Crack movement in layered composites under electric field affect

The variation principle is applied for defining a crack in the solid body. The methods proposed in [G. Sih, C. Chen, Non-self-similar crack growth in elastic–plastic finite thickness plate, Theoretical and Applied Fracture Mechanics 3 (1985) 125–139] extend to presence of electromagnetic fields in material. Crack propagation in non-homogeneous media has been considered. It is shown that electromagnetic fields in the material are essentially affecting the trajectory. The crack trajectory stability has been studied as function of fracture energy, phase portraits of the trajectory in different media have been built, and various attractor types have been revealed. Different crack morphologies from single straight and oscillating crack propagation to straight double crack propagation were theoretically founded. In compliance with the experimental data of [R. Niefanger, V.-B. Pham, G. Schneider, H.-A. Bahr, H. Balke, U. Bahr, Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory, Acta Materialia 52 (1) (2004) 117–127], it has been demonstrated that periodic electromagnetic field results in trajectory stochastization. This can be used for switching the crack over from the mode of mainline propagation into the mode of development of the field of diffused microcracks.     

Crack trajectory instability: Propagation in inhomogeneous medium

The problem of crack trajectory stabilization in composite material is investigated. The equation for a crack path is found from the variational principle. It is considered as a path along which the extreme amount of energy is generated during the destruction. This statement corresponds to the variational problem analogous to the Lagrange–d’Alembert principle of classic mechanics and to the Fermat principle in optic and acoustic. For a crack path in inhomogeneous medium, nonlinear differential equation is obtained. Stability of the crack propagation in the inhomogeneous medium is considered. In particular, a 2D crack propagating in a composite material is considered. The path of propagation is assumed to cross layers or fibres. For layered and piece-wise continuous composites, the resulting governing equation corresponds to different kind of Duffing’s equation. The bifurcations of the trajectory and instability of crack path are investigated numerically. Conditions of crack trajectory stabilization are found. Properties of the materials that stabilized the crack trajectory are found.     

Delamination of Composites along the Interface as Buckling Failure of the Stressed Layer

A refined model for free vibrations of a Griffith crack in layered composites is investigated. The delamination of the composites along an interface is studied in the context of growth of instability of the stressed layer. This is analogous to the bending of a beam on an elastic foundation. The second-order gradient terms are taken into account in the power-series expansion of deflections. These terms are responsible for nonlinear phenomena in the interaction zone. The zero-order frequency of free vibrations of the crack along the interface and the time of instability growth are determined.     

Geometric Characteristics of Fracture‐Associated Space and Crack Propagation in a Material

It is shown that fracture can be treated as a process occurring in the Finsler space. The use of the Finsler space allows one to construct a delaminated manifold whose characteristics are related to the defect structure of the medium. A method of determining the fractal dimension of fracture is developed using the concept of crack propagation along geodesics.     

Equation of the Crack Front with Allowance for the Metric Properties of the Material

The geometric representation of the crack front propagation is examined in a Finsler space in the context of the discontinuity theory. The structure of the medium is taken into account via the connectivity coefficients of the Finsler space and its metric. It is demonstrated that this approach leads to the construction of fiber spaces and allows the gauge invariance to be introduced correctly and noncontradictorily into the fracture theory. The Lie derivative is used to proceed from discontinuities to differentials. The equation of the front crack surface is retrieved.     

Influence of the Defect Structure of the Material on the Fracture and Crack Motion

The influence of the structure of the medium on the crack propagation in a Finsler space is examined in the context of the fracture theory. The structure of the medium is taken into account via the connectivity coefficient of the Finsler space and its metric. The deformation of the fibered space caused by the crack motion is analyzed.