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 金属学报 , 1986, Abstract: The fatigue dislocation structure in an alloy ferrite steel was studied by the method of electron diffraction contrast analysis. The dislocation structure features in annealed 12CrMo steel variate after 10~7 cycles under cyclic tensile stresses. The main features of fatigue dislocation structure are dislocation jog, dipole, Ioop, deformation band, tangle and banded dislocation structure. Alloy ferrite grains are broken into blocky-like microstructure regions.
 JIN Nengyun Shanghai Jiaotong University Jin Nengyun 金属学报(英文版) , 1989, Abstract: A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac-cording to this model,cyclic stress-strain responses and saturation dislocation structures of acrystal are associated with the modes and intensities of dislocation interactions between slipsystems active in the crystal; and,hence,may be predicted by the location of its tensile axis inthe crystallographic triangle.This model has successfully explained the different behaviours ofdouble-slip crystals and multi-slip behaviours of some crystals with orientations usually con-sidered as single-slip ones.
 Materials Research , 2001, DOI: 10.1590/S1516-14392001000200008 Abstract: the work hardening of metals subjected to complex processing paths is different from that in monotonic deformation. changes in the deformation mode can promote transients in the strain-hardening rate, leading to anomalous softening or hardening of the material. this paper investigates the influence of strain path changes on the tensile behavior of drawn 0.12% steel rods. annealed or predrawn specimens were submitted to cyclic twisting and then tested in tension. the results show that the cyclic deformation causes changes in the mechanical behavior of the metal, and the effect will depend on the previous "history" of the material. cyclic twisting causes hardening in annealed samples, but leads to softening of the drawn bars. these phenomena are in line with the corresponding substructural aspects.
 Materials Research , 2001, Abstract: The work hardening of metals subjected to complex processing paths is different from that in monotonic deformation. Changes in the deformation mode can promote transients in the strain-hardening rate, leading to anomalous softening or hardening of the material. This paper investigates the influence of strain path changes on the tensile behavior of drawn 0.12% steel rods. Annealed or predrawn specimens were submitted to cyclic twisting and then tested in tension. The results show that the cyclic deformation causes changes in the mechanical behavior of the metal, and the effect will depend on the previous "history" of the material. Cyclic twisting causes hardening in annealed samples, but leads to softening of the drawn bars. These phenomena are in line with the corresponding substructural aspects.
 金属学报(英文版) , 1989, Abstract: Cyclic stress-strain responses and dislocation structure of copper single crystals with varioustensile axes were systematically studied and compared with each other.Experimental resultsreveal that the evolution of microscopic dislocation configurations in a crystal and,accordingly,its macroscopic cyclic behaviours are closely related with its orientation.Re-markable secondary slip has been observed in some crystals with orientations well inside thecrystallographic triangle, which are usually considered as single-slip ones.Their cycliobehaviours and dislocation structures at saturation are similar to those of their neighbouringmulti-slip crystals.These results have constructed the experimental basis for the newly pro-posed dislocation interaction model Jor cyclic deformation of fee crystals,which will be des-cribed in the second part of this article.
 Mathematics , 2011, DOI: 10.1515/form.2011.159 Abstract: In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of products of locally indicable groups, extensions of $\mathbb{Z}^n$ by cyclic groups, and fuchsian groups. We take advantage of the torsion structure of these groups to use appropriate models of the universal space for proper actions which allow us, in turn, to extend some technology defined by Mislin in the case of one-relator groups.
 Jian Wang Mathematics , 2015, Abstract: Let $E$ be an elliptic defined over a number field $K$. Then its Mordell-Weil group $E(K)$ is finitely generated: $E(K)\cong E(K)_{tor}\times\mathbb{Z}^r$. In this paper, we will discuss the cyclic torsion subgroup of elliptic curves over cubic number fields.
 力学学报 , 1992, Abstract: In this paper, the cyclic hardening behavior of 45 # steel and LY-12CZ aluminum alloy under proportional and non-proportional combined loadings of tension and torsion at normal room temperature has been investigated.The experimental results show that the cyclic hardening levels are different for different loading paths. The least is for the pure torsion, while the highest is for the circular path. The authors have especially investigated the effect of different cyclic history on the amplitudes of stabilized stresses.
 金属学报(英文版) , 1989, Abstract: Cyclic deformation in symmetrical push-pull mode was carried out at room temperature in airusing a Schenck hydropuls machine.The total strain amplitude which was kept constant dur-ing the test ranged from ±0.004 to±0.012.The 0.2% offset yield stress σ_(0.2f) in tensionand σ_(0.2r) in compression and peak stress σ were measured from the stress-strain hysteresisloop at various cycles.The Bauschinger strenghth differential factor(BSDF)was then calcu-lated from σ_(0.2f) and σ_(0.2r).The energy loss △E of each cycle was determined fromhysteresis loop areas.These parameters,BSDF,σ and △E,appear to have two distinctivelydifferent stages.The dislocation structures were observed using TEM in specimens deformed cyclically,forvarious cycles.The observation shows that the dislocations pile-up mainly against grainboundaries and there exist large amount of deformation twins.The addition of 0.25 wt-% ni-trogen reduced the stacking fault energy of the alloy significantly.Cross-slip and climb aretherefore rather difficult to occur during the cyclic deformation at room temperature,andwell-defined dislocation cells and walls can only be seen at the final stage of fatigue.
 Matt Clay Mathematics , 2015, Abstract: We provide an upper bound on the $\ell^{2}$-torsion of a free-by-cyclic group, $-\rho^{(2)}(\mathbb{F} \rtimes_{\Phi} \mathbb{Z})$, in terms of a relative train-track representative for $\Phi \in \mathrm{Aut}(\mathbb{F})$. Our result shares features with a theorem of L\"uck-Schick computing the $\ell^{2}$-torsion of the fundamental group of a 3-manifold that fibers over the circle in that it shows that the $\ell^{2}$-torsion is determined by the exponential dynamics of the monodromy. In light of the result of L\"uck-Schick, a special case of our bound is analogous to the bound on the volume of a 3-manifold that fibers over the circle with pseudo-Anosov monodromy by the normalized entropy recently demonstrated by Kojima-McShane.
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