ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 120–131.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
V.M. Kornev, A.G. Demeshkin.
QUASI-BRITTLE FRACTURE OF COMPACT SPECIMENS
WITH SHARP NOTCHES AND U-SHAPED CUTS
V. M. Kornev and A. G. Demeshkin
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.
Keywords: brittle and quasi-brittle fracture, small-scale yielding, necessary and suﬃcient criteria
of fracture, elastoplastic material, edge crack, U-shaped cut.
The analysis of various systems used for fracture calculations within the framework of the linear fracture
mechanics (LFM) and nonlinear fracture mechanics (NLFM) [1, 2] shows that no simple schemes for calculating
structures made of quasi-brittle materials are available at the moment. It is desirable to use commonly accepted
characteristics of materials in calculations. Zhu and Joyce noted in their review paper  that the most important
parameters used in fracture mechanics are J-integral, the stress intensity factor K, crack width at the tip, and
angle at the crack tip. In LFM calculations of the critical stresses for specimens with suﬃciently long cracks, the
only governing parameter is the stress intensity factor (SIF).
Berto and Lazzarin  considered one-parameter local criteria of fracture of brittle and quasi-brittle solids
in the vicinity of stress concentrators.
Below we consider elastoplastic bodies under ultimate deformation. In studying fracture of quasi-brittle
bodies with small-scale yielding, one has to use quasi-linear fracture mechanics (QLFM). The proposed QLFM
version involves the use of the critical SIF and the classical stress–strain diagram with allowance for the ultimate
deformation of the examined material.
The goals of the present work are to derive relations for the critical stresses in compact specimens with
sharp cracks and to compare the theoretically predicted critical loads with experimental data obtained in the case
of fracture of compact specimens with U-shaped cuts.
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090
Russia; firstname.lastname@example.org; email@example.com. Translated from Prikladnaya Mekhanika i Tekhnicheskaya
Fizika, Vol. 59, No. 1, pp. 138–152, January–February, 2018. Original article submitted July 20, 2016; revision
submitted November 18, 2016.
2018 by Pleiades Publishing, Ltd.