A method for measuring the tensile strain at the bottom of a small beam based on four-point bending fatigue test

Abstract

The present invention discloses a method for measuring the tensile strain of the bottom of a small beam based on a four-point bending fatigue test, comprising: installing a small beam specimen in a four-point bending fatigue loading device of a universal testing machine, installing three displacement sensors on the upper surface of the small beam specimen in sequence, obtaining the vertical deflection of the small beam at the inner clamp by using the displacement sensors at both ends, obtaining the vertical deflection of the small beam at the mid-span by using the middle displacement sensor, making a difference between the two deflection values, and calculating the horizontal tensile strain of the bottom of the beam at the mid-span position of the small beam by using the deflection difference. The present invention eliminates the calculation error caused by the shear force between the two inner clamps by adopting the deflection difference method, and then uses the deflection difference to reversely calculate the horizontal tensile strain of the bottom of the small beam at the mid-span position, optimizes the strain calculation process and error, and makes the bending modulus calculation result more accurate; directly laying the displacement sensor at the mid-span position increases the measurement accuracy, and simultaneously measuring the deflection at the inner clamp by taking the average of two measured values, greatly reducing the measurement error.

Description

Technical Field

[0001] The invention relates to the field of road engineering materials, and in particular to a method for measuring the tensile strain of a small beam bottom based on a four-point bending fatigue test. Background Art

[0002] Fatigue is the phenomenon that materials crack or break under cyclic loads. In order to study the fatigue failure process mechanism, fatigue mechanical properties and evaluate the fatigue life of engineering structures, it is necessary to test the fatigue fracture performance of material samples. Due to the reasonable force and the actual road conditions, the four-point bending fatigue test has become the first choice for asphalt mixture beam fatigue testing.

[0003] The core of fatigue test is to establish fatigue model, in which the calculation of modulus is indispensable. The bending modulus of existing beams is calculated by stress / strain. Stress and strain need to be calculated by material mechanics. The influence of shear force is not considered in the strain calculation process. In the process of four-point bending fatigue test of asphalt mixture beams using universal material testing machine UTM, when load is applied, ideally, the mid-span position of the beam is in pure bending state, with only bending moment but no shear force. However, in actual situation, there is shear force between the two inner clamps. Therefore, the deflection of the beam between the two inner clamps includes both bending deflection and constant shear deflection. The deflection currently measured regards the total deflection as the deflection caused by bending stress only, which makes the calculated deflection value too large. In addition, due to the limitation of the matching clamps of the existing universal material testing machine, the mid-span deflection currently measured can only measure the deflection at the outer 1 / 6 position of the beam, and then use the deflection value at this position to inversely calculate the mid-span displacement. Due to factors such as uneven deformation of the beam material during bending, the calculation results have large errors. Summary of the invention

[0004] Purpose of the invention: In view of the above problems, the purpose of the present invention is to provide a method for measuring the tensile strain at the bottom of a small beam based on a four-point bending fatigue test. The vertical deflection difference is measured by three displacement sensors arranged at different positions, and the horizontal tensile strain is inversely calculated by changing the deflection measurement position and measuring the deflection difference, so that the tensile strain calculation is more accurate.

[0005] Technical solution: A method for measuring the tensile strain at the bottom of a small beam based on a four-point bending fatigue test of the present invention comprises: installing a small beam specimen in a four-point bending fatigue loading device of a universal testing machine, installing three displacement sensors in sequence on the upper surface of the small beam specimen, obtaining the vertical deflection of the small beam at the inner fixture using the displacement sensors at both ends, obtaining the vertical deflection at the mid-span of the small beam using the middle displacement sensor, subtracting the two deflection values, and calculating the horizontal tensile strain at the bottom of the beam at the mid-span position of the small beam using the deflection difference.

[0006] Furthermore, the second displacement sensor among the three displacement sensors is installed at the mid-span position on the upper surface of the small beam specimen, the first and third displacement sensors are symmetrically arranged on both sides of the second displacement sensor, the first and third displacement sensors are arranged on the inner sides of the two inner clamps, and the three displacement sensors fully contact the upper surface of the small beam.

[0007] Furthermore, using the displacement sensors at both ends to obtain the vertical deflection of the small beam at the inner clamp includes: using the first displacement sensor to measure the vertical deflection at the first inner clamp, using the third displacement sensor to measure the vertical deflection at the second inner clamp, and taking the average of the two deflection values ​​as the vertical deflection at the inner clamp.

[0008] Furthermore, the first displacement sensor is arranged close to the first inner fixture, and the distance between the two ranges from 1 to 2 centimeters.

[0009] Furthermore, the calculation of the horizontal tensile strain at the bottom of the beam at the mid-span position of the small beam using the deflection difference includes:

[0010] When the beam is subjected to four-point bending, the bending deflection between the inner clamp and the mid-span is expressed as:

[0011]

[0012] In the formula, F represents the concentrated load force, E represents the elastic modulus, I represents the moment of inertia, A represents the distance between adjacent clamps, A=l / 3; x represents the distance from any point of the beam specimen to the first outer clamp, and the first outer clamp is regarded as the position origin; l represents the distance between the two outer clamps, that is, the span of the beam;

[0013] Since the shear deflection cancels out, the deflection difference is the difference between the two bending deflections, which is substituted into the bending deflection formula:

[0014]

[0015] Where V represents the sum of shear deflection and bending deflection; L represents the length of the beam specimen, and L / 2 represents the mid-span position of the beam;

[0016] The expression of the mid-span bending deflection of the beam is:

[0017]

[0018] Where ε is the horizontal tensile strain at the bottom of the beam, and h is the height of the beam;

[0019] The horizontal tensile strain at the bottom of the beam is calculated by using the relationship between the deflection difference and the bending deflection at the mid-span position of the beam. The expression is:

[0020]

[0021] make Then the horizontal tensile strain expression of the bottom of the small beam in the above formula is:

[0022]

[0023] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0024] 1. The present invention adopts the method of deflection difference to eliminate the calculation error caused by the shear force between the two inner clamps, and then uses the deflection difference to reversely calculate the horizontal tensile strain at the bottom of the small beam in the span, optimizes the strain calculation process and error, and makes the bending modulus calculation result more accurate;

[0025] 2. The present invention directly lays the displacement sensor at the mid-span position to increase the measurement accuracy, and simultaneously measures the deflection at the inner fixture by taking the average of two measured values, thereby greatly reducing the measurement error. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the structure of the four-point bending fatigue test of asphalt mixture;

[0027] Figure 2 This is the main view of the position of each component of the test;

[0028] Figure 3 This is a schematic diagram of the deflection difference measurement in the test;

[0029] Figure 4 This is the modulus-load action number curve. DETAILED DESCRIPTION

[0030] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0031] The method described in this embodiment is a method for measuring the tensile strain at the bottom of a small beam based on a four-point bending fatigue test, comprising: installing the small beam specimen in a four-point bending fatigue loading device of a universal testing machine, installing three displacement sensors in sequence on the upper surface of the small beam specimen, using the displacement sensors at both ends to obtain the vertical deflection of the small beam at the inner clamp, using the middle displacement sensor to obtain the vertical deflection at the mid-span of the small beam, subtracting the two deflection values, and using the deflection difference to calculate the horizontal tensile strain at the bottom of the beam at the mid-span position of the small beam.

[0032] The preparation process of the small beam specimen used in this embodiment is as follows: using the wheel rolling molding experimental method, AC20 asphalt mixture is molded into a 300*400*70mm rutting plate, and after demolding and standing for a period of time, it is cut into four 380*65*50mm small beam specimens 1. After curing at 15℃ for 4 hours, it is installed in the UTM four-point bending fatigue loading device and fully aligned. A total of four fixtures are loaded on the small beam specimen 1, and the distances between adjacent fixtures are the same, such as Figure 1-2As shown, from left to right are the first outer fixture 2, the first inner fixture, the second inner fixture, and the second outer fixture. A displacement sensor bearing beam 3 is arranged above the displacement sensor, a load sensor is fixed on each fixture, and a load bearing plate is arranged below the load sensor.

[0033] The three displacement sensors are arranged on the upper surface of the beam specimen 1 from left to right, the second displacement sensor is installed at the mid-span position of the upper surface of the beam specimen 1, the first and third load bearing plates 6 are symmetrically arranged on both sides of the second displacement sensor, the first and third load bearing plates 6 are arranged on the inner side of the two inner clamps, and the three displacement sensors fully contact the upper surface of the beam, so that the reading of the displacement sensor is close to zero, otherwise the measured vertical deflection will be inaccurate. The first displacement sensor is arranged close to the first inner clamp, and the distance between the two is in the range of 1-2 cm; the third load bearing plate 6 is arranged close to the second inner clamp, and the distance between the two is in the range of 1-2 cm. If the distance is too close to the inner clamp, a large clamping deformation will occur, and if the distance is too far, the accuracy will be affected. In this embodiment, the test effect is more accurate within the range of 1-2 cm.

[0034] After placing the beam specimen 1 in the UTM four-point bending fatigue loading device, the 10Hz partial sine controlled strain loading method is selected to load the beam specimen 1. During the loading process, the magnitude of the applied force is controlled by the load sensor 4, and the load bearing plate 5 contacts the beam specimen 1. The displacement sensor is fixed on the load-bearing beam and laid at a specified position. 50 preloads are used, and the modulus of the 50th loading cycle is calculated as the initial modulus. The calculation method uses bending stress / bending strain, and finally the modulus-load action number curve is obtained, as shown in Figure 4 The curve shown.

[0035] Using the displacement sensors at both ends to obtain the vertical deflection of the small beam at the inner fixture includes: using the first displacement sensor to measure the vertical deflection at the first inner fixture, using the third load bearing plate 6 to measure the vertical deflection at the second inner fixture, and taking the average of the two deflection values ​​as the vertical deflection at the inner fixture, such as Figure 3 As shown, the expression is:

[0036]

[0037] Where Δ A1 , Δ A2 , Δ L / 2 Represent the two deflections measured at the inner fixture and the mid-span deflection respectively.

[0038] The calculation of the horizontal tensile strain at the bottom of the beam at the mid-span of the small beam using the deflection difference includes:

[0039] When the beam is subjected to four-point bending, the bending deflection between the inner clamp and the mid-span is expressed as:

[0040]

[0041] In the formula, F represents the load concentration force, E represents the elastic modulus, I represents the moment of inertia, A represents the distance between adjacent clamps, A=l / 3; x represents the distance from any point of the beam specimen to the first outer clamp, and the first outer clamp is regarded as the position origin; l represents the distance between the two outer clamps, that is, the span of the beam. Since the shear deflection between the two inner clamps is consistent and constant, the deflection effect caused by the shear stress can be eliminated by using this embodiment, and then the relationship between the difference in the bending deflection between the two and the mid-span bending deflection can be obtained according to the material mechanics formula, and then the calculation formula of the mid-span strain can be obtained.

[0042] Since the shear deflection cancels out, the deflection difference is the difference between the two bending deflections, which is substituted into the bending deflection formula:

[0043]

[0044] Where V is the sum of shear deflection and bending deflection; L is the length of the beam specimen, and L / 2 is the mid-span position of the beam.

[0045] The expression of the mid-span bending deflection of the beam is:

[0046]

[0047] Where ε is the horizontal tensile strain at the bottom of the beam, and h is the height of the beam;

[0048] The horizontal tensile strain at the bottom of the beam is calculated by using the relationship between the deflection difference and the bending deflection at the mid-span position of the beam. The expression is:

[0049]

[0050] make Then the horizontal tensile strain expression of the bottom of the small beam in the above formula is:

[0051]

[0052] Where C is a fixed coefficient. Each time the deflection difference is measured by the displacement sensor, the horizontal tensile strain value at the bottom of the beam can be directly calculated using the above formula.

[0053] In the calculation of horizontal tensile strain of four-point bending beams of asphalt mixtures, the existing technical tests back-calculate the horizontal tensile strain through the mid-span deflection, and the deflection values ​​used include bending deflection and shear deflection. This method eliminates the influence of shear force by taking the deflection difference method, and then back-calculates the horizontal tensile strain at the bottom of the mid-span beam, thereby optimizing the strain calculation and making the bending modulus calculation more accurate.

[0054] In the calculation of horizontal tensile strain of four-point bending beams of asphalt mixture, the existing technology uses the deflection measured at the outer 1 / 6 point to back-calculate the mid-span deflection in the test, which causes a large error. The present method directly lays the sensor at the mid-span to increase the measurement accuracy, and at the same time measures the deflection at the inner fixture by taking the average of two measured values, which greatly reduces the measurement error.

Claims

1. A method for measuring the tensile strain at the bottom of a small beam based on a four-point bending fatigue test, characterized in that: include: The small beam specimen is installed in the four-point bending fatigue loading device of the universal testing machine, and three displacement sensors are installed on the upper surface of the small beam specimen in sequence. The displacement sensors at both ends are used to obtain the vertical deflection of the small beam at the inner fixture, and the middle displacement sensor is used to obtain the vertical deflection of the small beam in the middle span. The two deflection values ​​are subtracted, and the horizontal tensile strain of the bottom of the beam at the mid-span position of the small beam is calculated using the deflection difference. The calculation of the horizontal tensile strain at the bottom of the beam at the mid-span of the small beam using the deflection difference includes: When the beam is subjected to four-point bending, the bending deflection between the inner clamp and the mid-span is expressed as: In the formula, F represents the concentrated load force, E represents the elastic modulus, I represents the moment of inertia, A represents the distance between adjacent clamps, A=l / 3; x represents the distance from any point of the beam specimen to the first outer clamp, and the first outer clamp is regarded as the position origin; l represents the distance between the two outer clamps, that is, the span of the beam; Since the shear deflection cancels out, the deflection difference is the difference between the two bending deflections, which is substituted into the bending deflection formula: Where V represents the sum of shear deflection and bending deflection; L represents the length of the beam specimen, and L / 2 represents the mid-span position of the beam; The expression of the mid-span bending deflection of the beam is: Where ε is the horizontal tensile strain at the bottom of the beam, and h is the height of the beam; The horizontal tensile strain at the bottom of the beam is calculated by using the relationship between the deflection difference and the bending deflection at the mid-span position of the beam. The expression is: make Then the horizontal tensile strain expression of the bottom of the small beam in the above formula is:

2. The method for measuring the tensile strain at the bottom of a small beam according to claim 1, characterized in that: The second displacement sensor of the three displacement sensors is installed at the mid-span position on the upper surface of the small beam specimen, the first and third displacement sensors are symmetrically arranged on both sides of the second displacement sensor, the first and third displacement sensors are arranged on the inner sides of the two inner clamps, and the three displacement sensors fully contact the upper surface of the small beam.

3. The method for measuring the tensile strain at the bottom of a small beam according to claim 2, characterized in that: Using the displacement sensors at both ends to obtain the vertical deflection of the small beam at the inner clamp includes: using the first displacement sensor to measure the vertical deflection at the first inner clamp, using the third displacement sensor to measure the vertical deflection at the second inner clamp, and taking the average of the two deflection values ​​as the vertical deflection at the inner clamp.

4. The method for measuring the tensile strain at the bottom of a small beam according to claim 3, characterized in that: The first displacement sensor is arranged close to the first inner fixture, and the distance between the two is in the range of 1-2 cm.

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