Method for analyzing tensile fracture of polypropylene fiber concrete at mesoscopic scale

Abstract

The application discloses a kind of polypropylene fiber concrete tensile fracture analysis method on mesoscale, comprising the following steps: polypropylene fiber reinforced concrete tensile fracture stress characteristic determination and mesoscopic component division;Determine the fracture parameter of each mesoscopic component;Establish the three-phase and four-phase mesoscopic geometric model of polypropylene fiber reinforced concrete;Based on the material constitutive parameter of each mesoscopic component of cohesive force constitutive model calculation;The fracture parameter and material constitutive parameter of each mesoscopic component are given to the three-phase and four-phase mesoscopic geometric model of polypropylene fiber reinforced concrete, and model boundary condition is established to carry out model rationality checking;Polypropylene fiber concrete tensile fracture analysis is carried out, and analysis result is obtained.The significant effect is: reduce the computer calculation cost while meeting the calculation accuracy requirement, quantify the inherent nature of low-dosage polypropylene fiber to concrete reinforcement and the weakening effect of high-dosage fiber on concrete.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of concrete finite element simulation, and particularly relates to a method for analyzing tensile fracture of polypropylene fiber concrete at a mesoscale. BACKGROUND

[0002] As the most widely used engineering 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. 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 material is brittle and has low tensile strength, and concrete is prone to cracking under the action of tensile stress and is difficult to repair. Concrete is usually combined with steel bars to form a load-bearing member, and the expansion of cracks in the member will lead to steel bar corrosion when encountering adverse environmental factors. The greater the crack width, the greater the contact area between the steel bar and the adverse environment, which promotes further corrosion of the steel bar. In a reinforced concrete structure, the cracking of the concrete section and the corrosion of the steel bar will greatly weaken the stiffness, ductility and load-carrying capacity of the structure. In a structure with severe cracking and corrosion, even brittle failure may occur, which seriously affects the performance and durability of the structure and even causes unpredictable engineering accidents.

[0004] Therefore, some people have developed fiber reinforced concrete to overcome the above-mentioned defects. Fiber reinforced concrete is a multi-phase non-homogeneous cementitious material that uses fiber material as a reinforcing material and is composed of cement, coarse and fine aggregates, and admixtures. Compared with ordinary concrete, it has higher ductility, strength and durability. Among the many fibers, polypropylene fiber is considered to be a secondary material for reinforcing concrete. Due to the low price, light weight, easy mixing, and significant improvement in the mechanical properties of concrete, polypropylene fiber reinforced concrete has been widely used in key projects such as construction, bridges, and water conservancy.

[0005] Although the mechanical properties of concrete can be improved by adding polypropylene fiber, the problem of cracking in concrete members under extreme conditions cannot be completely avoided. The addition of polypropylene fiber improves the crack resistance of concrete, but the composition of polypropylene fiber reinforced concrete is more complex than that of concrete. On the one hand, polypropylene fiber has low elastic modulus and soft texture. During the mixing, pouring and vibrating of concrete, the distribution of polypropylene fiber in concrete is dispersed and not in a single shape. On the other hand, the randomness of the physical and mechanical properties of each phase of polypropylene fiber reinforced concrete and its distribution leads to a high degree of randomness, heterogeneity, porosity and complex interface at the mesoscale. 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 need to be carried out, which consumes a lot of manpower and resources. Therefore, it is urgent to establish a calculation model of FRC cracking.

[0006] The process of understanding the internal mechanism of concrete material failure is slow. From linear elasticity to elastoplastic damage mechanics and fracture mechanics, from homogeneous isotropic materials to heterogeneous anisotropic materials, from small deformation simulation based on small deformation assumption to large deformation simulation based on large deformation failure, from macroscopic mechanics model to mesoscopic mechanics analysis model and the establishment of the equivalent relationship between the two, with the continuous development 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 is gradually deepened.

[0007] At the mesoscale, 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 mesoscopic analysis model, all actual mesoscopic structure geometric characteristics (including randomly distributed fibers, initial defects, etc.) should be accurately considered and simulated. When considering discrete fibers, the model is composed of multiple random systems of fibers, aggregates and ITZ. The fibers should be placed between irregularly distributed aggregates, ensuring that the fibers do not overlap with the aggregates and that the fibers do not overlap with each other. Covering all characteristics in a random system will lead to modeling difficulties.

[0008] The existing mesoscopic simulation methods of fiber reinforced concrete can be mainly divided into two types:

[0009] (1) According to the above method and concrete mix proportion, only a small number of large-diameter fibers are added. However, this method is very limited in the types of fibers that can be studied. 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 microscopic model study of fiber-reinforced concrete, the number of fibers directly determines the complexity of the model. A large number of micrometer-sized fibers require extremely high computer requirements for model generation, mesh generation, and model calculation. During the mixing, pouring, and vibration of concrete, polypropylene fibers are not distributed in a single shape inside the concrete due to the extrusion of aggregates. Therefore, this method is not suitable for simulating polypropylene fiber-reinforced concrete, whether from the perspective of calculation cost or irregular fiber geometric model distribution.

[0010] (2) Treating the initial defects in fibers and mortar as part of the mortar, a fiber-modified mortar matrix is ​​prepared. The material parameters of the matrix and the interfacial transition zone are quantified by physical experiments to establish a three-phase microstructure model of concrete, namely: mortar (fiber modified), aggregate, and the interfacial transition zone between fiber-modified mortar and aggregate (fiber modified interfacial transition zone). However, the material properties of each microstructure component in this method are not determined by experiments, and the accuracy of the simulation results cannot be guaranteed. Summary of the Invention

[0011] To address the shortcomings of existing technologies, the purpose of this invention is to provide an analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale. By establishing a microscopic analysis model suitable for polypropylene fiber reinforced concrete, the inherent strengthening effect of low-dosage polypropylene fibers on concrete and the weakening effect of high-dosage fibers on concrete can be quantified. This method not only reduces computer computation costs while meeting computational accuracy requirements, but also ensures the accuracy of simulation results.

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

[0013] A method for analyzing the tensile fracture of polypropylene fiber reinforced concrete at a microscale, the key of which includes the following steps:

[0014] Step 1: Determination of tensile fracture stress characteristics and microstructure composition of polypropylene fiber reinforced concrete.

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

[0016] Step 3: Using two-dimensional image recognition of concrete slices and three-dimensional digital simulation based on Python random numbers, establish three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete.

[0017] Step 4: Calculate the material constitutive parameters of each microstructure component based on the cohesive constitutive model;

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

[0019] Step 6, using the three-phase and four-phase micro-geometric models that pass the checking, perform tensile fracture analysis of polypropylene fiber reinforced concrete to obtain the analysis results.

[0020] Further, in step 1, the tensile fracture stress characteristics of the polypropylene fiber reinforced concrete are characterized by type I cracks, and the micro-constituents of the polypropylene fiber reinforced concrete include aggregates, mortar, and interfacial transition zones, wherein the polypropylene fibers are uniformly distributed in the mortar.

[0021] Further, in step 2, the steps for determining the fracture parameters of each micro-constituent are as follows:

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

[0023] Step 2.2, perform material fracture tests on the 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-constituent under tensile fracture conditions.

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

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

[0027] Step 3.1, obtain the finite element calculation model of polypropylene fiber reinforced concrete through two-dimensional image recognition technology of concrete sections;

[0028] Step 3.2, based on the Python programming environment, use random number generation technology to construct the three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete.

[0029] Further, the three-phase micro-geometric model of polypropylene fiber reinforced concrete includes aggregate models, polypropylene fiber-containing mortar models, and interfacial transition zone models, and the four-phase micro-geometric model of polypropylene fiber reinforced concrete includes aggregate models, polypropylene fiber-containing mortar models, interfacial transition zone models, and fiber-mortar interface models.

[0030] Further, the construction steps of the aggregate model are as follows:

[0031] A1. Randomly generate spherical aggregates;

[0032] A2. Use 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 polyhedral aggregates based on the vertex triangle faces;

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

[0035] A5. Determine whether the random polyhedral aggregate exceeds the boundary. If it does not exceed the boundary, proceed to step A6.

[0036] A6. Determine whether there is any interference between the randomly placed polyhedral aggregate and the previously placed random polyhedral aggregate. If there is no interference, proceed to step A7.

[0037] A7. Repeat steps A2-A6 until the volumetric rate is qualified, then terminate and generate the aggregate model.

[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 geometry.

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

[0041] Furthermore, during the process of placing fibers on the aggregate model, it is necessary to avoid the fibers crossing each other and not overlapping with the already placed random polyhedral aggregates.

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

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

[0044] B2. Based on the microstructure of polypropylene fiber reinforced concrete, establish a non-statistical analysis and perform mesh generation, then insert the generated cohesive elements into the initial mesh.

[0045] B3. Simulate concrete cracking by imposing different traction-separation softening laws;

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

[0047] The significant effects of this invention are:

[0048] (1) For the weak part of polypropylene fiber reinforced concrete, namely the transition zone of fiber modified mortar-rock interface, the present invention designs a method for experimentally determining its fracture parameters and establishes a microscopic analysis model applicable to polypropylene fiber reinforced concrete, which reduces the computer calculation cost while meeting the calculation accuracy requirements.

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

[0050] (3) Based on the cohesive constitutive model and the above geometric model, a set of calculation methods applicable to tensile fracture of polypropylene fiber concrete was established. This method not only quantifies the intrinsic nature of low-dosage polypropylene fiber reinforcement of concrete and the weakening effect of high-dosage fiber on concrete, but also shows that the established model is reliable when compared with the experimental results.

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

[0052] (5) The material properties of each micro-component in the established micro-analysis model are determined by experiments, which can ensure the accuracy of the simulation results. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method of the present invention;

[0054] Figure 2 It is a detailed design drawing of the specimen;

[0055] Figure 3 This is a schematic diagram of material performance testing at the microscale;

[0056] Figure 4 This is a schematic diagram showing the influence of polypropylene fibers on the fracture parameters of mortar and the interface transition zone.

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

[0058] Figure 6 This is a schematic diagram of the shape of random polyhedral aggregates with different numbers of vertices;

[0059] Figure 7 This is a schematic diagram for judging interference from polyhedral aggregates;

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

[0061] Figure 9 This is a schematic diagram of the PFRC four-phase microscopic model;

[0062] Figure 10 This is a schematic diagram of two types of cohesive units in a concrete microcrack model;

[0063] Figure 11 It is a schematic diagram of a three-dimensional concrete model with different cohesive interface units;

[0064] Figure 12 It is a schematic diagram of a two-dimensional concrete model with different cohesive interface units;

[0065] Figure 13 This is a schematic diagram of the constitutive response of a cohesive unit;

[0066] Figure 14 This is a constitutive schematic diagram of the cohesive unit under mixing effects;

[0067] Figure 15 These are comparison images of crack morphology in three-phase and four-phase microscopic models;

[0068] Figure 16 These are stress-strain diagrams for three-phase and four-phase microscopic models;

[0069] Figure 17 This is a schematic diagram of the fracture process in a two-dimensional finite element model.

[0070] Figure 18 This is a schematic diagram of the fracture process in a three-dimensional finite element model. Detailed Implementation

[0071] The specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.

[0072] like Figure 1 As shown in the figure, this invention proposes an analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale, and the specific steps are as follows:

[0073] Step 1: Determination of tensile fracture stress characteristics and microstructure composition of polypropylene fiber reinforced concrete.

[0074] This embodiment, in its in-depth study of the tensile fracture characteristics of polypropylene fiber reinforced concrete, found that its fracture mode mainly exhibits Type I cracking, i.e., open cracking. From a microscopic perspective, polypropylene fiber reinforced concrete can be considered as a three-phase heterogeneous composite material system consisting of aggregate, mortar (in which polypropylene fibers are uniformly distributed), and an interfacial transition zone. The aggregate provides the basic skeleton of the concrete, the mortar serves as the filling and bonding medium, and the addition of polypropylene fibers significantly improves the crack resistance of the mortar. The interfacial transition zone, located between the aggregate and the mortar, has a significant impact on the overall mechanical properties of the material.

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

[0076] Given the complex structure of polypropylene fiber-reinforced concrete, a series of experimental measurements are necessary to accurately evaluate its material properties, especially its Type I fracture characteristics. This includes detailed testing and analysis of the aggregate strength and stiffness, the fracture properties of the polypropylene fiber-modified mortar, and the bond strength in the interfacial transition zone. These experiments allow for the acquisition of key material parameters for each microstructure under Type I fracture conditions, such as fracture energy, tensile strength, elastic modulus, and fracture toughness, thus providing solid data support for the study of the fracture mechanism of polypropylene fiber-reinforced concrete.

[0077] Since the methods for obtaining fracture parameters of rocks and mortars are relatively conventional, this embodiment focuses on the method for obtaining fracture parameters in the interface transition zone. The details are as follows:

[0078] Step 2.1: With the fiber volume ratio in polypropylene fiber-reinforced concrete as a variable, design fiber-reinforced mortar specimens and rock-fiber modified mortar mixed specimens with different fiber volume ratios.

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

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

[0081] See the specimen loading diagram. Figure 3 (a) and 3(b), flexural strength test materials and equipment such as Figure 3 As shown in (c) and 3(d), the materials and equipment for the splitting tensile strength test are as follows: Figure 3 As shown in (e) and 3(f).

[0082] Step 2.3: Record the load-deflection curve and calculate the fracture parameters of each microstructure under tensile fracture conditions.

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

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

[0085] In the formula, W0 is the load P (δ) The energy produced W1+W2 represents the work done by the gravity of the experimental beam between the two supports; W3 represents the work done by the gravity of the loading head.

[0086] For mortar specimens, during the fracture process, the experimental beam consists of two parts: W1≈W2=1 / 2mgδ. max The fracture energy G per unit area of ​​the mortar sample is then... FM for:

[0087]

[0088] In the formula, mg is the weight of the specimen between the two supports; δ max denoted as the maximum deflection at mid-span when the specimen fails; A is the area of ​​the beam fracture zone, 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 precast crack surface during the fracture process is not equal, W1=1 / 2m1gδ max W2=1 / 2m2gδ max Then the fracture energy G per unit area of ​​ITZ FI for:

[0090]

[0091] In the formula, m1g is the weight of a portion of the mortar from the support to the precast crack surface, and m2g is the weight of another portion of the rock from the support to the precast crack surface.

[0092] The tensile strength is:

[0093]

[0094] In the formula, T m denoted as σt, where σt is the tensile strength of the specimen, in MPa; P is the maximum load, in N; and C is the side length of the cube, in mm.

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

[0096] Step 3: Using two-dimensional image recognition of concrete slices and three-dimensional digital simulation based on Python random numbers, establish three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete.

[0097] To delve into the microstructure of polypropylene fiber-reinforced concrete and its impact on material properties, this embodiment employs advanced image recognition technology and digital simulation methods to construct accurate mesoscopic geometric models. Therefore, the process of establishing the three-phase and four-phase mesoscopic geometric models of polypropylene fiber-reinforced concrete is as follows:

[0098] Step 3.1: Using two-dimensional image recognition technology on concrete slices, details of the internal structure of the concrete are captured, including the distribution of aggregates, the filling of mortar, and the distribution of polypropylene fibers. After cutting the concrete sample, the cut surface is photographed with a digital camera. Figure 5 As shown in (a), the image is then processed to determine the boundaries of the aggregate, as shown in (a). Figure 5 As shown in (b), after image enhancement processing, importing the image into ABAQUS yields the finite element model of polypropylene fiber-reinforced concrete, as follows: Figure 5 As shown in (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 fibers), and the interface transition zone. In the four-phase model, in addition to the above three phases, the fiber-mortar interface, a key phase, is specifically added to more comprehensively reflect the role mechanism of polypropylene fibers in enhancing concrete performance. That is, the three-phase micro-geometric model of polypropylene fiber-reinforced concrete includes an aggregate model, a polypropylene fiber-containing mortar model, and an interface transition zone model; the four-phase micro-geometric model of polypropylene fiber-reinforced concrete includes an aggregate model, a polypropylene fiber-containing mortar model, an interface transition zone model, and a fiber-mortar interface model.

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

[0102] A1. Randomly generate spherical aggregates;

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

[0104]

[0105] In the formula: 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 represents the minimum and maximum aggregate particle size within a certain particle size range; rand is a random function.

[0106] A2. Use 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 represented as in equation (6).

[0108]

[0109] In the formula: (x mp ,y mp ,z mp ) represents the coordinates of the reference sphere center, r mp Let α be the radius of the reference sphere. p = rand[0, 2π], β p = rand[0, π].

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

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

[0112] A5. Determine whether the random polyhedral aggregate exceeds the boundary. If it does not exceed the boundary, proceed to step A6.

[0113] A6. Determine whether there is any interference between the randomly placed polyhedral aggregate and the previously placed random polyhedral aggregate. If there is no interference, proceed to step A7.

[0114] After generating random polyhedral aggregates, 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 subsequently generated aggregate and the coordinates of the center point of the previously generated aggregate be greater than the sum of the radii of the two circumscribed spheres, as shown in equation (7):

[0115]

[0116] In the formula: (x mp ,y mp ,z mp ), (x nq ,y nq ,z nq ) represent the coordinates of the center of the already generated aggregate and the center of the aggregate to be generated, respectively; r mp r nq These are the radii of the already generated aggregate and the radii of the aggregate to be generated, respectively; d m ζ represents the distance between the centers of the aggregates already generated and those yet to be generated; ζ is the aggregate crossover discrimination coefficient. The larger the coefficient, the lower the probability of aggregate crossover, but it also limits the aggregate volume fraction.

[0117] This method produces aggregates with low volume fractions. It stores vertex coordinate data when generating random polyhedra and calculates the minimum distance d between all vertices of two aggregates. min As shown in equation (8), the interference judgment diagram is as follows: Figure 7 As shown.

[0118]

[0119] In the formula, Let p be the vertex coordinates of the generated aggregate. Let n be the vertex coordinates for generating aggregate q, n be the number of vertices in the polyhedron, and N be the number of aggregates. When the number of aggregate vertices is large enough and l0 = 0, all vertices will not contact each other, and the aggregates will not penetrate each other. However, it is not certain that the number of aggregate vertices will reach the ideal situation when generating aggregates. To avoid aggregate penetration, the number of vertices can be increased appropriately. However, to ensure that there is no interference between aggregates, the value of l0 can be increased appropriately.

[0120] A7. Repeat steps A2-A6 until the volumetric rate is qualified, then terminate and generate the aggregate model.

[0121] The three-phase microstructure model of fiber-reinforced concrete can be established using the method described above. Figure 8 As shown, to establish a four-phase fiber-reinforced concrete model, fiber modeling should be completed based on the above. Therefore, the process of establishing the fiber model in the fiber-mortar interface model described 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 geometry, as shown in equation (9):

[0123]

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

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

[0126]

[0127] In the formula, x1 and 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 midpoint coordinates of the fiber, the fiber's orientation angle is randomly generated, and the fiber endpoint coordinates are generated in the positive and negative directions of the generated angle, respectively. Assume the angle between the fiber and the Z-axis is α, α∈[0,π], and the angle between the fiber's projection onto 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 shown in equation (11):

[0129]

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

[0131] Fiber placement needs to avoid fiber crossings, therefore fiber endpoint coordinates (x) have been generated. mi / j ,y mi / j ,z mi / j ), the coordinates of the fiber endpoint (x) to be generated ni / j ,y ni / j ,z ni / j The coordinates of any point m and n on the two fibers are given by 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 discrimination condition is as shown in equation (14):

[0134]

[0135] In the formula: d fib The diameter 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 aggregate that has already been added. This article stipulates that the distance from the fiber to the center of the reference ball should not be less than 1.1 times the length of half a pound of the reference ball, as shown in formula (15):

[0137]

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

[0139] Step 4: Calculate the material constitutive parameters of each microstructure component based on the cohesive constitutive model;

[0140] The microscopic geometric model established using the above method can intuitively display the internal structure of polypropylene fiber-reinforced concrete. Furthermore, the parametric design of the model allows us to study the effects of fiber content, length, shape, and distribution on concrete performance, providing a powerful tool for optimizing the design of polypropylene fiber-reinforced concrete. However, to accurately analyze the fracture of this microscopic model under external forces, corresponding material constitutive parameters should be assigned to each microscopic component. The specific steps are as follows:

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

[0142] B2. Based on the microstructure of polypropylene fiber reinforced concrete, establish a non-statistical analysis and perform mesh generation, then insert the generated cohesive elements into the initial mesh.

[0143] B3. Simulate concrete cracking by imposing different traction-separation softening laws;

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

[0145] In practical implementation, cohesive elements and solid elements are connected by mesh topology and can represent independent constitutive models. The finite element model based on cohesive elements can effectively simulate damage caused by crack propagation. Cohesive elements can be embedded between mortar-mortar elements to simulate mortar cracking, or embedded between aggregate-aggregate elements to simulate aggregate crushing, such as... Figure 10 As shown in (a), the mortar-aggregate interface can also be inserted to simulate the weak point in concrete (ITZ), such as... Figure 10 As shown in (b).

[0146] In the commercial software ABAQUS, the specific implementation method involves first outputting an .inp file, reading and numbering the element nodes, inserting cohesive elements between shared nodes, renumbering all nodes, and then writing the result back into the .inp file to establish a finite element model containing cohesive interface elements. Taking a three-dimensional mesoscopic concrete specimen as an example, a finite element model containing cohesive interface elements (CIE) is established, as follows: Figure 11 As shown. First, different sets are created for the concrete microstructure model, namely aggregate and mortar. Then, the mesh is generated, as shown in the example mesh. Figure 11 As shown in (a), the three sets of cohesive elements CIE_AGG (Aggregate), CIE_MOR (Mortar), and CIE_ITZ are then inserted into the initial mesh, as shown in (a). Figure 11 As shown in (b), (c), and (d), different traction-separation softening laws can be applied to simulate concrete cracking. The same principle applies to the two-dimensional mesoscopic model. Figure 12 As shown.

[0147] For quasi-brittle materials, such as cement mortar and aggregates, a bilinear traction-separation relationship is adopted, and the constitutive models of cohesive units in uniaxial tension / compression and shear modes are as follows: Figure 13 As shown, Figure 13 (a) is a type I predominant bilinear cohesive model, which assumes that the separation of material interfaces is controlled by displacements perpendicular to the interfaces. Figure 13 (b) is a type II-dominant bilinear model, which assumes that the separation of the material interface is related to the displacement of the interface tangency.

[0148] The traction-separation stage of the cohesive unit corresponds to Figure 13 In the straight upward segment, before the stress exceeds the damage strength, the cohesive elements exhibit linear elastic constitutive behavior. The normal and tangential constitutive behaviors of the cohesive elements are shown in equations (16) and (17):

[0149]

[0150] In the formula, t n and t s These represent the normal stress and shear stress of the cohesive element, respectively; < and > represent Macaulay brackets, which are 0 under compression; δ n and δ s Indicates positive opening and shear slip displacement; This represents the penalty stiffness of a cohesive element.

[0151] Once the element stress state satisfies the damage initiation criterion, the element enters the damage evolution phase. This study adopts the second nominal stress criterion, expressed as follows:

[0152]

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

[0154] When the stress of the cohesive element exceeds the damage initiation strength t n0 and t s0 (t t0 When damage occurs in the element following the table, its stiffness can be expressed as:

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

[0156] In the formula, K represents the damage stiffness; D represents the stiffness damage factor, D=0 represents no damage, and D=0 represents complete element failure.

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

[0158]

[0159] In the formula, This represents the maximum effective relative displacement obtained during the loading process. These represent the effective relative displacements at the onset of damage and at the point of final failure, respectively. The damage evolution caused by the combined action of normal and tangential forces is expressed as follows:

[0160]

[0161] because Determining this is quite complex, as it reflects the fracture energy release rate of an element under mixed stress conditions. BK (Benzeggagh-Kenane) proposed a fracture criterion suitable for describing quasi-brittle materials from an energy perspective. Therefore, the constitutive response of a cohesive element in a mixed mode is as follows: Figure 14 , It can be represented as:

[0162]

[0163] In the formula G Ⅰ and G Ⅱ G represents the tensile (Type I) and shear (Type II) fracture energies, respectively; n and G s These represent the work done by the tensile force and the shear force, respectively; η is the correction parameter for the BK criterion.

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

[0165] Step 6: Using the verified three-phase and four-phase micro-geometric models, perform tensile fracture analysis of polypropylene fiber reinforced concrete and obtain the analysis results.

[0166] The 3D concrete model was built as a 50×50×50mm cube, and the 2D slice model was 50×50×1mm. The left surface of the model was fully constrained, and the right surface was coupled to a reference point, to which an axial displacement was applied. The final displacement was set to 0.1mm. The curves of the reference point reaction force and displacement over time were read and combined. For the 3D concrete model, the equivalent stress result was expressed as the nodal reaction force divided by the cross-sectional area; for the 2D concrete model, the equivalent stress result was expressed as the nodal reaction force divided by the length of the coupled edge. The equivalent strain of the concrete was expressed as the ratio of the reference point displacement to the model edge length in the elongation direction. Quasi-static calculation analysis was performed using the ABAQUS / Explicit explicit solver, with the displacement applied using the "smooth analysis" option.

[0167] A comparative analysis was conducted on polypropylene fiber reinforced concrete with a fiber volume ratio of 0.4% using two methods: three-phase and four-phase microscopic geometric models. The crack morphology of the microscopic geometric models calculated by the two methods is as follows: Figure 15 As shown, where Figure 15 (a) and Figure 15 (c) shows the crack morphology of the three-phase microscopic geometric model. Figure 15 (b) and Figure 15 (d) shows the cracking morphology of the three-phase microscopic geometric model; the PFRC stress-strain curve is as follows: Figure 16 As shown, the crack paths of PFRC under different fiber volume ratios were calculated as follows: Figure 17 and18 As shown.

[0168] In summary, this invention establishes a microstructure analysis model applicable to polypropylene fiber reinforced concrete, reducing computer computation costs while meeting computational accuracy requirements. It quantifies the intrinsic strengthening effect of low-dosage polypropylene fibers on concrete and the weakening effect of high-dosage fibers on concrete. Furthermore, the material properties of each microstructure component in the established microstructure analysis model are determined experimentally, ensuring the accuracy of the simulation results.

[0169] The technical solution provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make several improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for analyzing the tensile fracture of polypropylene fiber reinforced concrete at a microscale, characterized in that, Includes the following steps: Step 1: Determination of tensile fracture stress characteristics and microstructure composition of polypropylene fiber reinforced concrete. Step 2: Conduct material fracture tests and determine the fracture parameters of each microstructure component; The steps for determining the fracture parameters of each microstructure component in step 2 are as follows: Step 2.1: With the fiber volume ratio in polypropylene fiber-reinforced concrete as a variable, design fiber-reinforced mortar specimens and rock-fiber modified mortar mixed specimens with different fiber volume ratios. Step 2.2: Conduct 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 microstructure under tensile fracture conditions; Step 3: Using two-dimensional image recognition of concrete slices and three-dimensional digital simulation based on Python random numbers, establish three-phase and four-phase micro-geometric models of polypropylene fiber reinforced concrete. Step 4: Calculate the material constitutive parameters of each microstructure component based on the cohesive constitutive model; Step 5: Assign the fracture parameters and material constitutive parameters of each microstructure component to the three-phase and four-phase microstructure geometric models of polypropylene fiber reinforced concrete, and establish model boundary conditions to verify the rationality of the model. Step 6: Using the verified three-phase and four-phase micro-geometric models, perform tensile fracture analysis of polypropylene fiber reinforced concrete and obtain the analysis results. The three-phase micro-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a polypropylene fiber-containing mortar model, and an interface transition zone model. The four-phase micro-geometric model of polypropylene fiber reinforced concrete includes an aggregate model, a polypropylene fiber-containing mortar model, an interface transition zone model, and a fiber-mortar interface model.

2. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale 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 microstructure of polypropylene fiber reinforced concrete includes aggregate, mortar, and interface transition zone, in which polypropylene fibers are uniformly distributed in the mortar.

3. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale according to claim 1, characterized in that: The fracture parameters include fracture energy, tensile strength, elastic modulus, and fracture toughness.

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

5. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale according to claim 1, characterized in that: The steps for constructing the aggregate model are as follows: A1. Randomly generate spherical aggregates; A2. Use 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 polyhedral aggregates based on the vertex triangle faces; A4. Randomly generate the coordinates of the aggregate center point within the reference sphere, and place random polyhedral aggregates according to the coordinates of the center point. A5. Determine whether the random polyhedral aggregate exceeds the boundary. If it does not exceed the boundary, proceed to step A6. A6. Determine whether there is any interference between the randomly placed polyhedral aggregate and the previously placed random polyhedral aggregate. If there is no interference, proceed to step A7. A7. Repeat steps A2-A6 until the volumetric rate is qualified, then terminate and generate the aggregate model.

6. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale according to claim 1 or 5, 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 geometry. After calculating the number of fibers, the fibers are generated and placed on the aggregate model.

7. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale according to claim 6, characterized in that: During the process of placing fibers on the aggregate model, it is necessary to avoid the fibers crossing each other and not overlapping with the already placed random polyhedral aggregates.

8. The analytical method for tensile fracture of polypropylene fiber reinforced concrete at the microscale according to claim 1, characterized in that: The steps in step 4 for calculating the material constitutive parameters of each microstructure component based on the cohesive constitutive model are as follows: B1. Based on ABAQUS software, establish a finite element model of the cohesive interface element; B2. Based on the microstructure of polypropylene fiber reinforced concrete, establish a non-statistical analysis and perform mesh generation, then insert the generated cohesive elements into the initial mesh. B3. Simulate concrete cracking by imposing different traction-separation softening laws; B4. Calculate the material constitutive parameters of each microscopic component.

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