CN112906083A - Modeling method of 2.5-dimensional braided composite material geometric topological model - Google Patents

Modeling method of 2.5-dimensional braided composite material geometric topological model Download PDF

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CN112906083A
CN112906083A CN202110203671.8A CN202110203671A CN112906083A CN 112906083 A CN112906083 A CN 112906083A CN 202110203671 A CN202110203671 A CN 202110203671A CN 112906083 A CN112906083 A CN 112906083A
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weft
composite material
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weft yarns
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张宏建
杨皓
崔海涛
温卫东
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a modeling method of a 2.5-dimensional braided composite material geometric topological model, which comprises the following steps: firstly, acquiring a 2.5-dimensional woven composite material latitudinal slice diagram by using an XCT technology; secondly, measuring and counting the weft yarn positions on the same layer in the section obtained in the first step; thirdly, measuring and counting the positions of the two upper weft yarns relative to the lower weft yarns of the two adjacent layers in the section obtained in the step one; fourthly, based on the weft yarn positions obtained in the second step and the third step, a cosine function curve is adopted to simulate the warp yarn track and the weft yarn contour in the slice layer; fifthly, three-dimensional stretching is carried out on the warp and weft two-dimensional structure model built in the step four to obtain a weft straight three-dimensional model, and finite element dispersion is carried out to obtain a three-dimensional finite element model; and sixthly, modifying surface weft yarns of the three-dimensional finite element model by utilizing the grid grouping to bend the surface weft yarns at the interweaving positions of the surface weft yarns and the warp yarns, and finally establishing a model close to the geometric topological structure of the 2.5-dimensional woven composite material.

Description

Modeling method of 2.5-dimensional braided composite material geometric topological model
Technical Field
The invention belongs to the technical field of composite materials, and particularly relates to a modeling method of a 2.5-dimensional braided composite material geometric topological model.
Background
The 2.5-dimensional braided composite material is characterized in that the fiber bundles in different layers are mutually orthogonally interwoven in different directions, so that the layers are hinged, the shearing strength of the material is improved, and the performance in the thickness direction is enhanced. Because the braided composite material has a complex structure, scientific and reasonable mechanical property analysis needs to fully consider the internal geometric structure of the material, the mechanical property of internal component materials, the stress condition of the material and the like, the prediction of the performance of the braided composite material is more complicated due to the internal structural nonuniformity caused by the interweaving of yarns, for example, the mechanical property of a curved section of a fiber bundle is reduced compared with that of a straight section, a resin poor area, a resin rich area and the like exist in a net-shaped structure, so that the mechanical property of the braided composite material needs to be firstly researched when the braided composite material is researched, the weaving process of the three-dimensional braided composite material is always periodical in order to improve the production efficiency in the forming process, the internal structure of the three-dimensional braided composite material is also periodical generally, the research on the structure in the minimum period of the braided material replaces the research on the whole material to reduce the calculation scale, this minimal periodic unit, also known as a "unit cell," reduces computational cost and improves computational efficiency by studying a unit cell instead of studying the entire material.
Disclosure of Invention
Aiming at the defects of the existing 2.5-dimensional braided composite material modeling method, the invention provides a new 2.5-dimensional braided composite material geometric topological model modeling method, so that the established geometric model is close to the actual geometric topological structure of the material.
In order to achieve the purpose, the invention adopts the following technical scheme:
a2.5-dimensional braiding composite material geometric topological model modeling method comprises the following steps:
step one, obtaining a 2.5-dimensional woven composite material latitudinal slice diagram by using an XCT technology;
step two, measuring and counting the weft yarn positions on the same layer in the section obtained in the step one;
step three, measuring and counting the positions of two upper weft yarns relative to the lower weft yarns of two adjacent layers in the section obtained in the step one;
step four, based on the positions of the weft yarns on the same layer measured in the step two and the positions of the weft yarns on the upper layer and the weft yarns on the lower layer of the two adjacent layers measured in the step three, simulating the warp track and the weft yarn contour in the XCT slice diagram obtained in the step one by adopting a cosine function curve, and establishing a warp and weft yarn two-dimensional structure model;
step five, performing three-dimensional stretching on the warp and weft two-dimensional structure model established in the step four by using software to obtain a 2.5-dimensional braided composite material three-dimensional model with straight weft, and performing finite element dispersion to obtain a three-dimensional finite element model;
and step six, based on the three-dimensional finite element model established in the step five, modifying the weft yarns on the surface layer of the three-dimensional finite element model by utilizing grid grouping, bending the weft yarns on the surface layer at the interweaving positions with the warp yarns, and finally establishing a model close to the geometric topological structure of the 2.5-dimensional woven composite material.
Further, in the first step, the slice taken by XCT includes more than one unit cell structure.
In the first step, in the slice taken by XCT, the double-lens hypothesis is adopted for the weft section in the inner layer, the rectangular section hypothesis is adopted for the weft section in the surface layer that is not interwoven with the warp, and the double-lens hypothesis is adopted for the weft section in the surface layer that is interwoven with the warp.
Furthermore, in the second step, five reference lines are divided according to the number of weft layers in the slice, and the relative height of the weft in the same layer from the reference line in the same layer is measured and counted to compare the relative positions of the weft in the same layer.
Furthermore, in the third step, a vertical reference line is established by using a center point of a certain weft yarn, and the horizontal distance between two weft yarns on the upper layer and the lower layer of the two adjacent layers is measured and counted to compare the relative positions of the weft yarns on the adjacent layers.
Further, in the fourth step,
the warp yarn path is described by a cosine function: (x) Acos (ω x) + g;
the weft contour is described using a cosine function: g (x) ═ Acos (ω x) + h;
wherein A, omega, g and h are unknown parameters; the amplitude A is the mean value of the difference between the coordinates of the highest point and the lowest point of the curve, omega is related to the curve period, g and h are the relative positions of the curve and the local coordinate system, so that the following are provided:
Figure BDA0002948953940000021
Figure BDA0002948953940000022
in the formula w2w、w2jThe height (mm) of the cross section of the weft yarn and the warp yarn respectively; t is the minimum period of a trigonometric function and is related to the weft distance of the same layer; h iswThe height between two adjacent layers of weft yarns is related to the number of layers of the weft yarns:
Figure BDA0002948953940000023
in the formula, H is the integral thickness of the 2.5-dimensional braided composite material, NwThe number of layers of the weft yarn is,
Figure BDA0002948953940000031
the horizontal distance between two wefts in the upper layer of the two adjacent layers is half of the horizontal distance between the wefts in the lower layer.
Further, in the fifth step, the finite element discretization includes the following steps: and (3) carrying out grid discretization on the 2.5-dimensional woven composite material three-dimensional model with straight weft yarns by using software, and regrouping the surface weft yarns and the matrix grid of the three-dimensional finite element model to modify the surface weft yarn tracks.
Drawings
FIG. 1 is a flow chart of the geometric topological structure modeling method based on 2.5-dimensional braided composite material of the present invention;
FIG. 2 is a drawing of an XCT slice of a 2.5-dimensional braided composite material with a backing warp;
FIG. 3 is a schematic view of the statistics of weft yarn positions in a slice; wherein, FIG. 3a is a statistical schematic diagram of the relative positions of weft yarns in two adjacent layers in a section; FIG. 3b is a statistical representation of the weft yarn positions in the same layer in a slice;
FIG. 4 is a schematic view of warp yarn path strike;
FIG. 5 is a warp view of a 2.5 dimensional woven composite with flat weft yarns
FIG. 6 is a schematic illustration of surface layer flat weft modification for a three-dimensional finite element model, wherein FIG. 6a is a 2.5 dimensional woven composite three-dimensional model warp view with the surface layer weft flat prior to modification; FIG. 6b is a slice of an XCT versus test piece taken in the warp direction; FIG. 6c is a three-dimensional model warp view of the surface weft yarns after modification in bending;
FIG. 7 is a 2.5 dimensional braided composite geometric topological model established by the present invention, wherein FIG. 7a is an established weft yarn model; FIG. 7b is the established warp and inlay warp yarn model; FIG. 7c is the established matrix model; fig. 7d is the complete model finally built.
Advantageous effects
The modeling of the traditional 2.5-dimensional woven composite material is generally that all yarn trends are drawn in a two-dimensional plane, the two-dimensional plane is stretched, and different yarns are grouped to obtain a final three-dimensional model of the woven material, while the 2.5-dimensional woven composite material researched by the method has certain fluctuation in the warp direction and the weft direction, which brings certain difficulty to the modeling of a geometric model by using the traditional method, and the geometric model established by using the method can better reflect the geometric topological structure of the material by considering the bending trend of weft yarns.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the modeling method of the 2.5-dimensional braided composite material geometric topological model of the present invention is specifically as follows:
the method comprises the following steps: the method is characterized in that the XCT material internal structure is utilized to carry out slice scanning, as shown in figure 2, the double-lens assumption is adopted for the weft yarn section of the inner layer, the rectangular section assumption is adopted for the weft yarn section of the 2.5-dimensional woven composite material surface layer which is not interwoven with the warp yarn, and the double-lens assumption is adopted for the weft yarn section of the 2.5-dimensional woven composite material surface layer which is interwoven with the warp yarn;
step two: the position of the weft yarns in the same layer in the section obtained in the step one is determined as shown in a figure 3(b), and the measurement result of the distance between the center measuring point of the weft yarns in the same layer and the reference line is as follows:
TABLE 1 distance of center measuring point of inner weft yarn from reference line
Figure BDA0002948953940000041
Through statistics of measurement results, although the distances between the weft yarns positioned on the same layer and the reference line are vertically floated, the dispersion degrees are within 0.2, and therefore the weft yarns positioned on the same layer are assumed to be on the same horizontal line.
Step three: measuring and counting the relative positions of weft yarns of two adjacent layers in the section image obtained in the step one; randomly selecting 7 groups of weft yarns in a weft section picture shot by XCT, wherein each group of weft yarns comprises three weft sections of two adjacent layers, two adjacent weft yarns are positioned on an upper layer, one weft yarn is positioned on a lower layer and is positioned between the two weft yarns on the upper layer, the central point of the weft yarn is selected as a measuring point, the 7 groups of selected weft yarns comprise the weft yarns of all layers in the thickness direction, the relative positions of the two adjacent layers of weft yarns in the section picture are measured as shown in figure 3(a), and the relative distance measurement results of the two adjacent layers of weft yarns are as follows:
TABLE 2 statistics of relative distances between adjacent weft yarns
Figure BDA0002948953940000042
For the positions of the upper weft yarn and the lower weft yarn, the upper weft yarn and the lower weft yarn are supposed to be distributed in a staggered way and the weft yarn of the lower layer is positioned at the central position of the two weft yarns of the upper layer,
in which the weft yarns of the same layerAt a spacing of
Figure BDA0002948953940000051
d1 represents the horizontal distance from the center point of the lower weft yarn to the center point of the left weft yarn of the upper layer; d2 represents the horizontal distance from the center point of the lower weft yarn to the center point of the left weft yarn of the upper layer;
Figure BDA0002948953940000052
representing the mean values of d1 and d 2.
Step four: based on the weft yarn position of the same layer determined in the second step and the relative position of the weft yarns of the two adjacent layers determined in the third step, simulating the warp yarn track and the weft yarn contour in the section by adopting a cosine function curve, and establishing a warp yarn and weft yarn two-dimensional structure model;
the description using the cosine function for the warp yarn path is shown in FIG. 4: (x) Acos (ω x) + g;
the weft yarn contour is described by adopting a cosine function: g (x) ═ Acos (ω x) + h;
wherein A, omega, g and h are unknown parameters.
For trigonometric functions, the amplitude A can be seen as the mean of the difference between the coordinates of the highest and lowest points of the curve, ω1Relating to the curve period, g and h are relative positions of the curve and the local coordinate system, so that:
Figure BDA0002948953940000053
Figure BDA0002948953940000054
in the formula w2w、w2jHeight (mm) of the weft and warp sections, respectively, T being the minimum period of a trigonometric function related to the weft pitch of the same layer, hwThe height between two adjacent layers of weft yarns is related to the number of layers of the weft yarns:
Figure BDA0002948953940000055
in the formula, H is the whole thickness of the test piece, NwThe number of layers of the weft yarn is,
Figure BDA0002948953940000056
half the distance between adjacent wefts, as determined by the statistics of step three. All warp yarn paths in the structure are drawn in a two-dimensional plane, see figure 4.
Step five: and D, performing three-dimensional stretching by utilizing UG to obtain a 2.5-dimensional braided composite material three-dimensional model with straight weft yarns according to the 2.5-dimensional braided composite material two-dimensional structure diagram obtained in the step four, wherein a warp direction view of the model is shown in figure 5.
Step six: and (3) carrying out grid discretization on the 2.5-dimensional woven composite three-dimensional model with the straight weft yarns obtained in the step five by using hypermesh software, regrouping the surface weft yarns on the surface of the three-dimensional finite element model and the matrix grid to modify the surface weft yarn tracks, wherein the process is shown in figure 6, and finally establishing a model which is close to the 2.5-dimensional woven composite geometric topological structure shown in figure 7.

Claims (7)

1. A2.5-dimensional braiding composite material geometric topological model modeling method is characterized by comprising the following steps:
step one, obtaining a 2.5-dimensional woven composite material latitudinal slice diagram by using an XCT technology;
step two, measuring and counting the weft yarn positions on the same layer in the section obtained in the step one;
step three, measuring and counting the positions of two upper weft yarns relative to the lower weft yarns of two adjacent layers in the section obtained in the step one;
step four, based on the positions of the weft yarns on the same layer measured in the step two and the positions of the weft yarns on the upper layer and the weft yarns on the lower layer of the two adjacent layers measured in the step three, simulating the warp track and the weft yarn contour in the XCT slice diagram obtained in the step one by adopting a cosine function curve, and establishing a warp and weft yarn two-dimensional structure model;
step five, performing three-dimensional stretching on the warp and weft two-dimensional structure model established in the step four by using software to obtain a 2.5-dimensional braided composite material three-dimensional model with straight weft, and performing finite element dispersion to obtain a three-dimensional finite element model;
and step six, modifying the weft yarns on the surface layer of the three-dimensional finite element model by utilizing grid grouping based on the three-dimensional finite element model established in the step five, so that the weft yarns are bent at the interweaving positions with the warp yarns, and finally establishing a model close to the geometric topological structure of the 2.5-dimensional woven composite material.
2. The method of claim 1, wherein in the first step, the slice pattern of XCT contains more than one unit cell structure.
3. The modeling method for the geometric topological model of 2.5-dimensional woven composite material according to claim 1, wherein in the first step, in the slice taken by XCT, the double lens assumption is adopted for the weft yarn section of the inner layer of the 2.5-dimensional woven composite material, the rectangular section assumption is adopted for the weft yarn section of the surface layer of the 2.5-dimensional woven composite material, which is not interwoven with the warp yarn, and the double lens assumption is adopted for the weft yarn section of the surface layer of the 2.5-dimensional woven composite material, which is interwoven with the warp yarn.
4. The modeling method of the 2.5-dimensional braided composite geometric topological model according to claim 1, wherein in the second step, five reference lines are divided according to the number of weft layers for the slice, and the relative height of the weft in the same layer from the reference line in the layer is measured and counted to compare the relative positions of the weft in the same layer.
5. The modeling method of 2.5-dimensional weaving composite geometric topological model according to claim 1, characterized in that in the third step, a vertical reference line is established by a certain weft yarn center point, and the horizontal distance between two weft yarns at the upper layer and the lower layer of two adjacent layers is measured and counted to compare the relative position of the weft yarns at the adjacent layers.
6. The modeling method for 2.5-dimensional braided composite geometric topological model according to claim 1, wherein in said step four,
the warp yarn path is described by a cosine function: (x) Acos (ω x) + g;
the weft contour is described using a cosine function: g (x) ═ Acos (ω x) + h;
wherein A, omega, g and h are unknown parameters; the amplitude A is the mean value of the difference between the coordinates of the highest point and the lowest point of the curve, omega is related to the curve period, g and h are the relative positions of the curve and the local coordinate system, so that the following are provided:
Figure FDA0002948953930000021
Figure FDA0002948953930000022
in the formula w2w、w2jThe height (mm) of the cross section of the weft yarn and the warp yarn respectively; t is the minimum period of a trigonometric function and is related to the weft distance of the same layer; h iswThe height between two adjacent layers of weft yarns is related to the number of layers of the weft yarns:
Figure FDA0002948953930000023
in the formula, H is the integral thickness of the 2.5-dimensional braided composite material, NwThe number of layers of the weft yarn is,
Figure FDA0002948953930000024
the horizontal distance between two wefts in the upper layer of the two adjacent layers is half of the horizontal distance between the wefts in the lower layer.
7. The modeling method of 2.5 dimensional braided composite geometric topological model according to claim 1, characterized in that in said step five, finite element discretization includes the following steps: and (3) carrying out grid discretization on the 2.5-dimensional woven composite material three-dimensional model with straight weft yarns by using software, and regrouping the surface weft yarns and the matrix grid of the three-dimensional finite element model to modify the surface weft yarn tracks.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050018885A1 (en) * 2001-05-31 2005-01-27 Xuesong Chen System and method of anatomical modeling
CN105808893A (en) * 2016-05-30 2016-07-27 江苏理工学院 Rigidity predicting method for 2.5-D woven composite
CN108717727A (en) * 2018-05-29 2018-10-30 南京航空航天大学 A kind of identification of D braided composites precursor structure and modeling method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050018885A1 (en) * 2001-05-31 2005-01-27 Xuesong Chen System and method of anatomical modeling
CN105808893A (en) * 2016-05-30 2016-07-27 江苏理工学院 Rigidity predicting method for 2.5-D woven composite
CN108717727A (en) * 2018-05-29 2018-10-30 南京航空航天大学 A kind of identification of D braided composites precursor structure and modeling method

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