Method for establishing constitutive equation of plastic modified concrete material considering compaction process

Abstract

The application relates to the technical field of protective materials, in particular to a method for establishing a plastic modified concrete constitutive equation considering a compaction process. The stress-strain curve of a plastic modified concrete sample is obtained through one-dimensional strain SHPB (split Hopkinson pressure bar) experiment, the stress-strain curve is divided into a linear elastic section, a pore compaction section and a dense section, the relationship between the compression yield strength and the strain rate is fitted in sections, and the plastic modified concrete constitutive equation considering the compaction process is established. It is verified that the constitutive equation obtained by the application can truly reflect the relationship between the compression yield strength and the strain rate of the plastic modified concrete, wherein the upper threshold and the lower threshold of the pore compaction section reflect the high and low of the porosity, and provide a technical basis for evaluating the protective performance of the plastic modified concrete.

Description

Technical Field

[0001] This invention relates to protective material technology, specifically a method for establishing the constitutive equation of plastic-modified concrete material that takes into account the compaction process. Background Technology

[0002] Foamed concrete, as a new type of energy-absorbing material, has been widely used in various protective engineering projects. However, foamed concrete uses foaming agents to create pores, and after the addition of organic foaming agents, its porosity is difficult to control, resulting in uneven energy absorption performance. In addition, after a period of use, certain liquid impurities are mixed into the pores of foamed concrete, which will cause the strength of the foamed concrete to change and lose its energy absorption performance.

[0003] Because of the above problems with foamed concrete, in order to simplify the production process of porous concrete, reduce costs, and further improve the energy absorption capacity of foamed concrete, a type of plastic modified concrete has been developed. This type of concrete is made by dispersing plastic particles into concrete and then mixing and solidifying it.

[0004] The physical significance of constitutive equations lies in describing the macroscopic mechanical response characteristics of materials through mathematical relationships. They serve as a bridge connecting the microstructure and macroscopic mechanical behavior of materials, providing crucial basis for engineering analysis.

[0005] Currently, there are no constitutive equations for plastic-modified concrete materials in existing technologies. Summary of the Invention

[0006] In view of the problems pointed out in the background art, the purpose of this invention is to provide a method for establishing the constitutive equation of plastic modified concrete material considering the compaction process. Through the method provided by this invention, the correct constitutive equation of plastic modified concrete can be obtained, providing a technical basis for the application of plastic modified concrete.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for establishing the constitutive equation of plastic-modified concrete considering the compaction process includes the following steps: S1. Prepare plastic-modified concrete specimens; the mass composition of the specimens is as follows: X parts concrete; Y parts water; Z parts plastic granules; the specimen shape is a cylinder with length H and diameter D; S2. Using irreversible loading and unloading, a one-dimensional strain SHPB test with lateral constraints is performed on the specimen, and the stress-strain curve of the specimen under one-dimensional strain conditions is obtained through the test. S3. Based on the stress P during the compaction process, the stress-strain curve of the specimen under one-dimensional strain conditions is divided into the linear elastic segment, the pore compaction segment, and the dense segment. S4. The stress should be converted into hydrostatic pressure and then into volumetric deformation. The stress deviator of plastic modified concrete adopts an ideal elastic-plastic model. Based on the stress-strain curve of the specimen under one-dimensional strain conditions, the relationship between compressive yield strength and strain rate of the linear elastic segment, pore compaction segment and dense segment is fitted respectively, and the constitutive equation of plastic modified concrete considering the compaction process is established.

[0008] Step S2 is as follows: The plastic-modified concrete specimen is placed into a rigid sleeve with an inner diameter of D. Both ends of the rigid sleeve are sealed with disc-shaped concrete blocks of diameter D, and the two disc-shaped concrete blocks abut against the two end faces of the plastic-modified concrete specimen. The plastic-modified concrete specimen, the disc-shaped concrete blocks, and the rigid sleeve constitute a combined specimen. A one-dimensional strain SHPB test device is used, and the combined specimen is installed between the input rod and the output rod of the one-dimensional strain SHPB test device. The launch rod is launched in a shooting manner, and the launch rod impacts the input rod to input the load.

[0009] Step S3 is as follows: The upper limit of the stress threshold for the linear elastic segment is set as P1, and the upper limit of the stress threshold for the pore compaction segment is set as P2. If P≤P1, it is a linear elastic segment; if P1<P<P2, it is a pore compaction segment; if P≥P2, it is a dense segment after the pores disappear.

[0010] In step S4, the linear elastic segment is reversible due to loading and unloading, and its mathematical expression is as follows: .in The compression ratio is... , The initial density of the material, The density of the material after compression. This represents the initial elastic modulus of the material.

[0011] In step S4, the pore compaction section follows different paths during loading and unloading. The pore compaction process is described by the residual volume deformation after unloading, and its mathematical expression is as follows: Loading , During uninstallation , ; Indicates the tangential volume modulus of the compacted section. It is the unloading modulus of the compaction section.

[0012] In step S4, the mathematical expression for the dense segment is as follows: Assuming the material's plastic volume is incompressible in the dense segment, its loading and unloading curves will develop along the same path, therefore:

[0013] It is the initial compression ratio of the dense section of the material. , , , These are the fitting coefficients.

[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention proposes to describe the pore compaction process using an irreversible loading-unloading PV relationship. Through laterally constrained one-dimensional strain SHPB tests, a strain constitutive equation for plastic-modified concrete considering the compaction process is established. Verification shows that the constitutive equation obtained by this invention is basically consistent with the actual material properties and can be used to evaluate the protective performance of plastic-modified concrete, providing a technical basis for its application. In this invention, the upper and lower thresholds of the pore compaction section reflect the porosity; experiments show that the above constitutive model also applies to plastic-modified concrete. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention.

[0016] Figure 2 This is a schematic diagram of the one-dimensional strain SHPB test apparatus in Example 1.

[0017] Figure 3 This is a structural diagram of the specimen for Example 1.

[0018] Figure 4 for Figure 3 A magnified view of part A.

[0019] Figure 5 The stress-strain curve of the specimen under one-dimensional strain conditions is obtained from the one-dimensional strain SHPB test according to Example 1.

[0020] Figure 6 The waveform of the incident wave is shown in Example 1 when the velocity of the incident rod is 11 m / s.

[0021] Figure 7 The transmitted wave waveform is shown in Example 1 when the incident rod velocity is 11 m / s.

[0022] Figure 8 The waveform of the incident wave is shown in Example 1 when the velocity of the incident rod is 10 m / s.

[0023] Figure 9 The waveform of the transmitted wave is shown in Example 1 when the incident rod velocity is 10 m / s. Detailed Implementation

[0024] The present invention will now be clearly and completely described with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] like Figure 1 As shown, this invention provides a method for establishing the constitutive equation of plastic-modified concrete materials that considers the compaction process. To clearly illustrate the principle of this invention, the process of Embodiment 1 is described in detail below.

[0026] Example 1

[0027] Example 1 uses plastic-modified concrete with a porosity φ of 0.45. The method for preparing the plastic-modified concrete specimens is as follows: Concrete, water, and plastic particles are mixed according to the mass ratio, stirred evenly, and then molded into cylindrical specimens of length H and diameter D. After the specimens are prepared, they are subjected to... Figure 2 The SHPB apparatus shown performs one-dimensional strain SHPB tests on the specimen at different incident velocities. The stress waveforms at both ends of the specimen are analyzed by measuring the strain signals on the input and output rods. During the one-dimensional strain test, as... Figure 3 , Figure 4 As shown, a plastic-modified concrete specimen is sandwiched between concrete specimens of the same diameter, and then placed inside a rigid sleeve (a steel sleeve is used in this example) to form a composite specimen. During the test, because the steel sleeve is rigid, the plastic-modified concrete specimen is in a one-dimensional strain state. The concrete specimen is 50 mm long, and the plastic-modified concrete specimen is 25 mm long. Figure 4 As shown, a plastic film is placed between the plastic-modified concrete specimen and the rigid sleeve, and a lubricant is applied between the plastic film and the rigid sleeve.

[0028] The experiment was conducted on a large-diameter one-dimensional strain gauge SHPB device, which is existing technology. Both the input and output rods had a diameter of 100 mm, an elastic modulus E1 of 200 GPa, and a density of 7.8 g / cm³. The incident rod was 18.8 cm long and had the same diameter as the input and output rods. The electronic strain gauge had a sensitivity coefficient of 2.14, and the incident channel calibration coefficient was 1000ue = 1.00 V. The transmission channel calibration coefficient was 1000ue = 1.01 V. The input rod was 4499 mm long, and the output rod was 6535 mm long. The strain gauges were attached to the input rod at a distance of 1000 mm from the specimen and to the output rod at a distance of 800 mm from the specimen, respectively.

[0029] During the experiment, the incident rod was launched at seven different velocities, and seven tests were conducted. When the incident rod was launched at a velocity of 11 m / s, the incident wave waveform was as follows: Figure 6 As shown, the transmitted wave waveform is as follows: Figure 7 As shown; when the launch velocity of the incident rod is 10 m / s, the incident wave waveform is as follows. Figure 8 As shown, the transmitted wave waveform is as follows: Figure 9 As shown. Table 1 shows the peak values ​​of incident wave stress and transmitted wave stress of plastic-modified concrete specimens and concrete blocks under different impact velocities under one-dimensional stress conditions of single-layer materials.

[0030] Table 1. Comparison of peak stress attenuation in concrete and plastic-modified concrete.

[0031] The stress-strain curves of the specimen under one-dimensional strain conditions were obtained through experiments, such as... Figure 4 ,Will Figure 4 The stress in the concrete, when converted to hydrostatic pressure, should be transformed into volumetric deformation to obtain the P-ε of the plastic-modified concrete with a porosity φ of 0.45. V The curve, the P-ε V The main parameters of the curve are shown in Table 2 below.

[0032] Table 2 Plastic modified concrete mainly parameter

[0033] The stress deviator of plastic-modified concrete is modeled using an ideal elastoplastic model, and the relationship between compressive yield strength and strain rate can be fitted using experimental results:

[0034] In the formula To compress the yield strength, The initial compressive yield strength, For strain rate, Let A be the initial strain rate and A be the formula fitting coefficient. hour, , , .

[0035] The parts of this invention not described in detail are prior art.

Claims

1. A method for establishing the constitutive equation of plastic-modified concrete considering the compaction process, characterized in that: Includes the following steps: S1. Prepare plastic-modified concrete specimens; the mass composition of the plastic-modified concrete specimens is as follows: X parts concrete; Y parts water; Z parts plastic particles; the specimen shape is a cylinder with length H and diameter D; S2. Using irreversible loading and unloading, a one-dimensional strain SHPB test with lateral constraint was conducted on plastic modified concrete specimens, and the stress-strain curves of the specimens under one-dimensional strain conditions were obtained through the experiment. S3. Based on the stress P during the compaction process, the stress-strain curve of the specimen under one-dimensional strain conditions is divided into the linear elastic segment, the pore compaction segment, and the dense segment. S4. The stress should be converted into hydrostatic pressure and then into volumetric deformation. The stress deviator of plastic modified concrete adopts an ideal elastic-plastic model. Based on the stress-strain curve of the specimen under one-dimensional strain conditions, the relationship between compressive yield strength and strain rate of the linear elastic segment, pore compaction segment and dense segment is fitted respectively, and the constitutive equation of plastic modified concrete considering the compaction process is established.

2. The method for establishing the constitutive equation of plastic-modified concrete material considering the compaction process according to claim 1, characterized in that: Step S2 is as follows: The plastic-modified concrete specimen is inserted into a rigid sleeve with an inner diameter of D. Both ends of the rigid sleeve are sealed with disc-shaped concrete blocks of diameter D, and the two disc-shaped concrete blocks abut against the two end faces of the plastic-modified concrete specimen. The plastic-modified concrete specimen, the disc-shaped concrete blocks, and the rigid sleeve constitute a combined specimen. A one-dimensional strain SHPB experimental device is used, and the combined specimen is installed between the input rod and the output rod of the one-dimensional strain SHPB experimental device. The launch rod is launched in a shooting manner, and the launch rod impacts the input rod to input the load.

3. The method for establishing the constitutive equation of plastic-modified concrete considering the compaction process according to claim 1, characterized in that: The specific steps of step S3 are as follows: set the upper limit of the stress threshold of the linear elastic segment to P1, and the upper limit of the stress threshold of the pore compaction segment to P2. If P≤P1, it is a linear elastic segment; if P1<P<P2, it is a pore compaction segment; if P≥P2, it is a dense segment after the pores disappear.

4. The method for establishing the constitutive equation of plastic-modified concrete material considering the compaction process according to claim 1, characterized in that: In step S4, the linear elastic segment is reversible due to loading and unloading, and its mathematical expression is as follows: ; The compression ratio is... , The initial density of the material, The density of the material after compression. This represents the initial elastic modulus of the material.

5. The method according to claim 1, characterized in that: In step S4, the pore compaction section follows different paths during loading and unloading. The pore compaction process is described by the residual volume deformation after unloading, and its mathematical expression is as follows: Loading , During uninstallation , ; Indicates the tangential volume modulus of the compacted section. It is the unloading modulus of the compaction section.

6. The method for establishing the constitutive equation of plastic-modified concrete material considering the compaction process according to claim 1, characterized in that: In step S4, the mathematical expression for the dense segment is as follows: Assuming the material's plastic volume is incompressible in the dense segment, its loading and unloading curves will develop along the same path, therefore: It is the initial compression ratio of the dense section of the material. , , , These are the fitting coefficients.

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