Combining the caustic method with high-speed photography is an efficient optical measurement technique to study the dynamic fracture behaviours of homogenous and isotropic material. In the last decade, the main emphasis is extended to study dynamic fracture of anisotropic material and dynamic propagation of multi-cracks and interface cracks in practical engineering materials. In this paper, the recent advances and applications about the dynamic caustic method in China are reviewed, such as impact response and dynamic fracture of composite materials (fibre composites, functionally gradient materials and nanometre composites), and dynamic interaction and propagation of multi-cracks and interface cracks. Particularly, some new numerical methods were developed to solve the complicated caustic equations by introducing both the maximum characteristic size and the relevant angles in caustic patterns. Also, some important experimental results in fracture mechanics are described, and the potential research prospects about dynamic caustics are included as well.

Recent application of caustics on experimental dynamic fracture studies

On a moving interface crack with a contact zone in a piezoelectric bimaterial

An interface crack of a finite length moving with a constant subsonic speed v along an interface of two semi-infinite piezoelectric spaces is considered. It is assumed that the bimaterial compound is loaded by a remote mixed mode mechanical loading and a thermoelectrical field and that a frictionless contact zone arises at the leading crack tip. Electrically permeable and electrically insulated cases of the open part of the crack are involved into the consideration. By introducing a moving coordinate system at the crack tip the problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved exactly. For both cases of the electrical conditions the transcendental equations are obtained for the determination of the real contact zone length, and moreover, the associated closed form asymptotic formulas are found for small values of this parameter. Variations of the contact zone length and the stress intensity factor with respect to the crack speed and the loading have been investigated both for electrically permeable and electrically insulated cases.

Contact Zone Approach for a Moving Interface Crack in a Piezoelectric Bimaterial under Thermoelectromechanical Loading

Theoretical development of the method of caustics for intersonically propagating interfacial crack

A plane strain problem for a crack with a frictionless contact zone at the leading crack tip expanding stationary along the interface of two anisotropic half-spaces with a subsonic speed under the action of various loadings is considered. The cases of finite and infinite-length interface cracks under the action of a moving concentrated loading at its faces are considered. A finite-length crack for a uniform mixed-mode loading at infinity is considered as well. The associated combined Dirichlet-Riemann boundary value problems are formulated and solved exactly for all above-mentioned cases. The expressions for stresses and the derivatives of the displacement jumps at the interface are presented in a closed analytical form for an arbitrary contact zone length. Transcendental equations are obtained for the determination of the real contact zone length, and the associated closed form asymptotic formulas are found for small values of this parameter. It is found that independently of the types of the crack and loading, an increase of the crack tip speed leads to an increase of the real contact zone length and the correspondent stress intensity factor. The latter increase significantly for an interface crack tip speed approaching the Ragleigh wave speed.

A. Noe

Papers

Analysis of dynamic mixed mode stress fields in bimaterials by the method of caustics