Creep deformation usually occurs over a period of time when a material (or structure) is subjected to constant load (or stress) (i.e. time-dependent deformation). Strain (or deformation) increases with load, temperature, relative humidity and time. Polymeric materials, such as adhesives can undergo creep deformation at room temperature (referred to as cold flow). Creep data is usually presented as a plot of creep versus time with stress and temperature constant (Figure 11). A schematic of creep versus time plot is shown in Figure 12.
Figure 11: Creep compliance curves for an epoxy adhesive at different levels of stress
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Regions Region I – First stage, or primary creep, starts at a rapid rate and slows with time. Region II – Second stage (secondary) creep has a relatively uniform rate (minimum gradient). Region III – Third stage (tertiary) creep has an accelerating creep rate and terminates by failure of material at time for rupture. |
Figure 12: Creep versus time plot
The creep curve can be divided into three regions. An induction period in which no deformation occurs, a period of logarithmic creep in which creep increases at a relatively uniform rate and finally an accelerated stage terminating in failure by stress rupture. If creep occurs in a bonded joint, there is typically a delay between initial loading and the onset of creep, as clearly shown in Figure 11. The length of this period is dependent on several factors of which the main factor is considered to be the time taken for the stress to redistribute along the overlap length of the adhesive joint.
As creep is defined as time-dependent deformation of a material (or structure) under a constant load, the design process should involve substituting creep modulus for stiffness (or Young’s modulus). The creep modulus is the apparent stiffness as determined by the total deformation to the time defined. Figure 13 compares the creep modulus for unidirectional and chopped strand mat (CSM) composite materials in tension.
Figure 13: Normalised creep modulus for composite materials loaded in tension
When the applied loads are approximately constant for the duration of loading, a “pseudo-elastic” design method may be used. Creep or time-dependent modulus:
(6)
may be modelled by the following relationship:
(7)
where ε(t) is the strain-time function, EO is initial (or 1 second) modulus and n is the creep index (an experimentally derived constant). The value of EO is obtained by extrapolation. This approach can be used for different loading modes and elastic properties.
The creep index n is a measure of viscoelastic behaviour and for adhesive bonds it is dependent on the adhesive and degree of cure, interfacial bonding (i.e. surface treatment) and environmental effects (i.e. temperature, moisture and aggressive chemicals). Creep index can be obtained from the gradient of E(t) versus log t (see Figure 13). Low values of n can be expected for elastic materials reinforced with continuous aligned fibres. The value of n is lower in the fibre direction for these materials. In fact, loading along the fibre direction is unlikely to result in significant creep deformation. For design purposes, creep modulus and creep index should be obtained from direct experiments on the composite or metallic system.
In addition to loss of stiffness as a consequence of creep, it is possible that strength reductions will occur. Creep rupture can occur at stress levels below the monotonic strength of the joined system. Tests need to be carried out to verify that the joined system will not fail as a result of stress rupture. Figure 14 shows the time-to-failure for an aluminium alloy strap joint bonded with an epoxy adhesive.
Figure 14: Creep rupture of an aluminium alloy/epoxy tapered strap joints
Note: Large bonded joints undergo minimal creep at loads approaching 80% of the quasi-static strength of the joint.
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. 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) and thereby preventing creep strain accumulating. 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. Creep within the low stress region of the bonded region should be kept to a minimum.
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