On materials destruction criteria

TL;DR

This paper develops a nonlinear fracture mechanics model for materials, demonstrating that force and energy criteria derived without linear assumptions can effectively describe material fracture behavior.

Contribution

It introduces a discrete-structure fracture model based on energy conservation, linking nonlinear fracture criteria to classical linear fracture mechanics.

Findings

Crack resistance and fracture toughness are derived from energy conservation.

The nonlinear energy criterion $G_{1c}$ exceeds the linear one $K_{1c}^2/E$.

The model provides a more accurate description of material fracture beyond linear assumptions.

Abstract

In terms of nonlinear material fracture mechanics, the real (discrete)-structure material fracture model has been developed. The model rests on the demonstration of the fact that crack resistance $K_{1c}=2\sigma \sqrt l$ and fracture toughness are $G_{1c}=J_{1c}=2\sigma l$ obtained on the basis of energy conservation law and derived without linear material fracture mechanics assumptions can be respectively taken as force and energy criteria for non-linear fracture mechanics. It is shown that $G_{1c}=K_{1c}^2/E$ is the energy criterion of linear fracture mechanics of material and it is sufficiently less than $G_{1c} = J_{1c}=2\sigma l$.