LOW CYCLE FATIGUE BEHAVIOR
At relatively large plastic strain ranges from 10"4 to 10" 2 and short fatigue lives, the cyclic response of UFG materials is described by the Coffin-Manson law.[1] as illustrated in Fig. 9 for UFG Cu and 5056 Al-Mg alloy. Although the data in Fig. 9a are compiled from the results obtained by different researchers on differently processed samples, one can see a reasonable agreement between these results. Samples in the as-received state after ECAP demonstrate notable degradation in low cycle fatigue (LCF) life when compared to the ordinary coarse-grain samples. This is not surprising in view of their lower ductility and poor resistance to macroscopic and microscopic plastic instabilities such as necking, shear banding, cracking, etc. Such behavior is typical of metals with low levels of strain hardening (recall Consideres criterion). As will be discussed in detail below, a postprocessing heat treatment can significantly improve the LCF properties. Remarkably, UFG Ti obtained by ECAP did not reveal a significant degradation in low-cyclic fatigue performance in the plastic strain controlled testing, and the Coffin-Manson lines were practically indistinguishable for the samples before and after ECAP[35] This result agrees with the general observation in the sections ”Introduction” and ”Background,” that non-f.c.c. metals can exhibit greater improvement in their fatigue performance if both LCF and HCF regimes is of major concern.
Fig. 9 Coffin-Manson plots for ultrafine grain Cu (a) and 5056 Al-Mg alloy (b) obtained by SPD (reprinted with permission). Arrows indicate the improvement of fatigue life after post-ECAP heat treatment.
Cyclic Softening and Hardening
The cyclic stress-strain curves (CSSC) of NC materials can be represented by a power law in the same way as for other polycrystalline metals (see Refs. [4,5] and references therein).
This relation is essentially the same as that used to describe the monotonic stress-stress curve
where Kb, nb, K, and n are materials constants, and the subscript index b stands for the basic CSSC. Fig. 10 summarizes some currently available cyclic stress strain data for ECAP metals. It has been observed in a former communication[32] that the slopes of the CSSC in logarithmic scale for the same material (Fe-36Ni Invar alloy) subjected to different number of ECA pressings between 2 and 12 are approximately the same, i.e., the cyclic strain hardening exponent nb values are nearly equal for all samples regardless of the preimposed strain. Fig. 11 compares the monotonic and CSSC for ECAP Fe-36 Ni Invar alloy (only the initial part of the tensile stress-strain curve is shown). The relative position of the monotonic and cyclic stress-strain curves delivers information on the materials cyclic hardening/softening behavior under different strain amplitudes. In the region of strain amplitudes where the CSSC lies above the monotonic strain-stress curve, the material cyclically hardens.[5] On the other hand, in the regions where the CSSC is positioned below the monotonic stress-strain curve, the material cyclically softens. Hence it becomes obvious that the ECAP materials are prone to cyclic softening at any imposed plastic strain amplitude.
Fig. 10 Basic cyclic stress-strain curves for several UFG ECAP metals.
Fig. 11 Fragments of tensile stress-strain curves and CSSC for ECAP Fe-36Ni Invar alloy after 2 and 12 ECA passes.
Softening is common for cyclic deformation of prestrained f.c.c. metals.[4,5.51] It has been also clearly observed in many ECAP f.c.c. metals such as cop-per,[20-22,26] Ni,[29] single-phase Al-Mg 5056[3°31] and Fe-36Ni Invar alloys,[32] and precipitation-hardened
Fig. 12 Cyclic hardening/softening curves of some selected SPD metals with UFG structures.
Cu0.44Cr0.2Zr alloy.[36] However, the detailed characteristics of cyclic softening, its phenomenology, and microscopic mechanisms vary broadly depending on the material and processing. Fig. 12 shows the cyclic hardening-softening curves for various NC ECAP metals tested under plastic strain control. The very first investigations of LCF behavior of ECAP materials revealed that the cyclic response strongly depends on processing and the initial UFG structure. Vinogradov et al.[18] observed no cyclic softening in ECAP Cu under plastic strain amplitudes Aepl/2=5 x 10"4 and 10"3. Furthermore, some light hardening was noticed on the early stage of straining (Fig. 12). However, Agnew and Weertman[20] observed pronounced cyclic softening in similar UFG Cu produced by ECAP. The degree of softening appears to depend on the temperature, time, and plastic strain amplitude, and can vary from material to material.[23] The mechanism of cyclic softening of UFG f.c.c. metal is largely associated with a complex effect of dislocation recovery, cyclically induced dynamic ”recrystallization,” and grain coarsening, which is more pronounced at higher strain amplitudes/ ,,,] Interestingly, cyclic softening and the associated coarsening facilitates the formation of dislocation structures typical for ordinary metals, i.e., cellular and ladder-like dislocation arrange-ments[20,23] (Fig. 4b). Thiele et al.[29] performed a detailed structural investigation of the fatigue-induced structures in UFG Ni and the dependence of the grain size. Using X-ray diffraction peak profile analysis, they detected a reduction of internal stresses in the course of cycling. It was demonstrated that there is a lower threshold grain size dth of 1 mm, above which dislocation patterning takes place with a length scale 500 nm) nearly independent of the initial grain size. For materials with d< dth, the cyclic stress-strain curve obeys the Hall-Petch relation.
Not surprisingly, the SPD structure can be stabilized and the rate of cyclic softening can be reduced by: 1) annealing at an intermediate temperature, i.e., reducing the stored strain energy prior to cyclic loading;[19,22,26,30,33,44] 2) using solid solution alloys instead of pure metals;[31,32] and 3) precipitation.[36] The numerous large-scale shear bands, which are observed in the fatigued ECAP Fe-36Ni alloy, may contribute to the cyclic softening in that alloy. Hoppel and Mughrabi,[55] using Vickers microhardness measurements, have convincingly shown that the material in the shear band of a cyclically deformed ECAP Cu sample is softer than its surroundings. The values are in line with the concept of cyclically induced dynamic recrystallization and grain growth.[22,23,26] Similar measurements have been performed by Vinogradov on the fatigued ECAP Fe-36Ni alloy. It has been demonstrated that the main reason for rapid cyclic softening of the UFG under- or peak-aged CuCrZr alloy (Fig. 12) is related to dislocation cutting of the fine strengthening precipitates.[36] The degree of softening is substantially lowered in overaged samples; however, the monotonic mechanical properties (strength and ductility) are degraded in this case.
FATIGUE DAMAGE AND STRAIN LOCALIZATION
Internal stresses in metals increase during monotonic straining, finally leading to microvoid nucleation or crack initiation as the resources of plastic deformation exhaust in local volumes of the material. Thus it may come as a surprise to some readers that the cyclic deformation of UFG metals fabricated by SPD may reduce the level of internal stress (as indicated by X-ray diffraction measures of rms strains[29] and the general cyclic softening behavior referred to above), yet the end result is still a fatigue fracture. The answer, in its general form, is actually trivial: fracture occurs as a result of inhomogeneity in the plastic deformation manifesting itself as strain localization. The gradients of plastic deformation are often connected with grain boundaries, which may serve as barriers to dislocation motion as well as effective sources and sinks of lattice dislocations. These concepts are supported by atomic force microscopy (AFM) observations of fine traces of plastic deformation in UFG copper and nickel where: 1) dislocation activity is particularly visible at the grain boundaries;[16,33,52] and 2) dislocation slip is terminated at the grain boundary and is not transferred to an adjacent grain. TEM observations have also demonstrated some reduction of the dislocation density near the grain boundary during fatigue (compare Fig. 5a and b, for example). Reducing the excess dislocation density around grain boundaries may explain the observed cyclic softening and the decrease of root mean square internal stress levels and, ironically, it may ultimately promote intergranular cracking. Fracture surface analysis and the surface crack morphology shows that failure in the SPD metals indeed occurs intergranu-larly.[16,32,35]
Strain localization in the ECA-processed materials is frequently observed during both monotonic and cyclic deformation.[10-15,44] Fig. 13 shows shear bands oriented at 45° to the loading axis in pure Cu after fatigue at Aepl/ 2=5 x 10"3 and 5056 Al-Mg alloy after monotonic deformation. These bands commonly appear shortly after yielding in tensile deformation or at the end of saturation in cyclic testing. Fatigue cracks initiate and propagate along this kind of shear band (Fig. 13a).[25] Although shear banding is the major form of fatigue damage in wavy-slip UFG materials, these bands play a twofold role in fracture: on one hand, they promote crack nucleation due to strain localization and stress concentration; on the other hand, they reduce the overall elastic stresses, as evidenced by the reduction in stress at the end of saturation in strain controlled tests. Therefore it is unclear if suppression of the susceptibility to shear banding would delay or accelerate fatigue failure because cracking is a likely alternative mechanism for stress relaxation when other plastic mechanisms are exhausted. For instance, in UFG titanium or precipitation-hardened CuCrZr alloy, large-scale shear bands are not observed. However, a large population of surface microcracks is observed on the late stage of fatigue.
Fig. 13 SEM micrographs showing the shear bands in fatigued ECAP Cu (a) and in the tensile tested ECAP 5056 Al-Mg alloy (b). Final crack propagating along the shear band is shown in (a).
The microstructural nature of shear bands has been investigated in detail, at least for UFG Cu. Agnew et al.[21] observed that the shear bands in UFG copper appear like ordinary persistent slip bands (PSBs) in coarse-grain poly-and single crystals. For instance, the shear bands were removed by electropolishing, and then they reappeared on the same places during subsequent cyclic loading, indicating materials softening associated with shear bands. Furthermore, careful structural observations have shown that the shear bands in UFG copper can have essentially the same ladder-like dislocation structure as the PSBs in ordinary crystals. The TEM image shown in Fig. 4b demonstrates the dislocation walls separated by dislocation-free channels in fatigued UFG copper. Hoppel et al.[23] investigated the microstructural aspects of shear banding in UFG copper, including the dependence of strain amplitude and temperature, and have found that grain coarsening and shear banding are more pronounced at high strain amplitudes, which agrees with the observed faster cyclic softening. Thus pure f.c.c. UFG metals first exhibit relaxation and coarsening during cyclic softening, along with the formation of the low-energy configurations typical of conventional fatigued crystals, i.e., ordinary PSBs may occur. Finally, microcracks appear to initiate on intrusions and then behave similarly to those in conventional metals.
Although a similar scenario is applicable to those UFG metals exhibiting considerable grain coarsening during cycling,[16,21-23,29] conflicting observations have been reported by Vinogradov et al.[54] and Wu et al.,[27,28] who did not observe any gross structural coarsening in fatigued ECAP Cu. Furthermore, using TEM, SEM, and electron channeling contrast imaging (ECCI), it was shown that the dimensions of protrusions on the surface did not match the dimensions of the grains. In fact,numerous questions remain unanswered as to which elements govern the fatigue behavior in the complex UFG microstructure.
Fig. 14 SEM image of the shear offset on the surface of fatigued Fe-36Ni (Aepl/2 = 3 x 10— 3) (a). AFM image illustrating the large-scale displacement of adjacent grains along the grain boundary in the shear direction (b). The dislocation slip in the grain interior is clearly visible.
There are at least two kinds of plastic instabilities which manifest themselves in various NC metals under various testing conditions: 1) the PSB-like shear bands that appear during fatigue as a result of slow large-scale structural rearrangement involving grain coarsening as a prerequisite for ladder structure formation; and 2) the shear bands that arise both in monotonic and cyclic testing, and phenomenologically (if not structurally) resemble twinning events. Shear bands of the second kind are not crystallographic and are not miroscopically straight (Fig. 14a). They emerge very suddenly at free surfaces along grain boundaries in adiabatic fashion and are accompanied by significant acoustic emissions.[54,56] The possibility of grain boundary sliding at ambient temperature in UFG SPD materials has been speculated in the literature[2,43] in terms of enhanced diffusion and grain boundary mobility associated with heavily distorted grain boundaries. However, it is of particular importance to note the traces of dislocation slip of 1-10 nm height in the grain interior (Fig. 14b): that the slip lines are confined to a single grain, and the slip does not transfer through the boundary.[33] Thus the AFM observations1-16,33,52-1 highlight the fact that conventional intragranular dislocation activity cannot be neglected as the most important mechanism of plastic deformation of UFG metals.
Shear bands in NCs may emerge to a free surface in a way similar to the shear bands commonly observed in metallic glasses during inhomogeneous plastic flow,[57] which is also accompanied by intensive acoustic emission,[58] and the morphology of shear bands in metallic glasses is very similar to that in NCs; however, this similarity may be completely coincidental because the concept of thick amorphous boundaries has not been justified by direct structural observations, particularly for metals fabricated by SPD. Wu et al.[25,27] and Vinogradov et al.[54] have found that the shear bands tend to align themselves with the plane of simple shear on the last ECA pressing, i.e., these bands are sensitive to the structure and its inhomogeneities formed during the last pass through the die. This leads to a conclusion that the careful control over processing (strain path, temperature, velocity, etc.) may allow control of the material’s resistance to shear banding. Indeed, the nanostructure with equiaxied grains is less susceptible to rapid adiabatic shear banding than the structure with the grains (cells, fragments, etc.) elongated in the direction of last shear. Furthermore, UFG copper manufactured using different die sets (with round and rectangular corner) and different processing routes (but the same number of ECA passes and nearly the same grain size) exhibited different shear banding susceptibility: the softer UFG copper, which saturated at 120 MPa and then cyclically softened at Aepl=1 x 10— 3, did not reveal the shear bands during either cyclic or monotonic loading,[59] while the stronger copper saturated at 250 MPa and demonstrated many shear band on late stage of fatigue at the same plastic strain amplitude.[18,54]
Annealing of as-processed UFG copper at an intermediate temperature for a short time, which does not give rise to substantial grain growth, resulted in the disappearance of adiabatic shear bands and accompanying acoustic emission.[56] Despite the considerable difference in the microscopic mechanisms resulting in the two kinds of shear bands, they both appear as precursors of micro-cracks and serve as a preferred sites of crack nucleation.
