Gaussian curve ultrasonic fatigue specimen, design method and test method thereof

Abstract

The application discloses a Gaussian curve ultrasonic fatigue test sample, a design method and a test method thereof, and belongs to the technical field of metal material ultrahigh cycle fatigue performance testing. The application is aimed at the Gaussian curve ultrasonic fatigue test sample, and firstly solves the size design problem thereof, deduces a sample end length formula under the condition of satisfying ultrasonic frequency resonance, and then obtains a stress amplitude formula; further, a stress conversion formula between the Gaussian curve sample and the hourglass-shaped sample is deduced, and the stress amplitude control of the Gaussian curve sample is realized by using existing equipment and software. Under the condition of similar sample size or volume, the control volume of the Gaussian curve sample is larger than that of the dog bone-shaped sample and the hourglass-shaped sample, so that a more safe fatigue strength evaluation result can be obtained when the Gaussian curve sample is used for evaluating the ultralong life of a metal material structure.

Description

Technical Field

[0001] This invention belongs to the field of ultra-high cycle fatigue performance testing technology for metallic materials, and more specifically, relates to the design and stress control of a Gaussian curve ultrasonic fatigue specimen. Background Technology

[0002] Ultrasonic fatigue testing is a new technology for testing the fatigue properties of materials. It uses an ultrasonic generator to produce 2.0 × 10⁻⁶ ultrasonic waves. 4 A piezoelectric ceramic transducer converts a Hz electrical signal into a mechanical vibration of the same frequency. This vibration is amplified by a displacement amplifier and transmitted to the sample, generating a resonant wave within the sample, thus giving the sample a frequency of 2.0 × 10⁻⁶. 4 Hz represents the axial displacement and stress that vary sinusoidally, such as... Figure 1 Ultrasonic fatigue testing operates at extremely high frequencies, which can greatly improve the efficiency of fatigue testing. It has been widely used in ultra-long life durability design and service safety assessment in fields such as aerospace, nuclear power, railway wheel axles and tracks.

[0003] Generally, low-cycle fatigue (<10) 5 ) and high-cycle fatigue (<10) 7 When the applied stress is large, fatigue failure tends to initiate from the sample surface, such as... Figure 2 As shown, when the load is reduced, it is insufficient to induce surface crack initiation in the specimen. The fatigue crack initiation site shifts from the specimen surface to the interior of the specimen. At this point, the fatigue life extends from the high-cycle range to the ultra-high-cycle range (>10). 7 Therefore, ultra-high cycle fatigue tends to initiate cracking from internal defects in the specimen, such as... Figure 3 As shown. Generally, high-cycle fatigue strength is referred to as surface fatigue strength, while ultra-high-cycle fatigue strength is referred to as volumetric fatigue strength.

[0004] The stress distribution of the specimen is defined as 0.9σ. max ~σ max The volume region is called the control volume V. Generally speaking, the larger the control volume of the specimen, the lower the probability of defects inside the specimen, and the lower its ultra-high cycle fatigue strength. Therefore, when evaluating the ultra-long life of a material structure, the control volume of the specimen should be as large as possible in order to obtain a safer ultra-high cycle fatigue strength value.

[0005] Due to the excessively high vibration frequency, ultrasonic fatigue specimens can only be designed to be very small. Currently, the commonly used rod-shaped ultrasonic fatigue specimens are dog-bone and hourglass shapes. The disadvantage of these two types of specimens is that the stress distribution in their working section is not uniform. Figure 4 and Figure 5 As shown, the control volume of the sample is relatively small, resulting in a higher ultra-high cycle fatigue strength value, which may lead to a dangerous fatigue strength assessment result. Summary of the Invention

[0006] To address the issue of relatively small control volumes in dog-bone and hourglass-shaped specimens, this invention designs a Gaussian curve ultrasonic fatigue specimen. The working segment of the Gaussian curve specimen exhibits a uniform stress distribution, and its contour is derived based on the uniform stress distribution conditions. Under similar specimen size or volume conditions, the control volume of the Gaussian curve specimen is larger than that of dog-bone and hourglass-shaped specimens. Therefore, when using it for ultra-long-life assessment of metallic material structures, more reliable fatigue strength assessment results can be obtained.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for designing a Gaussian curve ultrasonic fatigue specimen is provided, comprising:

[0008] The density and dynamic elastic modulus of the test material are measured, and the relevant parameter values ​​are calculated based on the density and dynamic elastic modulus.

[0009] Based on the preset working section length L3 and the initial working section diameter D2, the Gaussian curve section diameter equation is obtained by analytical calculation. Based on the Gaussian curve section diameter equation, the control volume of the working section is obtained by integration. The integrated working section control volume is used as the preset control volume value. The Gaussian curve of the sample working section is designed based on the preset control volume value.

[0010] Based on the designed working section Gaussian curve and the preset end diameter D1 and transition arc length L2, the end length L1 of the Gaussian curve specimen is derived, thus completing the size design of the Gaussian curve ultrasonic fatigue specimen.

[0011] In some optional implementations, the profile of the cylindrical end of the Gaussian curve specimen is obtained by D(x) = D1, -(L1+L2)≤x≤-L2; 2L3+L2≤x≤2L3+L2+L1, and the profile of the transition arc segment of the Gaussian curve specimen is obtained by D(x) = D2cosh(αx), -L2≤x≤0; 2L3≤x≤2L3+L2, where...

[0012] In some alternative implementations, by The cross-sectional area s3(x) at point x of the Gaussian curve is obtained from... The equation for the cross-sectional diameter at point x on the Gaussian curve is obtained as D3(x), where S0 represents the area constant related to the boundary conditions, k represents the ratio of ω to C, i.e., k = ω / C, ω represents the angular frequency, and C represents the propagation speed of the resonant wave in the sample.

[0013] In some alternative implementations, by The control volume V of the working section is obtained, and erf(x) represents the error function.

[0014] In some alternative implementations, by The length of the sample end L1 is obtained, and N = D1 / D2.

[0015] According to another aspect of the present invention, a Gaussian curve ultrasonic fatigue specimen is provided, which is obtained by the design method of Gaussian curve ultrasonic fatigue specimen as described in any one of the above claims.

[0016] According to another aspect of the present invention, a test method for ultrasonic fatigue specimens based on the above-described Gaussian curve is provided, comprising:

[0017] The end displacement amplitude U0 is preset, and the stress amplitude calculation formula for the Gaussian curve specimen is obtained based on the relationship between stress amplitude and end displacement amplitude.

[0018] A stress conversion formula between Gaussian curve specimens and hourglass-shaped specimens is derived to convert the stress amplitude of the Gaussian curve ultrasonic fatigue specimens into the corresponding stress amplitude of the hourglass-shaped specimens, thereby achieving stress amplitude control of Gaussian curve ultrasonic fatigue.

[0019] In some alternative implementations, by The formula for calculating the stress amplitude of the Gaussian curve specimen is obtained, where σ is the stress amplitude of the working segment of the Gaussian curve specimen, and N = D1 / D2. E d This indicates the dynamic elastic modulus of the sample.

[0020] In some alternative implementations, by A stress transformation formula between Gaussian curve specimens and hourglass specimens is derived, where σ is the stress amplitude of the working segment of the Gaussian curve specimen. This represents the stress amplitude of an hourglass-shaped specimen under the same displacement amplitude. D1 0 Indicates the diameter of the end of the hourglass-shaped sample. Indicates the initial diameter of the working section of the hourglass-shaped specimen, l b l represents half the length of the variable cross-section of the hourglass-shaped specimen. d Indicates the length of the end of the hourglass-shaped sample, such as Figure 4 As shown.

[0021] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0022] 1. The stress distribution in the working section of the Gaussian curve ultrasonic fatigue specimen described in this invention is more uniform. Under similar specimen size or volume conditions, the control volume of the Gaussian curve specimen is larger than that of the dog bone-shaped specimen and the hourglass-shaped specimen. When using it to evaluate the ultra-long life of metallic materials, a safer fatigue strength evaluation result can be obtained.

[0023] 2. Based on the working principle of ultrasonic fatigue testing, the stress amplitude of the Gaussian curve specimen is converted into the stress amplitude of the hourglass specimen. No software upgrade is required, and stress control of the Gaussian curve ultrasonic fatigue specimen can be achieved using existing equipment and software. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of an ultrasonic fatigue test principle provided by an embodiment of the present invention, wherein: 1: industrial control computer; 2: ultrasonic generator; 3: piezoelectric transducer; 4: displacement amplifier; 5: ultrasonic fatigue specimen; 6: end of ultrasonic fatigue specimen; a: axial stress distribution of specimen; b: axial displacement distribution of specimen.

[0025] Figure 2 This is a high-cycle fatigue fracture surface provided in an embodiment of the present invention, N f <10 7 ;

[0026] Figure 3 This is an ultra-high cycle fatigue fracture surface provided in an embodiment of the present invention, N f >10 7 ;

[0027] Figure 4 This is an hourglass-shaped ultrasonic fatigue specimen provided in an embodiment of the present invention, wherein a represents the stress distribution and b represents the displacement distribution;

[0028] Figure 5 This is a dog bone-shaped ultrasonic fatigue specimen provided in an embodiment of the present invention, wherein a represents the stress distribution and b represents the displacement distribution;

[0029] Figure 6 This invention provides a Gaussian curve ultrasonic fatigue specimen, wherein: 1: cylindrical end of the specimen with a straight outline; 2: transition arc segment of the specimen with a catenary outline; 3: working segment of the specimen with a Gaussian curve outline; D1: end diameter; D2: initial diameter (or minimum diameter) of the working segment; L1: end length of the specimen; L2: length of the transition arc segment; L3: half the length of the working segment. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0031] This invention addresses the issue of dimensional design for Gaussian curve ultrasonic fatigue specimens. It first derives the formula for the specimen end length under ultrasonic frequency resonance conditions, then calculates the stress amplitude formula, and further derives the stress conversion formula between Gaussian curve specimens and hourglass-shaped specimens. Finally, it utilizes existing equipment and software to achieve stress amplitude control for Gaussian curve specimens.

[0032] Figure 6 The technical solution provided by this invention for the Gaussian curve ultrasonic fatigue specimen consists of two parts: Gaussian curve specimen size design and stress amplitude control.

[0033] In this embodiment of the invention, the design of the Gaussian curve sample size is accomplished from the following three aspects.

[0034] 1: First, measure the density and dynamic elastic modulus of the test material, and then calculate the relevant parameter values ​​based on the density and dynamic elastic modulus;

[0035] 2: Design the working section of the sample, i.e. the Gaussian curve section. According to the preset working section length L3 and the initial diameter D2, the Gaussian curve section diameter equation is obtained by analytical calculation. According to the Gaussian curve section diameter equation, the control volume of the working section is obtained by integration. The integrated working section control volume is used as the preset control volume value. Based on this, the Gaussian curve of the working section of the sample can be designed by the preset control volume value. According to Equation (10), the preset control volume value is obtained by adjusting D2 and L3.

[0036] 3: Based on the designed working section Gaussian curve and the preset end diameter D1 and transition arc length L2, the end length L1 of the Gaussian curve specimen is derived, thus completing the size design of the Gaussian curve ultrasonic fatigue specimen.

[0037] In this embodiment of the invention, after the dimensional design is completed, the stress amplitude control is accomplished from the following two aspects.

[0038] 1: Preset the end displacement amplitude U0, and obtain the stress amplitude calculation formula for the Gaussian curve specimen based on the relationship between stress amplitude and end displacement amplitude;

[0039] 2: Further, the stress conversion formula between Gaussian curve specimens and hourglass specimens is derived, and the stress amplitude of the Gaussian curve ultrasonic fatigue specimen is converted into the stress amplitude of the hourglass specimen on the control software. The existing equipment and software are used to complete the stress amplitude control of Gaussian curve ultrasonic fatigue.

[0040] The technical solution will be described in detail below.

[0041] 1. To Figure 6 The Gaussian curve specimen shown in the invention includes the following steps in the method for designing the size of the Gaussian curve specimen:

[0042] 1.1) Test the density ρ and dynamic elastic modulus E of metallic materials. d The system's vibration frequency f = 2.0 × 10⁻⁶ 4 Hz, composed of ρ and E d We can find ω = 2πf from f. Where ω is the angular frequency; C is the propagation velocity of the resonant wave in the sample, which can be further calculated as follows:

[0043] 1.2) Design of Gaussian curve segments

[0044] The Gaussian curve sample is divided into three parts, such as... Figure 6 As shown in the image.

[0045] Part-1 is the cylindrical end with a straight outline, and Part-2 is the transition arc with a catenary outline.

[0046]

[0047] in

[0048] Part-3 is the working section, and its outline is a Gaussian curve. Preset D1, D2, L2, and L3, where D1 is the diameter of the sample end, D2 is the initial diameter (or minimum diameter) of the working section, L2 is the length of the transition arc, and L3 is half the length of the working section.

[0049] The one-dimensional longitudinal wave equation is:

[0050]

[0051] Assuming the sample satisfies the resonance condition, u(x,t) is separated into variables u(x,t)=u(x)e iωt Substituting into equation (1), we get:

[0052] u" "x" + P(x)u'(x) + k 2 u(x)=0 (2)

[0053] in, u(x) is the displacement amplitude at point x of the sample, and s(x) is the cross-sectional area at point x of the sample.

[0054] From equation (2), we can calculate the expression for s(x) as follows:

[0055]

[0056] Where S0 represents the area constant related to the boundary conditions.

[0057] The ultrasonic fatigue specimen has relatively low stress and exhibits linear elasticity. The working section of the specimen is designed to have uniform stress; therefore, the displacement distribution within the working section is linear and can be expressed as:

[0058] u(x)=A(kx)+B (4)

[0059] Here, A and B are constants that depend on the boundary conditions.

[0060] From equation (4), equation (3) can be simplified to:

[0061]

[0062] in, c = k -1 .

[0063] Let u3(x) represent the displacement amplitude of the working segment, i.e., the Gaussian curve segment. Due to the symmetry condition, the displacement amplitude in the middle of the sample is 0, that is:

[0064] u3(L3)=0 (6)

[0065] From equations (4) and (6), we can obtain:

[0066] B / A = -kL3 (7)

[0067] Substituting equation (7) into equation (5), we can obtain the cross-sectional area and diameter of the Gaussian curve segment as follows:

[0068]

[0069]

[0070] D3(x) is in Figure 6 The diameter of the cross section at position x in the coordinate system shown.

[0071] Integrating equation (8) yields the volume of the working segment, i.e., the Gaussian curve segment, i.e., the control volume V.

[0072]

[0073] Where erf(x) represents the error function.

[0074] 1.3) Calculation of the end length of the Gaussian curve specimen

[0075] Depend on Figure 1 It can be seen that at the cross-section of the sample and the displacement amplifier, i.e. Figure 6 At x = -(L1 + L2), the displacement amplitude of the specimen is U0 and the stress amplitude is 0, that is:

[0076]

[0077] Where u1 and u'1 represent the displacement and strain amplitude distribution of Part-1, i.e., the end cylinder, respectively.

[0078] From the interface between Part-1 and Part-2, i.e. Figure 6 The continuity conditions for displacement and strain at x = -L2 can be obtained as follows:

[0079]

[0080] Where u2 and u'2 represent the displacement and strain amplitude distributions of Part-2, i.e., the transition arc segment, respectively.

[0081] From the interface of Part-2 and Part-3, that is Figure 6 The continuity conditions for displacement and strain at x=0 can be obtained as follows:

[0082]

[0083] Where u3 and u'3 represent the displacement and strain amplitude distributions of Part-3, i.e., the working section, respectively.

[0084] From equations (11) to (13), the expression for the end length L1 of the ultrasonic fatigue specimen satisfying the Gaussian curve under the ultrasonic frequency resonance condition can be obtained:

[0085]

[0086] Where N = D1 / D2,

[0087] Thus, the design of the Gaussian curve sample size is completed, that is, the sample end length L1 is obtained from the preset D1, D2, L2, L3 and equation (14). The control volume value can be obtained from equation (10).

[0088] 2. The above describes a design method for ultrasonic fatigue specimens with Gaussian curves, applicable to stress ratios of -1 and vibration frequencies of f = 2.0 × 10⁻⁶. 4 The axial tensile-compression ultrasonic fatigue test at Hz ensures that the Gaussian curve specimen can resonate on the ultrasonic fatigue testing machine. The following describes a stress control method for the Gaussian curve specimen, converting the stress amplitude of the Gaussian curve ultrasonic fatigue specimen into the stress amplitude corresponding to the hourglass-shaped specimen in the control software, and utilizing existing equipment and software to achieve stress control of the Gaussian curve specimen.

[0089] After designing the dimensions D1, D2, L2, L3, and L1 of the Gaussian curve specimen, the displacement amplitude U0 at the specimen end is preset. The stress distribution function of the Gaussian curve specimen can be obtained by differentiating the displacement amplitude function, and the stress amplitude of the Gaussian curve specimen can be further calculated as follows:

[0090]

[0091] Where σ is the stress amplitude of the working section of the Gaussian curve specimen, and N = D1 / D2,

[0092] Ultrasonic fatigue testing controls the stress amplitude by controlling the displacement amplitude at the end of the specimen. Therefore, for a Gaussian curve specimen with a preset stress amplitude σ, the end displacement amplitude U0 is first determined by equation (15).

[0093] Figure 4 The image shows an hourglass-shaped sample in the system control software, with its dimensions defined as D1. 0 D0 0 , l b , l d The relationship between the maximum stress amplitude and the end displacement amplitude of the hourglass-shaped specimen working section is as follows:

[0094]

[0095] in,

[0096] The stress amplitude of the hourglass-shaped specimen with the same displacement amplitude as the Gaussian curve specimen can be obtained from equations (15) and (16):

[0097]

[0098] In the formula: σ represents the stress amplitude of the Gaussian curve specimen; This represents the stress amplitude of an hourglass-shaped specimen under the same displacement amplitude.

[0099] Equation (17) can be used to convert the stress amplitude of the Gaussian curve specimen into the stress amplitude of the hourglass specimen in the system control software, so that the stress amplitude control of the Gaussian curve specimen can be achieved using existing equipment and software.

[0100] Example 1

[0101] Taking a low-alloy high-strength weather-resistant steel used in train bogies as an example, in order to evaluate its fatigue strength during its ultra-long service life, a Gaussian curve ultrasonic fatigue test specimen was designed to test its ultra-long service fatigue life. The implementation steps are as follows:

[0102] 1. The dynamic elastic modulus E of low-alloy high-strength weather-resistant steel was measured. d =210GPa, density ρ=7850kg / m³ 3 .

[0103] 2. Design as follows Figure 6The Gaussian curve specimen shown was subjected to an axial tensile-compression ultra-high cycle fatigue test with a stress ratio of -1 using an ultrasonic fatigue testing machine. Preset Gaussian curve dimensions: length of the transition arc L2 = 10 mm; half the length of the working section L3 = 24 mm; end diameter D1 = 11 mm; initial diameter of the working section D2 = 5 mm. According to equation (14), the end length L1 of the specimen is calculated to be 7.69 mm, and the cross-sectional diameter of the Gaussian curve segment of the working section is... The control volume of the sample, V = 1051 mm, is obtained by solving equation (10). 3 .

[0104] 3. Process according to the Gaussian curve equation and the equivalent values ​​of D1, D2, L1, L2, and L3. Figure 6 The ultrasonic fatigue specimen with the Gaussian curve shown was polished after processing to achieve a surface finish R. a =0.2μm.

[0105] 4. The preset loading stress amplitude is 300MPa, and the corresponding end displacement amplitude is 43.3μm obtained by solving equation (15).

[0106] 5. Open the ultrasonic fatigue system control software, select the hourglass-shaped specimen, and determine the dimensional parameters of the hourglass-shaped specimen. b =20mm, The control software determines the end length l of the hourglass-shaped specimen. d = 9.86mm.

[0107] 6. The stress amplitude of the hourglass-shaped specimen under the same displacement amplitude is obtained from equation (17). It is 894 MPa.

[0108] 7. Install the processed specimen in the displacement amplifier of the ultrasonic fatigue testing machine, adjust the cooling air nozzle, and spray cooling air onto the working section of the specimen.

[0109] 8. After setting all test parameters in the control system software, begin the axial tensile-compression ultrasonic fatigue test of the Gaussian curve specimen. The vibration frequency is 20 kHz, and the test duration is 1.38 × 10⁻⁶. 7 After several cycles, the sample broke.

[0110] Example 2

[0111] Taking 3D-printed aluminum alloy as an example, in order to evaluate its fatigue strength during ultra-long service life, a Gaussian curve ultrasonic fatigue specimen was designed to test its ultra-long service fatigue life. The implementation steps are as follows:

[0112] 1. The dynamic elastic modulus E of the 3D printed aluminum alloy material was measured. d =76.6 GPa, density ρ = 2770 kg / m³3 .

[0113] 2. Design as follows Figure 6 The Gaussian curve specimen shown was subjected to an axial tensile-compression ultra-high cycle fatigue test with a stress ratio of -1 using an ultrasonic fatigue testing machine. Preset Gaussian curve dimensions: length of the transition arc L2 = 10 mm; half the length of the working section L3 = 20 mm; end diameter D1 = 20 mm; initial diameter of the working section D2 = 10 mm. According to equation (14), the end length of the specimen is calculated to be 12.13 mm, and the cross-sectional diameter of the Gaussian curve segment of the working section is... The control volume of the sample, V = 3392 mm², is obtained by solving equation (10). 3 .

[0114] 3. Process according to the Gaussian curve equation and the equivalent values ​​of D1, D2, L1, L2, and L3. Figure 6 The ultrasonic fatigue specimen with the Gaussian curve shown was polished after processing to achieve a surface finish R. a =0.2μm.

[0115] 4. The preset loading stress amplitude is 120MPa, and the corresponding end displacement amplitude is 42.7μm obtained by solving equation (15).

[0116] 5. Open the ultrasonic fatigue system control software, select the hourglass-shaped specimen, and determine the dimensional parameters of the hourglass-shaped specimen. b =20mm, The control software determines the end length l of the hourglass-shaped specimen. d = 9.86mm.

[0117] 6. The stress amplitude of the hourglass-shaped specimen under the same displacement amplitude is obtained from equation (17). It is 321 MPa.

[0118] 7. Install the processed specimen in the displacement amplifier of the ultrasonic fatigue testing machine, adjust the cooling air nozzle, and spray cooling air onto the working section of the specimen.

[0119] 8. After setting all test parameters in the control system software, begin the axial tensile-compression ultrasonic fatigue test of the Gaussian curve specimen. The vibration frequency is 20kHz, and the test lasts for 2.52 × 10⁻⁶ hours. 7 After several cycles, the sample broke.

[0120] The above is a detailed description of the embodiments of the present invention. Through the above implementation measures, the size design of the Gaussian curve ultrasonic fatigue specimen and the stress amplitude control based on the existing control software can be completed. The above implementation measures are only examples, and the present invention is not limited to the specific embodiments of the Gaussian curve specimen with the above materials, shapes and sizes.

[0121] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0122] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing a Gaussian curve ultrasonic fatigue specimen, characterized in that, include: The density and dynamic elastic modulus of the test material were measured, and the angular frequency was calculated based on the density and dynamic elastic modulus. ω The propagation speed of the resonant wave in the sample C Among them, the cylindrical end of the sample has a straight outline; the transition arc section of the sample has a catenary outline; and the working section of the sample has a Gaussian curve outline. According to the preset working section length 2 L 3 and the initial diameter of the working section D 2. The equation for the diameter of the Gaussian curve section is obtained through analytical calculation. Based on this equation, the control volume of the working section is obtained by integration. This integrated control volume is used as the preset control volume value. The Gaussian curve of the working section of the sample is then designed based on this preset control volume value. Gaussian curves are obtained x Cross-sectional area at point ,Depend on Gaussian curves are obtained x Equation of the cross-sectional diameter at point , This represents the area constant related to the boundary conditions. express ω and C The ratio, i.e. k = ω / C ; The Gaussian curve of the designed working section and the preset end diameter D 1 and the length of the transition arc segment L 2. Derive the end length of the Gaussian curve specimen. L 1. Complete the dimensional design of the Gaussian curve ultrasonic fatigue specimen, wherein, by Obtain the length of the sample end , N = D 1 / D 2, .

2. The design method according to claim 1, characterized in that, Depend on Obtain the control volume of the working section , .

3. A Gaussian curve ultrasonic fatigue specimen obtained by the design method of the Gaussian curve ultrasonic fatigue specimen according to claim 1 or 2.

4. A test method for an ultrasonic fatigue specimen based on the Gaussian curve described in claim 3, characterized in that, include: Preset end displacement amplitude U 0. Based on the relationship between stress amplitude and end displacement amplitude, the formula for calculating the stress amplitude of the Gaussian curve specimen is obtained, where, from The formula for calculating the stress amplitude of the Gaussian curve specimen is obtained. σ The stress amplitude of the working section of the Gaussian curve specimen. N = D 1 / D 2, , Indicates the dynamic elastic modulus of the specimen; A stress conversion formula between Gaussian curve specimens and hourglass-shaped specimens was derived to convert the stress amplitude of the Gaussian curve ultrasonic fatigue specimens into the corresponding stress amplitude of the hourglass-shaped specimens, thereby achieving stress amplitude control in Gaussian curve ultrasonic fatigue. The stress transformation formula between Gaussian curve specimens and hourglass-shaped specimens is derived. σ The stress amplitude of the working section of the Gaussian curve specimen. This represents the stress amplitude of an hourglass-shaped specimen under the same displacement amplitude. , Indicates the diameter of the end of the hourglass-shaped sample. This indicates the initial diameter of the working section of the hourglass-shaped sample. l b This represents half the length of the variable cross-section of the hourglass-shaped specimen. l d This indicates the length of the end of the hourglass-shaped sample.

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