Analysis method for tensile fracture of polypropylene fiber concrete on microscopic scale

Abstract

The invention discloses a method for analyzing tensile fracture of polypropylene fiber reinforced concrete on a microscopic scale. The method comprises the following steps: determining tensile fracture stress characteristics of the polypropylene fiber reinforced concrete and dividing microscopic components; the fracture parameters of all the mesoscopic components are measured; establishing three-phase and four-phase mesoscopic geometric models of the polypropylene fiber reinforced concrete; calculating material constitutive parameters of each mesoscopic component based on the cohesion constitutive model; the fracture parameters and the material constitutive parameters of all the mesoscopic components are endowed with three-phase and four-phase mesoscopic geometric models of the polypropylene fiber reinforced concrete, and model boundary conditions are established for model rationality checking calculation; and carrying out tensile fracture analysis on the polypropylene fiber concrete to obtain an analysis result. The method has the remarkable effects that the calculation cost of a computer is reduced, meanwhile, the calculation precision requirement is met, and the intrinsic essence of the low-doping-amount polypropylene fibers on concrete reinforcement and the weakening effect of the high-doping-amount fibers on the concrete are quantified.

Description

Technical Field

[0001] The invention relates to the technical field of concrete finite element simulation, and in particular to an analysis method for tensile fracture of polypropylene fiber concrete on a microscopic scale. Background Art

[0002] As the most widely used engineering and construction material in today's society, concrete has many advantages, such as low price, mature technology, mechanized mass production and transportation, high compressive strength, good durability and high strength grade, etc. Therefore, in addition to the field of civil engineering, it has also been widely used in the fields of mechanical industry, offshore platform construction and geothermal engineering.

[0003] However, ordinary concrete materials are brittle and have low tensile strength. Concrete is very easy to crack under tensile stress and is difficult to repair. Concrete is usually combined with steel bars to form load-bearing components. The expansion of cracks in the components will cause steel corrosion when encountering adverse environmental factors. The wider the crack width, the larger the contact area between the steel bar and the adverse environment, which promotes further corrosion of the steel bar. In reinforced concrete structures, cracking of concrete sections and corrosion of steel bars will greatly weaken the rigidity, ductility and bearing capacity of the structure. In structures with severe cracking and corrosion of sections, brittle failure may even occur, seriously affecting the performance and durability of the structure, and even causing unpredictable engineering accidents.

[0004] To this end, fiber-reinforced concrete has been developed to overcome the above defects. Fiber-reinforced concrete is a multiphase heterogeneous cementitious material composed of cement, coarse and fine aggregates, and admixtures with fiber materials as reinforcement. Compared with ordinary concrete, it has higher ductility, strength and durability. Among many fibers, polypropylene fiber is considered to be a secondary material for concrete reinforcement. Due to the advantages of polypropylene fiber-reinforced concrete such as low price, light weight, easy mixing, and obvious improvement in the mechanical properties of concrete, it has been widely used in key projects such as construction, bridges, and water conservancy.

[0005] Even though polypropylene fiber reinforced concrete can improve the mechanical properties of concrete, it cannot change the fact that concrete is not tensile, and the problem of cracking of concrete components under extreme conditions cannot be completely avoided. The addition of polypropylene fiber improves the crack resistance of concrete, but the material composition of polypropylene fiber reinforced concrete is more complex than that of concrete. On the one hand, polypropylene fiber has a low elastic modulus and a soft texture. Due to the extrusion of aggregates during the mixing, pouring and vibration of concrete, the distribution of polypropylene fiber in concrete is large and the distribution is not in a single shape inside the concrete; on the other hand, the physical and mechanical properties of each phase of polypropylene fiber reinforced concrete and the randomness of its distribution lead to highly random, heterogeneous, porous and complex interfaces on a microscopic scale. This series of factors makes the cracking mechanism of polypropylene fiber reinforced concrete more complex than that of concrete. In order to obtain the accurate mechanical properties of polypropylene fiber reinforced concrete, a large number of experiments are required, which consumes a lot of manpower and material resources. Therefore, it is urgent to establish a set of calculation models for FRC cracking.

[0006] The process of people's understanding of the internal mechanism of concrete material failure and destruction is slow, from linear elastic mechanics to elastoplastic damage mechanics and fracture mechanics, from homogeneous isotropic materials to heterogeneous anisotropic materials, from simulation calculations based on small deformation assumptions to simulation calculations based on large deformation destruction, from macroscopic mechanical models to microscopic mechanical analysis models and the establishment of an equivalent relationship between the two. With the continuous in-depth research of these basic theories and the continuous development of material science, experimental methods and simulation technology, people's understanding of the internal mechanism of concrete material failure and destruction has gradually deepened.

[0007] At the microscopic level, fiber reinforced concrete is a multiphase composite material composed of aggregate, mortar, fiber, interface transition zone and initial defects (pores, microcracks and bubbles). Therefore, in an ideal microscopic analysis model, all actual microscopic structural geometric features (including disordered fibers, initial defects, etc.) should be accurately considered and simulated. When considering the modeling of discrete fibers separately, the model consists of multiple random systems of fibers, aggregates, and ITZ. The fibers should be placed between irregularly randomly distributed aggregates. While checking that the fibers and aggregates do not overlap, it should also be ensured that the fibers do not overlap with each other. Covering all characteristics in a random system will lead to modeling difficulties.

[0008] There are two main methods for microscopic simulation of existing fiber concrete:

[0009] (1) According to the above method and concrete mix ratio, only a small number of large-diameter fibers are added. However, this method is very limited in the study of fiber types. For fibers with a diameter of micrometers (such as polypropylene fibers), due to the small fiber diameter, millions of fibers are often required in reality. In the study of fiber concrete microscopic model, the number of fibers directly determines the complexity of the model. A large number of micrometer-level fibers have extremely high computer requirements in model generation, mesh division, and model calculation. Polypropylene fibers are not distributed in a single shape inside the concrete due to the extrusion of aggregates during the mixing, pouring, and vibration of concrete. Therefore, this method is not suitable for the simulation of polypropylene fiber concrete, whether from the perspective of computational cost or irregular fiber geometric model distribution;

[0010] (2) Considering the initial defects in the fibers and mortar as part of the mortar, a fiber-modified mortar matrix is ​​prepared, and the material parameters of the matrix and the interface transition zone are quantified by physical experiments to establish a three-phase mesoscopic model of concrete, namely: mortar (fiber-modified), aggregate, and the interface transition zone between the mortar and aggregate under fiber modification (fiber-modified interface transition zone). However, the material properties of each mesoscopic component of this method are not measured based on experiments, and the accuracy of the simulation results cannot be guaranteed. Summary of the invention

[0011] In view of the shortcomings of the prior art, the purpose of the present invention is to provide an analysis method for the tensile fracture of polypropylene fiber concrete on a microscopic scale. By establishing a microscopic analysis model suitable for polypropylene fiber reinforced concrete, the intrinsic nature of the reinforcement of concrete by low-dosage polypropylene fibers and the weakening effect of concrete by high-dosage fibers are quantified. This can not only reduce the computer calculation cost while meeting the calculation accuracy requirements, but also ensure the accuracy of the simulation results.

[0012] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0013] A method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale includes the following steps:

[0014] Step 1: Determine the tensile fracture stress characteristics of polypropylene fiber reinforced concrete and divide its microscopic components;

[0015] Step 2: Conduct material fracture tests to determine the fracture parameters of each microscopic component;

[0016] Step 3: Using concrete slice 2D image recognition and Python random number based 3D digital simulation method, three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete are established;

[0017] Step 4, calculating the material constitutive parameters of each microscopic component based on the cohesive constitutive model;

[0018] Step 5, assign the fracture parameters and material constitutive parameters of each micro-component to the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete, and establish the model boundary conditions to verify the rationality of the model;

[0019] Step 6: Use the verified three-phase and four-phase micro-geometric models to conduct tensile fracture analysis of polypropylene fiber concrete and obtain analysis results.

[0020] Furthermore, in step 1, the tensile fracture stress characteristics of the polypropylene fiber reinforced concrete are manifested as type I cracks, and the microscopic components of the polypropylene fiber reinforced concrete include aggregate, mortar, and interface transition zone, wherein the polypropylene fibers are uniformly distributed in the mortar.

[0021] Furthermore, the steps of determining the fracture parameters of each microscopic component in step 2 are as follows:

[0022] Step 2.1, taking the fiber volume ratio in polypropylene fiber reinforced concrete as a variable, designing fiber reinforced mortar specimens and rock-fiber modified mortar mixed specimens with different fiber volume ratios;

[0023] Step 2.2, performing material fracture tests on fiber-reinforced mortar specimens and rock-fiber-modified mortar mixed specimens;

[0024] Step 2.3, record the load-deflection curve, and calculate the fracture parameters of each micro-component under tensile fracture conditions.

[0025] Furthermore, the fracture parameters include fracture energy, tensile strength, elastic modulus and fracture toughness.

[0026] Furthermore, the steps for establishing the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete in step 3 are as follows:

[0027] Step 3.1, obtaining a finite element calculation model of polypropylene fiber reinforced concrete by using a two-dimensional image recognition technology of concrete slices;

[0028] Step 3.2: Based on the Python programming environment, the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete are constructed using random number generation technology.

[0029] Furthermore, the three-phase meso-geometric model of the polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fibers, and an interface transition zone model, and the four-phase meso-geometric model of the polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fibers, an interface transition zone model, and a fiber-mortar interface model.

[0030] Furthermore, the steps of constructing the aggregate model are as follows:

[0031] A1. Randomly generate spherical aggregates;

[0032] A2. Take the generated spherical aggregate as a reference sphere and randomly generate a certain number of vertices on the reference sphere;

[0033] A3. After generating vertices, use the "convhulln" function to generate random polyhedron aggregates based on the vertex triangle faces;

[0034] A4. Randomly generate the coordinates of the center point of aggregate within the range of the reference sphere, and place random polyhedral aggregate according to the coordinates of the center point;

[0035] A5, determine whether the random polyhedral aggregate exceeds the boundary, if not, proceed to step A6;

[0036] A6, judging whether there is interference between the random polyhedral aggregate placed later and the random polyhedral aggregate placed previously, if there is no interference, proceeding to step A7;

[0037] A7. Repeat steps A2-A6 until the volume rate is qualified and the aggregate model is generated.

[0038] Furthermore, the process of establishing the fiber model in the fiber-mortar interface model is as follows:

[0039] The number of fibers placed in a fixed size is calculated based on the fiber volume ratio and fiber geometric size;

[0040] After the number of fibers is calculated, the fibers are generated and placed on the aggregate model.

[0041] Furthermore, in the process of placing the fibers on the aggregate model, it is necessary to avoid crossing between the fibers and avoiding overlapping with the placed random polyhedral aggregates.

[0042] Furthermore, the steps for calculating the material constitutive parameters of each microscopic component based on the cohesive force constitutive model in step 4 are as follows:

[0043] B1. Based on ABAQUS software, establish the finite element model of the cohesive interface unit;

[0044] B2. According to the microscopic components of polypropylene fiber reinforced concrete, the statistical sum is established, and the grid is divided, and the divided cohesive elements are inserted into the initial grid;

[0045] B3, assigning different traction-separation softening laws to simulate concrete cracking;

[0046] B4. Calculate the material constitutive parameters of each microscopic component.

[0047] The remarkable effects of the present invention are:

[0048] (1) The present invention designs a method for experimentally determining the fracture parameters of the weak part of polypropylene fiber concrete, namely, the fiber-modified mortar-rock interface transition zone, and establishes a micro-analysis model suitable for polypropylene fiber reinforced concrete, thereby reducing the computer calculation cost while meeting the calculation accuracy requirements.

[0049] (2) The three-phase and four-phase micro-geometric models of polypropylene fiber concrete were established by using two-dimensional image recognition of concrete slices and three-dimensional digital simulation method based on Python random numbers.

[0050] (3) Based on the cohesive constitutive model and the above-mentioned geometric model, a calculation method suitable for the tensile fracture of polypropylene fiber concrete was established. This method not only quantified the intrinsic nature of the reinforcement of concrete by low-content polypropylene fibers and the weakening effect of concrete by high-content fibers, but also compared with the experimental results, it was found that the established model was reliable.

[0051] (4) The established model can clearly reproduce the initiation and development of cracks in the tensile fracture process of polypropylene fiber concrete, and finally the concrete fracture after the microcracks penetrate, which can improve the predictability of tensile cracking damage of polypropylene fiber concrete.

[0052] (5) In the established mesoscopic analysis model, the material properties of each mesoscopic component are determined based on experiments, which can ensure the accuracy of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of the method of the present invention;

[0054] Figure 2 It is the meso-scale specimen design drawing;

[0055] Figure 3 It is a schematic diagram of meso-scale material performance testing;

[0056] Figure 4 This is a schematic diagram of the effect of polypropylene fiber on the fracture parameters of mortar and interface transition zone;

[0057] Figure 5 It is a schematic diagram of two-dimensional finite element modeling of concrete;

[0058] Figure 6 It is a schematic diagram of the shapes of random polyhedral aggregates with different vertex numbers;

[0059] Figure 7 It is a schematic diagram of polyhedral aggregate interference judgment;

[0060] Figure 8 It is a schematic diagram of the three-phase mesoscopic model of PFRC;

[0061] Fig. 9 It is a schematic diagram of the PFRC four-phase mesoscopic model;

[0062] Fig.10 It is a schematic diagram of two types of cohesive elements in the concrete mesoscopic crack model;

[0063] Fig.11 is a schematic diagram of a three-dimensional concrete model with different cohesive interface elements;

[0064] Fig.12 is a schematic diagram of a two-dimensional concrete model with different cohesive interface elements;

[0065] Fig.13 is a schematic diagram of the constitutive response of the cohesive unit;

[0066] Fig.14 is the constitutive diagram of the cohesive unit under mixing;

[0067] Fig.15 This is a comparison of the cracking morphology of the three-phase and four-phase mesoscopic models;

[0068] Fig.16 are the stress-strain diagrams of the three-phase and four-phase mesoscopic models;

[0069] Fig.17 It is a schematic diagram of the fracture process of the two-dimensional finite element model;

[0070] Fig.18 It is a schematic diagram of the fracture process of the three-dimensional finite element model. DETAILED DESCRIPTION

[0071] The specific implementation manner and working principle of the present invention are further described in detail below with reference to the accompanying drawings.

[0072] like Figure 1 As shown, the embodiment of the present invention proposes an analysis method for tensile fracture of polypropylene fiber concrete at a microscopic scale, and the specific steps are as follows:

[0073] Step 1: Determine the tensile fracture stress characteristics of polypropylene fiber reinforced concrete and divide its microscopic components;

[0074] When this embodiment deeply studies the tensile fracture characteristics of polypropylene fiber reinforced concrete, it is found that its fracture mode is mainly manifested as type I crack, that is, opening crack. From a microscopic perspective, polypropylene fiber reinforced concrete can be regarded as a three-phase heterogeneous composite material system composed of aggregate, mortar (in which polypropylene fibers are evenly distributed in the mortar), and interface transition zone. Aggregate provides the basic skeleton of concrete, mortar serves as a filling and bonding medium, and the addition of polypropylene fibers significantly improves the crack resistance of the mortar. The interface transition zone is between the aggregate and the mortar, which has an important influence on the overall mechanical properties of the material.

[0075] Step 2: Conduct material fracture tests to determine the fracture parameters of each microscopic component;

[0076] In view of the complex structure of polypropylene fiber reinforced concrete, a series of experimental measurements must be carried out to accurately evaluate its material properties, especially the type I fracture characteristics. This includes detailed testing and analysis of the strength and stiffness of aggregates, the fracture properties of polypropylene fiber modified mortar, and the bond strength of the interface transition zone. Through these experiments, the key material parameters of each mesoscopic component under type I fracture conditions, such as fracture energy, tensile strength, elastic modulus and fracture toughness, can be obtained, thus providing solid data support for the study of the fracture mechanism of polypropylene fiber reinforced concrete.

[0077] Since the fracture parameter acquisition methods of rock and mortar are relatively conventional, this embodiment focuses on the fracture parameter acquisition method of the interface transition zone. The details are as follows:

[0078] Step 2.1, taking the fiber volume ratio in polypropylene fiber reinforced concrete as a variable, designing fiber reinforced mortar specimens and rock-fiber modified mortar mixed specimens with different fiber volume ratios;

[0079] The fiber-reinforced mortar was designed with the fiber volume ratio as a variable. The interface transition zone was designed as a rock-mortar mixed specimen. The size of the mixed specimen for testing fracture energy was designed to be 160 mm × 40 mm × 40 mm, 80 mm × 40 mm × 40 mm for mortar, and 80 mm × 40 mm × 40 mm for limestone. The natural bonding surface is 40 mm high, including a 30 mm bonding surface and a 10 mm prefabricated notch. Figure 2 As shown in (a), in order to ensure the uniformity of the prefabricated notch, a steel sheet with a specific thickness is used to prefabricate the notch. The size of the steel sheet is as follows: Figure 2 (b) The size of the mixed specimen for testing tensile strength is 100mm×100mm×100mm, the mortar is 100mm×100mm×50mm, and the limestone is 100mm×100mm×50mm. The size is as follows Figure 2 (c) as shown.

[0080] Step 2.2, performing material fracture tests on fiber-reinforced mortar specimens and rock-fiber-modified mortar mixed specimens;

[0081] Specimen loading diagram Figure 3 (a) and 3(b), flexural test materials and equipment such as Figure 3 (c) and 3(d), the splitting tensile strength test materials and equipment are as follows Figure 3 (e) and 3(f).

[0082] Step 2.3, record the load-deflection curve, and calculate the fracture parameters of each micro-component under tensile fracture conditions.

[0083] In this case, the load-deflection is recorded as a continuous curve and the fracture energy is defined as the energy consumed to produce a unit crack, which can be obtained by calculating the area under the curve.

[0084] W=W0+W1+W2+W3 (1)

[0085] Where W0 is the load P (δ) The energy generated, W1+W2 is the work done by the gravity of the test beam between the two supports; W3 is the work done by the gravity of the loading head.

[0086] For the mortar specimen, the fracture process of the experimental beam is W1≈W2=1 / 2mgδ max ; then the fracture energy per unit area of ​​the mortar specimen G FM for:

[0087]

[0088] Where mg is the weight of the specimen between the two supports; δ max is the maximum deflection at the mid-span when the specimen is damaged; A is the fracture area of ​​the beam, A=b(ha).

[0089] For the mixed specimen, the work done by the mortar and rock gravity from the two supports of the experimental beam to the prefabricated crack surface during the fracture process is not equal, W1 = 1 / 2m1gδ max , W2=1 / 2m2gδ max , then the fracture energy per unit area of ​​ITZ G FI for:

[0090]

[0091] In the formula, m1g is the weight of the mortar from one part of the support to the prefabricated crack surface, and m2g is the weight of the rock from the other part of the support to the prefabricated crack surface.

[0092] The tensile strength is:

[0093]

[0094] Where, T m is the tensile strength of the specimen, MPa; P is the maximum load, N; C is the side length of the cube, mm.

[0095] The fracture results of polypropylene fiber modified mortar and modified interface transition zone test are as follows Figure 4 As shown, Figure 4 (a) shows the flexural strength parameter, Figure 4 (b) shows the splitting tensile strength parameter, Figure 4 (c) shows the fracture energy parameters.

[0096] Step 3: Using concrete slice 2D image recognition and Python random number based 3D digital simulation method, three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete are established;

[0097] In order to deeply explore the microstructure of polypropylene fiber reinforced concrete and its influence on material properties, this embodiment adopts advanced image recognition technology and digital simulation methods to construct an accurate micro-geometric model. Therefore, the process of establishing the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete is as follows:

[0098] Step 3.1: Use the two-dimensional image recognition technology of concrete slices to capture the details of the internal structure of the concrete, including the distribution of aggregates, the filling of mortar, and the distribution of polypropylene fibers. After cutting the concrete sample, use a digital camera to take a picture of the cut surface. Figure 5 (a) is shown, and then the image is processed to determine the boundaries of the aggregate. Figure 5 As shown in (b), after image enhancement processing, the finite element calculation model of polypropylene fiber reinforced concrete can be obtained by importing it into ABAQUS, as shown in Figure 5 (c)

[0099] Step 3.2: Based on the Python programming environment, a three-dimensional digital simulation method was developed. This method uses random number generation technology to construct three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete.

[0100] In the three-phase model, this embodiment mainly considers the interaction between aggregate, mortar (containing polypropylene fiber) and interface transition zone; in the four-phase model, in addition to the above three phases, the key phase of fiber-mortar interface is also added to more comprehensively reflect the mechanism of action of polypropylene fiber in enhancing concrete performance. That is, the three-phase meso-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fiber and an interface transition zone model, and the four-phase meso-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fiber, an interface transition zone model, and a fiber-mortar interface model.

[0101] In an embodiment of the present invention, the steps of constructing the aggregate model are as follows:

[0102] A1. Randomly generate spherical aggregates;

[0103] The center coordinates and interval radius parameters of the spherical aggregate are as shown in formula (5):

[0104]

[0105] Where: x1, x2 (y / z) are the starting and ending values ​​of the interval range in the x (y / z) direction in the three-dimensional model; r min ,r max is the minimum and maximum value of aggregate particle size within a certain particle size range; rand is a random function.

[0106] A2. Take the generated spherical aggregate as a reference sphere and randomly generate a certain number of vertices on the reference sphere;

[0107] Vertex coordinates Euler space polar angle α i and azimuth β i It is expressed as formula (6).

[0108]

[0109] Where: (x mp ,y mp ,z mp ) is the coordinate of the center of the reference sphere, r mp is the radius of the reference sphere, α p =rand[0,2π],β p =rand[0,π].

[0110] A3. After generating vertices, use the "convhulln" function to generate random polyhedron aggregates based on the vertex triangle faces. The shapes of random polyhedron aggregates with different vertex numbers are as follows: Figure 6 As shown;

[0111] A4. Randomly generate the coordinates of the center point of aggregate within the range of the reference sphere, and place random polyhedral aggregate according to the coordinates of the center point;

[0112] A5, determine whether the random polyhedral aggregate exceeds the boundary, if not, proceed to step A6;

[0113] A6, judging whether there is interference between the random polyhedral aggregate placed later and the random polyhedral aggregate placed previously, if there is no interference, proceeding to step A7;

[0114] After random polyhedral aggregates are generated, the key to their placement lies in step A6. The most common method requires that the distance between the coordinates of the center point of the later generated aggregate and the coordinates of the center point of the previously generated aggregate is greater than the sum of the radii of the two circumscribed spheres, as shown in formula (7):

[0115]

[0116] Where: (x mp ,y mp ,z mp ), (x nq ,y nq ,z nq ) are the coordinates of the center of the sphere of the generated aggregate and the center of the sphere of the aggregate to be generated respectively; r mp 、r nq are the radius of the generated aggregate and the radius of the aggregate to be generated respectively; d m is the distance between the center of the generated aggregate and the center of the aggregate to be generated; ζ is the aggregate crossover discrimination coefficient. The larger the coefficient is, the smaller the probability of aggregate crossover is, but it also limits the volume ratio of aggregate.

[0117] This method generates a lower volume ratio of aggregates. When generating random polyhedrons, the vertex coordinate data is stored and the minimum distance d between all vertices of two aggregates is calculated. min As shown in formula (8), the interference judgment diagram is as follows Figure 7 shown.

[0118]

[0119] In the formula, are the vertex coordinates of the generated aggregate p, is the vertex coordinate of the next generated aggregate q, n is the number of polyhedron orthopedic vertices, and N is the number of aggregates. When the number of aggregate vertices is large enough and l0=0, all vertices do not touch, and the aggregates will not penetrate. However, when generating aggregates, it is not certain that the number of aggregate vertices reaches the ideal state. In order to avoid penetration of aggregates, it can be appropriately increased. However, in order to ensure that there is no interference between aggregates, the l0 value can be appropriately increased.

[0120] A7. Repeat steps A2-A6 until the volume rate is qualified and the aggregate model is generated.

[0121] According to the above method, the three-phase microscopic model of fiber concrete can be established. Figure 8 As shown, if you want to establish a four-phase model of fiber concrete, you should also complete the fiber modeling on the above basis. Therefore, the process of establishing the fiber model in the fiber-mortar interface model in this example is as follows:

[0122] The number of fibers placed in a fixed size is calculated based on the fiber volume ratio and fiber geometric size, as shown in formula (9):

[0123]

[0124] Where: L is the length of the specimen; W is the width of the specimen; H is the height of the specimen; ρ f is the fiber volume ratio; l f is the fiber length; d f is the fiber diameter; N is the calculated number of fibers, which is an integer.

[0125] The generation and placement of fibers are carried out on the basis of the above-mentioned aggregates. First, three-dimensional random fibers are generated as shown in formula (10):

[0126]

[0127] Where x1, x2(y / z) are the starting and ending values ​​of the interval range in the x(y / z) direction in the three-dimensional model.

[0128] After generating the fiber midpoint coordinates, the direction angle of the fiber is randomly generated, and the fiber endpoint coordinates are generated in the positive and negative directions of the generated angles. Assuming that the angle between the fiber and the Z axis is α, α∈[0,π], and the angle between the fiber projection on the XOY plane and the X axis is β, β∈[0,2π], the fiber endpoint coordinates (x mi / j ,y mi / j ,z mi / j ) as formula (11):

[0129]

[0130] In the formula: α=rand·180, β=rand·360.

[0131] The placement of fibers needs to avoid crossing between fibers, so the fiber endpoint coordinates (x mi / j ,y mi / j ,z mi / j ), the fiber endpoint coordinates to be generated (x ni / j ,y ni / j ,z ni / j ), the coordinates of any point m and n on the two fibers are as shown in equations (12) and (13):

[0132]

[0133] In this embodiment, each fiber is evenly divided into 10 equal parts, and the minimum distance between any points m and n on two fibers is greater than 3 times the fiber diameter. The judgment condition is as shown in formula (14):

[0134]

[0135] Where: d fib is the fiber diameter.

[0136] While ensuring that the fibers do not cross each other, it is also necessary to ensure that they do not overlap with the placed aggregates. This paper stipulates that the distance from the fiber to the center of the reference sphere should not be less than 1.1 times the weight of the reference sphere, as shown in formula (15):

[0137]

[0138] Where: (x mp ,y mp ,z mp ) is the center of the reference ball; (x0, y0, z0), (x0, y0, z0), (x0, y0, z0) are the coordinates of the midpoint and two end points of the fiber respectively; d agg-fib(0) d agg-fib(i) d agg-fib(j) are the distances from the center of the reference sphere to the midpoint and two end points of the fiber respectively. The four-phase micro-geometric model of polypropylene fiber reinforced concrete is established as follows: Fig. 9 shown.

[0139] Step 4, calculating the material constitutive parameters of each microscopic component based on the cohesive constitutive model;

[0140] The mesoscopic geometric model established by the above method can intuitively display the internal structure of polypropylene fiber reinforced concrete. In addition, the parametric design of the model also allows us to study the influence of fiber dosage, length, shape and distribution on the performance of concrete, providing a powerful tool for optimizing the design of polypropylene fiber reinforced concrete. However, in order to accurately analyze the fracture of the mesoscopic model under the action of external forces, the corresponding material constitutive parameters should be assigned to each mesoscopic component. The specific steps are as follows:

[0141] B1. Based on ABAQUS software, establish the finite element model of the cohesive interface unit;

[0142] B2. According to the microscopic components of polypropylene fiber reinforced concrete, the statistical sum is established, and the grid is divided, and the divided cohesive elements are inserted into the initial grid;

[0143] B3, assigning different traction-separation softening laws to simulate concrete cracking;

[0144] B4. Calculate the material constitutive parameters of each microscopic component.

[0145] In the specific implementation process, the cohesive force unit and the solid unit have a grid topological connection, and can represent independent constitutive models respectively. The finite element model based on the cohesive force unit can well simulate the damage caused by crack expansion. The cohesive force unit can be embedded between mortar-mortar units to simulate the cracking of mortar, or embedded between aggregate-aggregate units to simulate the crushing of aggregates, such as Fig.10 As shown in (a), the mortar-aggregate interface can also be inserted to simulate the weak defect location (ITZ) in concrete, such as Fig.10 (b) as shown.

[0146] The specific implementation method in the commercial software ABAQUS is to first output the inp file, read the unit nodes and number them, insert the cohesive force unit between the shared nodes, renumber all the nodes and write them into the inp file to establish a finite element model containing the cohesive interface unit. Taking the three-dimensional micro-concrete specimen as an example, a finite element model containing the cohesive interface element (CIE) is established, such as Fig.11 First, different sets of concrete micro-model structures are established, namely aggregate and mortar, and then meshing is performed. The mesh is as follows Fig.11 As shown in (a), three groups of cohesive elements CIE_AGG (Aggregate), CIE_MOR (Mortar) and CIE_ITZ are then inserted into the initial grid, as shown in Fig.11 (b), (c) and (d), and finally different traction-separation softening laws are given to simulate concrete cracking. The two-dimensional microscopic model is similar as Fig.12 shown.

[0147] For quasi-brittle materials, such as cement mortar and aggregate, a bilinear traction-separation relationship is used, and the constitutive law of the cohesive element in uniaxial tension-compression mode and shear mode is as follows: Fig.13 As shown, Fig.13 (a) is a bilinear cohesive force model based on type I. This model assumes that the separation of the material interface is controlled by the displacement perpendicular to the interface. Fig.13 (b) is a bilinear model based on type II, which assumes that the separation of the material interface is related to the displacement of the interface tangent.

[0148] Correspondence of the traction-separation phase of the cohesive unit Fig.13 In the straight rising section, before the stress exceeds the damage strength, the cohesive force unit in this range exhibits a linear elastic constitutive law. The normal and tangential constitutive laws of the cohesive force unit are as shown in equations (16) and (17):

[0149]

[0150] In the formula, t n and t s Represent the normal stress and shear stress of the cohesive unit respectively; < > is the Macaulay bracket, which is 0 in the compression state; δ n and δ s represents the positive opening and shear slip displacements; Represents the cohesive element penalty stiffness.

[0151] When the element stress state meets the damage initiation criterion, the element enters the damage evolution. This study adopts the quadratic nominal stress criterion, which is expressed as:

[0152]

[0153] In the formula, t n ,t s ,t t represents the cohesive normal and two tangential stresses, t n0 ,t s0 (t t0 ) represents tensile strength and shear strength.

[0154] When the cohesive element stress exceeds the damage initiation strength t n0 and t s0 (t t0 ) After the unit is damaged, the stiffness can be expressed as:

[0155] K=(1-D)K 0 (19)

[0156] Where K represents the damage stiffness; D represents the stiffness damage factor, D = 0 represents no damage, and D = 0 represents complete unit failure.

[0157] For the bilinear model, D is expressed as:

[0158]

[0159] In the formula, is the maximum effective relative displacement obtained during the loading process, are the effective relative displacements at damage initiation and final failure, respectively. is the damage evolution caused by the combined action of normal and tangential directions, and its expression is:

[0160]

[0161] because It is more complicated to determine, which reflects the fracture energy release rate of the unit under mixed stress state. BK (Benzeggagh-Kenane) proposed a fracture criterion suitable for describing quasi-brittle materials from the energy perspective. Therefore, the constitutive response of the cohesive unit of the mixed mode is as follows: Fig.14 , It can be expressed as:

[0162]

[0163] Where G Ⅰ and G Ⅱ represent the tensile (type I) and shear (type II) fracture energies, respectively; G n and G s They represent the work done by tensile force and shear force respectively; η is the correction parameter of BK criterion.

[0164] Step 5, assign the fracture parameters and material constitutive parameters of each micro-component to the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete, and establish the model boundary conditions to verify the rationality of the model;

[0165] Step 6: Use the verified three-phase and four-phase micro-geometric models to conduct tensile fracture analysis of polypropylene fiber concrete and obtain analysis results.

[0166] The three-dimensional concrete model was established as a 50×50×50mm cubic specimen, and the two-dimensional slice model size was 50×50×1mm. The left surface of the model was fully constrained, and the right surface was coupled with the reference point to apply an axial displacement to the reference point. The final displacement was set to 0.1mm. The reference point reaction force and displacement time curves were read and combined. For the three-dimensional concrete model, the equivalent stress result was expressed as the node reaction force divided by the cross-sectional area, and the equivalent stress result of the two-dimensional concrete model was expressed as the node reaction force divided by the length of the coupling side. The equivalent strain of concrete was expressed as the ratio of the reference point displacement to the length of the model side in the elongation direction. The ABAQUS / Explicit explicit solver was used for quasi-static calculation and analysis, and the displacement was applied using the "smooth analysis" option.

[0167] The three-phase and four-phase micro-geometric models were used to compare and analyze the cracking morphology of the micro-geometric models calculated by the two methods for polypropylene fiber concrete with a fiber volume ratio of 0.4%. Fig.15 As shown, Fig.15 (a) and Fig.15 (c) is the cracking morphology of the three-phase micro-geometric model. Fig.15 (b) and Fig.15 (d) is the crack morphology of the three-phase micro-geometric model; the PFRC stress-strain curve is shown in Fig.16 As shown in the figure, the crack paths of PFRC under different fiber volume ratios are calculated as follows: Fig.17 and18 shown.

[0168] In summary, the present invention establishes a mesoscopic analysis model suitable for polypropylene fiber reinforced concrete, which reduces computer calculation costs while meeting calculation accuracy requirements, quantifies the intrinsic nature of low-dosage polypropylene fiber reinforcement on concrete and the weakening effect of high-dosage fiber on concrete. At the same time, in the established mesoscopic analysis model, the material properties of each mesoscopic component are determined based on experiments, which can ensure the accuracy of the simulation results.

[0169] The technical solution provided by the present invention is described in detail above. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, the present invention can also be improved and modified in a number of ways, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale, characterized in that: The steps include: Step 1: Determine the tensile fracture stress characteristics of polypropylene fiber reinforced concrete and divide its microscopic components; Step 2: Conduct material fracture tests to determine the fracture parameters of each microscopic component; Step 3: Using concrete slice 2D image recognition and Python random number based 3D digital simulation method, three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete are established; Step 4, calculating the material constitutive parameters of each microscopic component based on the cohesive constitutive model; Step 5, assign the fracture parameters and material constitutive parameters of each micro-component to the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete, and establish the model boundary conditions to verify the rationality of the model; Step 6: Use the verified three-phase and four-phase micro-geometric models to conduct tensile fracture analysis of polypropylene fiber concrete and obtain analysis results.

2. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 1, characterized in that: In step 1, the tensile fracture stress characteristics of polypropylene fiber reinforced concrete are manifested as type I cracks. The microscopic components of polypropylene fiber reinforced concrete include aggregate, mortar, and interface transition zone, among which polypropylene fibers are evenly distributed in the mortar.

3. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 1, characterized in that: The steps for determining the fracture parameters of each microscopic component in step 2 are as follows: Step 2.1, taking the fiber volume ratio in polypropylene fiber reinforced concrete as a variable, designing fiber reinforced mortar specimens and rock-fiber modified mortar mixed specimens with different fiber volume ratios; Step 2.2, performing material fracture tests on fiber-reinforced mortar specimens and rock-fiber-modified mortar mixed specimens; Step 2.3, record the load-deflection curve, and calculate the fracture parameters of each micro-component under tensile fracture conditions.

4. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 3, characterized in that: The fracture parameters include fracture energy, tensile strength, elastic modulus and fracture toughness.

5. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 1, characterized in that: The steps for establishing the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete in step 3 are as follows: Step 3.1, obtaining a finite element calculation model of polypropylene fiber reinforced concrete by using a two-dimensional image recognition technology of concrete slices; Step 3.2: Based on the Python programming environment, the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete are constructed using random number generation technology.

6. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 5, characterized in that: The three-phase micro-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fibers, and an interface transition zone model. The four-phase micro-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a mortar model containing polypropylene fibers, an interface transition zone model, and a fiber-mortar interface model.

7. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 6, characterized in that: The steps for constructing the aggregate model are as follows: A1. Randomly generate spherical aggregates; A2. Take the generated spherical aggregate as a reference sphere and randomly generate a certain number of vertices on the reference sphere; A3. After generating vertices, use the "convhulln" function to generate random polyhedron aggregates based on the vertex triangle faces; A4. Randomly generate the coordinates of the center point of aggregate within the range of the reference sphere, and place random polyhedral aggregate according to the coordinates of the center point; A5, determine whether the random polyhedral aggregate exceeds the boundary, if not, proceed to step A6; A6, judging whether there is interference between the random polyhedral aggregate placed later and the random polyhedral aggregate placed previously, if there is no interference, proceeding to step A7; A7. Repeat steps A2-A6 until the volume rate is qualified and the aggregate model is generated.

8. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 6 or 7, characterized in that: The process of establishing the fiber model in the fiber-mortar interface model is as follows: The number of fibers placed in a fixed size is calculated based on the fiber volume ratio and fiber geometric size; After the number of fibers is calculated, the fibers are generated and placed on the aggregate model.

9. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 8, characterized in that: In the process of placing the fibers on the aggregate model, it is necessary to avoid crossing between the fibers and not overlapping with the placed random polyhedral aggregates.

10. The method for analyzing tensile fracture of polypropylene fiber concrete at a microscopic scale according to claim 1, characterized in that: The steps for calculating the material constitutive parameters of each microscopic component based on the cohesive constitutive model in step 4 are as follows: B1. Based on ABAQUS software, establish the finite element model of the cohesive interface unit; B2. According to the microscopic components of polypropylene fiber reinforced concrete, the statistical sum is established, and the grid is divided, and the divided cohesive elements are inserted into the initial grid; B3, assigning different traction-separation softening laws to simulate concrete cracking; B4. Calculate the material constitutive parameters of each microscopic component.

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