A method for calculating the healable critical size of fatigue crack of viscoelastic material under torsional cyclic loading

Abstract

The application discloses a kind of viscoelastic material fatigue crack healable critical size calculation methods under torsional cyclic loading, specifically: apparent configuration mechanics response is used to determine the real recoverable pseudo strain energy density of real configuration, and the volume free energy change equation is calculated according to the real recoverable pseudo strain energy density;Based on surface energy and crack healing area, the surface free energy change equation is constructed;The total free energy change equation is constructed in combination with volume free energy change equation and surface free energy change equation;According to the principle that the total free energy change in the fatigue crack healing process of viscoelastic material is 0, the fatigue crack healable critical size of viscoelastic material is derived, and the healable critical size can be calculated and determined by the maximum apparent internal stress of material at intermittent initial moment, maximum apparent recovery pseudo strain increment, material surface energy, sample size.The method of the application can be popularized to various engineering materials, and has wide engineering application potential and popularization value.

Description

Technical Field

[0001] This invention belongs to the field of solid mechanics technology, and in particular relates to a method for calculating the critical size of fatigue crack healing in viscoelastic materials under torsional cyclic loading. Background Technology

[0002] Viscoelastic materials, especially asphalt, are widely used in road engineering. Under the coupled effects of cyclic loading and environmental factors, asphalt is prone to fatigue cracking, which eventually leads to material failure as the cracks propagate. Notably, asphalt materials possess significant self-healing capabilities, a property that plays a crucial role in inhibiting crack propagation and delaying pavement damage. Current research on the self-healing of asphalt materials mainly focuses on three aspects: first, research on improving material self-healing, including modification through the incorporation of nanomaterials such as silica, the use of microencapsulation technology to release repair agents, and the use of induction heating technology to promote material healing; second, research on the mechanism of material self-healing, proposing theories such as surface energy, molecular diffusion, and capillary flow to describe the crack healing behavior from microscopic to macroscopic scales; and third, research on the evaluation of material self-healing, with existing technologies typically using indicators such as modulus recovery rate, activation energy, and cumulative dissipated energy ratio to assess the self-healing ability of different asphalt materials.

[0003] However, current technologies mainly focus on improving material self-healing, studying the mechanism of material self-healing, and evaluating material self-healing. They have not yet constructed a theoretical framework that describes the relationship between energy evolution and crack size development during the healing process of asphalt materials, nor have they determined the critical conditions for asphalt materials to transition from a healable to an unhealable state. This means that the critical size for the healable fatigue crack cannot be calculated using existing theoretical methods, thus limiting the definition of the self-healing limit of asphalt materials. If the calculation and definition of the critical size for the healable fatigue crack in asphalt materials could be achieved theoretically, it would help maximize the self-healing potential of materials and extend their service life. Summary of the Invention

[0004] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a method for calculating the critical size of healable fatigue cracks in viscoelastic materials under torsional cyclic loading.

[0005] Technical solution: This invention discloses a method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading, specifically as follows:

[0006] Based on the recoverable pseudo-strain energy density of viscoelastic materials, an equation for the change of volume free energy of viscoelastic materials during the healing stage under torsional cyclic loading is constructed.

[0007] In viscoelastic materials, the geometric region containing cracks during the healing process is considered the apparent configuration, while the solid region without cracks is considered the true configuration.

[0008] The true recoverable pseudo-strain energy density of the real configuration is solved by using the apparent configuration mechanical response;

[0009] An equation for the change of surface free energy is constructed based on surface energy and crack healing area;

[0010] Substitute the real recoverable pseudo-strain energy density of the real configuration into the volume free energy change equation, and construct the total free energy change equation based on the volume free energy change equation and the surface free energy change equation.

[0011] Based on the principle that the total free energy change during the fatigue crack healing process of viscoelastic materials is 0, the critical size for the healing of fatigue cracks in viscoelastic materials is calculated.

[0012] Furthermore, we construct the equation for the change in volume free energy. Specifically:

[0013] ;

[0014] in, This is the region where volumetric strain energy is stored during the healing process. For cylindrical viscoelastic materials at any radial position The recoverable pseudo-strain energy density at the location; The expression is as follows:

[0015] ;

[0016] in, This is the initial stage of healing; At a certain moment in the healing process, The maximum radius of the cylindrical viscoelastic material The recoverable pseudo-strain energy density at the location, For cylindrical viscoelastic materials at any radial position The internal stress, For cylindrical viscoelastic materials at any radial position Recovery pseudo-strain:

[0017] ;

[0018] ;

[0019] in, The maximum radius of the cylindrical viscoelastic material The internal stress, The maximum radius of the cylindrical viscoelastic material The recovery pseudo-strain.

[0020] Furthermore, the solution for the true recoverable pseudo-strain energy density of the actual configuration is as follows: based on the volume free energy change equation, using a cylindrical viscoelastic material at any radial position... The true recoverable pseudo-strain energy density at the location Substituting into the equation for the change in volume free energy, we get:

[0021] ;

[0022] The expression is:

[0023] ;

[0024] in, This is the initial stage of healing; For any moment in the healing process, and These represent any radial position of the actual configuration. Internal stress and pseudo-strain of the actual configuration;

[0025] Constructing the torque balance equation during the healing phase:

[0026] ;

[0027] in, Any time during the healing process The apparent configuration of torque; Any time during the healing process The torque of the actual configuration:

[0028] , ;

[0029] in, Any time during the healing process The internal stress of the apparent configuration at radius r; for Place Internal stress in the actual configuration at any given moment. For the true configuration radius, and Substituting the expression into the torque balance equation, we get:

[0030] ;

[0031] Will and Substituting the expression into the torque balance equation, the resulting equation is then substituted into... The expression yields the result at any moment in the healing process. , Internal stress of the apparent configuration at the location At any time during the healing process , Internal stress of the actual configuration at the location The relationship between them:

[0032] ;

[0033] Will and Substitute the relationship into The expression yields:

[0034] ;

[0035] in, It is Euler's constant; For proportional parameters, Any time during the healing process , Pseudo-strain of apparent configuration at the location:

[0036] ;

[0037] in, Any time during the healing process , The pseudo-strain of the true configuration at the location.

[0038] Furthermore, the equation for the change in surface free energy is constructed as follows:

[0039] When the fatigue crack size of a viscoelastic material approaches the healable critical point, the minute amount of fatigue crack healing at this point is defined as... The equation for the change in surface free energy is:

[0040] ;

[0041] in, This is the change in surface free energy. For surface free energy, This refers to the critical size at which fatigue cracks can heal in viscoelastic materials. , This is the actual configuration radius.

[0042] Furthermore, the equation for the total change in free energy is constructed as follows:

[0043] When the fatigue crack size of a viscoelastic material approaches the healable critical point, assuming that the apparent recoverable pseudo-strain energy density is uniformly distributed within the recoverable region, the equation for the change in volume free energy is rewritten as follows:

[0044] ;

[0045] in, Position in the true configuration The true recoverable pseudo-strain energy density at the location;

[0046] right Differentiate:

[0047] ;

[0048] right Differentiate:

[0049] ;

[0050] The change in volume free energy is as follows The rate of change is defined as positive, and the change in surface free energy is as follows: The rate of change is defined as negative. The equation for the change of total free energy during the healing process under torsional cyclic loading is as follows:

[0051] ;

[0052] in, This represents the total change in free energy during the healing process.

[0053] Furthermore, the critical size for fatigue crack healing in viscoelastic materials. The expression is as follows:

[0054] ;

[0055] Where r is the radius of the apparent configuration, For the height of the viscoelastic material, and These represent the internal stress and pseudo-strain of the largest apparent configuration, respectively; represent The increment at the initial stage of healing, Any time during the healing process The pseudo-strain of the apparent configuration at position r Let Euler's constant be 1. This is a proportional parameter.

[0056] A computer device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the steps of the method for calculating the critical size of fatigue crack healing in a viscoelastic material under torsional cyclic loading.

[0057] A computer-readable storage medium storing a computer program, characterized in that, when executed by a processor, the computer program implements the steps of the method for calculating the critical size of fatigue crack healing in a viscoelastic material under torsional cyclic loading.

[0058] Beneficial effects:

[0059] This invention can accurately describe the self-healing limit of viscoelastic materials under torsional cyclic loading, providing a new design index for maximizing the self-healing performance of viscoelastic materials and extending their service life.

[0060] This invention can predict the self-healing limit of viscoelastic materials and can be used to predict whether the fatigue damage currently generated by viscoelastic materials has entered an irreversible stage, providing an indicator for the cracking and deterioration inflection point of viscoelastic materials.

[0061] The method for calculating the critical size of fatigue crack healing established in this invention can be extended to various engineering materials such as polymer composites, and has broad engineering application potential and promotion value.

[0062] The fatigue crack healing critical size of the viscoelastic material proposed in this invention can be used as an evaluation index for self-healing performance, and can be used to evaluate the self-healing ability of conventional asphalt materials or self-healing reinforced modified asphalt materials. Attached Figure Description

[0063] Figure 1 Figure (a) shows the internal stress distribution of the apparent material, and Figure (b) shows the internal stress distribution of the intact material.

[0064] Figure 2 A calculation formula for the critical size at which fatigue cracks in asphalt materials can heal under torsional cyclic loading, and an explanation of its physical quantities;

[0065] Figure 3 Flowchart for fatigue and creep recovery testing;

[0066] Figure 4 Flowchart for fatigue and creep-zero strain rate testing;

[0067] Figure 5 The critical size for the healing of fatigue cracks in asphalt mortar under different working conditions. Detailed Implementation

[0068] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0069] This invention analyzes the changes in volume free energy and surface free energy of asphalt materials during fatigue crack healing, derives a mathematical expression for the total free energy, and proposes a method for calculating the critical size for the healing of fatigue cracks in asphalt materials under torsional cyclic loading. This achievement provides theoretical and technical support for evaluating the self-healing performance of asphalt materials, assessing the healing effect of self-healing additives, and developing crack-resistant optimization design methods for materials with ultimate healing capabilities.

[0070] In this embodiment, asphalt-based materials are used as an example of viscoelastic materials. The specific method is as follows:

[0071] Asphalt materials undergo fatigue cracking under torsional cyclic loading, and the cracks heal after unloading. During this process, the total free energy change of the material system consists of two parts: firstly, the change in strain energy stored in the asphalt material during healing, called the volumetric free energy change, which is related to internal stress and recoverable strain; secondly, the change in free energy before and after the healing process on the upper and lower surfaces of the asphalt crack, called the surface free energy change, which is related to the material's surface energy and the crack area.

[0072] First, the volume free energy change of a cylindrical asphalt material specimen under torsional cyclic loading during the healing stage is derived. During the fatigue crack healing process of the asphalt material, the free energy change is calculated at any radial position of the specimen. The internal stress at the maximum radius r has the following relationship:

[0073] (1)

[0074] In the formula: For any radial position of the cylindrical sample; The maximum radius of the sample; For any radial position of the cylindrical sample Internal stress at the location; The maximum radius of the cylindrical specimen The internal stress at that point.

[0075] Any radial position of a cylindrical specimen The recovered strain and recovered pseudo-strain at the maximum radius r are related by the following formula:

[0076] (2)

[0077] In the formula: For any radial position of the cylindrical sample Recovery strain; The maximum radius of the cylindrical specimen Recovery strain at the location; For any radial position of the cylindrical sample The recovery of pseudo-strain; The maximum radius of the cylindrical specimen The recovery pseudo-strain at the location.

[0078] The change in volumetric free energy of asphalt material under torsional cyclic loading can be calculated using the following formula:

[0079] (3)

[0080] In the formula: This is the region where volumetric strain energy is stored during the healing process; For any radial position of the cylindrical sample The recoverable pseudo-strain energy density at the location.

[0081] in, The calculation method is as follows:

[0082] (4)

[0083] In the formula: This is the initial stage of healing; This refers to a specific moment in the healing process. The maximum radius of the cylindrical specimen The recoverable pseudo-strain energy density at the location.

[0084] In the healing process of asphalt material, the geometric region containing cracks is considered the apparent configuration (apparent material, i.e., the entire area of ​​the specimen), while the solid region without cracks is considered the true configuration (intact material). (Appendix) Figure 1 The diagram shows the internal stress distribution of the apparent and intact materials, where light gray areas represent undamaged regions and dark gray areas represent damaged regions. (Attached) Figure 1 In this context, the superscripts A and T represent the apparent and true mechanical responses, respectively; the subscript i represents the healing process; t represents any moment during the healing process; and the non-subscript T represents the torque applied to the specimen. The apparent mechanical response of a material can be directly determined experimentally, while the true mechanical response characterized by an intact material must be obtained through theoretical calculations and derivations.

[0085] Based on equation (3), this invention uses the real recoverable pseudo-strain energy density to calculate the recoverable pseudo-strain energy of asphalt material during the healing process, as shown below:

[0086] (5)

[0087] In the formula: For any radial position of the cylindrical sample The recoverable pseudo-strain energy density of the true configuration at the location.

[0088] The true recoverable pseudo-strain energy density of asphalt materials can be calculated using the following formula:

[0089] (6)

[0090] In the formula: and These represent the internal stress of the true configuration and the recovered pseudo-strain of the true configuration, respectively.

[0091] To determine the recoverable pseudo-strain energy density of the true configuration, the torque balance equation for the asphalt material during the healing stage after torsional cyclic loading is established as follows:

[0092] (7)

[0093] In the formula: Any time during the healing process The apparent torque; Any time during the healing process The true torque.

[0094] The torque of the apparent and intact materials can be calculated from the internal stresses distributed across the cross-section of the asphalt sample, using the following formula:

[0095] (8)

[0096] In the formula: Any time during the healing process , radial arbitrary position Apparent internal stress at a location (internal stress of the apparent configuration); Any time during the healing process , radial arbitrary position The actual internal stress at the location (the internal stress of the actual configuration); The radius of the complete material; The radius of the apparent material is the radius of the sample.

[0097] By integrating equation (8), we can derive... and The expression is as follows:

[0098] (9)

[0099] In the formula: for Place Apparent internal stress at a given time; for Place The actual internal stress at any given moment.

[0100] Substituting equation (9) into equation (7), we get:

[0101] (10)

[0102] Substituting equation (10) into equation (6), we get:

[0103] (11)

[0104] The apparent pseudo-strain and the true pseudo-strain have the following relationship:

[0105] (12)

[0106] In the formula: It is Euler's constant; This is a proportional parameter with a value of 14.

[0107] Therefore, the true recoverable pseudo-strain energy density can be calculated using the following formula:

[0108] (13)

[0109] , The following relationship exists between the fatigue crack critical size and the healable fatigue crack size:

[0110] (14)

[0111] In the formula: This refers to the critical size at which fatigue cracks in asphalt materials can heal.

[0112] When the fatigue crack size of the asphalt material approaches the healable critical point, assuming that the minute amount of fatigue crack healing at this point is... Since the recoverable region at the critical point is very small, it is assumed that the apparent recoverable pseudo-strain energy density is uniformly distributed within the recoverable region. Equation (5) can be further written in the following form:

[0113] (15)

[0114] In the formula: Radial position of the cylindrical sample The true recoverable pseudo-strain energy density at the point can be determined by equation (13).

[0115] Equation (15) Differentiating, we get the following equation:

[0116] (16)

[0117] Furthermore, the change in surface free energy can be determined by the surface energy and the crack healing area:

[0118] (17)

[0119] In the formula: This represents the change in surface free energy during the healing process. For surface free energy, The height of the sample;

[0120] Equation (17) for Differentiating the derivative yields the following equation:

[0121] (18)

[0122] This invention uses the change in volume free energy as... The rate of change is defined as positive (volume free energy storage), and the change in surface free energy is as follows: The rate of change is defined as negative (surface free energy release). Therefore, the rate of change of total free energy during the fatigue crack healing process of asphalt material under torsional cyclic loading can be expressed as follows:

[0123] (19)

[0124] In the formula: This represents the total change in free energy during the healing process.

[0125] Assuming the total free energy change rate during the fatigue crack healing process of asphalt material is 0, the calculation formula for the critical size at which fatigue cracks in asphalt material can heal is obtained as follows:

[0126] (20)

[0127] In the formula: and These are the maximum apparent internal stress and the maximum apparent recovered pseudo-strain, respectively. represent The increment at the initial stage of healing; It is the surface energy of the material; The radius of the sample; The height is the specimen height. The healable critical size can be calculated and determined by the maximum apparent internal stress, the maximum apparent recovery pseudo-strain increment, the material surface energy, and the specimen size at the initial moment of the interval.

[0128] The formula for calculating the critical size for the healing of fatigue cracks in asphalt materials under torsional cyclic loading, and its explanation of the physical quantities proposed in this invention, are attached. Figure 2 As shown, it can be determined by material properties (surface energy) Mechanical response during the healing phase (maximum apparent internal stress) With large apparent recovery pseudo-strain ) and geometric dimensions (sample height) and radius The critical size for the healing of fatigue cracks in asphalt materials under torsional cyclic loading is uniquely determined. It increases with the increase of the material's surface energy and decreases with the increase of the maximum apparent internal stress and the maximum apparent pseudo-strain.

[0129] In one embodiment of the present invention, the asphalt matrix is ​​selected as No. 70 base asphalt, and the technical indicators of No. 70 asphalt are tested and verified according to the specifications of the "Technical Specification for Construction of Highway Asphalt Pavement" (JTG E40-2004). The mineral powder filler is limestone mineral powder produced in Jingmen, Hubei, China, whose main component is calcium carbonate powder, and the volume content of mineral powder is 27%. The various performance indicators of the mineral powder are tested and verified according to the requirements of the "Test Procedure for Aggregates in Highway Engineering" (JTG E42 2005).

[0130] The preparation steps of asphalt mastic are as follows: (1) Place the mineral powder in an oven at 105℃ for 4 hours and place the asphalt in an oven at 135℃ for 2 hours; (2) Place the hot asphalt in a high-speed shear disperser, set the instrument speed to 2000 rpm, and stir for 2 minutes beforehand; (3) Add the heated mineral powder slowly in batches to the hot asphalt being stirred until all the mineral powder is incorporated into the hot asphalt; (4) Finally, shear and mix the asphalt mastic for 30 minutes to make the mineral powder and asphalt evenly mixed.

[0131] This study primarily used a Dynamic Shear Rheometer (DSR) from TA Instruments to test asphalt mastic samples. The selected parallel plate had a diameter of 8 mm, and the prepared asphalt mastic samples had a diameter of 8 mm and a height of 2 mm. The tests were conducted in accordance with the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025).

[0132] Fatigue and creep recovery tests were conducted on asphalt mortar, including fatigue loading, non-destructive creep, and recovery phases. The specific test procedures are detailed in the attached document. Figure 3As shown in the diagram. First, a time-scan test with controlled strain was conducted on the asphalt mastic under damaged shear strain. The test temperatures were 20℃ and 25℃, and the loading frequency was 10Hz. Second, the damage density development of the asphalt mastic during fatigue loading was tracked in real time. Once the set damage density was reached, a non-destructive creep load was reapplied for 10 seconds. Finally, a recovery test (i.e., unloading, with the creep load at 0) was conducted on the asphalt mastic to obtain the recovery strain during the healing stage. Furthermore, before conducting the fatigue and creep recovery tests, a non-destructive creep test was performed on the asphalt mastic to determine its relaxation modulus for pseudo-strain calculation.

[0133] Fatigue and creep-zero strain rate tests were conducted on asphalt mortar, including fatigue loading, non-destructive creep, and zero strain rate tests. The specific test procedures are detailed in the attached document. Figure 4 As shown. First, the fatigue loading section, non-destructive creep section, and the first two sections of the fatigue and creep recovery test are controlled to be consistent to ensure that the specimens reach the same damage state. Then, a zero-strain rate test is performed, in which the shear strain level is controlled to remain constant (i.e., zero strain rate) to obtain the internal stress corresponding to the recovery strain in the healing stage. The shear strain level in the zero-strain rate test is controlled to be the initial recovery strain level in the fatigue and creep recovery test.

[0134] Appendix Figure 3 and 4 In the above, 5% is the strain load level of the asphalt mastic during the fatigue loading stage. Under this load level, the asphalt mastic will suffer fatigue damage, which is manifested as a continuous decrease in stress amplitude. The moment marks the boundary between the fatigue loading stage and the non-destructive creep loading stage; The moment is the dividing point between non-destructive creep loading and zero-load creep loading or zero strain rate; To restore the initial value of strain, and also to control the level of shear strain in zero strain rate tests.

[0135] The surface energies and their components of asphalt, limestone powder, and the test liquid are shown in Table 1. Combining the surface energies of asphalt and limestone powder, the bonding energy of asphalt and the adhesion energy between asphalt and the powder can be calculated, with values ​​of 17.9 mJ / m. 2 and 112.3 mJ / m 2 Finally, the total surface energy of the asphalt mortar was determined to be 43.4 mJ / m. 2 .

[0136] Table 1. Surface energy and composition of asphalt, limestone powder and test liquid

[0137] Material <![CDATA[Non-polar component (mJ / m 2 )]]> <![CDATA[Lewis acidity component (mJ / m 2 )]]> <![CDATA[Lewis basic component (mJ / m 2 )]]> <![CDATA[Polar component (mJ / m 2 )]]> <![CDATA[Surface energy (mJ / m 2 )]]> asphalt 13.0 3.6 1.7 4.9 17.9 limestone powder 58.1 401.2 1.8 53.2 111.3 water 21.8 25.5 25.5 51 72.8 formamide 39.0 2.3 39.6 19.0 58.0 Ethylene glycol 29.0 1.9 47.0 19.0 48.0

[0138] After obtaining the recoverable strain and corresponding internal stress of the asphalt mastic during the healing stage, its maximum apparent recoverable pseudo-strain energy density under different working conditions can be calculated. Substituting the maximum apparent recoverable pseudo-strain energy density and surface energy under different working conditions into equation (20), the critical size for fatigue crack healing under torsional cyclic loading can be obtained. The results of the critical size for fatigue crack healing under various working conditions determined by the examples of this invention are attached. Figure 5 As shown in the figure, the critical size for fatigue crack healing of asphalt mortar increases with increasing temperature. This is because as the temperature increases, the fluidity of the asphalt mortar itself increases, which helps the material flow on the crack surface, making its self-healing performance better at lower temperatures.

[0139] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading, characterized in that, Specifically: Based on the recoverable pseudo-strain energy density of viscoelastic materials, an equation for the change of volume free energy of viscoelastic materials during the healing stage under torsional cyclic loading is constructed. In viscoelastic materials, the geometric region containing cracks during the healing process is considered the apparent configuration, while the solid region without cracks is considered the true configuration. The true recoverable pseudo-strain energy density of the real configuration is solved by using the apparent configuration mechanical response; An equation for the change of surface free energy is constructed based on surface energy and crack healing area; Substitute the real recoverable pseudo-strain energy density of the real configuration into the volume free energy change equation, and construct the total free energy change equation based on the volume free energy change equation and the surface free energy change equation. Based on the principle that the total free energy change during the fatigue crack healing process of viscoelastic materials is 0, the critical size for the healing of fatigue cracks in viscoelastic materials is calculated.

2. The method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading according to claim 1, characterized in that, Construct the equation for the change in volume free energy Specifically: ； in, This is the region where volumetric strain energy is stored during the healing process. For cylindrical viscoelastic materials at any radial position The recoverable pseudo-strain energy density at the location; The expression is as follows: ； in, This is the initial stage of healing; At a certain moment in the healing process, The maximum radius of the cylindrical viscoelastic material The recoverable pseudo-strain energy density at the location, For cylindrical viscoelastic materials at any radial position The internal stress, For cylindrical viscoelastic materials at any radial position Recovery pseudo-strain: ； ； in, The maximum radius of the cylindrical viscoelastic material The internal stress, The maximum radius of the cylindrical viscoelastic material The recovery pseudo-strain.

3. The method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading according to claim 1, characterized in that, The solution for the true recoverable pseudo-strain energy density of the real configuration is as follows: based on the volume free energy change equation, using a cylindrical viscoelastic material at any radial position... The true recoverable pseudo-strain energy density at the location Substituting into the equation for the change in volume free energy, we get: ； The expression is: ； in, This is the initial stage of healing; For any moment in the healing process, and These represent any radial position of the actual configuration. Internal stress and pseudo-strain of the actual configuration; Constructing the torque balance equation during the healing phase: ； in, Any time during the healing process The apparent configuration of torque; Any time during the healing process The torque of the actual configuration: ， ； in, Any time during the healing process The internal stress of the apparent configuration at radius r; for Place Internal stress in the actual configuration at any given moment. For the true configuration radius, and Substituting the expression into the torque balance equation, we get: ； Will and Substituting the expression into the torque balance equation, the resulting equation is then substituted into... The expression yields the result at any moment in the healing process. , Internal stress of the apparent configuration at the location At any time during the healing process , Internal stress of the actual configuration at the location The relationship between them: ； Will and Substitute the relationship into The expression yields: ； in, Here is Euler's constant; For proportional parameters, Any time during the healing process , Pseudo-strain of apparent configuration at the location: ; in, Any time during the healing process , The pseudo-strain of the true configuration at the location.

4. The method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading according to claim 1, characterized in that, The equation for the change in surface free energy is constructed as follows: When the fatigue crack size of a viscoelastic material approaches the healable critical point, the minute amount of fatigue crack healing at this point is defined as... The equation for the change in surface free energy is: ； in, This is the change in surface free energy. For surface free energy, This refers to the critical size at which fatigue cracks can heal in viscoelastic materials. , This is the actual configuration radius.

5. The method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading according to claim 4, characterized in that, The equation for the total change in free energy is constructed as follows: When the fatigue crack size of a viscoelastic material approaches the healable critical point, assuming that the apparent recoverable pseudo-strain energy density is uniformly distributed within the recoverable region, the equation for the change in volume free energy is rewritten as follows: ； in, Position in the true configuration The true recoverable pseudo-strain energy density at the location; right Differentiate: ； right Differentiate: ； The change in volume free energy is as follows The rate of change is defined as positive, and the change in surface free energy is as follows: The rate of change is defined as negative. The equation for the change of total free energy during the healing process under torsional cyclic loading is as follows: ； in, This represents the total change in free energy during the healing process.

6. The method for calculating the critical size for the healing of fatigue cracks in viscoelastic materials under torsional cyclic loading according to claim 1, characterized in that, Critical size for fatigue crack healing in viscoelastic materials The expression is as follows: ； Where r is the radius of the apparent configuration, For the height of the viscoelastic material, and These represent the internal stress and pseudo-strain of the largest apparent configuration, respectively; represent The increment at the initial stage of healing, Any time during the healing process The pseudo-strain of the apparent configuration at position r Let Euler's constant be 1. This is a proportional parameter.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for calculating the critical size of fatigue crack healing in viscoelastic materials under torsional cyclic loading as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for calculating the critical size of fatigue crack healing in a viscoelastic material under torsional cyclic loading as described in any one of claims 1 to 6.

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