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High-Cycle Fatigue in Polycrystalline Materials: The Grain-Boundary Formulation Voronoi grain-boundary representation.
The above expression can also be expressed in discrete terms, considering the accumulation of damage over a finite number of cycles DN.
Fig.2 shows the average damage for the two tested specimens versus the number of load cycles as function of the amplitude of the applied cyclic stress (average damage is defined as surface average of the local damage over all the grains interfaces).
a b c Fig.2: Average damage versus number of cycles at different amplitudes of the applied cyclic stress. a) Convex specimen; b) Non-convex specimen; c) s-N curves for the tested specimens.
Since only meshing of the grain boundaries is required, simplification in data preparation and reduction in the number of DoFs are attained, with consequential computational benefits, appealing in the context of micro/multiscale simulations.

With developing of nanocrystalline materials, there was a hope that superplasticity could be obtained in a number of pure metals.
Recently, it was concluded that superplastic behavior in pure nickel is not related to the presence of sulfur at grain boundaries or a liquid phase at grain boundaries.
Superplasticity is known as strong grain size dependent phenomenon.
The RQ nickel possesses an equiaxed grain structure with a mean grain size of 1-2 µm showing well defined grain boundaries.
Pshenichnyuk Superplasticity and grain boundaries in ultrafine-grained materials.

The recrystallization microstructures consisted of equiaxed grains and a large number of the annealing twins.
Texture evolution during the recrystallization and grain growth.
Then, in the subsequent grain growth stage, the similar preferential growth occurs on the grains with the same orientation as the as-rolled texture since these grains can form the 40˚<111> GBs with the grains in the primary recrystallization texture.
However, they did not find the texture return by the grain growth.
Regarding the texture evolution by the subsequent grain growth, observed was the tendency that the {110} texture components appeared during the grain growth [17].

Fatigue tests with small dog-bone-shaped specimens were conducted under fully reversed axial loading (R = -1) with a constant stress amplitude and were interrupted when the first slip bands occurred and at defined numbers of load cycles, respectively.
Introduction Fatigue crack initiation in ductile materials depends on local plastic deformation and starts either at grain boundaries or at slip bands within a single grain.
Using the long distance microscope allows interrupting the fatigue tests when the first slip bands occurred or at defined numbers of load cycles, respectively (Figure 2).
Figure 2: Damage accumulation in a ferritic grain The surface topography of individual grains with interesting slip band formations was measured afterwards with a white light interferometer.
Even the slight height differences between grains can be illustrated.

The grain size also starts to become small.
It can be seen from Fig.2(a) that the grains is relatively coarse and the effect of grain refinement is not very good.
A large number of Ti and B enrich at the grain boundaries, which makes grain coarsen, dendrite arm spacing widen, and Al2Cu phase unevenly distribute.
However, when the holding temperature is above 740℃, a large number of Ti and B will enrich at grain boundaries.
With the increase of the holding time, a large number of Al3Ti phase and Al2Cu phase occur.

For such nanometre scale grain sizes, the volume fraction of grain boundaries (GBs) becomes significant and the mechanical properties of nc materials exhibit unique properties when compared to their coarser grained counterparts.
With decreasing grain sizes, a transition from dislocation mediated plasticity within the grains, towards a plasticity that is primarily accommodated by the GB structure is to be expected.
Simulating nanocrystalline microstructures There exist a number of techniques to construct computer generated nc systems [6,7].
Fig. 1 displays the two-theta spectrum for two computer generated nc samples, one containing 15 grains with a computed average grain size of 12 nm and another containing 125 grains with a computed average grain size of 5 nm [14].
More recently, collective processes such as cooperative grain boundary sliding via the formation of shear planes spanning several grains have been observed [17,18].

This method is called the templated grain growth (TGG) method.
Therefore, the origin of the splitting is related to the template grains since the increased intensity of these peaks is based primarily on the diffraction from the oriented grains [9].
This kind of grain boundary is called “flat” grain boundary [8].
Therefore, the flat grains contribute the evolution of grain oriented growth.
Increases in the number and size of grains with flat boundaries are directly related to an increase in the texture fraction.

In order to optimize performance in use, an austenitic grain size of 5 or finer is now expected in most cases, with a maximum of 10 percent of individual grains of sizes 3 and 4 partially permissible [2].
This requirement means that fine grained steels with appropriate fine grain stability have to be used [3].
Table 1: Chemical composition of investigated case hardening steels, mass contents in % For heat B, which largely complies with requirements at that time except as regards titanium content, it was shown in numerous grain growth trials that fine grain stability can be reliably achieved up to 1050 °C with a holding time of 25 hours, provided that the tolerance range with 5 percent of grains with the ASTM number 3 and 4 can be exploited.
Table 2 summarizes the coarse grain fractions observed, i.e. grains with a coarseness of ASTM number 4 and coarser.
Table 2: Comparison of grain growth behaviour of heats A (conventional case hardening steel) and B (microalloy case hardening steel); the fraction of grains with an ASTM grain number of 4 or coarser is shown in % Heats A and B are identical in terms of their production paths and the dimensions produced as forged steel bar, so that the alloy typical fine grain stability can be significantly increased in this case by the microalloying elements, both in laboratory and industrially produced case hardening steels.

In a number of studies [4,15–18], twinning was observed at a fist stage of nucleation and continued to develop during the grain growth until the completion of recrystallization.
The number of Σ3-twin boundaries increased greatly (Fig. 3 g-m) to the end of the recrystallization.
The number of special boundaries Σ3 decreased insignificantly and it was due to HAGB between the grains, while the Brandon criterion decreased 5 times.
The role of special boundaries having a large number of coincident sites during recrystallization of FCC metals is described in [6].
Thompson, A comparison of grain boundary evolution during grain growth in fcc metals, Acta Mater. 61 (2013) 3936–3944.

Research shows that the addition of rare earth elements to gold can refine the grains.
The oxides are dissolved out on the grains boundaries during annealing and inhibit the growth of the grains, therefore improving the strength of pure gold[7].
It was approximately directly proportional to the ratio of the numbers of gold and solute atoms at a particular weight percentage.
They increased the undercooling of metals on the crystallisation frontier, the nucleation rate at any given time, and the number of grains formed during solidification.
Owing to the deformation strengthening being primarily caused by the obstacles posed by the grain boundaries to dislocation slip, the small grain size and large amount of grains boundaries in modified pure gold intensified the hardening effect.