Dynamic and static universal loading path design method for true triaxial mechanical test

Abstract

The invention provides a dynamic and static universal loading path design method for a true triaxial mechanical test. Loading path design is carried out in the stress space, the principal stress space is sectioned into a set of a series of stress meridian plane spaces, and conversion from a three-dimensional design environment to a two-dimensional design environment is achieved; on the basis of the two-dimensional design environment, dynamic and static universal loading paths in three different loading modes of triaxial compression, triaxial stretching and tension-compression combination are designed; and converting the design result in the two-dimensional design environment into a final three-dimensional design result. And the comparability between dynamic and static true triaxial mechanical test results can be realized. And the distribution of dynamic and static true triaxial mechanical test loading paths in a stress space can be set as required.

Description

Technical Field

[0001] The present invention relates to the application field of high-end equipment, in particular to the field of mechanical testing, and specifically to the design of static and dynamic true triaxial mechanical testing loading schemes for solid materials such as rock, concrete, metal, ceramic, polymer, etc. Background Art

[0002] True triaxial mechanical test is an important research method for studying the mechanical properties of solid materials. This test can provide a theoretical basis for geotechnical engineering, mining engineering, concrete structure engineering, metal processing and other fields. In actual engineering, solid materials such as rocks and concrete 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. At present, the static true triaxial mechanical test system is mainly based on the Mogi true triaxial test machine configuration. The loads in the three axes of the test machine can be independently controlled. In theory, a highly free loading path can be achieved by regulating the stress time history curves of each axis.

[0003] like Figure 1 As shown in the figure, the common loading scheme of the static true triaxial test system is: first load three axial loads to make the specimen reach a certain stress state, maintain the second and third principal stresses The level remains unchanged, and then continue to load to increase the first principal stress Until the specimen stress reaches the test requirements.

[0004] This loading path meets the research needs of most static true triaxial mechanical tests, but is not suitable for dynamic true triaxial mechanical tests, especially dynamic tests with high loading rates or strain rates, because it is difficult to achieve precise control of dynamic stress during a short dynamic loading process. For example, the dynamic loading time of the Hopkinson bar test is extremely short (microseconds), and its loading time history curve is a shock wave with a fixed waveform. Generally, only the pulse width (loading time) and amplitude (load size) 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 dynamic true triaxial mechanical test research and realize the comparative analysis of the dynamic and static mechanical properties of solid materials, it is necessary to develop a dynamic and static universal loading path design method so that the designed loading path can be applied to dynamic true triaxial test systems, static true triaxial test systems, and dynamic and static combined true triaxial test systems. Summary of the invention

[0006] In order to solve the problems in the prior art, the present invention provides a dynamic and static universal loading path design method for true triaxial mechanical tests. Step 1: In the principal stress space, from arrive Select within the range 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 numerical 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 regions corresponding to different loading modes in each stress meridian space; the division of various loading mode regions in the stress meridian space is determined by 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: Combining the above design process, complete the total Design of dynamic and static universal loading path for true triaxial mechanical tests on test materials.

[0007] As a further improvement of the present invention, 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.

[0008] As a further improvement of the present invention, in step 3, different loading modes include triaxial compression, triaxial tension, and tension-compression combination; wherein the area corresponding to the triaxial compression loading mode is specifically 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-axis of the axis; the area corresponding to the tension-compression composite 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.

[0009] 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 composite 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.

[0010] As a further improvement of the present invention, in step 4, in each stress meridian plane, a region corresponding to the triaxial compression loading mode is arranged 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.

[0011] As a further improvement of the present invention, in step 6, a total of Design of dynamic and static universal loading path for true triaxial mechanical test of sandstone.

[0012] The beneficial effects of the present invention are: The loading path design method provided by the present invention is beneficial in that: Innovation 1: It can make the dynamic and static true triaxial mechanical test results comparable. Based on the high strain rate characteristics and load time history curve characteristics of the dynamic true triaxial Hopkinson bar test, a loading path design method suitable for both dynamic true triaxial tests and static true triaxial tests was established, achieving comparability between dynamic and static test results.

[0013] like Figure 7 As shown in Figure 2, by controlling the dynamic and static loading, the ratio of the three axial stresses increases synchronously in time. Equal, realizing that the dynamic and static true triaxial mechanical loading paths are the same ray in the stress space; Innovation 2: The distribution of dynamic and static true triaxial mechanical test loading paths in stress space can be set as needed. Loading path design is carried out in stress space. The loading path design process uses the method of stress space visualization and proposes a three-dimensional stress state in the stress meridian plane. and the three-dimensional stress state in the principal stress space The coordinate transformation formula is used to cut the principal stress space into a set of stress meridian plane spaces, realizing the transformation from a three-dimensional design environment to a two-dimensional design environment. Based on the above two-dimensional design environment, dynamic and static universal loading paths under different loading modes (triaxial compression, triaxial tension, tension-compression combination) 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. .

[0014] like Figure 8 As shown in Figure 2, this is specifically manifested by controlling the ratio of the three axial stresses to increase synchronously in time during the loading process. By changing the directional area and distribution density of multiple loading paths in the stress space in dynamic and static true triaxial mechanical tests, it is possible to adjust the change; thus providing an experimental basis for simulating the stress state and loading path of engineering objects under complex static loads and complex dynamic disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of common loading schemes for static true triaxial test studies, including stress-time history curves of two static loading paths and the loading paths in the principal stress space; Figure 2 Schematic diagram of cubic specimen loading in static and dynamic true triaxial tests; Figure 3 Different Lode angles in principal stress space Schematic diagram of the corresponding stress meridian plane and deviatoric plane; Figure 4 It is a schematic diagram of the division of different loading modes in the stress meridian plane; Figure 5 In the principal stress space at the Lode angle Schematic diagram of the designed loading path on the corresponding stress meridian plane; Figure 6 A schematic diagram of a dynamic and static universal loading scheme for a true triaxial mechanical test provided by the present invention, including a stress time history curve of a dynamic loading path and a static loading path and a loading path 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 is expressed as a ray in the principal stress space; Figure 7 A schematic diagram of a dynamic and static universal loading scheme for a true triaxial mechanical test provided by the present invention, including a stress time history curve of a dynamic loading path and a static loading path and a loading path in the principal stress space, and by controlling the ratio of the synchronous increase of the three axial stresses in dynamic and static loading in time are equal, the loading path is the same ray in the principal stress space; Figure 8 A schematic diagram of a dynamic and static universal loading scheme for a true triaxial mechanical test provided by the present invention, including two groups of loading paths with different directional areas and distribution densities; Fig. 9 The Lode angle designed in the embodiment The corresponding three loading paths are distributed on the stress meridian plane; Fig.10 The Lode angle designed in the embodiment , = Stress-time history curve results of the verification test of the loading path; Fig.11 The Lode angle designed in the embodiment , = Test verification results of loading paths on stress meridian planes; Fig.12 The Lode angle designed in the embodiment Corresponding test verification results of three loading paths on the stress meridian plane. DETAILED DESCRIPTION

[0016] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0017] like Figure 2As shown, the embodiment of the present invention takes the dynamic triaxial compression strength pre-experiment of sandstone as an example, and stipulates that in this embodiment, the stress is positive when it is compressed. The test equipment is a dynamic true triaxial test system based on the Hopkinson bar. The load loading method is to apply impact stress wave loads by three axial square cross-section waveguide rods. A titanium alloy cube specimen with the same material as the waveguide rod is used for pre-experimentation to verify the feasibility of the designed loading path.

[0018] The dynamic and static universal loading path design method for true triaxial mechanical test of the present invention is used to design and implement the test loading scheme as follows: Step 1: Figure 3 As shown in the figure, in the principal stress space, a space angle bisector is determined, which passes through the origin and has equal angles with the three coordinate axes; any plane perpendicular to the space angle bisector is the stress deviatoric plane, and any plane perpendicular to the stress deviatoric plane and containing the space angle bisector is the stress meridian plane, which contains the coordinate axes The Lode angle corresponding to the stress meridian plane = ; Note: The mathematical expression for the definition of the Lode angle is as shown in equation (1). arrive Select 3 Lode angles from the range and its corresponding stress meridian plane, set it to be evenly distributed, that is, the adjacent meridian planes correspond to the Lode angle interval of 30 degrees ; Step 2: In the three stress meridian spaces selected in step 1, establish Axis and The plane rectangular coordinate system composed of the axes, and mean principal stress In terms of numerical value, it is a multiple relationship. Equivalent stress (or generalized shear 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: If Figure 4 As shown in the figure, the areas corresponding to different loading modes (triaxial compression, triaxial tension, and tension-compression combination) are delineated in each stress meridian space; 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 division of various loading mode areas in the stress meridian space depends on their corresponding Lode angle For example, the slope of the boundary between the triaxial compression loading area and the tension-compression combined loading area is With Lord's Point The triaxial compression loading area is reduced as the angle increases. Taking the corresponding stress meridian plane as an example, the area corresponding to the triaxial compression loading mode is the slope in the first quadrant And the ray with the origin as its endpoint is The area enclosed between the positive semi-axes; Step 4: Figure 5 As shown in the figure, three loading paths are arranged in the area corresponding to the triaxial compression loading mode in each stress meridian plane. Specifically, three loading paths are selected with the zero coordinate point as the endpoint and the slope as The rays are the dynamic and static general load paths; the ... Taking the corresponding stress meridian plane as an example, the slopes of the three selected rays are 0.40, 0.55 and 0.70, which are all less than , which belongs to the category of triaxial compression loading mode; Step 5: There are 9 loading paths determined in step 4 above, each of which corresponds to a Lode angle. and the slope of the ray in stress meridian space , 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 , 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. As shown in Table 1, Table 1 lists some of the data. Table 1 is the result of calculation and normalization by formula (2).

[0019] Cape Lord ,design Take the loading path as an example, select the loading path that satisfies MPa stress state point, calculated according to the slope MPa, and the stress state point is expressed in principal stress space coordinates as follows: = MPa, normalized calculation of the ratio of stress synchronous increase = ; like Figure 6 and Figure 7 As shown in Figure 1, firstly, this design method changes the amplitude of the stress time history curve by designing the shape of the stress time history curve to remain unchanged, that is, controlling the three axial stresses to increase synchronously in time during the loading process, so that the dynamic and static loading paths are expressed in the form of rays in the stress space (principal stress space and stress meridian plane space) (such as Figure 6 As shown), when the dynamic and static true triaxial mechanical tests are carried out according to the same ratio When loading, the same loading path in the principal stress space and the stress meridian plane space is the same ray, that is, dynamic and static loading can be realized as the same loading path (such as Figure 7 As shown). Secondly, this design method adjusts the distribution of the loading path in the stress space (principal stress space and stress meridian plane space) by controlling the change in the ratio of the synchronous increase of the three axial stresses in time during the loading process, that is, the direction in which the above rays extend in the stress space; the final design result of this method is: during the dynamic and static true triaxial mechanical test loading process, the ratio of the synchronous increase of the three axial stresses in time is expressed by Each ratio corresponds to a fixed loading path in the stress space.

[0020] Step 6: Based on the above design process, a total of 9 dynamic and static universal loading path designs for true triaxial mechanical tests of sandstone were completed, located at Lord Point On the corresponding three stress meridian planes, the Lode angle The corresponding three loading paths on the stress meridian plane rectangular coordinate system are distributed as follows: Fig. 9 As shown; Step 7: Take 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. Fig.10 As shown; 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 Fig.11 As shown; 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 Fig.12 shown.

[0021] 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.

[0022] Table 1 Results of dynamic and static universal loading path design for true triaxial mechanical test

[0023] 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: Combining the above design process, 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-axis of the axis; the area corresponding to the tension-compression composite 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.

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 is 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.

Images