CN105823686A - Method for measuring tensile strength and fracture toughness of cement mortar or concrete - Google Patents

Abstract

The invention discloses a method for simultaneously measuring the tensile strength and fracture toughness of cement mortar or concrete, including pouring test pieces, cutting out cracks, static loading and peak load recording, and calculating nominal strength <i>σ</i> _n , calculate the equivalent crack length <i>a</i> _e and other steps, and finally obtain the tensile strength <i>f</i> _t and fracture toughness <i> of cement mortar or concrete at the same time through regression analysis K</i> _IC . The method of the invention is simple in form, easy to operate in the test, has sufficient precision, and is easy to judge the rationality of the result. The tensile strength <i>f</i> _t and fracture toughness <i>K</i> _IC of cement mortar and concrete can be determined at the same time only from the peak load of small-sized specimens.

Description

Method for Simultaneous Determination of Tensile Strength and Fracture Toughness of Cement Mortar or Concrete

technical field

The invention relates to the technical field of civil engineering and hydraulic engineering material properties, in particular to a method for simultaneously measuring the tensile strength and fracture toughness of cement mortar or concrete.

Background technique

A large number of studies have shown that there is an obvious size effect on the strength and fracture toughness of cement mortar and concrete. To obtain real material parameters independent of the size of the specimen, it is necessary to cast a larger size specimen. Therefore, the test results of small-scale cement mortar specimens cannot be directly used to evaluate the real material properties of cement mortar and concrete.

At present, the tensile strength of cement mortar and concrete generally needs to be tested with axial tensile specimens, and the fabrication and testing of axial tensile specimens are relatively difficult. Due to the heterogeneity of cement mortar and concrete, even if the specimen can be geometrically centered, it often cannot be truly physically centered, thus forming an actual eccentric stress state.

On the other hand, for the test of the fracture toughness of cement mortar and concrete, according to the US ASTME399 standard, if the condition of linear elastic fracture mechanics is satisfied, the fracture toughness of the material without size effect is measured, and the thickness B of the sample is used, and the crack length a ₀ , The ligament size Wa ₀ must satisfy the following formula:

$\left.\begin{array}{c}\mathrm{<span\; class="notranslate">\; B</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right\}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 2.5</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; C</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

Among them, K _IC is the fracture toughness of the material, f _t is the tensile strength of the material. To determine the K _IC of cement mortar according to ASTM regulations, the size W of the test piece should generally reach about 500mm; while the size W of the concrete test piece should generally exceed 1000mm. If small-sized specimens are used, the size effect of parameters such as fracture toughness is unavoidable. How to determine the true fracture toughness of materials without size effect from small-sized specimens under elastic-plastic fracture conditions, such as (Wa ₀ )/d _max =3-10, is a scientific problem to be solved urgently.

In addition, in the fracture toughness test, there are strict restrictions on the type of specimen, loading fixture, loading method, and test system. Make the production cost of the test sample and the test workload increase greatly.

It should also be emphasized that different types of specimens and loading methods are currently used to determine the tensile strength and fracture toughness of cement mortars and concrete. However, the method of simultaneously determining the tensile strength and fracture toughness of cement mortar and concrete with the same test method and sample has not been reported yet.

Contents of the invention

At present, the determination of the tensile strength of cement mortar or concrete has high requirements for the test specimen and test system. On the other hand, the test specimen size required for the determination of the fracture toughness without size effect is very large, and it is difficult to complete the test under ordinary laboratory conditions. Such pouring and testing work. In order to overcome the deficiencies of the existing measuring methods, the present invention proposes a testing method that can simultaneously determine the tensile strength and fracture toughness of cement mortar or concrete.

In order to solve the problems of the technologies described above, the present invention adopts the following technical solutions:

Design a kind of method of measuring cement mortar or concrete tensile strength and fracture toughness simultaneously, it is characterized in that, comprises the following steps:

(1) According to the given cement mortar or concrete mix ratio requirements, pour a certain number of cement mortar or concrete three-point bending beam specimens with dimensions of W×B×L, where W is the height of the specimen and B is the specimen height. The thickness of the test piece, L is the effective length of the test piece, and the test piece satisfies L/W=2.5, 4 or 8;

(2) After curing the test piece obtained in step (1) to the specified age, use a cutting machine to cut out cracks on the test piece respectively. The length of the crack is a ₀ , and the slit height ratio of the test piece is α=a ₀ / W ranges from 0.02 to 0.75; select 5 to 8 specimens with different seam height ratios, and each seam height ratio corresponds to 3 to 5 specimens; the value method of the seam height ratio α of the specimens It is: random value within the range of 0.02 to 0.75, uniform distribution;

(3) On a common pressure testing machine or a universal testing machine, load according to the static loading test method and until the specimen is destroyed, record the peak load P _max of each specimen during the test;

(4) Calculate the nominal strength σ _n of each specimen based on the peak load of each specimen obtained in step (3);

(5) Calculate the equivalent crack length a _e of each specimen;

(6) Bring the different σ _n and a _e values obtained in step (4) and step (5) into the following formula (1) for regression analysis,

The tensile strength f _t and fracture toughness K _IC of cement mortar or concrete can be obtained simultaneously.

Preferably, in the step (2), the values of the slit height ratio α=a ₀ /W are 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7.

Preferably, in said step (4), the nominal strength σ _n of each test piece is calculated by the following formula (2),

In formula (2), W ₁ =Wa ₀ ; W ₂ =W ₁ -(γ·d _max ); W ₃ =W ₁ +(γ·d _max ); P _max is the measured peak load of each specimen; B is The thickness of the specimen; a ₀ is the initial crack length, γ·d _max is the initial crack expansion corresponding to the peak load P _max ; d _max is the maximum particle size of the aggregate.

Preferably, in said formula (2), when γ=1.0, the average value of cement mortar or concrete strength and toughness is calculated from a statistical point of view;

When γ = 0.2, 0.4, 0.6, 0.8...2.0, from the discrete point of view of the material properties of cement mortar or concrete, the exact value of the strength and toughness of cement mortar or concrete can be calculated.

Preferably, in the step (5), the equivalent crack length a _e of each test piece is calculated by the following formulas (3a) to (3d):

When L/W=2.5,

When L/W=4,

When L/W=8, Y(α)=1.106-1.552α+7.71α ² -13.53α ³ +14.23α ⁴

- Formula (3d).

The beneficial effects of the present invention are:

1. In the method of the present invention, small-sized samples are adopted, and the size of the test piece does not need to meet the strict requirement that the height, thickness, initial crack length, etc. of the test piece should be greater than a certain value under the condition of linear elastic fracture of existing norms.

2. The present invention adopts a sample and a test method to simultaneously determine the tensile strength and fracture toughness of cement mortar or concrete. It overcomes the need to use different types of samples and loading methods to determine the tensile strength and fracture toughness of cement mortar and concrete.

3. For the formation of the initial cracks in the fracture toughness test, it is only necessary to use a cutting machine to cut the cracks, instead of prefabricating the cracks when pouring the specimen. The difficulty of processing the cracks of the sample is greatly reduced, and the corresponding workload is reduced.

4. Considering the amount of crack growth corresponding to the peak load through the parameter γ·d _max , so that the dispersion of the overall test results can be accurately estimated, and the tensile strength and fracture toughness of a single specimen can be calculated, that is, the value γ is taken from a statistical point of view =1.0, the average value of the overall test can be calculated; when the tensile strength and fracture toughness of each specimen are accurately calculated, then γ can take values of 0.2, 0.4, 0.6, 0.8...2.0.

5. The method of the present invention is simple in form, easy to operate in the test, has sufficient precision, and is easy to judge the rationality of the result. This method only needs to determine the tensile strength f _t and fracture toughness K _IC of cement mortar simultaneously from the peak load of a small-sized specimen. It is not necessary to meet the strict regulations on the size, type and loading conditions of test specimens in current domestic and foreign standards.

Description of drawings

Fig. 1 is the stress distribution figure when the specimen shape of the present invention and peak load;

Figure 2 is a schematic diagram of the value of λ·d _max : among them, Figure 2a shows the value when γ=1.0 in a statistical sense; Figure 2b shows the exact value when γ=0.2, 0.4, 0.6, 0.8...2.0;

Fig. 3 is the schematic diagram of tensile strength and fracture toughness of cement mortar determined by the regression of test data in Example 1: wherein, Fig. 3a is the tensile strength and fracture toughness of the first series of test pieces L * B * W = 400 * 50 * 100mm Toughness; Figure 3b is the tensile strength and fracture toughness of the second series of test pieces L×B×W=240×50×60mm;

Fig. 4 is a schematic diagram of concrete tensile strength and fracture toughness determined by regression of test data in Example 2.

detailed description

The specific implementation of the present invention will be described below in conjunction with the accompanying drawings and examples, but the following examples are only used to describe the present invention in detail, and do not limit the scope of the present invention in any way. Some of the steps or methods involved in the following examples are conventional methods in the art unless otherwise specified, and the materials and equipment involved are conventional materials and equipment unless otherwise specified.

First, according to the given cement mortar mix ratio, 15 to 40 concrete mortar or concrete three-point bending beam specimens with dimensions of W×B×L are poured, where W is the height of the specimen and B is the thickness of the specimen , L is the effective length of the specimen, and the specimen satisfies L/W=2.5, 4 or 8. Under the premise of meeting the test accuracy requirements of the testing machine and other supporting measuring instruments, the size W of the test piece can be small enough.

After curing the above test pieces to the required age, use a cutting machine to cut out cracks on the test pieces respectively. The length of the cracks is a ₀ , and the slit height ratio of the test pieces α=a ₀ /W is in the range of 0.02 to 0.75 Inner value; select 5 to 8 specimens with different seam height ratios, and each seam height ratio corresponds to 3 to 5 specimens.

Example 1: The maximum particle size of the cement mortar aggregate used in the test of Example 1 is d _max =2.5mm. There are two series: the first series L×B×W=400×50×100mm, initial seam height ratio α=a ₀ /W=0.03～0.72, W/d _max =40. The second series L×B×W=240×50×60mm, initial seam height ratio α=a ₀ /W=0.04～0.68, W/d _max =24.

Referring to Fig. 1, considering that cement mortar is a quasi-brittle material, the stress distribution at peak load is shown in Fig. 1, and the corresponding crack extension Δa _fic = γ·d _max . Based on the following formula (2), the nominal strength σ _n of each specimen can be calculated from the measured peak load P _max :

Considering γ=1.0 from a statistical point of view, the average value of tensile strength and fracture toughness of cement mortar can be calculated, see Figure 2a. Considering the discretization of the cement mortar test results and solving it accurately, γ=0.2, 0.4, 0.6, 0.8...2.0 can be used to calculate the exact values of the tensile strength and fracture toughness of the cement mortar, see Figure 2b.

The equivalent crack length a _e of each specimen can be calculated by the following formulas (3a)~(3d):

When L/W=2.5,

When L/W=4,

When L/W=8, Y(α)=1.106-1.552α+7.71α ² -13.53α ³ +14.23α ⁴

- Formula (3d).

After obtaining different σ _n and a _e , put them into the formula (1) for regression analysis, and the tensile strength f _t and fracture toughness K _IC of cement mortar can be obtained at the same time:

The results of the cement mortar tensile strength and fracture toughness determined by the regression of test data in Example 1 are shown in Fig. 3, wherein Fig. 3a shows the tensile strength and fracture toughness of the first series of test pieces L×B×W=400×50×100mm Degree; Figure 3b shows the tensile strength and fracture toughness of the second series of test pieces L×B×W=240×50×60mm. The determined tensile strength and fracture toughness data of cement mortar are shown in Table 1 below.

The cement mortar tensile strength and fracture toughness that table 1 embodiment 1 determines

It can be seen that, from a statistical point of view, when γ=1.0, the tensile strength and fracture toughness of cement mortar can be consistent with the average value measured in the test. If the discreteness of each different specimen in the test is considered, then γ=0.6,0.8...2.0.

Example 2: The maximum particle size of the concrete aggregate used in the test of Example 2 is d _max =19mm. The size of the test piece is L×B×W=1143×76.2×305mm, the initial seam height ratio α=a ₀ /W=0.36～0.68, W/d _max =16.

The stress distribution of the specimen at the peak load is shown in Fig. 1, and the corresponding crack growth Δa _fic = γ·d _max . Based on formula (2), the nominal strength σ _n of each specimen can be calculated from the measured peak load.

Considering γ=1.0 from a statistical point of view, the average value of concrete tensile strength and fracture toughness can be calculated. Considering the discretization of the concrete test results and solving it accurately, then make γ=0.6,0.8...2.0, and calculate the exact values of concrete tensile strength and fracture toughness.

The equivalent crack length a _e of each specimen can be calculated by formulas (3a)~(3d).

After obtaining different σ _n and a _e , put them into formula (1) for regression analysis, and then obtain the tensile strength f _t and fracture toughness K _IC of concrete at the same time. The formulas (1), formula (2), and formulas (3a) to (3d) referred to in the embodiment (2) are the same as those in the embodiment 1.

Referring to Fig. 4, it is the results of concrete tensile strength and fracture toughness determined by regression of test data in Example 2. The specific data of the determined concrete tensile strength and fracture toughness are shown in Table 2 below.

The concrete tensile strength and fracture toughness that table 2 embodiment 2 determines

gamma f _t /MPa K _IC /MPa m ^1/2 0.2 7.00 1.26 0.4 5.84 1.32 0.6 5.13 1.38 0.8 4.55 1.49 1.0 4.10 1.63 1.2 3.73 1.91

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Many modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. a method for measuring cement mortar or concrete tensile strength and fracture toughness simultaneously, is characterized in that, comprises the following steps: (1) According to the given cement mortar or concrete mix ratio requirements, pour a certain number of cement mortar or concrete three-point bending beam specimens with dimensions of W×B×L, where W is the height of the specimen and B is the specimen height. The thickness of the test piece, L is the effective length of the test piece, and the test piece satisfies L/W=2.5, 4 or 8; (2) After curing the test piece obtained in step (1) to the specified age, use a cutting machine to cut out cracks on the test piece respectively. The length of the crack is a ₀ , and the slit height ratio of the test piece is α=a ₀ / W ranges from 0.02 to 0.75; select 5 to 8 specimens with different seam height ratios, and each seam height ratio corresponds to 3 to 5 specimens; (3) On a common pressure testing machine or a universal testing machine, load according to the static loading test method and until the specimen is destroyed, record the peak load P _max of each specimen during the test; (4) Calculate the nominal strength σ _n of each specimen based on the peak load of each specimen obtained in step (3); (5) Calculate the equivalent crack length a _e of each specimen; (6) Bring the different σ _n and a _e values obtained in step (4) and step (5) into the following formula (1) for regression analysis, The tensile strength f _t and fracture toughness K _IC of cement mortar or concrete can be obtained simultaneously. 2. the method for simultaneously measuring cement mortar or concrete tensile strength and fracture toughness according to claim 1, is characterized in that, in described step (2), described seam height ratio α=a ₀ /W The values are 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7. 3. the method for simultaneously measuring cement mortar or concrete tensile strength and fracture toughness according to claim 1, is characterized in that, in described step (4), calculates each specimen by following formula (2) The nominal strength σ _n of In formula (2), W ₁ =Wa ₀ ; W ₂ =W ₁ -(γ·d _max ); W ₃ =W ₁ +(γ·d _max ); P _max is the measured peak load of each specimen; B is The thickness of the specimen; a ₀ is the initial crack length, γ·d _max is the initial crack expansion corresponding to the peak load P _max ; d _max is the maximum particle size of the aggregate. 4. the method for simultaneously measuring cement mortar or concrete tensile strength and fracture toughness according to claim 3, is characterized in that, in described formula (2), when γ=1.0, calculate from statistical point of view The average value of cement mortar or concrete strength and toughness; When γ = 0.2, 0.4, 0.6, 0.8...2.0, from the discrete point of view of the material properties of cement mortar or concrete, the exact value of the strength and toughness of cement mortar or concrete can be calculated. 5. the method for measuring cement mortar or concrete tensile strength and fracture toughness simultaneously according to claim 1, is characterized in that, in described step (5), the equivalent crack length a of each test _piece is by The following equations (3a) ~ (3d) calculation: When L/W=2.5, When L/W=4, When L/W=8, Y(α)=1.106-1.552α+7.71α ² -13.53α ³ +14.23α ⁴ - Formula (3d); In the above formula, a ₀ is the initial fracture length; α is the fracture height ratio; Y(α) is the geometric influence parameter. 6. The method for simultaneously measuring cement mortar or concrete tensile strength and fracture toughness according to claim 1, characterized in that, in the step (1), the number of poured specimens is 15 to 40.