Quasi-brittle material dynamic fracture behavior and parameter prediction method based on equivalent area

Abstract

The invention relates to a method for predicting dynamic fracture behaviors and parameters of a quasi-brittle material based on an equivalent area, and aims to solve the technical problems that in the prior art, a dynamic fracture parameter test of quasi-brittle materials such as concrete is remarkable in size effect and complex in test process, and multiple groups of test pieces and special equipment are needed. According to the method, a technical means of taking an equivalent area Ae as a core design parameter is adopted, two groups of quantitative test pieces with a specific Ae value ratio are designed, a linear analysis model of a peak load and the equivalent area is established, the dynamic fracture toughness KIC and the tensile strength ft without a size effect are synchronously determined, and a fracture total curve with 95% reliability is constructed. The method has the technical effects that the real dynamic fracture parameters of the material can be accurately measured only by a small number of laboratory small-size test pieces, the size effect is effectively eliminated, the test process is remarkably simplified, the equipment requirement is reduced, and the reliable prediction of the fracture behaviors of engineering structures with different geometric sizes is realized.

Description

Technical Field

[0001] This invention relates to the field of quasi-brittle material performance testing technology, and in particular to a method for predicting the dynamic fracture behavior and parameters of quasi-brittle materials based on equivalent area. Background Technology

[0002] Concrete, as the most widely used quasi-brittle material in civil engineering, inevitably endures dynamic loads such as earthquakes, explosions, and impacts during its service life. Under these high strain rate conditions, concrete structures are prone to tensile-dominated fracture failure, which is often sudden and catastrophic, seriously threatening the safety and durability of the structure. Therefore, accurately assessing the fracture performance of concrete under dynamic loads, especially its fracture toughness without size effects, is crucial. K IC ) and tensile strength ( f t This is a key scientific issue for ensuring the reliable design and safety evaluation of engineering structures.

[0003] Currently, several mature fracture mechanics models have been proposed and widely applied for the fracture behavior of concrete under static or quasi-static conditions, such as the two-parameter model, the effective crack model, and the crack zone model. These models, by introducing the concept of the fracture process zone (FPZ), overcome to some extent the size effect problem existing in traditional linear elastic fracture mechanics when describing quasi-brittle materials, and can reasonably determine the intrinsic fracture parameters of the material. However, most of these models are based on static loading conditions and are difficult to directly apply to dynamic loading scenarios.

[0004] Because concrete exhibits significant strain rate sensitivity, its compressive and tensile strengths show a marked upward trend under medium-to-high strain rate conditions (i.e., dynamic enhancement effect). Simultaneously, the evolution mechanism of the fracture process zone, crack propagation rate, and failure mode also undergo significant changes. Existing dynamic fracture models typically focus only on determining apparent fracture parameters under specific specimen geometry and loading rates, lacking a systematic consideration of the influence of specimen size, crack height ratio, loading rate, and other factors, leading to inaccurate results. K IC and f t The values ​​still exhibit a strong size dependence. Furthermore, tests at different loading rates often require different testing equipment (such as split Hopkinson bar systems, drop hammer devices, electro-hydraulic servo systems, etc.), resulting in high data acquisition costs and poor comparability, which limits the extraction of intrinsic property parameters of uniform materials.

[0005] More importantly, there is currently no universally applicable method to accurately invert the true, size-effect-free dynamic fracture parameters of concrete from conventional small-sized quantitative laboratory specimens without relying on a large number of specimens of different sizes. On the one hand, large-sized specimens are difficult to fabricate and the experiments are complex; on the other hand, small-sized specimens are significantly affected by boundary and size effects, and their measured nominal strength cannot truly reflect the intrinsic properties of the material. Therefore, how to overcome the interference of specimen geometry, loading method, and strain rate on the determination of dynamic fracture parameters, and achieve efficient and accurate determination of the intrinsic dynamic fracture characteristics of concrete materials from standard laboratory specimens, has become a technical bottleneck restricting the design and evaluation of the dynamic performance of concrete structures. Summary of the Invention

[0006] This invention addresses the technical problems of existing methods being unable to accurately determine the dynamic fracture parameters of quasi-brittle materials, the results being affected by specimen size effects, and the high cost and complexity of operation. It introduces an equivalent area... A e By using these as core parameters and establishing corresponding simplified calculation models, we were able to simultaneously and accurately obtain the dynamic fracture toughness and tensile strength of materials without size effects using only two sets of standard quantitative specimens with specific equivalent area ratios. This enabled us to achieve the technical effect of predicting fracture behavior across scales from the laboratory to engineering structures.

[0007] According to one aspect of this disclosure, a method for determining dynamic fracture parameters of quasi-brittle materials based on equivalent area is provided, comprising the following steps: (1) Prepare at least two groups with different equivalent areas A e The laboratory quantitative test specimens, the equivalent areas of each group of test specimens satisfy a preset proportional relationship; (2) Fracture tests were conducted on each group of specimens at different loading rates to obtain their corresponding peak loads. P max ; (3) Based on the equivalent area A e and the corresponding peak load P max The dynamic fracture toughness of the quasi-brittle material without size effect at the corresponding loading rate is simultaneously determined using the following solution model. K IC and dynamic tensile strength f t : ; ; In the formula, The characteristic crack length of the specimen. The characteristic particle size is denoted as .

[0008] In some embodiments of this disclosure, the preset ratio is 2:1.

[0009] In some embodiments of this disclosure, the equivalent area of ​​each group of specimens is calculated based on the following formula. : ; In the formula, W The height of the specimen. S The span of the specimen. B For the thickness of the specimen, For the seam height ratio, The characteristic crack length of the specimen. These are the geometric parameters of the specimen. This represents the virtual crack propagation amount of the specimen.

[0010] In some embodiments of this disclosure, the virtual crack propagation amount Determined by the following formula: ; In the formula, The average particle size of the aggregate; n The value for the aggregate expansion quantity; The empirical parameter calculation formula to take into account the effect of loading rate is as follows: ,in, The strain rate of the specimen. This is the reference value for the strain rate of the specimen.

[0011] In some embodiments of this disclosure, the The characteristic crack length is determined by the following formula: ; In the formula, For concrete, the characteristic particle size is... Take the average aggregate particle size .

[0012] In some embodiments of this disclosure, the geometric parameters Determined by the following formula: ; In the formula, For seam height ratio; For geometric shape factor; The expression for the loaded type parameter is: .

[0013] According to another aspect of this disclosure, a method for predicting the dynamic fracture behavior of quasi-brittle materials based on quantitatively designed specimens is provided, comprising the following steps: (1) Dynamic fracture toughness determined using the above method K IC and dynamic tensile strength f t Constructing based on geometric structural parameters a e With characteristic crack length The ratio is shown on the x-axis, with nominal stress as the metric. The broken full curve is represented by the ordinate; (2) Calculate the geometric parameters of the actual structure to be predicted using the following formula. a e : ; In the formula, α For seam height ratio; Y ( α ) represents the geometric shape factor; A ( α ) represents the loading type parameter, and its expression is: ; (3) The geometric parameters of the actual structure to be predicted Substitute the complete fracture curve into the value to predict the nominal stress at that loading rate. and fracture modes.

[0014] In some embodiments of this disclosure, in step (1), the nominal stress σ n Determined by the following formula: ; In the formula, W The height of the specimen. S The span of the specimen. B For the thickness of the specimen, α For the seam height ratio, This represents the virtual crack propagation amount of the specimen.

[0015] In some embodiments of this disclosure, in step (3), the fracture mode is determined based on the following characteristics: Nominal stress σ n Corresponding to a e / In the region <0.1, the fracture of the actual structure to be predicted is under the control of tensile strength; nominal stress σ n Corresponding to a e / In the region where the stress is greater than 10, the fracture toughness is controlled; nominal stress σn Corresponding to 0.1< a e / If the value is less than 10, it is considered a quasi-brittle fracture region, where fracture is controlled by both tensile strength and fracture toughness.

[0016] Compared with the prior art, the beneficial technical effects achieved by the present invention are as follows: 1. It realizes the size-effect-free inversion of dynamic fracture parameters, solving the fundamental problem that traditional test results are constrained by geometric dimensions.

[0017] For the first time, the equivalent area A e As a core design parameter, it is defined as a normalized index that comprehensively reflects the influence of specimen height, crack length, ligament height, and geometric configuration. This is achieved by constructing a peak load and... A e The functional relationship between them was established, including the intrinsic parameters of the material. K IC and f t The analytical expression. Based on this, it is only necessary to select two groups with the same material composition but... A e By conducting dynamic loading tests on quantitative laboratory specimens with a ratio of 2, a unique set of solutions that are unaffected by specimen size can be obtained through simultaneous analysis. K IC and f t This method fundamentally eliminates the drift of fracture parameters caused by changes in specimen size, enabling laboratory measurements to truly reflect the dynamic fracture characteristics of the material itself.

[0018] 2. A unified virtual crack length calculation model is proposed, which enhances the adaptability and accuracy of the method under different loading rates and crack height ratios.

[0019] To address the deficiency in existing models regarding the lack of rate correlation in determining virtual crack length, this paper innovatively introduces a loading rate factor and a ligament relative height correction term, constructing a unified formula for calculating virtual crack length applicable to a wide range of strain rate conditions. This model fully considers the lag effect in fracture zone development under dynamic loading and the variation of local stress concentration with crack height, ensuring accurate calculation of virtual crack length under different specimen configurations and loading rates. A e The physical meaning remains consistent, thus ensuring the stability and consistency of the parameter inversion process.

[0020] 3. Significantly reduced testing requirements, improving the practicality and scalability of the project.

[0021] Compared to traditional methods that require conducting multiple sets of tests on specimens of different sizes, this invention only requires two sets of tests to meet the requirements. A e All parameters can be identified using a design specimen with a ratio of 2, greatly reducing the number of experiments, time, and resource consumption. It is particularly suitable for scenarios with limited experimental conditions (such as those where large-scale dynamic experiments cannot be carried out), providing a feasible technical path for small and medium-sized laboratories and significantly improving the practical operability and popularization potential of the method.

[0022] 4. A statistically reliable full-curve fracture prediction system was constructed, enabling accurate prediction of structural fracture behavior.

[0023] Based on the determined size-free effect K IC and f t This invention further develops a full-curve fracture model encompassing multiple fracture modes, and combines it with statistical analysis methods ( Envelope curves with upper and lower limits and a 95% confidence level were established for the interval. This system can not only accurately predict the peak bearing capacity and failure mode of specimens or actual structures with arbitrary geometric configurations at different loading rates, but also quantify the dispersion of the results, providing a probabilistic basis for structural safety assessment and significantly enhancing the engineering guidance value of the model.

[0024] 5. It has been thoroughly validated and possesses good universality and transferability.

[0025] By back-calculating and verifying publicly available experimental data from other researchers, the results show that the inverted... K IC and f t The errors between the values ​​and the literature benchmarks were all controlled within 5%, demonstrating the high accuracy and cross-dataset applicability of the method. Furthermore, the method is not dependent on specific specimen types (such as three-point bending beams, compact tensile specimens, etc.), as long as the following conditions are met... A e The design principle of a ratio of 2 can be extended to various standard or non-standard specimen forms, demonstrating excellent versatility.

[0026] In summary, this invention introduces an equivalent area A eUsing this method as the core bridge, a systematic design framework integrating loading rate effects, geometric parameter influences, and statistical reliability was constructed, successfully achieving a precise mapping from finite laboratory specimens to the intrinsic dynamic fracture properties of materials. This method not only solves the long-standing problem of the coupling of "size effect-dynamic response-parameter uniqueness" in the field of concrete fracture mechanics, but also provides theoretical support and technical tools for the performance characterization and structural design of quasi-brittle materials under complex dynamic loading environments, possessing significant academic value and broad application prospects. Attached Figure Description

[0027] Figure 1 This represents the specimen size effect ratio under different loading rates in the embodiments of this disclosure.

[0028] Figure 2 This is the crack propagation region of the specimen under peak load in the embodiments of this disclosure. A schematic diagram of its expansion path under different loading rates.

[0029] Figure 3 For concrete specimens under laboratory conditions in the embodiments of this disclosure P max time exhibit.

[0030] Figure 4 This is a schematic diagram illustrating the prediction of concrete fracture behavior at different loading rates based on standardized specimens in an embodiment of this disclosure.

[0031] Figure 5 This is a flowchart illustrating the determination of size-free dynamic fracture parameters of concrete at different loading rates based on quantitative laboratory specimens in this embodiment of the present disclosure.

[0032] Figure 6 The results of concrete material parameters under different loading rates were determined using quantitative laboratory specimens in this embodiment of the present disclosure.

[0033] Figure 7 The results of concrete material parameters under different loading rates were determined by multiple sets of laboratory specimens in this embodiment of the present disclosure.

[0034] Figure 8 This is a fracture failure curve established based on a quantitatively designed specimen in an embodiment of this disclosure. Detailed Implementation

[0035] To better understand the technical solution of this application, the above technical solution will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1: Construction of a dynamic fracture prediction model for concrete considering size effects 1. Determine the dynamic properties of concrete materialsK IC and f t Theoretical basis Concrete specimens prepared under laboratory conditions exhibit significant heterogeneity, leading to complex nonlinear behavior during fracture. The fracture parameters of concrete materials at different loading rates (…) K IC and f t The fracture process zone (FPZ) exhibits a significant size effect. This phenomenon is closely related to the dynamic evolution of the fracture process zone at the crack tip (FPZ) of concrete specimens. The FPZ is the region of stress and strain concentration when a material is subjected to force, and its microstructure and mechanical properties have a decisive influence on the fracture behavior of concrete. Within the FPZ, the nonlinear behavior of the material is particularly prominent, manifested as the initiation, propagation, closure, and interaction of microcracks, and the responses of these processes differ significantly under different loading rates.

[0037] The increased loading rate significantly altered the dynamic fracture behavior of the FPZ (fiber optic zone), making the size effect phenomenon in concrete materials more complex. Under high-speed loading, the relationship between fracture parameters and specimen size in concrete specimens exhibited a drastically different trend compared to low-speed loading; for example... Figure 1 As shown. Specifically, under high-speed loading conditions, due to the hindered propagation of microcracks, the fracture toughness and tensile strength of large-sized specimens are relatively improved, while the performance improvement of small-sized specimens is not significant, which is related to the relative size and distribution of FPZ. Under low-speed loading, the fracture parameters change relatively gradually with the specimen size.

[0038] At a close scale, concrete exhibits two typical failure modes: circumgranular failure and transgranular failure. Circumgranular failure refers to the behavior where, when cracks in the mortar matrix extend to the edges of aggregate particles, the aggregate particles cannot crack or penetrate through them, causing the cracks to propagate through the interface transition zone, thus forming interface cracks. Transgranular failure refers to the behavior where, when cracks in the mortar matrix extend to the edges of aggregate particles, the aggregate particles crack and are penetrated, thus forming aggregate cracks. Under dynamic loading conditions, the rate sensitivity of concrete material strength cannot be ignored; that is, concrete material strength exhibits a significant strain rate effect.

[0039] Therefore, this example, combining boundary effect theory, studies and discovers the linear relationship between virtual crack propagation and aggregate particle size under peak loads at different loading rates, and establishes an analytical calculation model that can determine the true fracture toughness and tensile strength of the material under different loading rates. This model uses the equivalent area... A e As an important design parameter, only A eBy conducting fracture tests on two groups of specimens that meet certain thresholds, the strength and toughness parameters under different loading rates can be determined. The unified analytical expression for the analytical calculation model of the true fracture toughness and tensile strength under different loading rates proposed in this example is: (1); In the formula, P max For the peak fracture load, W The height of the specimen. S The span of the specimen. B For the thickness of the specimen, The characteristic crack length of the specimen. a e These are the geometric parameters of the specimen. This represents the virtual crack propagation of the specimen. Numerous experimental studies have shown that... P max At that time, FPZ development was insufficient, only expanding to a few aggregate sizes, which were denoted as ,like Figure 3 The red area is shown. , and a e The calculation method is shown in equations (2) - (4).

[0040] As the load increases, the fracture process zone develops in the stable damage zone at the crack front, such as... Figure 2 The virtual crack propagation length reflects the morphology of a continuous, irregular microcrack. The processes of aggregate frictional interlocking and pull-out leading to cohesion on the crack surface during virtual crack propagation mainly occur around the aggregate particles and exhibit strain rate effects. Under low strain rates, crack propagation primarily manifests as intergranular failure. However, at medium to high loading rates, as the strain rate of the specimen increases, an inertial effect occurs, and the crack exhibits transgranular failure, penetrating and breaking all aggregates along the propagation path. The influence of the loading rate on the specimen cannot be ignored; therefore, we consider incorporating the empirical parameters of the loading rate effect into the virtual crack propagation corresponding to the peak load. However, compared to FPZ, Its formation is short-lived and its expansion is unstable. Under different loading rates, it is difficult to capture its true form. For ease of design and application, [further measures are needed]. The specific calculation formula is as follows: (2); In the formula, d av The average aggregate particle size is calculated as follows: First, the aggregate content for each particle size is calculated using the Fuller & Thompson formula. Then, the sieve retention rate for each particle size is determined. Finally, the weighted average method is used to calculate the average aggregate size. dav . n The calculation method for determining the aggregate expansion quantity is shown in Table 1 and... Figure 3 . To account for the influence of loading rate, the empirical parameter is calculated as follows: .in, The strain rate of the specimen. This is a reference value for the strain rate of the specimen, which is related to the strain rate level at which the specimen is loaded. When the specimen is at a low strain rate (10... -5 s -1 ~ 10 0 s -1 When conducting the experiment, When the specimen is subjected to a strain rate (10... 0 s -1 ~ 10 2 s -1 When conducting the experiment, When the specimen is subjected to a high strain rate (10... 2 s -1 ~ 10 4 s -1 When conducting the experiment, .

[0041] According to the literature (X. Hu, Q. Li, Z. Wu and S. Yang, Modelling fracture processzone width and length for quasi-brittle fracture of rock, concrete and ceramics, Eng Fract Mech 259(2022) 108158.), the formula for calculating the characteristic crack length is: (3); In the formula, C cr For concrete, the characteristic particle size is... C cr Take the average aggregate particle size d av .

[0042] a eThe geometric structural parameters of the specimen are given by the following analytical expressions (JF Guan, XZ Hu, CPXie, QB Li and ZM Wu, Wedge-splitting tests for tensile strength and fracture toughness of concrete, Theor Appl Fract Mec 93(2018) 263-275.): (4); In the formula, α The seam height ratio, i.e. a 0 and W The ratio; A ( α ) represents the loading type parameter, and its expression is as follows: (5).

[0043] Table 1 Δ a fic Specific design methods .

[0044] Y ( α () represents the geometric shape factor, and the specimen type is 3-pb. Y ( α The expression is shown below (J. Guan, Z. Song, M. Zhang, X. Yao, L. Li and S. Hu, Concrete fracture considering aggregate grading, Theor Appl Fract Mec 112(2021)102833.): (6); (7); (8); (9); (10); From equation (1), we can see that P max and A e Once determined, the concrete specimens under different loading rates f t It can be obtained by linear fitting (y=Ax).

[0045] The fracture toughness of specimens without size effect under different loading rates can be derived from equation (3). K IC The calculation formula is as follows: (11).

[0046] In summary, the size-free effect of concrete under different loading rates can be calculated using equations (1) - (10). f t The obtained specimens f t Substituting into equation (11) yields the size-free properties of concrete at different loading rates. K IC .

[0047] 2. Predicting Dynamic Fracture Behavior of Concrete Based on Laboratory Quantitative Design of Specimens Related studies have shown that Δ a fic The material parameters determined using a rectangular stress distribution are basically consistent with those determined using triangular, trapezoidal, or other nonlinear distribution patterns, thus meeting design accuracy requirements. P max When considering Δ a fic nominal stress of influence The calculation expression is: (12).

[0048] Based on the design method proposed in this example, through... A e The concrete determined by the design specimen with a ratio of 2 K IC and f t From equations (2) to (12), a complete fracture curve reflecting the relationship between dynamic fracture parameters and structural properties of concrete materials under different loading rates can be constructed. a e / In the region where the tensile strength is less than 0.1, the fracture of the specimen is under the control of tensile strength. a e / In the region >10, the fracture of the specimen was under the control of fracture toughness; 0.1 < a e / The region with a fracture strength <10 is considered a quasi-brittle fracture zone, where the fracture is controlled by both tensile strength and fracture toughness. The geometric parameters of large-size specimens or actual structures are calculated using equation (4). ae Then, by substituting the pre-constructed fracture curve, the nominal stress of large-sized specimens or large engineering structures can be predicted. That is, by establishing a complete fracture curve through quantitative design of specimens, the fracture behavior of large-sized specimens or engineering-scale components can be accurately predicted; such as... Figure 4 As shown.

[0049] 3. Determine the dynamic properties of concrete materials K IC and f t Simplified design method When domestic and international scholars determine the size-effect-free fracture parameters of concrete through experiments, multiple sets of concrete specimens are often required to avoid the influence of factors such as specimen size, loading type, operation method, and measurement error on the results. Based on a certain amount of experimental data, the dynamic fracture parameters of concrete without size effects are determined by linear fitting. However, in designing experiments, there is still a lack of unified standards on how to determine the number of specimens and sets to obtain the best data fit and thus optimize cost-effectiveness. In view of this, this invention aims to fill this knowledge gap and proposes a method for determining the size-effect-free fracture parameters of concrete based on quantitative laboratory specimens. K IC and f t A simplified design method is proposed. The proposed method significantly reduces the number of specimens while maintaining data accuracy, thereby reducing testing costs and workload. The testing procedure is as follows: Figure 5 As shown.

[0050] The first step is to design and test the specimens: design two groups. A e For specimens with a ratio of 2, the specimen size, crack length, and loading rate can be arbitrarily adjusted according to the test plan. Subsequently, fracture tests are performed on the cast concrete specimens, and the fracture characteristics of the concrete specimens under different loading rates are recorded. P max .

[0051] The second step is to calculate key parameters: This involves analyzing concrete specimens obtained from experiments at different loading rates. P max Then the concrete specimens d av Substituting into equation (2), the two sets of design specimens can be determined. A e1 , A e2 ) of ∆ a fic Secondly, the results are calculated using equations (3) and (4) respectively. anda e Then set the parameters S , W , B , α , , and a e Substituting into equations (1) - (4) yields the following result. A e The value; The third step is to calculate the dynamic fracture parameters: The calculated parameters will be used in conjunction with the dynamic fracture parameters. A e and the experimentally measured P max Substituting into equation (1) yields the specimen considerations. Impact f t Then f t Substituting into equation (11) yields the size-free properties of concrete at different loading rates. K IC .

[0052] The fourth step is to predict fracture behavior: based on the quantitative specimens under different loading rates... K IC and f t The complete fracture curve of concrete can be established, and the fracture behavior of the specimen or engineering structure can be determined based on the complete fracture curve.

[0053] In summary, the simplified design method proposed in this example considers different loading rates. The influence of size effects on concrete materials was investigated, and the selection strategy for laboratory specimens was optimized, aiming to obtain dynamic data on concrete materials without size effects. K IC and f t It provides an efficient and economical path.

[0054] Example 2: Model Application The model of this invention uses equivalent area A e As an important design parameter, it can more comprehensively reflect the size effect of concrete strength and toughness parameters under dynamic loads. A total of 10 sets of small-size quantitative concrete specimens were designed for laboratory use. A e The ratios are all 2, and the loading rates range from 0.02 to 200 mm / min. Based on equation (1), different combinations of designed specimens ( A e1 and Ae2 Linear regression analysis was used to determine the size-free properties of concrete under different loading rates. K IC and f t This paper incorporates the research results of other scholars' dynamic fracture tests on concrete. The dynamic fracture parameters determined based on the above model are presented. K IC and f t Fitting analysis with multiple sets of data from the conducted experiments determined that K IC and f t A comparison was made. Meanwhile, the results determined based on the method of this invention were... K IC and f t According to the cited references K IC and f t A comparison was made.

[0055] Information on concrete quantitative design specimens at different loading rates is detailed in Table 2. Based on the design method proposed in this invention, calculations can be performed to obtain the strength and toughness parameters of the quantitative design specimen (DG17) at different loading rates. K IC and f t The results of determining the strength and toughness parameters of concrete at different loading rates using quantitative design specimens are as follows: Figure 6 As shown. To verify the rationality and applicability of the design method proposed in this invention, a fitting analysis was performed on all fracture test data of DG17 under different loading rates to determine the... K IC and f t like Figure 7 As shown. Furthermore, the quantitative specimens and multiple sets of specimens determined... K IC and f t Compared with the original literature, the quantitative specimens and multiple sets of specimens were obtained respectively. K IC and f t Relative error analysis was used to compare the two sets of results. The relative error was calculated as: relative error = (design group results - multiple sets of specimen results) / multiple sets of specimen results. The comparison results are shown in Table 3. It can be seen that the results determined using quantitative concrete specimens... K IC The errors are all within ±5%. f tThe errors are all within ±5%. In summary, the calculation results from the cited literature are in good agreement with the calculation results using the two-point method proposed in this invention. The dynamic concrete properties determined using the design method proposed in this invention are... K IC and f t It is accurate and reasonable.

[0056] Table 2. Detailed information on laboratory concrete design specimens (loading rate 0.02~200 mm / min) Note: The data in the table comes from publicly available literature (S. Yang, M. Wang, T. Lan, S. Liu and Z. Sun, Fracture model for predicting tensile strength and fracturetoughness of concrete under different loading rates, Constr Build Mater365(2023) 129978).

[0057] Table 3 Comparison of material parameters under different loading rates (loading rate 0.02~200 mm / min) .

[0058] Example 3: Prediction of Structural Fracture Behavior Based on Quantitative Design Specimens This embodiment demonstrates how the method of the present invention can be used to accurately predict the fracture behavior of actual engineering structures by quantitatively designing specimens in the laboratory.

[0059] Based on the method proposed in this invention, by designing a system that satisfies the equivalent area ratio A e2 : A e1 Two sets of laboratory specimens with a strength of 2 can determine the true strength and toughness parameters (fracture toughness) of quasi-brittle materials such as concrete under different loading rates. K IC With tensile strength f t Furthermore, based on these parameters, reliable prediction models can be established to evaluate the fracture behavior of actual engineering structures.

[0060] Verification results and analysis: Figure 8 The complete fracture curves constructed from test data by design group DG17 are presented. The results show that all specimen data fall within the range provided by [the data source]. K IC and ft Within a jointly controlled quasi-brittle fracture region. It is noteworthy that this region possesses 95% reliability. The prediction range almost completely covered the experimental data of all concrete specimens, which shows that the model and method established in this invention can effectively predict the fracture failure of quasi-brittle materials.

[0061] To verify the engineering applicability of the method, the geometric parameters of the large-size specimen were calculated according to equation (4). a e And substitute it into the fracture curve and the corresponding Upper and lower limit curves. Through this process, the nominal stress of the specimen under different loading rates was obtained. σ n The predicted values ​​and their 95% reliability range. From Figure 8 It can be seen that the concrete specimens under different loading rates calculated by equation (12) All measured values ​​fell within the predicted range established based on the quantitatively designed specimens, thus fully verifying the accuracy and rationality of the method of the present invention in predicting actual structural fracture failure.

[0062] To address the vulnerability of actual engineering structures to various dynamic loads during service, this invention considers the geometric differences between laboratory specimens and actual structures, using an equivalent area... A e Using these as core design parameters, a system was established to determine the size-effect-free dynamic fracture parameters of concrete using small-sized laboratory specimens. K IC and f t The method and supporting fracture model were proposed. The main conclusions are as follows: (1) By incorporating microstructural parameters such as aggregate gradation, crack length, and specimen geometry, as well as load characteristic parameters such as strain rate and loading rate, into the calculation expression, a simplified design method and calculation model for simultaneously determining the strength and toughness parameters of concrete based on peak load of small-sized laboratory specimens were established. Only two sets of quantitative specimens with an equivalent area ratio of 2 are needed to accurately determine the size-free strength parameters of concrete under different loading rates. K IC and f t .

[0063] (2) Laboratory specimen verification at different loading rates, based on research data from relevant scholars, shows that the method determined by this invention... K IC and f t Compared with the results in the literature, the errors were all controlled within 5%, which confirmed the accuracy of the method.

[0064] (3) Based on certainty K IC and f t The established fracture curve with 95% reliability can accurately predict the failure behavior of actual structures. Through the fracture curve... The upper and lower limits can not only predict the fracture behavior of laboratory specimens and actual structures, but also effectively characterize the dispersion of the results. The verification of experimental data by relevant scholars further proves the rationality of this method.

[0065] This invention successfully solves the problem that the dynamic fracture parameters of concrete determined by existing design methods are easily affected by specimen size, loading method and loading rate, and thus cannot reflect the true performance of the material. It breaks through the technical bottleneck of unified testing of dynamic fracture toughness and tensile strength of concrete, and provides an innovative solution for evaluating the fracture performance and strength characteristics of quasi-brittle material engineering structures through laboratory quantitative variable geometry specimens.

Claims

1. A method for determining dynamic fracture parameters of quasi-brittle materials based on equivalent area, characterized in that, Includes the following steps: (1) Prepare at least two groups with different equivalent areas A e The laboratory quantitative test specimens, the equivalent areas of each group of test specimens satisfy a preset proportional relationship; (2) Fracture tests were conducted on each group of specimens at different loading rates to obtain their corresponding peak loads. P max ; (3) Based on the equivalent area A e and the corresponding peak load P max The dynamic fracture toughness of the quasi-brittle material without size effect at the corresponding loading rate is simultaneously determined using the following solution model. K IC and dynamic tensile strength f t : ； ； In the formula, The characteristic crack length of the specimen. C cr The characteristic particle size is denoted as .

2. The determination method according to claim 1, characterized in that, The preset ratio is 2:

1.

3. The determining method according to claim 1 or 2, characterized in that, The equivalent area of ​​each group of specimens is calculated based on the following formula. A e : ； In the formula, W The height of the specimen. S The span of the specimen. B For the thickness of the specimen, For the seam height ratio, The characteristic crack length of the specimen. a e These are the geometric parameters of the specimen. This represents the virtual crack propagation amount of the specimen.

4. The determination method according to claim 3, characterized in that, The virtual crack propagation amount Δ a fic Determined by the following formula: ； In the formula, d av The average particle size of the aggregate; n The value for the aggregate expansion quantity; The empirical parameter calculation formula to take into account the effect of loading rate is as follows: ,in, The strain rate of the specimen. This is the reference value for the strain rate of the specimen.

5. The determination method according to claim 3, characterized in that, The The characteristic crack length is determined by the following formula: ； In the formula, C cr For concrete, the characteristic particle size is... C cr Take the average aggregate particle size d av .

6. The determining method according to claim 3, characterized in that, The geometric parameters a e Determined by the following formula: ； In the formula, For seam height ratio; Y ( ) represents the geometric shape factor; A ( ) represents the loading type parameter, and its expression is: .

7. A method for predicting the dynamic fracture behavior of quasi-brittle materials based on equivalent area, characterized in that, Includes the following steps: (1) Using the dynamic fracture toughness determined by any one of claims 1 to 6 K IC and dynamic tensile strength f t Constructing based on geometric structural parameters a e With characteristic crack length The ratio is shown on the x-axis, with nominal stress as the metric. The broken full curve is represented by the ordinate; (2) Calculate the geometric parameters of the actual structure to be predicted using the following formula. a e : ； In the formula, For seam height ratio; Y ( ) represents the geometric shape factor; A ( ) represents the loading type parameter, and its expression is: ; (3) The geometric parameters of the actual structure to be predicted a e Substitute the complete fracture curve into the value to predict the nominal stress at that loading rate. and fracture modes.

8. The prediction method according to claim 7, characterized in that, In step (1), the nominal stress Determined by the following formula: ； In the formula, W The height of the specimen. S The span of the specimen. B For the thickness of the specimen, For the seam height ratio, This represents the virtual crack propagation amount of the specimen.

9. The prediction method according to claim 7, characterized in that, In step (3), the fracture mode is determined based on the following characteristics: Nominal stress Corresponding to a e / In the region < 0.1, the fracture of the actual structure to be predicted is under the control of tensile strength; nominal stress Corresponding to a e / In the region > 10, the fracture toughness is controlled; nominal stress Corresponding to 0.1 < a e / If the value is less than 10, it is considered a quasi-brittle fracture region, where fracture is controlled by both tensile strength and fracture toughness.

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