A Design Method for Static and Dynamic Universal Loading Paths in True Triaxial Mechanical Tests

Abstract

The present invention provides a method for designing a dynamic and static universal loading path for true triaxial mechanical tests. The loading path design is carried out in the stress space. The principal stress space is sliced into a set of stress meridian plane spaces, realizing the conversion from a three-dimensional design environment to a two-dimensional design environment. Based on the above two-dimensional design environment, the dynamic and static universal loading paths under three different loading modes of triaxial compression, triaxial tension, and tension-compression compound are designed respectively. The design results in the two-dimensional design environment are converted into three-dimensional final design results. It can make the results of dynamic and static true triaxial mechanical tests comparable. The distribution of the dynamic and static true triaxial mechanical test loading paths in the stress space can be set as needed.

Description

Technical Field

[0001] The present invention relates to the application field of high-end equipment, particularly to the field of mechanical tests, and specifically to the design of static and dynamic true triaxial mechanical test loading schemes for solid materials such as rocks, concretes, metals, ceramics, polymers, etc. Background Art

[0002] The true triaxial mechanical test is an important research method for studying the mechanical properties of solid materials, and this test can provide a theoretical basis for fields such as geotechnical engineering, mine engineering, concrete structure engineering, metal processing, etc. In actual engineering, solid materials such as rocks and concretes not only bear static loads but are often also affected by various dynamic disturbances. Therefore, the results of static and dynamic true triaxial mechanical tests are of great research significance for the scientific construction and healthy operation and maintenance of engineering. Currently, the static true triaxial mechanical test system is mainly based on the Mogi-type true triaxial test configuration. The loads in the three axial directions of this testing machine can be independently controlled, and theoretically, a highly free loading path can be achieved by regulating the stress time history curves in each axial direction.

[0003] As Figure 1 shown, a common loading scheme using the above-mentioned static true triaxial test system is as follows: First, apply three axial loads to make the specimen reach a certain stress state, maintain the second and third principal stress at a constant level, and then continue to apply a load to increase the first principal stress until the stress of the specimen reaches the test requirements.

[0004] This loading path meets the research requirements of most static true triaxial mechanical tests, but it is not applicable to dynamic true triaxial mechanical tests, especially dynamic tests with a relatively high loading rate or strain rate. The reason is that it is very difficult to achieve precise control of dynamic stress during a short-time dynamic loading process. For example, the dynamic loading duration of the Hopkinson bar test is extremely short (in the microsecond level), and its loading time history curve is a shock wave with a fixed waveform. Generally, only the pulse width (loading duration) and amplitude (load magnitude) of the waveform can be adjusted, and the loading path of the traditional static true triaxial mechanical test cannot be achieved.

[0005] Therefore, in order to facilitate the development of dynamic true triaxial mechanical test research and simultaneously achieve the comparative analysis of the static and dynamic mechanical properties of solid materials, it is necessary to develop a loading path design method that is applicable to both static and dynamic tests, so that the designed loading path can be applied to not only the dynamic true triaxial test system but also the static true triaxial test system and the true triaxial test system combining static and dynamic tests. Summary of the Invention

[0006] In order to solve the problems in the prior art, the present invention provides a loading path design method for true triaxial mechanical tests that is applicable to both static and dynamic tests,

[0007] Step 1: In the principal stress space, starting from Select within the range of and select Lode angles and their corresponding stress meridional planes, and set their uniform distribution according to requirements, or customize the non-uniform arrangement of stress meridional planes; the mathematical expression for the definition of the Lode angle is as shown in Equation (1);

[0008]

[0009] Step 2: In the stress meridional plane space selected in Step 1, establish a plane rectangular coordinate system composed of axis and axis, where has a multiple relationship with the mean principal stress numerically, has a multiple relationship with the equivalent stress numerically, with the unit of MPa, and the calculation formula is as follows:

[0010]

[0011]

[0012] Therefore, the combination of the coordinates of any point in the stress meridional plane space and the Lode angle corresponding to the stress meridional plane can also represent the three-dimensional stress state ;

[0013] Step 3: Define the regions corresponding to different loading modes in each stress meridional plane space; among them, the division of various loading mode regions in the stress meridional plane space varies with the change of the corresponding Lode angle ;

[0014] Step 4: Arrange loading paths in each stress meridional plane space, specifically represented as rays with the coordinate origin as the endpoint and the slope of ;

[0015] Step 5: Use the loading path parameters determined in Step 4, that is, the Lode angle corresponding to the stress meridional plane where the ray is located and the slope of the ray, so as to determine the three-dimensional stress state at any point on each loading path. The three-dimensional stress state can be represented in the main stress space coordinates through coordinate transformation. The coordinate transformation calculation formula is as shown in Equation (2),

[0016]

[0017] Then the three-dimensional stress state According to perform normalization processing, so that the ratio of the synchronous increase of the stresses on the three principal stress axes corresponding to each loading path can be obtained ,

[0018] Step 6: Based on the above design process, complete the design of the true triaxial mechanical test dynamic and static universal loading paths for a total of test materials

[0019] As a further improvement of the present invention, Step 1: In the principal stress space, select from to the range of Lode angles and their corresponding stress meridional planes, and their uniform or non-uniform distribution can be set

[0020] As a further improvement of the present invention, in Step 3, different loading modes include triaxial compression, triaxial tension, and tension-compression compound; among them, the area corresponding to the triaxial compression loading mode is specifically the area enclosed between a ray with the origin as an endpoint in the first quadrant and the positive semi-axis of the axis; the area corresponding to the triaxial tension loading mode is specifically the area enclosed between a ray with the origin as an endpoint in the second quadrant and the

[0021] negative semi-axis of the axis; the area corresponding to the tension-compression compound loading mode is the area between the area corresponding to the triaxial compression loading mode and the area corresponding to the triaxial tension loading mode As a further improvement of the present invention, in Step 3, the slope of the boundary line between the triaxial compression loading area and the tension-compression compound loading area decreases with the increase of the Lode angle , and here the slope is positive, so that the range of the triaxial compression loading area is continuously reduced; the slope of the boundary line between the triaxial tension loading area and the tension-compression compound loading area decreases with the increase of the Lode angle

[0022] is negative, so that the range of the triaxial tension loading area is continuously increased; the change of the range of the tension-compression compound loading area is determined according to the changes of the above two As a further improvement of the present invention, in Step 4, arrange loading paths in the area corresponding to the triaxial compression loading mode in each stress meridional plane, specifically select rays with the coordinate origin as an endpoint and a slope of

[0023] These rays are the dynamic and static universal loading paths Design of a universal loading path for dynamic and static true triaxial mechanical tests on a test sandstone

[0024] The beneficial effects of the present invention are as follows:

[0025] The beneficial aspect of the loading path design method provided by the present invention lies in:

[0026] Innovation point 1: It enables comparability between the results of dynamic and static true triaxial mechanical tests. Based on the high strain rate characteristics and the load-time history curve characteristics of the dynamic true triaxial Hopkinson bar test, a loading path design method applicable to both dynamic and static true triaxial tests is established, achieving comparability between dynamic and static test results.

[0027] As Figure 7 shown, by controlling the ratio of the synchronous increase in time of the three axial stresses in dynamic and static loading to be equal, the dynamic and static true triaxial mechanical loading paths are the same ray in the stress space;

[0028] Innovation point 2: It can set the distribution of the dynamic and static true triaxial mechanical test loading paths in the stress space as needed. Loading path design is carried out in the stress space. The stress space visualization method is used in the loading path design process, and coordinate transformation formulas for the three-dimensional stress state in the stress meridian plane and the three-dimensional stress state in the principal stress space are proposed. The principal stress space is sliced into a set of stress meridian plane spaces, realizing the conversion from a three-dimensional design environment to a two-dimensional design environment. Based on the above two-dimensional design environment, the universal loading paths for different loading modes (triaxial compression, triaxial tension, tension-compression combination) are designed. The design results in the two-dimensional design environment are converted into the final three-dimensional design results, that is, the ratio of the synchronous increase in time of the three axial stresses .

[0029] As Figure 8 shown, specifically, by controlling the change in the ratio of the synchronous increase in time of the three axial stresses during the loading process , it is possible to adjust the pointing area and the distribution density of multiple loading paths in the stress space in dynamic and static true triaxial mechanical tests; thus providing an experimental basis for simulating the stress state and loading path of engineering objects under complex static loads and complex dynamic disturbances. Description of the Drawings

[0030] Figure 1 Schematic diagram of common loading schemes for static true triaxial test research, including the stress-time history curves of two static loading paths and their loading paths in the principal stress space;

[0031] Figure 2 Schematic diagram of loading a cubic specimen for static and dynamic true triaxial tests

[0032] Figure 3 For different Lode angles in the principal stress space Schematic diagram of the stress meridian plane and the deviatoric plane corresponding thereto

[0033] Figure 4 Schematic diagram of the division of different loading modes in the stress meridian plane

[0034] Figure 5 In the principal stress space at the Lode angle Schematic diagram of the designed loading path on the corresponding stress meridian plane

[0035] Figure 6 Schematic diagram of a universal static and dynamic loading scheme for true triaxial mechanical tests provided by the present invention, including the stress time history curves of one dynamic loading path and one static loading path and their loading paths in the principal stress space, and by controlling the three axial stresses of dynamic and static loading to increase synchronously in time, the loading path appears as a ray in the principal stress space

[0036] Figure 7 Schematic diagram of a universal static and dynamic loading scheme for true triaxial mechanical tests provided by the present invention, including the stress time history curves of one dynamic loading path and one static loading path and their loading paths in the principal stress space, and by controlling the ratio of the three axial stresses of dynamic and static loading to increase synchronously in time to be equal, and the loading path is the same ray in the principal stress space

[0037] Figure 8 Schematic diagram of a universal static and dynamic loading scheme for true triaxial mechanical tests provided by the present invention, including two groups of loading paths with different pointing regions and distribution densities

[0038] Figure 9 For the stress meridian plane corresponding to the designed Lode angle in the embodiment Distribution of three loading paths

[0039] Figure 10 For the stress meridian plane corresponding to the designed Lode angle in the embodiment , = Results of the stress time history curves of the verification test of the loading path

[0040] Figure 11 For the stress meridian plane corresponding to the designed Lode angle in the embodiment , = Test verification results of the loading path on the stress meridian plane

[0041] Figure 12 The Lode angle designed in the embodiment Experimental verification results of three loading paths on the corresponding stress meridian plane Specific implementation manners

[0042] The following combines the accompanying drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention

[0043] As Figure 2 shown, in the embodiment of the present invention, the pre-experiment of the dynamic triaxial compression strength of sandstone is taken as an example, and it is stipulated that in this embodiment, the stress is positive under compression. The test equipment is a dynamic true triaxial test system based on Hopkinson bars. The load loading method is to apply impact stress wave loads by three axial square-section waveguide bars. A titanium alloy cube specimen with the same material as the waveguide bar is used for the pre-experiment to verify the feasibility of the designed loading path

[0044] The implementation process of the test loading scheme design is as follows by using a method for designing a static and dynamic universal loading path for a true triaxial mechanical test of the present invention

[0045] Step 1: As Figure 3 shown, in the principal stress space, determine a spatial angle bisector that passes through the origin of coordinates and has equal angles with the three coordinate axes; any plane perpendicular to this spatial angle bisector is a stress deviatoric plane, and any plane perpendicular to the stress deviatoric plane and containing the spatial angle bisector is a stress meridian plane, where the stress meridian plane containing the coordinate axis corresponds to the Lode angle = ; Note: The mathematical expression for the definition of the Lode angle is as shown in formula (1). Select three Lode angles from to and their corresponding stress meridian planes, and set them to be evenly distributed, that is, the Lode angle interval between adjacent meridian planes is 30 degrees ;

[0046]

[0047] Step 2: In the space of the three stress meridian planes selected in Step 1, establish a plane rectangular coordinate system composed of the axis and the axis, where has a multiple relationship with the mean principal stress numerically, and has a multiple relationship with the equivalent stress (or generalized shear stress) numerically, with the unit of MPa. The calculation formulas are as follows

[0048]

[0049]

[0050] Thus, the combination of the coordinates of any point in the stress meridian plane space and the corresponding Lode angle of this stress meridian plane can also represent the three-dimensional stress state ;

[0051] Step 3: As shown in Figure 4 , delimit the regions corresponding to different loading modes (triaxial compression, triaxial tension, combined tension and compression) in each stress meridian plane space; among them, the region corresponding to the triaxial compression loading mode is specifically the region enclosed between a ray with the origin as an endpoint in the first quadrant and the positive semi-axis of the axis; among them, the division of the regions of various loading modes in the stress meridian plane space varies with the change of the corresponding Lode angle , for example, the slope of the boundary line between the triaxial compression loading region and the combined tension and compression loading region decreases with the increase of the Lode angle , so that the range of the triaxial compression loading region continuously shrinks. Taking the stress meridian plane corresponding to the Lode angle as an example, the region corresponding to the triaxial compression loading mode is the region enclosed between the ray with a slope and the origin as an endpoint in the first quadrant and the positive semi-axis of the axis;

[0052] Step 4: As shown in Figure 5 , arrange 3 loading paths in the region corresponding to the triaxial compression loading mode in each stress meridian plane, specifically select 3 rays with the coordinate origin as an endpoint and a slope of , and these rays are the general-purpose dynamic and static loading paths; taking the stress meridian plane corresponding to the Lode angle as an example, the slopes of the 3 selected rays are 0.40, 0.55, and 0.70 respectively, all of which are less than , belonging to the category of the triaxial compression loading mode;

[0053] Step 5: Each of the 9 loading paths determined in the above Step 4 corresponds to a Lode angle and the slope of the ray in the stress meridian plane space, so that the three-dimensional stress state at any point on each loading path can be determined, and can be represented as the three-dimensional stress state in the principal stress space coordinates through coordinate transformation, and the coordinate transformation calculation formula is as shown in Equation (2); then the three-dimensional stress state is arranged according to Normalization is performed so that the ratio of the synchronous increase in stress along the three principal stress axes corresponding to each loading path can be obtained. , as shown in Table 1. Table 1 lists some of the data, and Table 1 is the result of calculation using formula (2) and then normalization.

[0054]

[0055] Taking the Lode angle , design of the loading path as an example, stress state points satisfying MPa on the loading path are selected, and MPa is calculated according to the slope. Substituting it into the formula, the stress state point is represented in the principal stress space coordinates as = MPa, and the ratio of synchronous stress increase obtained by normalization is = ;

[0056] As Figure 6 and Figure 7 show, first, in this design method, by keeping the shape of the designed stress time history curve unchanged while changing the amplitude, that is, controlling the synchronous increase of the three axial stresses in time during the loading process, the dynamic and static loading paths are shown as rays in the stress space (principal stress space and stress meridian plane space) (as Figure 6 shows). When the dynamic and static true triaxial mechanical tests are loaded according to the same ratio , the same loading path in the principal stress space and stress meridian plane space is the same ray, that is, the dynamic and static loadings can be the same loading path (as Figure 7 shows). Second, in this design method, by controlling the change of the ratio of the synchronous increase of the three axial stresses in time during the loading process, the distribution of the loading path in the stress space (principal stress space and stress meridian plane space) is adjusted, that is, the extension direction of the above ray in the stress space; the final design result of this method is: during the loading process of the dynamic and static true triaxial mechanical tests, the ratio of the synchronous increase of the three axial stresses in time, and this ratio is represented by . Each ratio corresponds to a fixed loading path in the stress space.

[0057] Step 6: Based on the above design process, the dynamic and static universal loading path design for a total of 9 tested sandstones is completed, which are respectively located on the three stress meridian planes corresponding to the Lode angle . Among them, the distribution of the three loading paths on the plane rectangular coordinate system of the stress meridian plane corresponding to the Lode angle is as shown in Figure 9 ;

[0058] Step 7: Taking the Lode angle Taking the design result in the corresponding stress meridian plane as an example, the incident stress wave amplitude of the Hopkinson bar is adjusted according to the designed loading path, and the Lode angle is used as the Taking the loading path of as an example, the incident stress wave waveform is controlled to be consistent and the amplitude ratio is 13.02:7.01:1.00. Figure 10 As shown;

[0059] So that the stress in each principal stress axis is in accordance with the design ratio When the stress of the titanium alloy specimen increases synchronously, the dynamic stress state of the titanium alloy specimen moves along the ray corresponding to the loading path in the stress meridian plane and the principal stress space, as shown in Figure 11 As shown;

[0060] Complete Lord Point The loading tests of the three loading paths in the corresponding stress meridian plane under small and large amplitude dynamic loads verified the feasibility of the dynamic and static universal loading path designed by this method, such as Figure 12 shown.

[0061] In summary, the loading path design is carried out in the stress space, and the principal stress space is cut into a collection of a series of stress meridian plane spaces to realize the conversion from the three-dimensional design environment to the two-dimensional design environment; based on the above two-dimensional design environment, the dynamic and static universal loading paths under three different loading modes of triaxial compression, triaxial tension, and tension-compression composite are designed respectively; the design results in the two-dimensional design environment are converted into the final three-dimensional design results, that is, the ratio of the synchronous increase of the three axial stresses in time equal.

[0062] Table 1 Results of dynamic and static universal loading path design for true triaxial mechanical test

[0063] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A dynamic and static universal loading path design method for true triaxial mechanical tests, characterized by: Step 1: In the principal stress space, select from -30° to 30° Lord's Point and its corresponding stress meridian plane, set its uniform distribution according to requirements, or customize the non-uniform arrangement of stress meridian plane; the mathematical expression of the Lode angle definition is as shown in formula (1); Step 2: In the stress meridian space selected in step 1, establish Axis and The plane rectangular coordinate system composed of the axes, and mean principal stress In terms of value, it is a multiple relationship. Equivalent stress The numerical value is a multiple relationship, the unit is MPa, and the calculation formula is as follows: Therefore, the coordinates of any point in the stress meridian space correspond to the Lode angle of the stress meridian. The combination of can also represent the three-dimensional stress state ; Step 3: Delineate the areas corresponding to different loading modes in each stress meridian space; The division of various loading mode areas in the stress meridian space depends on their corresponding Lode angles. varies with changes in Step 4: Arrange in each stress meridian space The loading path is specifically characterized by a zero point as the endpoint and a slope of of rays; Step 5: Substitute the loading path parameter determined in step 4, i.e., the Lode angle corresponding to the stress meridian plane where the ray is located. and the slope of the ray , so that the three-dimensional stress state at any point on each loading path can be determined , which can be expressed as a three-dimensional stress state by coordinate transformation into the principal stress space coordinates , transformed into the three-dimensional parameters of the ray in the principal stress space, the coordinate transformation calculation formula is shown in formula (2): Then the three-dimensional stress state according to After normalization, the ratio of the synchronous increase of stress in the three principal stress axes corresponding to each loading path can be obtained. , Step 6: Combine the above steps to complete the total Design of dynamic and static universal loading path for true triaxial mechanical tests on test materials.

2. The method for designing a dynamic and static universal loading path for a true triaxial mechanical test according to claim 1, characterized in that: Step 1: In the principal stress space, from arrive Range selection Lord's Point and its corresponding stress meridian plane, which can be set to be uniformly or non-uniformly distributed.

3. The method for designing a dynamic and static universal loading path for a true triaxial mechanical test according to claim 2, characterized in that: In step 3, different loading modes include triaxial compression, triaxial tension, and tension-compression combination; the area corresponding to the triaxial compression loading mode is specifically the area between a ray with the origin as the endpoint in the first quadrant and The area enclosed by the positive semi-axis of the axis; the area corresponding to the triaxial tensile loading mode is specifically the area between a ray with the origin as the endpoint in the second quadrant and The area enclosed by the negative half-axes of the shaft; the area corresponding to the tension-compression combined loading mode is the area between the above two.

4. The method for designing a dynamic and static universal loading path for a true triaxial mechanical test according to claim 3, characterized in that: In step 3, the slope of the boundary between the triaxial compression loading area and the tension-compression combined loading area is With Lord's Point decreases with the increase of is a positive value, so the triaxial compression loading area is continuously reduced; the slope of the boundary line between the triaxial tensile loading area and the tension-compression combined loading area With Lord's Point decreases with the increase of is a negative value, so the range of the triaxial tensile loading area continues to increase; the change in the range of the tension-compression composite loading area is determined according to the changes of the above two.

5. The method for designing a dynamic and static universal loading path for a true triaxial mechanical test according to claim 4, characterized in that: In step 4, arrange the Loading paths, specifically select The line has the zero coordinate point as its endpoint and the slope is These rays are the dynamic and static general-purpose load paths.

6. A dynamic and static universal loading path design method for true triaxial mechanical testing according to claim 5, characterized in that: In step 6, complete the total Design of dynamic and static universal loading path for true triaxial mechanical test of sandstone.

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