Relationship between the fatigue cracking probability and the grain-boundary category

Polycrystalline materials with grain boundaries (GBs), involving excess free energy because of their structural imperfection, can reduce their energy by the nanoscopic structural changes of the GBs via impurity segregation. Those local changes at GBs can stabilize non-equilibrium nanostructures, resulting in the drastic change in the macroscopic properties of those materials. The mechanism of GB segregation is, however, far from being understood due to difficulties in characterizing both crystallographic and chemical properties of the same GB at atomistic levels. We have therefore developed an analytical method to determine the impurity segregation ability on the same GB at the same nanoscopic location by a joint use of scanning transmission electron microscopy (STEM) and atom probe tomography (APT) combined with ab-initio calculations, and discussed the segregation mechanism in terms of bond distortions at the GB. In the present work, we examined the GBs in Si ingots used for solar cells. They have serious impacts on the solar cell efficiency via the segregation of detrimental impurity atoms, such as oxygen and transition metals introduced inevitably during crystal growth and cell processing, depending on their structural condition at those GBs. Accordingly, precise understanding of the segregation mechanism of impurity atoms is one important issue to produce cost-effective solar cells by engineering the structural condition of impurity atoms segregating at GBs. Three-dimensional distribution of impurity atoms was systematically determined at the typical large-angle GBs (i.e., Σ3{111}, Σ5{013}, Σ9{221}, Σ9{114}, Σ9{111}/{115}, and Σ27{552}) [1-3] and small-angle GBs [3-5] by APT with a low impurity detection limit (0.01 at.% on a GB plane) simultaneously with a high spatial resolution (about 0.4 nm), and it was correlated with the atomic stresses around the GBs estimated by ab-initio calculations based on atomic-resolution scanning TEM data (for large-angle GBs [2]) and by calculations with the elastic theory based on dark-field TEM data (for small-angle GBs [4]). It was hypothesized that oxygen atoms segregate at the bond-centered positions under tensile stresses above about 2 GPa so as to attain more stable bonding network by reducing the local stresses [6]. The number of segregating atoms per unit GB area (N GB ) is in proportion to both the number of the stressed positions per unit GB area (n bc) and the average concentration of oxygen atoms around the GB ([Oi]) with N GB ~ 50n bc[Oi]. This indicates that the probability of oxygen atoms at the segregation positions would be, on average, fifty times larger than in bond-centered positions in defect-free regions. This nanoscopic finding may provide a general guidance to control compositions and band structures at GBs via oxygen segregation.

The role of grain boundaries on fatigue crack initiation – An energy approach

Perhaps the most thoroughly studied feature of cyclic plasticity has been persistent slip bands (PSBs) formed in some metals during cyclic loading. The aim of this paper is to delimit the conditions for the occurrence of the PSBs and to discuss their role in the fatigue process in all its stages, that is in cyclic hardening resulting in a saturated stress–strain response, in initiation of fatigue microcracks and in propagation of fatigue cracks. The PSBs are zones of high cyclic slip activity. Therefore the cyclic stress–strain response depends on their volume fraction and on the ratio of cyclic slip activities within the PSBs to those outside the PSB. The cyclic plastic deformation within the PSBs leads to the formation of surface extrusions and intrusions along the traces of the active slip planes; fatigue microcracks start from the surface intrusions. Thus the PSBs play a crucial role in the process of crack initiation. Stage I fatigue cracks usually run along the PSBs. At very early stages of crack propagation these PSBs are formed before the cracks are initiated; later the PSBs are formed in the plastic zones ahead of the cracks. Stage II fatigue cracks often follow the PSBs on the microscopic level in the threshold region.

The microstructurally short-crack initiation and early propagation were studied on the metastable β-Ti alloy TimetalĽB in the solution heat-treated bcc β microstructure under symmetrical pull-push fatigue testing. By means of a finite-element treatment in combination with local displacement measurements applying a laser interferometric strain-displacement gauge (ISDG), it was shown that elastic anisotropy gives rise to high mechanical stresses at certain grain boundaries (GBs). Large-angle GBs were observed to be preferred sites for short-crack initiation. Two modes of fatigue crack initiation were found: one is crack formation along slip bands, often resulting in transgranular crack propagation; the second is intergranular cracking of GBs. Using electron back-scattered diffraction (EBSD), local crystallographic orientations were determined and hence the role of GB types in the process of short crack initiation and growth could be taken into account. On the basis of the experimental observations and measurements, the preferred crystallographic conditions for short crack initiation and growth were revealed. The ISDG system was applied to measure the local crack opening displacements of short cracks in order to characterize the dependence of the short-crack closure phenomena on the applied load.

Higher fatigue cracking resistance of twin boundaries than grain boundaries in Cu bicrystals

Electron channeling contrast imaging of dislocation structures in fatigued austenitic stainless steels

Effects of grain boundary on wear of graphene at the nanoscale: A molecular dynamics study

The secondary slip behavior ahead of crystallographic fatigue cracks and its effect on the crack growth near the grain boundaries (GBs) in $$[12\bar 1]$$ tilt nonsymmetrical aluminum bicrystals under constant cyclic stress amplitude have been systematically examined. The displacement field ahead of short crack tips near the interfaces in two specimens has been measured by using a microfiducial grid technique. It has been observed that the critical persistent slip band (PSB) ahead of a short crack tip near the GB in a middle misoriented bicrystal was able to develop as long as the primary one and resulted in a temporary stage II growth. As a longer crystal- lographic crack grew into the grain boundary affected zone (GBAZ), activation of the critical slip ahead of the crack front and crack branching along the critical PSB occurred in all groups of the aluminum bicrystals, which reveals a crucial role of the critical slip in increasing the crack opening and triggering the slip in the adjacent grain. On the other hand, cross slip became the dominant slip mode ahead of the crystallographic crack front near the GB in a bicrystal of larger misfit angles and drove the crack along the cross PSB, a steep path with a remarkably high growth rate, until it propagated into the GBAZ. The resultant stress on the secondary slip system ahead of a crack front near the interface contributed by the internal stress due to both intergranular and intragranular incompatible strain, as well as the enhanced crack tip stress, has been evaluated and rationalizes the activation of the secondary slip systems.

Shear stress driven grain boundary (GB) migration was found to be a ubiquitous phenomenon in small grained polycrystalline materials. Here we show that the GB displacement shift complete (DSC) dislocation mechanism for GB shear coupled migration is still functioning even if the geometry orientation of the GBs deviates a few degrees from the appropriate coincidence site lattice (CSL) GBs. It means that any large angle GB can have a considerable chance to be such a “CSL-related GB” for which the shear coupled GB migration motion can happen by the GB DSC dislocation mechanism. We conclude that the CSL-DSC bi-crystallographic lattice structure in GB is the main reason that GB can migrate under shear stress.

How a crack initiates from the smooth surface of single crystals subjected to uniaxial cyclic loading is unclear. Experiments were conducted to observe in detail the dislocation microstructures during the saturation stage of cyclic deformation in a copper single crystal using scanning electron microscopy and the electron channeling contrast (SEM–ECC) technique. Some dark zones were found in the dislocation microstructures, which were located either at the edge region of the specimen or within the persistent slip bands (PSBs) at the matrix/PSB interfaces. Hence, fatigue cracks will initiate at these sites with high stress concentrations, i.e., the dark zones. Also, dislocation dynamics (DD) simulation was adopted to calculate internal stress distributions induced by dislocations, and finite element analysis (FEA) used to obtain stress distribution at the matrix/PSB interfaces and neighboring micro-regions caused by an externally applied load. Simulation results show that the external shear stresses distribute uniformly in all specimens; while near the free-surface regions, the maximum value of internal stresses not only occurs at interfaces between PSBs and dislocation matrix, but also at locations where these interfaces cross the freesurface. Consequently, the interfaces are most probable sites for nucleated cracks. Finally, the simulation results agree well with experimental observations.

The effect of a geometrical relationship between a grain boundary (GB) plane and a tensile axis on intergranular fatigue cracking along Σ3(1 1 2) twin boundaries has been investigated in Fe-30%Cr alloy crystals. Fatigue experiments were carried out on the three kinds of the specimens containing the Σ3(1 1 2) twin boundary. It was found that the fatigue cracking behavior was sensitive to the geometry of the GB plane. In a specimen where both the GB plane and a slip vector lying in the GB plane in adjacent grains are inclined to the tensile axis at 45°, the fatigue cracks were nucleated preferentially along the twin boundary at a stress amplitude of 170 MPa. The specimen with the GB plane normal to the tensile axis showed that the fatigue crack was initiated from a slip band formed within a constituent grain at a stress amplitude of 300 MPa. When the GB plane was inclined to the tensile axis but the slip vector lying in the GB plane was normal to the tensile axis, development of additional slips formed perpendicular to the GB plane were observed at a specific site of the GB. Initiation of intergranular fatigue cracks at the site was recognized at a stress amplitude of 250 MPa. It can be suggested that the GB plane normal to the tensile axis provides the highest fatigue performance among them. The difference in the cracking property among these specimens could be understood in terms of the effective Schmid factor derived from elastically incompatible stress.

Grain boundaries (GBs) are important microstructure features and can significantly affect the properties of nanocrystalline materials. Molecular dynamics simulation was carried out in this study to investigate the shear response and deformation mechanisms of symmetric and asymmetric Σ11<1 1 0> tilt GBs in copper bicrystals. Different deformation mechanisms were reported, depending on GB inclination angles and equilibrium GB structures, including GB migration coupled to shear deformation, GB sliding caused by local atomic shuffling, and dislocation nucleation from GB. The simulation showed that migrating Σ11(1 1 3) GB under shear can be regarded as sliding of GB dislocations and their combination along the boundary plane. A non-planar structure with dissociated intrinsic stacking faults was prevalent in Σ11 asymmetric GBs of Cu. This type of structure can significantly increase the ductility of bicrystal models under shear deformation. A grain boundary can be a source of dislocation and migrate itself at different stress levels. The intrinsic free volume involved in the grain boundary area was correlated with dislocation nucleation and GB sliding, while the dislocation nucleation mechanism can be different for a grain boundary due to its different equilibrium structures.

Low cycle fatigue of a copper bicrystal under constant plastic strain control

Fatigue crack growth rate in axial, torsional and multiaxial mode in 316L austenitic steel

Quantitative measurement of persistent slip band profiles and crack initiation