CN115130360B - A method for establishing a high-fidelity unit cell model of carbon fiber fabric - Google Patents
A method for establishing a high-fidelity unit cell model of carbon fiber fabric Download PDFInfo
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Abstract
本发明涉及一种碳纤维织物高保真单胞模型建立方法，根据所使用的纤维织物选取最小不重复织物单胞结构，根据光学图像获取纤维织物厚度、纤维束横截面面积以及织物编织方式；使用等效体积将纤维束离散为指定数量的代表性纤维丝，并根据纤维织物编织方式对代表性纤维丝进行相同形式编织；对该模型施加适当的周期性边界条件，结合指定的工况条件进行动力学仿真；根据仿真后代表性纤维丝的分布状态进行纤维束重构；对纤维束干涉部分进行干涉消除，最终获取指定工况下的高保真单胞RVE模型。
The present invention relates to a method for establishing a high-fidelity unit cell model of carbon fiber fabric. The method comprises the following steps: selecting a minimum non-repetitive unit cell structure of the fabric according to the fiber fabric used, obtaining the thickness of the fiber fabric, the cross-sectional area of the fiber bundle and the fabric weaving method according to an optical image; discretizing the fiber bundle into a specified number of representative fiber filaments using an equivalent volume, and weaving the representative fiber filaments in the same form according to the fiber fabric weaving method; applying appropriate periodic boundary conditions to the model, and performing dynamic simulation in combination with specified working conditions; reconstructing the fiber bundle according to the distribution state of the representative fiber filaments after simulation; and eliminating interference of the interference part of the fiber bundle, so as to finally obtain a high-fidelity unit cell RVE model under the specified working condition.
Description
Technical Field
The invention belongs to the field of resin-based carbon fiber reinforced composite material simulation modeling, and relates to a method for establishing a high-fidelity unit cell model of a carbon fiber fabric.
Background
The resin-based carbon fiber reinforced composite material has the advantages of high specific strength, high specific modulus, good fatigue resistance, corrosion resistance, good designability and the like, and the light weight and the high strength of the resin-based carbon fiber reinforced composite material enable the resin-based carbon fiber reinforced composite material to have unique application advantages in the advanced industrial manufacturing fields of aerospace, vehicles, ships and the like.
Wherein, the carbon fiber fabric is used as a reinforcing phase to be compounded with resin by a corresponding molding technology to manufacture a composite material product. In the manufacturing process, the two-dimensional carbon fiber fabric is usually manufactured into a fiber preform with a specific design shape, and then resin infiltration and solidification and subsequent processes are carried out, so that the product manufacturing is finally completed. The flow of resin in the fiber preform is influenced by the structure of the fiber preform, and the corresponding flow process can influence the generation of void defects in the mold filling process, so that the establishment of a fiber fabric unit cell model under specified working conditions is important for the prediction and control of the related process.
In order to save the manufacturing cost and reduce the manufacturing period, the numerical simulation is carried out before the process scheme is determined, so that the numerical simulation has a very reference value for determining the process parameters and optimizing the process path. Because of the periodically repeating structural features of the fiber fabric, the associated analysis often uses a fabric unit RVE (REPRESENTATIVE VOLUME ELEMENT ) model. However, most of the RVE models of the fabrics are modeled by combining fiber bundles with constant geometric cross sections with the weaving mode of the fabrics, and the RVE models have a larger gap from the actual structure of the fabrics under actual working conditions, so that correlation analysis based on the models is not accurate enough, and the corresponding numerical simulation has insufficient application value in actual engineering. How to build the RVE model of the fabric under different specified working conditions is a precondition for accurately predicting and analyzing the seepage behavior of the resin in the preform, and meanwhile, building the corresponding RVE model with high fidelity according to the macro-microstructure of the fabric is a necessary condition for analyzing the multi-scale mechanical properties of the fabric.
The invention provides a two-dimensional carbon fiber fabric high-fidelity single cell RVE model building method, which comprises the steps of firstly dispersing fiber bundles in a single cell of a fabric into a plurality of representative fiber filaments, carrying out dynamic compaction simulation on the discrete fiber filaments to obtain fiber filament distribution, then carrying out corresponding section reconstruction and fiber bundle generation on the fiber bundles to which the discrete fiber filaments belong, and carrying out interference elimination and clearance control on fiber bundle models to complete the construction of the high-fidelity single cell RVE model under specified working conditions.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a method for establishing a high-fidelity unit cell model of a carbon fiber fabric, and provides a method for establishing a two-dimensional high-fidelity unit cell RVE model of the carbon fiber fabric.
Technical proposal
A method for establishing a high-fidelity single cell model of a carbon fiber fabric is characterized by comprising the following steps:
Step 1, processing digital images of fiber fabrics to obtain data of fabric thickness, length, short axis, area and porosity of the section of warp and weft fiber bundles;
Step 2, dispersing the warp and weft yarn fiber bundles into a plurality of representative fiber filaments according to the sectional area and the porosity of the warp and weft yarn fiber bundles, wherein the representative virtual fiber filament radius is as follows:
Sf＝π·rf 2
S is the cross-sectional area of single-bundle fibers, S f is the cross-sectional area of single discrete fibers, N is the number of discrete fibers, r f is the radius of a representative virtual fiber, Is the volume fraction of fiber filaments in the fiber bundle;
Step 3, according to the weaving mode and the single-cell size of the fabric, establishing discrete representative virtual fiber yarn central line control node space coordinates along the warp and weft yarn beam paths of the fabric, and carrying out spline curve interpolation and radius assignment to complete discrete fiber three-dimensional model construction;
Step4, importing the built three-dimensional model of the discrete fiber wires into dynamics simulation software, placing the model into two rigid plates, building each fiber wire into a digital chain which is in non-pin connection by a plurality of beam units, and endowing periodic boundary conditions according to the following conditions:
Uai=Ubi,i=1,2,3,4,5,6
wherein a, b represent fiber bundle end points of the connecting line, U represents the degree of freedom, and i represents the direction of the degree of freedom of the corresponding end points;
Then fixing the rigid lower plate, applying specified displacement to the rigid upper plate, controlling the thickness of the compacted discrete fiber yarn through the relative displacement of the two plates, and applying a load condition with proper concentration force to one end of the compacted discrete fiber yarn in the process;
Step 5, firstly, guiding out and reconstructing the compacted and simulated discrete fiber yarns, and summarizing representative fiber yarns belonging to the same bundle of warp yarns or weft yarns into a collection, namely a fiber bundle;
dividing each fiber bundle into a plurality of sections along the axial direction of the central line of the fiber bundle, wherein the sections are perpendicular to the central line of the fiber at the sections, and obtaining corresponding intersection points of representative fiber filaments on the sections;
Highly reconstructing a fiber bundle section with concave and convex features using a roping algorithm based on a force bias principle;
And 6, combining the warp and weft yarn fiber bundle models according to the weaving mode of the selected fabric to construct a single-cell fabric model, and adopting an interference elimination algorithm to realize interference elimination and gap insertion of micro areas of the model, thereby finally completing reconstruction of the single-cell fabric model.
The rope winding algorithm based on the force bias principle comprises the steps of firstly establishing a closed flexible rope wrapping fiber yarn collection, dispersing the rope into a ball chain formed by a series of balls with the radius r, arranging virtual stretching and bending springs between the balls, giving corresponding spring characteristics to maintain smoothness and continuity of the ball chain in the motion process, applying a centripetal force to the flexible rope to enable the discrete balls on the flexible rope to move towards the center of a surrounding area of the flexible rope at the same time, simultaneously arranging repulsive force related to overlapping degree between peripheral small balls and fibers, calculating the total force born by the small balls in the moving process, including stretching spring force, bending spring force, repulsive force and centripetal force, configuring the small displacement in the same direction for the small balls according to the total force born by the small balls, finally stopping motion when the total force of all the small balls reaches balance, performing overlapping deletion when the ball center distance is smaller than the radius r of the balls, performing ball interpolation when the distance between the adjacent balls is larger than 2r, finally performing discrete fiber yarn in the same bundle to wrap the fiber yarn, stopping the whole ball chain in the state when the potential energy reaches the minimum balance state, outputting the contour of the fiber bundle warp, and reconstructing the fiber bundle in the whole curve.
The interference elimination algorithm process is as follows, the fiber bundle surface is discretized into a dense point cloud set, an in-plane space area is defined as omega, a bundle of fiber bundle surface is defined as zero potential energy surface phi 0, euclidean distance field is constructed, potential energy is defined as negative for a point in the fiber bundle, otherwise, the potential energy is positive, and the potential energy is related to the distance d between the point p and the zero potential energy surface, namely:
Φ=-kd,p∈Ω
Firstly, for the minimum distance between the point with negative potential energy and the zero potential energy surface and the unit normal vector corresponding to the corresponding point on the zero potential energy surface, the unit normal vector is perpendicular to the curved surface Solving to make the point followAnd then, judging the potential energy of the point with the potential energy which is not zero, namely keeping the position when the potential energy is larger than a set value phi t, otherwise, moving the point along a corresponding method direction on a zero potential energy surface of the fiber until the potential energy is larger than the set value phi t, thereby realizing the insertion and control of the fiber bundle gap, wherein the minimum gap is d min, namely:
Φt＝k*dmin。
The spring characteristic is a tensile or flexural spring restoring force.
Advantageous effects
The invention provides a carbon fiber fabric high-fidelity unit cell model building method, which comprises the steps of selecting a minimum non-repeated fabric unit cell structure according to a used fiber fabric, obtaining the thickness of the fiber fabric, the cross-sectional area of a fiber bundle and the weaving mode of the fabric according to an optical image, dispersing the fiber bundle into a designated number of representative fiber filaments by using an equivalent volume, weaving the representative fiber filaments in the same mode according to the weaving mode of the fiber fabric, applying a proper periodic boundary condition to the model, carrying out dynamics simulation in combination with a designated working condition, carrying out fiber bundle reconstruction according to the distribution state of the representative fiber filaments after simulation, carrying out interference elimination on an interference part of the fiber bundle, and finally obtaining a high-fidelity unit cell RVE model under the designated working condition.
Drawings
FIG. 1 satin two-dimensional planar fabric sample
FIG. 2 discrete representative filaments
FIG. 3A is a flow chart of simulation of compaction of a discrete fiber model
(A) Discrete fibers and their applied force fields;
(b) Periodic boundary condition applying method
(C) Fiber compaction process
(D) Results of fiber compaction
FIG. 4 initial state of the roping algorithm
FIG. 5A roping algorithm to obtain the cross-sectional profile of the fiber bundle
FIG. 6 Multi-section surface interpolation of fiber bundle section profiles
FIG. 7 interference and cancellation between fiber bundles
(A) Interference between fiber bundles
(B) Interference cancellation and gap control
FIG. 8A-C satin weave pattern
Detailed Description
The invention will now be further described with reference to examples, figures:
the method comprises the following specific steps:
And 1, acquiring an image of the fiber fabric, wherein the image contains information such as a fiber fabric knitting mode, fabric thickness, fabric warp and weft cross section and the like. And processing the image by using image processing software in combination with a size calibration piece to obtain parameters such as fabric thickness, the length and the short axis of the cross section of the warp and weft yarn fiber bundles, the area, the porosity and the like.
Step 2, dispersing the warp and weft yarn fiber bundles into a plurality of representative virtual fiber yarns according to the sectional area of the warp and weft yarn fiber bundles and the volume fraction of the fiber yarns in the bundles, wherein the radius of the representative virtual fiber yarns is calculated according to the following formula:
Sf＝π·rf 2
S is the cross-sectional area of single-bundle fibers, S f is the cross-sectional area of single discrete fibers, N is the number of discrete fibers, r f is the radius of a representative virtual fiber, Is the fiber volume fraction in the fiber bundle.
And 3, establishing discrete representative virtual fiber yarn central line control node space coordinates along the warp and weft yarn beam path of the fabric by combining the weaving mode of the used fabric and the single-cell size of the fabric, and carrying out spline curve interpolation and radius assignment to complete the construction of a discrete fiber three-dimensional model.
And 4, importing the built three-dimensional model of the discrete fiber wires into dynamics simulation software, placing the model into two rigid plates, building each fiber wire into a digital chain which is subjected to non-pin linkage by a plurality of beam units, and giving periodic boundary conditions as shown in fig. 3 (b) according to the following formula.
Uai=Ubi,i=1,2,3,4,5,6
Wherein a, b represent fiber bundle end points of connecting lines in the figure, U represents the degree of freedom, and i represents the direction of the degree of freedom of the corresponding end points.
And fixing the rigid lower plate, applying specified displacement to the rigid upper plate, controlling the thickness of the compacted discrete fiber yarn through the relative displacement of the two plates, and applying a load condition with proper concentration force to one end of the compacted discrete fiber yarn in the process.
Step 5, firstly, guiding out and reconstructing the compacted and simulated discrete fiber yarns, and summarizing representative fiber yarns belonging to the same bundle of warp yarns or weft yarns into a collection, namely a fiber bundle. And dividing each fiber bundle into a plurality of sections along the axial direction of the central line of the fiber bundle, wherein the sections are perpendicular to the central line of the fiber, and obtaining corresponding intersection points of representative fiber filaments on the sections. In order to acquire the cross section of the discrete fiber model and solve the problem of poor curvature continuity of the traditional convex hull algorithm, the cross section of the fiber bundle with concave and convex characteristics is highly reconstructed, and a rope winding algorithm based on a force bias principle is used. The algorithm is mainly implemented by firstly establishing a closed flexible rope (wrapped fiber yarn set) and dispersing the rope into a ball chain consisting of a series of spheres with radius r. Virtual tension and bending springs are arranged between the balls, and corresponding spring characteristics (tension and bending spring restoring force) are given to the balls so as to maintain smoothness and continuity of the ball chain during movement. Wherein the tension spring restoring force and the bending spring force are both related to the deformation of the spring. A centripetal force is applied to the flexible cord to move the discrete beads thereon simultaneously toward the center of the flexible cord surrounding area. And meanwhile, repulsive force (related to overlapping degree) between the peripheral small balls and the fibers is set so as to ensure that the small balls and the fibers do not overlap as much as possible in centripetal motion. During the movement, the resultant force to which all the pellets are subjected is calculated, including the tension spring force, the bending spring force, the repulsive force and the centripetal force. And according to the resultant force applied to the device, the device is provided with tiny displacement in the same direction. Eventually stopping the movement when the total force of all the pellets reaches equilibrium. When the distance between the sphere centers of adjacent discrete spheres is smaller than the radius r of the sphere, overlapping and deleting are carried out, when the distance between the adjacent sphere centers is larger than 2r, sphere interpolation and supplement are carried out, finally, discrete fiber filaments in the same bundle are wrapped, and when the whole sphere chain reaches the balance state with the minimum potential energy, the movement of the sphere is stopped, and the cross section profile of the fiber is output. And (3) performing curved surface insertion on the fiber bundle profile to reconstruct the complete warp yarn and weft yarn fiber bundles in the single unit fabric.
And 6, combining the warp yarn fiber bundle models according to the weaving mode of the selected fabric to construct a fabric unit cell model, wherein in the process, micro-area interference can occur between warp yarn fiber bundles and weft yarn fiber bundles due to the inherent limitation introduction problem of dynamic numerical simulation. In order to enable the model to be widely applied to numerical simulation prediction, an interference elimination algorithm is adopted to realize interference elimination and gap insertion of a micro area of the model, and finally reconstruction of the single-cell model of the fabric is completed. The main process of the algorithm is that the surface of the fiber bundle is discretized into a dense point cloud set, the in-plane space area is defined as omega, a bundle of fiber bundle surface is defined as zero potential energy surface phi 0, a Euclidean distance field is constructed, potential energy is defined as negative for points in the fiber bundle, otherwise, the potential energy is positive, and the potential energy is related to the distance d between the point (p represents the point) and the zero potential energy surface, namely:
Φ=-kd,p∈Ω
Firstly, for the minimum distance between the point with negative potential energy and the zero potential energy surface and the unit normal vector corresponding to the corresponding point on the zero potential energy surface Solution (defined as outward perpendicular to the surface) to cause the point to followWhen all the negative potential energy points are moved so that the potential energy is zero, the interference between the fiber bundles and other fiber bundles is eliminated. And then, judging the potential energy of a point with potential energy not being zero, and keeping the position when the potential energy is larger than a set value phi t, otherwise, enabling the point to move along a corresponding method direction on a zero potential energy surface of the fiber until the potential energy is larger than the set value phi t, thereby realizing the insertion and control of the fiber bundle gap, wherein the minimum gap is d min, namely:
Φt＝k*dmin。
in the embodiment, a satin fiber fabric shown in fig. 1 is taken as an example, five wefts in satin form are satin, and a two-dimensional plane fabric high-fidelity single cell model building method is described with reference to the accompanying drawings.
1. A region with the size of 4cm multiplied by 4cm and containing the single-cell fabric is selected from the satin fabric to prepare a sample, the single-layer satin fabric is placed between two transparent acrylic plates, the thickness between the plates is controlled by a gasket, and the fixed thickness is fastened by using bolts.
2. The knitting mode of the satin fabric is recorded by using a camera and dimension calibration, and the knitting mode comprises the information of fabric thickness, fabric warp and weft yarn cross section and the like.
3. And (3) processing the image by using image processing software, and calibrating parameters such as the thickness of the fabric, the length, the short axis, the area and the volume fraction of the fiber yarns in the warp and weft fiber bundles.
4. According to the cross-sectional area S of the warp and weft yarn fiber bundles and the volume fraction of fiber filaments in the bundlesThe warp and weft yarn bundles were discretized into 61 representative filaments as shown in fig. 2, and the filament radii were calculated according to the following formula:
Sf＝π·rf 2
s is the cross section area of the single-beam fiber Shu Wei, Is the fiber volume fraction within the fiber bundle, S f is the individual discrete fiber cross-sectional area, and r f is the representative fiber radius.
5. And (3) establishing a discrete representative fiber center line control node space coordinate and path by combining the weaving mode of the used fabric, and carrying out spline curve interpolation and radius assignment to complete the construction of the discrete fiber three-dimensional model shown in fig. 2.
6. The built three-dimensional model of discrete filaments is imported into dynamics simulation software, which is placed in two rigid plates as in fig. 3 (c), and each filament is built as a digital chain with non-pin links by several beam units, and periodic boundary conditions as shown in fig. 3 (b) are given according to the following formula.
Uai=Ubi,i=1,2,3,4,5,6
Where a, b denote the fiber bundle end points of the wire in fig. 3 (b), U denotes the degree of freedom, and i denotes the direction of the degree of freedom of the corresponding end point.
And then fixing the rigid lower plate, applying specified displacement to the rigid upper plate, controlling the thickness of the compacted discrete fiber yarn through the relative displacement of the two rigid plates, applying a load condition of fixing one end of the discrete fiber yarn and applying a proper amount of concentrated force to the other end of the discrete fiber yarn in the process, determining the fiber density and the elastic modulus according to the parameters of the actually used fabric materials, and performing mass scaling definition under the condition that the simulation result does not change obviously to amplify the fiber mass by 10 times, wherein the result is shown in fig. 3 (d).
7. The compacted and simulated discrete filaments are led out and reconstructed and a collection of representative filaments belonging to the same bundle of warp or weft yarns is summarised, called a bundle. And dividing each fiber bundle into a plurality of sections along the axial direction of the central line of the fiber bundle, wherein the sections are perpendicular to the central line of the fiber, and obtaining corresponding intersection points of representative fiber filaments on the sections. As shown in fig. 4 and 5, the warp and weft yarn fiber bundle cross-sectional profile acquisition is performed by using a roping algorithm.
8. As shown in fig. 6, the obtained fiber bundle cross-sectional profile is subjected to multi-section curved surface interpolation to reconstruct the fiber bundle.
9. As shown in fig. 7, the warp and weft yarn fiber bundles are combined, and the fiber bundle micro interference elimination and the designated gap insertion are performed by adopting a fiber bundle interference elimination algorithm, so that the single cell model establishment of the satin two-dimensional plane fabric shown in fig. 8 is finally completed.
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