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Streszczenie:
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.

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

Streszczenie:
The paper presents analytical pullout analysis for Carbon nanotube-cement composite based on Shear-lag assumptions. The composites under study are cement matrix composites reinforced by means of unidirectional Carbon nanotubes (CNT). The interface is assumed to be a material line with constitutive behaviour characterized by a relation between sliding stress and relative sliding displacement. Frictional sliding at the interface region is described by three different interface models: (i) Constant-τ model; (ii) Linear slip-hardening model and, (iii) Linear slip-softening model. The pullout analysis is performed considering static loading. The numerical examples are performed for concrete geometrical and material characteristics for CNT/cement composite. The obtained results are illustrated by figures and discussed.

Słowa kluczowe:
Carbon nanotube cement reinforced composites, Interface sliding models, Pullout analysis, Shear-lag model, Static loading

Streszczenie:
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.

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

Streszczenie:
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.

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

Streszczenie:
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.

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

Streszczenie:
The behaviour of the interface of a pre-cracked bi-material ceramic-metal structure under static axial loading is an object of interest in the present paper. To solve the problem for interface delamination of the structure and to determine the debond length along the interface, a 2D BEM code was created and applied. The interface plate is assumed as a very thin plate comparing with the others two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. First, the obtained numerical results are compared with analytical ones from 1D. Shear lag analysis of the considered structure. The respective comparison is illustrated in figures and shows a good agreement. The comparison between the calculated using 2D BEM code elastic-brittle debond lengths with Song's experimental data for the bi-material structure Zinc/Steel as well as with respective results from FEM simulation shows good coincidence.

Słowa kluczowe:
BEM, Shear lag analysis, bi-material structure, debond length

Streszczenie:
This article is concerned with the effect of imperfect interfaces on the decay of end effect for heat conduction in non-symmetric sandwich strip with - layers. The constituent layers are isotropic and the interface conditions between the layers are assumed to be either LC-type or HC-type at vanishing temperature at the bottom and top side of the strip. The characteristic decay length in all considered cases for three-layered sandwich strip is numerically calculated and represented by the smallest real and positive root of a corresponding transcendental equation. The results of parametric analysis of decay rate depending on volume fraction and heat conductivity of constituents provided for three-layered sandwich strip are illustrated in figures and discussed. Some optimal parameters for the considered structure at which the maximal value of the decay rate is reached are proposed.

Słowa kluczowe:
decay rate of end effects, heat condition, semi-infinite sandwich structure

Streszczenie:
The behaviour of the interface of a pre-cracked bi-material ceramic - metal structure under static axial loading is an object of interest in the present paper. To solve the problem for an interface de lamination of the structure and to determine the debond length along the interface, own 2D BEM code is created and applied. The interface plate is assumed as a very thin plate comparing with others two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. The obtained numerical results are compared with analytical one from 1D Shear-lag analysis of considered structure. The respective comparison is illustrated in figures and shows a good coincidence.

Słowa kluczowe:
BEM, Shear-lag analysis, Layered structure