International Review of Mechanical Engineering (I.RE.M.E.), Vol. xx, n. x Manuscript received January 2007, revised January 2007 Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved A Phenomenological Approach for Fatigue Damage Accumulation of CF/PEEK Laminates under Two-stage Loading Dimitrios G. Pavlou 1 , Kyriakos I. Kourousis 2 Abstract – The life of composite materials (CM) subjected to fatigue conditions is associated with the gradual damage of their structure. Since the damage accumulation is reflected by changes in CM properties, the derivation of damage accumulation curves may be based on test results providing the reduction of the residual strength. Examined in this work is a non-linear fatigue damage accumulation function for cross-ply CF/PEEK laminates. This damage function is specified with respect to damage parameters derived by the strength decrease during fatigue for the CF/PEEK. Taking into account this concept, an improvement of the theory of isodamage lines is proposed. Since the nonlinearity of the derived damage function depends on an exponent that is a function of the fatigue stress amplitude, the effect of the loading order and the previous damage history on the total fatigue life is investigated. Numerical examples of fatigue life prediction under two-stage loading conditions and a damage accumulation map for the CP/PEEK are presented and discussed. Copyright © 2013 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Damage, Fatigue, CF/PEEK, Residual Strength, Non-linear model, Two-stage Loading I. Introduction Fatigue failure of composite materials (CM) is difficult to be predicted especially when the stress amplitude is not constant. Therefore, modern NDT techniques e.g. [1] - [3] have been today used for the evaluation of accumulated fatigue damage. For analytical fatigue life prediction the assumption that fatigue loading stages with different stress amplitude will result to total damage equal to the sum of the damage increments occurring at each individual loading level has been adopted by most of the researchers e.g. [4]. According to this assumption, failure occurs when a dimensionless function D reflecting the accumulated damage reaches the critical value D=1. However, the proper selection of the damage function D is not straightforward. The success of the damage function selection depends on the degree of understanding the fundamental damage micro-mechanisms and its mathematical modeling. In practice, damage accumulation models based on micro-mechanical observations are not in common use due to their complexity e.g. [5], [6]. Miner’s [7] damage accumulation rule is still widely used because of its simplicity. However, since this model is linear, it doesn’t take into account the previous damage history and the influence on damage accumulation of the loading order. In the present work, a phenomenological model based on the correlation of the material property degradation [4], [8] - [10] with the fatigue damage accumulation is exhibited. Since the reduction of residual strength reflects the material property degradation, a fatigue life prediction procedure based on the evolution of the residual strength during fatigue will be proposed. II. Cumulative Fatigue Damage Function Experimental observations have shown that the damage accumulation rate is slow at the early fatigue stage, while at the final stage before failure it is rapid. The above non-linear path-dependent nature of damage evolution means that the fatigue life is strongly affected by the load sequence [11]. Therefore, any damage increment ΔD is a function of the actual state of damage D, the stress amplitude σα, the number of loading cycles n applied in the past and the increment of the loading cycles Δn causing ΔD, i.e.: ( , ,, ) a D fD n n     (1) Assuming that the relative increase of damage ΔD/D is a linear function of the relative increase of the number of loading cycles, i.e.: ( ) a D n f D n     (2)