Applicability range of Stoney’s formula and modified formulas for a film/substrate bilayer

Zhang, Yin; Zhao, Ya‐Pu

doi:10.1063/1.2178400

Cited by 42 publications

(32 citation statements)

References 29 publications

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“…The exact nonlinear curvature definition is κ = w xx /(1 + w 2 x ) 3/2 . Curvature κ is directly related to the strain of bending beam, and thus system potential energy [36][37][38]. For the structures of tension-dominant nonlinearity and large aspect ratio, such linear curvature ap-proximation is sufficiently accurate [45] and this curvatureinduced nonlinearity in the structures of tension-dominant nonlinearity is also shown negligible in our results.…”

Section: Tension-dominant Nonlinearitysupporting

confidence: 52%

“…The built-in strain [16], fabrication process [18,36], residual stress [37] and surface stress [38] dx is the tension due to (nonlinear) midplane stretching [39]. The beam is modeled as the EulerBernoulli beam which requires the relatively large aspect ratio of length to thickness/radius and the shear effects are thus neglected.…”

Section: Tension-dominant Nonlinearitymentioning

confidence: 99%

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Nonlinear dynamic response of beam and its application in nanomechanical resonator

2011

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Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity The project was supported by the National Natural Science Foundation of China (10721202 and 11023001) can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.

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Section: Tension-dominant Nonlinearitysupporting

confidence: 52%

Section: Tension-dominant Nonlinearitymentioning

confidence: 99%

Nonlinear dynamic response of beam and its application in nanomechanical resonator

2011

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“…Stoney's formula [68][69][70][71][72][73] was extensively used to describe the residual stress of the film-substrate system produced by thermal change/phase transition/shrinkage of devices during the preparation and post-treatment process. The formula is the theoretical basis of curvature-based technique to evaluate the interface stress status in the film-substrate system.…”

Section: Stoney's Formulamentioning

confidence: 99%

Mechanical Analyses and Structural Design Requirements for Flexible Energy Storage Devices

Mao

Meng

Ahmad

et al. 2017

Advanced Energy Materials

192

146

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degree of the entire electronic systems. In the integrated flexible electronic system, energy storage devices [14,[16][17][18][19][20] play important roles in connecting the preceding energy harvesting devices and the following energy utilization devices (Figure 1). Rechargeable secondary batteries and supercapacitors (SCs) are two typical energy storage devices. [21] Several excellent review papers [21][22][23][24][25][26] reported significant progresses achieved in flexible lithium-ion batteries (LIBs) and SCs by taking advantage of novel electrode materials, current collectors, and solid-state electrolytes. The application areas and lifetime of flexible power sources strongly depend on their mechanical deformation tolerance and the electrical property retention under deformation. Qualified flexible power sources should be able to endure high strain induced by external mechanical deformation, such as bending, compressing, stretching, folding, and twisting, while maintaining their electrochemical performance stability and structural integrity. Therefore, the mechanical reliability assessment and electrical property analysis of flexible devices need to be given much attention for future application.Tolerance in bending into a certain curvature is the major mechanical deformation characteristic of flexible energy storage devices. Thus far, several bending characterization parameters and various mechanical methods have been proposed to evaluate the quality and failure modes of the said devices by investigating their bending deformation status and received strain. Some of these mechanical metrologies were derived from the early research on flexible semiconductor devices of micro-electromechanical system (MEMS) [27,28] and TFTs. [29] However, comparing those numerous measurement data with one another is difficult because of the various theories and methods adopted by different research groups and the lack of unified assessment criteria. [26] The flexibility of flexible devices is generally realized not only by use of intuitive soft electrode materials but also by optimizing their mechanical structural design. [25] Detailed analysis on bending mechanics combining experimental and theoretical results provide not only reliable test methods to describe the bending state but also guidance for configuration design of devices against mechanical failure.The current review emphasizes on three main points: (1) key parameters that characterize the bending level of flexible energy storage devices, such as bending radius, bending Flexible energy storage devices with excellent mechanical deformation performance are highly required to improve the integration degree of flexible electronics. Unlike those of traditional power sources, the mechanical reliability of flexible energy storage devices, including electrical performance retention and deformation endurance, has received much attention. To provide the guideline for the construction design of devices, the strain distribution and failure modes in the entire architecture should b...

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“…In this paper the immovable edge constraint is imposed, which also implicitly indicates that the film edges are not delaminated. The boundary conditions and the film length also play important roles of the film/substrate bilayer deflection induced by the interfacial stress [22] , which are also incorporated in this model. It is noticed that in Huang and Suo's perturbation solutions [18,19] periodic boundary conditions are implicitly assumed.…”

Section: Introductionmentioning

confidence: 99%

Local bending of thin film on viscous layer

Yin

Liu

2010

Acta Mechanica Solida Sinica

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Effects of deposition layer position and number/density on local bending of a thin film are systematically investigated. Because the deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the socalled local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection case. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.

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Applicability range of Stoney’s formula and modified formulas for a film/substrate bilayer

Cited by 42 publications

References 29 publications

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Mechanical Analyses and Structural Design Requirements for Flexible Energy Storage Devices

Local bending of thin film on viscous layer

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