Mathematical Problems in Engineering

Volume 2015, Article ID 964062, 7 pages

http://dx.doi.org/10.1155/2015/964062

## Damage Monitoring and Analysis of the Structure Effect on Strength of Composite Laminates

Kaohsiung University of Applied Sciences, 414 Chien Kung Road, Sanmin District, Kaohsiung City 80778, Taiwan

Received 25 September 2014; Accepted 12 December 2014

Academic Editor: Mo Li

Copyright © 2015 Chia-Chin Chiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Carbon fiber reinforced polymer (CFRP) composite materials have been widely used in industries in recent years. The design of composite structures, and open-holes for joining are also widely used. Understanding of open-hole behavior is very necessary for the design of complex structures. In this paper, the initial damage, progressive damage analysis, and the effect of structure on strength of composite laminates are investigated. Based on Hashin’s criteria, three-dimensional model of composite laminates containing a central open-hole is developed. The model is conducted by finite element analysis, commercial Abaqus software to simulate the whole process of initial damage, propagation of damage, and analysis of the effect of a few structures on strength of composite laminates containing open-hole.

#### 1. Introduction

Composite materials have been extensively used in engineering and become an important material in aeronautic, automotive, and astronautic structures. There are many different shapes fabricated from composite structure in that kind of open-holes which are typical. During the using time, stress concentrations will appear around the holes and the surrounding areas. This is a phenomenon causing accumulation of damage and decreasing the strength of composite structures. The primary consideration of the structure is the evaluation of its load carrying capacity. Because analyzing stress, failure, and damage’s structure is the best method used, in this work the composite laminates containing a central open-hole subjected to tension are investigated. Many previous studies about the damage of the composite material have been introduced [1–3]. There are some fracture-mechanistic models that are proposed to study propagation crack in composite laminates with an open-hole. The propositions were significantly studied by previous researchers [4–11]. The authors developed a two-dimensional progressive damage model considering three different failure modes to predict the accumulation of damage and the strength of the composite laminates containing unloaded holes and loaded holes by integrating failure criteria of Yamada-Sun and Hashin. Although the failure of the plies was evaluated, the delamination of the composite structures was not considered in these analyses. The model needed the ply orientation of the laminates which must be symmetric with respect to the middle plane of the plate. Two-dimensional model cannot accurately analyze stress around open-holes. The layer orientations and delamination as well as damage of the composite laminates can be solved by three-dimensional finite element method with the commercial Abaqus. Therefore, the objective of this investigation is to predict the initial damage, progressive damage analysis, and the effect of a few structures on strength of composite laminates.

#### 2. Materials and Methods

##### 2.1. Progressive Damage Analysis

In this study, in order to predict the initial damage, progressive damage analysis and the effect of a few structures on strength of composite laminates are investigated. Based on Hashin’s failure criteria and numerical model are presented as follows.

###### 2.1.1. Damage Initiation

The onset of damage in Abaqus is detected by Hashin and Rotem initial damage criteria in terms of apparent (Cauchy) stress “,” which is calculated by progressive damage analysis code. Damage initiation refers to the onset of stiffness degradation at a material point [2, 12]. The consideration of damage laminates by Hashin’s criteria in four cases is assumed to be uncoupled as follows:fiber tension ()fiber compression ()matrix tension and/or shear ()matrix compression ()where , , and are the components in-plane longitudinal, transverse, and shear stress; , are the compressive and tensile strength in the fiber direction; , are the compressive and tensile strength in the matrix direction; , are the transverse and longitudinal shear strength; and determines the contribution of the shear stress to the fiber tensile criterion. To obtain the model proposed by Hashin and Rotem, it set and . is the loading functions for different failure mechanisms adopted in the form of Hashin’s criteria. These indexes , , , and indicated whether a damage initiation criterion in a damage model has been satisfied or not. Damage initiation occurs, when any one of the four indices exceeds 1. The effect of damage is taken into account with reducing the values of the stiffness coefficients [2, 12] as follows:where represents a tensor double contraction and damaged stiffness is given byin which where is the apparent stress, is the strain, is the damaged stiffness matrix, , are the moduli in the fiber direction and perpendicular to the fiber, respectively, is the shear modulus, and are Poisson’s ratios, , , , , and are damage variables of the fiber, matrix, and shear damage, in tension and compression, respectively. The shear damage variable is not independent but is given by (6) in terms of the remaining damage variables.

The variables damages , and , , which characterize fiber and matrix damage in tension and compression, corresponding to the four damage initiation modes are represented in (1)~(4). , , , , , and are six values of the strength. In this work, in order to predict damage initiation, progressive damage analysis, and the effect of structure on strength of composite laminates accurately, the values of strength of CFRP T300/134-C material are used [3]. The mechanical properties of this material are listed in Table 1.