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The basic aspects of the
J
-
A
concept of elastoplastic two-parameter fracture mechanics based on a three-term asymptotic description of the stress field at the crack tip are presented. It is noted that the field of elastoplastic stresses at the crack tip is controlled by two parameters of fracture mechanics, namely,
J
-integral and parameter
A
. Parameter
A
is a measure of the deviation of the stress field from the
HRR
stress field and can be considered a parameter of elastoplastic constraint at the crack tip under conditions of both small- and large-scale yielding. The results of studying the influence of the exponent of the strain hardening of the material, crack aspect ratio, and the thickness of standard specimens with a crack on the elastoplastic stress intensity factor and parameter
A
are presented. A two-parameter elastoplastic
J
-
A
fracture criterion based on the relationship between
J
-integral and strain (stress) on the surface of the crack-notch and the principle of linear summation of damage is formulated. To reflect the crack-tip constraint, the parameter
A
is introduced into the criterion equation as a function of applied failure stresses. The elastoplastic fracture toughness as a function of the crack-tip constraint in the fracture criterion is interpreted as the corrected elastoplastic fracture toughness of a specimen with the corresponding constraint parameters
A
. The results of studying the normalized corrected fracture toughness as a function of failure stresses, crack aspect ratio, and strain hardening exponent of the material are presented.