A novel method to measure the residual stress in a corrosion film formed on metallic substrates

Abstract

This paper theoretically proposed a series of formulae for a novel tensile testing method to extract the residual stress in the surface film on metallic substrates. Finite element calculations were conducted to verify the accuracy and reliability of the proposed formulae. From the tensile stress–strain curves of metallic substrates with and without a surface film, one can evaluate the residual stress in the film using these formulae. A tarnish film on a brass substrate formed after immersion in Mattsson’s solution was tested to demonstrate these methods, and the obtained residual stress showed a low difference below 6.8%.

Introduction

Residual stress in a film is a key characteristic related to its mechanical properties. Many techniques have been proposed to measure the residual stress in films by researchers for over a century, such as X-ray or electron diffraction techniques [1], [2], [3] and beam bending methods [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21].

Corrosion product film-induced stress and the residual stress in films deposited by electrolysis are important in the corrosion research and the electrolysis industry. However, the X-ray diffraction technique is not suitable to measure the residual stress in the corrosion product film due to the amorphous nature. The beam bending method is widely used to measure the stress in the corrosion product film [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15] or electrolysis layer [16], [17], [18], [19], [20], [21] on a metal substrate, based on the formula:

$$\sigma =\frac{{\mathit{Et}}^2\delta }{3(1-v^2)L^{2}d}$$

where δ is the deflection at the free end of the foil, E and ν are the Young’s modulus and Poisson’s ratio of the metal substrate, L and t are the length and thickness of the substrate and d is the thickness of the film layer where the stress is generated.

The beam bending method was first proposed by Stoney [16] to measure the stress in metallic films deposited by electrolysis. It has been widely used to determine the stress in films formed on metallic materials during the anodic oxidation [4], [5], [6], [7], [8], [9], [10], [11] and stress corrosion cracking [12], [13], [14], [15] processes. However, mechanical assumptions and geometric restrictions must be taken into account before the beam bending method is applied. Eq. (1) is only valid for a film with thickness much smaller than the substrate; typically a thickness ratio of 1/20 is acceptable [21]. Additionally, the length-to-width ratio has to be as large as possible so that the influence of transverse deformation can be neglected [22].

In using the beam bending method, a metallic strip specimen is coated on one side with a lacquer to make that side inert. One end of the strip is fixed, and a small mirror is attached to the free end. When the uncoated side of the strip specimen is exposed to the solution, a film is formed on the uncoated surface and a stress is generated in the film that causes the strip to bend and the free end to move. By measuring the deflection of the free end of the strip using a laser beam, the stress in the film can be extracted using Eq. (1). However, in practice, the beam bending method is actually quite troublesome. Experimental error is introduced into the measured stress that causes significant scatter due to the uncontrolled lacquer characterization (such as the thickness and the mechanical properties of the lacquer) on the inert side, and the reflection of the laser beam.

The flow stress in metallic materials is only dependent on plastic strain. If a metallic strip is loaded above its yield stress ${\sigma }_{\text{Y}}$, the inter-atomic bonds stretch. If the load is then removed, the inter-atomic bonds recover to their initial state and any plastic strain (${\sigma }_{\text{pl}}$) remains, as shown in Fig. 1. Prior to unloading, the total strain for the flow stress ${\sigma }_{\text{f}}$ is ${\epsilon }_{\text{f}}={\epsilon }_{\text{pl}}+{\epsilon }_{\text{el}}$ (${\epsilon }_{\text{el}}={\sigma }_{\text{f}}/E\text{,}$ E is Young’s modulus). When the specimen is reloaded, the dislocation generation and movement does not occur again until the applied stress reaches the flow stress ${\sigma }_{\text{f}}$ prior to unloading. During repetitive loading and unloading, a stress–strain curve is created similarly, as shown in Fig. 1a.

When a film forms on a metallic substrate, a residual stress ${\sigma }_{\text{r}}^{\text{film}}$ is generated in the film. According to the force balance, a stress ${\sigma }_{\text{b}}^{\text{sub}}$ with the opposite sign will be generated within the substrate. When the metallic substrate is placed in tension, the applied stress ${\sigma }_{\text{A}}$, with a balance stress${\sigma }_{\text{b}}^{\text{sub}}$, in the substrate act together to deform the substrate. The stress–strain curve changes compared to the substrate without surface film, as shown in Fig. 1b. Based on the distinguishing characteristics of the stress–strain curves of the substrate with and without the surface film, the residual stress in the film can be extracted.

The objective of this paper is to examine a novel method to measure the residual stress in the film formed on a metallic substrate using tensile tests. A theoretic analysis formula relating the yield and the flow stress in the metallic substrate with and without a surface film and the residual stress in the surface film is derived first. A finite element method (FEM) was used to check the accuracy and reliability of the proposed method. A tarnish film formed on a brass substrate by immersing in Mattsson’s solution was tested to demonstrate the proposed method. The residual stress in the film was extracted from the experimental stress–strain curves of the substrate with and without the tarnish film.