JP3770844B2 - Simple biaxial property measurement method for plain woven fabric - Google Patents

Description

[0001]
【Technical field】
The present invention relates to a method for simply measuring an elastic modulus when a tensile force is applied to a plain woven fabric in both the warp and weft directions using a uniaxial tensile tester.
[0002]
[Prior art and its problems]
For example, film structures such as bellows, diaphragms, and tents are made of a composite material in which a plain woven fabric as a reinforcing material is embedded in a rubber base material made of low elastic modulus rubber. Since the elastic modulus ratio between the plain woven fabric and the rubber material is different by 10 ³ to 10 ⁴ , the properties of the membrane structure are dominated by the properties of the plain woven fabric. Therefore, the analysis of the characteristics of the plain woven fabric is indispensable for the analysis of the characteristics when the membrane structure is subjected to pressure and is in a multiaxial stress state.
[0003]
The characteristics of the plain woven fabric are desirably measured in a biaxial stress state (stress ratio of 1: 1) in which a tensile force is applied to each of the warp and the weft. However, the biaxial testing machine is not only large and expensive, but also the test method itself is difficult.
[0004]
OBJECT OF THE INVENTION
An object of the present invention is to obtain a method for measuring an elastic modulus at an arbitrary stress ratio in a biaxial stress state of a plain woven fabric using a simple uniaxial tensile tester.
[0005]
SUMMARY OF THE INVENTION
In the method of the present invention, a plain woven fabric specimen having warp and weft is pulled in the warp direction in a plurality of different restraint states with different degrees of restraint in the weft direction, and the relationship between strain and elastic modulus at each restraint is obtained. 1st step; 2nd step which calculates | requires the relationship between the said restraint degree in the center part and the stress ratio of a warp and a weft based on the finite element method; and each restraint degree calculated | required by the 1st step A third step for determining the relationship between the stress ratio and the elastic modulus at each strain from the relationship between the strain and the elastic modulus and the relationship between the strain and the stress ratio at each degree of restraint determined in the second step. It is said. According to this method, the elastic modulus when the stress ratio between the warp and the weft is 1: 1, that is, the elastic coefficient of the plain woven fabric in the biaxial stress state can be obtained.
[0006]
DETAILED DESCRIPTION OF THE INVENTION
The present invention will be described based on specific examples.
"First step"
1 to 4 show a state in which a plain woven fabric test piece TP is pulled in the warp direction while varying the degree of restraint in the weft direction using a uniaxial tensile tester. The uniaxial tensile tester is a tester that linearly moves a pair of cross heads (chucks) 11 holding both ends of a plain woven fabric test piece TP in a direction away from each other. The moving direction of the cross head 11 and the warp direction X of the plain woven fabric test piece TP coincide with each other. FIG. 1 shows a tensile state when the weft restraint degree r = 0 (when the weft thread is not restrained at all). In this uniaxial tension state, the plain woven fabric test piece TP extends in the load direction (warp direction X) and contracts in the weft direction Y orthogonal to the warp direction X.
[0007]
2 and 3 show a state (constraint degree r = 1) in which the shrinkage of all the fibers in the weft direction Y of the plain woven fabric test piece TP is restrained in the uniaxial tension state of FIG. Both ends of the yarn in the weft direction Y of the plain woven fabric test piece TP are bonded to one longitudinal restraint plate 12, and both ends of the pair of longitudinal restraint plates 12 are supported by the cross head 11. The distance between the pair of vertical restraint plates 12 is fixed. This tensile state is equivalent to applying a strain equal to the lateral strain generated in the uniaxial stress state in the weft direction Y, and the plain woven fabric test piece TP is in the biaxial stress state. However, in this state, the stress ratio between the warp and the weft is only 1: ν (Poisson's ratio). The present embodiment proposes a method for measuring the elastic modulus of a plain woven fabric test piece TP in a biaxial stress state with a stress ratio of 1: 1 while using a uniaxial tensile tester.
[0008]
FIG. 4 shows a specific example in which the degree of restraint in the weft direction Y of the plain woven fabric test piece TP is varied. Between the pair of cross heads 11, a plurality of (more preferable) lateral restraint plates 13 in the weft direction Y are positioned at equal intervals as much as possible. In the bonding areas 13 a at both ends of the lateral restraint plates 13, Both ends of the yarn in the weft direction Y of the plain woven fabric test piece TP are bonded. When the total length in the warp direction X of the bonding area 13a by the lateral restraint plate 13 is Σp, and the total length in the warp direction X of the plain woven fabric test piece TP not restrained by the lateral restraint plate 13 is Σq, Σp / (Σq + Σp ) Is the degree of restraint r. The fibers in the weft direction Y bonded to the bonding area 13a of the lateral restraint plate 13 cannot be shrunk. Making the degree of restraint different means making the number and total width of the lateral restraint plates 13 different. The method of changing the degree of restraint using the lateral restraint plate 13 is not strict, but in this measurement method, a sufficient degree of pseudo restraint can be obtained if necessary.
[0009]
A specific example of the plain woven fabric specimen TP is cut out from the plain woven fabric with a constant width (for example, 45 mm), and the same number of warps from both ends so that the number of warps is a constant (for example, 70, width 25 mm) The both ends of the wefts that have been removed and separated are used as bonding portions to the bonding area 13 a of the lateral restraint plate 13.
[0010]
FIG. 5 shows the stress at each degree of restraint obtained by conducting a simple biaxial extension test with the number of samples n = 3 for five kinds of restraint degrees r = 0, 0.25, 0.5, 0.63 and 1. -Strain diagram. The strain was calculated as the strain in the load direction from the moving distance of the crosshead 11. The stress is defined as a load value per fiber bundle. From this graph, it is recognized that the stress value of the warp is remarkably increased as the degree of restraint of the weft is increased.
[0011]
FIG. 6 is a graph in which the test result of FIG. 5 is replaced with an elastic coefficient-strain relationship at each degree of constraint. That is, by dividing the stress by the strain, the relationship between the strain and the elastic modulus is obtained for each degree of constraint. From this graph, in the region where the strain is as small as less than 1%, there is a sudden change in the elastic modulus of the plain woven fabric specimen TP, and there is a need to investigate the behavior by obtaining the elastic modulus in the biaxial stress state. I can reason. It is also necessary to consider the strain dependence of the elastic modulus.
[0012]
"Second step"
As described above, the elastic modulus that can be obtained by the above analysis is up to the state where the stress ratio is 1: ν (Poisson's ratio), and the plain weave when the stress ratio is 1: 1 and the stress ratio is 1: 1. The elastic modulus of the cloth test piece TP cannot be obtained. Therefore, in the second step, the relationship between the degree of restraint of the plain woven fabric test piece TP and the stress ratio is obtained based on the finite element method. In the finite element method, a plain woven fabric specimen TP was treated as an orthotropic material, and a two-dimensional plane stress analysis was performed in consideration of material nonlinearity of the fabric. FIG. 7 is a conceptual diagram thereof, in which the left end (end portion in the warp direction) of the test piece model TP is completely restrained, and a forced displacement in the warp direction X is given to the right end. The upper and lower ends restrained only the weft direction Y. The degree of restraint r was defined by the ratio of the total number of nodes at the free ends of both ends in the weft direction Y of a small element (finite element) divided into rectangles to the number of restrained nodes. The Poisson's ratio ν of the plain woven fabric test piece TP was ν = 0.41, and the elastic modulus E was given the value shown in FIG. 6 according to the strain increment.
[0013]
In the central part of this analytical specimen model TP, no restraint effect is observed. FIG. 8 is a graph showing the relationship between the stress ratio and the degree of restraint at the center of the analytical specimen model TP by the finite element method when the Poisson's ratio ν = 0.41. It can be seen that the stress ratio when the constraint degree r = 1 converges to the Poisson's ratio ν = 0.41.
[0014]
"Third step"
In the third step, the elastic modulus-strain relationship at each degree of restraint obtained in the first step above is combined with the relation between the degree of restraint obtained in the second step and the stress ratio, and the degree of restraint is excluded from the parameters. The relationship between the stress ratio in strain and the elastic modulus is obtained. FIG. 9 is a graph thereof. The maximum stress ratio obtained in the actual measurement of the first step is 1: ν (Poisson's ratio), but by extrapolating the stress ratio-constraint relationship obtained in the second step, the stress ratio The elastic modulus of the plain woven fabric test piece TP when the ratio is 1: 1 can be obtained for each strain.
[0015]
In the above embodiment, the transverse restraint plate 13 is used to vary the degree of restraint of the weft of the plain woven fabric test piece TP. Instead, a pair of longitudinal restraint plates having a number of clips arranged in the warp direction are used. Even if the both ends of the weft are selectively restrained with respect to the large number of clips, the degree of restraint of the weft can be made different. FIG. 10 is a schematic view of this type of testing machine that is commercially available. A number of clip members 21 are movably supported by a pair of tension direction guides 20 provided parallel to the tension direction. A clip 21 a for holding the weft of the plain woven fabric test piece TP is provided at the tip of 21. Both ends in the warp direction X of the plain woven fabric test piece TP are held by the cross head 11 and given a tensile force. In this testing machine, the restraint degree r can be changed by the number and interval of the clip members 21.
[0016]
【The invention's effect】
As described above, according to the present invention, the elastic modulus at an arbitrary stress ratio in the biaxial stress state of the plain woven fabric can be easily measured using the uniaxial tensile tester.
[Brief description of the drawings]
FIG. 1 is a conceptual perspective view of a state in which a plain woven fabric test piece is pulled at a constraint degree r = 0 by a uniaxial tensile tester.
FIG. 2 is a conceptual perspective view of a state of pulling at the same constraint degree r = 1.
3 is a conceptual cross-sectional view taken along line III-III in FIG.
FIG. 4 is a conceptual plan view when pulling with different degrees of restriction.
FIG. 5 is a graph showing examples of measurement results of stress-strain relationships at different degrees of constraint.
6 is a graph obtained by converting the result of FIG. 5 into an elastic coefficient-strain relationship at each degree of constraint.
FIG. 7 is a plan view for explaining the degree of restraint by a finite element method on a plain woven fabric test piece.
FIG. 8 is a graph showing the relationship between the degree of restraint of a plain woven fabric test piece and the stress ratio obtained by the finite element method.
9 is a graph showing the relationship between the elastic modulus-stress ratio for each strain obtained from the results of FIGS. 6 and 8. FIG.
FIG. 10 is a conceptual diagram showing an example of another tensile tester for plain woven fabric test pieces.
[Explanation of symbols]
TP plain weave test piece X Warp direction Y Weft direction

Claims (2)

A first step in which a plain woven fabric specimen having warp and weft is pulled in the warp direction in a plurality of different restrained states with different degrees of restraint in the weft direction, and the relationship between strain and elastic modulus at each restraint is obtained;
Based on the finite element method, a second step for determining the relationship between the degree of restraint and the stress ratio between the warp and the weft in the central portion of the plain woven fabric specimen; and each of the steps determined in the first step A third step for determining the relationship between the stress ratio and the elastic modulus at each strain from the relationship between the strain and the elastic modulus in the degree of constraint and the relationship between each degree of constraint and the stress ratio obtained in the second step;
A simple biaxial property measuring method for plain woven fabrics, comprising: 2. The simple biaxial characteristic measuring method according to claim 1, wherein, in the third step, the plain woven fabric is obtained by obtaining an elastic coefficient when the stress ratio between the warp and the weft is 1: 1.

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