem of plane theory of elasticity for anisotropic wedge. Proc. Natl. Acad. Sci. Armen. Mech. 53(2), 10–15 (2000)
Atkinson, C., Bourne, J.P.: Stress singularities in angular sectors of viscoelastic media. Int. J. Eng. Sci. 28(7), 615–630 (1990)
Atzori, B., Lazzarin, P.: Notch sensitivity and defect sensitivity under fatigue loading: two sides of the same medal. Int. J. Fract. 107, L3–L8 (2000)
Ayatollahi, M.R., Nejati, M.: Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method. Int. J. Mech. Sci. 53(3), 164–177 (2011)
Banks-Sills, L., Sherer, A.: A conservative integral for determining stress intensity factors of a bimaterial notch. Int. J. Fract. 115(1), 1–25 (2002)
Banks-Sills, L., Yang, Y.Y., Munz, D.: An influence function for stress intensity factors of bimaterial notched bodies. Int. J. Fract. 85(4), 333–350 (1997)
Bansal, A., Kumosa, M.: Analysis of double edge-cracked iosipescu specimens under biaxial loads. Eng. Fract. Mech. 59(1), 89–100 (1998)
Barber, J.R.: Elasticity, 2nd edn. Kluwer Academic Publishers, New York (2002)
Barone, M.R., Robinson, A.R.: Determination of elastic stresses at notches and cornes by integral equations. Int. J. Solids Struct. 8, 1319–1338 (1972)
Belubekyan, V.M., Belubekyan, M.V., Terzyan, S.A.: Stress state in the vicinity of the elastic wedge vertex. Proc. Natl. Acad. Sci. Armen. Mech. 54(2), 8–21 (2001)
Benthem, J.: On the stress distribution in anisotropic infinite wedges. Q. Appl. Math. 21(3), 189–198 (1963)
Benthem, J.P.: Stresses in the region of rounded corners. Int. J. Solids Struct. 23(2), 239–252 (1987)
Berto, F., Lazzarin, P., Matvienko, Y.G.: J-integral evaluation for U- and V-blunt notches under mode I loading and materials obeying a power hardening law. Int. J. Fract. 146(1), 33–51 (2007)
Blanco, C., Martinez-Esnaola, J.M., Atkinson, C.: Analysis of sharp angular notches in anisotropic materials. Int. J. Fract. 93(1–4), 373–386 (1998)
Blinowski, A., Rogaczewski, J.: On the order of singularity at V-shaped notches in anisotropic bodies. Arch. Mech. 52(6), 1001–1010 (2000)
Blinowski, A., Wieromiej-Ostrowska, A.: On the singularities at the tips of orthotropic wedges in plane elasticity - I. Technol. Sci. 8, 107–124 (2005)
Bogy, D.B.: Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 35, 460–466 (1968)
Bogy, D.B.: Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. 38, 377–386 (1968)
Bogy, D.B.: The plane solution for anisotropic elastic wedges under normal and shear loading. J. Appl. Mech. 39, 1103–1109 (1972)
Bogy, D.B., Wang, K.C.: Stress singularities at interface corners in bonded dissimilar isotropic elastic materials. Int. J. Solids Struct. 7(8), 993–1005 (1971)
Bourne, J.P., Atkinson, C.: Stress singularities in viscoelastic media 2. Plane-strain stress singularities at corners. IMA J. Appl. Math. 44(2), 163–180 (1990)
Brahtz, A.H.A.: Stresses at two-dimensional corners for various force distributions. Ph.D. thesis, California Institute of Technology, Pasadena California (1932)
Brahtz, J.H.A.: Stress distribution in a reentrant corner. Trans. ASME 55, 31–37 (1933)
Brahtz, J.H.A.: Stress distribution in wedges with arbitrary boundary forces. J. Appl. Phys. 4(2), 56–65 (1933)
Broberg, K.B.: Cracks and Fracture. Academic Press, San Diego (1999)
Carpenter, W.C.: Calculation of fracture parameters for a general corner. Int. J. Fract. 24(1), 45–58 (1984)
Carpenter, W.C.: A collocation procedure for determining fracture mechanics parameters at a corner. Int. J. Fract. 24(4), 255–266 (1984)
Carpenter, W.C.: Mode I and mode II stress intensities for plates with cracks of finite opening. Int. J. Fract. 26(3), 201–214 (1984)
Carpenter, W.C.: The eigenvector solution for a general corner or finite opening crack with further studies on the collocation procedure. Int. J. Fract. 27, 63–73 (1985)
Carpenter, W.C.: Comments on the eigenvalue formulation of problems with cracks, V-notched cracks, and corners. Int. J. Fract. 68(1), 75–87 (1994)
Carpenter, W.C., Byers, C.: Path independent integral for computing stress intensities for V-notched cracks in a bi-material. Int. J. Fract. 35(4), 245–268 (1987)
Carpinteri, A., Paggi, M., Pugno, N.: Numerical evaluation of generalized stress intensity factors in multi-layered composites. Int. J. Solids Struct. 43(3–4), 627–641 (2006)
Cartwright, D.J., Rooke, D.P.: Evaluation of stress intensity factors. J. Strain Anal. 10(4), 217–224 (1975)
Chang, J.H., Wu, W.H.: Calculation of mixed-mode stress filed at a sharp notch tip using \(M_{1\varepsilon }\)-integral. Comput. Mech. 31, 419–427 (2003)
Chao, Y.J., Yang, S.: Singularities at the apex of a sharp V-notch in a linear strain hardening material. Int. J. Fract. 57(1), 47–60 (1992)
Chen, D., Ushijima, K.: Plastic stress singularity near the tip of a V-notch. Int. J. Fract. 106(2), 117–134 (2000)
Chen, D.H., Nisitani, H.: Mode I and II singular stress fields near a corner of jointed dissimilar materials. JSME Int. J. 35, 392–398 (1992)
Chen, D.H., Nisitani, H.: Singular stress field near the corner of jointed dissimilar materials. J. Appl. Mech. 60(3), 607–613 (1993)
Chen, D.H., Nisitani, H.: Body force method. Int. J. Fract. 86(1), 161–189 (1997)
Chen, Y.H., Lu, T.J.: On the path dependence of the J-integral in notch problems. Int. J. Solids Struct. 41, 607–618 (2004)
Cheng, C., Niu, Z., Zhou, H., Recho, N.: Evaluation of multiple stress singularity orders of a V-notch by the boundary element method. Eng. Anal. Bound. Elem. 33(10), 1145–1151 (2009)
Cherepanov, G.P.: Mekhanika khrupkogo razrusheniya (Mechanics of brittle fracture). Nauka, Moscow (1974)
Cherepanov, G.P.: Mechanics of Brittle Fracture. McGraw Hill, New York (1979)
Chiang, C.R.: Stress field around a rounded crack tip. J. Appl. Mech. 58(3), 834–836 (1991)
Chiang, C.R.: The stress field for a blunt crack in an anisotropic material. Int. J. Fract. 68(2), R41–R46 (1994)
Cho, S.B., Kim, J.K.: A study on stress singularities for V-notched cracks in anisotropic and/or pseudo-isotropic dissimilar materials. Int. J. Korean Soc. Precis. Eng. 3(2), 22–32 (2002)
Chuang, W.Y., Sung, J.C., Chung, W.G.: Stress singularities of two special geometries of wedges with free-mixed boundary conditions. Comput. Struct. 81(3), 167–176 (2003)
Chue, C.H., Liu, C.I.: A general solution on stress singularities in an anisotropic wedge. Int. J. Solids Struct. 38(38–39), 6889–6906 (2001)
Chue, C.H., Liu, C.I.: Stress singularities in a bimaterial anisotropic wedge with arbitrary fiber orientation. Compos. Struct. 58(1), 49–56 (2002)
Chue, C.H., Weng, S.M.: Stress singularities in anisotropic three-material wedges and junctions with applications. Compos. Struct. 58(4), 443–456 (2002)
Chue, C.H., Tseng, C.H., Liu, C.I.: On stress singularities in an anisotropic wedge for various boundary conditions. Compos. Struct. 54, 87–102 (2001)
Cormack, D.E., Rosen, D.: Gauge conditions and the analysis of singular fields with boundary integral equations. Eng. Anal. Bound. Elem. 18(1), 1–8 (1996)
Creager, M., Paris, P.C.: Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int. J. Fract. Mech. 3, 247–252 (1967)
De Chen, C., Chue, C.H.: Singular stresses near apex of wedge by finite element analysis. J. Chin. Inst. Eng. 26(4), 423–434 (2003)
Della-Ventura, D., Smith, R.N.L.: Some applications of singular fields in the solution of crack problems. Int. J. Numer. Methods Eng. 42, 927–942 (1998)
Dempsey, J., Sinclair, G.: On the stress singularities in the plane elasticity of the composite wedge. J. Elast. 9(4), 373–391 (1979)
Dempsey, J., Sinclair, G.: On the singular behavior at the vertex of a bi-material wedge. J. Elast. 11(3), 317–327 (1981)
Denisyuk, I.T.: Stress singularities of anisotropic plates with angular cuts. Int. Appl. Mech. 32(1), 41–45 (1996)
Ding, S., Meekisho, L., Kumosa, M.: Analysis of stress singular fields at a bimaterial wedge corner. Eng. Fract. Mech. 49(4), 569–585 (1994)
Dini, D., Hills, D.: The effect of a crack-tip radius on the validity of the singular solution. Proc. Inst. Mech. Eng. Part C: Mech. Eng. Sci. 218(7), 693–701 (2004)
Dini, D., Hills, D.: When does a notch behave like a crack? Proc. Inst. Mech. Eng. Part C: Mech. Eng. Sci. 220(1), 27–43 (2006)
Dini, D., Hills, D.A.: Asymptotic characterization of nearly-sharp notch root stress fields. Int. J. Fract. 130, 651–666 (2004)
Dundurs, J.: Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1(3), 310–322 (1967)
Elliott, D., Johnston, P.R.: Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals. J. Comput. Appl. Math. 203(1), 103–124 (2007)
Elliott, D., Johnston, P.R.: Gauss-Legendre quadrature for the evaluation of integrals involving the Hankel function. J. Comput. Appl. Math. 211(1), 23–35 (2008)
Elschner, J., Stephan, E.P.: A discrete collocation method for Symm’s integral equation on curves with corners. J. Comput. Appl. Math. 75(1), 131–146 (1996)
Fan, Z., Long, Y.: Sub-region mixed finite element analysis of V-notched plates. Int. J. Fract. 56, 333–344 (1992)
Fett, T.: Weight function for cracks ahead of sharp notches. Int. J. Fract. 74(1), 11–16 (1995)
Fett, T.: Weight functions for cracks at sharp notches and notch intensity factors. Int. J. Fract. 77, R27–R33 (1996)
Fett, T., Munz, D.: Stress intensity factors and weight functions. Advances in Fracture Mechanics. Computational Mechanics Publications Inc., Southampton (1997)
Filippi, S., Ciavarella, M., Lazzarin, P.: An approximate, analytical approach to the ‘HRR’-solution for sharp V-notches. Int. J. Fract. 117(3), 269–286 (2002)
Filippi, S., Lazzarin, P., Tovo, R.: Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int. J. Solids Struct. 39(17), 4543–4565 (2002)
Fukui, T.: On corner solutions by indirect BIEM. Boundary elements V. In: Proceedings of the 5th International Conference, pp. 929–938. Springer, Berlin (1983)
Gecit, M.R.: An integral equation approach for simultaneous solution of rectangular hole and rectangular block problems. Int. J. Eng. Sci. 21(9), 1041–1051 (1983)
Gevorkyan, S.K.: Investigation of singularities in the solutions of some problems of the theory of elasticity for anisotropic solids. Proc. Nat. Acad. Sci. Armen. Mech. 21(4), 30–39 (1968)
Givoli, D., Rivkin, L.: The DtN finite element method for elastic domains with cracks and entrant corners. Comput. Struct. 49, 633–642 (1993)
Givoli, D., Rivkin, L., Keller, J.B.: A finite element method for domains with corners. Int. J. Numer. Methods Eng. 35(6), 1329–1345 (1992)
Glinka, G.: Energy density approach to calculation of inelastic strain-stress near notches and cracks. Eng. Fract. Mech. 22(3), 485–508 (1985)
Glinka, G., Ott, W., Nowack, H.: Elastoplastic plane strain analysis of stresses and strains at the notch root. J. Eng. Mater. Technol. 110, 195–204 (1988)
Gómez, F.J., Elices, M.: A fracture criterion for blunted V-notched samples. Int. J. Fract. 127(3), 239–264 (2004)
Gospodinov, G., Drakaliev, P., Kerelezova, I.: A singular boundary element for a general corner case. In: Proceedings of the Anniversary Scientific Conference 50 Faculty of Hydrotechnics of the University of Architecture, Civil Engineering and Geodesy, Sofia, pp. 113–120 (1999)
Gross, B., Mendelson, A.: Plane elastostatic analysis of V-notched plates. Int. J. Fract. Mech. 8(3), 267–276 (1972)
Groth, H.: Stress singularities and fracture at interface corners in bonded joints. Int. J. Adhes. Adhes. 8(2), 107–113 (1988)
Gumerov, K.M., Kolesov, A.V., Gnidin, V.A.: Stress-strain state in the vicinity of a concentrator such as dihedral angle. In: Voprosy svarochnogo proizvodstva (Questions of welding production), pp. 3–8. Chelyabinsk (1987)
Hasebe, N., Iida, J.: Intensity of corner and stress concentration factor. J. Eng. Mech. 109(1), 346–356 (1983)
Hasebe, N., Kutanda, Y.: Calculation of stress intensity factors from stress concentration factor. Eng. Fract. Mech. 10, 215–221 (1978)
Hasebe, N., Nakamura, T., Iida, J.: Notch mechanics for plane and thin plate bending problems. Eng. Fract. Mech. 37(1), 87–99 (1990)
Hein, V., Erdogan, F.: Stress singularities in a two-material wedge. Int. J. Fract. Mech. 7(3), 317–330 (1971)
Helsing, J., Jonsson, A.: On the computation of stress fields on polygonal domains with V-notches. Int. J. Numer. Methods Eng. 53(2), 433–453 (2002)
Helsing, J., Ojala, R.: Corner singularities for elliptic problems: integral equations, graded meshes, quadrature, and compressed inverse preconditioning. J. Comput. Phys. 227(20), 8820–8840 (2008)
Hills, D., Dini, D.: Characteristics of the process zone at sharp notch roots. Int. J. Solids Struct. 48(14), 2177–2183 (2011)
Hufenbach, W., Kroll, L.: Stress analysis of notched anisotropic finite plates under mechanical and hygrothermal loads. Arch. Appl. Mech. 69(3), 145–159 (1999)
Huth, J.H.: The complex-variable approach to stress singularities. J. Appl. Mech. 20, 561–562 (1953)
Hwu, C., Kuo, T.L.: A unified definition for stress intensity factors of interface corners and cracks. Int. J. Solids Struct. 44(18), 6340–6359 (2007)
Irwin, G.R.: Fracture. In: Flügge, S. (ed.) Encyclopedia of Physics. Elasticity and Plasticity, vol. 6, pp. 551–590. Springer, Berlin (1958)
Johnston, P.R., Elliott, D.: A sinh transformation for evaluating nearly singular boundary element integrals. Int. J. Numer. Methods Eng. 62, 564–578 (2005)
Ju, S.: Finite element calculation of stress intensity factors for interface notches. Comput. Meth. Appl. Mech. Eng. 199(33), 2273–2280 (2010)
Ju, S.H.: Calculation of notch H-integrals using image correlation experiments. Exp. Mech. 50(4), 517–525 (2010)
Ju, S.H., Chung, H.Y., Jhao, B.J.: Experimental calculation of mixed-mode notch stress intensity factors for anisotropic materials. Eng. Fract. Mech. 76(14), 2260–2271 (2009)
Ju, S.H., Chiu, C.Y., Jhao, B.J.: Determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments. Int. J. Solids Struct. 47(7), 894–900 (2010)
Ju, S.H., Chung, H.Y., Liu, S.H.: Determining 2D notch SIFs by the image-correlation method. J. Chin. Inst. Eng. 34(4), 503–514 (2011)
Kalandiya, A.I.: Remarks on the singularity of elastic solutions near corners. J. Appl. Math. Mech. 33(1), 127–131 (1969)
Karp, S.N., Karal, F.C.J.: The elastic-field behaviour in the neighbourhood of a crack of arbitrary angle. Commun. Pure Appl. Math. 15(4), 413–421 (1962)
Kazberuk, A.: Stress concentration around an oval hole. Acta Mech. Autom. 1, 25–30 (2007)
Kazberuk, A.: Determining parameters of fracture toughness of quasibrittle materials using specimens with notches. Acta Mech. Autom. 3(3), 28–31 (2009)
Kazberuk, A.: Stress intensity factors for cracks at the vertex of a rounded V-notch. Mater. Sci. 45(5), 676–687 (2009)
Kazberuk, A.: Dwuwymiarowe zagadnienia mechaniki pȩkania ciał z karbami (Two-dimensional problems of fracture mechanics of bodies with notches). Bialystok University of Technology, Bialystok (2010)
Kazberuk, A., Niedźwiedź, M.: Stress distribution on the edge of a rounded v-shaped notch. In: Proceedings of the V International Symposium on Damage Mechanisms in Materials and Structures. Białystok, pp. 56–58 (2009)
Kazberuk, A., Niedźwiedź, M.: The influence of the shape of the notch on stress distribution on the boundary. Acta Mech. Autom. 3(1), 38–41 (2009)
Kazberuk, A., Savruk, M.P.: Selected problems of fracture mechanics of bodies with V-notches. In: Fatigue and Fracture Mechanics: Proceedings of the XXIII Symposium University Technology and Life Sciences, Bydgoszcz, pp. 67–68 (2010)
Kazberuk, A., Savruk, M.P.: Stress concentration in vertexes of notches in complex stress states. In: Proceedings of the XIII Conference on Fracture Mechanics, Opole, pp. 104–106 (2011)
Kazberuk, A., Savruk, M.P., Tarasiuk, G.: Concentration of stresses in the rounded corners of the notches and holes under antiplane deformation. In: Fatigue and Fracture Mechanics: Proceedings of the XXIV Symposium on University of Technology and Life Sciences. Bydgoszcz, pp. 69–70 (2012)
Keer, L.M., Chantaramungkorn, K.: An elastic half plane weakened by a rectangular trench. J. Appl. Mech. 42(3), 683–687 (1975)
Kim, J.K., Cho, S.B.: An analysis of eigenvalues and eigenvectors for V-notched cracks in pseudo-isotropic dissimilar materials. Int. J. Korean Soc. Precis. Eng. 3(2), 33–44 (2002)
Klusák, J., Knésl, Z.: Determination of crack initiation direction from a bi-material notch based on the strain energy density concept. Comput. Mater. Sci. 39(1), 214–218 (2007)
Klusák, J., Knésl, Z.: Reliability assessment of a bi-material notch: strain energy density factor approach. Theor. Appl. Fract. Mech. 53(2), 89–93 (2010)
Klusák, J., Profant, T., Kotoul, M.: A comparison of two direct methods of generalized stress intensity factor calculations of bi-material notches. Key Engineering Materials, vol. 385, pp. 409–412. Trans Tech Publications (2008)
Knésl, Z., Klusák, J., Náhlık, L.: Crack initiation criteria for singular stress concentrations, part i: a universal assesment of singular stress concentrations. Eng. Mech. 14(6), 399–408 (2007)
Knésl, Z., Klusák, J., Náhlık, L.: Crack initiation criteria for singular stress concentrations, part ii: stability of sharp and bimaterial notches. Eng. Mech. 14(6), 409–422 (2007)
Koshelev, V., Ghassemi, A.: Wedge boundary elements for 2D problems with corner points. Eng. Anal. Bound. Elem. 32(2), 168–175 (2008)
Kouzniak, N.V., Rossmanith, H.P., Savruk, M.P.: Plastic strain distribution near a tip of a sharp V-notch in a power hardening material. Mechanism and Mechanics of Damage and Failure, pp. 355–360. EMAS, London (1996)
Kouznyak, N.V., Rossmanith, H.P., Savruk, M.P.: Singular stresses at a tip of a sharp notch in power hardening materials under anti-symmetric load. Mater. Sci. 31(6), 693–701 (1995)
Kuang, Z.B., Xu, X.P.: Singular behavior of a sharp V-notsh tip in power hardening material. In: Sih G.C., Nisitani H., Ishihara T. (eds.) Role of Fracture Mechanics in Modern Technology, pp. 477–484. Elsevier, Netherlands (1987)
Kuang, Z.B., Xu, X.P.: Stress and strain fields at the tip of a sharp V-notch in a power-hardening material. Int. J. Fract. 35(1), 39–53 (1987)
Kullmer, G.: Elastic stress fields in the vicinity of a narrow notch with circular root. In: Proceedings of the European Conference on Reliability and Structural Integrity of Advanced Materials, ECF 9, Varna, Bulgary, vol. 2, pp. 905–910 (1992)
Kullmer, G., Richard, H.A.: Influence of the root radius of crack-like notches on the fracture load of brittle components. Arch. Appl. Mech. 76, 711–723 (2006)
Labossiere, P.E.W., Dunn, M.L.: Calculation of stress intensities at sharp notches in anisotropic media. Eng. Fract. Mech. 61(5–6), 635–654 (1998)
Labossiere, P.E.W., Dunn, M.L.: Stress intensities at interface corners in anisotropic bimaterials. Eng. Fract. Mech. 62(6), 555–576 (1999)
Lazzarin, P., Filippi, S.: A generalized stress intensity factor to be applied to rounded V-shaped notches. Int. J. Solids Struct. 43(9), 2461–2478 (2006)
Lazzarin, P., Tovo, R.: A unified approach to the evaluation of linear elastic stress fields in the neibourhood of cracs and notches. Int. J. Fract. 78(1), 3–19 (1996)
Lazzarin, P., Zambardi, R.: The equivalent strain energy density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity. Fatigue Fract. Eng. Mater. Struct. 25(10), 917–928 (2002)
Lazzarin, P., Tovo, R., Filippi, S.: Elastic stress distributions in finite size plates with edge notches. Int. J. Fract. 91(3), 269–282 (1998)
Lazzarin, P., Zappalorto, M., Berto, F.: Generalised stress intensity factors for rounded notches in plates under in-plane shear loading. Int. J. Fract. 170(2), 123–144 (2011)
Lebedev, D.F.: Brittle fracture of the composite elastic plane with a V-shaped notch. Proc. Natl. Acad. Sci. Armen. Mech. 43(2), 12–22 (1990)
Li, J., Zhang, X.B., Recho, N.: Stress singularities near the tip of a two-dimensional notch formed from several elastic anisotropic materials. Int. J. Fract. 107(4), 379–395 (2001)
Li, Y., Song, M.: Method to calculate stress intensity factor of V-notch in bi-materials. Acta Mech. Solida Sinica 21(4), 337–346 (2008)
Lin, K.Y., Tong, P.: Singular finite elements for the fracture analysis of V-notched plate. Int. J. Numer. Methods Eng. 15(9), 1343–1354 (1980)
Lin, S., Hills, D.A.: Stress intensity factors for cracks emanating from a semicircular notch in a half-plate. J. Strain Anal. 31(6), 433–439 (1996)
Livieri, P.: A new path independent integral applied to notched components under mode I loading. Int. J. Fract. 123(3–4), 107–125 (2003)
Livieri, P., Segala, F.: Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading. Int. J. Fract. 148(1), 57–71 (2007)
Livieri, P., Segala, F.: Evaluation of stress intensity factors from elliptical notches under mixed mode loadings. Eng. Fract. Mech. 81, 110–119 (2012)
Loghin, A., Joseph, P.F.: Asymptotic solutions for mixed mode loading of cracks and wedges in power law hardening materials. Eng. Fract. Mech. 68(14), 1511–1534 (2001)
Lum, C., Foschi, R.O.: Arbitrary V-notches in orthotropic plates. J. Eng. Mech. 114(4), 638–655 (1988)
Maz’ya, V.G., Soloviev, A.A.: Boundary integral equations on contours with peaks. Birkhäuser, Boston (2010)
Mikhailov, S.E.: On a plane problem for the two connected anisotropic wedges. Mech. Solids 13(4), 155–160 (1978)
Mikhailov, S.E.: The asymptotic behavior of solutions of some integral equations and plane elasticity problems near the corners under given stresses on the boundary. Mech. Solids 24(3), 33–43 (1989)
Mitra, A.K., Ingber, M.S.: A multiple-node method to resolve the difficulties in the boundary integral equation method caused by corners and discontinuous boundary conditions. Int. J. Numer. Methods Eng. 36(10), 1735–1746 (1993)
Mohammed, I., Liechti, K.M.: The effect of corner angles in bimaterial structures. Int. J. Solids Struct. 38(24), 4375–4394 (2001)
Munz, D., Yang, Y.Y.: Stresses near the edge of bonded dissimilar materials described by two stress intensity factors. Int. J. Fract. 60(2), 169–177 (1993)
Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity, 2nd edn. Noordhoff International Publishing, Leyden (1977)
Nachname, M., Hohe, J., Becker, W., et al.: A closed-form analysis of material and geometry effects on stress singularities at unsymmetric bimaterial notches. Proc. Appl. Math. Mech. 2(1), 210–211 (2003)
Neskorodev, N.M., Neskorodev, R.N.: Stress singularities in the neighborhood of corners of orthotropic plates. J. Math. Sci. 101(1), 2785–2788 (2000)
Neuber, H.: Die halbeelliptische Kerbe mit Riß als Beispiel zur Korrelation von Mikro- und Makrospannungskonzentrationen. Ing.-Arch. 46, 389–399 (1977)
Nisitani, H.: The two-dimensional stress problem solved using an electric digital computer. Bull. JSME 11(43), 14–23 (1968)
Nisitani, H.: Solutions of notch problems by body force method. In: Sih, G.C. (ed.) Stress Analysis of Notch Problems. Mechanics of Fracture, vol. 5, pp. 1–68. Noordhoff International Publishing, Alphen aan den Rijn (1978)
Niu, Z., Ge, D., Cheng, C., Ye, J., Recho, N.: Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials. Appl. Math. Model. 33, 1776–1792 (2009)
Niu, Z.R., Recho, N., Yang, Z.Y., Cheng, C.Z.: Elastic-plastic stress singularities of plane V-notches in power-hardening materials. Key Eng. Mater. 465, 105–110 (2011)
Noda, N.A., Oda, K., Inoue, T.: Analysis of newly-defined stress intensity factors for angular corners using singular integral equations of the body force method. Int. J. Fract. 76(3), 243–261 (1996)
Nui, L.S., Chehimi, C., Pluvinage, G.: Stress field near a large blunted tip V-notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials. Eng. Fract. Mech. 49(3), 325–335 (1994)
Ovcharenko, Y.N.: Teoriya i praktika V-obraznykh vyrezov v mekhanike razrusheniya (Theory and practice of V-shaped notches in fracture mechanics). TSU, Tula (2003)
Ovcharenko, Y.N.: The elastic stress-strain state and strain energy density at the vertex of extremely narrow U-notches. Proc. Tula State Univ. Nat. Sci. 2, 97–108 (2010)
Panasyuk, V.V., Savruk, M.P., Datsyshin, A.P.: Raspredeleniye napryazhenii okolo treshchin v plastinakh i obolochkakh (Stress distribution around cracks in plates and shells). Naukova dumka, Kyiv (1976)
Panasyuk, V.V., Savruk, M.P., Kazberuk, A.: Stress concentration near sharp and rounded V-notches. Mater. Sci. 49(6), 711–722 (2014)
Parton, V.Z., Morozov, E.M.: Elastic-Plastic Fracture Mechanics. Mir, Moscow (1978)
Petkov, Z.B., Gospodinov, G.K.: Evaluation of fracture mechanics parameters for a general corner using a weight function method. Acta Mech. 93, 145–155 (1992)
Ping, X.C., Chen, M.C., Xie, J.L.: Singular stress analyses of V-notched anisotropic plates based on a novel finite element method. Eng. Fract. Mech. 75, 3819–3838 (2008)
Pluvinage, G.: Mekhanika uprugoplasticheskogo razrysheniya (Mechanics of elastic-plastic fracture). Mir, Moscow (1993)
Portela, A., Aliabadi, M.H., Rooke, D.P.: Efficient boundary element analysis of sharp notched plates. Int. J. Numer. Methods Eng. 32, 445–470 (1991)
Prößdorf, S., Rathsfeld, A.: Quadrature and collocation methods for singular integral equations on curves with corners. Z. Anal. Anwendungen 8(3), 197–220 (1989)
Providakis, C.P.: Boundary element analysis of creeping V-notched metallic plates in bending. Eng. Fract. Mech. 64(2), 129–140 (1999)
Providakis, C.P.: Creep analysis of V-notched metallic plates: boundary element method. Theor. Appl. Fract. Mech. 32(1), 1–7 (1999)
Qian, Z.Q.: On the evaluation of the free-edge stress intensity factors for a joint subjected to a uniform change in temperature. J. Therm. Stress. 23(5), 463–481 (2000)
Qian, Z.Q.: On the evaluation of wedge corner stress intensity factors of bi-material joints with surface tractions. Comput. Struct. 79(1), 53–64 (2001)
Qian, Z.Q., Akisanya, A.R.: Wedge corner stress behaviour of bonded dissimilar materials. Theor. Appl. Fract. Mech. 32(3), 209–222 (1999)
Radaj, D., Zhang, S.: On the relations between notch stress and crack stress intensity in plane shear and mixed mode loading. Eng. Fract. Mech. 44(5), 691–704 (1993)
Rao, A.K.: Stress concentrations and singularities at interface corners. ZAMM J. Appl. Math. Mech. 51(5), 395–406 (1971)
Rice, J.R.: A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 35(2), 379–386 (1968)
Rooke, D.P., Baratta, F.I., Cartwright, D.J.: Simple methods of determining stress intensity factors. Eng. Fract. Mech. 14(2), 397–426 (1981)
Rösel, R.: On the wedge/notch eigenvalue. Int. J. Fract. 33(1), 61–71 (1987)
Rudge, M.R.H.: Interfacial stress singularities in a bimaterial wedge. Int. J. Fract. 63(1), 21–26 (1993)
Rudge, M.R.H., Tiernan, D.M.: Interfacial stress singularities in a bimaterial wedge. Int. J. Fract. 74(1), 63–75 (1995)
Rudge, M.R.H., Tiernan, D.M.: Stress singularities in composite wedge-shaped materials. Fatigue Fract. Eng. Mater. Struct. 22(1), 11–15 (1999)
Rzasnicki, W., Mendelson, A.: Application of boundary integral method to elastoplastic analysis of V-notched beams. Int. J. Fract. 11(2), 329–342 (1975)
Sargsyan, A.M.: On stress singularity in one problem of elasticity theory for the wedge. Proc. Natl. Acad. Sci. Armen. Mech. 61(1), 48–53 (2008)
Savruk, M.P.: Dvumernyye zadachi uprugosti dla tel s treshchinami (Two-dimensional problems of elasticity for bodies with cracks). Naukova dumka, Kyiv (1981)
Savruk, M.P.: Koeficienty intensivnosti napryazhenii v telakh s treshchinami (Stress intensity factors in bodies with cracks). Naukova dumka, Kyiv (1988)
Savruk, M.P.: Solving planer problems of crack theory for regions with angular points. Mater. Sci. 24(1), 39–49 (1988)
Savruk, M.P., Datsyshin, A.P.: Interaction between a system of cracks and the boundaries of an elastic body. Int. Appl. Mech. 10(7), 755–761 (1974)
Savruk, M.P., Kazberuk, A.: Relationship between the stress intensity and stress concentration factors for sharp and rounded notches. Mater. Sci. 42(6), 725–738 (2006)
Savruk, M.P., Kazberuk, A.: Stress concentration around a rounded notch for arbitrary vertex curvature. Acta Mech. Autom. 1(1), 90–102 (2007)
Savruk, M.P., Kazberuk, A.: Stress intensity factors at the apex of the diamond hole in the stretched plane. In: Proceedings of the IV International Symposium on Damage Mechanisms in Materials and Structures, pp. 233–236. Bialystok (2007)
Savruk, M.P., Kazberuk, A.: Stress intensity factors at the apex of the diamond hole in the stretched plane. Acta Mech. Autom. 1(2), 37–40 (2007)
Savruk, M.P., Kazberuk, A.: A unified approach to problems of stress concentration near V-shaped notches with sharp and rounded tip. Int. Appl. Mech. 43(2), 182–197 (2007)
Savruk, M.P., Kazberuk, A.: A unified approach to the problem of the distribution of stresses near sharp and rounded V-shaped notches. In: Mhitarian, S.M. (ed.) Aktual’nye problemy mekhaniki sploshnoy sredy, pp. 359–363. Erevanskiy gos. un-t arhitektury i stroitel’stva, Erevan (2007)
Savruk, M.P., Kazberuk, A.: Plane periodic boundary-value problem of elasticity theory for a half-plane with curvilinear edge. Mater. Sci. 44(4), 461–470 (2008)
Savruk, M.P., Kazberuk, A.: Problems of fracture mechanics of solid bodies with V-shaped notches. Mater. Sci. 45(2), 162–180 (2009)
Savruk, M.P., Kazberuk, A.: Stress concentration problems for elastic domains with V-shaped notches. In: Panasyuk, V.V. (ed.) Mekhanika ruinuvannya materialiv i mitsnist’ konstruktsii (Fracture mechanics of materials and strength of structures), pp. 75–86. Lviv (2009)
Savruk, M.P., Kazberuk, A.: Stresses in an elastic plane with a periodic system of closely located holes. Mater. Sci. 45(6), 831–844 (2009)
Savruk, M.P., Kazberuk, A.: On some problems of fracture mechanics in bodies with sharp and rounded V-notches. Acta Mech. Autom. 4(2), 113–123 (2010)
Savruk, M.P., Kazberuk, A.: Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches. Int. J. Fract. 161, 79–95 (2010)
Savruk, M.P., Kazberuk, A.: Antisymmetric stress distribution in an elastic body with a sharp or a rounded V-shaped notch. Mater. Sci. 46(6), 711–722 (2011)
Savruk, M.P., Kazberuk, A.: Distribution of stresses near V-shaped notches in the complex stressed state. Mater. Sci. 47(4), 476–487 (2012)
Savruk, M.P., Osiv, P.M.: Numerical solution of the singular integral equations for plain problems of the theory of cracks with angular points on the boundary contours. Mater. Sci. 25(3), 294–301 (1989)
Savruk, M.P., Zelenyak, V.M.: Dvovymirni zadachi termopruzhnosti dla kuskovo-odnoridnykh til z trishchynamy (Two-dimensional problem of thermoelasticity for piecewise homogeneous bodies with cracks). Rastr-7, Lviv (2009)
Savruk, M.P., Osiv, P.M., Prokopchuk, I.V.: Chislennyy analiz v ploskikh zadachakh teorii treshchin (Numerical analysis in plane problems of theory of cracks). Naukova dumka, Kyiv (1989)
Savruk, M.P., Shkarayev, S.V., Madenci, E.: Stress near apex of dissimilar material with bilinear behavior. Theor. Appl. Fract. Mech. 31(3), 203–212 (1999)
Savruk, M.P., Kazberuk, A., Niedźwiedź, M.: Stress distribution around sharp and rounded corners notches for complex stress state. Matematychni problemy mekhaniky neodnoridnykh struktur (Mathematical problems of mechanics of nonhomogeneous structures), pp. 81–83. Lviv (2010)
Savruk, M.P., Kazberuk, A., Tarasiuk, G.: Distribution of stresses over the contour of rounded V-shaped notch under antiplane deformation. Mater. Sci. 47(6), 717–725 (2012)
Savruk, M.P., Kazberuk, A., Tarasiuk, G.: Stress concentration near holes in the elastic plane subjected to antiplane deformation. Mater. Sci. 48(4), 415–426 (2013)
Seweryn, A.: Asymptotic methods of determining stress intensity factors for V-notches in plane problems in the theory of elasticity. Rozprawy Inżynierskie (Eng. Trans.) 38, 467–486 (1990)
Seweryn, A.: Modeling distributions of stresses and displacements in the vicinity of the V-notch apex in plane problems in the theory of elasticity - I. Rozprawy Inżynierskie (Eng. Trans.) 38, 351–376 (1990)
Seweryn, A.: Modeling distributions of stresses and displacements in the vicinity of the V-notch apex in plane problems in the theory of elasticity - II. Rozprawy Inżynierskie (Eng. Trans.) 38, 377–396 (1990)
Seweryn, A.: Kumulacja uszkodzeń i pȩkanie elementów konstrukcyjnych w złożonych stanach obcia̧żeń (Accumulation of damage and fracture of structural elements in complex states of loading). Bialystok University of Technology, Bialystok (1997)
Seweryn, A.: Modeling of singular stress fields using finite element method. Int. J. Solids Struct. 39(18), 4787–4804 (2002)
Seweryn, A.: Metody numeryczne w mechanice pekania (Numerical methods in fracture mechanics). Institute of Fundamental Technological Research. Polish Academy of Sciences, Warsaw (2003)
Seweryn, A., Adamowicz, A.: Modelling of stress fields in the elements with cracks and sharp notches. Przeglad Mechaniczny (Mech. Rev.) 1, 36–41 (2002)
Seweryn, A., Adamowicz, A.: On analytic constraints and elements methods in modeling stresses near the tips of cracks and V-notches. Mater. Sci. 41(4), 462–478 (2005)
Seweryn, A., Łukaszewicz, A.: Numerical modeling methods of problems of linear fracture mechanics. Przeglad Mechaniczny (Mech. Rev.) 5–6, 36–42 (2000)
Seweryn, A., Molski, K.: Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Eng. Fract. Mech. 55(4), 529–556 (1996)
Shin, K.C., Kim, W.S., Lee, J.J.: Application of stress intensity to design of anisotropic/isotropic bi-materials with a wedge. Int. J. Solids Struct. 44(24), 7748–7766 (2007)
Sih, G.C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10(3), 305–321 (1974)
Sih, G.C., Liebowitz, H.: Mathematical theories of brittle fracture. In: Liebowitz, H. (ed.) Fracture, vol. 2, pp. 67–190. Academic Press, New York (1968)
Sinclair, G.B.: A remark on the determtnation of mode I and mode II stress intensity factors for sharp re-entrant corners. Int. J. Fract. 27(3), 81–85 (1985)
Sinclair, G.B., Okajima, M., Griffin, J.M.: Path independent integrals for computing stress intensity factors at sharp notches in elastic plates. Int. J. Numer. Methods Eng. 20, 999–1008 (1984)
Song, C., Tin-Loi, F., Gao, W.: A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges. Eng. Fract. Mech. 77(12), 2316–2336 (2010)
Strandberg, M.: A numerical study of the elastic stress field arising from sharp and blunt V-notches in SENT-specimen. Int. J. Fract. 100(4), 329–342 (1999)
Szabó, B.A., Yosibash, Z.: Numerical analysis of singularities in two dimensions. Part 2: computation of generalized flux/stress intensity factors. Int. J. Numer. Methods Eng. 39(3), 409–434 (1996)
Teh, L.S., Brennan, F.P.: Evaluation of mode I stress intensity factors for edge cracks from 2-D V-notches using composition of constituent SIF weight functions. Int. J. Fatigue 29(7), 1253–1268 (2007)
Teh, L.S., Love, A.J., Brennan, F.P.: Mode I stress intensity factors for edge cracks emanating from 2-D U-notches using composition of SIF weight functions. Int. J. Fatigue 28(4), 355–365 (2006)
Theocaris, P.S.: The order of singularity at a multi-wedge corner of a composite plate. Int. J. Eng. Sci. 12(2), 107–120 (1974)
Theocaris, P.S., Ioakimidis, N.I.: The V-notched elastic half-plane problem. Acta Mech. 32(1–3), 125–140 (1979)
Tur, M., Fuenmayor, J., Mugadu, A., Hills, D.A.: On the analysis of singular stress fields. Part 1: finite element formulation and application to notches. J. Strain Anal. 37(5), 437–444 (2002)
Ufland, Y.S.: Integral’nye preobrazovaniya v zadachakh teorii uprogosti (Integral transforms in problems of the theory of elasticity). Nauka, Moscow (1967)
Ushijima, K., Chen, D.H., Kitte, N.: Intensity of a plastic singular stress field at the notch tip. JSME Int. J. A Solid Mech. Mater. Eng. 45(2), 170–176 (2002)
Vable, M., Maddi, J.R.: Boundary element analysis of inclusions with corners. Eng. Anal. Bound. Elem. 31(9), 762–770 (2007)
Vorovich, I.I.: On some problems of stress concentration. Kontsentratsiya napryazheniy (Stress concentration), vol. 2, pp. 45–53. Naukova dumka, Kyiv (1968)
Vorovich, I.I.: Formulation of boundary-value problems in the theory of elasticity for an infinite energy integral and basic properties of homogeneous solutions. Mekhanika deformiruyemykh tel i konstruktsii (Mechanics of solids and structures), pp. 112–128. Mashinostroyeniye, Moskow (1975)
Wang, W., Kuang, Z.: Higher order asymptotic fields at the tip of a sharp V-notch in a power-hardening material. Acta. Mech. Solida Sinica 15(2), 102–110 (2002)
Wieghardt, K.: über das spalten und zerreißen elastischer körper. Z. Math. Phys. 55(2), 60–103 (1907)
Williams, M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19(4), 526–530 (1952)
Williams, M.L.: The complex variable approach to stress singularities. J. Appl. Mech. 23, 477–478 (1956)
Wu, K.C., Chang, F.T.: Near-tip fields in a notched body with dislocations and body forces. J. Appl. Mech. 60(4), 936–941 (1993)
Wu, K.C., Chen, C.T.: Stress analysis of anisotropic elastic V-notched bodies. Int. J. Solids Struct. 33(17), 2403–2416 (1996)
Wu, Z., Liu, Y.: Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material. Eng. Fract. Mech. 75(8), 2367–2384 (2008)
Wu, Z., Liu, Y.: Asymptotic fields near an interface corner in orthotropic bi-materials. Int. J. Fract. 156(1), 37–51 (2009)
Wu, Z., Liu, Y.: Singular stress field near interface edge in orthotropic/isotropic bi-materials. Int. J. Solids Struct. 47(17), 2328–2335 (2010)
Xia, L., Wang, T.C.: Singular behaviour near the tip of a sharp V-notch in a power law hardening material. Int. J. Fract. 59(1), 83–93 (1993)
Xu, J.Q., Liu, Y.H., Wang, X.G.: Numerical methods for the determination of multiple stress singularities and related stress intensity coefficients. Eng. Fract. Mech. 63(6), 775–790 (1999)
Xu, X.X., Cai, Q.G., Su, Y., Ma, W.D.: Notch root strain and stress distributions in power hardening materials. Int. J. Fract. 41(4), 275–282 (1989)
Yang, S., Chao, Y.J.: Asymptotic deformation and stress fields at the tip of a sharp notch in an elastic-plastic material. Int. J. Fract. 54(3), 211–224 (1992)
Yosibash, Z., Schiff, B.: A superelement for two-dimensional singular boundary value problems in linear elasticity. Int. J. Fract. 62(4), 325–340 (1993)
Yosibash, Z., Schiff, B.: Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities. Finite Elem. Anal. Des. 26(4), 315–335 (1997)
Yosibash, Z., Szabó, B.: Numerical analysis of singularities in two-dimensions part 1: computation of eigenpairs. Int. J. Numer. Methods Eng. 38(12), 2055–2082 (1995)
Yosibash, Z., Szabó, B.A.: Generalized stress intensity factors in linear elastostatics. Int. J. Fract. 72(3), 223–240 (1995)
Yosibash, Z., Szabó, B.A.: A note on numerically computed eigenfunctions and generalized stress intensity factors associated with singular points. Eng. Fract. Mech. 54(4), 593–595 (1996)
Yu, T., Shi, L.: Determination of sharp V-notch stress intensity factors using the extended finite element method. J. Strain Anal. 47(2), 95–103 (2012)
Yuan, H.: Singular stress fields at V-notch tips in elastoplastic pressure-sensitive materials. Acta Mech. 118(1–4), 151–170 (1996)
Yuan, H., Lin, G.: Analysis of elastoplastic sharp notches. Int. J. Fract. 67(3), 187–216 (1994)
Zargaryan, S.S.: Plane elasticity problem for simply connected domains with corners for given external forces on the boundary. Rep. Acad. Sci. Armen. SSR 60(1), 43–50 (1975)
Zargaryan, S.S.: Singularities of solutions of a system of singular integral equations in plane elasticity theory for given stresses on the boundary. Rep. Acad. Sci. Armen. SSR 77(4), 167–172 (1983)
Zargaryan, S.S., Maz’ya, V.G.: The asymptotic form of the solutions of the integral equations of potential theory in the neighbourhood of the corner points of a contour. J. Appl. Math. Mech. 48(1), 120–124 (1984)
Zhang, N., Joseph, P.F.: A nonlinear finite element eigenanalysis of singular plane stress fields in bimaterial wedges including complex eigenvalues. Int. J. Fract. 90(3), 175–207 (1998)
Zhang, S.W., Chen, Y.Z., Lin, W.Z.: Investigation of shear stress distribution in notch problem under sliding mode case. Int. J. Fract. 56(1), 85–92 (1992)
Zhu, H., Xu, J., Feng, M.: Singular fields near a sharp V-notch for power law creep material. Int. J. Fract. 168(2), 159–166 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Savruk, M.P., Kazberuk, A. (2017). Stress Distribution in Elastic Plane with a Semi-infinite Notch. In: Stress Concentration at Notches. Springer, Cham. https://doi.org/10.1007/978-3-319-44555-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-44555-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44554-0
Online ISBN: 978-3-319-44555-7
eBook Packages: EngineeringEngineering (R0)