We present a survey of the results of investigations of the concentration of stresses in elastic bodies weakened by curvilinear holes and notches with nonsmooth contours. Special attention is given to the asymptotic approach to the investigation of stress distributions near stress concentrators in the case where the stress intensity factors at sharp vertices are found by using the stress concentration factors at the rounded vertices of V-notches.
Similar content being viewed by others
References
H. Neuber, Kerbspannungslehre: Theorie der Spannungskonzetration; genaue Berechnung der Festigkeit, Springer, Berlin (1985).
G. N. Savin, Distribution of Stresses near Holes [in Russian], Naukova Dumka, Kiev (1968).
D. W. Pilkey and D. F. Pilkey, Peterson’s Stress Concentration Factors, Wiley, New York (2008).
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1989).
M. P. Savruk and A Kazberuk, Concentration of Stresses in Solids with Notches, in: V.V. Panasyuk (editor), Fracture Mechanics and Strength of Materials, [in Ukrainian], Vol. 14, SPOLOM, Lviv (2012).
M. P. Savruk and A Kazberuk, Stress Concentration at Notches, Springer, Cham (2017).
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1953).
M. P. Savruk, Two-Dimensional Problems of Elasticity for Cracked Bodies [in Russian], Naukova Dumka, Kiev (1981).
J. P. Benthem, “Stresses in the region of rounded corners,” Int. J. Solids Struct., 23, No. 2, 239–252 (1987).
K. Wieghardt, “Über das Spalten und Zerreissen elastischer Körper,” Z. Math. Physik, 55, No. 2, 60–103 (1907).
M. L. Williams, “Stress singularities resulting from various boundary conditions in angular corners of plates in extension,” J. Appl. Mech., 19, 526–530 (1952).
G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw Hill, New York (1979).
A. Kazberuk, Dwuwymiarowe Zagadnienia Mechaniki Pękania Ciał z Karbami, Oficyna Wydawnicza Politechniki Białostockej, Białystok (2010).
M. P. Savruk and A. Kazberuk, “Relationship between the stress intensity and stress concentration factors for sharp and rounded notches,” Fiz.-Khim. Mekh. Mater., 42, No. 6, 17–26 (2006); English translation: Mater. Sci., 42, No. 6, 725–738 (2006).
M. P. Savruk and A. Kazberuk, “A unified approach to problems of stress concentration near V-shaped notches with sharp and rounded tip,” Prikl. Mekh., 43, No. 2, 70–87 (2007); English translation: Int. Appl. Mech., 43, No. 2, 182–196 (2007).
M. P. Savruk and A. Kazberuk, “Antisymmetric stress distribution in an elastic body with a sharp or a rounded V-shaped notch,” Fiz.-Khim. Mekh. Mater., 46, No. 6, 5–15 (2010); English translation: Mater. Sci., 46, No. 6, 711–722 (2010).
M. P. Savruk and A. Kazberuk, “Distribution of stresses near V-notches in the complex stressed state,” Fiz.-Khim. Mekh. Mater., 47, No. 4, 52–61 (2011); English translation: Mater. Sci., 47, No. 4, 476–487 (2012).
M. P. Savruk, A. Kazberuk, and G, Tarasiuk, “Distribution of stresses over the contour of a rounded V-shaped notch under antiplane deformation,” Fiz.-Khim. Mekh. Mater., 47, No. 6, 7–14 (2011); English translation: Mater. Sci., 47, No. 6, 717–725 (2012).
M. P. Savruk and A. Kazberuk, “Problems of fracture mechanics of solid bodies with V-notches,” Fiz.-Khim. Mekh. Mater., 45, No. 2, 23–39 (2009); English translation: Mater. Sci., 45, No. 2, 162–180 (2009).
M. P. Savruk and A. Kazberuk, “Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches,” Int. J. Fract., 161, No. 1, 79–95 (2010).
M. P. Savruk and A. Kazberuk, Stress concentration problems for elastic domains with V-shaped notches, in: V. V. Panasyuk (editor), Fracture Mechanics of Materials and Structural Integrity [in Ukrainian], Karpenko Physicomechanical Institute, National Academy of Sciences of Ukraine, Lviv (2009), pp. 75–86.
M. P. Savruk and A. Kazberuk, “O pewnych zagadnieniach mechaniki pękania ciał z ostrymi i zaokrąglonymi karbami V,” Acta Mech. Autom., 4, No. 3, 113–123 (2010).
M. P. Savruk, A. Kazberuk, and G, Tarasiuk, “Stress concentration near holes in the elastic plane subjected to antiplane deformation,” Fiz.-Khim. Mekh. Mater., 48, No. 4, 5–13 (2012); English translation: Mater. Sci., 48, No. 4, 415–426 (2013).
V. S. Kravets and M. P. Savruk, “Axisymmetric problem of torsion of an elastic space with smooth and acute-angled notches,” Fiz.-Khim. Mekh. Mater., 49, No. 5, 21–30 (2013); English translation: Mater. Sci., 49, No. 5, 577–588 (2014).
M. P. Savruk and A. B. Chornenkyi, “Plane problem of the theory of elasticity for a quasiorthotropic body with cracks,” Fiz.-Khim. Mekh. Mater., 51, No. 3, 17–24 (2015); English translation: Mater. Sci., 51, No. 3, 311–321 (2015).
M. Zappalorto and P. Lazzarin, “In-plane and out-of-plane stress field solutions for V-notches with end holes,” Int. J. Fract., 168, 167–180 (2011).
G. Kullmer, “Elastic stress fields in the vicinity of a narrow notch with circular root,” in: Reliability and Structural Integrity of Advanced Materials. Proc. of the 9th Biennial Europ. Conf. on Fracture (ECF 9), Vol. 2 (1992), pp. 905–910.
G. Kullmer and H. A. Richard, “Influence of the root radius of crack-like notches on the fracture load of brittle components,” Arch. Appl. Mech., 76, 711–723 (2006).
M. P. Savruk, “Longitudinal shear of an elastic wedge with cracks and notches,” Fiz.-Khim. Mekh. Mater., 38, No. 5, 57–65 (2002); English translation: Mater. Sci., 38, No. 5, 672–684 (2002).
V. M. Mirsalimov, “Influence of unloading holes on the propagation of cracks,” Probl. Prochn., No. 4, 18–19 (1971).
E. Smith, “The Mode III elastic stress distribution near the root of (a) an intrusion-type notch and (b) a key-hole notch,” Int. J. Eng. Sci., 44, 340–344 (2006).
F. Berto, “Fictitious notch rounding concept applied to V-notches with end holes under mode 3 loading,” Int. J. Fat., 38, 188–193 (2012).
C. R. Chiang, “Stress field around a rounded crack tip,” J. Appl. Mech., 58, No. 3, 832–836 (1991).
D. Taylor, The Theory of Critical Distances: A New Perspective in Fracture Mechanics, Elsevier, Oxford (1977).
A. Carpinteri, P. Cornetti, N. Pugno, A. Sapora, and D. Taylor, “A finite fracture mechanics approach to structures with sharp V-notches,” Eng. Fract. Mech., 75, 1736–1752 (2008).
D. Taylor, “The theory of critical distances,” Eng. Fract. Mech., 75, 1696–1705 (2008).
M. R. Ayatollahi and A. R. Torabi, “Brittle fracture in rounded-tip V-shaped notches,” Mater. Design, 31, 60–67 (2010).
M. R. Ayatollahi and A. R. Torabi, “Investigation of mixed mode brittle fracture in rounded-tip V-notched components,” Eng. Fract. Mech., 77, No. 16, 3087–3104 (2010).
P. Cornetti, N. Pugno, A. Carpinteri, and D. Taylor, “Finite fracture mechanics: A coupled stress and energy failure criterion,” Eng. Fract. Mech., 73, 2021 –2033 (2006).
A. Sapora, P. Cornetti, A. Carpinteri, and D. Firrao, “Blunt V-notch brittle fracture: An improved finite fracture mechanics approach,” Adv. Mater. Res., 1105, 237–244 (2015).
A. Kazberuk, “Stress intensity factors for cracks at rounded V-notch vertex,” Fiz.-Khim. Mekh. Mater., 45, No. 5, 61–70 (2009); English translation: Mater. Sci., 45, No. 5, 676–687 (2009).
D. Gallagher, “A crack at the apex of a V-shaped notch,” Int. J. Fract., 69, No. 4, R81–R87 (1995).
M. P. Savruk and A. Kazberuk, “Współczynniki intensywnosci naprężeń w wierzchółku rombowego otworu w rozciąganej plaszczyznie,” Acta Mech. Autom., 1, No. 2, 37–40 (2007).
N. A. Noda, K. Oda, and T. Inoue, “Analysis of newly-defined stress intensity factors for angular corners using singular integral equations of the body force method,” Int. J. Fract., 76, 243–261 (1996).
V. S. Kravets, Study of the stressed state of an infinite plate with square hole, in: Fracture Mechanics and Physics of Construction Materials and Structures [in Ukrainian], Vol. 5, Kamenyar, Lviv (2002), pp. 95–105.
Y. Kohno and H. Ishikawa, “Singularities and stress intensities at the corner point of a polygonal hole and rigid polygonal inclusion under antiplane shear,” Int. J. Eng. Sci., 33, No. 11, 1547–1560 (1995).
N. F. Morozov, Mathematical Questions of the Theory of Cracks [in Russian], Nauka, Moscow (1984), 256 pp.
A. Kazberuk, “Koncentracja naprężeń wokół owalnego otworu,” Acta Mech. Autom., 1, No. 2, 25–30 (2007).
V. D. Kuliev, “A singular problem of elasticity theory for a semiinfinite rectangular notch,” Prikl. Mat. Mekh., 44, No. 5, 952–957 (1980).
V. A. Kryven, A. R. Boiko, and A. V. Kaplun, “Development of plastic strips in the process of shear deformation of a body with narrow rectangular slot,” Fiz.-Khim. Mekh. Mater., 50, No. 4, 49–54 (2014); English translation: Mater. Sci., 50, No. 4, 527–535 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 57, No. 3, pp. 41–52, May–June, 2021.
Rights and permissions
About this article
Cite this article
Savruk, M.P. Stress Concentration Near Curvilinear Holes and Notches with Nonsmooth Contours. Mater Sci 57, 331–343 (2021). https://doi.org/10.1007/s11003-021-00548-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-021-00548-9