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Abstract:
The paper deals with the elastic and cohesive interface behavior of pre-cracked bi-material ceramic-metal structures under dynamic time harmonic load. The shear lag model as well as the Fourier method is applied to find the dynamic response of the considered bi-material structure, assuming the cohesive interface behaviour, accompanied before of the elastic-brittle one. In both cases, the growth of debond length is not considered, e.g. at a given loading condition the only corresponding debond length is found. The inertia forces of the already elastic debond parts of the bi-material structure are neglected. Appropriate contact conditions are proposed in order to fit together both elastic and cohesive solutions. The numerical predictions for the cohesive debond length of the bi-material structures is calculated by the aid of the corresponding value of the elastic debond length at the same loading condition. The influence of loading characteristics i.e. frequencies and amplitude fluctuations on the debond length and the interface shear stress distribution is discussed. The parametric analysis of the results obtained is illustrated by examples of the modern ceramic-metal composites on metal substrates and is depicted in figures.

Keywords:
Dynamic behaviour of bi-material structure, cracked plate, shear lag model, elastic-brittle and cohesive interface delamination, debond length

Abstract:
The interface cohesive behaviour and interface delamination in a bi-material structure consisting of two plates and material interface with zero thickness under time harmonic load is studied. Previously, the authors studied the elasto-brittle interface behaviour, from both sides of a crack, initially normal to the interface, when the elastic-brittle interface debonding appeared. Now, it is again assumed that the restriction for the ratio of energy release rates of the second plate and interface allowing the occurrence of an interface cohesive delamination before the initiation of the normal crack in the second plate is satisfied. The shear lag model is adopted and applied to find the dynamic response of the considered structure, assuming the cohesive interface behaviour, accompanied before of the elastic-brittle one. In both cases, the growth of debond length is not considered e.g. at a given loading condition the corresponding single debond length is found. The inertia forces of the already debonded interface elasto-brittle cracks (mode II) are neglected. The appropriate contact conditions are proposed in order to fit together both elastic and cohesive solutions. The Laplace inverse transform is applied to obtain the original of cohesive debond length by the aid of the already obtained elastic value of debond length at the same loading condition. Parametric analysis of the results obtained is illustrated by examples of the modern ceramic-metal composite on metal substrate. The influence of frequencies and amplitude fluctuations on the cohesive debond length and the interface shear stress distribution are discussed.

Keywords:
dynamic behaviour of bi-material structure, cracked plate, shear lag model, Laplace transform, cohesive interface delamination, cohesive debond length

Abstract:
The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper. Firstly, it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading. Secondly, the “shear-lag model” is applied to the structure under dynamic loading. To solve the problem for an interface delamination of the structure and to determine the debond length along the interface, our own 2D boundary element method (BEM) code is proposed in the case of static loading, and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading. The interface layer is assumed as a very thin plate compared with the other two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model. In the dynamic case, the influence of loading characteristics, i.e., frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time, is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite, namely cermet, and depicted in figures.

Keywords:
Debond length, Precracked bi-material structure, Shear-lag model, Delamination, BEM

Abstract:
The interface behaviour between two layers of 2D elastic structure under dynamic time-harmonic load is studied. The “shear lag model” is adopted and applied to the dynamic response of bi-material structure, assuming the elastic-brittle behaviour of the interface. The Laplace transforms together with half-analytical calculations are used to obtain the shear stress and elastic debond lengths along the interface at sinusoidal load. Parametric analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite, so called cermet, and depicted in figures. The influence of loading characteristics, i.e. frequencies and amplitude fluctuations on the shear stress and the value of debond length for a small interval of time, is discussed.

Keywords:
Dynamic behaviour of bi-material structure, cracked plate, shear lag model, elastic-brittle interface delamination, debond length