Characteristics of surface roughening during plane strain compression of polycrystalline iron

Shimizu, Ichiro; Abe, Takeji; Nosho, Takayoshi; Wakayama, Masahiro

doi:10.1007/bf03026427

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…We further assume conservation of the area of the free surface, i.e., as the slab is compressed, the surface concertinas between stress concentrators. (Qualitatively similar roughening behavior has been observed for polycrystalline metal under compressive plane strain [39].) Setting the lattice constant s equal to the largest lengthscale over which shear strain is constant in this model, namely λ d /2, , we then find c = 1− (1 + K −1 c ) −1/2 = 38% (mean-field theory) and = 30% (renormalization group), which bracket 33%.…”

Section: Rsupporting

confidence: 76%

Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition

Engstrom

Schwarz

2017

EPL

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Harnessing a model from composite materials science, we show how point-like cusped surface features arise as quasi-particle excitations, termed "ghost fibers", on the surface of a homogeneous soft elastic material. These deformations appear above a critical compressive strain at which ghost fiber dipoles unbind, analogous to vortices in the Kosterlitz-Thouless transition. Finite-length creases can be described in the same framework. Our predictions for crease surface profiles and onset strain agree with previous experiments and simulations, and further experimental tests are proposed.PACS numbers: 46.35.+z, 62.20.mq, 68.35.Rh, 82.60.Nh, 87.15.Zg Cusped inward folds known as creases form on compressed surfaces of a variety of soft elastic materials [1], including natural rubber [2,3], polymer gels [4-6], silicone elastomers [7][8][9][10][11][12], starchy foods [13,14], and the developing mammalian brain [11,12,15,16]. In the latter context, creases are called "sulci". Unlike the long-wavelength buckling of a compressed beam, or the smooth sinusoidal wrinkles observed on the skin of drying fruit or a tensioned elastic sheet [17][18][19], creases are sharply localized in both their elastic deformation and stresses, thereby defying a linear perturbation analysis [3,7,13,20,21]. Owing to this difficulty, numerical minimization of a nonlinear neo-Hookean energy functional has become the standard theoretical tool for investigating the onset of creases [7, 11-13, 15, 20-22]. A central claim in much of this work is that creasing is a fundamentally new, nonlinear instability with no scale [20,21]. Experimental work has also studied the growth of pre-existing long creases, describing these behaviors in analogy to crack propagation [8,9].Here we develop a new quasi-particle framework for shear stress focusing in surface-compressed solids, assuming planar geometry and neglecting surface tension. We apply our theory to the creasing instability, obtaining a markedly different picture than [20,21]. We find evidence that (i) creasing onset maps to the Kosterlitz-Thouless (KT) transition [23], (ii) nonlinear elasticity is needed only within a small region analogous to a vortex core, and (iii) compression-induced shear strain fluctuations set the fundamental, microscopic lengthscale in the problem. Our theory makes contact with experimental and simulation results on critical strain, surface profiles, and crease patterns. In particular, we obtain a universal critical compressive plane strain above which creases emerge, in reasonable agreement with the measured value of 35% [5,13,21]. Finally, the theory points to a set of minimal physical ingredients for creasing, and suggests a possible unification with ridging (formation of localized surface protrusions) [24], and dimple crystallization [25,26].Our point of departure from prior work is to consider a distinct regime of zero-length creases, qualitatively similar to those observed in [6][7][8], immediately upon nucleation, and those in [15], as the critical point is approached f...

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Section: Rsupporting

confidence: 76%

Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition

Engstrom

Schwarz

2017

EPL

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“…Free surface of polycrystalline metal becomes roughened after plastic deformation. It is known that the surface roughening is closely related to the inhomogeneity of polycrystalline metals, that is, to the inhomogeneous plastic deformation of respective grains [1][2][3][4][5][6] as well as that in the grains [5][6][7][8][9][10]. Therefore, the experimental study of the surface roughening is also important for the understanding of microscopic deformation behavior of polycrystalline metals.…”

Section: Introductionmentioning

confidence: 99%

Observation of Microscopic Plastic Deformation of Polycrystalline Aluminum during Uniaxial Tension by Confocal Laser-Scanning Microscope

Song

Abe

Shimizu

et al. 2004

KEM

Self Cite

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Microscopic plastic deformation behavior of aluminum sheet during uniaxial tension is experimentally investigated by a confocal laser-scanning microscope. The surface roughening is closely related to the inhomogeneity of polycrystalline metals, that is, to the inhomogeneous plastic deformation of respective grains. Image measuring method of rigid rotation of grain is proposed. It is shown that the averaged grain rotation on the surface plane is much less than the averaged grain rotation out of the surface plane. The averaged grain rotation, the grain-area strain and the mean size strain and the standard deviations of these parameters increase statistically in proportion to the applied strain. The grain rotation in the material is less than that on the surface, thus it is considered that deformation inhomogeneity of grains in the material is less than that of grains on the surface of the material. This fact may indicate that the surface roughness is mainly affected by inhomogeneous deformation of the surface layer. Discussions are made on the grain rotation, the inhomogeneous deformation of the grains and the free surface roughening mechanism.

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Study of Microtopography of Free Surface of if-Steel at the Uniaxial Stretching

BELOV,

GUBAREV,

KRIVKO

et al. 2021

Černaâ metallurgiâ. Bûlletenʹ naučno-tehničeskoj informacii

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Study of the process of final microtopography of automobile-body sheet surface forming revealed increase of roughness of free surface of sheet at its uniaxial deformation. A necessity to account this factor was noted, since the regulation ranges of microtopography parameters of some kinds of sheet products are narrow. Results of the study of variation of microtopography surface of automobile-body sheet of IF-steel depending on grain size and value of uniaxial deformation presented. It was shown that with the growth of ε, a complicated character of forming of free surface microtopography at various scale levels is observed. Amplitude values (Ra, Rq) and step (Rрc) parameters increase in a nonlinear way when ε grows for high frequency component of microtopography. While ε grows, on the surface of IF steel the grains form structural elements of deformation (SED). The step parameters of SED increase while ε grows slightly, whereas the amplitude parameters of SED show considerable growth. Stages of variation of surface microtopography of IF-steel at uniaxial stretching considered. It was shown that at early stages of deformation, intensive formation of ledges of micro-asperity of rough layer and forming of SED boundaries on the surface takes place. During next stages of deformation, the process of spatial decomposition of the roughness profile asperities at the constant spatial parameters of SED takes place. The intensity of growth of the rough layer roughness heights decreases and that of growth of height sizes of SED increases. At the stages close to destruction, the roughness profile is becoming even and the amplitude characteristics are increasing sharply. The amplitude characteristics of SED profile Raгарм considerably exceed the analogue characteristics of the roughness profile Raслуч.The results of the study should be used to take into consideration formation of free surface microtopography during production of cold-rolled sheet.

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Characteristics of surface roughening during plane strain compression of polycrystalline iron

Cited by 3 publications

References 8 publications

Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition

Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition

Observation of Microscopic Plastic Deformation of Polycrystalline Aluminum during Uniaxial Tension by Confocal Laser-Scanning Microscope

Study of Microtopography of Free Surface of if-Steel at the Uniaxial Stretching

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