CN103018160A - Flexure testing method and flexure testing device for quantitatively characterizing interface binding property of thin-film material - Google Patents

Abstract

The invention relates to a buckling test method and device for quantitatively characterizing the interfacial bonding properties of thin film materials, and belongs to the technical field of experimental mechanics and material mechanical performance characterization. The invention uses a universal material testing machine to perform axial uniaxial compression on the sample, and records the stress and strain values of the sample, and simultaneously uses a CCD camera to observe the cross section of the sample during the loading process in real time, and records the buckling process in real time The relationship between the coating-substrate stress-strain history and the peeling characteristics is established to characterize the interface bonding performance of the coating-substrate. The CCD camera, monitor, image processing card, computer, data processing card, load sensor and universal material testing machine of the device of the invention are connected in sequence. The invention has the advantages of simple principle, simple sample preparation, clear model, easy operation and the like.

Description

Buckling test method and device for quantitatively characterizing interfacial bonding properties of thin film materials

technical field

The invention relates to a buckling test method and device for quantitatively characterizing the interfacial bonding properties of thin film materials, and belongs to the technical field of experimental mechanics and material mechanical performance characterization.

Background technique

With the rapid development of science and technology, thin film/substrate systems are widely used in surface modification and material science. During the use of thin film materials, due to the differences in microstructure and other aspects of substrate materials, the mechanical load, thermal Under various complex environments such as loading, there will be a mismatch of stress and strain, which will eventually lead to the failure of the thin film coating material. In engineering applications, the typical failure mode of the film/substrate system is: the film or coating peels off from the substrate. Whether the interfacial bonding of the film/substrate system is good or not determines the service life of the material to a large extent, so the characterization of the interfacial bonding performance is of great significance to the practical application of the material.

The characterization of the interfacial bonding performance of the film/substrate material is the basis for studying the failure mechanism of the film interface and preventing its failure. It involves interdisciplinary subjects such as materials, mechanics, and physics. The complexity of the film failure problem, the diversity of failure phenomena, and the unpredictability , making the characterization of the interfacial bonding properties of thin films a recognized difficult problem. Internationally renowned scholars such as Evans, Hutchinson, and Nix have made outstanding contributions in this field. In China, the country has also funded a number of National Natural Science Foundation projects to carry out research work related to thin film interfaces. However, so far, the binding properties of thin films The characterization of is still in the stage of theoretical and experimental exploration. Quantitative characterization of the interfacial bonding properties of thin-film substrate systems is the unanimous goal pursued by many researchers and users. However, due to the diversity of thin-film types and thin-film technologies, efforts to pursue a single characterization parameter and characterization method have not yet shown signs of success. In some national standards, it even has to be recommended to use a simple number of bending times to determine the firmness of the bond between the film and the substrate. This not only makes engineers at a loss, but also makes researchers feel ashamed.

At present, there are more than 200 methods for characterizing the interfacial bonding properties of film/substrate materials, such as tensile method, scratch method, peeling method, indentation method, bulge method, etc., but there is no standard characterization method suitable for each A film/substrate material system. The tensile method is suitable for brittle/ductile and brittle/brittle systems with weak interfaces, and is meaningful only when the interfacial bond strength is less than the bond strength. The indentation method is suitable for brittle film/rigid substrate, brittle film/brittle substrate material system, some theoretical mechanisms, the characterization of interface bonding strength and the influence of various factors on critical load, etc. If these problems cannot be solved well, indentation The application of the trace method will be limited. The exfoliation method is suitable for brittle and ductile films. Although it is intuitive and easy to implement, it is difficult to extract the interfacial crack propagation energy. Although the bulging method can quantitatively measure the interfacial bonding performance of the thin film, its sample preparation is relatively difficult, which increases the difficulty of the experiment. A characterization method is urgently needed to quantitatively characterize the interfacial bonding performance of the film-substrate system.

Contents of the invention

Aiming at the deficiencies of the prior art, the invention provides a buckling test method and device for quantitatively characterizing the interfacial bonding properties of thin film materials.

A buckling test method for quantitatively characterizing the interfacial bonding properties of thin film materials, the specific steps are as follows:

a. prepare the coating sample to be tested by coating, and polish the uncoated surface of the sample until the mirror surface is smooth with sandpaper;

b. Clamp the prepared sample coated with the coating to be tested on the universal material testing machine, and point the CCD camera at the cross section of the sample to be tested, adjust the position and focal length of the CCD camera so that the sample to be tested Form a clear image in the middle of the field of view of the CCD camera;

c. Perform axial uniaxial compression on the sample, and the universal material testing machine records the stress and strain values of the sample in real time. At the same time, the CCD camera performs synchronous real-time observation of the cross-section of the sample during the loading process, and records the buckling process in real time. The critical stress, deflection and peeling characteristics of crack length;

d. Establish the relationship between the coating-substrate stress-strain history and the peeling characteristics to characterize the interface bonding performance of the coating-substrate; the energy release rate G of the interface when the coating buckles can be calculated by the following formula:

$\frac{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G\; G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">G</figure-callout></span><figure-callout\; id="0"\; label="G\; G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">\; </figure-callout>}}{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">G</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h\&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ;</span>$

Wherein E _f is the modulus of elasticity of the coating, the unit is Pa, υ _f is Poisson's ratio, h is the thickness of the coating, the unit is m, G ₀ is the strain energy release rate under the plane strain situation, the unit is J/ m ² , σ ₀ is the stress applied in the coating during the loading process, in Pa, and σ _cr is the critical stress in the coating when the coating begins to buckle, in Pa;

The corresponding phase angle ψ is:

$\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}$

where ω is the material mismatch phase angle in °, and ξ is a dimensionless function of the buckling deflection. ω is related to the mismatch parameters α and β of the coating and the base material. According to the different values of α and β, the value of ω also changes accordingly. See the table below for details of the specific values:

Table 1 ω and α, β relationship table

α, β, ξ, σ _cr are calculated with the following formula:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}$

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="HDA00002558354700021.png"\; state="\{\{state\}\}">f</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA00002558354700021.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 12</span>}}\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

分别为平面应变情况下涂镀层和基底的弹性模量，单位为Pa，υ_f,υ_s分别为涂镀层和基底的泊松比，μ_f,μ_s分别为涂镀层和基底的剪切模量，单位为Pa，E_f,E_s分别为涂镀层和基底的弹性模量，单位为Pa，ξ为屈曲挠度的一个无量纲化函数，ω_max为试样涂镀层屈曲中心点的挠度，单位为m，h为涂镀层的厚度，单位为m，σ₀为加载过程中涂镀层内的应力，单位为Pa，σ_cr为涂镀层刚开始发生屈曲时的临界应力，单位为Pa，b为屈曲时的裂纹半长，单位为m。in

are the elastic modulus of the coating and the substrate under the plane strain condition respectively, and the unit is Pa, υ _f , υ _s are the Poisson’s ratios of the coating and the substrate respectively, μ _f , μ _s are the shear moduli of the coating and the substrate respectively The unit is Pa, E _f , E _s are the elastic modulus of the coating and the substrate respectively, the unit is Pa, ξ is a dimensionless function of the buckling deflection, ω _max is the deflection of the buckling center point of the sample coating, The unit is m, h is the thickness of the coating, the unit is m, σ ₀ is the stress in the coating during the loading process, the unit is Pa, σ _cr is the critical stress when the coating just begins to buckle, the unit is Pa, b is the half-length of the crack during buckling, in m.

The base length of the coating sample to be tested is 10 mm, the width is 5 mm, and the thickness is 5 mm.

The photographing frequency of the CCD camera is 1-2 seconds/frame.

The loading mode of the universal material testing machine is load loading, the loading rate is 3000N/min, and the maximum compression displacement is 1~2mm.

A buckling test device for quantitatively characterizing the interfacial bonding properties of thin film materials, in which a CCD camera, a monitor, an image processing card, a computer, a data processing card, a load sensor and a universal material testing machine are connected in sequence.

The photographing frequency of the CCD camera is 1-2 seconds/frame.

The loading mode of the universal material testing machine is load loading, the loading rate is 3000N/min, and the maximum compression displacement is 1~2mm.

The beneficial effects of the present invention are:

In the present invention, the universal material testing machine is used to perform axial uniaxial compression on the sample, so that the coating layer buckles at the weak point of the interface, and at the same time, the cross-section of the sample during the loading process is synchronously observed by a CCD camera to establish The relationship between coating-substrate stress-strain history and peeling characteristics is used to characterize the coating-substrate interface bonding performance, which has the advantages of simple principle, simple sample preparation, clear model, and easy operation.

Description of drawings

Fig. 1 is the schematic diagram of device structure of the present invention;

Figure 2 is a schematic diagram of the observation area of the CCD camera;

Fig. 3 is the stress-strain curve that sample is pressed in embodiment;

Fig. 4 is the picture recorded in real time of the sample in the uniaxial compression process in the embodiment; wherein Fig. 4a is the picture when no buckling occurs during the compression process of the sample, Fig. 4b is the picture when the sample just buckled, and Fig. 4c It is a picture of the buckling expansion of the sample; Figures 4a, 4b, and 4c correspond to the states of A, B, and D in Figure 3, respectively.

Labels in the figure: 1-Universal material testing machine; 2-Cold light source; 3-CCD camera; 4-Monitor; 5-Image processing card; 6-Computer; 7-Data processing card; 8-Load sensor; 9- Indenter of universal testing machine; 10-support of universal testing machine; 11-coating part of sample; 12-base part of sample.

Detailed ways

The present invention provides a buckling test method and device for quantitatively characterizing the interfacial bonding properties of thin film materials. The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

A buckling test method for quantitatively characterizing the interfacial bonding properties of thin film materials, the specific steps are as follows:

a. prepare the coating sample to be tested by coating, and polish the uncoated surface of the sample until the mirror surface is smooth with sandpaper;

b. Clamp the prepared sample coated with the coating to be tested on the universal material testing machine, and point the CCD camera at the cross section of the sample to be tested, adjust the position and focal length of the CCD camera so that the sample to be tested Form a clear image in the middle of the field of view of the CCD camera;

c. Perform axial uniaxial compression on the sample, and the universal material testing machine records the stress and strain values of the sample in real time. At the same time, the CCD camera performs synchronous real-time observation of the cross-section of the sample during the loading process, and records the buckling process in real time. The critical stress, deflection and peeling characteristics of crack length;

d. Establish the relationship between the coating-substrate stress-strain history and the peeling characteristics to characterize the interface bonding performance of the coating-substrate; the energy release rate G of the interface when the coating buckles can be calculated by the following formula:

$\frac{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G\; G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">G</figure-callout></span><figure-callout\; id="0"\; label="G\; G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">\; </figure-callout>}}{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G"\; filenames="HDA00002558354700011.png,HDA00002558354700021.png"\; state="\{\{state\}\}">G</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h\&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ;</span>$

Wherein E _f is the modulus of elasticity of the coating, the unit is Pa, υ _f is Poisson's ratio, h is the thickness of the coating, the unit is m, G ₀ is the strain energy release rate under the plane strain situation, the unit is J/ m ² , σ ₀ is the stress applied in the coating during the loading process, in Pa, and σ _cr is the critical stress in the coating when the coating begins to buckle, in Pa;

The corresponding phase angle ψ is:

$\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}$

where ω is the material mismatch phase angle in °, and ξ is a dimensionless function of the buckling deflection. ω is related to the mismatch parameters α and β of the coating and the substrate material. According to the different values of α and β, the value of ω also changes accordingly. See the table below for details of the specific values:

Table 1 ω and α, β relationship table

α, β, ξ, σ _cr are calculated with the following formula:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}$

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="HDA00002558354700021.png"\; state="\{\{state\}\}">f</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA00002558354700021.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 12</span>}}\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&upsi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

分别为平面应变情况下涂镀层和基底的弹性模量，单位为Pa，υ_f,υ_s分别为涂镀层和基底的泊松比，μ_f,μ_s分别为涂镀层和基底的剪切模量，单位为Pa，E_f,E_s分别为涂镀层和基底的弹性模量，单位为Pa，ξ为屈曲挠度的一个无量纲化函数，ω_max为试样涂镀层屈曲中心点的挠度，单位为m，h为涂镀层的厚度，单位为m，σ₀为加载过程中涂镀层内的应力，单位为Pa，σ_cr为涂镀层刚开始发生屈曲时的临界应力，单位为Pa，b为屈曲时的裂纹半长，单位为m。in

are the elastic modulus of the coating and the substrate under the plane strain condition respectively, and the unit is Pa, υ _f , υ _s are the Poisson’s ratios of the coating and the substrate respectively, μ _f , μ _s are the shear moduli of the coating and the substrate respectively The unit is Pa, E _f , E _s are the elastic modulus of the coating and the substrate respectively, the unit is Pa, ξ is a dimensionless function of the buckling deflection, ω _max is the deflection of the buckling center point of the sample coating, The unit is m, h is the thickness of the coating, the unit is m, σ ₀ is the stress in the coating during the loading process, the unit is Pa, σ _cr is the critical stress when the coating just begins to buckle, the unit is Pa, b is the half-length of the crack during buckling, in m.

The base length of the coating sample to be tested is 10 mm, the width is 5 mm, and the thickness is 5 mm.

The photographing frequency of the CCD camera is 1-2 seconds/frame.

The loading mode of the universal material testing machine is load loading, the loading rate is 3000N/min, and the maximum compression displacement is 1~2mm.

A buckling test device for quantitatively characterizing the interfacial bonding properties of thin film materials, in which a CCD camera 3, a monitor 4, an image processing card 5, a computer 6, a data processing card 7, a load sensor 8 and a universal material testing machine 1 are connected in sequence.

The photographing frequency of the CCD camera 3 is 1 to 2 seconds per sheet.

The loading mode of the universal material testing machine 1 is load loading, the loading rate is 3000N/min, and the maximum compression displacement is 1~2mm.

Example 1

Consider a specific situation: the nickel film-low-carbon steel system is used as the coating-substrate, the thickness of the nickel film is h=6×10 ^-5 m, the elastic modulus is E _f =2.2×10 ¹¹ Pa, and the thickness of the low-carbon steel substrate is Elastic modulus E _s =2×10 ¹¹ Pa, Poisson's ratio υ _f =υ _s =0.3. The critical buckling stress σ _cr =4.46×10 ⁸ Pa, the stress in the membrane when loading σ ₀ =6×10 ⁸ Pa, for the nickel film-low carbon steel substrate system, α≈0, β≈0, according to the data in the table ω=52.1° can be obtained, and the deflection ω _max of the buckling center point of the sample coating coating is 6.7×10 ^-5 m substituted into the above formula to obtain the interface binding energy of the nickel film-low carbon steel substrate system G=37.1J/m ² , Phase angle Ψ=-637°.

Claims (7)

1. the flexing method of testing of a quantitatively characterizing membraneous material interfacial combined function is characterized in that concrete steps are as follows:

A. prepare plating coated layer sample to be measured, with sample not the face of plating with sand papering to mirror-smooth;

B. with the sample holder of the plating coated layer to be measured for preparing on universal testing machine, and the CCD camera aimed at the xsect of sample to be tested, regulate position and the focal length of CCD camera, make sample to be tested become clearly image in the centre of CCD viewing field of camera;

C. sample is carried out axial uniaxial compression, the ess-strain numerical value of universal testing machine real time record sample, by the CCD camera xsect of sample in the loading procedure is carried out synchronous real-time monitored, the release characteristics of limit stress, amount of deflection and crack length in the real time record flexing process simultaneously;

D. the relation between coated layer-base stress strain history and the release characteristics set up characterizes the interfacial combined function of coated layer-substrate; The energy release rate G at interface can be calculated by following formula during the coated layer flexing:

$\frac{G}{G_0}=(1+3\frac{{\mathrm{\&sigma;}}_{\mathrm{cr}}}{{\mathrm{\&sigma;}}_0})(1-\frac{{\mathrm{\&sigma;}}_{\mathrm{cr}}}{{\mathrm{\&sigma;}}_0})$ ， $G_0=\frac{(1-{\mathrm{\&upsi;}}_f^2)h{\mathrm{\&sigma;}}_0^2}{2E_f}$ ；

E wherein _fBe the elastic modulus of coated layer, unit is Pa, υ _fBe Poisson ratio, h is the thickness of coated layer, and unit is m, G ₀Be the strain energy rate in the plane strain situation, unit is J/m ², σ ₀For being applied to the stress in the coated layer in the loading procedure, unit is Pa, σ _CrBe applied to limit stress in the coated layer when just having begun flexing occurs for coated layer, unit is Pa;

Corresponding phase angle ψ is:

$\tan \mathrm{\&psi;}=\frac{4\cos \mathrm{\&omega;}+\sqrt{3}\mathrm{\&xi;}\sin \mathrm{\&omega;}}{-4\sin \mathrm{\&omega;}+\sqrt{3}\mathrm{\&xi;}\cos \mathrm{\&omega;}}$

Wherein ω is the material phase-displacement angle, and unit is ^o, ξ is a nondimensionalization function of flexing amount of deflection.

2. method according to claim 1, it is characterized in that: the base length of described plating coated layer sample to be measured is 10 mm, and width is 5 mm, and thickness is 5 mm.

3. method according to claim 1 is characterized in that: the frequency of taking pictures of described CCD camera is 1 ~ 2 second/.

4. method according to claim 1 is characterized in that: the loading mode of described universal testing machine is that load loads, and loading speed is 3000 N/min, and the maximum displacement of compression is 1 ~ 2 mm.

5. the flexing proving installation of a quantitatively characterizing membraneous material interfacial combined function, it is characterized in that: CCD camera (3), monitor (4), video processing board-card (5), computing machine (6), data processing card (7), load transducer (8) and universal testing machine (1) link to each other in turn.

6. device according to claim 5 is characterized in that: the frequency of taking pictures of described CCD camera (3) is 1 ~ 2 second/.

7. device according to claim 5 is characterized in that: the loading mode of described universal testing machine (1) is that load loads, and loading speed is 3000 N/min, and the maximum displacement of compression is 1 ~ 2 mm.

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