Nonlocal criterion of bridged cracks growth: analytical analysis

Abstract

A nonlocal fracture criterion with accounting of the work during bonds deformation at the fracture process zone has been implemented analytically for analysis of bridged cracks growth. This criterion consists of two conditions: (1) the necessary energy condition of the crack tip limit equilibrium, which takes into account the energy release rate to the crack tip and the rate of deformation energy consumed by bonds in the crack bridged zone; (2) the sufficient condition is the equality of the crack opening at the bridged zone trailing edge to the bond limit stretching. Subcritical and quasi-statical regimes of bridged cracks growth have been formulated on these fracture conditions. Regimes of bridged cracks growth are analyzed in detail for the case of an internal straight bridged crack in homogeneous material with bonds traction, which is constant and independent of the external loading. Analytical expressions are obtained for the deformation energy release rate and for the rate of deformation energy consumed by bonds. The main fracture parameters, the critical external load and the crack bridged zone size in the limit equilibrium state are determined and analyzed. The limit cases of a crack which is filled with bonds and a crack with a small-scale bridged zone are considered. A comparative study with the well-known force fracture criterion for bridged crack growth is performed.

Modeling of Materials Self-Healing

“…The healing time and efficiency are dependent on the chemical reaction rate of the healing agent, the crack size and the external loads. The non-local fracture criterion [1,5,6] is used to evaluate the fracture toughness and the critical external loading in the frames of the bridged crack model. The model can be used for the evaluation of composite materials healing and durability.…”

“…4 values of SIF for cracks with bonds were scaled by SIF for the same crack length without bonds, Analysis of the healing process in finite size structures can be performed by boundary elements method [2]. Growth prediction of healed cracks can be performed on the basis of the bridged cracks growth criterion [5,6].…”

Criterion of Interfacial Bridged Cracks Initiation and Quasistatic Growth

“…The non-local fracture criterion [1,3,4] is used to evaluate the fracture toughness and the critical external loading in the frames of the bridged crack model. The state of the crack limit equilibrium corresponds to the condition (  is the total potential energy, ()…”

“…It can be determined from condition (1) while the searching for the critical load needs additional conditions of the bond rupture. In the general case the strain energy release rate can be defined through the stress intensity factors, [1,4].…”

“…The main features of the nonlocal fracture criterion are the accounting of energy consumed by bonds during cracks growth and the analysis on this ground of non self-similar crack growth. This criterion has implemented in the frames of the bridged crack model with assumption of singularity at the crack tip, but it includes the cohesive model as the special case, see [3,4]. The application of the nonlocal fracture criterion will be helpful for cracks filled with bonds in the most part of its length.…”