Keywords: layered composite beam, delamination, contact, friction, mechanical fatigue, thermal fatigue, fatigue, finite element.

Fatigue of composite materials is considered as the main result of their degradation under cyclic mechanical, thermal or cyclic coupled thermomechanical loads and, since that, is usually a very complicated process in theoretical analysis. The need of the material fatigue damage and durability research is especially required in the aerospace industry, where the composite structures subjected to some coupled cyclic phenomena must satisfy the very high reliability conditions. There exist many empirical and semi-empirical deterministic and even statistical models of fatigue failure derived initially for metals and next modified or adopted for various composites. Some models identify fatigue phenomena with the fatigue micro-crack growth using the fracture mechanics approach and, then, account the micro-crack effect in mechanical properties reduction. These models contain nonlinear differential equation (of deterministic or stochastic character) describing the fatigue crack growth rate as a function of dominant crack length, stress variations and the specimen material parameters. The influence of crack-like defects on the overall material behavior is evaluated using fatigue models based on the damage mechanics by identification of this process as a damage accumulation process. Other approaches measure composite stiffness degradation directly as a function of the fatigue cycle number. Furthermore, the results of fatigue experiments show considerably large statistical scatter and that is why the stochastic modeling is widely accepted to analyze materials fatigue problems. Stochastic modeling of materials fatigue consists of the following main steps: (a) a choice of the appropriate stochastic process (stationary or non-stationary) to build the mathematical fatigue model; (b) description of the probabilistic properties of the model (its probability distribution or lifetime distribution); (c) a connection between the stochastic model and a variety of the empirical data. There exists an opportunity to distinguish the random fatigue load models, evolutionary probabilistic models based on the Markow processes theory, cumulative jump models and the differential models resulting from the corresponding deterministic models randomization. Some stochastic simulation methods are used to model fatigue phenomena, too. For instance, the Monte Carlo Simulation (MSC) technique was successfully applied to the lifetime prediction and variability of bundles of parallel elements and parallel-lay ropes. The comprehensive numerical study on the first-order probability of mixed- mode fatigue failure calculation from reliability index by a constrained optimization problem solution has been implemented into Probabilistic Finite Element Method (PFEM) based on the First Order Second Statistical Moment analysis.

Since the most of fatigue studies are done theoretically, the paper is devoted to the computational FEM-based simulation of composite delamination process. The similar composite material configuration to that presented in [1] is proposed as a curved composite beam built up from the homogenized boron/epoxy composite laminate on homogeneous aluminum structure to study its fatigue life under mechanical loading with constant amplitude and, at the same time, the thermal cycling. Adhesive FM®73M usually used in that connection is modeled as zero thickness layer and its properties are not accounted now in the analysis. The components are assumed to be linearly elastic transversely isotropic; the composite interface is concerned as a possible location of high stress gradients leading to failure by delamination. Thus, the failure process is assumed to be numerically modeled by the interface crack growth. The advantage of the present concept is the possibility of crack propagation direction modeling compared to the existing analytical approaches. The composite delamination problem is modeled as a contact problem[2] with friction due to shear load and the curved specimen geometry. That is why, the numerical analysis problem is geometrically nonlinear with elastic contact between delaminated crack surfaces what requires incremental computational analysis. Such an approach is the only method to analyze this problem since the analytical solutions in this area usually based on the Hankel's transform are available for composites with longitudinal or plane interfaces only. All computational illustrations are carried out by using the Finite Element Method (FEM)[3] displacement-based program ANSYS[4]. The results of the simulation make it possible estimation of fracture parameter range describing a fatigue crack propagation and, as a result, calculation of the corresponding fatigue cycles by the use of the modified Paris-Erdogan law.

1

S.W. Johnson et al., "Application of fracture mechanics to the durability of bonded composite joints", Report DOT/FAA/AR-97/56, OAR, Washington, D.C., 1998.

2

R. Buczkowski, M. Kleiber, "A stochastic model of rough surfaces for finite element contact analysis", Computer Methods in Applied Mechanics anf Engineering, 169, 43-59, 1999. doi:10.1016/S0045-7825(98)00175-3

3

K.J. Bathe, "Finite Element Method Procedures", Prentice Hall, 1996.

4

ANSYS v.5.5, "User's Manual", 1999.

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