Delamination analysis of multilayered viscoelastic beam exposed to chemical degradation

Delamination of multilayered viscoelastic non-homogeneous beam structure subjected to chemical degradation is analysed in this paper. The creep behaviour is treated by using a linear viscoelastic model. The influence of chemical degradation is taken into account by decreasing the elasticity modulus and the coefficient of viscosity with time. The time-dependent delamination fracture under chemical degradation is studied by analysing the strain energy release rate. The strain energy is used to obtain the strain energy release rate that accounts for the creep and for the chemical degradation. The solution is verified by applying the compliance method with considering of the chemical degradation.


Introduction
Multilayered non-homogeneous structural materials are made of adhesively bonded layers of different non-homogeneous materials (for example, layers of fibre reinforced polymer composites). Very modern non-homogeneous materials are functionally graded materials [1,2,3,4,5]. These novel materials have a wide application in current engineering mainly due to their specific behaviour involving high strength-to-weight and stiffness-to-weight ratios [6,7,8,9,10,11]. Therefore, multilayered non-homogeneous materials are used in advanced load-bearing structures where low weight is of special significance [12,13,14,15,16,17].
It should be noted, however, that multilayered materials are employed with caution because of their poor delamination fracture behaviour [18,19,20,21,22,23,24,25]. The delamination cracks drastically reduce the load-bearing capacity of the multilayered structure. Thus, the safety and reliability of multilayered non-homogeneous constructions depend largely on their delamination fracture behaviour.
The goal of the paper is to analyse the delamination fracture of a multilayered non-homogeneous viscoelastic beam configuration that is exposed to influence of aggressive chemical agent. It should be mentioned that such analysis is important since multilayered beam structures frequently are in contact with various chemical substances in their life-time. It should also be mentioned that previous publications do not consider the influence of chemical degradation on time-dependent delamination of non-homogeneous viscoelastic beam structural components [26,27,28]. Therefore, a time-dependent analytical expression of the strain energy release rate that accounts for the chemical degradation of the viscoelastic multilayered non-homogeneous material in a delaminated beam is presented in the paper.

Influence of chemical degradation on delamination of multilayered viscoelastic beam
The delamination crack in the multilayered non-homogeneous viscoelastic beam shown in figure 1 is under consideration. The crack has length, a . The lower and the upper crack arms have thickness, 1 h and 2 h , respectively. The beam has width, b , and thickness, h . The beam is with length, l .
The multilayered non-homogeneous viscoelastic beam structure is exposed to the influence of aggressive chemical agent which leads to chemical degradation of the material in layers. Thus, i L E and i L η decrease with time on exponential laws [30]: where U is the strain energy in the beam structure, da is an elementary increase of the length of the  It should be noted that solution (5) is time-dependent since the strain energy densities in the layers are functions of the time.
The strain energy release rate that accounts for the chemical degradation of the viscoelastic multilayered beam is found also through the compliance method. According to this method, the strain energy release rate is written as The strain energy release rate obtained by (11) is in excellent agreement with that calculated by (5) which prove the correctness of analysis performed.

Numerical results
The time-dependent analysis described in section 2 of the paper is applied here in order to evaluate the influence of the chemical degradation of the multilayered viscoelastic material on the delamination fracture behaviour. Figure 3. The non-dimensional strain energy release rate presented as a function of nondimensional time (curve 1 -for multilayered inhomogeneous viscoelastic beam exposed to chemical degradation, curve 2 -for multilayered inhomogeneous viscoelastic beam that is not exposed to chemical degradation).
The strain energy release rate is expressed in non-dimensional form by using the formula Calculations of the strain energy release rate are carried-out for a three-layered cantilever beam exposed to chemical degradation. The thickness of each layer is d h . The following data are used:

Conclusions
A time-dependent delamination analysis of a multilayered non-homogeneous viscoelastic beam configuration subjected to chemical degradation is developed. The beam is made of adhesively bonded non-homogeneous viscoelastic layers of different thicknesses and material properties. The beam is exposed to influence of aggressive chemical agent. This leads to chemical degradation of the material in layers of the beam. As a result of the chemical degradation, the elasticity modulus and the coefficient of viscosity decrease with time. The time-dependent delamination fracture behaviour is studied by analysing the strain energy release rate with considering of the chemical degradation. For this purpose, the strain energy is used to derive the strain energy release rate. The strain energy is calculated by taking into account the chemical degradation. In this way, the solution obtained accounts for both the creep behaviour of the non-homogeneous structure and the chemical degradation of the material. The compliance method with considering of the chemical degradation of the multilayered non-homogeneous viscoelastic material is applied to verify the solution. The change of the strain energy release rate with time is analysed. The analysis reveals that the strain energy release rate increases with time (this behaviour is due to the creep and to the chemical degradation). Concerning the influence of material non-homogeneity, the calculations show that the strain energy release rate increases with increasing of 1 L p and 1 L q under chemical degradation.