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Cyclic Fatigue

Fatigue 5:  Typical S-N curve with fatigue or endurance limit

Fatigue damage or creep (see creep modelling) in an adhesive layer can be avoided, or at least minimised, by ensuring that the adhesive remains in an elastic state for most of its service life.  Repeated cyclic loading to high plastic strains can result in creep failure occurring within a relatively short number of cycles due to the cumulative effect of cyclic shear strains.  This effect is more pronounced as the frequency of loading is reduced.  From a design perspective, a sufficiently long overlap length will ensure that most of the adhesive remains elastic.  The elastic region acts as an elastic reservoir during unloading, enabling the bond layer to recover (i.e. stress relief) to its unstrained state, thus preventing accumulation of shear strain.  Provided the minimum shear stress at the middle of the overlap remains within the elastic limit of the adhesive and the maximum shear strain at the ends of the overlap is limited to a value below the adhesive yield strain, then the joint should be suitable for use under cyclic loading conditions. 

Ideally, significant plastic deformation of the adhesive should only be permitted when the joint is stressed to the limit load.  Where the limit load is the highest load expected to be experienced during the service life of the structure.  Even at the ultimate load, which is 1.5 times the limit, the strain in the adhesive should not approach the failure strain.  Provided stress levels are sufficiently low (i.e. below the “endurance limit”) then fatigue should not to be a problem.

It is recommended that verification of fatigue and creep performance should be undertaken on critical joints to demonstrate that the joint can carry the ultimate load required throughout its design life, under representative conditions of stress, temperature and humidity [1].  Design of bonded joints is still far from the point where fatigue and creep performance can be inferred from data obtained for simple coupon tests (e.g. single-lap joints), which can only provide comparative data.   In the absence of test data, the EUROCOMP Code [2] suggests that the safety factors given in Table 2 should be multiplied by an additional factor gm5 - dependent on the level of inspection of the joint in service.

In assessing the fatigue performance of an adhesive joint, it is important to determine the fatigue behaviour of the substrate material under representative loading and environmental conditions.  When designing an adhesive joint, it is unsatisfactory to consider the adhesive on its own.

Cyclic fatigue loading can be in the form of either constant amplitude or variable amplitude spectrum loading.

Constant Amplitude Loading is defined by the following terms (see also Figure 6):

Figure 6:  Nomenclature for stress parameters for constant amplitude cyclic loading

Figure 7:  Direct tension-tension cyclic loading of a bonded aluminium T-joint

(left: normalised S-N data; right: bonded T-joint)

Figure 7 shows an S-N curve (R = 0.1 and test frequency f = 5 Hz) that was obtained for a bonded 2014-T6 aluminium T-joint (Figure 7) bonded with XD4601 epoxy adhesive subjected to constant amplitude tension-tension loading.  The loading mode was direct tension (i.e. pull-off) - see [3-4].  The S-N curve has been normalised with respect to the ultimate failure load of specimens tested under monotonic loading at an equivalent loading rate to the fatigue cycling.  The gradient of the slope k is the fractional loss in strength per decade of cycles and is dependent on the joint geometry and loading conditions.

Normalised S-N curves (see Figure 7) can be approximated by the following relationship:

                       (2)

where P_MAX is the maximum load applied to the specimen, P_ULT is the ultimate strength of the joint and N_f is the number of cycles to failure.  The value of k was » 0.10.

Fatigue performance of an adhesive joint can be approximated by (rule of thumb) Equation (2) where k the fractional loss in strength per decade of cycles is a measure of fatigue resistance of the joint.  The lower the k value the better the fatigue performance.  Table 3 shows typical k values for a number of metal and composite joints bonded with epoxy adhesives. 

A scarf joint with an angle of 15° with respect to the horizontal where failure is dominated by shear stresses has a far better fatigue performance than tests where peel or hydrostatic tensile stresses are the major cause of failure (e.g. T-peel joints and 60° scarf joints).

Table 3: Typical k Values for Bonded Joints (R = 0.1 and f = 5 Hz)

Constant-life diagrams are often used to represent the effects of mean stress and stress amplitude on fatigue performance of adhesive joints.  Different combinations of normalised stress amplitude, DP/P_ULT , and the normalised mean stress, P_MEAN /P_ULT , are plotted to give constant fatigue life curves.  Figure 8 shows normalised stress-amplitude plots for different mean stress values that were obtained for tension-tension fatigue of a unidirectional GFRP composite material (E-glass/913 epoxy).  In this case, stress values were normalised with respect to the ultimate tensile strength, s_UTS , of the material.  In principle, the curves should converge to the static strength of the material on the mean stress axis (i.e. when the mean load is increased to the static strength then no amplitude is required to cause failure).

Figure 8:  Stress amplitude-life plots for different mean stress values for E-glass/913

A number of models have been suggested for determining stress amplitude-life plots of polymeric materials [5].  Crocombe et al. [6] have shown a Goodman type curve to be a valid method of representing the effect of mean stress and stress amplitude on fatigue performance of single-lap and T-peel joints.  The Goodman relation is given below:

                  (3)

where P_A is the stress amplitude (for a non-zero mean stress), P_FS is the fatigue strength (for a fixed life), P_MEAN is the mean stress and P_ULT is the ultimate strength of the material.

An alternative approach for estimating fatigue life is to apply a model originally developed for polymer matrix composites known as the normalised life prediction model.

Next: Variable Amplitude Spectrum Loading

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