Size effect in mesoscopic epitaxial ferroelectric structures: Increase of piezoelectric response with decreasing feature size

S. Bühlmann; B. Dwir; J. Baborowski; P. Muralt

doi:10.1063/1.1475369

Size-Effect in Mesoscopic Epitaxial Ferroelectric Structures: Increase of Piezoelectric Response with Decreasing Feature-Size

Integrated Ferroelectrics ◽

10.1080/743817662 ◽

2002 ◽

Vol 50 (1) ◽

pp. 261-267 ◽

Cited By ~ 7

Author(s):

S. Bühlmann ◽

B. Dwir ◽

J. Baborowski ◽

P. Muralt

Keyword(s):

Size Effect ◽

Piezoelectric Response ◽

Feature Size

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Feature Size Effect on Formability of Multilayer Metal Composite Sheets under Microscale Laser Flexible Forming

Metals ◽

10.3390/met7070275 ◽

2017 ◽

Vol 7 (7) ◽

pp. 275 ◽

Cited By ~ 7

Author(s):

Huixia Liu ◽

Wenhao Zhang ◽

Jenn-Terng Gau ◽

Zongbao Shen ◽

Youjuan Ma ◽

...

Keyword(s):

Size Effect ◽

Metal Composite ◽

Feature Size ◽

Flexible Forming ◽

Multilayer Metal

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FE Analysis of Size Effect on Deformation Behavior of Metal Microtube Considering Surface Roughness in Flaring Test

Materials Science Forum ◽

10.4028/www.scientific.net/msf.623.79 ◽

2009 ◽

Vol 623 ◽

pp. 79-87 ◽

Cited By ~ 1

Author(s):

Mohammad Ali Mirzai ◽

Kenichi Manabe

Keyword(s):

Surface Roughness ◽

Size Effect ◽

Wall Thickness ◽

Size Effects ◽

Fe Analysis ◽

Material Behavior ◽

Test Results ◽

Feature Size ◽

Analysis And Design ◽

Smoothing Process

Reliable test results that show the material characteristics of a micromaterial are necessary for the accurate analysis and design of microforming processes. The size effects in the microforming are predicted to have a significant impact on the material behavior. Two size effects are explored in metallic materials. One is the grain size effect, and the other is the feature/specimen size effect. In this study, the feature size effect on the smoothing process with the consideration of tool surface roughness is investigated numerically for metal microtubes by the flaring test. Stainless-steel (SUS 316L) microtubes with the same outer diameter of 500 μm and different wall thicknesses of 50, 25 and 10 μm were used in the FE analysis to study the feature size effect on the microscale by the flaring test. The surface roughnesses of the inner and outer surfaces of the microtube, as well as the surface asperity of the conical tool, were modeled in the cyclic concave-convex configuration. It is found, in the flaring test with using rough and fine tools, that the smoothing process on the inner surface of the microtube (ISM), as well as the plastic strain in the wall thickness of microtube, is affected owing to the rigidity of the microtube, which decreases as the wall thickness of the microtube decreases. These results suggest that the feature size affects the flaring test results for the metal microtube.

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The Size-Dependent Electromechanical Coupling Response in Circular Micro-Plate due to Flexoelectricity

Journal of Mechanics ◽

10.1017/jmech.2016.104 ◽

2016 ◽

Vol 33 (6) ◽

pp. 873-883 ◽

Cited By ~ 1

Author(s):

X. Ji ◽

A.-Q. Li

Keyword(s):

Size Effect ◽

Natural Frequency ◽

Circular Plate ◽

Electromechanical Coupling ◽

Initial Conditions ◽

Couple Stress Theory ◽

Piezoelectric Response ◽

Induced Voltage ◽

Cylindrical Coordinates ◽

Size Dependent

AbstractFlexoelectricity, the coupling of strain gradient to polarization, enhances the properties of piezoelectric response desirable for advanced MEMS dramatically even in centrosymmetric dielectrics. In this paper, the general formulations of the flexoelectric couple stress theory presented by Hadjesfandiari in orthogonal curvilinear coordinate system are derived, and are then specified for the case of cylindrical coordinates. A size-dependent flexoelectric model of circular plate is established based on the current formulations in cylindrical coordinates. The governing equations, boundary conditions and initial conditions are derived by applying Hamilton's principle. The static bending and free vibration problems of a simply supported axisymmetric circular plate are carried out to illustrate the applicability of the present model. Numerical results reveal that a homogeneous electric field between the up and down surfaces of the circular plate is induced indeed. The generated deflection, induced voltage and natural frequency show obvious size effect, but the size effect is almost diminishing as the thickness of the plate is far greater than the material length scale parameter. As the increase of the flexoelectric coefficient, the induced voltage increases evidently and the generated deflection and the natural frequency increase weakly.

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Size Effects on Formability of Copper Foil in Flexible Micro-Bending Process

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.723.207 ◽

2016 ◽

Vol 723 ◽

pp. 207-213

Author(s):

You Juan Ma ◽

Xiao Wang ◽

Qing Qian ◽

Zong Bao Shen

Keyword(s):

Grain Size ◽

Size Effect ◽

Size Effects ◽

Copper Foil ◽

Testing Machine ◽

Coarse Grained ◽

Feature Size ◽

Fine Grained ◽

Microhardness Distribution ◽

Different Grain Size

The occurrence of size effects in the microforming leads to the uncertainties in process determination and quality control. In this research, a series of experiments were conducted in UTM4104 testing machine to investigate the grain size effect and feature size effect in micro-bending. Different grain size (d), thickness to grain size ratio () and micro-mold feature size (W) were prepared to explore size effects on formability of copper foil. The formability characterized by forming depth, deformation uniformity and surface integrity was discussed. It was found that the normalized forming depth presented a gradually rise and then declined markedly when N value further decreased to 0.79. The ductile fracture mode was observed for all grain-sized workpiece and the corresponding limit forming depth decreased with increasing grain size. Besides, the thickness thinning distribution and microhardness distribution showed the similar variation tendency like M. Both the standard deviation of thickness reduction and the roughed degree of surface topography indicated the worsening deformation uniformity of the foils with a larger grain size. The inhomogeneous plastic flow of material may be the reason to explain the depression near fracture location which is only observed in coarse-grained workpiece. Overall, it is concluded that the fine-grained copper exhibited better formability as the coarse-grained workpiece experienced severe strain incompatibility.

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