A system and method for measuring fracture toughness at the crack tip of a moving crack in a transparent cylindrical shell

Abstract

The present application relates to a kind of system and method for measuring transparent cylindrical shell motion crack tip fracture toughness, it is related to the field of dynamic fracture mechanics, system includes: cold light source, DC stabilized power supply, speckle target surface, external force loading device, high-speed camera and computer;Cold light source is used to illuminate the speckle target surface under the power supply of DC stabilized power supply;Speckle target surface has black and white interlaced paint speckle;Transparent cylindrical shell is placed in front of speckle target surface;The axis of transparent cylindrical shell is perpendicular to the direction of light path;External force loading device is used to load transparent cylindrical shell;Transparent cylindrical shell is equipped with motion crack;High-speed camera and computer are connected, computer stores digital speckle software;Light emitted by cold light source occurs diffuse reflection on speckle target surface, after passing through transparent cylindrical shell, it is received by high-speed camera and imaged, then the fracture toughness is determined by computer.The present application can accurately measure the fracture toughness of cylindrical shell structure motion crack tip.

Description

Technical Field

[0001] This invention relates to the field of dynamic fracture mechanics, and in particular to a system and method for measuring the fracture toughness at the tip of a moving crack in a transparent cylindrical shell. Background Technology

[0002] Cylindrical shell structures possess varying degrees of inherent defects. Under sudden dynamic loads such as explosions, impacts, and seismic loads, these defects can cause partial cracking or overall structural failure, leading to catastrophic consequences. Quantitative analysis of the fracture parameters of moving cracks in cylindrical shell structures is crucial for assessing their safety. Currently, the determination of the fracture toughness at the tip of a moving crack in a transparent cylindrical shell structure primarily employs strain gauge measurement. This method involves attaching multiple strain gauges to the component under test and measuring the strain values ​​in the region near the moving crack path to infer the fracture toughness. However, this method requires attaching strain gauges for each measurement, making the process cumbersome. Transmission-based digital gradient sensitivity testing technology is a novel optical measurement technique based on coherent gradient sensitivity and digital image correlation to obtain deformation information at the crack tip. There is an urgent need to develop a method combining transmission-based digital gradient sensitivity and high-speed imaging technology to more conveniently measure the fracture toughness at the tip of a moving crack in a transparent cylindrical shell structure, thereby assessing the safety of the cylindrical shell. Summary of the Invention

[0003] The purpose of this invention is to provide a system and method for measuring the fracture toughness of the moving crack tip of a transparent cylindrical shell. By combining transmission-type digital gradient sensing and high-speed imaging technology, the fracture toughness of the moving crack tip of a cylindrical shell structure can be accurately measured.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A system for measuring the fracture toughness of the tip of a moving crack in a transparent cylindrical shell includes: a cold light source 1, a DC regulated power supply 2, a speckle target 3, an external force loading device 5, a high-speed camera 6, and a computer 7.

[0006] The cold light source 1 is used to illuminate the speckle target surface 3 under the power supply of the DC regulated power supply 2; the speckle target surface 3 has black and white paint spots; the transparent cylindrical shell 4 is placed in front of the speckle target surface 3; and the axis of the transparent cylindrical shell 4 is perpendicular to the light path direction; the external force loading device 5 is used to apply a load to the transparent cylindrical shell 4; the transparent cylindrical shell 4 is provided with motion cracks 8; the high-speed camera 6 is connected to the computer 7, and the computer 7 stores digital speckle software;

[0007] The light emitted by the cold light source 1 is diffusely reflected on the speckle target surface 3, passes through the transparent cylindrical shell 4, and is received and imaged by the high-speed camera 6. The computer 7 then calculates the fracture toughness of the moving crack tip of the transparent cylindrical shell structure based on the image.

[0008] A method for measuring the fracture toughness at the tip of a moving crack in a transparent cylindrical shell, the method being applied to the system for measuring the fracture toughness at the tip of a moving crack in a transparent cylindrical shell, the method comprising:

[0009] Adjust the position and focal length of the high-speed camera 6 so that the speckle target surface 3 presents a speckle image in the center of the field of view of the high-speed camera 6;

[0010] The number of pixels corresponding to each millimeter in the speckle image is calibrated;

[0011] The transparent cylindrical shell 4 was loaded with an external force loading device 5, causing the crack to propagate.

[0012] Continuous images of crack propagation were acquired using a high-speed camera 6.

[0013] Based on the number of pixels corresponding to each millimeter and the crack propagation image, computer 7 calculates the displacement field in the X direction and the displacement field in the Y direction of the speckle target surface.

[0014] The light deflection displacement components in two perpendicular directions of the tip region of the moving crack 8 are obtained based on the displacement fields in the X and Y directions.

[0015] The fracture toughness of the crack tip of the transparent cylindrical shell structure at different times is determined based on the light deflection displacement component.

[0016] Optionally, the fracture toughness includes Type I fracture toughness and Type II fracture toughness.

[0017] Optionally, the Type I fracture toughness is determined by the following formula:

[0018] K IC =A(-U0 cosβ-U 90 sinβ+B cos 2 β)

[0019] Among them, K IC For type I fracture toughness, β is the angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell, U0 is the light deflection displacement component in the X direction of the speckle target surface, U 90 Let A and B be the light deflection displacement components in the Y direction of the speckle target surface, where A and B are geometric coefficients.

[0020] Optionally, the Type II fracture toughness is determined by the following formula:

[0021] KIIC =A(U0sinβ-U 90 cosβ-B sin βcosβ)

[0022] Among them, K IIC For type II fracture toughness, β is the angle between the extension of the moving crack and the circumferential direction of the cylindrical shell, U0 is the light deflection displacement component in the X direction of the speckle target surface, U 90 Let A and B be the light deflection displacement components in the Y direction of the speckle target surface, where A and B are geometric coefficients.

[0023] Optionally, the geometric coefficient A is determined by the following formula:

[0024]

[0025] Where Δ is the distance between the transparent cylindrical shell and the speckle target surface, c is the elastic optical constant of the transparent cylindrical shell material, h is the wall thickness of the transparent cylindrical shell, and r is the distance between the test point and the crack tip.

[0026] Optionally, the geometric coefficient B is determined by the following formula:

[0027]

[0028] Where h is the wall thickness of the transparent cylindrical shell, R is the radius of the transparent cylindrical shell, a is the length of the moving crack, r is the distance from the test point to the crack tip, and n is the refractive index of the transparent cylindrical shell material.

[0029] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0030] The transmission-type digital gradient sensing technology employed in this invention is a non-contact measurement technique. Compared to traditional strain gauge measurement methods, it eliminates the cumbersome process of attaching strain gauges each time, making the measurement steps of this system more convenient and simpler. Compared to other optical mechanical measurement techniques such as digital image correlation and caustics, crack tips are easier to identify, and experimental results are more reliable. For measuring the fracture toughness of the moving crack tip in a transparent cylindrical shell structure, this invention adds a correction term for the geometric parameters of the cylindrical shell compared to traditional methods, resulting in more accurate results. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1This is a schematic diagram illustrating the structural principle of the system for measuring the fracture toughness at the tip of a kinematic crack in a transparent cylindrical shell according to the present invention.

[0033] Figure 2 This is the optical path diagram of the transmissive digital gradient sensing technology of the present invention.

[0034] Symbol Explanation: 1-Cold light source; 2-DC regulated power supply; 3-Speckle target surface; 4-Transparent cylindrical shell; 5-External force loading device; 6-High-speed camera; 7-Computer; 8-Moving crack; a-Moving crack length; β-Angle between the moving crack and the cylindrical shell in the circumferential direction; δx-Component of the light deflection displacement caused by the strain gradient field at the crack tip along the local coordinate x′ direction on the speckle target surface; δy-Component of the light deflection displacement caused by the strain gradient field at the crack tip along the local coordinate y′ direction on the speckle target surface; δ0-Additional light deflection displacement caused by the curvature of the cylindrical shell along the global coordinate X direction on the speckle target surface; r-Distance from the center of the digital speckle calculation region to the crack tip; θ-Angle between the line connecting the center of the digital speckle calculation region and the crack tip and the crack extension line. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] The purpose of this invention is to provide a system and method for measuring the fracture toughness of the moving crack tip of a transparent cylindrical shell. By combining transmission-type digital gradient sensing and high-speed imaging technology, the fracture toughness of the moving crack tip of a cylindrical shell structure can be accurately measured.

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Figure 1 This is a schematic diagram illustrating the structural principle of the system for measuring the fracture toughness at the tip of a kinematic crack in a transparent cylindrical shell, as described in this invention. Figure 1 As shown, the system includes a cold light source 1 for illumination, a DC regulated power supply 2, a speckle target surface 3, an external force loading device 5, a high-speed camera 6, and a computer 7 containing digital speckle-related software. The cold light source 1 illuminates the speckle target surface 3 under the power supply of the DC regulated power supply 2, and a transparent cylindrical shell 4 is placed in front of the speckle target surface 3. The light emitted by the cold light source 1 undergoes diffuse reflection on the speckle target surface 3, passes through the transparent cylindrical shell 4 containing the moving crack 8, and is received and imaged by the high-speed camera 6, and then stored by the computer 7.

[0039] For digital speckle correlation software, please refer to the literature Yao XF, Meng LB, Jin JC, Yeh HY. Full-field deformation measurement of fiber composite pressure vessel using digital speckle correlation method. Polymer Testing 2005, 24(2):245-251.

[0040] Based on the above structure, the method provided by the present invention includes the following steps:

[0041] 1) Spray black and white paint spots onto the speckle target surface as a speckle marker.

[0042] 2) Fix the transparent cylindrical shell on the external force loading device so that the axis of the cylindrical shell is perpendicular to the direction of the light path.

[0043] 3) Aim the high-speed camera at the transparent cylindrical shell and the speckle target behind it, adjust the position and focal length of the high-speed camera so that the speckle target is in the center of the high-speed camera's field of view to form a clear speckle image, mark how many pixels each millimeter corresponds to in the image, and take a picture.

[0044] 4) Apply an external force loading device to the transparent cylindrical shell to cause the crack to expand, and take continuous photos using a high-speed camera.

[0045] 5) The displacement fields in the X and Y directions of the speckle target surface were calculated using digital speckle correlation software, and the light deflection displacement components in the two perpendicular directions in the region near the tip of the moving crack on the speckle target surface were obtained.

[0046] 6) The fracture toughness of the crack tip of the transparent cylindrical shell structure at different times is obtained from the light deflection displacement component.

[0047] In calculating fracture toughness, it is assumed that U0 and U 90 Let be the light deflection displacement components in the X and Y directions of the speckle target surface, respectively. The center of the digital speckle calculation region is located on the extension line of the moving crack, and the distance from the crack tip is r, that is, the distance from the test point to the crack tip is r. Then, the type I fracture toughness K at the tip of the moving crack in the cylindrical shell structure is... IC Type II fracture toughness K IIC They are respectively:

[0048] K IC =A(-U0cosβ-U 90 sinβ+Bcos 2 β)

[0049] K IIC=A(U0sinβ-U 90 cosβ-Bsinβcosβ)

[0050] Where β is the angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell, and the coefficients A and B are calculated using the following formula:

[0051]

[0052]

[0053] Where c and n are the elastic optical constants and refractive index of the transparent cylindrical shell material, respectively; h and R are the wall thickness and radius of the cylindrical shell component, respectively; Δ is the distance between the cylindrical shell and the speckle target surface; and a is the length of the moving crack.

[0054] Figure 2 This diagram illustrates the light ray deflection near the tip of a moving crack caused by light passing through a cylindrical shell component. `oxyz` is a local coordinate system fixed at the tip of the moving crack in the cylindrical shell, with the x-axis along the crack extension line, the y-axis perpendicular to the crack extension line, and the z-axis along the light ray propagation direction. `o′x′y′` is a local coordinate system fixed on the speckle target surface corresponding to `oxy`, and `OXY` is a global coordinate system fixed on the speckle target surface. According to the theory of plate and shell fracture mechanics, when an external force load causes crack propagation in the cylindrical shell, the stress state at the tip of the moving crack in any direction is as follows:

[0055]

[0056]

[0057]

[0058] Wherein K represents the normal stress along the x-axis, the normal stress along the y-axis, and the shear stress, respectively. IC K IIC θ represents the dynamic fracture toughness at the tip of a moving crack in a cylindrical shell, where r and θ are polar coordinates with the crack tip as the origin.

[0059] Based on the principles of elastic optics, the strain gradient field at the crack tip causes a change in the optical path difference, resulting in a deflection of light rays in the vicinity. According to the Maxwell-Neumann law and the generalized Hooke's law, the components of the light ray deflection displacement caused by the strain gradient field at the moving crack tip along the local coordinates x′ and y′ on the speckle target surface are as follows:

[0060]

[0061] Where c is the elastic optical constant of the transparent cylindrical shell material, h is the wall thickness of the cylindrical shell component, and Δ is the distance between the cylindrical shell and the speckle target surface.

[0062] Substituting formula ① into formula ②, the components of the light ray deflection displacement along the x′ and y′ directions on the extension line of the moving crack (i.e., θ=0°) can be simplified as:

[0063]

[0064] Based on the coordinate transformation relationship, the components of the ray deflection displacement along the global coordinates X and Y directions on the speckle target surface are:

[0065]

[0066] Where β is the angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell.

[0067] According to the principles of geometric optics imaging, such as Figure 2 In the global coordinate system OXY, the additional ray deflection displacement along the X direction on the speckle target surface caused by the curvature of the cylindrical shell is:

[0068]

[0069] Where n is the refractive index of the transparent cylindrical shell material, and R is the radius of the cylindrical shell component.

[0070] Considering the combined effects of the strain gradient field near the crack in an arbitrary direction of movement of the cylindrical shell structure and the curvature of the cylindrical shell on light deflection, assuming U0 and U 90 Let X and Y be the light ray deflection displacement components along the X and Y directions at a distance r from the tip of the moving crack on the extension line of the crack in the cylindrical shell under test. Solve the simultaneous equations:

[0071]

[0072] The type I fracture toughness K at the tip of a kinematic crack in a cylindrical shell structure IC Type II fracture toughness K IIC They are respectively:

[0073]

[0074] Where β is the angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell, and the coefficients A and B are calculated using the following formula:

[0075]

[0076]

[0077] This invention employs digital gradient sensing technology, using a high-speed camera to record in real time the black and white speckle pattern on the speckle target surface behind the transparent cylindrical shell structure. By measuring the light deflection displacement field near the tip of the moving crack, the fracture toughness of the moving crack tip of the transparent cylindrical shell structure at different times is obtained.

[0078] The digital gradient sensing technology used in this invention belongs to non-contact, full-field real-time optical mechanical measurement technology. Compared with traditional strain electrical measurement methods, it eliminates the cumbersome process of pasting strain gauges, making the measurement steps simpler and more convenient.

[0079] This invention addresses the dynamic fracture problem of transparent cylindrical shell structures by proposing a method for measuring the fracture toughness of moving crack tips based on digital gradient sensing technology. This method comprehensively considers the influence of the strain gradient field near the moving crack in any direction and the curvature of the cylindrical shell on the deflection of light, making the experimental results more accurate.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0081] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A system for measuring the fracture toughness at the tip of a kinematic crack in a transparent cylindrical shell, characterized in that, include: Cold light source (1), DC regulated power supply (2), speckle target surface (3), external force loading device (5), high-speed camera (6), and computer (7); The cold light source (1) is used to illuminate the speckle target surface (3) under the power supply of the DC regulated power supply (2); the speckle target surface (3) has black and white paint spots; the transparent cylindrical shell (4) is placed in front of the speckle target surface (3); and the axis of the transparent cylindrical shell (4) is perpendicular to the light path direction; the external force loading device (5) is used to apply a load to the transparent cylindrical shell (4); the transparent cylindrical shell (4) is provided with motion cracks (8); the high-speed camera (6) is connected to the computer (7), and the computer (7) stores digital speckle software; Aim the high-speed camera at the transparent cylindrical shell and the speckle target behind it, adjust the position and focal length of the high-speed camera so that the speckle target is in the center of the high-speed camera's field of view to form a clear speckle image, mark how many pixels each millimeter corresponds to in the image, and take a picture. The external force loading device applies force to the transparent cylindrical shell, causing the crack to propagate, and a high-speed camera is used to continuously capture photographs; The digital speckle software calculates the displacement fields in the X and Y directions of the speckle target surface, and obtains the light deflection displacement components in two perpendicular directions in the region near the moving crack tip on the speckle target surface. The fracture toughness of the moving crack tip of the transparent cylindrical shell structure at different times is obtained from the light deflection displacement components. The light emitted by the cold light source (1) is diffusely reflected on the speckle target surface (3), passes through the transparent cylindrical shell (4), and is received and imaged by the high-speed camera (6). The computer (7) then calculates the fracture toughness of the moving crack tip of the transparent cylindrical shell structure based on the image. The fracture toughness includes Type I fracture toughness and Type II fracture toughness; The type I fracture toughness K IC Type II fracture toughness K IIC They are respectively: Among them, U0 and U 90 These represent the light deflection displacement components in the X and Y directions of the speckle target surface, respectively. β Let A and B be the angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell. The coefficients A and B are calculated using the following formula: Where r is the distance from the test point to the crack tip, c and n are the elastic optical constants and refractive index of the transparent cylindrical shell material, h and R are the wall thickness and radius of the cylindrical shell component, Δ is the distance from the cylindrical shell to the speckle target surface, and a is the length of the moving crack.

2. A method for measuring the fracture toughness at the tip of a kinematic crack in a transparent cylindrical shell, characterized in that, The method is applied to the system for measuring the fracture toughness at the tip of a kinematic crack in a transparent cylindrical shell as described in claim 1, the method comprising: Adjust the position and focal length of the high-speed camera (6) so that the speckle target surface (3) presents a speckle image in the center of the field of view of the high-speed camera (6); The number of pixels corresponding to each millimeter in the speckle image is calibrated; The transparent cylindrical shell (4) is loaded with an external force loading device (5), causing the crack to expand; Crack propagation images were continuously acquired using a high-speed camera (6); Based on the number of pixels corresponding to each millimeter and the crack propagation image, the computer (7) calculates the displacement field in the X direction and the displacement field in the Y direction of the speckle target surface (3). The light deflection displacement components in two perpendicular directions of the tip region of the moving crack (8) are obtained based on the displacement field in the X direction and the displacement field in the Y direction. The fracture toughness of the crack tip of the transparent cylindrical shell structure at different times is determined based on the light deflection displacement component. The fracture toughness includes Type I fracture toughness and Type II fracture toughness; The Type I fracture toughness is determined by the following formula: in, Type I fracture toughness, β The angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell. U 0 represents the light deflection displacement component in the X direction of the speckle target surface. U 90 Let A and B be the light deflection displacement components in the Y direction of the speckle target surface, where A and B are geometric coefficients. Type II fracture toughness is determined by the following formula: in, It has type II fracture toughness. β The angle between the extension line of the moving crack and the circumferential direction of the cylindrical shell. U 0 represents the light deflection displacement component in the X direction of the speckle target surface. U 90 Let A and B be the light deflection displacement components in the Y direction of the speckle target surface, where A and B are geometric coefficients. The geometric coefficient A is determined by the following formula: The geometric coefficient B is determined by the following formula: Where Δ is the distance between the transparent cylindrical shell and the speckle target surface. c The elastic optical constants of the transparent cylindrical shell material; h Let be the wall thickness of the transparent cylindrical shell, and r be the distance from the point to be measured to the crack tip. R Let be the radius of the transparent cylindrical shell. a The length of the moving crack. n is the refractive index of the transparent cylindrical shell material.

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