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Review Article

# Delamination Under Fatigue Loads in Composite Laminates: A Review on the Observed Phenomenology and Computational Methods

[+] Author and Article Information
Brian L. V. Bak

Department of Mechanical and
Manufacturing Engineering,
Aalborg University,
Fibigerstraede 16,
DK-9220 Aalborg East, Denmark;
Siemens Wind Power,
Assensvej 11,
Aalborg East DK-9220, Denmark
e-mail: brianbak@m-tech.aau.dk

University of Girona,
Campus Montilivi s/n,
Girona 17071, Spain

Albert Turon

University of Girona,
Campus Montilivi s/n,
Girona 17071, Spain
e-mail: albert.turon@udg.edu

Josep Costa

University of Girona,
Campus Montilivi s/n,
Girona 17071, Spain
e-mail: josep.costa@udg.edu

In the original paper [23], the factor $δ·n$ was not presented due to a misprint [135].

Manuscript received December 2, 2013; final manuscript received April 28, 2014; published online June 20, 2014. Assoc. Editor: Toshio Nakamura.

Appl. Mech. Rev 66(6), 060803 (Jun 20, 2014) (24 pages) Paper No: AMR-13-1097; doi: 10.1115/1.4027647 History: Received December 02, 2013; Revised April 28, 2014

## Abstract

Advanced design methodologies enable lighter and more reliable composite structures or components. However, efforts to include fatigue delamination in the simulation of composites have not yet been consolidated. Besides that, there is a lack of a proper categorization of the published methods in terms of their predictive capabilities and the principles they are based on. This paper reviews the available experimental observations, the phenomenological models, and the computational simulation methods for the three phases of delamination (initiation, onset, and propagation). It compiles a synthesis of the current state-of-the-art while identifying the unsolved problems and the areas where research is missing. It is concluded that there is a lack of knowledge, or there are unsolved problems, in all categories in the field, but particularly in the category of computational methods, which in turn prevents its inclusion in the structural design process. Suggested areas where short-term and midterm research should be focused to overcome the current situation are identified.

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## Figures

Fig. 1

Cyclic variation of the energy release rate with the minimum and maximum energy release rates used for determining the load ratio, R

Fig. 2

Typical fatigue crack growth curve

Fig. 3

Typical fatigue crack onset curve

Fig. 4

Schematic representation of the influence of the mixed-mode ratio in delamination onset (a) and propagation (b) curves

Fig. 5

Schematic representation of the variation of the Paris law coefficient m as a function of the mixed-mode ratio (qualitative representation from the data presented in Refs. [39,40,49] for carbon/epoxy laminates)

Fig. 6

Schematic representation based on the results reported in Ref. [40] of the influence of the mixed-mode ratio in delamination onset (a) and propagation (b) curves taking into account the nonmonotonic variation of the Paris law coefficients and the independence of the fatigue threshold Gth with the mixed-mode ratio

Fig. 7

Schematic representation of the influence of the load ratio in delamination onset (a) and propagation (b) curves. Subscripts 1 and 2 refer to two different loading conditions with different load ratios

Fig. 8

Schematic representation of the influence of matrix toughness in delamination onset (a) and propagation (b) curves

Fig. 9

Comparison between the fatigue crack propagation curves given by a model capturing the entire propagation curve and a Paris' law enclosed by the threshold energy release rate and the fracture toughness

Fig. 10

Exponential and bilinear equivalent one dimensional cohesive laws

Fig. 11

Fig. 12

Sketch of the cohesive zone and damage distribution, (a) damage distribution in the DPZ before fatigue damage, (b) after fatigue damage, and (c) after static equilibrium is obtained

Fig. 13

Equivalent one dimensional bilinear law with a stiffness degrading damage parameter

Fig. 14

Equivalent one dimensional bilinear law with a traction degrading damage parameter

Fig. 15

Equivalent one dimensional bilinear law with an onset traction degrading damage parameter

Fig. 16

Cylinder model for testing performance of envelope load damage models [132]. M is the applied moment, r is the cylinder radius, θ is the angle of rotation, and Δl is the distance between spring elements.

Fig. 17

Fig. 18

Cohesive law for initiation and propagation simulation. The active domain for the initiation model and propagation model are shown.

Fig. 19

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