Abstract
A two-parameter (coupled) discrete-integral criterion of fracture is proposed. It can be used to construct fracture diagrams for compact specimens with sharp cracks. Curves separating the stress–crack length plane into three domains are plotted. These domains correspond to the absence of fracture, damage accumulation in the pre-fracture region under repeated loading, and specimen fragmentation under monotonic loading. Constants used for the analytical description of fracture diagrams for quasi-brittle materials with cracks are selected with the use of approximation of the classical stress–strain diagrams for the initial material and the critical stress intensity factor. Predictions of the proposed theory are compared with experimental results on fracture of compact specimens with different radii made of polymethylmethacrylate (PMMA) and solid rubber with crack-type effects in the form of U-shaped cuts.
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References
V. V. Panasyuk, A. E. Andreikin, and V. Z. Parton, Fracture Mechanics and Material Strength: Reference Book, Vol. 1: Fundamentals of Material Fracture Mechanics (Naukova Dumka, Kiev, 1988) [in Russian].
X.-K. Zhu and J. A. Joyce, “Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization,” Eng. Fracture Mech. 85, 1–46 (2012).
F. Berto and P. Lazzarin, “Recent Developments in Brittle and Quasi-Brittle Failure Assessment of Engineering Materials by Means of Local Approaches,” Mater. Sci. Eng. R 75, 1–48 (2014).
M. Ya. Leonov and V. V. Panasyuk, “Development of the Smallest Cracks in Solids,” Prikl. Mekh. 5 (4), 391–401 (1959).
D. S. Dugdale, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids 8, 100–104 (1960).
G. Neuber, Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung (Springer-Verlag, Berlin, 1937).
V. V. Novozhilov, “On the Necessary and Sufficient Criterion of Brittle Strength,” Prikl. Mat. Mekh. 33 (2), 212–222 (1969).
V. D. Kurguzov and V. M. Kornev, “Construction of Quasi-Brittle and Quasi-Ductile Fracture Diagrams Based on Necessary and Sufficient Criteria,” Prikl. Mekh. Tekh. Fiz. 54 (1), 179–195 (2013) [J. Appl. Mech. Tech. Phys. 54 (1), 156–170 (2013)].
I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Fundamentals of Experimental Fracture Mechanics (Izd. Mosk. Gos. Univ., Moscow, 1989) [in Russian].
V. M. Kornev, “Assessment Diagram of Quasi-Brittle Fracture of Bodies with a Hierarchy of Structures. Multiscale Necessary and Sufficient Criteria of Fracture,” Fiz. Mezomekh. 13 (1), 47–59 (2010).
V. M. Kornev and A. G. Demeshkin, “Quasi-Brittle Fracture Diagram of Structured Bodies in the Presence of Edge Cracks,” Prikl. Mekh. Tekh. Fiz. 52 (6), 152–164 (2011) [J. Appl. Mech. Tech. Phys. 52 (6), 975–985 (2011)].
M. P. Savruk, Fracture Mechanics and Material Strength: Reference Book, Vol. 2: Stress Intensity Factors in Cracked Bodies (Naukova Dumka, Kiev, 1988) [in Russian].
Stress Intensity Factors Handbook, Ed. by Y. Murakami (Pergamon Press, Oxford, 1986).
V. M. Kornev, “Diagrams of Quasi-Brittle Fracture of Bent Structural Elements with Cracks,” Probl. Mashinostr. Nadezh. Mashin, No. 2, 38–46 (2015).
S. E. Kovchik and E. M. Morozov, Fracture Mechanics and Material Strength: Reference Book, Vol. 3: Characteristics of Short-Time Fracture Toughness of Materials and Methods of their Determination (Naukova Dumka, Kiev, 1988) [in Russian].
V. M. Kornev, “Critical Fracture Curves and Effective Diameter of the Structure of Brittle and Quasi-Brittle Materials,” Fiz. Mezomekh. 16 (5), 25–34 (2013).
V. M. Kornev, “Fracture Diagrams for Bodies with Short Microcracks. Embrittlement of the Material during Fatigue Fracture,” Fiz. Mezomekh. 19 (2), 80–99 (2016).
M. Eleces, G. V. Guinea, J. Gomez, and J. Planas, “The Cohesive Zone Model: Advantages, Limitations and Challenges,” Eng. Fracture Mech. 69, 137–163 (2002).
G. I. Barenblatt, “Mathematical Theory of Equilibrium Cracks Formed during Brittle Fracture,” Prikl. Mekh. Tekh. Fiz., No. 4, 3–56 (1961).
V. Z. Parton and E. M. Morozov, Elastoplastic Fracture Mechanics: Fundamentals of Fracture Mechanics (Izd. LKI, 2008) [in Russian].
V. M. Kornev and N. S. Astapov, “Model of Fracture of a Piecewise–HomogeneousMedium during Delamination of Elastoplastic Structured Materials,” Mekh. Kompoz. Mater. Konstr. 16 (3), 347–360 (2010).
V. M. Kornev, V. D. Kurguzov, and N. S. Astapov, “Fracture Model of Bimaterial under Delamination of Elasto-Plastic Structured Media,” Appl. Compos. Mater. 20 (2), 129–143 (2013).
A. G. Demeshkin, V. M. Kornev, and N. S. Astapov, “Strength of a Glued Composite with Crack-Type Defects,” Mekh. Kompoz. Mater. Konstr. 19 (3), 445–458 (2013).
V. M. Kornev, “Delamination of Bimaterial and Critical Curves of Quasi-Brittle Fracture in the Presence of Edge Cracks,” Adv. Materials Sci. Appl. 3 (4), 164–176 (2014).
N. S. Astapov, V. D. Kurguzov, and V.M. Kornev, “Modeling of Bimaterial Delamination Induced by Transverse Shear,” Mekh. Kompoz. Mater. Konstr. 22 (1), 40–53 (2016).
N. S. Astapov, V. M. Kornev, and V. D. Kurguzov, “Model of Delamination of a Cracked Bimaterial with Different Moduli,” Fiz. Mezomekh. 19 (4), 49–57 (2016).
M. M. Shakirtov, A. P. Shabanov, and V. M. Kornev, “Construction of Fracture Diagrams for Plates with a Crack-Like Cut with the Use of Necessary and Sufficient Criteria,” Prikl. Mekh. Tekh. Fiz. 54 (2), 163–170 (2013) [J. Appl. Mech. Tech. Phys. 54 (2), 308–314 (2013)].
V. M. Kornev, “Quasi-Brittle Fracture Diagrams due to Fatigue (Two-Frequency Loading),” Fiz. Mezomekh. 15 (6), 45–58 (2012).
V. M. Kornev, “Quasi-Brittle Fracture Diagrams under Low-Cycle Fatigue (Variable Amplitude Loadings),” Eng. Failure Anal. 35, 533–544 (2013).
A. Yu. Larichkin, V. M. Kornev, and A. G. Demeshkin, “Changes in Plasticity Regions and Damage Accumulation in the Course of Crack Propagation in Quasi-Brittle Materials under Low-Cycle Loading,” Fiz. Mezomekh. 19 (4), 38–48 (2016).
V. M. Kornev, “Diagrams of Quasi-Brittle Fracture ofWelded Joints under Low-Cyclic Fatigue Loading,” Mekh. Kompoz. Mater. Konstr. 19 (4), 568–581 (2013).
V. M. Kornev, “Damage Accumulation and Fracture of Welded Joints under Low-Cyclic Loading Conditions,” Appl. Mech. Mater. 784, 179–189 (2015).
O. N. Romaniv, S. Ya. Yarema, G. N. Nikiforchin, N. A. Makhutov, and M. M. Stadnik, Fracture Mechanics and Material Strength: Reference Book, Vol. 4: Fatigue and Cyclic Fracture Toughness of Structural Materials (Naukova Dumka, Kiev, 1990) [in Russian].
V. V. Bolotin, Mechanics of Fatigue (CRC Press, Boka Raton, London, 1998).
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Original Russian Text © V.M. Kornev, A.G. Demeshkin.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 138–152, January–February, 2018.
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Kornev, V.M., Demeshkin, A.G. Quasi-Brittle Fracture of Compact Specimens with Sharp Notches and U-Shaped Cuts. J Appl Mech Tech Phy 59, 120–131 (2018). https://doi.org/10.1134/S0021894418010157
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DOI: https://doi.org/10.1134/S0021894418010157