Short fiber composite material RVE modeling method considering fiber curvature and distribution

Abstract

The invention provides a short fiber composite material RVE modeling method considering fiber curvature and distribution, and belongs to the field of composite material simulation calculation. The method comprises the following steps: firstly, collecting model parameters, randomly generating a curvature of a first fiber and obtaining a fiber bending function of the first fiber, randomly generating a fiber direction, randomly placing the first fiber in an RVE region, randomly generating a curvature of a new fiber and placing a new fiber, judging whether the new fiber interferes with the existing fiber or not, and if so, placing the new fiber again; if no interference exists, the next new fiber is placed until the fiber volume fraction requirement is met, and finally a fiber geometry is drawn and combined with the base body to form the RVE model of the short fiber composite material. According to the method, the microstructure characteristics of the short fibers are considered, the fiber curvature is quantitatively described based on the fiber curvature distribution function and the fiber bending function, the RVE model of the short fiber composite material can be more accurately established, and an effective tool is provided for accurate prediction of the performance of the short fiber composite material.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of composite material simulation calculation, and relates to a short fiber composite material RVE modeling method considering fiber curvature and distribution. BACKGROUND

[0002] Short fiber composite material has high specific strength and specific stiffness, and compared with continuous fiber composite material, it can form a structure with complex shape, and thus is widely applied in the industrial fields of aerospace, ship, automobile and medical instrument. Therefore, it is of great significance to establish a model capable of accurately predicting the performance of short fiber composite material for engineering application of the material. The representative volume element (RVE) model based on micromechanics can accurately describe various micromechanical features of the composite material, and is a commonly used prediction method. Therefore, how to establish an RVE model capable of accurately describing various micromechanical features of the short fiber composite material is the first step for material performance prediction, and is also a research difficulty.

[0003] The existing short fiber composite material RVE modeling method usually considers common micromechanical features such as fiber diameter, fiber length, fiber orientation and fiber volume fraction. However, researches show that fiber bending may occur in the micromechanical structure of the short fiber composite material. Although some modeling algorithms can establish the RVE of the short fiber composite material, they usually regard the fiber bending as completely random or a certain fixed value, and lack quantitative description. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a short fiber composite material RVE modeling method considering fiber curvature and distribution. The method considers common micromechanical features of the short fiber (fiber diameter, fiber length, fiber orientation and fiber volume fraction), and quantitatively describes the fiber curvature based on a given fiber curvature distribution function (such as normal distribution, uniform distribution, etc.) and fiber bending function, so that the RVE model of the short fiber composite material can be more accurately established, and an effective tool is provided for accurate prediction of the performance of the short fiber composite material.

[0005] The technical scheme adopted by the present application is as follows:

[0006] A short fiber composite material RVE modeling method considering fiber curvature and distribution comprises the following steps:

[0007] Step 1, collect model parameters, including fiber diameter and length, fiber orientation tensor, fiber volume fraction, size of RVE, and fiber bending type; wherein the fiber bending type includes half-sine, 3 / 4-sine and full-sine, and the fiber orientation tensor B uses a second-order orientation tensor:

[0008] B = diag(b1, b2, b3), b1+b2+b3 = 1 (1)

[0009] where b1, b2, b3 represent the probability of the fiber direction along the X, Y and Z axes of the global coordinate system, respectively.

[0010] Step 2, randomly generate the curvature of the first fiber and obtain its fiber bending function.

[0011] Taking the starting point of the fiber as the origin and the line connecting the starting point and the ending point as the X axis, a local coordinate system is established. The fiber bending function corresponding to different fiber bending patterns is:

[0012] 1) For the half-sine bending pattern, the fiber bending function is represented by the half-sine function shown in equation (2):

[0013]

[0014] where A represents the amplitude of fiber bending, L is the effective length of the fiber, and (x, y) represents the coordinates of each point on the fiber in the local coordinate system.

[0015] The bending of the fiber is defined by the curvature corresponding to the point with the maximum bending degree on the fiber. For the half-sine function, the point with the maximum bending degree is , and the curvature k at this point is calculated by equation (3):

[0016]

[0017] where the first derivative y' and the second derivative y" corresponding to y are calculated by equation (4):

[0018]

[0019] Therefore, the curvature k at point can be expressed as:

[0020]

[0021] Transforming equation (5), the fiber bending amplitude A is expressed as a function of the fiber curvature k, as shown in equation (6):

[0022]

[0023] Therefore, the fiber bending function of the half-sine bending pattern, i.e. equation (2), can be converted into a quantitative relationship related to the fiber curvature:

[0024]

[0025] 2) For 3 / 4 sinusoidal bending pattern, the fiber bending function is expressed by 3 / 4 sinusoidal function as shown in equation (8):

[0026]

[0027] The bending of the fiber is defined by the curvature at the point where the fiber has the maximum bending. For 3 / 4 sinusoidal function, the point where the bending is maximum is at The curvature k at this point is calculated by equation (3):

[0028] where y' and y" are calculated by equation (9):

[0029]

[0030] The curvature k at this point can be expressed as:

[0031]

[0032] Therefore, the fiber bending function for 3 / 4 sinusoidal bending pattern, i.e. equation (8), is converted to a quantitative relationship with the fiber curvature as:

[0033]

[0034] 3) For full sinusoidal bending pattern, the fiber bending function is expressed by full sinusoidal function as shown in equation (12):

[0035]

[0036] The bending of the fiber is defined by the curvature at the point where the fiber has the maximum bending. For full sinusoidal function, the point where the bending is maximum is at The curvature k at this point is calculated by equation (3):

[0037] where y' and y" are calculated by equation (13):

[0038]

[0039] The curvature k at this point can be expressed as:

[0040]

[0041] Therefore, the fiber bending function for full sinusoidal bending pattern, i.e. equation (12), is converted to a quantitative relationship with the fiber curvature as:

[0042]

[0043] ​​According to the given fiber curvature distribution function, the fiber curvature of the first fiber is randomly generated, and the fiber bending function of the first fiber is determined according to the bending type.

[0044] Step 3, randomly generate the direction of the fiber according to the fiber orientation tensor, randomly place the first fiber in the RVE region, and obtain the initial coordinates of the first fiber in the global coordinate system.

[0045] Select equidistant points on the fiber axis as control points of the fiber bending, then the fiber axis is divided into N parts by the control points, and the coordinates of each control point in the local coordinate system can be calculated by the fiber bending function:

[0046]

[0047] In the formula, i represents the serial number of the control point.

[0048] According to the size of the RVE, the RVE region is constructed in the global coordinate system, and the first fiber is randomly placed in the RVE region; through coordinate transformation, the initial coordinates of each control point of the first fiber in the global coordinate system are obtained:

[0049]

[0050] In the formula, represents the initial coordinates of the control point in the global coordinate system, represents the coordinates of the drawing point of the fiber in the local coordinate system, which is calculated by the following formula:

[0051]

[0052] According to the fiber orientation tensor, the orientation angle θ and are randomly generated. Rotate the fiber, wherein the orientation angle θ is the included angle between the first and last lines of the fiber curve and the Z axis in the global coordinate system, and the orientation angle is the included angle between the first and last lines of the fiber curve and the Y axis in the global coordinate system, then the coordinates of the control points of the fiber in the global coordinate system after rotation are As shown in formula (19):

[0053]

[0054] In the formula, (x,y,z) T represents the coordinates of the starting point of the fiber in the global coordinate system.

[0055] Step 4, repeat the operation steps 2 and 3 to randomly generate the curvature of the new fiber and randomly place the new fiber in the RVE region.

[0056] Step 5, judge whether the new fiber interferes with the existing fiber.

[0057] The minimum distance between the new fiber and the existing fiber is calculated by using the control points of the fiber, as shown in equation (20):

[0058]

[0059] In the equation: represents the i-th control point of the m-th fiber, represents the j-th control point of the s-th fiber, represents the distance between the two points.

[0060] According to equation (21), judge whether the new fiber interferes with the existing fiber, if it interferes, regenerate the curvature and place the new fiber, if it does not interfere, go to the next step.

[0061]

[0062] In the equation: d i represents the diameter of the i-th fiber, d j represents the diameter of the j-th fiber.

[0063] Step 6, keep the information of the new fiber, and judge whether the fiber volume fraction in the RVE region reaches the fiber volume fraction requirement in step 1, if it does not reach the requirement, return to step 4 to continue placing the new fiber, if it reaches the requirement, go to the next step.

[0064] Step 7, draw the fiber geometry according to the information of all fibers, and combine it with the matrix to form the RVE model of the short fiber composite material. The drawing process of the fiber geometry is: connect the control points on the fiber axis in turn to draw a spline curve, draw a circle with the fiber axis as the center and the fiber diameter on the plane perpendicular to the spline curve, and sweep the circle along the spline curve to draw the fiber geometry.

[0065] The effects and benefits of the present application are:

[0066] 1. The present application introduces a quantitative relationship between the fiber curvature and the fiber bending function, so that the size and distribution of the fiber curvature can be directly considered in the RVE model of the short fiber composite material.

[0067] 2. The present application fully considers various microstructure characteristics of the fiber: fiber diameter and length, fiber volume fraction, fiber orientation distribution, fiber curvature and distribution, etc.

[0068] 3. The present application establishes a short fiber composite material RVE modeling algorithm considering fiber curvature and its distribution based on the idea of random sequence adsorption algorithm, which provides an effective modeling tool for performance prediction of short fiber composite materials. Attached Figure Description

[0069] Figure 1 This defines the fiber in the global coordinate system.

[0070] Figure 2 This is a schematic diagram of the fiber.

[0071] Figure 3 RVE diagram

[0072] Figure 4 This is a diagram showing the distribution of fiber curvature in RVE. Detailed Implementation

[0073] The technical solution of the present invention will be further described below with reference to the embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0074] This embodiment uses the generation of a 200×200×200μm short fiber composite RVE model as an example to further illustrate the method of the present invention. The fiber orientation tensor and fiber curvature follow a normal distribution: k~N(10,2) 2 )mm -1 .

[0075] A method for RVE modeling of short fiber composites considering fiber curvature and distribution includes the following steps:

[0076] Step 1: Collect model parameters, including: fiber diameter of 7 μm, fiber length of 100 μm, fiber volume fraction of 10%, RVE size of 200×200×200 μm, fiber bending type including three types: half sine, 3 / 4 sine and full sine, and fiber orientation tensor B as diag(1 / 3, 1 / 3, 1 / 3).

[0077] Step 2: Randomly generate the curvature of the first fiber and obtain its fiber bending function.

[0078] With the fiber's starting point as the origin and the line connecting its starting and ending points as the X-axis, a local coordinate system is established. The fiber bending functions corresponding to the three fiber bending types are shown in Equations (7), (11), and (15), respectively.

[0079] The fiber curvature of the first fiber is randomly generated based on a given fiber curvature distribution function, and its fiber bending function is determined according to its bending pattern. In this embodiment, the fiber curvature follows a normal distribution: k ~ N(10,2). 2 )mm -1 .

[0080] Step 3, randomly generate the direction of the fiber according to the fiber orientation tensor, randomly place the first fiber in the RVE region, and obtain the initial coordinates of the first fiber in the global coordinate system.

[0081] Select equidistant points on the fiber axis as control points of fiber bending (such as Figure 2 ), then the fiber axis is divided into N parts by the control points, and the coordinates of each control point in the local coordinate system can be calculated by the fiber bending function, such as equation (16).

[0082] According to the size of the RVE, the RVE region is constructed in the global coordinate system, and the first fiber is randomly placed in the RVE region; through coordinate transformation, the initial coordinates of each control point of the first fiber in the global coordinate system are obtained as shown in equation (17).

[0083] Randomly generate the orientation angle θ and of the fiber according to the fiber orientation tensor. Rotate the fiber, where the orientation angle θ is the angle between the line connecting the beginning and end of the fiber curve and the Z axis in the global coordinate system, and the orientation angle is the angle between the line connecting the beginning and end of the fiber curve and the Y axis in the global coordinate system, as shown in Figure 1 , then the coordinates of the control points of the fiber in the global coordinate system after rotation are as shown in equation (19).

[0084] Step 4, repeat the operation steps 2 and 3 to randomly generate the curvature of the new fiber and randomly place the new fiber in the RVE region.

[0085] Step 5, determine whether the new fiber interferes with the existing fiber.

[0086] Calculate the minimum distance between the new fiber and the existing fiber using the control points of the fiber, as shown in equation (20).

[0087] According to equation (21), determine whether the new fiber interferes with the existing fiber, if there is interference, regenerate the curvature and place the new fiber, if there is no interference, then proceed to the next step.

[0088] Step 6, retain the information of the new fiber, and determine whether the fiber volume fraction in the RVE region reaches the fiber volume fraction collected in step 1, if it does not reach the requirement, return to step 4 to continue placing new fibers, if it reaches the requirement, then proceed to the next step.

[0089] Step 7, draw the fiber geometry according to the information of all fibers, and combine it with the matrix to form the RVE model of the short fiber composite material, as shown in Figure 3The drawing process of the fiber geometry is as follows: connecting the control points on the fiber axis in sequence to draw a spline curve, drawing a circle with the fiber axis as the center and the fiber diameter on the plane perpendicular to the spline curve, and drawing the fiber geometry by sweeping the circle along the spline curve.

[0090] It is verified that the distribution of the fiber curvature in the obtained RVE model is as shown in Figure 4 , which conforms to the preset normal distribution.

[0091] The above only describes some embodiments of the present application, and does not limit the implementation and protection scope of the present application. Any improvement and modification made by those skilled in the art without departing from the scope of the present application should be within the protection scope of the present application.

Claims

1. A method for RVE modeling of short fiber composite materials considering fiber curvature and distribution, characterized in that, The process includes the following steps: First, collect model parameters, randomly generate the curvature of the first fiber, randomly place the first fiber in the RVE region, then randomly generate the curvature of a new fiber and place the new fiber, determine whether the new fiber interferes with the existing fibers, if there is interference, regenerate and place the new fiber, if there is no interference, generate and place the next new fiber, until the fiber volume fraction requirement is met, and finally draw the fiber geometry and merge it with the matrix to form the RVE model of the short fiber composite material.

2. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 1, characterized in that, Includes the following steps: Step 1: Collect model parameters; Step 2: Establish a local coordinate system with the fiber's starting point as the origin and the line connecting its starting and ending points as the X-axis, and construct a quantitative relationship between the fiber bending function and the fiber curvature; randomly generate the fiber curvature of the first fiber according to the given fiber curvature distribution function, and determine its fiber bending function. Step 3: Randomly generate the fiber orientation based on the fiber orientation tensor, randomly place the first fiber in the RVE region, and obtain the initial coordinates of the first fiber in the global coordinate system. By selecting equally spaced points on the fiber axis as control points for fiber bending, the fiber axis is divided into N equal parts by these control points. The coordinates of each control point in the local coordinate system can be calculated using the fiber bending function. In the formula: i represents the sequence number of the control point; Construct the RVE region in the global coordinate system based on the RVE size, and randomly place the first fiber in the RVE region; obtain the initial coordinates of each control point of the first fiber in the global coordinate system through coordinate transformation: In the formula: This represents the initial coordinates of the control point in the global coordinate system. The coordinates of the fiber's plotting point in the local coordinate system are calculated using the following formula: The fiber orientation angles θ and φ are randomly generated based on the fiber orientation tensor. The fiber is then rotated according to these orientation angles θ and φ. Here, orientation angle θ is the angle between the line connecting the beginning and end of the fiber curve in the global coordinate system and the Z-axis, and orientation angle φ is the angle between the line connecting the beginning and end of the fiber curve in the global coordinate system and the Y-axis. The coordinates of the control points of the fiber after rotation in the global coordinate system are then determined. As shown in equation (19): in, (x,y,z) T This indicates the coordinates of the fiber origin in the global coordinate system; Step 4: Repeat steps 2 and 3 to randomly generate the curvature of new fibers and randomly place new fibers in the RVE region; Step 5: Determine whether there is any interference between the new fiber and the existing fiber; The minimum distance between the new fiber and the existing fiber is calculated using the control points of the fiber. According to Equation (21), it is determined whether there is interference between the new fiber and the existing fiber. If there is interference, the curvature is regenerated and the new fiber is placed. If there is no interference, proceed to the next step. In the formula: This represents the i-th control point of the m-th fiber. This represents the j-th control point of the s-th fiber. d represents the distance between the two points. i d represents the diameter of the i-th fiber. j This represents the diameter of the j-th fiber; Step 6: Retain the information of the new fiber and determine whether the fiber volume fraction in the RVE area meets the fiber volume fraction requirement in Step 1. If the requirement is not met, return to Step 4 to continue placing new fibers. If the requirement is met, proceed to the next step. Step 7: Draw the fiber geometry based on the information of all fibers, and merge it with the matrix to form the RVE model of the short fiber composite material.

3. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that, In step 1, the model parameters include: fiber diameter and length, fiber orientation tensor, fiber volume fraction, RVE dimensions, and fiber bending pattern.

4. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 3, characterized in that, The fiber orientation tensor B is as follows: B=diag(b1, b2, b3), b1+b2+b3=1 (1) Where b1, b2, and b3 represent the probabilities of the fiber direction along the X-axis, Y-axis, and Z-axis of the global coordinate system, respectively.

5. The RVE modeling method for short fiber composite materials considering fiber curvature and distribution according to claim 3, characterized in that, The bending patterns of fibers include half-sine, 3 / 4 sine, and full sine.

6. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that, For the semi-sine fiber bending type, the quantitative relationship between the fiber bending function and the fiber curvature is established as follows: The fiber bending function is represented by the half-sine function shown in equation (2): In the formula: A represents the bending amplitude of the fiber, L is the effective length of the fiber, and (x,y) represents the coordinates of each point on the fiber in the local coordinate system; The curvature of a fiber is defined by the curvature corresponding to the point of maximum curvature on the fiber. For a half-sine function, the point... The curvature is greatest at point , and the curvature k at that point is calculated by equation (3): In the formula, the first derivative y′ and the second derivative y″ corresponding to y are calculated by equation (4): Then point The curvature k at that point can be expressed as: Transforming equation (5), the fiber bending amplitude A is expressed as a function of the fiber curvature k, as shown in equation (6): Therefore, the fiber bending function of the semi-sine bending type, i.e., equation (2), can be converted into a quantitative relationship related to fiber curvature:

7. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that, For the 3 / 4 sinusoidal fiber bending type, the quantitative relationship between the fiber bending function and the fiber curvature is established as follows: The fiber bending function is represented by the 3 / 4 sine function shown in equation (8): The curvature of a fiber is defined by the curvature corresponding to the point of maximum curvature on the fiber. For a 3 / 4 sine function, the point... The curvature is greatest at point 3, and the formula for calculating the curvature k at that point is shown in equation (3): In the formula, the first derivative y′ and the second derivative y″ corresponding to y are calculated by equation (9): Then point The curvature k at that point can be expressed as: Therefore, the fiber bending function of the 3 / 4 sinusoidal bending type, i.e., equation (8), is converted into a quantitative relationship related to fiber curvature:

8. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that, For the sinusoidal fiber bending type, the quantitative relationship between the fiber bending function and the fiber curvature is established as follows: The fiber bending function is represented by the full sine function shown in equation (12): The curvature of a fiber is defined by the curvature corresponding to the point of maximum curvature on the fiber. For a full sine function, the point... The curvature is greatest at point , and the curvature k at that point is given by equation (3): In the formula, the first derivative y′ and the second derivative y″ corresponding to y are calculated by formula (13): Then point The curvature k at that point can be expressed as: Therefore, the fiber bending function of the full sinusoidal bending type, i.e., equation (12), is converted into a quantitative relationship related to fiber curvature:

9. A method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that... As shown in equation (20):

10. The method for RVE modeling of short fiber composite materials considering fiber curvature and distribution according to claim 2, characterized in that, In step 7, the process of drawing the fiber geometry is as follows: connect the control points on the fiber axis in sequence to draw the spline curve, draw a circle with the fiber axis as the center and the fiber diameter on the plane perpendicular to the spline curve, and sweep the circle along the spline curve to obtain the fiber geometry.

Images