KR20200045335A - System for calculating plastic stress intensity factor - Google Patents

Abstract

Disclosed is a system for calculating a plastic stress intensity factor, which calculates a plastic stress intensity factor for a structure where mechano-luminescence (ML) paint is applied and plastic deformation occurs. The system for calculating a plastic stress intensity factor comprises: a photographing unit; an image processing unit which receives images of the structure from the photographing unit, calculates cumulative ML intensity from a preset initial time to the present, generates a cumulative ML isointensity image, and analyzes the cumulative ML isointensity image to extract pieces of information necessary to calculate the presence or absence of cracks in the structure and the plastic stress intensity factor; a storage unit for storing therein effective stress information according to the cumulative ML intensity of the structure and information on a material constant of the structure; and an operation processing unit for calculating the plastic stress intensity factor (K^P_M) of the structure by using the information provided from the image processing unit and the information stored in the storage unit.

Description

Plastic stress expansion coefficient calculation system {SYSTEM FOR CALCULATING PLASTIC STRESS INTENSITY FACTOR}

The present invention relates to a system capable of calculating a plastic stress expansion coefficient using a piezoelectric material for a structure that is elastically deformed.

The stress intensity factor (SIF) value is calculated from the distance between the longest point on the fringe loop and the rotation angle between the longest point and the crack extension line in a given iso-chormatic pattern near the crack tip and the typical crack tip. Since Irwin was found to be calculable, many researchers have attempted to measure mode I fracture toughness (KI) values from isochromatic patterns to analyze static and dynamic problems near the crack tip stress field. Has been made.

In addition, optical methods for evaluating stress intensity factor values for similar purposes have been developed through studies of cracking in the elastic and plastic regions. Specifically, optical methods such as a method based on the moiré pattern, a method using distortion on a deformed surface, an optical interference method, and a holography method have been proposed. However, none of these methods, including these optical methods, is expensive and requires complex and heavy equipment, complex pre- and / or post-processing of specimens and tested data, lack of means of evaluating local or global strain, crack propagation is common. Problems such as the relatively slow speed of the response required to determine if it is a cognitive dynamic case could not be overcome.

To overcome the technical difficulties of crack monitoring, a method using mechano-luminescence (ML) has been proposed. The method using piezoelectricity has the advantage of being able to perform an overall inspection, show an immediate response, perform non-contact measurement, and have a low crack measurement ratio, as well as evaluate stress distribution in areas close to the crack tip based on fracture mechanics. Therefore, technical problems of the conventional methods can be avoided.

However, all fracture studies based on piezoelectric metals have been limited to the elastic behavior of Mode I cracks due to the complexity of nonlinear firing and mixing modes. Fracture generally involves areas of plastic deformation in the anterior portion of the crack tip of the actual structure to which tension is applied, as well as shear and torsion that cause mixed mode interactions, so the piezoelectricity for elastoplastic cracks under mixed mode An evaluation method is required.

An object of the present invention is to provide a system capable of real-time calculation of non-destructive crack detection and plastic stress expansion coefficient in the vicinity of a crack tip for a structure in which plastic deformation occurs.

)를 산출하는 연산처리부를 포함한다. The plastic stress expansion coefficient calculation system according to an embodiment of the present invention may calculate the plastic stress expansion coefficient for a structure in which plastic deformation is applied with mechano-luminescence (ML) paint, and a constant time interval for the structure An imaging unit continuously capturing an image; After receiving the images of the structure from the imaging unit, calculate a cumulative piezoelectric emission intensity from a preset initial time to the present, generate a cumulative piezoelectric intensity image, and analyze the cumulative piezoelectric intensity image to the structure An image processing unit for extracting information required to calculate the existence of a crack and a plastic stress expansion coefficient; A storage unit for storing effective stress information according to the cumulative piezoelectric strength of the structure and information about a material constant of the structure; And plastic stress expansion coefficient of the structure using information provided from the image processing unit and information stored in the storage unit (

).

In one embodiment, the image processing unit calculates the cumulative piezoelectric emission intensity from a preset initial time to the present after receiving images of the structure captured by the imaging unit, and then uses the cumulative piezoelectric intensity image An image generating unit to generate; And an image analysis unit for analyzing the cumulative piezoelectric intensity image generated by the image generation unit and extracting first information necessary to calculate the existence of a crack and a plastic stress expansion coefficient for the structure, and cracking the structure. If present, the image analysis unit generates polar coordinates for a first point located on an isochromatic fringe pattern located in a plastic core field located near the tip of the crack, and the Using the cumulative piezo-intensity image, the growth direction of the crack can be determined, and then the plastic mixing parameter M _P may be calculated therefrom.

)를 산출할 수 있다. In one embodiment, the calculation processing unit is applied to the following equation 1a or equation 1b equation, the plastic stress expansion coefficient of the structure (

).

[Equation 1a]

[Equation 1b]

는 θ, M_P 및 m를 변수로 포함하는 무차원 유효 응력을 나타내며,

이다.In Equations 1a and 1b, σ _e and τ _xy represent 'effective stress' and 'effective shear stress' at the first point, respectively, and r, θ, and M _P are polar coordinates of the first point. ) Components and the plastic mixing parameters, respectively, σ ₀ and m represent the yield stress and strain hardening component of the structure material,

Represents a dimensionless effective stress including θ, M _P and m as variables,

to be.

)를 표시하는 표시부를 더 포함할 수 있다. In one embodiment, the plastic stress expansion coefficient calculation system is a plastic stress expansion coefficient calculated by the calculation processing unit (

) May further include a display unit.

In one embodiment, the structure may include a bridge, a large machine tool or a building made of a material capable of plastic deformation.

According to the plastic stress expansion coefficient calculation system of the present invention, it is possible not only to perform non-destructive crack detection for a structure in which plastic deformation occurs, but also by simultaneously measuring light emission of a mechano-luminescence (ML) paint applied to the structure. The plastic stress intensity factor near the existing crack tip can be calculated in real time.

1 is a block diagram illustrating a plastic stress expansion coefficient calculation system according to an embodiment of the present invention.
2 is a view showing the produced two 4-point shear specimens (a, b) and one tension specimen (c).
Figure 3a is a graph showing the results of a tensile test explaining the mechanical properties of a core portion made of SAO and acrylic resin in a tension specimen, Figure 3b is a cumulative ML strength and measured in a 4-point shear test using a non-notched shear specimen It is a graph showing the relationship between effective shear stress.
4 (a) to 4 (d) are images showing ML luminescence near the crack tip of a 4-point shear specimen for external stresses of 0 N, 689 N, 829 N, and 872 N. ) To (g) are images representing the surface-strength profile of ML specified from the ML images of (b) to (d), respectively.
5 (a) to 5 (c) are discontinuous constant intensity images generated by accumulating ML luminescence from 0 to 689N, 829N, and 871N, respectively, using MATLAB software, which are virtual crack tip It represents the elastic long distance field in front of.
(A) and (c) of FIG. 6 are discontinuous iso-intensities and isochromatics collected for analysis of the plastic near field in front of the actual crack tip using ML from the plastic region in FIGS. 5 (e) and (f). It shows ML images accumulated in the form of contour lines.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. The present invention can be applied to various changes and may have various forms, and specific embodiments will be illustrated in the drawings and described in detail in the text. However, this is not intended to limit the present invention to a specific disclosure form, and it should be understood that all modifications, equivalents, and substitutes included in the spirit and scope of the present invention are included. In describing each drawing, similar reference numerals are used for similar components.

The terms used in the present application are only used to describe specific embodiments and are not intended to limit the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "include" or "have" are intended to indicate the presence of features, steps, actions, components, parts or combinations thereof described in the specification, one or more other features or steps. It should be understood that it does not preclude the existence or addition possibility of the operation, components, parts or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by a person skilled in the art to which the present invention pertains. Terms such as those defined in a commonly used dictionary should be interpreted as having meanings consistent with meanings in the context of related technologies, and should not be interpreted as ideal or excessively formal meanings unless explicitly defined in the present application. Does not.

In the present invention, the “stress intensity factor (SIF)” is a value that quantifies and indicates the degree to which cracks are likely to grow, and when the average tensile stress σ _{∞, which} is very far apart, is loaded, at the tip of the crack. It means the coefficient indicating how much the stress concentration of affects the fracture.

1 is a block diagram illustrating a plastic stress expansion coefficient calculation system according to an embodiment of the present invention.

Referring to FIG. 1, the plastic stress expansion coefficient calculation system 100 according to an embodiment of the present invention performs non-destructive crack detection for a structure in which plastic deformation occurs by measuring light emission of a mechano-luminescence (ML) paint. In addition, it is possible to simultaneously calculate the plastic stress expansion coefficient in the vicinity of the crack tip existing in the structure, and as a result, it is possible to simultaneously evaluate and evaluate the fracture characteristics of the deteriorated structure in real time.

The structure may include a bridge, a large machine tool, a building, etc. made of a material that can undergo plastic deformation, and the piezoelectric paint may be applied to the surface. The piezoelectric paint is a functional material that emits fluorescence corresponding to it when mechanical stress is applied, and a known piezoelectric paint material can be applied without limitation.

In one embodiment, the plastic stress expansion coefficient calculation system 100 may include an imaging unit 110, an image processing unit 120, a storage unit 130, a calculation processing unit 140, and a display unit 150. .

The imaging unit 110 may capture a continuous image at regular time intervals for the structure. In one embodiment, the imaging unit 110 may include a camera capable of high-speed imaging, for example, a CMOS camera.

The image processing unit 120 calculates the cumulative photoluminescence intensity from a preset initial time to the present after receiving the images of the structure imaged by the imaging unit 110, and then uses the accumulated photoluminescence intensity image It can be generated, and by analyzing the generated cumulative piezo-intensity image, it is possible to extract various information necessary to calculate the presence or absence of cracks in the structure and the plastic stress expansion coefficient for the structure.

In one embodiment, the image processing unit 120 receives the images of the structure imaged by the imaging unit 110 and calculates the cumulative photoluminescence intensity from a preset initial time to the present, and then uses it To analyze the cumulative piezoelectric intensity image generated by the image generator 121 and the image generator 121 to generate a cumulative piezoelectric intensity image, to calculate the presence or absence of cracks in the structure and the plastic stress expansion coefficient It may include an image analysis unit 122 for extracting a variety of necessary information.

In one embodiment, when a crack is present in the structure, the image analysis unit 122 may be disposed on an isochromatic fringe pattern located in a plastic core field located near the tip of the crack. You can create polar coordinates for one point. In this case, the image analysis unit 122 uses the tip of the crack as the origin and the axis of the crack as a reference line, the distance (r) between the origin and the first point, and the axis of the crack and the origin from the The polar coordinates of the first point can be generated by calculating the angle θ in the counterclockwise direction of the line connecting the first point.

On the other hand, the image analysis unit 122 may determine the growth direction of the crack and calculate the plastic mixing parameter M _P therefrom. The plastic mixing parameter is a parameter having a value of 0 or more and 1 or less, and indicates the degree of mixing between mode I in which tensile stress is applied in the near field of the crack tip and mode II in which shear stress is applied. The calcination mixing parameter can be calculated by a known method from the cumulative piezoelectric intensity images (see Shih, CF (1973) 'analysis of combined mode crack problems').

The storage unit 130 may store effective stress (σ _c ) information according to the cumulative piezoelectric strength of the structure, information about a material constant, and the like.

The material constant may include information such as yield stress (σ ₀ ), elastic modulus (young's modulus, E), and strain-hardening constant (m) of the structure material.

)를 산출할 수 있다. The calculation processing unit 140 applies the information provided from the image analysis unit 122 and the information stored in the storage unit 130 to the equations of Equation 1a or Equation 1b below to calculate the plastic stress expansion coefficient (

).

[Equation 1a]

[Equation 1b]

는 θ, M_P 및 m를 변수로 포함하는 무차원 유효 응력을 나타내며,

이다. 한편,

는 하기 수식 2의 미분방정식을 이용하여 산출할 수 있다. In Equations 1a and 1b, σ _e and τ _xy are values representing 'effective stress' and 'effective shear stress' at the first point, respectively, and accumulate the cumulative light intensity for the structure stored in the storage unit 130. According to the effective stress (σ _e ) information and the cumulative piezoelectric intensity image generated by the image generation unit 121, r, θ, and M _P are polar coordinate components of the first point And the plastic mixing parameters, respectively. These information can be provided from the image analysis unit 122, and σ ₀ and m are values representing the yield stress and strain hardening component of the structure material. These information can be provided from the low government 130,

Represents a dimensionless effective stress including θ, M _P and m as variables,

to be. Meanwhile,

Can be calculated using the differential equation of Equation 2 below.

[Equation 2]

In Equation 2, Φ _s represents the angular variable of the stress tensor component.

)를 사용자가 확인할 수 있도록 표시할 수 있다. The display unit 150 is a plastic stress expansion coefficient calculated by the calculation processing unit 140 (

) Can be displayed for the user to check.

According to the plastic stress expansion coefficient calculation system of the present invention, it is possible not only to perform non-destructive crack detection for a structure in which plastic deformation occurs, but also by simultaneously measuring light emission of a mechano-luminescence (ML) paint applied to the structure. The plastic stress intensity factor near the existing crack tip can be calculated in real time.

Hereinafter, examples and experimental examples of the present invention will be described. However, the examples described below are only reference materials for explaining the effectiveness of the present invention and should not be construed as limiting the scope of the present invention to the following examples.

[Example]

Two 4-point shear specimens (a, b) and one as shown in FIG. 2 using a material in which 30 wt% of SAO phosphor (SrAl ₂ O ₃ : Eu) and the remaining acrylic resin are uniformly mixed. The core parts of the tension specimen (c) were prepared.

First, the material was hot-pressed at 180 ° C under a 45 KN condition using a caliber mounting machine to prepare a disc-shaped product having a diameter of 50 mm and a thickness of 3 mm, followed by a length of 36 mm, a width of 25 mm, and a thickness of 3 mm. By cutting with a rectangular plate having, a core portion of a 4-point shear specimen was prepared and expanded using an epoxy resin to prepare a 4-point shear specimen (141 mm long, 25 mm wide, 3 mm thick). In one of the two 4-point shear specimens, a blunt notch tip with a 500 μm radius was intentionally introduced using a machining center to provide an extended firing area and uniform tip field during shearing.

Subsequently, a tension specimen with a length of 12 mm, a width of 6 mm, and a thickness of 3 mm was also fabricated to evaluate the mechanical properties of the core portion from the non-notched shear specimen according to ASTM E8M-04.

In the fracture test, a 4-point shear specimen bearing mechanical cracks was placed on a universal tension test device with a shear-shaped loading stage. The core portion was irradiated for 10 minutes by an ultraviolet lamp of 365 nm wavelength, and relaxed in the dark for 5 minutes to reduce the basic fluorescence to a stable intensity before applying the shear stress. The specimen was then sheared until complete failure occurred at a cross-head speed of 0.5 mm / s. The core portion containing the notch tip was photographed at a rate of 60 frames per second under static shear stress conditions and at a rate of 1000 frames per second under conditions of quasi-dynamic cracking using a high-speed CMOS camera.

In addition, to compensate for the piezoelectricity and elastoplastic behavior of the core portion, images were stored at 60 frames per second and under similar experimental conditions including mechanical loading of 0.1 mm / s for tension and 0.5 mm / s for shear. Traditional tension tests and 4-point shear tests were performed using tension and non-notched shear specimens.

<Experimental Example 1: Mechanical properties and corrected ML (Mechano-luminescence) curve>

Figure 3a is a graph showing the results of a tensile test explaining the mechanical properties of the core portion made of SAO and acrylic resin in the tension specimen.

Referring to Figure 3a, in the tensile test, the tension specimen clearly shows a yield stress of 30 MPa according to the Ramberg-Osgood equation (yield stress, σ ₀ ), a Young's modulus (E) of 1.26 GPa, It exhibited an elasto-plastic behavior with a strain-hardening constant of 13.

3B is a graph showing the relationship between cumulative ML strength and effective shear stress measured in a 4-point shear test using a non-notched shear specimen. In the relationship between the cumulative ML strength and the effective shear stress, the description of the corrected curve or the details of the image processing procedure have been previously described in the results of the previous study and are therefore omitted in this application specification.

”를 기초로 추론된 곡선(빨강색 일점쇄선)과 일치하는 것으로 나타났다. Referring to FIG. 3B, the correction curve (solid black line) derived from the shear ML results was found to coincide with the curve (black dotted line) according to the existing theoretical extrapolation method, and the correction indirectly derived from the tensile ML results The curve (solid blue line) is “

It was found to coincide with the curve (red dot-dashed line) inferred based on ”.

”의 관계를 이용하여 플라스틱 영역 내에서 대응되는 유효 전단 응력으로 변환될 수 있음을 알 수 있다. Therefore, due to the peculiarity of the crack tip, the cumulative ML strength in the vicinity of the crack tip is clearly greater than the cumulative ML strength in the non-notched sample.

Using the relationship ”, it can be seen that it can be converted into the corresponding effective shear stress in the plastic region.

<Experimental Example 2: Tracking Virtual Crack Tip Expansion Through ML>

4 (a) to 4 (d) are images showing ML luminescence near the crack tip of a 4-point shear specimen for external stresses of 0 N, 689 N, 829 N, and 872 N. ) To (g) are images representing the surface-strength profile of ML specified from the ML images of (b) to (d), respectively.

Referring to (b) to (d) of FIG. 4, in a specimen in which three external rods of 689N, 829N, and 872N were applied, a peanut-shaped elasto-plastic ML arranged vertically near the front end of the shear crack It was confirmed that luminescence appeared.

The ML strength was found to increase slightly non-linearly as the applied shear load increased, indicating that the relationship between the elastoplastic loading and the ML strength is not simply a linear relationship to the elastic or plastic region.

Referring to (e) to (g) of FIG. 4, ML peak coordinates were found to change in parallel with the crack axis according to the evolution of the firing core field, and it was found to be inconsistent with the actual position of the crack tip. Considering Irwin's suggestion for plasticity correction in fractures, 'When plastic deformation occurs at the crack tip, the crack behaves as if it is larger than the actual physical size', the above-mentioned misalignment in the length and position of the crack The only way to describe the match is to introduce a virtual crack tip image extending to the ML peak coordinates within the firing region.

To demonstrate the hypothesis for crack extension in the firing region using the ML technique as described above, including the actual deviations evaluated from FIG. 4 for the external loads of 689N, 829N, and 872N and the plasticity correction of the effective crack length. The theoretical deviations predicted from conventional models are listed in Table 1.

method crack extension formula Extended crack length (mm) 689N 829N 872N ML method - 1.06 1.42 1.60 Irwin's model

0.85 1.23 1.36 Dugdale's model

1.04 1.52 1.68 New PZE method

0.72 1.10 1.24

Referring to Table 1, it can be seen that the deviations Δa evaluated from the pixel intensity coordinates in the image of FIG. 4 are in good agreement with the theoretical deviations predicted from the conventional models. In particular, the deviations (Δa) evaluated from the pixel intensity coordinates in the image of FIG. 4 showed almost the same results as the prediction based on the Dugdale method.

Summarizing the above, it is judged that introducing a virtual crack cracked image derived from an ML intensity image can be a useful method.

<Experimental Example 3: Elastic ML specificity>

5 (a) to 5 (c) are discontinuous constant intensity images generated by accumulating ML luminescence from 0 to 689N, 829N, and 871N, respectively, using MATLAB software, which are virtual crack tip It represents the elastic long distance field in front of.

5 (a) to (c), unlike the instantaneous ML image shown in FIGS. 4 (b) to (d), as the 4-point shear progresses and the peanut shape expands in the vertical direction It was found that the overall brightness of the accumulated ML images increased rapidly. These discontinuous ML images show the shape and size of the stress field near the crack tip according to the typical Mode II elastic field, and it can be confirmed that the elastic region can be successfully quantified under Mode II.

5 (d) to 5 (f) show discontinuous iso-strength images in the vicinity of the virtual crack tip derived based on the accumulated ML intensity for the external loads of 689N, 829N, and 872N.

5 (d) to (f), the four isochromatic contours closest to the firing criterion were selectively extracted using the MATLAB software in discontinuous iso-intensity images and using the accumulated ML far field Therefore, the elastic ML singularity may be evaluated based on the equation 3 below.

In the images (d) to (f) of FIG. 5, the intersection point of the Y line which is the vertical axis and the X line which is the horizontal axis represents the physical crack tip, and the intersection point of Y and another horizontal axis X1 is specified from the ML brightness profile of the surface. It represents a virtual crack tip.

[Equation 3]

내지

는 하기 수식 4-1 내지 4-14로 각각 정의될 수 있다. In Equation 3 above

To

Can be respectively defined by the following formulas 4-1 to 4-14.

[Formula 4-1]

[Formula 4-2]

[Formula 4-3]

[Formula 4-4]

[Formula 4-5]

[Formula 4-5]

[Formula 4-7]

[Equation 4-8]

[Equation 4-9]

[Formula 4-10]

[Formula 4-11]

[Equation 4-12]

[Formula 4-13]

[Formula 4-14]

)및 응력 확대 계수(K)의 변화율이 제로(0)로 동일하므로, 상기 수식 3은 하기 수식 4으로 변경될 수 있다. For static shear cracks, crack tip acceleration (

) And the rate of change of the stress expansion coefficient K is equal to zero (0), so Equation 3 can be changed to Equation 4 below.

[Equation 4]

To determine the mode I stress intensity factor K _I , the mode II stress intensity factor K _Ⅱ , and the far field stress value σ _ox , within the x-axis region of -45 ° θ <45 ° on the virtual crack tip and the second contour line After taking several points, K _I , K _Ⅱ and σ _ox were calculated using the nonlinear least squares method, which are _presented in Table 2 as K _I ^ML , K _Ⅱ ^ML and σ _ox ^ML .

In addition to the stress intensity factor (SIF-ML) calculated from the ML isochromatic pattern, the stress intensity factor (SIF-analytical) calculated using the analytical method (Murakami, 1987) defined in other studies for modes I and II is shown. It is shown in 1.

Applied load (N) ML method
SIF-ML Analytical method
SIF-analytical K _I ^ML K _Ⅱ ^ML σ _ox K _I ^Anal K _Ⅱ ^Anal 689 0.08 1.15 -0.05 0.12 1.26 829 0.15 1.35 -0.15 0.14 1.52 872 0.16 1.40 -0.20 0.15 1.60

Referring to Table 3, although the K _Ⅱ ^ML values of 1.15, 1.35, and 1.40 MPam ^1/2 calculated from the external shear rods 689N, 827N, and 872N were all slightly smaller than the K _Ⅱ ^Anal values, the elastic K-domain region The error with the K _II ^Anal values within was found to be small enough to be acceptable. It is judged that all K _II ^ML values are slightly smaller than K _II ^Anal values due to the influence of the virtual crack along with the plastic J-domain.

On the other hand, as shown in Table 3, despite the external shear mode II loading parallel to the crack axis, negligible values of the mode I stress intensity factor (K _I ^ML ) and the far field stress (σ _ox ) were obtained.

In addition, the ratio of the mode II stress intensity factor (K _II ^Anal ) to the mode I stress intensity factor (K _I ^Anal ) in values calculated from the analysis methods defined in other studies (Murakami, 1987) is approximately 10.5, almost constant. Although maintained, the ratio of the mode II stress intensity factor (K _II ^ML ) to the mode I stress intensity factor (K _I ^ML ) for the values calculated from the ML contours is continuously from about 14 to about 9 at 689N, 827N, and 872N. Decreased. It is believed that this phenomenon suggests a transition from Mode II to Mode I in the cracking process that defines the twisting angle.

To demonstrate the elastic shape of the stress field at the crack tip along with the magnitude of the elastic stress intensity factor (SIF), the critical effective stresses selected in Table 3 and K _I ^ML , K _II ^ML , σ _ox ^ML from Table 2 were used. The theoretical isochromatic patterns were superimposed in Figs. 5 (d) to (f).

Applied load (N) Elastic second contour Plastic second contour Acc.ML (A.U) Effective shear stress
(MPa) Acc.ML (A.U) Effective shear stress
(MPa) 689 1.57 9.8 - - 829 2.59 12.4 6.98 19.68 872 3.02 13.4 8.32 21.36

The elastoplastic boundary obtained from Von Mises yield criterion was also internalized and corresponded to the inner most theoretical contour. Fracture parameters were obtained using the second contour line, while the first and third contour lines were chosen to demonstrate experimentally calculated breakthrough parameters.

Despite partial mismatches, FIG. 5 (b) in terms of size and shape shows acceptable agreement between experimentally obtained contour plots and theoretically obtained contour plots, and local deviation Is mainly attributed to the evolution of the plastic stress field in front of the physical crack tip, along with the unrealistic sharpness of the crack tip in the shear specimen. On the other hand, when the physical crack tip is used to determine K _I ^ML , K _II ^ML and σ _ox ^ML , the shape and size values indicate the total mismatch not presented here, and this mismatch is virtual in the plastic region. It can be corrected by the introduction of a crack tip and by the nullification of the linear elastic fracture mechanism in the vicinity of the plastic region.

<Experimental Example 4: Plastic ML specificity>

(A) and (c) of FIG. 6 are discontinuous iso-intensities and iso-colors collected for analysis of the plastic near field in front of the actual crack tip using ML from the plastic region in FIGS. 5 (e) and (f). It shows ML images accumulated in the form of contour lines.

Referring to FIGS. 6A and 6C, the evolutionary trend in overall ML strength and shape associated with cumulative plastic ML images can be compared to ML strength and shape in the elastic distant field, as well as typical mode II. Compatible with plastic fields. Therefore, it is judged that even in the case of elasto-plastic crack under mode II, it can be quantified through ML technology through stress distribution and isotropic contours in the plastic region near the actual crack tip.

6 (b) and (d) are isochromatic discontinuous isochromatic images with yield criterions in front of the actual crack tip for FIGS. 6 (a) and 6 (c).

Referring to (b) and (d) of FIG. 6, when using the accumulated near field ML, plastic specificity (Plastic ML singularity) may be evaluated based on the following Equation 4-1 or Equation 4-2. Smaller contour lines shown in Figs.

[Equation 5-1]

[Equation 5-2]

는 θ, M_P 및 m를 변수로 포함하는 무차원 유효 응력을 나타내며,

이다. In Equations 5-1 and 5-2, σ _e , τ _xy , σ ₀ , K _M ^P , M _p and m are effective stress, effective shear stress, yield stress, plastic stress expansion coefficient, and near plastic mixing parameters (near), respectively. field plastic mixity parameter) and strain hardening component, r and θ indicate polar coordinate components at the crack tip,

Represents a dimensionless effective stress including θ, M _P and m as variables,

to be.

는 하기 수식 2의 미분방정식을 해결함에 의해 수치적으로 풀 수 있다. Meanwhile,

Can be solved numerically by solving the differential equation of Equation 2.

[Equation 2]

In Equation 2, Φs represents the angular variable of the stress tensor component.

The accumulated plastic ML strength values corresponding to the contour lines selected from the applied external load and effective stress can be found from the corrected curve shown in FIG. 3B, all of which are listed in Table 3.

Then, using the relationship between the plastic mixing coefficient (M ^P ) and the elastic mixing parameter (M ^e ), the plastic mixing coefficient (M ^P = 0.09) was evaluated from the elastic mixing parameter (M ^e = 0.07), and the corresponding The dimensionless effective stress (σ _s ) was predicted based on m = 13.

및

임)Finally, the plastic stress intensity factor (K _M ^p ) can be determined by measuring the distance between the actual crack tip and several points on the selected fringe loop in the isochromatic ML pattern along with the angle of inclination of the corresponding lines relative to the crack axis. there was. (For 872N and 829N respectively

And

being)

To demonstrate the effectiveness of the plastic stress intensity factor obtained from the isochromatic ML contour in the firing region, the plastic stress intensity factor was predicted indirectly from the elastic stress intensity factor using the J-integration method based on Equation 6.

[Equation 6]

In Equation 6, K _I and K _II represent the mode I elastic stress expansion coefficient and the mode II elastic stress expansion coefficient, respectively, which are listed in Table 2. And α, σ ₀ , and I _m are material constants, and yield stress and dimensionless constant of 0.9197 of 0.046 and 30 MPa, respectively.

Table 4 below shows the plastic stress expansion coefficient (K _M ^p ) measured directly from the ML plastic field and the plastic stress expansion coefficient (K _M ^pe ) indirectly predicted from the elastic stress expansion coefficient.

m = 3 ML method J-integral method Applied load (N) K _M ^p K _M ^pe 829 0.73 0.81 872 0.80 0.82

Referring to Table 4, although the indirect predicted plastic stress intensity factor (K _M ^pe ) from the elastic distal field was slightly larger than the plastic stress intensity factor (K _M ^p ) measured directly from the ML plastic field, their The deviation was found to be less than 11%. This discrepancy between K _M ^p and K _M ^pe is considered to be due to the different positions of the crack tip used to determine the elastic stress expansion coefficient and the plastic stress expansion coefficient. Specifically, when measuring the circumferential distance and the corresponding angle to evaluate the elasticity specificity, the virtual crack tip was considered as the origin, but when measuring the circumferential distance and the corresponding angle to evaluate the plastic specificity, the physical crack tip It was considered the origin. Similar to the fact that the application of an actual crack tip causes unacceptable results when determining the elastic stress intensity factor, when a hypothetical crack tip is applied to determine plastic specificity, such as the plastic stress intensity factor (K _M ^P ), This is because it has caused unacceptable results.

Summarizing the above, it is determined that the plastic stress intensity factor (K _M ^p ) can be effectively measured directly from the ML plastic field.

Although described above with reference to the preferred embodiments of the present invention, those skilled in the art may variously modify and change the present invention without departing from the spirit and scope of the present invention as set forth in the claims below. You will understand that you can.

100: plastic stress expansion coefficient calculation system
110: imaging unit 120: image processing unit
130: storage unit 140: arithmetic processing unit
150: display unit

Claims (5)

In the plastic stress expansion coefficient calculation system for calculating the plastic stress expansion coefficient for a structure where plastic deformation with mechano-luminescence (ML) paint applied occurs,
An imaging unit continuously capturing images at regular time intervals with respect to the structure;
After receiving the images of the structure from the imaging unit, calculate a cumulative piezoelectric emission intensity from a preset initial time to the present, generate a cumulative piezoelectric intensity image, and analyze the cumulative piezoelectric intensity image to the structure An image processing unit for extracting information required to calculate the existence of a crack and a plastic stress expansion coefficient;
A storage unit for storing effective stress information according to the cumulative piezoelectric strength of the structure and information about a material constant of the structure;
Plastic stress expansion coefficient of the structure using information provided from the image processing unit and information stored in the storage unit (

), A plastic stress expansion coefficient calculation system comprising a calculation processing unit for calculating. According to claim 1,
The image processing unit,
An image generating unit that receives the images of the structure imaged by the imaging unit and calculates a cumulative piezoelectric emission intensity from a preset initial time to the present, and then uses the image to generate a cumulative piezoelectric intensity image; And
And an image analysis unit that extracts first information necessary to calculate the existence of cracks and plastic stress expansion coefficients in the structure by analyzing the cumulative piezoelectric intensity image generated by the image generation unit,
When a crack is present in the structure, the image analysis unit may calculate polar coordinates for a first point located on an isochromatic fringe pattern located in a plastic core field located near the tip of the crack. Generating, determining the growth direction of the crack by using the cumulative piezoelectric intensity image, characterized in that to calculate the plastic mixing parameter (M _P ), plastic stress expansion coefficient calculation system. According to claim 2,
The calculation processing unit is applied to the equations 1a or 1b below to calculate the plastic stress expansion coefficient of the structure (

Plastic stress expansion coefficient calculation system, characterized in that to calculate):
[Equation 1a]

[Equation 1b]

In Equations 1a and 1b, σ _e and τ _xy represent 'effective stress' and 'effective shear stress' at the first point, respectively, and r, θ, and M _P are polar coordinates of the first point. ) Components and the plastic mixing parameters, respectively, σ ₀ and m represent the yield stress and strain hardening component of the structure material,

Represents a dimensionless effective stress including θ, M _P and m as variables,

to be. According to claim 1,
Plastic stress expansion coefficient calculated by the calculation processing unit (

), Further comprising a display unit for displaying, the plastic stress expansion coefficient calculation system. According to claim 1,
The structure comprises a bridge, a large machine tool or a building made of a material capable of plastic deformation, plastic stress expansion coefficient calculation system.

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