JP2003247198A - Calculation method for theoretical tensile strength of nonwoven fabric - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a calculation method that can quantitatively predict the mechanical properties in relation to the whole sheets of a non-woven fabric, thus individual constitutional elements are optimized on the basis of the method whereby the theoretic structure design of the nonwoven fabric and the production method of the nonwoven fabric can be optimized by comparing the theoretical values with the practical values. <P>SOLUTION: An intersectional possibility of one fiber crossing the other fibers is theoretically calculated to assume a model of the transmission of force through the individual cross sections and to calculate the vectors on the individual cross sections whereby the theoretical tensile strength of the nonwoven fabric is calculated. When necessary, the invalid cross section points near the surface are theoretically calculated and the effect is taken into the consideration or calculated or a possibility of the breakage with a certain force is taken into consideration for calculation. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a nonwoven fabric composed of fibers and a binder. Nonwoven fabrics are widely used for printed boards, various boards for building materials, filters, battery separators and the like.

[0002]

2. Description of the Related Art Nonwoven fabrics can be roughly classified into wet type and dry type, and the fibers to be used range widely from organic fibers such as olefin and aramid to inorganic fibers such as glass and ceramics. These non-woven fabrics are manufactured and used in various industrial fields, and are actually used for various purposes.

Nonwoven fabrics are manufactured in such a manner that various elements such as strength, density, thickness, and air permeability are brought close to the purpose in accordance with the usage form and required characteristics. For example, it is an effective means to consider the blending of fibers as a material, to optimize the size of fibers, and to improve the density and strength by a compression operation after forming a sheet.

However, in order to actually develop a non-woven fabric for a certain purpose by such a method, an experimental non-woven fabric is experimentally produced, and while the various properties are measured, the fiber mixture ratio,
At present, the method of determining the optimum value of each element such as the fiber diameter, the fiber length and the compression rate is taken.

Therefore, in order to obtain the target non-woven fabric, there is a possibility that the range of each element should be considered and the range of the experiment should be performed. I had to rely on my experience and intuition.

At the same time, with regard to the portion that has not been acquired as a know-how, it is necessary to search for an unknown non-woven fabric structure on the basis of qualitative inference based on the conventional way of thinking. Therefore, it is unavoidable that the time and energy required for development are always largely divided.

Further, when the new structure of the non-woven fabric is developed by relying on the above method, there is an adverse effect that the search range tends to fall into a predictable range to some extent. Fiber length, fiber diameter,
If a certain combination of elements such as density is not common sense, it is likely to be overlooked at the time of the idea, even if it brings a characteristic that has not been known until now.

[0008] To give specific examples, a non-woven fabric having a high strength while having a very high density, a non-woven fabric having an extremely low density and a bulkiness as compared with a non-woven fabric having the same basis weight, and a non-woven fabric having strength and maintaining a low density. Regarding how to make structure, etc., what kind of true density material is used, fiber length,
A more efficient way of thinking is required in selecting a multidimensional optimum value such as how to set each element such as fiber diameter, apparent density of non-woven fabric, binding force between fibers, basis weight, aspect ratio, etc. .

Therefore, if it is possible to quantitatively obtain the optimum values that meet the purpose of each of these elements by some theoretical calculation rather than the conventional prediction based on empirical common sense,
Not only is it possible to design non-woven fabrics much faster than experimentally confirmed, it not only speeds up development, but also designs non-woven fabrics with new characteristics by combining elements that have never been anticipated. It will be possible.

[0010]

The object of the present invention is to provide a theory by which the mechanical properties of a sheet having a non-woven fabric structure can be quantitatively predicted, and by optimizing each component based on the theory, The purpose is to make theoretical structure design of non-woven fabric possible.

[0011]

The present inventor has calculated the total intersection area by using the geometric stochastic intersection theory to model the nonwoven structure in order to enable numerical treatment of the nonwoven structure. This problem was solved by defining a stress transfer route and introducing a fracture condition.

The theory of the present invention will be described in detail below. If the radius of the fibers that make up the nonwoven fabric is rμm, then the cross-sectional area = πr ² (1) If the fiber length L (mm) and the fiber specific gravity d (g / cm ³ ), then the volume of one fiber = πr ² × L × 10 ³ (μm ³ ) ... (2) The weight of one fiber is m = πr ² × L × d × 10 ³ (g) (3).

The intersection probability in the XY direction of one fiber is P _XY
Then, the intersection theory of Kallmes and others (O.Kallmes and H.Cor
te; Tappi. September 1960 Vol.43, No.9),

[Formula 19]

[Equation 20] Here, the sheet area A (m ² ), the average number of intersection points c (pieces), the total number of fibers N (pieces), and the intersection point probability P for one fiber are shown. However, from a mathematical point of view, the formula devised by Kallmes et al.
It seems that the one-dimensional geometric stochastic consideration by the mathematician of the century Buffon about the probability of intersection of a long line segment on a plane and a short line segment randomly drawn around it has been applied to two dimensions.

The apparent thickness of a sheet of Mitsubo M (g / m ² ) is T
(μm), the apparent density G is

[Equation 21] On the other hand, considering the relationship between the bulkiness and the fiber axial ratio,

[Equation 22] Here, the fiber axial ratio means the ratio of the diameter of the fiber to the length (L / 2r) and is considered to be an element that influences the degree of freedom of rotation of the fiber. Therefore, the bulk height is linked to the fiber axial ratio. It is thought to change. From (6) and (7),

[Equation 23] Here, k ₁ is a constant peculiar to a certain fiber material and needs to be obtained in advance by actual measurement. The apparent density is generally expected to be smaller as the fiber length is longer, but the present inventor has found through experimentation that the formula (7) can be specifically applied. By applying this, the thickness can be theoretically calculated by the equation (8).

Assuming that the probability of actual fiber contact at one XY intersection is the intersection probability P _{Z in the} Z direction, FIG.
Than,

[Equation 24] Therefore, the intersection probability P is from (4) and (9),

[Equation 25] The assumption that the equation (9) is assumed from the figure is an idea found by the present inventors, and by this, the intersection probability can be expressed by a simple equation composed only of the fiber diameter, the fiber length, and the thickness. .

When the fiber orientation aspect ratio = τ and the area s of one intersection at the average fiber intersection angle is calculated,

[Equation 26] Can be expressed. FIG. 2 illustrates this equation.

The number N of fibers in the sheet 1 (m ² ) of M (g / m ² ) is
From (3),

[Equation 27] Therefore, the average value c of the number of intersections for one fiber is (5), (1
From (0) and (12),

[Equation 28] Therefore, the ideal total number of intersections C in the sheet is

[Equation 29]

However, in reality, since P _Z changes in the thickness direction as shown in FIG. 3, the number of intersections tends to decrease near the surface layer. In FIG. 1, it is the area of the surface layer 2r where the formation of the intersection is restricted, but since the actual sheet does not have such ideal packing, the bulkiness is taken into consideration in the same manner as the expression (6). There is a need. Therefore, if the number of decreasing intersections is the number of invalid intersections C _inval ,

[Equation 30] The formula (15) is the formula (8) for theoretically obtaining the thickness.
It is obtained by using the constant k₃Is the constant k₁Same as
It has the meaning like this, and it is obtained in advance by actual measurement. As well
Empirically obtained correction factor peculiar to a certain fiber system
C multiplied by C _invalAlso good. Also, the actual thickness
When giving it as a measured value or a given value, the following equation (15 ') is used.
You may use it instead of Formula (15).

[Equation 31] Thus, the calculation of the number of invalid intersections in the vicinity of the surface from FIG. 3 and the consideration of the bulkiness in that case are important assumptions first introduced by the present inventor.

Therefore, the number of effective intersections C _val is

[Equation 32] Therefore, the realistic total sheet intersection area S is

[Expression 33] It is represented by. In the above, if the sheet thickness is thick,
C _val = C may be used, but when the sheet is thin, it is preferable to use the equation (16) in consideration of the decrease in the intersection probability near the surface layer.

A fiber orientation aspect ratio τ is defined as a parameter representing the fiber orientation. In FIG. 4, when the fiber exists on the hypotenuse L, it corresponds to τ = L _Y / L _X. At this time, in the fiber of average crossing angle,

[Equation 34] The average intersection distance (small el) of one fiber is l ＝ L /
If c, then the Y-direction component l _Y can be expressed by the following equation (19). In the mathematical formula, l is displayed in italics.

[Equation 35]

Consider a transmission path of force f as shown in FIG. In this model, it is assumed that each fiber has an average orientation angle τ and that a defect occurs at an intersection of each fiber with a certain probability. The number of fibers from the sheet end surface to the distance E is N
Assuming (E), from equation (12),

[Equation 36] Is. Here, the number of fibers is the number of fiber center points in the range.

Therefore, the number Ne of fibers appearing on the end face of the sheet
(Book)

[Equation 37] Can be expressed as

In order to transmit the force over the span h (mm), n
Because the transmission of steps is necessary,

[Equation 38]

In each transmission process, the average stress applied to the intersections is defined as the average intersection stress f _A (kgf / piece). At this time
If you think like

[Formula 39] Can be disassembled as Here, the decomposition vector has the following properties. f _F : The force along the fiber, the tensile shear strength of the fiber with respect to the bond point f _C : The force related to rotational failure of the bond point, which is proportional to l / L according to the principle of leverage, and this force is the torsional shear strength f When _{R, f R = (l /} L) f C = f C / c and expressed. Therefore, from FIG.

[Formula 40] However, f _AF component which can be decomposed into f _F of f _A, f _AC is a component that can be decomposed into f _C of f _A.

From the definition,

[Formula 41] Where B _F is the binder tensile shear strength (kgf / cm ² ), B _F
R is the binder torsional shear strength (kgf / cm ² ). therefore,

[Equation 42] The binder tensile shear strength B _F is the strength at which the bond breaks when one fiber is pulled straight when considering two fibers that are bonded orthogonally at an intersection with an intersection area s. It is the strength converted into a unit area. The binder torsional shear strength B _R is the strength at which the bonded portion is destroyed by rotating one of them along the surface formed by two bonded fibers in the same bonding model. Therefore, it is necessary to determine these values in advance by actual measurement.

From the above definitions, the values of B _F and B _R are values including cohesive failure of the binder resin and interfacial failure at the interface between the binder resin and the fiber, and are specific to a certain fiber-binder system. It is a value.

There can be various mechanical methods for measuring the tensile shear strength B _F and the torsional shear strength B _R , but in the fracture mechanics, the accuracy of quantitative conversion can be improved by changing the size of the fracture surface or the scale of the load. It is preferable to consider the view that it decreases. That is, the present inventor prepares long fibers having the same fiber diameter as the actual product, attaches the binder resin in a microdroplet shape in the same size as when it is present in an actual nonwoven fabric, and loads it when pulling it out. The tensile shear strength was obtained by the method of measuring. Similarly, a binder resin was attached in the form of macro droplets at the intersections of two intersecting fibers, and the torsional shear strength was measured by rotating the fibers in the same plane. As described above, it is important for the present invention to model the state of force transmission through the intersections and to calculate the tensile strength of the sheet in consideration of the two-component vectors of the tensile strength and the shear strength of the binder and the fiber. This is a hypothesis and was first attempted by the present inventor.

When considering the transmission of force, the number of transmission stages affects the strength of one transmission route. Considering the population based on the normal distribution as shown in Fig. 7 where the number of break points at force f is n (f), the maximum load stress of one transfer route depends on the weakest point of the intersection, so the break condition Is

[Equation 43] Here, f _B is an intersection breaking stress (kgf / piece).

If the fracture probability at f is P (f), then n (f) = n P (f) and the probability density at that time is Q (f).
If the fracture probability at (f) and f _B is P (f _b ), consider as shown in FIG.

[Equation 44] Where σ is the standard deviation of n (f). Therefore, (27),
By finding f _B that satisfies the fracture condition from (28),

[Equation 45]

In the above equation (29), σ is obtained by actually measuring the strength. Thus, in a system of a fibrous material and a binder material, measured by 'to previously obtain the k ₄ of (29 below (29)' may be used).

[Equation 46] f _A means an ideal theoretical strength when an ideal break occurs in a homogeneous sheet having the same strength at every intersection, and f _B means that the strength of the intersection has a variation based on a normal distribution. It means the practical strength in consideration of the probability of breakage due to the weakest force at the weakest point.

By the way, from (21) and (22), the total number of intersections = Ne ×
n, the ideal total number of intersections = C from (14),

[Equation 47] Therefore, the modeling of the intersection points in the sheet is valid. That is, the intersection point theory of equations (1) to (17) and (1
Equation (30) is a combination of the force transmission theory of Equations 8) to (29).

However, it is necessary to take the number of effective intersections into consideration in the transmission of force. Replacing the number of effective intersections with the effective force transmission route, from (30),

[Equation 48] Here, Ne _val is an effective transmission route (book).

Therefore, the sheet breaking stress F _B (kgf) for measuring the span h and the test width w is obtained as follows.

[Equation 49]

In the above description, the most accurate theoretical value is
The value of f _B is calculated by using the equation (29), and C _Val is (15)
It is a theoretical value when calculated by the equation (16). This is the theoretical value 1. C _Val is relatively simple (15)
It is calculated by the equation (16), and f _B without using the equation (29)
= F _A calculated. This is the theoretical value 2. Non-woven fabric actually manufactured by a machine has a strength considerably lower than the theoretical value. The main cause is that the adhesion distribution to the fiber of the binder is not uniform, the fiber is not oriented in an ideal dispersion normal state, but as other causes, binding fiber, shot, the presence of broken fibers,
It is conceivable that the binder has bubbles and the contact area with the fiber is not sufficient.

When a sample is prepared experimentally by hand rather than by an actual papermaking machine, defective fibers are removed,
Since it is possible to eliminate defects in the adhesion between the binder and the fibers by applying a sufficient time and temperature for drying, the measured value is close to the theoretical value. For example, if prepared carefully enough, the measured value can be 90% or more (preferably 95% or more) of the theoretical value 1 and 80% or more (preferably 85% or more) of the theoretical value 2. Therefore, even in an actual papermaking machine, if the above-mentioned defects are eliminated, it is possible to obtain a measured strength close to that of handmade paper. In such a state, it is considered that the original performance possessed by the fibers and the binder material was exhibited. In this sense, by comparing the theoretical value of the present invention with the actual measured value, it becomes possible to judge whether or not the original performance of the material is exerted, and not only the selection of the material but also the improvement of the papermaking conditions, etc. Information is also available.

[0036]

EXAMPLES Next, the present invention will be specifically described according to the following examples.

<Example 1> E glass glass fiber chopped strands (manufactured by Nippon Electric Glass Co., Ltd., fiber diameter φ)
9 μm, φ13 μm, fiber length 3, 6, 9, 12, 18,
24 mm 2) was made into a sheet by a wet method of 90% by mass (relative to non-woven fabric). At this time, the fiber orientation aspect ratio was adjusted to 1. Next, an acrylate resin binder and γ-aminopropyltrimethoxysilane were added in an effective component mass ratio of 99:
The binder solution mixed in 1 was prepared, and sprayed onto this sheet by a spray method so that the effective solid content relative to the non-woven fabric was 10% by mass, dried and cured at 170 ° C for 2 hours to obtain a non-woven fabric with a basis weight of 50 g / m ^2. It was For this nonwoven fabric, the change in strength (kgf / 15 mm) with respect to the change in fiber length was compared with the theoretical value (Table 1).

[0038] Note that the theoretical value 1 in Table 1 was calculated using the values of f _B (29) equation, C _{V al} is (15) (1
It is a theoretical value when calculated by the equation (6). The theoretical value 2 is similar to that, but without using the equation (29), f _B
= F _A.

The apparent density (g
The change in / cm ³ ) was compared with the theoretical value (Table 2).

In the calculation of the theoretical value, the fiber specific gravity d = 2.54 (g
/ cm ³ ), binder specific drawing strength BF = 240 (kgf / cm ² ),
Binder specific rotational strength B _R = 120 (kgf / cm ² ), intersection break standard deviation σ = 0.00005 (pieces), fiber orientation ratio (aspect ratio) τ =
1.0, tensile test piece width w = 15 (mm), tensile span h = 100 (m
m).

[0041]

[Table 1]

[0042]

[Table 2]

[0043]

The theoretically predicted value derived from the theory of the nonwoven fabric structure of the present invention substantially agrees with the actually measured value obtained experimentally, and it was confirmed that its mechanical properties can be quantitatively predicted. . Therefore, by optimizing each component based on this theory, it became possible to design the theoretical structure of the nonwoven fabric.

[Brief description of drawings]

FIG. 1 is a schematic cross-sectional view of a nonwoven fabric.

FIG. 2 is a schematic diagram showing an intersection area where two fibers intersect.

FIG. 3 is a schematic diagram of changes in the Z direction intersection probability P _{Z in} the thickness direction.

FIG. 4 is a schematic diagram showing a fiber orientation aspect ratio.

FIG. 5 is a schematic diagram showing a force transmission model.

FIG. 6 is a schematic diagram showing force vectors.

FIG. 7 is a distribution chart of the number of break points n (f) at force f.

FIG. 8 is a diagram showing a relationship between probability density Q (f) and fracture probability P (f _b ).

Claims (8)

[Claims] 1. A non-woven fabric comprising fibers and a binder
In the calculation method of theoretical tensile strength,
Theoretical Tensile Strength Calculation of Nonwoven Fabrics characterized by using
Method. [Equation 1] However, in the above equation (32), F_BIs theoretical tensile strength
Degree, Ne_ValIs an effective transmission route (book), f_BIs the breaking stress at the intersection
(Kgf / piece), w represents the tensile test width (mm), respectively.
Equation (32) is calculated from the following equations. That is, (3
In the formula 2), Ne_ValIs calculated from equation (31), and (3
The n of the equation (1) is obtained from the equation (22), and the l of the equation (22) is obtained. _yIs
It is obtained from the equation (19). C in the equation (19) is the equation (5)
P of equation (5) was obtained from equation (4) and equation (9).
It is obtained by the equation (10), and N is obtained by the equation (12). Well
In addition, f in equation (32)_BIs f in equation (26)_AIs equal to
Rui is calculated from equation (29) or equation (29 ').
From the equation (11), s of the equation (26) is the same as that of the above.
It is obtained from the equation (5). C in equation (31)_ValIs the expression (14)
Equal to C or calculated from Eqs. (15) and (16)
Whether it is calculated from equations (15 ') and (16), or
It is a value obtained by multiplying C in the equation (14) by a correction coefficient. [Equation 2] [Equation 3] [Equation 4] [Equation 5] [Equation 6] [Equation 7] [Equation 8] [Equation 9] [Equation 10] [Equation 11] [Equation 12] [Equation 13] [Equation 14] [Equation 15] [Equation 16] [Equation 17] However, the above formula group is 1m non-woven fabric²Based on per calculation
Fiber radius r (μm), fiber length L (mm), fiber ratio
Heavy d (g / cm³), Average number of fiber intersections c (pieces), total number of fibers N
(Book), sheet tsubo M (g / m²), Apparent sheet thickness T (μ
m), apparent density G, fiber XY intersection probability P_XY, Z intersection of fibers
Probability P_Z, Fiber intersection probability P, fiber orientation aspect ratio = τ, average
Area of one intersection at fiber crossing angle s (μm^Two), In the sheet
Ideal total number of intersections C (pieces), number of invalid intersections C_inval(Pieces), valid exchange
Score C_val(Pieces), total sheet intersection area S (μm²), Seat edge
The force is transmitted through the number of fibers Ne that appear in
Number of steps n (steps), force transmission distance per step l_y(mm), each biography
Average intersection stress f at the intersection of reaching process_A (kgf / piece), buy
Under tensile shear strength B_F(kgf / cm²), Binder
Shear strength B_R(kgf / cm²), Crossing fracture stress f_B (kgf /
), Effective transmission route Ne_val(Book), tensile test width w (mm),
Sheet breaking stress F_B (kgf) Also, k₁, K₃, K_FourIs constant
It is a number and can be obtained by actual measurement or empirically determined from the actual measured value.
Set. Also, in equation (29), one force transmission route
N (f), where n (f) is the number of break points
Let σ be the standard deviation of. 2. The apparent thickness T (μm) of the sheet is calculated by the following equation (8) and the values are calculated as (10), (14),
It is used for each expression of (15), Claim 1 characterized by the above-mentioned.
The method for calculating the theoretical tensile strength of a nonwoven fabric according to. [Equation 18] However, k ₁ is a constant and is determined based on actual measurement. 3. The method for calculating theoretical tensile strength of a non-woven fabric according to claim 1, wherein C _{Val in the} equation (31) is obtained from the equations (15) and (16). 4. The method for calculating theoretical tensile strength of a non-woven fabric according to claim 1, wherein C _{Val in the} equation (31) is obtained from the equations (15 ′) and (16). 5. The method for calculating theoretical tensile strength of a non-woven fabric according to claim 1, wherein f _{B in the} equation (32) is calculated by the equation (29). 6. _Cval of equation (31) is obtained by equation (15) or equation (15 ′) and equation (16), and (32)
The method for calculating theoretical tensile strength of a non-woven fabric according to claim 1, wherein f _{B in the} equation is determined by the equation (29) or the equation (29 ′). 7. A non-woven fabric comprising a fiber and a binder, wherein in the calculation of claim 1, f _B = f _A, and C _Val is the theoretical tensile strength calculated by the equations (15) and (16), A non-woven fabric having a measured tensile strength of 80% or more. 8. A non-woven fabric comprising a fiber and a binder, wherein in the calculation of claim 1, the value of f _B is calculated using formula (29) and C _Val is calculated using formulas (15) and (16). The non-woven fabric is characterized in that the measured tensile strength is 90% or more with respect to the theoretical tensile strength of.