(5)Three approaches to designing adhesively bonded joints for cyclic fatigue loading are shown below:
Stress-life approach is an empirical method, which uses stress-cycle (S-N) curves to determine the fatigue or endurance limit (i.e. maximum fluctuating stress a material can endure for an infinite number of cycles without causing failure) of a material or structure. This approach is the most widely used of the above-mentioned techniques. Under constant amplitude loading conditions, most materials or structures exhibit a plateau in the stress-cycle curve (Figure 5), which typically occurs at N > 106 cycles. The plateau level corresponds to the fatigue or endurance limit. Below this limit, the material or structure can be cycled indefinitely without causing failure. In most engineering applications, designers aim to ensure that no fatigue cracks develop during the service life of the component; S-N approach works well in these cases.
Note: The joint should be designed so that fatigue loads are below the endurance limit with an appropriate safety factor to suit the in-service loading and environmental conditions.
In this approach, the adhesive joint is subjected to fatigue loading at different load (stress) levels relative to the joints quasi-static failure load measured at a rate equivalent to the frequency of the cyclic loading. It is possible to determine an average stress (taken as the applied load divided by the overlap area), however this is misleading as the average stress may be significantly lower than the stresses present at the ends of the joint overlap.
The performance of the joint depends on the joint geometry and the range of stresses that occur in the regions of peak stress (i.e. stress concentrations near ends of adhesive joints). The mean stress level and stress amplitude of the imposed fatigue cycle are known to play an important role in influencing the fatigue behaviour of engineered structures. Ideally, the range of stresses should be kept below the “endurance limit”. The stress levels should be sufficiently low for fatigue not to be a problem. It is possible to track not only the number of cycles to failure, but also the number of cycles to initiate cracking in the bond-line. The differences between fatigue crack initiation and total fatigue lives can be used to compare the fatigue resistance of adhesive joints.
The main proponents/users of stress-based design/analysis of bonded joints have been Goland and Reissner [9] and Hart-Smith [10-13]. Work in this area has focused on determining the shear and peel stresses within the adhesive layer under static loading conditions. Failure criteria (closed-form solutions) have been proposed for determining maximum shear and peel stresses in the adhesive layer of bonded joints [2].
Current design criteria recommend the elimination or drastic reduction of peel stresses, which are the main cause of failure within the adhesive layer or at the adhesive-adherend interface. Hart-Smith states that the bond strength is limited by the adhesive’s shear strain energy per unit bond area (with linear-elastic modelling this can be expected to be equated to a stress). Stress-based design has been incorporated into computerized design programs used by the aerospace/defence industry.
In this approach, the designer selects a standard detail (i.e. joint) that is expected to behave similarly to the new design and uses the fatigue strength that has been established for the standard detail. This approach is straightforward and usually very successful. Hence, it has widespread use for designing adhesively bonded and bolted metallic structures. However, the approach should only be considered for preliminary design purposes. Confirmation tests of assemblies representative of the actual structure need to be carried out to finalise the design.
For this approach to be used, a large (and reliable) database is required for the standard detail in order to determine design stress cycles for a given stress level, or vice-versa. The database needs to include the effects of different stress ratios on fatigue life and allow for out-of-plane deformation of the joint. FEA is used to determine the stress and strain distribution in the structure. The problem arises when the new detail does not match any standard details or new materials are involved, then fatigue strength becomes very uncertain. It is important that the joint geometry used to determine the endurance limit conservatively represents the joint design of interest. The limitation of this approach is it is difficult (if not impossible) to apply data from one joint configuration to another for the same adhesive system. This comment also applies to the use of S-N data.
Note: Designers/Engineers need to conduct verification tests on any final design of a fatigue-critical structure
A more fundamental approach is to relate fatigue life to a local failure criterion, such as maximum stress, maximum strain and hydrostatic stress in the adhesive. This approach is not used because a suitable local failure criterion has not been found (see Smart Manual 3).
Stress-based analysis assumes the material undergoes unconstrained deformation. In fact, engineering structures experience a certain degree of structural constraint, particularly in regions of high stress concentrations. In these situations, it is therefore more appropriate to assume strain-controlled conditions when modelling fatigue behaviour [5]. Strain-controlled fatigue is commonly used as a basis for structural design in components where cyclic fatigue crack initiation is of concern near stress concentrations.
The following strain-life model forms the basis of a widely used approach by industry for predicting the fatigue life of engineering alloys [5]:
(5)
where Δ ε/2 is the strain amplitude, ε’f is the fatigue ductility coefficient (approximately equal to the true fracture strain εf in monotonic tension), σ’f is the corresponding stress, E is the Young’s modulus, and b and c are constants. The model accounts for both elastic and plastic strain.
Note: Fatigue damage can be minimised by maintaining the adhesive in the elastic state for most of its service life. Design criteria in the aircraft industry require structures to withstand limit loads with no permanent deformation and ultimate loads without any failure. Limit load is the highest load expected during service life. The ultimate load is 1.5 times the limit load (even at this load the strain should not approach the failure strain).
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