Extensions of the Stoney formula for substrate curvature to configurations with thin substrates or large deformations

Freund, L. B.; Floro, J. A.; Chason, E.

doi:10.1063/1.123722

Cited by 286 publications

(216 citation statements)

References 11 publications

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“…Similar to deformation of a substrate, in-planes stresses can be introduced in a coating due to a mismatch in thermal expansion coefficients between the polymer and the metal substrate. Thus in-plane residual stresses of thermal origin were measured with the curvature based techniques [8][9][10][11], double cantilever test [2,[12][13][14] and other less common experimental methods [15][16][17]. High compressive stresses are also found in coatings deposited on various substrates.…”

Section: E-mail Address: Afedorov@rugnl (Av Fedorov)mentioning

confidence: 99%

Degradation and recovery of adhesion properties of deformed metal–polymer interfaces studied by laser induced delamination

Федоров¹,

Tijum²,

Vellinga³

et al. 2007

Progress in Organic Coatings

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Degradation and recovery of adhesion properties of deformed metal-polymer interfaces studied by laser induced delamination Fedorov, A. V.; van Tijum, R.; Vellinga, W. -P.; De Hosson, J. Th. M. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractAdhesion properties of polymer coatings on metals are of great interest in various industrial applications, including packaging of food and drinks. Particular interest is focused on polymer-metal interfaces that are subjected to significant deformations during manufacturing process. In this work steel samples laminated with polyethylene terephthalate (PET) were subjected to uniaxial tensile deformations followed by annealing treatments. The measurements have demonstrated degradation of adhesion of the metal-polymer interface as the strain introduced by the deformation increased. Moreover, it was observed that within the geometry used in the experiments tensile deformations of the metal substrate introduced in-plane compressive stresses in the bulk of the coating. After applying a thermal treatment restoration of the adhesion has been achieved.Laser induced delamination technique was used to monitor the adhesion properties. In this technique a coating is subjected to a series of infrared laser pulses with a stepwise increase of intensity. Upon increasing the laser pulse intensity, the pressure which is formed inside the blisters reaches a critical value, resulting in further delamination of the coating. To process the experimental data an elastic model was developed. From the analysis of the experimental data the critical stresses required for the delamination and the practical work of adhesion are derived. The model accounts for the compressive in-plane stress present in the coating of the deformed samples.

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Section: E-mail Address: Afedorov@rugnl (Av Fedorov)mentioning

confidence: 99%

Degradation and recovery of adhesion properties of deformed metal–polymer interfaces studied by laser induced delamination

Федоров¹,

Tijum²,

Vellinga³

et al. 2007

Progress in Organic Coatings

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show abstract

“…[7][8][9] Freund et al also noted that the assumption of a uniform curvature is not valid for large nonlinear deformations. 7,9 The validity of the kinematic assumption of a uniform curvature is examined in this paper. Two different models of the film/substrate system are examined and compared.…”

Section: Introductionmentioning

confidence: 99%

“…Stoney's formula has been modified many times for the purpose of evaluating bilayer and multilayer structures with arbitrary layer thickness ratios. [2][3][4][5][6][7][8][9][10][11][12][13] Klein made comments on the accuracy of some modified Stoney formulas mentioned above. 14 The assumption of a uniform curvature is explicitly or implicitly used in the context of bilayer or multilayer structures modeled as either beams or plates.…”

Section: Introductionmentioning

confidence: 99%

“…14 The assumption of a uniform curvature is explicitly or implicitly used in the context of bilayer or multilayer structures modeled as either beams or plates. [2][3][4][5][6][7][8][9][10][11][12][13]15,16 Among these studies, Freund et al, in particular, presented an excellent analysis of the film/substrate bilayer and multilayer deflection due to lattice mismatch. [7][8][9] Freund et al also noted that the assumption of a uniform curvature is not valid for large nonlinear deformations.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Zhao

2006

Journal of Applied Physics

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In addition to the layer thickness and effective Young's modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not ͑fully͒ included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney's formula and modified formulas is presented.

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“…Once deposited, the curvature radius of samples is measured again and stress is calculated at the interface using Stoney formula [10]: (1) Where R is the curvature radius after copper deposition; R 0 is the initial curvature; E s the substrate Young modulus; s the substrate Poisson's ratio; d s the substrate thickness and d f film thickness. We have to note that this expression is an approximation, whose validity is widely accepted however, under certain assumptions [11][12].…”

Section: Characterization and Measurementsmentioning

confidence: 99%

Stresses evolution at high temperature (200°C) on the interface of thin films in magnetic components

Doumit

Danoumbé

Capraro

et al. 2014

EPJ Web of Conferences

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Abstract.In the field of electronics, the increase of operating temperatures is a major industrial and scientific challenge because it allows reducing mass and volume of components especially in the aeronautic domain. So minimizing our components reduce masses and the use of cooling systems. For that, the behaviours and interface stresses of our components (in particular magnetic inductors and transformers) that are constituted of one magnetic layer (YIG) or an alumina substrate (Al 2 O 3 ) representing the substrate and a thin copper film are studied at high temperature (200°C). COMSOL Multiphysics is used to simulate our work and to validate our measurements results. In this paper, we will present stresses results according to the geometrical copper parameters necessary for the component fabrication. Results show that stresses increase with temperature and copper's thickness while remaining always lower than 200MPa which is the rupture stress value.

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Extensions of the Stoney formula for substrate curvature to configurations with thin substrates or large deformations

Cited by 286 publications

References 11 publications

Degradation and recovery of adhesion properties of deformed metal–polymer interfaces studied by laser induced delamination

Degradation and recovery of adhesion properties of deformed metal–polymer interfaces studied by laser induced delamination

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

Stresses evolution at high temperature (200°C) on the interface of thin films in magnetic components

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