TWI410629B - Measurement Method of Elastic Modulus of Coating - Google Patents

Abstract

A coating elastic modulus measuring method is disclosed. The coating is formed on a surface of a flat plate. A steel ball is placed on the coating for providing a load, so that the steel ball would push against the coating to define a contact radius and the contact radius would be measured. In this invention, because the thickness of the coating itself, the Poisson's ratio, the radius of the steel ball and the loading force are all known standard parameters, the elastic modulus of the coating can be calculated by further associating with the measured contact radius. The whole calculation process does not involve with or create any experience curve, and thus the present invention can effectively overcome statistical errors of the experience curve, so as to increase calculation convenience. Further, because the hardness of the coating is less than that of the flat plate or the steel ball, the elastic modulus of the coating would have a higher accuracy without being influenced by the Poisson's ratio and the elastic modului of the flat plate and the steel ball.

Description

Measuring method of coating elastic modulus

The invention relates to a method for measuring the modulus of elasticity, in particular to a method for measuring the modulus of elasticity of a coating.

The research and production of nano-coated materials is not only an emerging field, but also the scientific basis for the advancement of cutting-edge technology in the future. As cutting-edge technology becomes more sophisticated, miniaturized and highly functional, the demand for materials in the industry is becoming more and more molecular. Multi-layer coating technology is extremely important to the microelectronics industry. For example, on a very large integrated circuit, the coating is the carrier of the surface circuit; on the optical component, the multi-layer coating structure is the basic component of the variable refractive index passive component, so the basis of the coating Physical properties and related mechanical properties are major issues in today's academic and industrial circles.

The main measurement method of nano-coating is nano-indentation test. The nano-indentation test is one of the current measurement techniques for surface mechanical properties of nanometer. The indentation is mainly at the nanometer scale. The technique of applying a force to the coating to break the coating can immediately record the indentation load and the depth of the indentation, and further calculate material properties such as an elastic modulus and the like.

Please refer to Figure 1, as disclosed in the invention patent of No. I247100, "Integrated Nanoindentation System and Optical Interferometry for Measuring Material Properties", mainly to treat a material to be tested 100 and a known The mechanical materials 110 are combined to form a composite material 1, and then the composite material 1 is placed in a chamber 120 to regulate the temperature in the chamber 120 to an initial temperature by a temperature control unit 130; Applying a force (F) to the surface of the material to be tested 100 by the indenter 150 causes the surface of the material to be tested 100 to form a displacement (h) in the same direction as the direction of the force applied, and according to the above-mentioned applied force (F) and displacement ( The data of h) can obtain a reduced Modulus (E _r ) value from the unloading curve; then move the indenter 150 to separate from the material to be tested 100; and continue to use the temperature control unit 130 The temperature in the chamber 120 is adjusted to a test temperature; the deformation distribution of the material to be tested 100 is measured by an optical measuring unit 160.

Pass the following formula: 1/E _r =[(1-v ₁ ² )/E ₁ ]+[(1-v ₂ ² )/E ₂ ], where E ₁ and E ₂ are the indenter 150 and the test to be tested modulus of elasticity material 100, v ₁ and v ₂ respectively, the ram pump 150 and the bulk material to be tested than 100, E _r by equivalent elastic modulus of the unloading curve obtained, wherein E _1, v ₁ and E _r is It is known that after the calculation of the formula, the relationship between E ₂ and v ₂ of the material to be tested 100 can be known, and the relationship is substituted into the Deformation theory of multi-layered structure and utilized. The multi-point optical experimental data obtained, and then the numerical iteration, can be used to obtain the elastic modulus, the Pusson ratio and the thermal expansion coefficient of the material 100 to be tested.

However, the aforementioned reduced elastic modulus _Er is corresponding to the unloading curve, and the unloading curve belongs to the empirical curve, and is simultaneously subjected to the elastic modulus E ₁ , E ₂ of both the indenter 150 and the material to be tested 100. The influence cannot be calculated simply by calculating only the elastic modulus E _{2 of the} material to be tested 100, which is obviously inferior in accuracy; and it is also known in advance to know the elastic modulus E ₁ and the Pusong ratio v _{1 of} the indenter 150, and A large amount of experimental data is used for iteration, so the convenience is also poor.

Therefore, the object of the present invention is to provide a measurement method for the elastic modulus of a coating film, which can effectively overcome the error and has high accuracy.

Therefore, in the method for measuring the elastic modulus of the coating film of the present invention, the coating film is formed on the surface of a flat plate with a specific thickness and a Pusson ratio, and the hardness of the flat plate is larger than the plating film, and the measuring method comprises a pressing step. , a measurement step, a parameter acquisition step, and a calculation step.

First, the pressing step is performed, a steel ball having a hardness greater than the coating film is placed on the coating film, and a load is applied to the steel ball, and the steel ball is pressed against the coating film to define a contact radius, and the contact is The radius is less than the thickness of the coating; then the measuring step is performed to measure the contact radius; and the parameter obtaining step is performed to form an integral equation by using the Pusong ratio of the coating, and after integration, at least one specific gravity parameter is obtained. And the ratio of the contact radius to the thickness of the coating is defined as a diameter-thickness parameter, and the specific gravity parameter is matched with the diameter-thickness parameter to calculate a main parameter, and the Pusson ratio of the coating is also related to the elastic modulus of the coating. Cooperating to form an unknown parameter; finally performing the calculation step, forming the specific parameters, the known main parameters, the steel ball radius, the load force, and the contact radius into a specific equation, and solving the unknown parameter becomes It is known that the modulus of elasticity of the coating can be obtained by substituting the Pusson ratio of the coating.

The effect of the invention is that since the coating thickness of the coating itself and the Pusson ratio, the radius of the steel ball, and the load force are all known specifications, and the contact radius obtained by the measurement is matched, the calculation step can be used to estimate the coating. Elastic modulus, the whole process does not involve or establish any empirical curve, can effectively overcome the statistical error on the empirical curve, and improve the convenience of calculation, in addition, the coating hardness is less than the plate and the steel ball, so the coating elastic modulus will not It is affected by the elastic modulus of the above two and the Pusong ratio, and the accuracy is high.

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments.

Referring to FIG. 2 and FIG. 3 together, in a preferred embodiment of the method for measuring the elastic modulus of the coating film of the present invention, the plating film 31 is formed on the surface of a flat plate 32 with a specific thickness d and a Pusson ratio v , and the flat plate The hardness of 32 is larger than that of the plating film 31, and the flat plate 32 is an optically transparent plate, and the plating film 31 is also transparent.

The measuring method 2 includes a pressing step 21, a measuring step 22, a parameter obtaining step 23, and a calculating step 24. First, the pressing step 21 is performed to make a steel ball 33 having a hardness greater than that of the coating 31. Putting on the plating film 31, and applying a load to the steel ball 33, the steel ball 33 is pressed against the plating film 31 to define a contact radius a , and the contact radius a is smaller than the coating thickness d ; The measuring step 22 uses a laser light source 41 to irradiate the laser beam to the flat plate 32 from the outside of the surface of the steel plate 33 opposite to the outer surface of the steel ball 33, and penetrates the flat plate 32 and penetrates the flat plate 32. 32, the contact position of the steel ball 33 with the coating film 31 is observed, and the steel ball is measured and analyzed by using an image device 42 disposed on the outer side of the surface of the flat plate 32 opposite to the steel ball 33. The contact radius a between 33 and the coating 31.

Then, the parameter obtaining step 23 is performed to form an integral equation by the Poisson ratio v of the plating film 31, as shown in the following formula (1):

among them,

k =3-4 v ............................................ ................(3)

Since the Pusong ratio v of the plating film 31 is a known parameter, the k value of the formula (3) is also known, and in the formula (2), L (ω) can be made into a simple corresponding function of ω, and then Substituting into equation (1), after integration, c _m is obtained.

The m value is determined by the following conditions:

When ( i,j )=(0,1) or ( i,j )=(1,0), m = i + j =1;

When ( i,j )=(1,1), m = i + j =2.

Then, i, j, m, and c _m are substituted into the following formula (4), and after the integral calculation, two specific gravity parameters b ₁ and b _{2 are obtained} .

That is, b ₀₁ = b ₁₀ = b ₁ , b ₁₁ = b ₂ .

The ratio of the contact radius a to the coating thickness d is defined as a diameter parameter.

In general, the contact radius a is 0.9 times or less of the coating thickness d , that is,

Then the path thickness parameters γ and b ₁ , b _{2 are} substituted into the calculation equation of a main parameter D , as listed in the following formula (6):

In this way, the main parameter D can be made known, and since the diameter-thickness parameters γ and b ₁ and b _{2 are} all dimensionless and unitless values, the value obtained by calculating the main parameter D is also dimensionless. No unit.

Then, the radius of the steel ball is defined as R , the load force is W , the elastic modulus of the coating 31 is E , and the Pusson's ratio v of the coating 31 is matched with the elastic modulus E of the coating 31 to form an unknown parameter β. , as listed in the following formula (7):

Then, a final calculation step 24 is performed to form the above-mentioned unknown parameter β with the known main parameter D , the steel ball radius R , the load force W , and the contact radius a into a specific equation, as listed in the following formula (8):

Substituting the formula (7) into the formula (8) and finishing it, the formula (9) is obtained:

In the formula (9), the contact radius a is obtained by performing the measuring step 22, and the unit is m , and the radius R of the steel ball is a known control parameter value at the time of measurement, and the unit is also m. The load force W is also a control parameter value known at the time of measurement, and the unit is Newton N , and the main parameter D is a specific value obtained in the formula (6), and there is no dimension, no unit, and the coating 31 The Pusson's ratio v is also a known value without unit, so that the formula (9) can be solved to obtain the elastic modulus E of the coating film 31, and the unit thereof is N / m ² , that is, P _a .

In summary, the measuring method 2 for applying the elastic modulus of the coating of the present invention does not need to cooperate with the elastic modulus of the steel ball 33 to establish a reduced elastic modulus, and of course, does not involve or establish any elastic modulus. The empirical curve can effectively overcome the statistical error on the empirical curve; further, the measuring method 2 of the present invention is only required to have a known specification parameter - the coating thickness d of the coating 31 itself, the Poisson ratio v , the radius R of the steel ball, and the load. The force W , together with the contact radius a obtained by the measuring step 22, can be used to calculate the elastic modulus E of the coating 31 via the calculation step 24, and the numerical iteration is performed without using a large amount of experimental data. The measuring device is only the laser light source 41 and the imaging device 42, and the device is simple and the estimation process is quite fast. In addition, the present invention directly targets the coating film 31 by the hardness of the plating film 31 being smaller than the flat plate 32 and the steel ball 33. The elastic modulus is calculated and does not depend on the elastic modulus of the steel ball and the elastic modulus of the steel ball 33 for indirect estimation, that is, the elastic modulus of the coating 31 is not caused by the flat plate 32 and the steel ball 33 described above. Modulus of elasticity affected the ratio of Pu loose, so the accuracy is high, indeed can achieve the object of the present invention.

The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent.

2. . . Measuring method of coating elastic modulus

twenty one. . . Pressure step

twenty two. . . Measurement step

twenty three. . . Parameter acquisition step

twenty four. . . calculation steps

31. . . Coating

32. . . flat

33. . . Steel ball

41. . . Laser source

42. . . Imaging equipment

43. . . Beam splitter

R . . . Steel ball radius

W. . . Load capacity

a . . . Contact radius

d . . . Coating thickness

1 is a schematic structural view showing the measurement method of the invention patent case of "Improvement of Nano Indentation System and Optical Interference Method for Measuring Material Properties" in the publication No. I247100;

Figure 2 is a block diagram showing a preferred embodiment of the method for measuring the modulus of elasticity of the coating of the present invention;

Figure 3 is a schematic diagram showing the actual measurement state of the preferred embodiment.

2. . . Measuring method of coating elastic modulus

twenty one. . . Pressure step

twenty two. . . Measurement step

twenty three. . . Parameter acquisition step

twenty four. . . calculation steps

Claims (2)

A method for measuring a modulus of elasticity of a coating film formed on a surface of a flat plate with a specific thickness and a Poisson ratio, and the hardness of the flat plate is greater than the plating film, the measuring method comprising: a pressing step, a steel ball having a hardness greater than the coating is placed on the coating film, and a load is applied to the steel ball, the steel ball is pressed against the coating film to define a contact radius, and the contact radius is less than the thickness of the coating film; Measuring step, measuring the contact radius; a parameter obtaining step, forming an integral equation by using the Poisson ratio of the coating, after integrating, obtaining at least one specific gravity parameter, and then defining the ratio of the contact radius to the coating thickness For a diameter parameter, the specific gravity parameter is matched with the diameter parameter to calculate a main parameter, and the Poisson ratio of the coating is also matched with the elastic modulus of the coating to form an unknown parameter; and a calculation step Combine the above unknown parameters with the known main parameters, the radius of the steel ball, the load force, and the contact radius into a specific equation, and solve the problem to make the unknown parameter Known, then substituting the loose film Pu ratio can be obtained for the modulus of elasticity of the film; wherein, in the parameter acquiring step, to the pump's ratio v loose coating constituted an integral equation ,among them, , κ = 3-4 v , after integration, two specific gravity parameters b ₁ , b _{2 are obtained} , where b ₀₁ = b ₁₀ = b ₁ , b ₁₁ = b ₂ , and , m = i + j , then the path thickness parameter γ and b ₁ , b ₂ generation eight main parameters In the calculation equation, the main parameter D can be made known, and then the calculation step is performed so that the radius of the steel ball is R , the load force is W , the contact radius is a , the coating thickness is d , and the diameter and thickness parameters are , the Pusson ratio and elastic modulus of the coating are v and E , the main parameter is D , and the unknown parameter is , the specific equation is . According to the measuring method of the elastic modulus of the coating film according to the first aspect of the patent application, wherein the flat plate is an optical transparent plate, the coating film is also transparent, and the measuring step is to use a laser light source from the opposite side of the flat plate. The outer surface of the steel ball is irradiated, and an imaging device disposed on the outer side of the surface opposite to the steel ball is also used to measure and analyze the contact radius between the steel ball and the coating.