KR101332264B1 - Analysis method of plastic stress-strain curve based on indentation image analysis - Google Patents

Abstract

The flow curve acquisition method of the spherical indentation based on the indentation image analysis according to the present invention determines the contact boundary by imaging the spherical indentation generated by the spherical indentation in three dimensions, and the projection contact area inside the contact boundary A first step (S10) of dividing the indentation load to obtain a contact pressure, and analyzing the flow stress by dividing the contact pressure by a plastic confinement factor; A second step (S20) of analyzing the flow strain (ε _i ) by dividing the integral value A obtained by integrating the surface area inside the plastic strain field by the surface area A0 before the indentation strain projecting the surface area vertically; And a third step (S30) of obtaining a flow curve by showing a graph by pairing the flow stress and the flow strain as a pair, thereby obtaining the flow stress by imaging the spherical indentations in three dimensions. Using the area obtained by using the material stacking area as the ellipsoid or the inclined part of the triangular pyramid as part of the sphere or ellipsoid, the flow strain is analyzed to analyze the flow curve and ultimately calculate the deformation characteristics of the individual materials individually. .

Description

Analysis method of plastic stress-strain curve based on indentation image analysis based on indentation image analysis

The present invention relates to a method for obtaining a flow curve by analyzing the plastic flow of spherical indentation particles, and more specifically, 3 of indentation marks or craters or spherical indents formed on the surface of an object by spherical indentation particles. The present invention relates to a method for acquiring a flow curve of a spherical indentation based on an indentation image analysis, which enables to obtain a flow curve through flow stress and flow strain analyzed by dimensional image analysis.

In general, indentation hardness test is a method of non-destructive testing, and it is possible to obtain deformation and fracture properties by acquiring and analyzing the properties of the test object without destroying the test object to diagnose the safety of the structure in operation. have. Among these indentation hardness tests, there is an indentation test using spherical indentation particles, and the plastic flow of the object is obtained through this test.

The indentation test using this spherical indenter (Korean Patent No. 0418700) is the same as in FIG. 1 showing the indentation by the spherical indenter (not shown). The ideal diameter (d _t ) and depth (h _t ) of the indentation and the diameter (d _p ) and depth of the unloaded indentation when indenting through the indentation formed on the surface of the object with a spherical indenter having a diameter of 'd' ( h _p ) was obtained. Afterwards, based on this, ultimately, the flow curve was obtained through finite element analysis including stress and strain analysis of the object. In particular, by combining these finite element analysis with instrumentation indentation test, it is possible to evaluate the stress and strain of the contact part that corrects the pile-up phenomenon that is common in the indentation of the object. Interpretation was possible.

However, through finite element analysis, various deformation factors such as elastic modulus, yield strength, tensile strength, and work hardening index were limited to generalize the indentation deformation and material stacking (10) behavior of individual materials. Various metal materials had to be largely classified into several deformation characteristics. In addition, through the analysis results of the indentation load removal curve generated in the instrumentation indentation test and the correction of the factor related to the material stack (10) obtained from the finite element analysis, the contact properties can be evaluated without direct observation of the indentation remaining on the object surface. Limitations in finite element analysis cause problems with analytical methods. In addition, when the contact boundary 11 which comes into contact with each other when the spherical pressure particles and the object surface are deformed is determined, the stress and strain at which the flow is generated are calculated, and the flow stress is determined by the contact pressure as a plastic restraint factor (a constant value around 3.0). This flow stress is incomplete if the determination of the contact boundary 11 is uncertain. In addition, in case of indentation strain corresponding to each flow stress, a sin function or tan function is used at the contact angle (θ) between the spherical indentation particle and the object surface at each indentation depth, but this indentation strain is used in the conventional uniaxial tensile test. This is not supported by physical concepts such as the ratio of initial length to tensile length, which is commonly defined. As described above, there is a problem in that there is a limit in obtaining an analysis and a flow curve in the instrumentation indentation test and the nanoindentation test using the finite element analysis.

KR0418700 10

The present invention has been made to solve the above problems, in order to check the deformation characteristics of the individual material and to monitor the instrumentation indentation curve image of the indentation remaining on the surface of the object in three dimensions, and to stack the material around the indentation The purpose of this study is to provide a flow curve acquisition method of a spherical indentation based on the indentation image analysis which obtains the flow curve by obtaining the flow stress and the strain rate through the direct analysis of the contact properties in consideration of the image deformation.

Flow curve acquisition method of the spherical indentation based on the indentation image analysis according to the present invention for achieving the above object, to determine the contact boundary by imaging the spherical indentation generated by the spherical indenter in three dimensions, the contact boundary inside A first step (S10) of dividing the indentation load of the spherical pressure particles by the projected contact area of to obtain the contact pressure, and dividing the contact pressure by the plastic confinement factor to analyze the flow stress; A second step (S20) of analyzing the flow strain (ε _i ) by dividing the integral value A obtained by integrating the surface area inside the plastic strain field by the surface area A0 before the indentation strain projecting the surface area vertically; And a third step (S30) of obtaining a flow curve by showing a graph by pairing the flow stress and the flow strain.

Here, the flow strain (ε _i ) is

[Equation 1]

to be. (Where A is the surface area integral inside the plastic strain field, A0 is the surface area before indentation projecting the surface area inside the plastic strain field vertically)

In addition, the surface area A0 is the projected area excluding the surface roughness, and the surface area A0 is the image of the spherical indentation on a part of a specific figure, and the material stacking area of the spherical indentation edge is smooth to the surface before deformation. It is an area calculated by geometrically calculating the inclination part and the part of the inclination part which is a part of a specific figure which converges easily.

In addition, the image of a spherical indentation is a part of a sphere or an ellipsoid sphere, and the image of the material stacking area is an inclination part which is a part of an ellipse sphere or a triangular pyramid.

In addition, the plastic deformation length is an area corresponding to 2 kC (real number of k = 3 to 5) from the center of the spherical indentation including the material stacking area when the 3D image is 2C.

Here, the contact boundary is determined by connecting the points where the derivative value is '0' by differentiating the height change with distance from the center of the spherical indentation.

In addition, the first step (S10) includes the step of converting the three-dimensional image information of the spherical indentation to the three-dimensional cylindrical coordinate system of θ, r and z after each numerical data obtained by the rectangular coordinate system of the x, y and z axis do.

Where θ is

&Quot; (2) "

Is converted to r,

&Quot; (3) "

Is converted to.

In addition, the projection contact area is obtained by integrating the inside of the contact boundary.

In addition, the flow curves are superimposed on one graph with each pair of flow stresses and flow strains analyzed corresponding to a plurality of indentation depths for a spherical indentation.

As described above, according to the present invention, the spherical indentation is imaged in three dimensions to obtain the flow stress, and the area of the spherical indentation is formed as a part of a sphere or an ellipsoid, and the material stacking area is an inclination part of an ellipsoid or a triangular pyramid. By obtaining the flow strain, it is possible to obtain the flow curve and ultimately calculate the deformation characteristics of the individual materials individually.

In addition, through the instrumentation indentation test, the same flow stress and strain can be calculated regardless of the type of the object to be measured, and according to the problem of inferring contact boundary through the conventional finite element analysis or the deformation characteristic group of the object There is an effect that can eliminate the hassle of conventional flow curve analysis and acquisition method using the equation.

In addition, since the analysis through the direct observation of the spherical indentation present on the surface of the object, even if the deformation is incomplete due to the hard foreign matter or surface defects included in the object, the screening can be clearly identified as well as the flow after removing the incomplete deformation part in the image analysis It is effective to analyze the characteristics.

In addition, in the conventional case, the indentation load-displacement curve obtained as a result of the instrumentation indentation test is very important for analyzing and acquiring the flow characteristics, so that a close control experiment on the initial contact load is required, whereas the indentation image analysis of the present invention Since the flow acquisition method observes the deformation of the indentation in a real image, it is effective to accurately analyze and acquire the flow characteristics when only the maximum applied load information is accurate.

In addition, the flow strain concept included in the present invention has a clear physical support that is consistent with the conventional strain definition, and thus has an effect of excluding an uncertain factor such as an optimization constant introduced in the conventional strain definition.

In addition, the spherical indentations formed on the surface of the object can be averaged with respect to the indentation deformation by imaging the ellipsoid and a part of the triangular pyramid.

BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate preferred embodiments of the invention and, together with the description, serve to further the understanding of the technical idea of the invention, It should not be interpreted.
1 is a cross-sectional image of a spherical indentation in order to analyze and obtain the flow curve of the spherical indentation through the conventional finite element analysis.
2 is a diagram showing a cross-sectional image of a spherical indentation for the flow curve analysis and acquisition of the spherical indentation based on the indentation image analysis in accordance with a preferred embodiment of the present invention.
FIG. 3 is a diagram illustrating flow strain analysis through geometrical analysis of the deformation region of the spherical indentation shown in FIG. 2.

Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention. However, the detailed description of known functions and configurations incorporated herein will be omitted when it may unnecessarily obscure the subject matter of the present invention.

<Acquisition Method>

2 is a view showing a cross-sectional image of the spherical indentation for the flow curve analysis and acquisition of the spherical indentation based on the indentation image analysis according to a preferred embodiment of the present invention, Figure 3 is a view of the spherical indentation FIG. 5 is a diagram illustrating flow strain analysis through geometric analysis of deformation regions.

2 and 3, the method for acquiring the flow curve by the spherical indenter based on the indentation image analysis according to the present invention is a three-dimensional image analysis of the indentation (100; spherical indent) generated on the surface of the object by infiltration of the spherical indenter. It is a method to measure the flow stress and the strain rate based on In other words, indentation flow is performed in several indentation depth stages, and the pairs of the flow stress and the strain in each stage are paired, and when they are superimposed on one graph, the indentation flow is consistent with the flow curve obtained in the uniaxial tensile test. To obtain a curve. Here, as shown in FIG. 2, when the spherical indentation 100 is observed by the atomic force microscope, the spherical indentation 100 is formed by the spherical indenter 110, and the material is stacked around the spherical indentation. A pile up area is formed, and a contact boundary 120 and a slope up leage 121 of the spherical indentation 100 are formed in the material stacking area. More specifically, a curved portion having a gentle inclined portion 121 is formed around the outer side of the spherical indentation 100, wherein the spherical pressure particles 110 and the spherical indentation 100 are formed by a change in the inclination of the curved portion. The contact boundary 120 becomes obscure. At this time, the contact boundary 120 is made by connecting the maximum point of the material stacking close to the actual contact portion.

First, the flow stress is analyzed (S10).

For this purpose, the spherical indentation 100 is imaged, and the three-dimensional imaging of the spherical indentation 100 is a process performed to obtain a three-dimensional data value. That is, in order to perform this process, the area of the spherical indentation 100 is scanned about twice as much as the center of the spherical indentation 100 using the contact mode of the tactile atomic force microscope, and the image information of the spherical indentation 100 obtained therefrom is stored. do.

Then, the stored image information is obtained by each of the numerical data by the Cartesian coordinate system of the x, y and z axes, and then the three points of θ, r and z with the center of the indentation 100 as the origin in order to differentiate the spherical indentation 100 image. Convert to a dimensional cylindrical coordinate system. In this case, θ and r are converted through Equation 2 and Equation 3 below.

&Quot; (2) &quot;

&Quot; (3) &quot;

When the transformation of the coordinate system is completed as described above, the height difference of the surface of the indentation 100 is first-differentiated from the origin to the radial distance in order to continuously determine the highest points around the indentation 100. At this time, the conditions for continuously determining the highest point are as shown in [Equation 4].

&Quot; (4) &quot;

That is, the condition for determining the height change of the surface of the indentation 100 determines the contact boundary 120 by connecting the points where the derivative value is '0'. The derivative for determining this contact boundary 120 is called radial differentiation.

Then, the load-off projected contact area is calculated by integrating the internal area of the contact boundary 120 thus obtained, and the calculated projected contact area is applied to the spherical pressure particle 110. The contact pressure is calculated by dividing the indentation load. The contact pressure is divided by the restraint factor to determine the flow stress.

Next, the flow strain is analyzed (S20).

This strain is used by modifying the contact area incremental analysis technique presented in Milman et al. In detail, Milman et al. Described the strain corresponding to the indentation strain as the ratio of the surface area before the initial indentation to the actual surface area of the indentation 100 after the indentation. In other words, if the tensile strain defined in the uniaxial tensile test is the change ratio of the length, the change ratio of the surface area is an extension of the change ratio of the length in two dimensions. Using this, the present invention extends the indentation strain presented by Milman to the plastic strain field, and provides a method of calculating the surface area, which is a blind spot of the image analysis technology, in consideration of the geometric image of the spherical indentation 100. Here, the boundary of the plastic strain field around the spherical indentation 100 is obtained by using the ratio of the surface area integrated value A inside the plastic strain field and the surface area A0 before indentation deformation which is confirmed by projecting the surface area vertically. Equation 1] defines the flow strain (ε _i ). At this time, the plastic deformation length is a region corresponding to 2kC (real number of k = 3 to 5) from the center of the spherical indentation 100 including the material stacking area when the 3D image is 2C.

[Equation 1]

Here, in determining the surface area A of the indentation 100 including the strain field and the object surface area A0 before the initial deformation corresponding thereto, it is difficult to accurately calculate the deformation area in the problem of surface roughness and image analysis. In other words, in order to accurately calculate the strain, the influence of surface roughness should be included in the determination of A0.In image analysis, the surface area integration, like mensuration by division, is used to sum individual areas of triangles or squares. Overestimation of integral areas occurs frequently. In order to solve this problem, in the present invention, as shown in FIG. 3, the image of the spherical indentation 100 formed on the surface of the object is confirmed as a part of a sphere or ellipsoidal sphere 130 (ellipsoidal geometry, ES), and the material stacked around the indentation 100. The area is identified by an inclined portion 131 that is part of an ellipsoid or triangular pyramid that slowly converges to the surface before deformation. That is, the area of the ellipsoid 130 and the inclined portion 121 can be calculated geometrically, the surface area A0 before the corresponding indentation deformation may be utilized by using the projected area without consideration of surface roughness. As described above, the three-dimensional image of the spherical indentation 100 is analyzed through a simple geometric figure and represented as a flow strain, so that an overestimation of the flow strain generated by the classification quadrature method can be eliminated.

Finally, a flow curve is obtained (S30).

By drawing a pair of each of the flow stresses and flow strains analyzed as described above corresponding to the various indentation depth steps in a single graph, the final flow curve can be obtained without governing equations for conventional plastic deformation.

The flow curves thus obtained are ultimately used to calculate the deformation characteristics of individual materials individually.

As described above, those skilled in the art will appreciate that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. It is therefore to be understood that the above-described embodiments are illustrative and non-restrictive in all aspects. The scope of the present invention is clearly defined in the following claims rather than the detailed description, and all changes or modifications derived from the meaning and scope of the claims and equivalents should be construed as being included in the scope of the present invention.

100 ... spherical indentation, 110 ... spherical indenter,
120 contact boundary, 121 stacking ramp,
130 ... ellipsoid, 131 ... conical inclination.

Claims (12)

The spherical indentation 100 generated by the spherical indenter particles is imaged in three dimensions to determine the contact boundary 120, and the indentation load of the spherical indentation particle 110 is divided by the projected contact area inside the contact boundary 120. A first step (S10) of obtaining a contact pressure and dividing the contact pressure by a plastic confinement factor to analyze the flow stress;
A second step (S20) of analyzing the flow strain (ε _i ) by dividing the integral value A obtained by integrating the surface area inside the plastic strain field by the surface area A0 before the indentation strain projecting the surface area vertically; And
And a third step (S30) of obtaining a flow curve by showing a graph using the pair of the flow stress and the flow strain as a pair; a flow curve acquisition method of the spherical indentation based on the indentation image analysis. The method of claim 1,
The flow strain (ε _i ) is,
[Equation 1]

Acquiring the flow curve of the spherical indentation based on the indentation image analysis, wherein A is the surface area integral inside the plastic deformation field, and A0 is the surface area before indentation projecting the surface area inside the plastic deformation field vertically. Way. The method of claim 1,
The surface area A0 is a projected area excluding surface roughness, and
The surface area A0 is an inclination which is a part of a specific figure in which the image of the spherical indentation 100 is part of a specific figure, and the image of the material stacking area of the edge of the spherical indentation 100 is gently converged to the surface before deformation. After the portion 121, the partial curve and the flow curve acquisition method of the spherical indentation based on the indentation image analysis, characterized in that the area calculated by geometrically calculating the inclined portion (121). The method of claim 3,
The image of the spherical indentation 100 is a flow curve acquisition method of the spherical indentation based on the indentation image analysis, characterized in that the above part of the sphere or ellipse sphere. The method of claim 3,
The image of the material stacking area is an ellipsoid or a slanted portion of a triangular pyramid pyramid based on indentation image analysis, characterized in that the flow curve acquisition method of the indentation. The method of claim 1,
The plastic deformation field is an indentation image which is an area corresponding to 2 kC (real number of k = 3 to 5) from the center of the spherical indentation 100 including the material stacking area when the 3D image is 2C. Flow curve acquisition method of spherical indentation based on analysis. The method of claim 1,
The contact boundary 120 is a spherical indentation based on the indentation image analysis, characterized in that by determining the differential value by connecting the points that the derivative value is '0' by differentiating the height change according to the distance from the center of the spherical indentation 100 How to obtain the flow curve of. The method of claim 1,
In the first step (S10) is to obtain the three-dimensional image information of the spherical indentation 100 by the rectangular coordinate system of the x, y and z axes, and then to convert to the three-dimensional cylindrical coordinate system of θ, r and z Flow curve acquisition method of the spherical indentation based on the indentation image analysis, characterized in that it further comprises a step. 9. The method of claim 8,
Θ is
&Quot; (2) &quot;

Method of obtaining a flow curve of the spherical indentation based on the indentation image analysis, characterized in that converted to. 9. The method of claim 8,
R is
&Quot; (3) &quot;

Method of obtaining a flow curve of the spherical indentation based on the indentation image analysis, characterized in that converted to. The method of claim 1,
The projection contact area is a flow curve acquisition method of the spherical indentation based on indentation image analysis, characterized in that obtained by integrating the inside of the contact boundary (120). The method of claim 1,
The flow curve is based on the indentation image analysis, characterized in that the superimposed in the graph with a pair of each of the flow stress and the strain is analyzed to correspond to a plurality of indentation depths for the spherical indentation 100 Flow curve acquisition method of spherical indentation.

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