Damage evolution in cross-ply laminates under tension–compression and compression-compression cyclic loads

Abstract

Tension-Compression and Compression-Compression fatigue tests were carried out on glass/epoxy cross-ply laminates, with different values of the minimum to maximum load ratio R (−1, −3, −5, −7, −10 and 20). During the tests, the damage evolution in the 90° ply was monitored at the macro-and micro-scales. Three damage scenarios were observed, depending on the load ratio: i) initiation and propagation of transverse cracks for R ≥ −3, ii) initiation of multiple inclined short cracks for R = 20, iii) a mixed damage type with the presence of both transverse cracks and inclined short cracks for −10 ≤ R ≤ −5. Finite Element analyses of micro-scale Representative Volume Elements, combined with a recently developed crack initiation criterion, revealed the role of the Local Hydrostatic Stress in the matrix in controlling the different damage scenarios. Eventually, quantitative analyses showed a highly detrimental effect of the compressive part of the cycle on the transverse crack initiation and propagation.

Introduction

The fatigue life of multidirectional (MD) laminates made of unidirectional (UD) plies is characterised by a progressive damage evolution that leads to the loss of stiffness and culminates in the final failure. Under Tension-Tension (T-T) loadings, the damage scenario is very well known and understood. It involves the formation and propagation of multiple off-axis cracks, the crack density evolution up to a saturation condition, the delamination propagation, and the failure of the fibres, typically triggered or enhanced by the previous damage mechanisms. This kind of damage evolution is documented in several works in the literature (see, among the others, Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]). On the other hand, the fatigue damage evolution under Tension-Compression (T-C), especially for negative mean stresses, and under Compression-Compression (C-C) loadings is far less analysed and understood, perhaps due to the intrinsic difficulties in testing laminates under compressive loads.

Experimental campaigns were carried out focussing on the life to final failure of MD laminates under T-C and C-C loadings [11], [12], [13], [14], [15], [16], [17]. A general conclusion that can be drawn from those contributions is that the fatigue life is shorter as the compressive part of the cycle is increased while keeping the same maximum stress level. In other words, the S-N curves for the laminate failure, in terms of the maximum cyclic stress, shift downwards and become steeper as the minimum to maximum load ratio R decreases. Under C-C loadings, the S-N curve in terms of the absolute value of the minimum compressive stress is typically lower than that under T-T conditions (in terms of maximum cyclic stress), apart from the [±60]_3s laminates tested in Ref. [17].

In these works, the attention was focussed on the final failure only, and no indications were reported on the damage evolution at the ply- or micro-scale, which is fundamental to develop models for predicting the crack initiation and the stiffness loss in composite components. These phenomena are controlled by the matrix-dominated fatigue behaviour, for which only few detailed damage observations can be found in the literature concerning T-C and C-C loadings, as reviewed hereafter.

Useful information is provided by fatigue tests on UD laminates, for which the final failure and the first crack initiation coincide. In Refs. [18], [19] uniaxial fatigue tests were carried out on glass/epoxy and carbon/epoxy UD laminates with different off-axis angles and load ratios R equal to −1, 0.1, 0.5, and −1, 0, 0.5, respectively. In general, a shorter fatigue life was found for lower R values, for a given maximum cyclic stress. This means that, under T-T and T-C loadings, off-axis cracks in MD laminates are expected to initiate earlier as the load ratio is decreased. This is confirmed by the experimental observations reported in Refs. [20], [21], [22], [23], where transverse cracks were seen to initiate earlier and the crack density to evolve faster for R = -1 than for R ≥ 0. Gamstedt and Sjogren [21] analysed more in depth the effect of a compressive part of the loading cycle on the crack formation, relating the faster crack density increase under T-C loadings to micro-scale observations on a single fibre specimen under transverse T-T and T-C loadings. A fibre–matrix debond was indeed found to propagate faster under fully reversed loadings, because of the mode I contribution provided by the compressive part of the cycles for high debonding angles (the so-called “bubble”). In the authors’ view, the faster debond propagation may lead to a premature transverse crack formation. Following this idea, more detailed numerical calculations of the Energy Release Rate (ERR) for a debond crack under T-C loadings were carried out in Ref. [24], confirming Gamstedt and Sjogren’s intuition.

If the number of studies dealing with the T-C crack formation is limited, even less information is available on the damage evolution under C-C loadings. The fatigue life of UD laminates under a cyclic uniaxial load at 45° and 90° with respect to the fibre orientation was found to be much higher under C-C (R = 10) than under T-T and T-C loadings [25]. No analyses of the damage evolution were reported. In Refs. [20], [26], different scenarios were observed for quasi-isotropic and cross-ply laminates under T-C (R = -1) and C-C loadings in the later stages of the fatigue life. In particular, a significantly lower number of transverse cracks were observed prior to failure (or immediately after failure) under C-C than under T-C loadings. A more detailed characterisation was recently presented by Just et al. [23] on carbon/epoxy [0₂/90₇/0₂] laminates tested with R = 0, −1, −3.26, ∞. The transverse crack density evolution was found to be significantly slower under C-C than under T-T and T-C loadings. However, it is important to mention that, given the residual thermal stresses due to the autoclave moulding process, the actual load ratio in the 90° plies was not equal to that relevant to the global remote load. For instance, the local load ratio for the transverse stress in the 90° plies was calculated equal to −1.48 for the loading condition characterised by a global load ratio R=∞. Therefore, detailed analyses of the damage evolution in off-axis plies under an actual C-C load are not currently available in the literature.

A micromechanical perspective of the damage mechanisms under a compressive transverse load was provided by Correa and co-authors [27], [28], who did numerical calculations of the ERR for the debond propagation under compression. They showed that the debond initiation position changes with respect to that relevant to tensile loadings, and that the debond crack leaves the interface and kinks into the matrix at an angle of roughly 50° with respect to the loading direction (compared to roughly 90° under tension). This micro-scale damage scenario is confirmed by some observations made under a quasi-static compressive load [20], [29].

According to this brief review of the literature, the damage evolution both at the macro-scale (ply-level) and the micro-scale has not been thoroughly clarified under C-C fatigue. Under T-C loadings, it is well documented that off-axis cracks initiate and propagate faster than under T-T loads, even if experimental observations are typically related to a load ratio equal to −1. No information on the damage evolution was found, instead, for T-C loadings with a negative mean stress (R < -1). Accordingly, the aim of the present work is to analyse the damage evolution at the macro- and micro-scale under T-C and C-C fatigue in the transverse plies of glass/epoxy cross-ply laminates. Tests were carried out with load ratio R = -1, −3, −5, −7, −10 and 20. The damage evolution was monitored through the analysis of front images taken during the tests as well as micrographs taken on the specimens’ edges, revealing three different damage scenarios depending on the load ratio. In addition, the life to crack initiation, the crack growth rate and the crack density evolution were quantitatively analysed and compared for different loading conditions. Eventually, the switch between different damage scenarios observed in the tests was justified based on Finite Element (FE) analyses of micro-scale Representative Volume Elements (RVEs), combined with a previously developed crack initiation criterion [30], [31].