Interactions between geometrical defects and microstructure during high cycle fatigue of polycrystalline aluminium with different grain sizes

In this work, the influence of the geometrical defect size on the high cycle fatigue behavior of polycrystalline aluminium with different grain sizes is investigated, to better understand the role of internal length scales. Two sizes of grains and defect are used: 100 μm and 1000 μm, the grain size being controlled with thermomechanical treatments. Fully reversed stress-controlled fatigue tests are then carried out. According to fatigue test results, surface crack initiation is delayed when the grain size is reduced, while an approximation of the fatigue limit shows that it is not much influenced by the average grain size. The relative defect diameter (compared to the grain size) seems to be the leading parameter influencing fatigue crack initiation from a defect. Finally, Electron BackScattered Diffraction (EBSD) maps are collected for specimens with large grains and small defects. Fatigue crack initiation from a defect is found to be strongly impacted by the crystallographic orientation of the surrounding grain, crack initiation preferably occurring in crystals being favorably oriented for plastic slip.


Introduction
Defects in metallic alloys can originate from various factors [1,2,3,4], have either a geometrical (e.g. notches) or metallurgical (e.g. inclusions) nature and can be of various shapes and sizes. Because they act as stress concentrators, such defects usually have a detrimental influence on the high cycle fatigue (HCF) resistance of metallic alloys [5]. The fatigue resistance reduction associated with the presence of defects is however strongly dependent on their size: the reduction is higher for a larger defect, and there exists a critical size below which the fatigue limit is no longer affected [6,7]. Although the knowledge of the critical size is important to design fatigue-resistant structures, the dependence of this critical size regarding microstructural features remains unclear.
The role of microstructural features on the fatigue behavior in the absence of significant geometrical defects has been widely studied. For instance, the influence of grain size on the fatigue behavior of smooth specimens is largely documented [8,9,10]. The fatigue limit is usually found to increase when the grain size is reduced and the influence of grain size on the fatigue limit is often correctly described with an Hall-Petch [11,12] type of relation [13]. According to Chan [14], the influence of grain size is explained by the fact that polycrystals with large grains are more prone to initiate cracks in slip bands than their smaller grained counterparts, leading to earlier crack initiation in the former. Regarding the influence of grain size on fatigue crack propagation in aluminium polycrystals, several authors give contradictory results: Saga et al. [15,16] conclude that the larger the grains, the higher the crack growth rate and the lower the number of cycles to failure, whereas Thompson et al. [17] found no significant impact on the fatigue resistance at 10 6 cycles, in the range 20-200 µm. The interpretation of the latter is that cross slip can easily be activated in pure aluminium, and that the resulting cellular dislocation structures tend to hide grain boundaries in the crack propagation stage.
Few attempts have been made to investigate the impact of microstructure on the fatigue behavior of metallic specimens with geometrical defects. Guerchais et al. [18] studied the influence of local microstructure around the defect for different loading conditions, but only the defect size and local microstructure were varied, not the grain size. Sweeney et al. [19] and Wan et al.
[20] relied on a comprehensive experimental procedure, including HCF tests and systematic Electron BackScattered Diffraction (EBSD) maps, to set up numerical models in order to predict fatigue crack initiation. In their case, the microstructure is varied around the defect, but grain and defect sizes are held constant. To explore the connection between grain size and defect size, Karry et al. [21] carried out an experimental investigation on brass specimens with defects of different sizes and shapes, as well as on smooth specimens. They observed that when a defect is introduced, the decrease in fatigue limit compared to the corresponding smooth specimen was lower for a higher grain size. The defect sensitivity is thus higher for small grained microstructures. Lorenzino et al. [22] carried out fatigue tests on pure aluminium specimens with different grain and defect sizes. Besides the fact that a larger grain size and/or notch size reduces the fatigue limit, they showed that, as far as crack propagation is concerned, the governing parameter is the relative defect size (the defect size divided by the mean grain size) rather than the absolute physical one. Indeed, by normalizing the fatigue limit of specimens with defects by the fatigue limit of smooth specimens with the same grain size, and the defect size by the grain size, all data points fall onto the same line in a fatigue limit/notch size diagram. Vincent et al. [23], using various defect sizes and grain sizes, came to the same conclusion for commercially pure iron. Those two studies focus on the number of cycles to failure rather than to crack initiation, but they demonstrate the interest of varying both characteristic sizes.
In the present work, an experimental campaign is carried out to investigate the joint influence of geometrical surface defect size and grain size on the HCF behavior of pure aluminium polycrystals. In contrast with the work of Lorenzino et al. [22], who focused on crack propagation, this study concentrates on crack initiation in the presence of defects. Indeed, the influence of the defect is most important in the crack initiation stage, as it acts as a stress concentrator and a preferential crack initiation site; its influence becomes lower once a crack is initiated and starts to propagate. Also, to better understand the factors governing the initiation of a fatigue crack, Electron Backscattered Diffraction (EBSD) techniques are used to evaluate the influence of crystallographic orientation.
1 Experimental procedure

Material description
The material used in this study is commercial purity aluminium (AA1050), for which the aluminium weight concentration exceeds 99.5 %. The alloy is supplied in the form of 6 mm-thick cold-rolled sheets. The initial microstructure is composed of elongated grains along the rolling direction.
Two different thermomechanical sequences have been applied to control the grain size Φ, which is evaluated by the average grain intercept method. For the first sequence, in addition to the strain-hardening associated to the rolling process, aluminium samples are held at 550°C for 45 minutes and then air cooled. The resulting microstructure is referred to as "small" grain microstructure (denoted by subscript s) with an average grain size Φ s of about 100 µm along the rolling direction. For the second sequence, samples are firstly maintained at 550°C for 2 hours and then air-cooled. A tensile strain of 12 % is then applied at room temperature in the rolling direction, followed by a second heat treatment at 600° C for 2 hours, before a final air cooling. The corresponding grain size Φ l is approximately of 1000 µm along the rolling direction. This second microstructure is referred to as "large" grain microstructure (denoted by subscript l). Both sequences ending with a recrystallization treatment, they provide fully annealed microstructures with different grain sizes.
Grain sizes have been evaluated in the three principal sheet directions from several micrographs. For both microstructures, grain sizes along the rolling and transverse directions are identical. The average grain size is however smaller, by a factor of 2, along the normal direction. It should be noticed that, for a given microstructure, all samples have been extracted from the same aluminium sheet. Also, during the preparation stage, some samples have been randomly selected to check the repeatability of the preparation procedure.
Tensile tests have been performed on both microstructures, in the rolling direction, using a strain rate = 10 −3 −1 . The corresponding mechanical properties are presented in Table 1. One can note that the values of R p0.2 and R m are lower for a higher grain size, in accordance with the classical Hall-Petch law.

Specimen preparation
Fatigue specimens have been machined from previously prepared aluminium samples. The geometry of fatigue specimens is presented in Figure 1. The gauge section is 15 mm-long and 30 mm-wide, the thickness is 5 mm and the loading axis coincides with the rolling direction. For the large grain microstructure, particular care has been taken to extract the gauge part of fatigue specimens from the area where the applied tensile strain, hence the grain size, had been controlled. Geometrical defects have been introduced in the gauge area of fatigue specimens with a hemispherical drill, the defect size d being thus given by the drill diameter. A high cutting speed and a low translation speed (1 µm.s -1 ) have been used to ensure that the local microstructure is not affected by drilling operations. In the present work, two defect sizes have been considered: d s = 100 µm and d l = 1000 µm, where subscripts s and l denote respectively the small and the large defects. Defect depths and shapes have been systematically inspected with a 3D profilometer. For small defects, the relative difference between the nominal depth and the actual depth is under 5 % in most cases, and under 10 % in all cases. For large defects, this difference is always inferior to 1 %. Four different types of specimens are used: smooth specimens, specimens with a single large defect (denoted SLD specimens), specimens with multiple large defects (MLD specimens) and specimens with multiple small defects (MSD specimens). Respectively 4 and 5 defects are machined in one specimen, for MLD and MSD specimens. Figure 1 displays the location(s) of defect(s) relative to the center of the gauge section.
Fatigue specimens are then submitted to mechanical polishing (FEPA abrasives 600, 1200 and 2000), followed by a final heat treatment (260° C for 2 hours and air-cooling) to relieve the residual stresses resulting from machining and polishing operations. The temperature for this heat treatment is chosen low enough not to engage recrystallization and modify the grain size.

Experimental set-up
Fully reversed load-controlled push-pull fatigue tests (i.e. = −1) are carried out on an Instron 8802 servohydraulic testing machine. The tests are thus nominal-stress-controlled; for the sake of simplicity, they are referred to as "stress-controlled" in the following. Different tests frequencies, namely 1 Hz and 12 Hz, are used, depending on the kind of test performed.
To prevent buckling of the specimen while allowing elongation measurement by an extensometer, a specific anti-buckling fixture has been developed. As shown in Figure 2, it consists of two opposing asymmetrical steel plates which are assembled to exert a normal effort on the specimen during the compression stage. A teflon film is placed between the specimen and the fixture to reduce friction. Preliminary tests have been conducted on a specimen equipped with strain gauges to verify that, despite the additional effort due to the fixture, the stress state in the center of the gauge area is not altered. However, when no defect is introduced, cracks initiate and propagate from the interface between the specimen and the rectangular plate in a region where the stress field might be perturbed. As a result, smooth specimens cannot be used to characterize the fatigue behavior since the stress state might not be correctly controlled in the crack initiation area. Smooth specimens are thus solely used for the evaluation of the cyclic behavior.
For specimens with defects, the final failure of fatigue specimens does not always result from a defectinduced crack. As a consequence, when evaluating the influence of geometrical defects on the number of cycles to failure, only tests for which fatigue failure is caused by defects have been considered. This aspect is not problematic for large defects (d l = 1000 µm), as final failure is caused by defects in most cases. However, for small defects (d s = 100 µm), final failure often results from another crack than the one(s) initiated from the defect. As a consequence of the propagation of non defect-induced cracks, the stress field in the vicinity of defects can be strongly perturbed. Therefore, for small defects, only crack initiation, for which perturbations caused by cracks initiated away from defects are negligible, is investigated.
Different experimental configurations are used to investigate the influence of grain size and/or defect size. In the first one, the cyclic elastic-plastic behavior of pure aluminium is evaluated from smooth specimens of both grain sizes equipped with a clip-on Instron extensometer with a 12.5 mm spacing. The second configuration uses SLD specimens (d l = 1000 µm). This configuration aims at measuring the length of cracks having been initiated from the defect. For this application, the area surrounding the defect is observed with an optical camera and pictures are recorded every 1000 loading cycles. While an in-situ monitoring of the crack length is possible with this second configuration, the detection is limited to surface cracks with a minimum length of about 100 µm. Due to the potential influence of non defect-induced cracks, small defects are not studied in this configuration. The third configuration uses MLD and MSD specimens (d l = 1000 µm and d s =100 µm). For a given low stress amplitude, preventing macroscopic crack propagation, it allows determining the number of cracked defects from a posteriori Scanning Electron Microscopy (SEM) observations. Some of the MSD specimens are also selected to carry out EBSD observations of the microstructure surrounding the defect.

Smooth specimens
Fully reversed stress-controlled cyclic tests have been performed with a loading frequency of 1 Hz and a constant stress amplitude σ a , for both grain sizes, to investigate the influence of grain size on the cyclic elastic-plastic behavior of pure aluminium. Most tests have been stopped after 10 4 cycles, but some have been continued up to 10 5 or 2.10 5 cycles to determine whether elastic shakedown is observed or not. The evolution of the axial plastic strain range Δε p as a function of the number of cycles N is plotted for different stress amplitudes in Figures 3 and 4, respectively for small and large grains.

Specimens with a single large defect (SLD)
Stress-controlled fatigue tests have been carried out on SLD specimens (d l = 1000 µm) to evaluate the impact of grain size on fatigue crack initiation and specimen fracture. For these tests, the loading frequency is set to 12 Hz. In the absence of failure, fatigue tests have been interrupted after 10 6 cycles. The observation of the area surrounding the defect with the optical camera allows monitoring early crack propagation from the defect, on the specimen surface, as illustrated in Figure 5 for the (d l -Φ s , σ a = 30 MPa) configuration, for which failure occurred at 292,000 cycles. Based on fatigue test results, two different S-N diagrams have been plotted. The first S-N diagram, Figure 6, represents the evolution of the stress amplitude σ a as a function of the number of cycles to failure N f , the failure being defined as the separation of the specimen into two distinct parts. Note that for large grains (Φ l = 1000 µm), for respectively σ a = 30 MPa and σ a = 33 MPa, only 2 and 1 point(s) were representative (failure from the crack initiating from the defect). The evolution of the stress amplitude as a function of the number of cycles to crack initiation N i is displayed in a second S-N diagram, Figure 7. In the present work, the crack initiation criterion, defining Ni, is arbitrarily set to a total surface crack length of 100 µm, which is the shortest detectable crack length. One should note that, as a result, especially for the small grain microstructure, the number of cycles to crack initiation may include a portion of early crack propagation.  S-N curves for initiation, obtained for SLD specimens (d l = 1000 µm) and two sizes of microstructure. Crack initiation criterion: 100 µm-long surface crack. Arrows represent run-out specimens for which this criterion was not reached. Number indicates the superimposed points (above for Φ s , below for Φ l ).

Specimens with multiple defects (MLD and MSD)
To investigate the influence of defect size on fatigue crack initiation, some specimens with multiple defects have been submitted to stress-controlled fatigue tests. The fatigue tests are conducted with a frequency of 12 Hz and up to 10 6 loading cycles. In this case, both the grain size Φ and the defect size d are varied. Stress amplitudes are selected low enough to prevent macroscopic crack propagation (hence failure) and exclude interactions between defects.
After fatigue testing, SEM observations of each defect are carried out to determine whether a crack initiated or not. In comparison with the in-situ monitoring used earlier, short cracks are more accurately detected with SEM because it allows observing the bottom pole of hemispherical defects. The results obtained for different grain sizes, defect sizes and stress amplitudes are presented in Table 2, which shows the proportion of cracked defects in the different configurations. Based on these results, the stress amplitude corresponding to a 50 % probability of crack initiation to a defect, σ a (P 50 ), has been estimated for each d-Φ configuration, by linear interpolation (see Figure 8).

Influence of grain size and defect size
Based on the experimental results, the influence of grain size and/or defect size on the HCF behavior of pure aluminium is firstly discussed.
According to Figures 3 and 4, for both grains sizes, the cyclic behavior is composed of three successive stages: primary hardening, softening and secondary hardening. This specific behavior, which is explained by the formation and evolution of dislocation structures [24,25,26,27], has already been highlighted [28,29]. Figure 9 shows, for all SLD specimens that failed from the defect before 10 6 cycles, the ratio between the crack initiation life and the total fatigue life. Most of the fatigue life is spent in the propagation stage, the ratio N i /N f being under 0.1 in all cases. Since, as shown in Figure 6, the fatigue limit (estimated as the higher stress level for which no failure occurs) is not much influenced by grain size, this gives credit to the results of [17]. Fig. 9. Ratio between the number of cycles to surface crack initiation N i and the number of cycles to failure N f , as a function of the stress amplitude σ a , for all SLD specimens that failed from the defect before 10 6 cycles.
On the contrary, the crack initiation stage may be impacted by the average grain size. Indeed, as illustrated  Figure 7, the mean number of cycles to crack initiation N i is reduced when the grain size is increased. However, this last conclusion must be taken with caution, as it depends on the crack initiation criterion used. Indeed, as can be seen in Figure 8, there are no differences in the stress amplitudes necessary to initiate a crack from a large defect, between the two grain sizes. The different conclusions can be explained by the fact that a small portion of early crack propagation is necessary to reach the crack initiation criterion in the results of Figure 7, whereas the criterion used in the results of Figure 8 is more precise.
This influence of grain size on fatigue crack initiation is also observed for specimens with multiple defects. Indeed, as shown in Table 3, the stress amplitude corresponding to a 50 % crack initiation probability, σ a (P50), is lower for the large grain microstructure, when small defects are introduced (reduction of 1.8 MPa, i.e. 6.3 %, between both grain sizes). For large defects, however, the difference between both grain sizes is negligible (this difference with the in-situ crack monitoring approach on SLD specimens presented above being attributable to the different crack initiation criteria used, as discussed earlier). The small grain microstructure is thus more sensitive to defect size.  To compare the results from both microstructures, a normalized stress level is used, in a similar way to the works of Lorenzino et al. [22] and Vincent et al. [23]. As the fatigue limit of smooth specimens could not be determined due to the anti-buckling fixture, the yield strength of the smooth specimen is used. As can be seen on Table 3, when increasing the defect size, the change in normalized stress level is more significant for the small grain microstructure (relative reduction of 9 % and 3 %, from a small to a large defect, respectively for the small grain and the large grain microstructures). Figure 10 shows that, for a constant relative defect size d/Φ but different absolute sizes, the normalized stress level corresponding to a 50 % crack initiation probability is the same for both grain sizes. This is consistent with the results of Lorenzino et al. [22] and Vincent et al. [23] who observed that the relative defect size d/Φ is more relevant than the actual physical defect size d. The equivalence of the ratio between the stress amplitude necessary to initiate a crack and the yield strength suggests that, on a macroscopic point of view, regardless of the local microstructural features (e.g. crystallographic orientation, grain shape) which can influence variability of crack initiation behavior for a given d-Φ-σ a configuration, crack initiation is essentially governed by plasticity.

Influence of local microstructure
To better understand the role of local microstructure on fatigue crack initiation, EBSD analyses have been carried out on specimens which have been submitted to a reversed stress-controlled fatigue test up to 10 6 cycles. The analyses have been performed a posteriori on MSD specimens with large grains (d s -Φ l ). In this specific configuration, defects are usually embedded within a single grain. It is therefore possible to associate a unique crystallographic orientation to each defect (among the 33 defects studied, only one lies on a grain boundary, and was therefore excluded from the analysis). The same stress amplitude (σ a = 27 MPa) is used for all observed specimens. Fig. 11. Orientation of the grains embedding defects, regarding the loading axis, with values of the Schmid factor on the primary slip system.
To evaluate the influence of crystallographic orientation on fatigue crack initiation, the maximum Schmid factor has been determined for each defect. The maximum Schmid factor corresponds to the ratio between the shear stress acting on the primary slip system and the applied uniaxial stress. Grain orientations of cracked and uncracked defects are plotted in Figure 11 in the stereographic unit triangle. Crack initiation is found to be highly dependent on crystallographic orientation, as grains being favorably oriented for plastic slip are more prone to crack initiation.
To evaluate the possible influence of normal stresses, the ratio between the maximum normal stress acting on the slip systems and the applied uniaxial stress has been determined for each defect, with a similar approach. The results are presented in Figure 12. One can note that normal stresses have no obvious influence on fatigue crack initiation. A posteriori SEM observations of cracked defects often do not allow for a clear identification of the crack initiation plane. However, for one cracked defect, this plane can be identified. From EBSD data, the maximum Schmid factor has been calculated for each of the four {111} slip planes of the surrounding grain. Figure 13 shows this cracked defect, the slip planes traces (i.e. the directions of the intersections of slip planes with a surface parallel to the free surface, as is approximately the defect root), and the corresponding values of maximum Schmid factors. The crack at the defect root (circled one) is parallel to one of the two planes of maximum Schmid factors: the crack initiation plane does not correspond to the primary slip plane (with Schmid factor of 0.48), but to the secondary slip plane (with a slightly lower Schmid factor of 0.47). This observation, although limited to one specimen among all specimens tested, is in agreement with the previous remark regarding the influence of shear stresses on fatigue crack initiation.
The present analysis, which requires the determination of Schmid factors, assumes the stress state to be uniaxial. However, while this simple approach seems sufficient for interpreting the influence of crystallographic orientation in many situations, there are some uncracked defects for which the maximum Schmid factor is significant (up to 0.47, see Figure 11). Such results could be explained by the fact that the stress field is not strictly uniaxial because of the defect and microstructural heterogeneities. Further investigations will therefore be carried out using appropriate computational methods to obtain more accurate estimations of the stress field.

Conclusion
In this work, the impact of geometrical defects on the HCF behavior of pure aluminium (AA1050) has been investigated. More specifically, experimental efforts have been made to better understand the role of local microstructure on fatigue crack initiation in the presence of defects. Two sizes of microstructure (Φ s = 100 µm and Φ l = 1000 µm) and defect (d s = 100 µm and d l = 1000 µm) are used.
Stress-controlled fully reversed uniaxial HCF tests have then been carried out on specimens with defects and two grain sizes. According to fatigue test results, for a large defect, the number of cycles to obtain a 100 µmlong surface crack is higher when the grain size is reduced. However, fatigue limit, estimated as the higher stress level for which no failure occurs, is not much influenced by grain size, and the fatigue life is spent mostly in the propagation stage in all cases. The small grain microstructure is observed to be more sensitive to the defect size. Also, when the ratio between the defect size d and the grain size Φ is held constant, the normalized stress amplitude associated with a 50 % crack initiation probability to the defect (normalization by R p0.2 (Φ)) is equivalent for both grain sizes. This suggests a strong connection between fatigue crack initiation and plasticity (as usually observed for smooth specimens) even in the presence of defect.
Finally, EBSD maps of the defect surroundings microstructure have been collected to evaluate the influence of crystallographic orientation on fatigue crack initiation. The results show that, when the defect size is small compared to the grain size, crack initiation is strongly impacted by crystallographic orientation. More specifically, crack initiation preferably occurs in crystals being favorably oriented for plastic slip. Crack initiation thus seems to be governed mostly by shear stresses, a conclusion that is consistent with the observation of an actual crack initiation plane.