Influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors

A mathematical model for failure prediction and reliability assessment of coating-substrate system is developed based on a multidisciplinary approach. Two models for diffusion and bending of bi-layer cantilever beam have been designed separately based on the concepts of material science and solid mechanics respectively. Then, these two models are integrated to design an equation for debonding driving force under mesomechanics concepts. Mesomechanics seeks to apply the concepts of solid mechanics to microstructural constituent of materials such as coatings. This research takes the concepts of mesomechanics to the next level in order to predict the performance and assess the reliability of coatings based on the measure of debonding driving force. The effects of two parameters i.e. interface roughness and coating thickness on debonding driving force have been analysed using finite difference method. Critical/ threshold value of debonding driving force is calculated which defines the point of failure of coating-substrate system and can be used for failure prediction and reliability assessment by defining three conditions of performance i.e. safe, critical and fail. Results reveal that debonding driving force decreases with an increase in interface roughness and coating thickness. However, this is subject to condition that the material properties of coating such as diffusivity should not increase and Young's modulus should not decrease with an increase in the interface roughness and coating thickness. The model is based on the observations recorded from experimentation. These experiments are performed to understand the behaviour of debonding driving force with the variation in interface roughness and coating thickness.

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“…The equations are also analogous to equations derived by Xuan et al [56] for deformation of thin sensor films.…”

Section: Bending Model Of Bi-layered Cantilever -Application Of Solidmentioning

confidence: 75%

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

Nazir

Khan

Stokes

2015

Journal of Adhesion Science and Technology

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“…The concentration of diffusing species is controlled by the residual stress in the coating. The residual stress can either block the pathway of corrosive species (due to compressive behaviour when ∆T > 0) by constricting the aperture of pre-existing micro-cracks or can open the pathway of corrosive species (due to tensile behaviour when ∆T < 0) by exposing/opening the aperture of coating micro-cracks [32,34,35,58]. For the coating substrate system with pre-existing coating micro-cracks, the size of the micro-crack aperture is a linear function of residual stress due to mismatch strain between the coating and substrate and the bending moment introduced by diffusion.…”

Section: Experimental Observationsmentioning

confidence: 99%

“…⍺ c > ⍺ s , the positive temperature diversification (∆T > 0) from its fabrication temperature will induce compressive residual stress in the coating [9,[32][33][34][35]. The pre-exiting micro-cracks in coating will gradually contract with increasing compressive residual stress on temperature rise.…”

Section: Introductionmentioning

confidence: 99%

Analysing the coupled effects of compressive and diffusion induced stresses on the nucleation and propagation of circular coating blisters in the presence of micro-cracks

Nazir

Khan

Stokes

2016

Engineering Failure Analysis

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This paper presents the delamination of coating with micro-cracks under compressive residual stress coupled with diffusion induced stress. Micro-cracks in coating provide a passage for corrosive species towards the coating-substrate interface which in turn produces diffusion induced stress in the coating. Micro-cracks contract gradually with increasing compressive residual stress in coating due to thermal expansion mismatch which blocks the species diffusion towards the interface. This behaviour reduces the diffusion induced stress in the coating while the compressive residual stress increases. With further increase in compressive residual stress, micro-cracks reach to the point, where they cannot be constricted any further and a high compressive residual stress causes the coating to buckle away from the substrate resulting in delamination and therefore initiating blistering. Blistering causes the contracted micro-cracks to wide open again which increases diffusion induced stress along with high compressive residual stress. The high resultant stress in coating causes the blister to propagate in an axis-symmetric circular pattern. A two-part theoretical approach has been utilised coupling the thermodynamic concepts with the mechanics concepts. The thermodynamic concepts involve the corrosive species transportation through micro-cracks under increasing compression, eventually causing blistering, while the fracture mechanics concepts are used to treat the blister growth as circular defect propagation. The influences of moduli ratio, thickness ratio, thermal mismatch ratio, poisson's ratio and interface roughness on blister growth are discussed. Experiment is reported for blistering to allow visualisation of interface and to permit coupled (diffusion and residual) stresses in the coating over a full range of interest. The predictions from model show excellent, quantitative agreement with the experimental results.

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“…The driving force for diffusing species is the chemical potential of that species, so Equation (2) can now be modified using Maxwell-type relation, derivable from expression of Helmholtz free energy as [47]:…”

Section: Diffusion and Ionic Transport Modelmentioning

confidence: 99%

A unified mathematical modelling and simulation for cathodic blistering mechanism incorporating diffusion and fracture mechanics concepts

Nazir

Khan

Stokes

2015

Journal of Adhesion Science and Technology

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A novel mathematical model has been developed to understand the mechanism of blister initiation and propagation. The model employs a two-part theoretical approach encompassing the debondment of a coating film from the substrate, coupled with the design components incorporating diffusion and fracture mechanics, where the latter is derived from equi-biaxial tensile loading. Integrating the two components, a comprehensive mathematical design for the propagation of blister boundaries based on specific toughness functions and mode adjustment parameters has been developed. This approach provided a reliable and efficient prediction method for blister growth rate and mechanisms. The model provided a foundation for holistic design based on diffusion and mechanic components to enable better understanding of the debondment of thin elastic films bonded to a metallic substrate.

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Influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors

Cited by 20 publications

References 34 publications

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

Analysing the coupled effects of compressive and diffusion induced stresses on the nucleation and propagation of circular coating blisters in the presence of micro-cracks

A unified mathematical modelling and simulation for cathodic blistering mechanism incorporating diffusion and fracture mechanics concepts

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