Fatigue damage accumulation in carbon/epoxy laminated composites J. Aghazadeh Mohandesi, B. Majidi * Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran article info Article history: Received 22 May 2008 Accepted 5 September 2008 Available online 17 September 2008 Keywords: Laminates (B) Fatigue (E) abstract The precise prediction of fatigue damage progress and fatigue life in laminated composites has been always a concern to designers. The present work is focused on the fatigue damage mechanisms and dam- age accumulation rate in laminated composites. Results showed that the dominant damage mechanism depends on the applied stress and total delamination only observed under the cyclic stress of less than 0.7r UTS . Under high cyclic stress, transverse cracks in 45° ply appear and its density rapidly increases to the characteristic damage state (CDS). The obtained results showed that high-stress peaks (HSP) have remarkable effect on the fatigue life and predictions based on Palmgren–Miner’s rule showed consider- able deviations from experimental results, whereas the new cumulative damage model presented in this work provided acceptable consistency with experimental results in the entire range of applied stress. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Fatigue behavior in laminated composite materials with inho- mogeneous, anisotropic nature is more complicated than those of homogeneous and isotropic materials. Similar to the monolithic materials, to predict the fatigue life of composites under cyclic loading, a cumulative damage rule is required. The key to make a cumulative damage model is the representation of damage and its accumulation during complex fatigue loading through the use of a suitable damage function. Under a given frequency, tempera- ture, moisture and specimen geometry, the fatigue damage func- tion of a material, D, depends on the applied stress and the number of fatigue cycles, thus; D ¼ Dðn; rÞ¼ Dðn; NÞ ð1Þ where n is the number of fatigue cycles, N is number of cycles to failure under applied stress of r. Quantities related to damage, such as fiber–matrix debonding, crack length and density, modulus and residual strength which would vary during fatigue loading, may be used to assess the damage [1]. It is well known that Palmgren–Miner’s rule is adequate for pre- dicting the cumulative damage in metallic materials. However, it is inadequate for fiber-reinforced plastics (FRP composites) due to their dominant viscoelastic characteristics. When composites are subjected to spectrum loading or stepped loading, an important and critical effect called ‘load sequence effect’ influences the fati- gue life and strength degradation of composite material [2,3]. This ‘load sequence’ is the time-based arrangement of the load applica- tion sequence or the sequential order of the load applied onto the component. The ‘load sequence effect’ is due to contributions from the ‘boundary effect’, i.e. the difference between residual strength lev- els, and the ‘memory effect’, where the strength/fatigue properties of the composite are influenced by accumulation of the previous load history, considering the matrix is of viscoelastic nature. The viscoelastic properties of the composites, in combination with the load levels, load duration, temperature and moisture content can lead to substantial amounts of viscoelastic creep, relaxation, damping and damage which can accumulate to induce delayed failure. Many researchers have shown, for example [3–8], that when the Palmgren–Miner’s rule is applied to composites under a ‘low–high’ load sequence, i.e. low amplitude loading followed by high amplitude loading, the results are generally smaller than unity and for a ‘high–low’ load sequence, i.e. high amplitude load- ing followed by low amplitude loading, the results are greater than unity. However, it has been shown that ‘high–low’ sequence is not always less damaging than ‘low–high’ sequence [7,9]. This disparity is primarily due to memory effects and boundary effects which Palmgren–Miner rule does not address. Several mod- els have been developed to assess the damage accumulation and predictions of residual strength after applying a spectrum/step loads on FRP composites. Sendeckyj [9] briefly reviewed the avail- able fatigue accumulation models and compares the applicability and accuracy of each model. In this review paper, the life predic- tion models proposed by Hashin and Rotem [10], Wang et al. [11] and Broutman and Sahu [4] have been discussed. A model pro- posed by Hwang and Han [12] based on stiffness degradation and coined ‘fatigue modulus’ has been modified by Hwang et al. [13] by introducing another parameter to account for load sequencing. In 1997 Otani and Song [14] proposed a model for a composite 0261-3069/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2008.09.012 * Corresponding author. Tel.: +98 9126899651. E-mail address: behzadmajidi@aut.ac.ir (B. Majidi). Materials and Design 30 (2009) 1950–1956 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes