PSI - Issue 43

Stanislav Žák et al. / Procedia Structural Integrity 43 (2023) 23 – 28 Stanislav Žák and Alice Lassnig / Structural Integrity Pr ocedia 00 (2022) 000 – 000

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1. Introduction The use of thin films and layers application spans through numerous scientific and engineering fields, for example in fabrication and use of protective coatings, medical applications (wearable sensors) and modern, flexible electronics (see e.g. works by (Bang et al., 2021; Htwe and Mariatti, 2022; Oldroyd and Malliaras, 2022)). Such different application fields are connected with the use of micro- or nano-scale thin films and substrates consisting of largely different materials, introducing a high amount of elastic materials properties mismatch on the interfaces between films and substrates. A prime example of such elastically mismatched system can be a bio-sensor plate or bendable display, where to achieve desired mechanical properties of the whole device, a combination of a compliant (usually a polymer) substrate material and a metallic thin film is used. Moreover, such metallic-polymer interfaces are usually stacked in numerous multi-layers systems. The elastic material properties mismatch can be described by the Dundurs parameters α and β (Beom, 1995; Dundurs, 1967) with the thin film and substrate shear moduli μ 1 and μ 2 and their Poisson’s rati os ν 1 and ν 2 , respectively (for detailed description of the parameters α and β the reader is referred to the original paper). The modern applications can consist of a wide range of materials leading to a small elastic material properties mismatch (e.g. MgO coatings on Ni with α = 0.15 and β = -0.04) or a large elastic material properties mismatch (e.g. Au thin film on polyimide substrate for flexible electronics with α = 0.81 and β = 0.14). While the differences between two adhered materials can be the source of several erroneous effects decreasing the reliability of the whole device (e.g. differences between coefficients of thermal expansion, ductile vs. brittle materials or diffusion between the two materials), this work aims at investigating the elastic mismatch influence on the adhesion of the thin film on the substrate. The interface stability and small-scale loading of any device can affect the interface between functional thin films and the substrate as a supporting structure, causing the whole device to fail. Therefore, a precise assessment of the adhesion energy of the thin film is needed. A widely used method is the spontaneous buckling-induced delamination by (Hutchinson and Suo, 1992). The 30-years old model assumes the buckles spontaneously formed under the compressive residual stress σ in the film and with use of basic Euler’s beam theory (Euler, 1952) to evaluate adhesion energy Γ and the mode-mixity angle Ψ using the film material properties and thickness h together with the buckle height δ and width 2 b :

( ) ( ) ( 2 1 1 h  −

2

2

E h

b      



) (     −  +

)

,

3 with

  =

c 

=

(1)

1

(

)

c

c

2

2

12 1

E

−

1 

1

3





( ) 

( ) 

( ) ( ) i i Kh Kh  

4 cos

sin

+

Im Re

h

( )

tan

.

 =

=

(2)

3





( ) 

( ) 

4 sin

cos

−

+

h

Fig. 1. Scheme of the original buckling-induced delamination model by (Hutchinson and Suo, 1992) While the actual value of the adhesion energy Γ in eq. (1) is independent of the substrate material or geometrical properties, the mode-mixity angle describing the ratio between K II and K I stress intensity factors (SIFs) in eq. (2) is influenced by the elastic mismatch in two ways. First of all, for β ≠ 0 a complex SIF consisting of both modes I and II contribution and oscillatory singularity with parameter ε have to be used:

1 1 2 1     ln

  

− +

 

and

.

(3)

K K iK = +



=

I

II