Previous Variable Amplitude Work

Many variable amplitude fatigue tests have been carried out over the last 50 years or so, and a number of significant advances have been made since Miner’s damage rule for variable amplitude fatigue endurance was published in the early 1940’s. These variable amplitude fatigue tests have ranged from very simple single overload or underload experiments to true spectrum loading sequences of great complexity. The following review attempts to group these tests according to their loading characteristics, in order to educe from them their true contribution to the body of variable amplitude fatigue knowledge.

5.2.1 Single overload

The literature on single overload fatigue crack growth is extensive and as a consequence, it is possible to draw the general conclusion that an overload results in crack growth deceleration [Matsuoka et Tanaka, 1980, Suresh, 198.3, Shin et Fleck, 1987, and Vardar,1988]. Microscopic observation of the developments taking place at the crack tip tend to indicate that following an overload there is a short period of accelerated crack growth, after which deceleration takes place [Shin et Fleck, 1987, and Davidson, 1988]. The crack growth acceleration is attributed to the opening of the crack by the overload resulting in a decrease in AK^p so that the crack remains fully open during most or all of the stress cycle [Shin et Fleck, 1987]. It has also been suggested that the overload causes the formation of shear bands at the crack tip, and it is along one of these shear bands that the crack grows rapidly [Davidson, 1988]. There is evidence to suggest that in some instances the retardation following the accelerated period of crack growth is due to the residual compressive stresses caused by the overload (see Fig.5.1 [Shin et Fleck, 1987]). In the experiment described in Fig.5.1, a 3mm thick compact tension specimen made of BS4360:50B structural steel was fatigued at constant AK and then overloaded. On application of further CA cycles, the crack growth rate was seen to accelerate and then gradually decelerate below the CA crack growth rate. The specimen was then stress relieved for 1 hour at 650“C. Further CA testing revealed crack growth rates well over the steady state range. This tends to suggest that following overload there is a geometry change (crack opening) inducing accelerations and increasing residual stresses that facilitate subsequent retardation. Both of this would be influenced by the stress state.

Fig.5.1 only showing the effects under plane stress conditions. The hypothesis that retardation is a plasticity induced mechanism is further enforced by the findings of Matsuoka et Tanaka [Matsuoka et Tanaka, 1980]. Using aluminium (A5083) and steel (HT80) specimens of 4 different thickness (2 to 30mm) and applying an overload, they found that while the retardation effects in the plane strain region were constant for all specimens, these increased dramatically in the plane stress region. It was further observed that machining away the specimen’s surface significantly reduced the amount of retardation in aluminium but had a limited effect on steel. Finally, empirical attempts have been made to correlate the amount of retardation following overload to the ratio of overload to CA load (eg. [Vardar, 1988] and [Wheeler, 1972]) but these models have been developed from a limited amount of data and can only be used if the variable amplitude fatigue crack growth mechanisms involved are the same.

5.2.2 Single Underload

The literature on single underload is less extensive than for overload but there is enough evidence to confirm fatigue crack growth acceleration under these conditions [Suresh, 1985 & 1988, and Fleck, 1985]. Many reasons have been given for this acceleration. These include reduction of roughness induced closure due to the flattening of crack surface asperities [Suresh, 1988], introduction of a tensile residual stress [Suresh, 1985], crack tip sharpening [Fleck, 1985], and the raising of the mean stress caused by a low load excursion in the stress-strain curve [Fleck, 1985]. It has also been shown that in fatigue tests underloads can have detrimental effects even under compressive loading fatigue [Suresh, 1985]. Studies of this type have also been undertaken in fracture mechanics specimens. Reid et al [1979] showed that a single compressive overload in a 25mm thick mild steel compact tension specimen introduced a residual tension stress that caused fatigue cracks to initiate and propagate under cyclic compressive loading. The crack was only arrested when it grew to a size comparable to that of the plane stress plastic zone corresponding to the compressive overload. Recently, attempts have been made to establish the relationship between underload/mean load ratio and acceleration factor, and it has also been established that AGq, for compression fatigue crack initiation is lower than for tension fatigue [Suresh, 1985].

5.2.3 Periodic Overloads

From experiments involving single overload (see section 2.1 above) it is to be expected that a periodic overload would have a beneficial effect on fatigue crack growth and indeed this is generally true [Ewalds et Wanhill, 1986, Fleck, 1985]. However, this is not always the case, and fatigue crack growth accelerations have been observed under some circumstances [Fleck, 1985]. Fleck’s tests were carried out on BS4360:50B and BS1501:32A steel compact tension specimens and they showed that when one or up to three small cycles per overload were used acceleration occurred. The reason for this could be that following overload, a large crack tip opening displacement gives rise to accelerated crack growth and before the crack grows into a region of compressive residual stress, the following overload opens the crack tip again, thus denying the beneficial effects of retardation. Alternatively, it has been suggested that this may be due to strain hardening of material ahead of the crack tip due to the major stress cycles [Reck, 1985]. As the overloads become more infrequent, more advantage of the retardation caused by the overload may be gained and retarded crack growth rates are achieved.

5.2.4 Periodic Underloads

It has been stated above that a single underload gives rise to accelerated crack growth. It is therefore to be expected that periodic underload will give rise to faster crack growth rates. It remains to be seen, however, at what frequencies and underload/minor cycle ratios the effects are more pronounced. A study on 2014A-T4 aluminium, BS4360:50B and BS1501:32A steel compact tension specimens showed that most damage occurred when only 10 small cycles were introduced between each underload, and the most damaging ratio was 2 [Reck, 1985]. It has been suggested that the underloads cause the mean stress of the following minor cycles to rise, thus resulting in increased R ratio which in turn gives rise to faster crack growth [Reck, 1985] although this may not be the only mechanism active in this instance.

5.2.5 Programmed and Random Loading with Constant

Programmed and random loadings of the type shown in Fig.5.2 [McMillan et Pelloux, 1967] carried out on 2024-T3 aluminium centre-notched plates revealed acceleration factors (y) of about 2, only in the early stages of crack propagation, and no effect was noticed for the final stages of crack growth. It was also observed that the crack growth rates were independent of the order in which the cycles occurred so that sequences P3, P4, and P5 yielded the same growth rates. It was also seen that when a large cycle was followed by a smaller cycle, less crack closure developed but the crack growth due to that cycle remained unaltered. On the other hand, a study on similar 7075-T6 aluminium specimens with the load sequences shown in Fig.5.3 [Broek et Leis, 1981] revealed acceleration factors of 1.61. It was argued that the large cycles in each block result in some strain damage at the crack tip that gives rise to faster crack growth at the lower AS cycles. However, if that were the case, one would expect sequence B5 to be more damaging than B4 since the damage caused by each large cycle in B5 would influence each following cycle in the block, while in B4 this would only occur at the beginning of each block. In practice, B4 produced faster growth than B5 and either some other mechanism is at work or it is the sudden jump from a large cycle to a small one that delivers the damage.

5.2.6 Programmed and Random Loading with Constant K^„

Programmed loadings of the type shown in Fig.5.4 (sequences B l, B2 and B3 only) [Broek et Leis, 1981] were used on centre notched 7075-T6 aluminium plates resulting in accelerated growth. It may be interesting to note that in this instance the sequence containing decreasing and increasing Kn,„ (B3) was far more damaging than those containing only increase or decrease in (Bl and B2). This would tend to indicate that smooth variations at constant are more damaging than abrupt ones.

5.2.7 Change in Mean Stress

A number of tests have been performed using a series of CA load blocks of equal stress range but different mean stress. It has been observed that increasing the R

ratio produces faster FCGR’s while decreasing it reduces the FCGR’s [McMillan et Pelloux, 1967, and Nowack et al, 1979]. The accelerated FCG transient following an increase in R ratio has been associated with the relative decrease of K^p in comparison with so that the crack is fully open for a greater proportion of the cycle. Additionally, it has been suggested that the crack tip radius may also play an important role: this is sharper at Rj (R2>Ri) than it is at Rg (cf section 3.3). The first

cycle at R2 will therefore be enhanced by the sharper crack. After the first cycle at

the higher stress ratio, the crack reverts to its steady state crack tip radius and less pronounced FCGR’s are observed [McMillan et Pelloux, 1967]. This hypothesis would be in line with SEM observations of giant striations in such tests and also in simple overload experiments [McMillan et Pelloux, 1967, Koterazawa, 1981, and Kobayashi et al, 1981]. The slow FCGR’s experienced when decreasing the R ratio point to crack closure effects playing an important role in slowing down crack growth while the accelerations associated with a greater COD in the larger preceding cycles in overload tests have not been observed [Nowack et al, 1979]. As a result of this, attempts to describe this behaviour by means of crack closure and elastic-plastic COD alone have been successful [Kobayashi et al, 1981].

5.2.8 Fully Reversed Overload Cycles

Experiments involving fully reversed overload cycles are plentiful and varied. Koterazawa carried out experiments on 5052 aluminium, low and medium carbon steels, and high strength steels and found that two cycles of fully reversed peak-trough overload gave rise to accelerated crack growth in the following low amplitude CA cycles (Fig.5.2) [Koterazawa, 1981]. This is the more surprising since post overload fatigue crack growth below AK^ was observed. Accelerations were more pronounced in the lower strength materials (hundredfold) than in the higher strength ones (five times faster). Furthermore, this phenomenon was observed in specimens of diverse geometries: notched round bar, through thickness cracked plate and surface cracked plate, thus indicating a geometry independent effect. Crack closure measurements were taken and they were insufficient to explain such growths. A zigzag propagation mechanism acting in conjunction with a radial dislocation structure at the crack tip has been proposed but additional data would be needed to confirm this hypothesis. Similar tests in 0.54%C annealed and quenched and tempered steels [Nisitani et Takao, 1978] revealed accelerations (y=2) following 3 fully reversed overload cycles. Fractographic studies revealed depressed

Kop values and extensive crack opening due to overload which were claimed to be the cause of the accelerations observed. These effects were more pronounced in the annealed steel than in the quenched and tempered one. 7075-T6 aluminium centre notched plate tests were carried out to establish whether peak-trough overstress was more damaging than trough-peak overstress or viceversa [Broek et Leis, 1981]. In both cases faster FCGR’s were observed but the peak-trough overstress cycle was seen to be marginally more rapid.

5.2.9 Other Types of Loading

A number of programmed variable amplitude tests have been done in the past and since all the sequences being used have been different, different findings have emerged. Discrepancies between one set of results and another tend to stem from oversimplifications in attempts to equate different materials, slightly different sequences, and even different environments. A series of fatigue tests on BS4360:50B welds [Gurney, 1983] with simple stress wave patterns provided enough evidence to show that Miner’s damage summation rule may be unconservative in a number of instances. Unfortunately, no crack initiation nor propagation data was recorded and therefore his main contribution remains in endurance evaluation. Another programmed sequence by McMillan et Pelloux [McMillan et Pelloux, 1967] showed that when a number of stress cycles with different R ratios were put together in a random way, a faster FCGR resulted. These experiments were accompanied by SEM fractographic studies and the effects of a number of cycles were thus visualised in a quantifiable manner.

5.2.10 Spectrum Loading

The number of spectrum loading tests to date is very large and still increasing. This is partly due to the fact that more realistic service conditions can now be simulated in laboratory tests, and partly due to the fact that it is now recognised that CA fatigue data cannot accurately be used to model service loadings that are random by nature. The large amounts of VA data being generated has now made it a necessity to generate standard load sequences that can be used throughout the world in order to model a particular problem encountered by many engineering structures of the same type. As a direct result of this, there is a lot more data available on weldable structural steel specimens subjected to simulated offshore structure type loading and this section will concentrate on such type of data. In addition, in such tests

environmental conditions have also been modelled thus thrusting us into an area in which variable amplitude and corrosion fatigue mechanisms overlap and which we shall now refer to as variable amplitude corrosion fatigue (VACF).

Booth [1983] carried out some VACF test on BS4360:50 steel plate welded joints, using a narrow band random load sequence (C/12/20 with 10^ cycles per block). The joints were tested in sea water under freely corroding, intermittently immersed, and cathodically protected conditions. It was seen that when the mean stress was increased a reduction in life was observed.

Experiments were also carried out on 3 point bend fracture mechanics specimens made of the same steel and using the same narrow band load sequence (C/12/20 with lO'* cycles per block) in air and sea water (non-biological and also with bacteria and nutrient, both with cathodic protection) [Cowling et al, 1985]. The FCGR’s were all within the scatter range of the air and sea water lines. However, using broad band load histories (UKOSRP II) on the same type of specimens revealed a change of slope in the air da/dN vs AK curve and it required adjustments for frequency variations in the sea water tests [Hancock, 1987].

VACF tests in large scale tubular joints of the type used in offshore structures have been carried out here at UCL in the past [Kam, 1987, Austin et al, 1992, Vihas-Pich et al, 1992]. Kam found that while high equivalent stress ranges gave rise to shorter fatigue lives, lower stress ranges yielded extended fatigue lives in which crack plugging resulted in \&si run-outs. However, Austin et al have shown that even at the lower stresses, realistic service loadings may still yield endurances with Miner’s sums of less than 0.25 with respect to the air mean life. In the following chapter, in the discussion of the experimental results a comparison with these experimental programmes shall be made and these shall be described in more detail.