Method for calculating interface area content of fiber reinforced mortar based on binary particle doping

Abstract

The invention relates to the technical field of microstructure characterization of a fiber reinforced concrete system, and discloses a binary particle doping-based fiber reinforced mortar interface area content calculation method, which comprises the following steps of: 1, respectively defining parameters such as geometrical morphology, size distribution, interface area thickness and the like of short fiber particles and fine aggregate particles; 2, calculating the relative content of a surrounding interface area of the single-size short fiber particles; 3, calculating the relative content of the interface area around the multi-size fine aggregate particles; and 4, calculating the total relative content of an interface area around all particle components in the fiber reinforced mortar system. The invention provides a calculation method for rapidly obtaining the total relative content of the interface area around the two particle components of the fiber and the aggregate in the fiber reinforced system doped and accumulated with the multiple particles, the limitation that the interface area content prediction can only be carried out for a single-type aggregate particle accumulation system in the prior art is eliminated, and the applicable objects are more diversified; and the calculation precision is higher.

Description

Technical Field

[0001] The invention relates to the technical field of microstructure characterization of fiber reinforced concrete systems, and in particular to a method for calculating the content of an interface zone of fiber reinforced mortar based on binary particle doping. Background Art

[0002] Adding various short fibers to the matrix material is considered an important method to improve the mechanical properties of the material, such as tensile strength, toughness, and crack resistance. For the concrete system, the interfacial transition zone is a weak zone that is commonly found around the aggregate particles. Affected by factors such as the aggregate sidewall effect and micro-area water bleeding, the interfacial zone usually exhibits characteristics such as high porosity, high permeability, and low strength. Therefore, the amount and structural characteristics of the interfacial zone in the system have an important influence on the overall macroscopic properties of the material. As various short fibers are added to the concrete system, the fibers not only improve the mechanical properties of the material, but also form an interfacial zone of a certain thickness around the fiber particles, which leads to a further increase in the relative content of the interfacial zone in the entire system. In order to more comprehensively understand the mechanism of fiber enhancement on material performance, clarify the relationship between the relative content of the interfacial zone in the fiber-reinforced system and the multi-type particle components such as fiber and aggregate, and its effect on the macroscopic properties of the material, it is necessary to accurately evaluate and predict the amount of the interfacial zone in the system. However, due to the complex characteristics of the interface area around the aggregate in real materials, many factors cannot be absolutely ideally controlled during the experiment and the experimental results are highly discrete. At present, it is still impossible to directly use experimental methods to accurately measure the content of the interface area in the material. With the rapid development of computer technology, using computer simulation technology to construct a microscopic model of materials and combining relevant theories to study the structural characteristics of the interface area in the particle system has become an optional research method.

[0003] From a microscopic perspective, fiber-reinforced concrete materials can be regarded as a multiphase composite material composed of fiber particles, aggregate particles, overlapping interface regions, and a homogeneous cement matrix. To date, most numerical and theoretical studies on the content of the interface region around aggregates in concrete systems have been conducted on ordinary concrete systems. In the modeling process, all coarse and fine aggregates are usually simplified into particles with the same geometric morphology, and the entire system is composed of a single type of spherical or non-spherical particles. The influence of the incorporation of short fibers and the diversity of particle components on the relative content of the interface region around the particle components inside the material has not been considered, which greatly limits the applicability of existing related research results. Existing theoretical prediction models cannot be directly used to calculate the total relative content of the interface region around fibers and aggregates in fiber-reinforced concrete systems, and the calculation accuracy also needs to be improved.

[0004] Therefore, it is necessary to provide a method for calculating the interface area content of fiber-reinforced mortar based on binary particle doping to solve the above technical problems. Summary of the invention

[0005] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a method for calculating the interface area content of fiber-reinforced mortar based on binary particle doping, taking the fiber-reinforced mortar system as the object. The method regards the short fibers in the system as single-sized spherical particles with a certain width and length, and the fine aggregate as multi-sized ellipsoidal particles with a fixed geometric morphology and aspect ratio that meet a specific size distribution, and accurately theoretically predicts the relative content of the interface area around all particle components when the two are mutually doped. This method gets rid of the previous limitation that the interface area content can only be predicted for a single-type aggregate particle stacking system, and the applicable objects are more diverse and the calculation accuracy is higher.

[0006] The method for calculating the content of the interface area of ​​the fiber-reinforced mortar based on binary particle doping provided by the present invention comprises the following steps:

[0007] Step 1: Define the parameters such as the geometric morphology, size distribution and interface thickness of short fiber particles and fine aggregate particles respectively;

[0008] Step 2: Calculate the relative content of the interface area around the single-sized short fiber particles;

[0009] Step 3: Calculate the relative content of the interfacial zone around the multi-sized fine aggregate particles;

[0010] Step 4: Calculate the total relative content of the interface area around all particle components in the fiber-reinforced mortar system based on the relative content of the interface area obtained in steps 2 and 3.

[0011] Preferably, in step 1, the short fibers in the system are regarded as spherical cylinders with the same geometric shape and size. Such fiber particles are composed of three parts: a cylinder in the middle area and two hemispheres at the ends. The diameter D of the sphere is set to sf Represents the sum of fiber width, cylindrical area height and sphere diameter H sf Represents the length of the fiber, parameter ε = H sf / D sf represents the aspect ratio of this type of fiber, and the thickness of the interface area around the fiber particles is t sf ;

[0012] The fine aggregate in the system is regarded as a spheroid with the same geometric shape and aspect ratio, but the particle size distribution satisfies a specific distribution function. Set a, b and c as the semi-axis lengths of the fine aggregate particles, and a is always equal to b. The parameter η = c / a represents the aspect ratio of the fine aggregate particles. The maximum equivalent particle size and the minimum equivalent particle size of the fine aggregate are D eq,max,sa and Deq,min,sa , the thickness of the interface zone around the aggregate particles is t sa .

[0013] Preferably, in the step 2, the relative content of the interface area around the single-sized short fiber particles is calculated by the following formula:

[0014]

[0015] Where V si,sf is the relative content of the interface area around the single-sized spherical short fiber particles, V f,sf is the volume fraction of fiber particles, N V,sf is the number density of fiber particles, κ 1,sf ,κ 2,sf and κ 3,sf is the adjustment factor, where

[0016]

[0017] Preferably, in step 3, the relative content of the interface area around the multi-sized fine aggregate particles is calculated by the following formula:

[0018]

[0019] Where V si,sa is the relative content of the interface area around the multi-sized ellipsoidal fine aggregate particles, V f,sa is the volume fraction of aggregate particles, N V,sa is the number density of aggregate particles, κ 1,sa ,κ 2,sa and κ 3,sa is the adjustment factor, where

[0020]

[0021] In the formula, is the average volume of multi-sized aggregate particles, is the average surface area of ​​multi-sized aggregate particles, is the average equivalent diameter of aggregate particles of various sizes.

[0022] Preferably, the specific distribution functions corresponding to the particle size of the fine aggregate are EVF and Fuller function, respectively, and the number basis probability density functions corresponding to the two types of functions are:

[0023]

[0024] Where D eq,sa is the equivalent diameter of aggregate particles, which can be expressed as 2aη 1 / 3 , f N (D eq,sa) is the probability density function of the quantity basis.

[0025] Preferably, the average volume, average surface area and average equivalent diameter of the multi-sized ellipsoidal fine aggregate particles satisfying the EVF and Fuller distribution functions can be respectively

[0026]

[0027] Preferably, in step 4, the relative content value V of the interface area around the single-sized short fiber particles obtained in step 3 is si,sf (t sf ,V f,sf ) and the relative content value V of the interface area around the multi-sized fine aggregate particles obtained in step 4 si,sa (t sa ,V f,sa ) into the following formula, the total relative content of the interface area around the two particle components of fiber and fine aggregate in the fiber-reinforced mortar system can be calculated.

[0028] V f,si (t sf ,V f,sf ,t sa ,V f,sa )=V si,sf (t sf ,V f,sf )+V si,sa (t sa ,V f,sa )-V s,isf ( s t f ,V f,sf )·V si,sa ( s t a ,V f,sa ) (15)

[0029] Where V f,si It is the total relative content of the interface area around the two particle components of short fibers and fine aggregate in the fiber-reinforced mortar system.

[0030] Compared with the related art, the method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping provided by the present invention has the following beneficial effects:

[0031] 1. The existing theoretical technology does not involve the influence of the mutual doping of multiple types of particles on the relative content of the interface area around the particle components, and it is impossible to effectively predict the content of the interface area in the multi-particle mixed stacking system;

[0032] 2. In the method of the present invention, the fiber and fine aggregate are regarded as single-sized spherical cylinders and multi-sized ellipsoids respectively, and a calculation method for the relative content of the interface area in the fiber-reinforced mortar system based on the mixed accumulation of the two is established, which fully considers the influence of the synergistic effect of the two on the relative content of the interface area, and gets rid of the previous limitation that the interface area content can only be predicted for a single-type aggregate particle accumulation system;

[0033] 3. The method of the present invention provides a preliminary basis for further exploring the quantitative relationship between particle component characteristics, relative content of interface area and macroscopic properties of materials in fiber-reinforced concrete;

[0034] 4. The method of the present invention is simple in theory, easy to use, applicable to more diverse objects, and has higher calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of a single spherical-column-shaped fiber particle containing an interface region of equal thickness;

[0036] Figure 2 Schematic diagram of a single ellipsoidal fine aggregate particle containing an interface region of equal thickness;

[0037] Figure 3(a) shows the thickness of the interface region t sf =t sa =0.02mm, 0.05mm and 0.10mm, the relative content of the interface area V f,si With fiber content V f,sf Comparison of theoretical calculation results and numerical results of changes;

[0038] Figure 3(b) shows the thickness of the interface region t sf =t sa = 0.02mm and 0.05mm, when the size distribution of fine aggregate conforms to the Fuller function, the relative content V in the interface area f,si With aggregate content V f,sa Comparison of theoretical calculation results and numerical results of changes;

[0039] Figure 3(c) shows the aggregate volume fraction V f,sa = 0.25 and 0.45, the size distribution conforms to the Fuller and EVF functions, and the relative content V f,si Minimum equivalent particle size of aggregate D eq,min,sa Comparison of theoretical calculation results and numerical results of changes;

[0040] Figure 3(d) shows the aggregate volume fraction V f,sa = 0.25 and 0.45, the size distribution conforms to the Fuller and EVF functions, and the relative content V f,si Maximum equivalent particle size of aggregate D eq,max,saComparison of theoretical calculation results and numerical results of the changes. DETAILED DESCRIPTION

[0041] The present invention will be further described below in conjunction with the accompanying drawings and implementation modes.

[0042] Step 1: Define the parameters such as the geometric morphology, size distribution and interface thickness of short fiber particles and fine aggregate particles respectively;

[0043] Step 2: Calculate the relative content of the interface area around the single-sized short fiber particles;

[0044] Step 3: Calculate the relative content of the interfacial area around the multi-sized fine aggregate particles;

[0045] Step 4: Calculate the total relative content of the interface area around all particle components in the fiber-reinforced mortar system based on the relative content of the interface area obtained in steps 2 and 3.

[0046] In step 1 of this embodiment, the short fibers in the fiber-reinforced mortar system are regarded as spherical cylinders with the same geometric shape and size. The fiber particles are composed of three parts: a cylinder in the middle area and two hemispheres at the ends. The diameter D of the sphere is set to sf Represents the sum of fiber width, cylindrical area height and sphere diameter H sf Represents the length of the fiber, parameter ε = H sf / D sf represents the aspect ratio of this type of fiber, and the thickness of the interface area around the fiber particles is t sf , see Figure 1 .

[0047] The fine aggregate in the system is regarded as a spheroid with the same geometric shape and aspect ratio, but the particle size distribution satisfies a specific distribution function. Set a, b and c as the semi-axis lengths of the fine aggregate particles, and a is always equal to b. The parameter η = c / a represents the aspect ratio of the fine aggregate particles. The maximum equivalent particle size and the minimum equivalent particle size of the fine aggregate are D eq,max,sa and D eq,min,sa , the thickness of the interface zone around the aggregate particles is t sa ,join Figure 2 .

[0048] In step 2 of this embodiment, the relative content of the interface region around the single-sized spherical-column-shaped fiber particles can be calculated by the following formula:

[0049]

[0050] Where V si,sf is the relative content of the interface area around the single-sized spherical short fiber particles, V f,sf is the volume fraction of fiber particles, NV,sf is the number density of fiber particles, κ 1,sf ,κ 2,sf and κ 3,sf is the adjustment factor, where

[0051]

[0052]

[0053] In step 3 of this embodiment, the relative content of the interface area around the multi-sized ellipsoidal fine aggregate particles can be calculated by the following formula:

[0054]

[0055] Where V si,sa is the relative content of the interface area around the multi-sized ellipsoidal fine aggregate particles, V f,sa is the volume fraction of aggregate particles, N V,sa is the number density of aggregate particles, κ 1,sa ,κ 2,sa and κ 3,sa is the adjustment factor, where

[0056]

[0057] In the formula, is the average volume of multi-sized aggregate particles, is the average surface area of ​​multi-sized aggregate particles, is the average equivalent diameter of aggregate particles of various sizes.

[0058] In this embodiment, the size distribution of fine aggregate conforms to the EVF and Fuller functions respectively, and the number basis probability density functions corresponding to the two types of functions are:

[0059]

[0060] Where D eq,sa is the equivalent diameter of aggregate particles, which can be expressed as 2aη 1 / 3 , f N (D eq,sa ) is the probability density function of the quantity basis.

[0061] In this embodiment, the average volume, average surface area and average equivalent diameter of multi-sized ellipsoidal fine aggregate particles satisfying EVF and Fuller distribution function can be obtained by the following formulas:

[0062]

[0063] In step 4 of this embodiment, the relative content value V of the interface area around the single-sized spherical short fiber particles calculated in step 3 is si,sf (t sf ,V f,sf ) and the relative content value V of the interface area around the multi-sized fine aggregate particles calculated in step 4 si,sa (t sa ,V f,sa ) is substituted into the following formula, and the total relative content of the interface area around the two particle components of fiber and aggregate in the fiber-reinforced mortar based on binary particle doping can be finally calculated.

[0064] V f,si (t sf ,V f,sf ,t sa ,V f,sa )=V si,sf (t sf ,V f,sf )+V si,sa (t sa ,V f,sa )-V si,sf (t sf ,V f,sf )·V si,sa (t sa ,V f,sa ) (15)

[0065] Where V f,si It is the total relative content of the interface area around the two particle components of short fibers and fine aggregate in the fiber-reinforced mortar system.

[0066] It can be seen from the above implementation process that as long as the volume fraction, geometric shape, size, thickness of the surrounding interface area of ​​the fiber particles and the volume fraction, geometric shape, size distribution characteristics and thickness of the surrounding interface area of ​​the fine aggregate particles are clear, the method of the present invention can be used to predict and calculate the relative content of the interface area in different forms of fiber-reinforced mortar systems. The above parameters are set to different values, substituted into the corresponding formulas to obtain the theoretical calculation results of the relative content of the interface area around the fiber and aggregate in the fiber-reinforced mortar system under different situations, and the theoretical results are compared with the numerical results obtained by the random point sampling algorithm. The results are shown in Figures 3(a)-3(d).

[0067] Figure 3(a) shows the thickness of the interface region t sf =t sa =0.02mm, 0.05mm and 0.10mm, the relative content of the interface area V f,si With fiber content V f,sf Comparison of theoretical calculation results and numerical results; Figure 3(b) shows the thickness of the interface zone tsf =t sa = 0.02mm and 0.05mm, when the size distribution of fine aggregate conforms to the Fuller function, the relative content V in the interface area f,si With aggregate content V f,sa Comparison of theoretical calculation results and numerical results; Figure 3(c) shows the aggregate volume fraction V f,sa = 0.25 and 0.45, the size distribution conforms to the Fuller and EVF functions, and the relative content V f,si Minimum equivalent particle size of aggregate D eq,min,sa The comparison between the theoretical calculation results and the numerical results of the changes in the aggregate volume fraction V is shown in Figure 3(d). f,sa = 0.25 and 0.45, the size distribution conforms to the Fuller and EVF functions, and the relative content V f,si Maximum equivalent particle size of aggregate D eq,max,sa Comparison of theoretical calculation results and numerical results of the changes.

[0068] It can be found that no matter how the parameters of the fiber or aggregate change, the theoretical calculation results provided by the method of the present invention maintain good consistency with the numerical results, which also indirectly proves the effectiveness and accuracy of the method of the present invention.

[0069] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping, characterized in that: include: Step 1: Define the parameters such as the geometric morphology, size distribution and interface thickness of short fiber particles and fine aggregate particles respectively; Step 2: Calculate the relative content of the interface area around the single-sized short fiber particles; Step 3: Calculate the relative content of the interfacial area around the multi-sized fine aggregate particles; Step 4: Calculate the total relative content of the interface area around all particle components in the fiber-reinforced mortar system based on the relative content of the interface area obtained in steps 2 and 3.

2. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 1, characterized in that: In the step 1, the short fibers in the system are regarded as spherical cylinders with the same geometric shape and size. The fiber particles are composed of three parts: a cylinder in the middle area and two hemispheres at the ends. The diameter D of the sphere is set to sf Represents the sum of fiber width, cylindrical area height and sphere diameter H sf Represents the length of the fiber, parameter ε = H sf / D sf represents the aspect ratio of this type of fiber, and the thickness of the interface area around the fiber particles is t sf ; The fine aggregate in the system is regarded as a spheroid with the same geometric shape and aspect ratio, but the particle size distribution satisfies a specific distribution function. Set a, b and c as the semi-axis lengths of the fine aggregate particles, and a is always equal to b. The parameter η = c / a represents the aspect ratio of the fine aggregate particles. The maximum equivalent particle size and the minimum equivalent particle size of the fine aggregate are D eq,max,sa and D eq,min,sa , the thickness of the interface zone around the aggregate particles is t sa .

3. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 1, characterized in that: In the step 2, the relative content of the interface area around the single-sized short fiber particles can be calculated by the following formula: Where V si,sf is the relative content of the interface area around the single-sized spherical short fiber particles, V f,sf is the volume fraction of fiber particles, N V,sf is the number density of fiber particles, κ 1,sf ,κ 2,sf and κ 3,sf is the adjustment factor, where 4. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 1, characterized in that: In step 3, the relative content of the interface area around the multi-sized fine aggregate particles can be calculated by the following formula: Where V si,sa is the relative content of the interface area around the multi-sized ellipsoidal fine aggregate particles, V f,sa is the volume fraction of aggregate particles, N V,sa is the number density of aggregate particles, κ 1,sa ,κ 2,sa and κ 3,sa is the adjustment factor, where In the formula, is the average volume of multi-sized aggregate particles, is the average surface area of ​​multi-sized aggregate particles, is the average equivalent diameter of aggregate particles of various sizes.

5. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 2, characterized in that: The specific distribution functions are EVF and Fuller function, and the number basis probability density functions corresponding to the two types of functions are: Where D eq,sa is the equivalent diameter of aggregate particles, which can be expressed as 2aη 1 / 3 , f N (D eq,sa ) is the probability density function of the quantity basis.

6. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 4, characterized in that: The average volume, average surface area and average equivalent diameter of multi-sized ellipsoidal fine aggregate particles that satisfy the EVF and Fuller distribution functions can be calculated by the following formulas:

7. The method for calculating the content of the interface area of ​​fiber-reinforced mortar based on binary particle doping according to claim 1, characterized in that: In step 4, the relative content value V of the interface area around the single-size short fiber particles obtained in step 3 is si,sf (t sf ,V f,sf ) and the relative content value V of the interface area around the multi-sized fine aggregate particles obtained in step 4 si,sa (t sa ,V f,sa ) into the following formula, the total relative content of the interface area around the two particle components of fiber and fine aggregate in the fiber-reinforced mortar system can be calculated. V f,si (t sf ,V f,sf ,t sa ,V f,sa )=V si,sf (t sf ,V f,sf )+V si,sa (t sa ,V f,sa )-V s,isf ( s t f ,V f,sf )·V si,sa ( s t a ,V f,sa ) Where V f,si It is the total relative content of the interface area around the two particle components of short fibers and fine aggregate in the fiber-reinforced mortar system.

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