A calculation method for tear strength of coated fabric membrane materials for construction

Abstract

The present invention provides a method for calculating the tear strength of coated fabric membrane materials for construction. First, a relationship formula between the slit length and the tear strength of the membrane material is established based on a relevant theoretical model, and the relationship formula includes the unknown parameter critical strain energy release rate of the membrane material; then a central tear test of the membrane material is performed, and the critical strain energy release rate of the membrane material is calculated according to the area of ​​the sawtooth fluctuation parallelogram in the descending section of the tear load-displacement curve; finally, the critical strain energy release rate of the membrane material obtained by actual measurement is substituted into the relationship formula to realize the calculation of the tear strength value of the membrane material under any slit length. The tear strength value of any initial slit length can be directly calculated by the present invention without the need for a large number of experiments, which is more convenient for the evaluation of the tear resistance performance of the membrane material and the design of the membrane structure, saving time and effort, and can be used in the evaluation of the tear strength of the membrane material and the design of the membrane structure.

Description

Technical Field

[0001] The invention belongs to the technical field of deep foundation pit construction, and in particular relates to a method for calculating the tear strength of a coating fabric membrane material for construction. Background Art

[0002] Membrane structure is a structure that uses architectural membrane as the main load-bearing component. After decades of rapid development, it has become a vibrant new member of the large family of space structures. With the rapid development of membrane structures at home and abroad, its damage accidents also occur from time to time. Membrane structure is a soft structure, and most of the damage is caused by heavy snow or strong wind. A series of studies on large-scale damage to membrane structures found that although the local stress on the membrane surface exceeded the design value of the material strength during the damage, its value was only half of the tensile strength. They were all because the local tear of the membrane material expanded to the overall damage. For general fabric membrane materials, its tear resistance is far worse than its tensile resistance. The possible damage of broken wires, cracks, holes and creases in the membrane material during use causes the membrane material to produce stress concentration under excessive snow load and wind load, resulting in tearing, and the tearing expansion causes the overall damage of the membrane surface. Tearing failure is a major form of damage for flexible composite materials, and its tear strength is closely related to the length of damage such as the slit on its surface. At present, when conducting research in this area, a large number of tests need to be carried out to obtain the tear strength values ​​under different slit lengths, which is time-consuming, labor-intensive and inconvenient. Based on the above problems, the present invention designs a method for calculating the tear strength of architectural coated fabric membranes based on analytical formulas and tear tests. A more direct and simple method is used to establish a formula for the relationship between the tear strength of membranes and the slit length, which is applied to the evaluation of the tear resistance of membranes and the design of membrane structures. Summary of the invention

[0003] In view of the deficiencies in the prior art, the present invention provides a method for calculating the tear strength of coated fabric membrane materials for construction. The tear strength value for any initial slit length can be directly calculated without the need for a large number of tests, thereby facilitating the evaluation of the tear resistance performance of membrane materials and the design of membrane structures.

[0004] The present invention achieves the above technical objectives through the following technical means.

[0005] A method for calculating the tear strength of a coated fabric membrane material for construction includes the following steps:

[0006] Step 1: Obtain the relevant parameter data of the membrane material and input it into the integrated management system. The calculation unit of the integrated management system establishes a relationship formula between the membrane material slit length and the tear strength based on the relevant theoretical model and stores it in the storage unit. The relationship formula includes the unknown parameter critical strain energy release rate of the membrane material;

[0007] Step 2: The technicians conduct a center tear test on the membrane material to obtain the load-displacement curve. According to the area of ​​the sawtooth-shaped fluctuation parallelogram in the descending section of the load-displacement curve at the stable stage, the measured value of the critical strain energy release rate of the membrane material is calculated and input into the integrated management system;

[0008] Step 3: The calculation unit of the integrated management system receives the measured value of the critical strain energy release rate obtained in step 2 and substitutes it into the relationship formula of step 1 to calculate the tear strength value of the membrane material under any slit length, and visualizes the calculated value through the display unit for real-time viewing by technical personnel.

[0009] Furthermore, the principle of obtaining the relational formula in step 1 is as follows:

[0010] According to Griffith's energy balance principle, the strain energy U released by the fabric membrane due to the existence of the slit is e The surface energy U that is completely converted into the cut s , the energy balance is expressed as follows:

[0011]

[0012] in:

[0013] U s =2a·t·2γ (2)

[0014] Combining formula (1) and (2), we get:

[0015]

[0016] In the formula, γ represents the surface energy per unit crack surface, t represents the thickness of the film material, a represents the half length of the cut, 2γt represents the internal properties of the film material, and the critical strain energy release rate G is used. IC To express, as follows:

[0017]

[0018] At the moment of tear propagation, the strain energy released is equal to the external work W done to close the slit to the initial state, and its calculation formula is:

[0019]

[0020] In the formula, σ c is the tear strength; v(x) is the displacement of the slit surface relative to the initial closed state at the moment of tear extension;

[0021] Combined with the Hedgepeth model, W is calculated: First, convert equation (5) into the calculation form at the yarn level:

[0022]

[0023] Where n c represents the number of cut yarns, m represents the serial number of cut yarns, P0 represents the axial force of the yarn at the clamping end; V m (0) represents the axial displacement value of the yarn on the section where the cut is located; then transform equation (6) into the following form:

[0024]

[0025] Where, E is the elastic modulus of the membrane in the direction of external load, G xy is its shear modulus; n is the number of yarns in the tensile direction within the unit width of the specimen;

[0026] Substituting formula (7) into formula (4), we can finally obtain the tear strength value σ of the film material under any slit length 2a: c Its critical strain energy release rate G IC The relationship formula is:

[0027]

[0028] Furthermore, in step 2, The parallelogram area refers to the area of ​​the sawtooth fluctuation parallelogram in the descending section of the stable phase of the load-displacement curve obtained in the center tear test.

[0029] The present invention has the following beneficial effects:

[0030] The present invention adopts a more direct and simple method to establish a relationship formula between the tear strength of the membrane material and the slit length. The tear strength value for any initial slit length can be directly calculated without the need for a large number of tests. This makes it more convenient to evaluate the tear resistance of the membrane material and design the membrane structure, saving time and effort. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a schematic diagram of the Minami model;

[0032] Figure 2 The typical load-displacement curve and parallelogram diagram of center tearing;

[0033] Figure 3 It is a schematic diagram of parallelogram analysis;

[0034] Figure 4 Schematic diagram of the critical strain energy release rate of the unknown parameter of the film material calculated based on the parallelogram area in the center tear test in Example 2. DETAILED DESCRIPTION

[0035] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0036] Embodiment 1:

[0037] The method for calculating the tear strength of the architectural coated fabric membrane material of the present invention comprises the following steps:

[0038] Step 1: Obtain the relevant parameter data of the membrane material and input it into the integrated management system. The calculation unit of the integrated management system establishes the relationship between the membrane material slit length 2a and the tear strength σ based on the relevant theoretical model. c The relationship formula is stored in the storage unit, and the relationship formula contains the unknown parameter critical strain energy release rate G of the film material. IC ; The specific principle of obtaining the relationship formula is as follows:

[0039] According to Griffith's energy balance principle, the strain energy U released by the fabric membrane due to the existence of the slit (the slit length is set to 2a in this embodiment) is e will be completely converted into the surface energy U of the cut s , the energy balance is expressed as follows:

[0040]

[0041] When γ is used to represent the surface energy of a unit crack surface, then U s It is expressed as:

[0042] U s =2a·t·2γ (2)

[0043] Where, t represents the thickness of the film;

[0044] Combining formula (1) and (2), we can get:

[0045]

[0046] Where a represents the half length of the cut, 2γt represents the internal properties of the membrane, and the critical strain energy release rate G IC To express:

[0047]

[0048] For the moment of tear propagation, Minami believes that the strain energy released is equal to the external work W done to close the cut to the initial state, and its calculation formula is:

[0049]

[0050] In the formula, σ cis the clamping end stress value at the moment of tear propagation, that is, the tear strength; v(x) is the displacement value of the slit surface relative to the initial closed state at the moment of tear propagation, such as Figure 1 As shown;

[0051] Combined with the Hedgepeth model, the external work W is calculated as:

[0052] First, convert formula (5) into the calculation form of yarn level:

[0053]

[0054] Where n c represents the number of cut yarns, m represents the serial number of cut yarns, and P0 represents the axial force of the yarn at the clamping end. Because the tear propagation moment is investigated, P0 divided by the yarn spacing is equal to the tear strength value σ c ; V m (0) represents the axial displacement of the yarn on the section where the cut is located. Combined with the Hedgepeth model, formula (6) is finally transformed into the following form:

[0055]

[0056] Where, E is the elastic modulus of the membrane in the direction of external load, G xy is its shear modulus, which can be measured through tensile test and shear test of membrane material; n is the number of yarns in the tensile direction within the unit width of the sample.

[0057] Substituting formula (7) into formula (4), we can finally obtain the tear strength value σ of the film material under any slit length 2a: c Its critical strain energy release rate G IC The relationship formula is:

[0058]

[0059] Step 2: Measure G IC :Technical personnel conduct a center tear test on the membrane material to obtain the load-displacement curve. Based on the area of ​​the sawtooth-shaped parallelogram in the descending section of the load-displacement curve, the critical strain energy release rate G of the membrane material is calculated. IC values ​​and input them into the integrated management system.

[0060] Among them, the descending section of the load-displacement curve of the membrane center tear test will have clear and regular sawtooth fluctuations.

[0061] Reference Figure 2 This is the unique property of coated fabric membranes that distinguishes them from commonly used building materials such as steel and concrete: when the yarns break one by one, the tearing and propagation are very regular.

[0062] Figure 3 The enlarged partial image of the representative sawtooth fluctuation is shown. The use of straight line segments to depict this fluctuation does not cause a large error. In simple terms, the characteristics of the center tear can be described as when the external load rises to point A, the first yarn at the edge of the triangle area at the tip of the cut will reach the breaking elongation and break. Almost at the same time, the tear begins to expand and is accompanied by instantaneous unloading, and the corresponding load-displacement curve drops to point B; then, as the remaining yarns continue to bear the load, a new tear triangle will form, and the load-displacement curve will also rise to point C. According to this process, a sawtooth path P1 is formed: I→A→B→C→J; on the other hand, assuming that the yarn continues to bear the load without breaking after point A, the load-displacement curve also reaches point C, and a path P2 can be imagined: I→A→D→C→J. Obviously, the difference between paths P1 and P2 comes from the breakage of a single yarn; the extension line of IA and the extension line of JC are compared to point D. Assuming that IA∥BC and AB∥CJ, the quadrilateral ABCD is a parallelogram.

[0063] From the energy point of view, the area enclosed by the load-displacement curve and the horizontal axis is the strain energy stored in the specimen; therefore, it can be considered that the energy release represented by the approximate parallelogram area ΔS is the result of breaking a single yarn and is used to form a new crack surface in the yarn. Undoubtedly, this is an approximate conclusion, because ΔS inevitably contains a certain amount of plastic strain energy and kinetic energy, which are all ignored in this study. Obviously, the value of ΔS divided by the newly formed crack area (the crack area is numerically equal to the yarn spacing multiplied by the film thickness) is equal to the required critical strain energy release rate G IC The value of .

[0064] Step 3: The computing unit of the integrated management system receives the G measured in step 2 IC The value is substituted into analytical formula (8) to calculate the tear strength value of the membrane material under any slit length, and the calculated value is visualized through the display unit for real-time viewing by technicians. It can be used in the evaluation of the tear strength of membrane materials and the design of membrane structures without the need to conduct a large number of membrane tear tests as in traditional methods.

[0065] Embodiment 2:

[0066] This paper describes a type of P membrane material based on polyvinyl chloride (PVC) coated polyester fiber, which is commonly used in architectural membrane materials. Its thickness is 0.83mm, the weaving method is plain weave, and the density is 1050g / m 2 The weaving densities in warp and weft directions are 6.3 strands / cm and 6.4 strands / cm respectively.

[0067] (1) First, according to the "Technical Regulations for Membrane Structure Testing" DGT J08-2019-2007, the longitudinal tensile modulus E = 684N / mm 2 and shear modulus G xy =46N / mm 2 , n = 0.63 root / mm, substituting into formula (8) to obtain:

[0068]

[0069] (2) The central tear test was used to obtain Figure 2 The load-displacement curve shown in FIG. 1 shows that the sawtooth fluctuation in the initial descending section is relatively stable, which means that the corresponding parallelogram area value also remains approximately constant; subsequently, as the slit continues to expand, when the number of intact yarns remaining on the cross section where the slit is located is insufficient to form a complete triangular area, the shape of the sawtooth fluctuation begins to decay, resulting in a smaller and smaller parallelogram area; the two stages discussed above can be defined as a stable stage and a decaying stage, respectively; in the decaying stage, although the unloading amount from point A to point B does not change much, the further load-bearing capacity from point B to point C becomes weaker and weaker, resulting in a gradual decrease in the value of ΔS until the specimen is completely destroyed; therefore, in order to reduce the impact of the decaying stage, 1 / 3 of the number of intact yarns on the cross section where the slit is located is usually taken as the standard value to determine the range of the stable stage; finally, the parallelogram area in the stable stage is divided by the yarn spacing and the membrane thickness to obtain the corresponding critical strain energy release rate G IC value.

[0070] This embodiment also conducts a series of center tear tests based on the "Technical Specifications for Membrane Structure Testing" DGT J08-2019-2007 to test the measured G IC The stability of the value was studied, and the test variables were the clamping distance L of the sample, the stretching speed v, the initial number of cut yarns n c and the total number of yarns in the width direction of the sample n t , the parameters were changed by controlling the variables, each test was repeated twice, and L was set to 100 mm. G was calculated by the area of ​​all parallelograms in the stable stage of the test. IC The values ​​are summarized in Table 1 and Figure 4 In the table, the results are mapped by test number.

[0071] From the results of the chart, we can see that the G obtained based on the parallelogram area method of the center tear test IC Although the value has a certain degree of discreteness, it is relatively less affected by deformation energy and kinetic energy because it does not change with the variables L and n related to deformation energy. c and the variable v related to kinetic energy; more importantly, the obtained G ICThe value is not affected by n c The values ​​represent a significant influence of the slit length, which is a significant feature of the internal parameters of the coated fabric membrane.

[0072] Calculate G for all different parameters of the center tear test IC The mean value and standard deviation of the longitudinal G are shown in Table 2. IC The average value is 88N / mm, and the standard deviation is about 19.3N / mm. The discreteness of the test results is attributed to the fact that different yarns in the fabric are affected by various factors such as weaving process, sample preparation, test method and coating, which show certain differences. Finally, G IC The value was determined to be 88 N / mm.

[0073] Table 1 G calculated based on the center tear test IC Value Summary Table

[0074]

[0075]

[0076] Table 2 Calculated G IC Statistical results

[0077]

[0078] (3) G IC =88N / mm Substituting into formula (9) we can get the tear strength value of the membrane material under any slit length:

[0079]

[0080] This formula can be used to evaluate the tear strength of this type of P membrane material and design membrane structures.

[0081] The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims

1. A method for calculating the tear strength of a coated fabric membrane material for construction, characterized in that: The process includes the following: Step 1: Obtain the relevant parameter data of the membrane material and input it into the integrated management system. The calculation unit of the integrated management system establishes a relationship formula between the membrane material slit length and the tear strength based on the relevant theoretical model and stores it in the storage unit. The relationship formula includes the unknown parameter critical strain energy release rate of the membrane material; Step 2: The technicians conduct a center tear test on the membrane material to obtain the load-displacement curve. According to the area of ​​the sawtooth-shaped fluctuation parallelogram in the descending section of the load-displacement curve at the stable stage, the measured value of the critical strain energy release rate of the membrane material is calculated and input into the integrated management system; Step 3: The calculation unit of the integrated management system receives the measured value of the critical strain energy release rate obtained in step 2 and substitutes it into the relational formula of step 1 to calculate the tear strength value of the membrane material under any slit length, and visualizes the calculated value through the display unit for real-time viewing by the technicians; The relationship formula in step 1 is: Among them, σ c is the tear strength value, G IC is the critical strain energy release rate, E is the elastic modulus of the membrane in the direction of external load, G xy is its shear modulus, 2a is the slit length, and n is the number of yarns in the tensile direction within the unit width of the specimen; In the step 2, ； The parallelogram area refers to the area of ​​the sawtooth fluctuation parallelogram in the descending section of the stable phase of the load-displacement curve obtained in the center tear test.

2. The method for calculating the tear strength of a coated fabric membrane material for construction according to claim 1, characterized in that: The principle of obtaining the relationship formula in step 1 is as follows: According to Griffith's energy balance principle, the strain energy U released by the fabric membrane due to the existence of the slit is e The surface energy U that is completely converted into the cut s , the energy balance is expressed as follows: （1） in: （2） Combining formula (1) and (2), we get: （3） In the formula, γ represents the surface energy per unit crack surface, t represents the thickness of the film material, a represents the half length of the cut, 2γt represents the internal properties of the film material, and the critical strain energy release rate G is used. IC To express, as follows: （4） At the moment of tear propagation, the strain energy released is equal to the external work W done to close the slit to the initial state, and its calculation formula is: （5） In the formula, σ c is tear strength; v ( x ) is the displacement value of the slit surface relative to the initial closed state at the moment of tear propagation; Combined with the Hedgepeth model, W is calculated: First, convert equation (5) into the calculation form at the yarn level: （6） Where n c represents the number of cut yarns, m represents the serial number of cut yarns, P0 represents the axial force of the yarn at the clamping end; V m (0) represents the axial displacement value of the yarn on the section where the cut is located; Formula (6) is converted into the following form: （7） Where, E is the elastic modulus of the membrane in the direction of external load, G xy is its shear modulus; n is the number of yarns in the tensile direction within the unit width of the specimen; Substituting formula (7) into formula (4), we can finally obtain the tear strength value σ of the film material under any slit length 2a: c Its critical strain energy release rate G IC The relationship formula is: （8）。

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