KR100947176B1 - Fiber bridging analysis method and prediction method for uniaxial tension behavior of fiber reinforced composites based on the fiber bridging analysis - Google Patents

Abstract

PURPOSE: A fiber cross linkage reading method and a method for estimating the tensile performance of a fiber composite using the same are provided to estimate the tensile performance of the fiber composite using a result of the fiber cross linkage. CONSTITUTION: Those are calculated from the matrix mixed fiber that fiber elasticity coefficient, length of fiber, fiber diameter, fiber tensile strength, fiber content, matrix coefficient of elasticity, matrix tensile strength, matrix content, interfacial friction, coefficient of fiber and matrix, chemical adhesion coefficient, slipping stiffness coefficient, snubbing coefficient, strength reduction factor, probability density function about the fabric center location, probability density function about the fiber oriented direction, and fiber number resistivity correction factor(S210). The stress caused in fiber is calculated according to an angle which inclines to a predetermined crack opening displacement or the buried length of fiber(S230). If the strength is same or bigger than the fiber strength, the stress of the corresponding fiber is zero(S250). If the strength is smaller than the fiber strength, the stress is the stress of the corresponding fiber(S260). The stress of each fiber is numerically integrated and the cross linkage stress of the fiber at the crack opening displacement is produced(S270). The opening edge the upper part is provided for the final opening edge and if it is bigger than the opening edge(S280).

Description

FIBER BRIDGING ANALYSIS METHOD AND PREDICTION METHOD FOR UNIAXIAL TENSION BEHAVIOR OF FIBER REINFORCED COMPOSITES BASED ON THE FIBER BRIDGING ANALYSIS}

The present invention relates to a fiber crosslinking analysis method and a method for predicting the tensile performance of the fiber composite material by the fiber crosslinking analysis, and more specifically, to analyze the fiber crosslinking action in the crack surface of the fiber composite material and using the analysis results A method for predicting uniaxial tensile behavior of a fiber composite material.

)와 섬유 가교 작용에 의하여 소산된 에너지의 합과 같으며, 섬유 가교 곡선에서 상보 에너지(

)는 매트릭스 파괴 인성 보다 커야한다. 다중 균열 발생 현상은 이 두 조건에 의하여 설명될 수 있는데, 균열 가교 작용을 하는 섬유가 하중을 저항할 수 없으면 국부적인 파괴에 의하여 다중 균열 거동이 발생하지 않는다. 이에 반하여 균열 가교 작용을 하는 섬유가 하중을 저항할 수 있으면, 섬유 가교 작용 응력은 섬유와 매트릭스의 계면을 통하여 섬유로부터 매트릭스로 전달된다. 이렇게 유발된 응력은 또 다른 균열을 유발하고 이러한 과정은 섬유 가교 곡선의 연화 거동에 의하여 특정 균열면의 국부적인 파괴가 발생할 때까지 반복된다. Engineered Cementitious Composite (ECC), one of the toughest cement composites, has a strain hardening behavior of more than 2% by incorporating about 2% synthetic fiber into the cement composite. This ultimate tensile behavior is manifested by fiber crosslinking and multiple cracking of microcracks. In order to show the strain hardening behavior due to multiple cracks, two conditions must be satisfied. The first condition is the strength condition, and the highest crosslinking stress in the fiber crosslinking curve must be greater than the crack strength of the composite. If this condition is met, there is no immediate stress drop due to the pulling or breaking of the fiber after the first crack has occurred. The second condition is the energy condition, which is a steady-state cracking condition. If the energy condition is satisfied, the crack develops under constant stress and opening displacement. The energy condition is defined by the energy equilibrium condition between the work done externally, the energy required to propagate the matrix crack, and the energy dissipated by the fiber crosslinking action. In other words, what you did outside of the matrix

) And the energy dissipated by the fiber crosslinking action, and complementary energy (

) Must be greater than the matrix fracture toughness. Multiple cracking phenomena can be explained by these two conditions. If the fiber that is cracking crosslinking cannot withstand the load, local cracking does not cause multiple cracking behavior. In contrast, if the fibrous crosslinking fiber can resist the load, the fiber crosslinking stress is transferred from the fiber to the matrix through the interface between the fiber and the matrix. This induced stress causes another crack and this process is repeated until the local fracture of a particular crack surface occurs by the softening behavior of the fiber crosslinking curve.

As described above, since the tensile behavior of the composite is determined by the fiber crosslinking behavior, it is necessary to accurately predict or evaluate the fiber crosslinking behavior in order to design the ECC and predict the tensile performance. Factors affecting the fiber crosslinking curve include the fiber, the matrix, and the interfacial properties of the fiber and the matrix. The properties of the fiber are the length, diameter, elastic modulus, strength, and content of the fiber, and the properties of the matrix are strength and elastic modulus. Interfacial properties include chemical adhesion, friction adhesion, and slip hardening. In addition to these micromechanical variables, fiber distribution properties also affect fiber crosslinking.

When the fibers are arranged in three dimensions, the highest fiber crosslinking stress is 1/6 or 1/5 as compared with the case where the fibers are arranged in one dimension. Therefore, in order to evaluate or predict the fiber crosslinking behavior, it is necessary to properly assume the distribution of fiber orientation angles. The orientation angle of the fiber is influenced by the shape of the specimen, the casting method, the rheological properties of the composite, and the like. Most researchers, however, have used values that assume the distribution of fiber orientation angles in two- or three-dimensional arrays.

The probability density function P ([theta]) for the fiber orientation angle assumed in two dimensions is 2 / [pi], and the graph is the same as "PDF2-D" in FIG. In addition, the probability density function P (θ) for the fiber orientation angle assumed in three dimensions uses sin (θ), and the graph is the same as “PDF3-D” in FIG. 6. As described above, the probability density function for the fiber orientation angle assumed in two or three dimensions shows a large difference from the graph of the measured fiber orientation angle (“PDFmeas” in FIG. 6). Compared with the experimental value shows a significant difference (see Fig. 10) there was a significant difficulty in predicting the tensile performance of the fiber composite material through the fiber crosslinking action.

 Therefore, the present invention was devised to improve the above problems, and suggests a fiber crosslinking configuration model that can consider the fiber orientation angle and the number of fibers measured in the cross-section, so that the fiber crosslinking analysis can be more accurately analyzed. It is an object of the present invention to provide a method for predicting the tensile performance of a fiber composite material by a method and a fiber crosslinking analysis.

The present invention for achieving the object as described above relates to a fiber crosslinking analysis method, the fiber elastic modulus (E _f ), fiber length (L _f ), fiber diameter (d _f ) in a fiber composite material mixed with fibers and matrix ), Fiber tensile strength (σ _fu ), fiber content (V _f ), matrix elastic modulus (E _m ), matrix tensile strength (σ _m ), matrix content (V _m ), and interfacial friction coefficient (τ ₀₎ ), Chemical adhesion coefficient (G _D ), slip hardening coefficient (β), snubbing coefficient (f) and strength reduction coefficient (f '), probability density function for fiber center position (P (z)), fiber orientation Calculating a probability density function (P (θ)) and a fiber count correction coefficient α _nf ; Calculating the stress induced in the fiber according to the embedding length and inclination angle of the fiber for a predetermined crack opening displacement; Comparing the stress induced in each fiber with the fiber strength considering the effect of reducing the fiber strength according to the angle; Determining that the stress of the fiber is zero when the stress is greater than or equal to the fiber strength, and determining the stress as the stress of the fiber when the stress is less than the fiber strength; Numerically integrating the stress of each fiber to calculate the crosslinking stress of the fiber at the crack opening displacement; And ending the analysis when the opening displacement is greater than or equal to the last opening displacement by comparing the opening displacement with the final opening displacement.

On the other hand, the present invention for achieving the above object relates to a method for predicting the tensile performance of the fiber composite material by the fiber crosslinking analysis, calculating the crack spacing for the specimen made of a fiber composite material mixed with fibers and matrix Dividing the specimen into n elements; Imparting the stiffness of the fiber composite material and the stiffness obtained from the fiber crosslinking analysis method to each element; Applying a uniaxial tensile stress to the specimen to produce a predetermined displacement and calculating the stress induced in each element against the displacement based on the stiffness of the fiber composite material; Comparing the stress induced in each element with the crack strength of each element; If the stress induced in each element is greater than or equal to the crack strength, replacing the physical properties of the element with the stiffness obtained from the fiber crosslinking analysis method in the stiffness of the fiber composite material; And contrasting the stress induced in the element with the maximum crosslinking stress obtained by the fiber crosslinking analysis method.

The present invention relates to a treatment method for predicting / evaluating the tensile performance of a fiber composite material using the results of analyzing the fiber crosslinking behavior before designing a fiber composite material or performing a tensile test. If it is designed so that it is difficult to evaluate the tensile performance through the experiment can utilize the present invention.

Hereinafter, the specific content of the fiber crosslinking analysis method and the method for predicting the tensile performance of the fiber composite material by the fiber crosslinking analysis according to the present invention will be described in detail.

1 is a flowchart of a method for predicting tensile performance of a fiber composite material by fiber crosslinking analysis according to the present invention.

As shown, in the present invention, after evaluating the distribution characteristics of the fibers in the fiber composite material (step S100), and based on this evaluation of the fiber crosslinking curve (step S200), to evaluate the fiber uniaxial tensile performance (step S300) Proceed in order. Here, the distribution characteristics of the fiber may utilize an image processing technique described in detail in Korean Patent No. 0869469.

The image processing technique will be briefly described with reference to FIG. 2. First, a specimen is obtained from a fiber composite material, and then a fiber image is obtained through a fluorescence microscope (step S101).

Then, the fiber image is detected by the binarization technique (step S102), and the detected fiber image is classified by applying a water fountain algorithm (step S103). The water separation algorithm distinguishes fiber images through analysis of brightness peaks of the images.

By such a watershed algorithm, if the number of brightness vertices of the fiber image is 1 (step S104), the single type is classified (step S105). If the number of brightness vertices is 2 or more, it is classified as a complex type (step S106).

The categorical type is reclassified through a type classifier (step S107). That is, the classification type is classified into a first type (step S108), a second type (step S109), a third type (step S110), and a fourth type (step S112) by the type classifier (see Fig. 3).

In this case, an artificial neural network is used as the type classifier, and the artificial neural network is constructed by learning a database of extracted feature values. These feature values are shape descriptors that are invariant to the transformation, including rotation, movement, size change, and brightness change.

On the other hand, the fiber image classified into the third type is reclassified by applying a fractional algorithm (step S111).

The fiber images classified into the fourth type are reclassified by applying morphological reconstruction techniques (step S113) and watershed algorithms (step S114) sequentially. At this time, the morphological reconstruction technique removes the maximum and minimum values of the brightness values of the vertices in the fiber image, thereby preventing the fiber image from being excessively divided during the execution of the watershed algorithm.

Through the image processing technique as described above, it is possible to reclassify the fiber image to enable measurement and evaluation of the fiber distribution characteristics of the fiber composite material.

Next, we evaluate the fiber crosslinking curves which can explain the dynamic behavior of cracks in composite materials. 4 shows a flow chart for evaluating fiber crosslinking curves.

In order to evaluate the fiber crosslinking curves, the parameters necessary for the evaluation must be entered. Firstly, the parameters related to fibers include the fiber elastic modulus (E _f ), the fiber length (L _f ), the fiber diameter (d _f ), the fiber tensile strength (σ _fu ), and the fiber content (V _f : volume ratio). Here, except for the fiber content, the characteristic values related to the fiber may be input using a value determined according to the product. Since the fiber content is a value determined according to the blending conditions, the value determined in the blending is used as an input value.

Variables related to the matrix include matrix elastic modulus (E _m ), matrix tensile strength (σ _m ), and matrix content (V _m : volume ratio). The elastic modulus and tensile strength of the matrix are determined by testing according to the KS standard, and the matrix content is determined according to the compounding as the fiber.

The interfacial properties of the matrix and the fiber include snubbing to reflect the effect of increasing the resistive force according to the interfacial friction coefficient (τ ₀ ), the chemical adhesion coefficient (G _D ), the slip hardening coefficient (β), and the inclination angle of the fiber. Coefficient f, strength reduction coefficient f 'for reflecting the effect of reducing the strength of the fiber according to the inclination angle of the fiber, and the like.

Here, the coefficient of friction, chemical adhesion, slip hardening coefficient can be obtained through the drawing experiment of a single fiber well known to those skilled in the art. The snubing coefficient (f) was experimentally found to have a value between 0.2 and 0.8, and the strength reduction factor (f ') was found to be 0.3 in the fiber-matrix system.

Input values for the distribution characteristics of the fibers include a probability density function P (z) for the fiber center position, a probability density function P (θ) for the fiber orientation, and a fiber number correction coefficient α _nf . The probability density function (P (z)) for the fiber center position is 2 / L _f , and the probability density function (P (θ)) for the fiber orientation is obtained by using the image processing technique described in Korean Patent No. 869469. In the analysis of the shape of each fiber can be obtained by calculating the direction, in more detail can be obtained through the following [Equation 1].

Here, p and q are variables that determine the shape of the probability density function, and are automatically determined through image analysis. In more detail, the graph of the fiber orientation obtained through image analysis for the cross section of the specimen (corresponding to “PDFmeas” in FIG. 6) can be regressed as a function of sin and cosine as described above. By determining the p and q values through this regression analysis, a probability density function of the form “PDFfit” in FIG. 6 can be obtained. And, as shown in Figure 5, the θ representing the orientation of the fiber is in the range of 0 ° ~ 90 ° (0 ~ 1.57 in radians), θ _min is 0 °, θ _max is 90 ° It becomes

In addition, the fiber number correction coefficient α _nf can be obtained through Equation 2 below.

The fiber number correction coefficient α _nf of Equation 2 is derived by Equation 3 below.

Where N _m is the number of fibers measured using an image processing technique and A _m is the measured cross-sectional area (step S210).

When the input value is determined, a crack opening displacement δ is assumed (step S220), and as shown in FIG. 5, according to each embedding length L _e and the angle of inclination θ of the fiber with respect to the crack opening displacement. The stress (σ _f (θ)) induced in the fiber is calculated by the following Equation 4. If the crack opening displacement is larger than [Equation 5], the induced stress is calculated according to [Equation 6] (step S230).

It is determined whether the fiber is broken based on the stress induced in the fiber calculated in step S230 (step S240). At this time, if the stress induced on the fiber is greater than or equal to the fiber strength (σ _fu e ^{- f ' θ} ) considering the effect of decreasing the fiber strength depending on the angle, the load that the fiber can resist due to the fiber breakage becomes zero. (Step S250). In addition, if the stress induced on the fiber is smaller than the fiber strength (σ _fu e ^{- f ' θ} ), the load the fiber can resist is calculated as the stress induced on the current fiber (step S260).

Thus, when the stress of each fiber with respect to the current crack opening displacement (δ) is calculated, numerical integration is performed according to [Equation 7] or [Equation 8] to calculate the fiber crosslinking stress at the crack cross section. .

[Equation 8] is an equation calculated by dividing all lengths by L _f / 2 so as to apply to fibers having an arbitrary length in Equation 7 (step S270).

This process continues until the assumed fiber opening displacement δ reaches the last crack opening displacement δ _final . That is, the fiber opening displacement δ is compared with the last crack opening displacement δ _final (step S280), and if the fiber opening displacement δ is smaller than the last crack opening displacement δ _final , the predetermined crack displacement δ + Δδ is increased. (Step S290) The process is performed again from step S220.

Here, the maximum value of the _final aperture displacement (δ _final ) is equal to half the fiber length (L _f / 2). This is because when the opening displacement is greater than half of the fiber length (L _f / 2), the fiber crosslinking stress becomes zero because all the fibers are pulled out or broken at the crack surface.

The fiber crosslinking curves calculated in consideration of the distribution of the fiber orientation angle and the number of fibers as described above are illustrated in FIGS. 7 and 8. At this time, the mixing ratio of the two test chains wc60 and wc48 is shown in Table 1 below.

cement water sand Slag HRW HPMC V _f (%) wc60 1.0 0.60 0.8 0.25 0 0.001 2 wc48 1.0 0.48 0.8 0.25 0.02 0

Here, HRW is a high-range water-reducing admixture, HPMC is Hydroxypropylmethyl-cellulose. And other components except fibers represent weight ratios for cement.

The input values for the two specimens are shown in [Table 2].

Input value wc60 wc48 fiber( fiber ) Fiber length L _f (Mm) 12 Fiber diameter d _f (mm) 0.040 Modulus of fiber E _f (㎬) 40 Fiber Tensile Strength σ _fu (MPa) 1600 Fiber content V _f (%) 2 matrix( matrix ) Matrix modulus of elasticity E _m (㎬)  18.4 26.2 Matrix Tensile Strength σ _m (MPa)   3.54 4.70 Interfacial Characteristics of Matrix and Fiber Interfacial friction coefficient τ ₀ (MPa)   1.65 1.85 Chemical Friction Coefficient G _D (J / ㎡)   1.88 1.83 Slip Hardening Factor β   0.104 0.129 Snubbing coefficient f 0.30 Strength reduction factor f ' 0.3

The probability density function of the fiber orientation angle obtained by assuming two-dimensional fiber crosslinking curve evaluated based on the probability density function of the fiber orientation angle measured by the image processing technique ("PDFfit" in FIG. 6) for the two specimens. Overall behavior similar to the fiber crosslinking curve calculated theoretically based on the function (“PDF2-D” in FIG. 6) was shown (FIG. 7A and FIG. 8A). However, in the initial behavior up to the maximum crosslinking stress, the crack opening displacement corresponding to the maximum crosslinking stress of the fiber crosslinking curve evaluated by the image processing technique was evaluated to be larger than that obtained by assuming two-dimensional fiber orientation angles. 7 (b) and 8 (b)).

)의 크기를 결정하는 중요한 값이므로 인장 변형 성능을 예측하는데 결정적 요인이 된다. Kanda 등(2000년, Tensile Stress-Strain Modeling of Pseudo Strain-Hardening Cementitious Composites, Journal Materials in Civil Engineering, 12(2), pp.147-156.)은 균열 강도와 섬유 가교 곡선의 최고 섬유 가교 응력과 그때에 균열 개구변위를 이용하여 ECC의 인장응력과 변형률 관계를 간단하게 예측하는 이론적 방법을 제안한 바 있다. 따라서 본 발명에서는 이미지 분석을 바탕으로 보다 정확한 섬유의 배향각의 분포와 섬유 개수를 고려함으로써 ECC의 인장 응력과 변형률 관계를 보다 정확히 예측할 수 있게 된다.The difference in crack opening displacement corresponding to the maximum crosslinking stress is the complementary energy (

This is an important value for determining the size of) and is a critical factor in predicting tensile strain performance. Kanda et al. (10, Tensile Stress-Strain Modeling of Pseudo Strain-Hardening Cementitious Composites, Journal Materials in Civil Engineering, 12 (2), pp.147-156.) At the time, a theoretical method was proposed to simply predict the relationship between tensile stress and strain of ECC using crack opening displacement. Therefore, in the present invention, it is possible to more accurately predict the tensile stress and strain relationship of the ECC by considering the more accurate distribution of fiber orientation angles and the number of fibers based on image analysis.

As shown in FIG. 9, the uniaxial tensile performance of a fiber is evaluated using the fiber crosslinking curve computed as mentioned above. At this time, since the matrix and crack surface behavior used for ECC show actual nonlinearity, it is preferable to analyze it in consideration of nonlinearity in order to simulate accurate behavior.However, the matrix used for ECC is mortar made of fine silica sand, Since the nonlinearity of the cracked surface behavior does not have a significant effect on the analysis result, the matrix and the cracked surface behavior are assumed to be linear elastic behavior. In addition, in order to consider the uncertainty of the material, the physical properties of each element were randomly selected within a normal distribution with a 95% confidence interval.

In order to predict or evaluate the fiber uniaxial tensile performance, as described above, the fiber crosslinking curve and the crack spacing are required at the crack surface after the crack has occurred. At this time, the fiber crosslinking curve is calculated in the manner described above, and the crack spacing is calculated by [Equation 9] in consideration of the orientation of the fibers and the number of fibers.

이고, here

ego,

: orientation coefficient

,

: orientation coefficient

,

: orientation coefficient for frictional force

: orientation coefficient for frictional force

,

,

: orientation coefficient for pulley force

: orientation coefficient for pulley force

,

,

: probability density function for fiber orientation(섬유 방향성에 대한 확률밀도 함수),

probability density function for fiber orientation,

: fiber number coefficient(섬유 개수 보정계수),

: fiber number coefficient,

: correction factor for snubbing effect 로서 0.8의 값을 사용할 수 있다.

A value of 0.8 can be used as a correction factor for snubbing effect.

By calculating the crack spacing to be induced in the specimen by the equation (9), it is divided into n elements for the specimen shape to be predicted through this, and each end of the element is sequentially given to n + 1 node (step S310), Gives each element its properties. The physical properties impart the stiffness (K) as the stiffness (K _ci ) and the stiffness (K _fi ) obtained from the fiber crosslinking curve after cracking occurs (step S320). At this time, the stiffness of the fiber composite is randomly selected between the maximum value and the minimum value for the stress and crack spacing calculated for a plurality of specimens as the stress and crack spacing of the corresponding element, and a graph of the selected stress and crack spacing. Determined by the slope value at (σ _ci -δ).

In addition, the stiffness obtained from the fiber crosslinking curve is randomly selected between the maximum and minimum values for the highest crosslinking stress and crack spacing calculated for a plurality of specimens as the fiber crosslinking stress and crack spacing of the corresponding element, and the selected fiber crosslinking Determined by the slope value in the graph of stress and crack spacing (σ _Bi −δ).

If physical properties are given to each element, the displacement δ is assumed (step S330) and the stress (σ _idi ) induced for the displacement is calculated (step S340). The calculated stress (σ _idi ) is then calculated according to the calculation method by finite element analysis, which will be described in more detail as follows.

Compare the induced stress (σ _idi ) with the crack strength (σ _m ) (step S350) and if it is less than the crack strength (σ _m ), increase the displacement (step S360) to recalculate the induced stress and make it larger than the crack strength. When the physical properties are replaced with the physical properties obtained from the fiber crosslinking curve (step S370). In this case, the crack strength (σ _m ) may be a value obtained from an experiment, and the maximum stress value corresponding to the point of crack occurrence may be used in relation to the stress and displacement of the element.

_{Comparing the} induced stress (σ _idi ) with the maximum crosslinking stress (σ _{B, peak} ) (step S380), if it is less than the maximum crosslinking stress, increase the displacement (step S360) to calculate the induced stress and If it is the same, the analysis ends. At this time, the maximum crosslinking stress may be a value obtained from the relationship between the fiber crosslinking stress and the displacement of the element.

10 compares simulation results and experimental results by numerical analysis of uniaxial tensile behavior. The analytical results show multiple cracks and strain hardening behavior similar to the experimental results. In both wc60 and wc48 specimens, the analytical results showed that the maximum tensile strain was about 10% smaller than the experimental results. These results can be explained by the existing experimental results that the better the fiber dispersibility when the slag is added, it can be more accurately simulate the uniaxial tensile behavior when considering the fiber dispersibility quantitatively in the analysis process.

If the orientation of the fibers is assumed to be two-dimensional or three-dimensional, the maximum fiber crosslinking stress and corresponding crack opening displacement in the fiber crosslinking curve are smaller than the proposed fiber crosslinking model. That is, as shown in FIG. 10, the maximum tensile strain was about 50% smaller than the experimental result when the direction of the fiber was assumed to be two-dimensional, and when the three-dimensional assumption was assumed, the maximum tensile strain was compared with the experimental result. About 10% or less. Therefore, when comparing the analysis results and the experimental results, using the model proposed in the present invention, that is, the fiber crosslinking model in the cement composite considering the probability density function of the orientation angle of the reinforcing fibers, the direction of the fibers is assumed to be two-dimensional or three-dimensional. Compared to one case, the uniaxial tensile behavior of the fiber reinforced cement composite can be more accurately simulated.

The rights of the present invention are not limited to the embodiments described above, but are defined by the claims, and those skilled in the art can make various modifications and adaptations within the scope of the claims. It is self-evident.

1 is a flow chart of a method for predicting tensile performance of a fiber composite material by fiber crosslinking analysis according to the present invention;

2 is a flow chart for a method for evaluating fiber distribution characteristics according to the present invention;

3 shows the types of fibers classified according to FIG. 2, FIG.

4 is a flowchart illustrating a method for evaluating a fiber crosslink curve according to the present invention;

5 illustrates the orientation angle of fibers relative to the matrix;

6 is a graph showing the probability density function according to the compounding ratio;

7 is a graph showing the fiber crosslink for wc60,

8 is a graph showing the fiber crosslink for wc48,

9 is a flow chart for a method for evaluating the uniaxial tensile performance of the fiber according to the present invention,

10 is a graph comparing the experimental results of the axial tensile behavior and the experimental results predicted by the present invention, assuming that the direction and the number of fibers in two or three dimensions.

Claims (11)

Fiber elastic modulus (E _f ), fiber length (L _f ), fiber diameter (d _f ), fiber tensile strength (σ _fu ), fiber content (V _f ), matrix elastic modulus (E _m ), matrix tensile strength (σ _m ), matrix content (V _m ), interfacial friction coefficient (τ ₀ ) of matrix and fiber, chemical adhesion coefficient (G _D ), slip hardening coefficient (β), snubbing coefficient (f) and strength reduction coefficient (f '), probability density function (P (z)) for fiber center position, probability density function (P (θ)) for fiber orientation, and fiber number correction coefficient (α _nf ) Calculating; Calculating the stress induced in the fiber according to the embedding length and inclination angle of the fiber for a predetermined crack opening displacement; Comparing the stress induced in each fiber with the fiber strength considering the effect of reducing the fiber strength according to the angle; Determining that the stress of the fiber is zero when the stress is greater than or equal to the fiber strength, and determining the stress as the stress of the fiber when the stress is less than the fiber strength; Numerically integrating the stress of each fiber to calculate the crosslinking stress of the fiber at the crack opening displacement; And And ending the analysis if the opening displacement is greater than or equal to the last opening displacement in comparison with the final opening displacement. The method of claim 1, And a probability density function (P (z)) for the fiber center position is 2 / L _f . The method of claim 2, The probability density function (P (θ)) with respect to the fiber orientation is calculated by the following equation.

The method of claim 3, The fiber number correction coefficient α _nf is fiber crosslink analysis method, characterized in that calculated by the following equation.

The method of claim 4, wherein Calculating the stress induced in the fiber, Fiber crosslinking analysis method, characterized in that calculated by the following equation.

The method of claim 5, The crack opening displacement

If larger, the stress induced in the fiber is calculated by the following equation.

The method of claim 6, In the step of calculating the crosslinking stress of the fiber, the fiber crosslinking stress is calculated by the following equation.

The method of claim 6, In the step of calculating the crosslinking stress of the fiber, the fiber crosslinking stress is calculated by the following equation.

Dividing the specimen into n elements by calculating a crack spacing for the specimen made of a fiber composite mixed with fibers and a matrix; Imparting the stiffness of the fiber composite material and the stiffness obtained from the fiber crosslinking analysis method according to any one of claims 1 to 8 to each element; Applying a uniaxial tensile stress to the specimen to produce a predetermined displacement and calculating the stress induced in each element against the displacement based on the stiffness of the fiber composite material; Comparing the stress induced in each element with the crack strength of each element; If the stress induced in each element is greater than or equal to the crack strength, replacing the physical properties of the element with the stiffness obtained from the fiber crosslinking analysis method in the stiffness of the fiber composite material; And And contrasting the stress induced in the element with the maximum crosslinking stress obtained by the fiber crosslinking analysis method. 10. The method of predicting tensile performance of a fiber composite material by fiber crosslinking analysis comprising: a. The method of claim 9, The crack spacing is calculated by the following equation, the method of predicting the tensile performance of the fiber composite material by the fiber crosslinking analysis.

here

ego,

: orientation coefficient

,

: orientation coefficient for frictional force

,

: orientation coefficient for pulley force

,

probability density function for fiber orientation,

: fiber number coefficient,

: correction factor for snubbing effect, value of 0.8 The method of claim 10, The stiffness of the fiber composite material and the stiffness obtained from the fiber crosslinking analysis method are given by selecting an arbitrary value between the maximum value and the minimum value calculated from a test on a plurality of specimens. Method of predicting tensile performance of composite materials.

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