Simulation of delamination in composites under high-cycle fatigue

doi:10.1016/j.compositesa.2006.11.009

Composites Part A: Applied Science and Manufacturing

Volume 38, Issue 11, November 2007, Pages 2270-2282

https://doi.org/10.1016/j.compositesa.2006.11.009 Get rights and content

Abstract

A damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed. The basis for the formulation is a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate dA/dN. The damage state is obtained as a function of the loading conditions as well as the experimentally-determined coefficients of the Paris law crack propagation rates for the material. It is shown that by using the constitutive fatigue damage model in a structural analysis, experimental results can be reproduced without the need of additional model-specific curve-fitting parameters.

Section snippets

Introduction and motivation

High-cycle fatigue is a common cause of failure in aerospace structures. In laminated composite materials, the fatigue process involves several damage mechanisms that result in the degradation of the structure. One of the most important fatigue damage mechanisms is interlaminar damage (delamination).

There are two basic approaches for the analysis of delamination under fatigue loading: fracture mechanics and damage mechanics. Fracture mechanics relates the fatigue crack growth rate with the

Cohesive zone model approach

The CZM approach [15], [16], [17] is one of the most commonly used tools to simulate interfacial fracture. The CZM approach assumes that a cohesive damage zone develops near the tip of a crack.

Cohesive damage zone models relate tractions, τ, to displacement jumps, $\bar{Δ}$ , at an interface where a crack may occur. Damage initiation is related to the interfacial strength, τ^o. When the area under the traction–displacement jump relation is equal to the fracture toughness, G_c, the traction is reduced to

Kinematics and constitutive model for quasi-static loading

The displacement jump across the interface 〚u_i〛, is obtained from the displacements of the points located on the top and bottom sides of the interface, $u_{i}^{+}$ and $u_{i}^{-}$ , respectively: $〚 u_{i} 〛 = u_{i}^{+} - u_{i}^{-}$ where $u_{i}^{\pm}$ are the displacements with respect to a fixed Cartesian coordinate system. A co-rotational formulation is used to express the components of the displacement jumps with respect to the deformed interface. The coordinates ${\bar{x}}_{i}$ of the deformed interface can be written as [30]: ${\bar{x}}_{i} = X_{i} + \frac{1}{2} (u_{i}^{+} + u_{i}^{-})$ where X_i

Constitutive model for high-cycle fatigue

The damage evolution that results from a general loading history can be considered as the sum of the damage created by the quasi-static overloads and the damage created by the cyclic loads: $\frac{d d}{d t} = \dot{d} = {\dot{d}}_{static} + {\dot{d}}_{cyclic}$ The first term in the right hand side of Eq. (13) is obtained from the equations presented in previous section, while the second term has to be defined to account for cyclic loading. Using a damage mechanics framework, several authors have formulated the damage evolution that results

Results and discussion

The present model is implemented as a user-written finite element in ABAQUS^® [37] by adding the fatigue damage model to the constitutive behavior of a cohesive element previously developed [13], [14].

Several single-element tests were performed to verify the response of the fatigue damage model. Then, simulations of Mode I, Mode II and Mixed-Mode delamination tests were conducted to demonstrate that when the constitutive damage model is used in a structural analysis, the analysis can reproduce

Conclusions

A damage model suitable for both quasi-static and high-cycle fatigue delamination propagation was developed. The evolution of the damage variable was derived by linking damage mechanics and fracture mechanics, thus establishing a relation between damage evolution and crack growth rates. The damage evolution laws for cyclic fatigue were combined with the law of damage evolution for quasi-static loads within a cohesive element previously developed by the authors.

The model was validated using

Acknowledgements

This work has been partially funded by the Spanish government through DG-GICYT under contract: MAT2003-09768-C03-01.

The financial support of the Portuguese Foundation for Science and Technology (FCT) under the project PDCTE/50354/EME/2003 is acknowledged.

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View full text

Simulation of delamination in composites under high-cycle fatigue

Abstract

Section snippets

Introduction and motivation

Cohesive zone model approach

Kinematics and constitutive model for quasi-static loading

Constitutive model for high-cycle fatigue

Results and discussion

Conclusions

Acknowledgements

Eng Fract Mech

Microelectron Eng

Eng Fract Mech

Int J Fatigue

J Mech Phys Solids

J Mech Phys Solids

J Mech Phys Solids

Composites

Int J Solids Struct

Int J Solids Struct

Int J Solids Struct

Compos Sci Technol

Composites Part A

Compos Sci Technol

A rational analytical theory of fatigue

Trend Eng

Critical analysis of propagation laws

J Basic Eng

Fatigue crack growth during gross plasticity and the J-integral

ASTM STP

A cohesive model for fatigue crack growth

Int J Fract

Irreversible constitutive law for modeling the delamination process using interfacial surface discontinuities

Compos Struct