KR100736436B1 - Method for measuring indentation hardness through analysis of indentation shape - Google Patents

Abstract

A method for measuring indentation hardness through analysis of indentation shape is provided to minimize overestimation or underestimation of measuring contact area to obtain precise test result. A method for measuring indentation hardness through analysis of indentation shape includes the steps of shaping residual indentation generated by applying a load to a harden indenter in a three-dimensional shape through a shaping program to differentiate a height variation based on a distance from the indentation center, and estimating load removal hardness by determining a closed curvature of connecting contacting edges with differentiated value of zero to each other as a contact boundary, calculating a projected contacting area by integrating the inside of the contact boundary to divide the applied load with the projected contacting area. The method further includes the step of obtaining image information of the residual indentation as numeral data based on X-, Y-, and X-axes orthogonal coordinate and of converting the image information as three-dimensional cylindrical coordinate.

Description

Method for Calculating Indentation Hardness through Shape Analysis of Non-Destructive Surface Indentation Traces

1 is an exemplary view showing the indentation shape generated in the test material during the indentation test.

Figure 2 is an illustration of a state in which residual indentations were observed by the indentation test according to the present invention.

Figure 3 is an exemplary view showing a state in which material accumulation of residual indentation occurred in the indentation test according to the present invention.

Figures 4a to 4c is an illustration of a three-dimensional residual indentation shape implemented as surface information of the atomic force microscope in the indentation test according to the present invention.

Figures 5a to 5c is a diagram illustrating a state in which the surface height change is differentiated from the indentation center by the radial distance in the indentation test according to the present invention.

6a to 6c is a view illustrating a state where the contact boundary closed curves obtained through the differential packing method and the residual material pile surrounding contours in the indentation test according to the present invention overlap.

7a to 7b is a graph of the indentation load-displacement curve obtained in the indentation test according to the present invention.

8 is a graph of a state in which the conventional indentation test and the indentation hardness value evaluated through the indentation test according to the present invention.

The present invention relates to a method of calculating the indentation hardness through the shape analysis of the non-destructive surface indentation traces. Specifically, the residual indentation formed by the load applied by the hard indenter is analyzed in a more accurate three-dimensional shape, and more accurate indentation hardness can be calculated by considering the shape deformation caused by the stacking of material around the indentation. The present invention relates to a method of calculating the indentation hardness through the shape analysis of nondestructive surface indentation traces.

The indentation hardness test, which is applied as a method of nondestructive testing, can be tested without destroying the test object for deterioration and safety diagnosis of the equipment and structure in operation. In addition, the indentation hardness test is not an expert research area, but can be easily and economically handled to obtain or analyze simple physical properties without being an expert to apply to quality control and diagnosis of actual production lines and industrial sites. At the same time, it is characterized by a versatile analysis process that can obtain various deformation and fracture properties with only one test.

In this indentation hardness test, by applying a load to the rigid indenter of various forms to press the surface of the test material, by measuring the diagonal or diameter length of the indentation formed on the test object by the dead weight After calculating the contact area, the applied load is divided by the calculated contact area to calculate the indentation hardness of the contact pressure concept.

Here, the hard indenter (also referred to as "hard presser") is formed in various forms such as square pyramid, triangular pyramid, cone or sphere as shown in the general data shown in Table 1, in particular, diamond having a higher hardness than the test material B) It is known that it is formed of steel ball material. Indentations formed on the surface of the test material are also observed by an optical microscope and the indentation hardness is calculated by the formula shown in Table 1.

In the indentation hardness test method as described above, a complex contact boundary of a convex or concave is shown in the indentation test of a metal material as shown in FIG. 1. However, at the present indentation hardness test, the measuring contact area is smaller or larger than the actual contact area because only the diagonal length of the indentation is measured by optical microscope. That is, the phenomenon as described above causes an underestimation or underestimation error of the indentation hardness depending on the underestimation or overestimation of the measured contact area.

In particular, when the pile-up (phenomena in which the indentation is raised to a certain height) is severe around the indentation as shown in FIG. 1, the contact depth has a value greater than or equal to the maximum indentation depth. However, the current calculation of the indentation hardness is calculated without considering the shape deformation for this material stacking phenomenon. Accordingly, in the case of materials such as soft aluminum, which is heavily stacked, severe indentation hardness measurements of more than 50% have been reported.

As a result, the process of measuring and analyzing only the diagonal length of the indentation described above and the indentation hardness calculated in the state that the material stacking around the indentation is not taken into account is not accurate data, which lowers the reliability of the test results.

The present invention has been invented to solve the above problems, the residual indentation generated by applying a load to the hard indenter in a three-dimensional shape, and the method of calculating the indentation hardness considering the shape deformation generated by the stacking material around the indentation The purpose is to provide.

In order to achieve the above object, the present invention has the following features.

The present invention comprises the steps of: shaping the residual indentation generated by applying a load to a hard indenter to which a load is applied in a three-dimensional form through a shaping program to differentiate the height change according to the distance from the center of the indentation; Determining a closed curve connecting the edges of the contact portion at which the derivative value is zero as a contact boundary, and then calculating the projected contact area by integrating the determined contact boundary into the projected contact area to calculate the load removal hardness by dividing the applied load by the projected contact area; It is characterized by including.

Hereinafter, embodiments of the present invention to which the above features are applied will be described in detail with reference to the accompanying drawings.

Figure 2 is an illustration of a state in which residual indentations formed on the surface of the test material is observed to perform the indentation hardness calculation method according to the present invention. The residual indentation shown in the figure is observed after removing the load applied by the hard indenter. This is because it is difficult to accurately measure the exact contact boundary between the surface of the indenter and the surface of the test material under load.

Referring to the drawings, the residual indentation of the triangular pyramid observed by the atomic force microscope is a depression where the black part in the center is formed by the hard indenter. In addition, it can be seen that the white portion around the triangular shape is a material stacking portion protruding outward by the load of the triangular pyramid.

Here, the hard indenter for forming the residual indentation is to apply the form of a triangular pyramid. In addition, a tool for observing residual indentations is applied to a commercial nanoindentation system using a conventional atomic force microscope to measure the three-dimensional surface shape of the test material with atomic precision. In particular, the atomic microscope can observe the three-dimensional surface shape, and then transmit the observed data to a dedicated terminal (computer type having a configuration of a monitor, a CPU, etc.) and output the data through a monitor / printer. Apply what is there.

In particular, when material accumulation occurs on the outer side of the residual indentation, the contact angle under the maximum load by the hard indenter is formed with a curved portion having a gentle slope on the outer side of the triangular shape as shown in FIG. As shown in Fig. 5, the change of the slope obscures the contact boundary between the hard indenter and the residual indentation. In this state, the contact boundary designates the maximum point of the material stack close to the actual contact boundary as the contact boundary to perform the indentation hardness to be described later.

In the above process, the three-dimensional shaping is a process performed to obtain a three-dimensional data value. That is, in order to perform the above process, the shape information of the residual indent is stored by scanning an area of approximately twice the center of the indent as shown in FIG. 2 using the contact mode of the tactile atomic force microscope. At this time, the stored shape information can obtain respective numerical data by the rectangular coordinate system of the x, y and z axes. Table 2 shows an exemplary state of a data sheet in which numerical data is calculated by the rectangular coordinate system, and the state displayed by this data sheet is the same as in FIGS. 4A to 4C.

Data Size: 256 x 256 Surface Size: 4.0 x 4.0 X Unit: Micro meter Y Unit: Micro meter Z Unit: Nano meter X Y Z 0 0 5.198 0.0156 0 0.2974 0.0312 0 -0.3649 0.0469 0 4.2709 0.0625 0 5.7278 0.0781 0 0.1649 0.0938 0 -2.2192 0.1094 0 -4.3384 0.125 0 -5.9278

Figure 4a is a shape of a three-dimensional residual indentation realized by atomic force microscope surface information by selecting quartz (fused quartz) as a test material, Figure 4b is a tungsten monocrystal, Figure 4c is a selection of pure copper (pure copper) Shows the shape of the three-dimensional residual indentation formed.

Thereafter, in order to differentiate the residual indentation shape represented by the rectangular coordinate system described above, the indentation center is converted into a three-dimensional cylindrical coordinate system of θ, r, z. Here, θ and r are converted as in Equations 1 and 2 below.

When the transformation of the coordinate system is completed as described above, the height difference of the indentation surface from the origin is first-differentiated to the radial distance to continuously determine the peaks of the indentation edges (the peaks of the stacking points in the case of stacking). do. At this time, the conditions for continuously determining the highest point are as in Equation 3 below.

That is, the condition for determining the height change of the indentation surface is a contact boundary by connecting the points where the derivative value is zero. Accordingly, when the derivatives are connected to the zero points and are displayed in the original rectangular coordinate system, they appear as shown in FIGS. 5A to 5C.

5A illustrates a case in which the test material is selected from quartz as illustrated in the above-described three-dimensional residual indentation shape, FIG. 5B illustrates a case in which tungsten single crystal is selected and FIG. 5C illustrates pure copper.

As a result, such a closed curve can be superimposed on a two-dimensional contour representing the height of the residual indentation, as shown in FIGS. 6A-6C (FIG. 6A shows quartz described above, FIG. 6B shows a tungsten single crystal, and FIG. 6C shows pure copper). .

Thereafter, the inside of the contact boundary obtained as described above is integrated to calculate the load-off projected contact area. The load removal hardness is calculated by dividing the applied load for pressing the hard indenter by the calculated projected contact area.

<Test Example>

The following test was conducted by the indentation hardness calculation method of the above example.

a) There are no non-uniform elements such as grain boundaries, and there is no material stacking, and quartz can measure more accurate indentation hardness, tungsten single crystal with isotropic deformation characteristics, and 99.99% pure copper with outstanding material stacking. Choose.

b) Indentation is formed by using a hard indenter in the form of a triangular pyramid on a test material which has been subjected to a high-gloss polishing such as a mirror surface by a mechanical method. At this time, the indentation rate was used 250μN / sec, the maximum applied load was selected as shown in Table 3.

Type of test material Quartz Tungsten single crystal Pure copper Applied Load (mN) 10, 6, 3, 1 6, 2.5, 1 2, 1.5, 0.8, 0.4

Here, the indentation test was applied to the instrumentation indentation test when forming the indentation.

For reference, the instrumentation indentation test causes surface penetration of the indenter at a constant speed by using a precision motor or a micro actuator instead of applying a load of hard indenter at one time, and retreats from the surface at the same constant speed to remove the load. Means a test technique. At this time, the load sensor and the displacement sensor is mounted on the rear end or side of the hard indenter to continuously measure the applied load and displacement during the indentation deformation and recovery caused by the generated displacement in the micro-actuator to be described below. A curve can be formed.

In particular, in this detailed description, a test for applying hardness evaluation of a thin film having a thickness within μm by lowering the applied load of the instrumentation indentation test to mN level will be referred to as a "nanoindentation test". The test method means that given in the above-described examples.

c) 5 times of nanoindentation tests (test of the above-described examples) were repeated corresponding to each loading condition of each test material, and the indentation load-displacement curves except for the curves circumferentially outermost are shown in the graphs of FIGS. 7A to 7B. Got as 7A is a graph for quartz, FIG. 7B is a graph for tungsten single crystal, and FIG. 7C is a graph for pure copper.

d) Looking at the graph, the indentation load-displacement curves with a low applied load were superimposed on the curves with a high applied load, it was confirmed that the reproducibility of the nanoindentation test presented in the above example is excellent.

Comparative Test Example

7A to 7C obtained by the above test example, a graph of the indentation load-displacement curves of the conventional analytical results for each test material and the analytical results by the method presented in the present invention are graphically shown in FIG. 8. It was.

Referring to FIG. 8, in the case of quartz in which material stacking hardly occurs, the existing indentation curve analysis method shown in Equations 4 and 5 and the residual indentation differential method according to the present invention showed the same result. Therefore, the validity of the method of calculating the indentation hardness according to the present invention was confirmed in a hard material having a weak material stacking.

Equation 4 is for converting the projection contact area based on the geometric shape of the indenter, such as a triangular pyramid of a particular angle, Equation 5 is to calculate the indentation hardness by dividing the maximum load by the projection contact area. Equations 4 and 5 are already known, and the above description is omitted.

However, in the shallow indentation region, there was an effect by the difference between the load-on state and the load removal state. That is, in the shallow indentation (low load), the elastic recovery of the indentation was severe, the hardness was increased by the differential method.

Referring to the same figure, in the case of the tungsten single crystal and pure copper, material stacking was severely generated. In this case, it was confirmed that the above-described indentation curve analysis method exhibits an indentation hardness value overestimate at least 50% of the intrinsic hardness.

That is, according to the method of calculating the indentation hardness according to the present invention, it can be seen that the inherent hardness value of the surface of the material can be obtained more precisely and accurately in the case of a metal material having a severe material stacking.

As described above, the present invention analyzes residual indentations in a three-dimensional shape, thereby minimizing an excessive or underestimation error of the measured contact area. Therefore, it is effective to obtain more accurate test results.

In addition, the present invention, by obtaining a test result in consideration of the shape deformation caused by the stacking material around the indentation to obtain more accurate data, thereby improving the reliability of the calculated test results.

Claims (9)

Shaping the residual indentation generated by applying the load to the hard indenter to which the load is applied in a three-dimensional form through a shaping program to differentiate the height change according to the distance from the center of the indentation; Determining a closed curve connecting the edges of the contact portion at which the derivative value is zero as a contact boundary, and then calculating the projected contact area by integrating the determined contact boundary into the projected contact area to calculate the load removal hardness by dividing the applied load by the projected contact area; Indentation hardness calculation method through the shape analysis of the non-destructive surface indentation traces comprising a. The method of claim 1, In order to realize the residual indentation in the three-dimensional shape, the numerical information of the residual indentation is obtained by the rectangular coordinate system of the x, y and z axes, and then the cylindrical indentation of the three-dimensional shape θ, r, z is obtained. Method of calculating the indentation hardness through the shape analysis of the non-destructive surface indentation traces comprising the step of converting. The θ of the cylindrical coordinate system is

Method of calculating the indentation hardness through the shape analysis of the non-destructive surface indentation traces, characterized in that converted to. The method of claim 2, wherein r of the cylindrical coordinate system is

Method of calculating the indentation hardness through the shape analysis of the non-destructive surface indentation traces, characterized in that converted to. The method of claim 1, wherein performing the derivative

Method of calculating the indentation hardness through the shape analysis of the non-destructive surface indentation traces, characterized in that the first derivative of the equation. The method of claim 5, wherein the two-dimensional contact boundary closed curves are formed by connecting the points satisfying the determined differential value 0, and the projected contact area is calculated by integrating the inside of the contact boundary. Indentation hardness calculation method through. The method according to any one of claims 1 to 5, In the case where the material accumulation occurs outside the residual indentation and the exact contact point cannot be specified, the contact boundary specifies the maximum point of the material accumulation point adjacent to the actual contact boundary as the contact boundary. Indentation hardness calculation method through shape analysis. The method according to any one of claims 1 to 6, The residual indentation is calculated after removal of the load applied by the hard indenter to determine the exact contact boundary, the indentation hardness calculation method through the shape analysis of the non-destructive surface indentation traces. The method according to any one of claims 1 to 6, The tool for observing the residual indentation is applied to a commercial nanoindentation system using an atomic force microscope to measure the three-dimensional surface shape of the test material with atomic level precision. Hardness calculation method.

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