PSI - Issue 33

O.B. Naimark et al. / Procedia Structural Integrity 33 (2021) 1115–1122

1117

Naimark O.B. et al / Structural Integrity Procedia 0 component of the stress field, but also the nonsingular component, a parameter of local constraint of deformations at the crack tip. This leads to refining models and criteria of fracture mechanics, taking into account the two-parameter representation of the stress-strain state in the vicinity of the crack tip, as well as experimental methods that allow verification of this approach and determination of parameters of the models. Two-parameter representation of the stress-strain state in the process zone at the crack tip allowed the formulation a fracture criteria and propose a criterion equation for a generalized fracture assessment diagram (FAD) as following: , (2)

where

is the stress intensity factor at the top of the U-shaped notch under normal separation conditions;

is the local strength of the material, called cohesive strength;

is applied critical stress. The fracture

toughness in the presence of a notch

reads

,

(3)

where

is the fracture toughness under conditions of maximum deformation constraint at the crack tip, Kt is

the theoretical stress concentration factor. For a crack-like defect (

) the criterion equation (3) is

transformed into the following:

(4)

Two parameter fracture criteria reflect the deep aspects of criticality of the damage-failure transition related the stress singularity at the crack tip area and nonlinearity of damage kinetics in the process zone. It was shown by Naimark et al. (2021) that the variety of crack advance scenario occurs due to the presence of two types of the intermediate self-similar solutions (two attractors) that are the Irwin solution for the stress distribution at the crack tip and the blow-up damage localization kinetics pre-generated to daughter cracks origin. Kinetics of damage-failure transition in the process zone was described using the results of statistical thermodynamics of solid with typical defects (microcracks, microshears) that allowed the definition of the non equilibrium free energy of solid with defects and damage kinetics due to the free energy release nonlinearity. It was shown, that the final damage localization stage is described by the intermediate self-similar solution for the defect density parameter p , which coincides with the deformation caused by the defects. This self-similar solution has the blow-up nature and reads

,

(5)

where

is the so-called "peak time" (

at

for the self-similar profile

of defects localized

on the scale

),

,

are the parameters of non-linearity characterizing the free energy release. The

self-similar solution (5) describes the blow-up damage kinetics for

on the set of spatial scales

, where

and

stand for the “simple” and “complex” blow-up dissipative

structures. The scale represents the “quantization length” of damage localization in the process zone providing the variety of the crack paths in the presence of two singularities: intermediate asymptotic solution for stress distribution at the crack tip area and the blow-up damage localization kinetics in the process zone. The existence of two self-similar singular solutions was supported by the temporal recording of the stress in the point at the crack tip area in the course of the crack dynamics in the preloaded PMMA plate