CN105063885B - Three-dimensional braided material based on space group P4 symmetry - Google Patents
Three-dimensional braided material based on space group P4 symmetry Download PDFInfo
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- CN105063885B CN105063885B CN201510420547.1A CN201510420547A CN105063885B CN 105063885 B CN105063885 B CN 105063885B CN 201510420547 A CN201510420547 A CN 201510420547A CN 105063885 B CN105063885 B CN 105063885B
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Abstract
The invention discloses a three-dimensional braided material based on space group P4 symmetry. According to the braided material, a novel three-dimensional braided geometric structure meeting the space group P4 symmetry and derived by taking representative volume elements meeting point group 4 symmetry as basic structural units is adopted to analyze the motion law of a yarn carrier in a braiding process, and the novel three-dimensional braided material variety having higher fiber volume percentage than the traditional three-dimensional braided material is obtained through research on the technology feasibility and prediction of the fiber volume percentage of the corresponding three-dimensional braided fabric. Meanwhile, the braiding technological method is simple and convenient to implement, the geometric structure of the obtained three-dimensional braided material is more stable, and the mechanical properties are excellent.
Description
Technical field
The present invention relates to three-dimensional knitting material technical field, specifically one kind are based on space groupSymmetric three
Dimension braided material.
Background technology
D braided composites have high specific strength, specific modulus, high damage tolerance and fracture toughness, resistance to punching because of it
Hit, not stratified, cracking resistance and the advantages of resisting fatigue, be used widely in the high-temperature-resistant structures such as Aeronautics and Astronautics, and constantly
To medical treatment, physical culture, automobile and other industries extension.But at this stage due to being subject to processing the restriction of the factors such as technique, 3 D weaving is combined
The kind of material is very few, working (machining) efficiency is low and process costs are high, is unfavorable for optimizing the performance of composite.Combination property to be obtained
Preferably D braided composites, are badly in need of developing more 3 D weaving techniques, and what relevant new three dimensional knitting method was predicted grinds
Study carefully work also in the starting stage.
The crystal of different crystalline lattice structure shows different performances, can be entered crystal geometry using Crystals in Symmetry group
Row classification.With reference to the research method of symmetric group, to the in addition inductive research of the cell geometry of braided material, according to space group
Push away to obtain three-dimensional yarn crossovers method new in a large number with the symmetry operation of space group description, thus obtaining yarn continuously three-dimensional yarn
Intersect geometry.By be three-dimensional new fabric developmental research new direction.
Content of the invention
The purpose of the present invention is: provides one kind to be based on space groupSymmetric three-dimensional knitting material, to expand three-dimensional volume
The species of Woven composite, and improve its performance.
The present invention is to solve above-mentioned technical problem, and the technical scheme being adopted is: based on space groupSymmetric three-dimensional
Braided material, the braided geometry of this braided material is to extend, in three dimensions, the structure in continuous yarn being woven into, and compiles
Knit the symmetry that the yarn line segment in the representative volume unit in geometry meets the point of space group 4 description, braiding structure
Present representative volume unit space group on the wholeThe translational symmetry operation of description carries out translating the three dimensions obtaining
The 3 D weaving fabric being interweaved together.
The group element of described space group 4 is(or), group's
Generating unit is, in three-dimensional system of coordinatexyzDefined in z-axis be rotary shaft, space group 4 is a pure rotation symmetry group, space
The matrix of the group element of point group 4 is expressed as follows,,
,；
The symmetric representative volume unit of the described point meeting space group 4 description, it is derived and is based on space group 4
Group element description rotationally symmetrical operation be expressed as:
,,
,；
Represent the point on a certain yarn line segmentThe rotationally symmetrical operation put after being transformed to equal sign；
Described space groupThe translational symmetry operation of description is in three-dimensional system of coordinatexyzIn, by representative volume unit
Yarn line segment combination do following manner:
(1)
(u,v,wFor base vector) translational symmetry operation.
Yarn line segment combination in described representative volume unit has z to thicknessh,xoyCoordinate plane and parallel with it
Bundle of planes in, the section of representative volume unit is rhombus, and the translation of representative volume unit is along quadrangular z to heighth'sTranslate again, in three-dimensional knitting material, the dot matrix corresponding to representative volume unit is simple tetragonal dot matrix, ultimately forms and has
Space groupA kind of symmetric new space continuous yarn intersects geometry.
The representative volume unit of each yarn line segment combination includes internal representative volume unit, surface representative volume unit
With corner representative volume unit, monolayer knitted body representative volume unit sum is:
(2)
Corner representative volume unitNumber and surface representative volume unitNumber be respectively as follows:
,(3)
Internal representative volume unitNumber is
(4)
Wherein, m, n are the representative volume unit number on the adjacent both sides of braided material section tetragon.
Beneficial effect:
The braided material of the present invention is derived with meeting the symmetric representative volume unit of point group 4 for basic structural unit
Meet space groupSymmetric new 3 D weaving geometry, by the research to its technological feasibility with to corresponding
The prediction of the fiber volume percentage composition of three-dimensional braid, has obtained fiber volume percentage composition than conventional three-dimensional braided material more
High new three-dimensional knitting material kind.Meanwhile, its weaving method is simple, facilitate implementation, and the three-dimensional knitting material obtaining is several
What structure is more firm, and mechanical property is more excellent.
Brief description
Fig. 1 is the structural representation of representative volume unit in the present invention；
Fig. 2 is the structural representation of the simple tetragonal dot matrix in the present invention residing for representative volume unit；
Fig. 3 is the structural representation of usual representative volume unit yarn line segment combination；
Fig. 4 is to meet space groupp4 symmetric three-dimensional knitting material interior geometry schematic diagrams；
Fig. 5 is corresponding space grouppThe geometry schematic diagram of 4 three-dimensional knitting material；
Fig. 6 is the movement locus figure taking yarn device in basic preparation method；
Fig. 6 a takes the characteristics of motion schematic diagram of yarn device for the first kind；
Fig. 6 b takes the characteristics of motion schematic diagram of yarn device for Equations of The Second Kind；
The structural representation of the three dimensional fabric that Fig. 7 is prepared for the present invention；
Fig. 7 a is fabric construction figure corresponding with Fig. 6 a；
Fig. 7 b is fabric construction figure corresponding with Fig. 6 b；
The structural representation of representative volume unit in the fabric that Fig. 8 a is prepared for the present invention；
The structural representation of multiple adjacent representations gonosome product units in the fabric that Fig. 8 b is prepared for the present invention；
The fabric yarn lateral compression structural representation that Fig. 9 is prepared for the present invention；
The geometrical form schematic diagram formed by the extruding of fabric yarn that Figure 10 is prepared for the present invention；
The fabric extent partition structure schematic diagram that Figure 11 is prepared for the present invention；
Figure 12 is to simplify mutual relation structural representation in given coordinate system for the yarn geometry parameter；
Figure 13 is the structural representation simplifying yarn cell geometry model；
Reference: a in Figure 11: corner representative volume unit, b: surface representative volume unit, c: internal representative
Elementary volume, volume element.
Specific embodiment
Below in conjunction with the accompanying drawings explanation the present invention based on space groupThe specific embodiment party of symmetric three-dimensional knitting material
Formula: the unit in braided material refers to table gonosome product unit.Herein and in claimsRepresent identical containing with p4
Justice.
1st, meet the symmetric 3 D weaving geometry unit of point group 4
In three-dimensional system of coordinatexyzIn set z-axis as rotary shaft, meet braiding point group 4 group element be(or), four in point group 4 kind rotation process,Generation for point group 4
Unit it is believed that be aroundAxle turns overThe rotation at angle, the matrix of the group element of corresponding point group 4 is expressed as follows
,,
,.
The corresponding rotationally symmetrical operation of group element of space group 4 is expressed as
,,
,；
Represent the point on a certain yarn line segmentThe rotation process put after being transformed to equal sign.
As shown in Figure 1, the symmetry operation imposing space group 4 to yarn line segment 1 can be derived from the combination of remaining yarn line segment, this group
Close pattern as representative volume unit (abbreviation unit), the geometry of novel three-dimensional of can deriving braiding.
2nd, meet space groupSymmetric 3 D weaving geometry
2.1 corresponding space groupsThe usual unit of 3 D weaving geometry
The simple tetragonal dot matrix of Crystals in Symmetry group description is designated as(as shown in Figure 2) is mutually coordinated with space group 4.
Represent, with a lattice point, the unit meeting space group 4, then unit (as Fig. 1) is put into cubic dot matrix, verify the continuous of yarn
Property, and then form usual unit, i.e. usual representative volume unit yarn line segment combination.(as shown in Figure 3).
2.2 space groupCorresponding translational symmetry operation
Set up three-dimensional system of coordinate xyz, the symmetry operation in three dimensions is:
(u,v,wFor base vector) (1)
WhereinFor integer,For translation vector.The usual unit meeting the point-symmetry property of space group 4 is put
Enter simple tetragonal dot matrixPush away and must meet braiding space groupSymmetric 3 D weaving interior volume geometry
(as shown in Figure 4).If monolayer yarn line segment combination in the representative volume unit shown in Fig. 1zTo thicknessh,xoySit
Mark plane and bundle of planes parallel with it in, unit along z to be withhIntegral multiple translation.
2.3 space groupCorresponding new 3 D weaving geometry
Can be derived from the unit of this new 3 D weaving geometry by the symmetry operation of space group 4, this unit is put down
Move operation and obtain possible 3 D weaving interior geometry.During actual braiding, the seriality of yarn to be considered will
Ask, and study its rule, and then obtain a kind of brand-new 3 D weaving geometry (as shown in Figure 5).
3rd, the weaving research of new three-dimensional knitting material geometry
A kind of corresponding new three dimensional knitting method of geometry of new three-dimensional knitting material is it may first have to research meets fabric
The crisscross motion rule of the yarn of geometry.Fig. 6 elaborates the plane motion rule taking yarn device for carrying yarn movement.
EachRepresent one and take yarn device, arrow is oriented to the direction of motion taking yarn device, yarn device is taken in the hollow and solid expression of arrow
Packet.In braiding array of yarns, the yarn device of taking of same motion trajectory is classified as a class, is divided into two classes (such as Fig. 6 a, Fig. 6 b institute
Show).During braiding, the yarn device movement locus of taking of same track do not change.All take yarn device by classification along arrow side
To alternately moving once, complete a braiding circulation.
Every group of yarn in new three-dimensional braid is straight line, only bends (as shown in Figure 7) in boundary.Two classes are different
Yarn ultimately forms new 3 D weaving geometry in space substep intersection.As Fig. 7 a is fabric construction corresponding with Fig. 6 a
Figure；Fig. 7 b is fabric construction figure corresponding with Fig. 6 b.
4th, the cell geometry analysis model of new three-dimensional knitting material
New 3 D weaving geometry is expected to be used for making the enhancing phase of new D braided composites, and its performance is pre-
Survey is using the analysis model based on cell geometry.Here dividing elements method and conventional elements follow the example of slightly difference: this
Elementary boundary in the new fabric geometric model of invention all using complete yams, inlayed by complete yams by adjacent cells, rather than
Traditional yarn center line segmentation (as figures 8 a and 8 b show).The advantage of this division methods is: is not affecting geometry
Remain the complete symmetry of unit on the basis of description, can be entered using the theoretical mechanical property to material of group in follow-up study
Row research.
4.1 basic assumption
(1) the braiding yarn cross section, being subject to lateral compression is rhombus (as shown in Figure 9), and submissive enough, carries with braiding
The change of lotus produces geometry deformation.
(2), braiding process is sufficiently stable, and in the range of certain length, braided geometry is consistent.
(3), internal element accounts for the overwhelming majority of woven preform, with the increase of sectional dimension, ignores surface texture
Impact.
(4), internally in unit, every one thread is subject to the lateral load from different directions, the cross section of final yarns
It is squeezed into the geometry shown in Figure 10.The size of lateral compression degree will have influence on composite fiber volume basis and contain
Amount.
The region division of 4.2 3 D weaving fabrics and its unit
Braided fabric is divided into interior zone, surface region and folding corner region.Corresponding unit is referred to as internal element
(interior unit), surface cell (face unit) and corner unit (corner unit) (as shown in Figure 11).
4.3 structural parameters describing 3 D weaving fabric
The performance of this braided material can be described using the usual unit of cuboid.
4.3.1 the unit number of single layer weave fabric
If m, n are the unit number on the tetragon adjacent edge of braided fabric section.Monolayer knitted body representative volume unit is total
NumbernFor
(2)
Corner representative volume unitNumber and surface representative volume unitNumber be respectively
,(3)
Internal representative volume unitNumber is
(4)
4.3.2 D braided composites geometric model and fiber volume percentage composition
The performance of this braided material can be described using the usual unit of cuboid.
(1) volume of the usual unit of cuboidOverall length with yarnl
In the rectangular coordinate system of Figure 12, if the unit base length of side is respectively、, Hua Jiegao, braid angle is
(i.e. yam axis inThe angle of axle).The then volume of the usual unit of cuboidFor:
(5)
Geometrical relationship according to Figure 12, obtains unit yarn overall lengthFor
(6)
Geometric parameter、、、WithRelation be
(7)
(2) single yarn is in the sectional area of cell surface
As shown in figure 13, note yarn is in the sectional area of cell surfaceFor
(8)
Use symbolThe equivalent cross-sectional area of yarn after geometry changes in description knitted body, yarnWith's
Equivalent cross-sectional area is respectivelyWith. according to the geometrical relationship of Figure 12, Figure 13, push away to obtain yarnWithEquivalent cross-sectional area、For
(9)
(3) reduction coefficient of yarn cross sectionThe urgent factor with yarn:
The reduction coefficient of cross sectionBe description yarn weaving and make yarn occur geometry deformation to equivalent transversal
The influence degree in face, definition yarn cross section reduction coefficient:
(10)
Wherein,
(11)
For weaving the equivalent diameter (mm) of yarn it is resolved that line density in yarn() and bulk density().
Yarn fill factor, curve factorThe size of fiber volume percentage composition in reflection yarn.Yarn because jam-packed degree, have non-twist
Yarn and the difference of the twist, the numerical value of the urgent factor of yarn is also different.The fraction volume of fiber maximum of Untwisted yarn:
=(12)
Use symbolThere is the yarn cross-section area before geometry change in description knitted body.If the circular section of yarn exists
Only occur during braiding interfibrous to slide it is believed that fibre section is amassed and do not change before and after Yarn texturing, and institute
Account for that percent is constant, thus the cross section being approximately considered yarn does not change. i.e.:
(13)
In the void area of unit, the increasing with urgent load and the deformation of yarn, space will be finally different degrees of
Filling, now fraction volume of fiber reaches maximum.It is presented as yarn cross section reduction coefficient:
Or(14)
(4) in unit the cumulative volume of yarn and fiber cumulative volume
Geometrical relationship according to Figure 12, obtains the cumulative volume simplifying yarn line segment in unitFor
(15)
Before reduction, yarn cumulative volume is
(16)
If fraction volume of fiber is in yarn, the cumulative volume of fiber is
(17)
(5) fraction volume of fiber
Can be pushed away by formula (5), (12) and (17) and fraction volume of fiber in body unit must be woven:
(18)
HereFor fiber limiting volume percentage composition.The total fiber of simplification yarn line segment is amassed and is
(19)
Think that now fraction volume of fiber is minimum in knitted body:
(20)
(6) fraction volume of fiberValue
Cross section reduction coefficientSize, impact fiber volume percentage composition value.The fibre of woven composite
Dimension volumn concentrationUnder the jammed state of the limit, also it is not up to the numerical value of unidirectional yarn assembly body.Braid angle
Size, by the reduction coefficient to cross sectionImpact, and then affect fiber volume percentage composition size.Braid angle is got over
Greatly,Value is less, otherwise bigger.According to formula (13) understand it is assumed thatWhen taking maximum (1), corresponding braided material because
For it is loosely organized, fraction volume of fiber is very low；When taking minimum, fraction volume of fiber reaches maximum.
Claims (3)
1. it is based on the symmetric three-dimensional knitting material of space group p4, the braided geometry of this braided material is to prolong in three dimensions
Stretch the structure in continuous yarn being woven into it is characterised in that: the yarn in representative volume unit in braided geometry
Section meets the symmetry of the point of space group 4 description, and braided geometry presents on the whole by representative volume unit space
GroupThe translational symmetry operation of description carries out translating the 3 D weaving fabric that the three dimensions obtaining are interweaved together；
The group element of described space group 4 is, the generation unit of group is, in three-dimensional system of coordinatexyz
Defined in z-axis be rotary shaft, space group 4 is a pure rotation symmetry group, and the matrix of the group element of space group 4 represents such as
Under:,,
,；
The symmetric representative volume unit of the described point meeting space group 4 description, its group deriving based on space group 4
The rotationally symmetrical operation of element description is expressed as:
,,
,；
Represent the point on a certain yarn line segmentThe rotationally symmetrical operation put after being transformed to equal sign；
Described space groupThe translational symmetry operation of description is in three-dimensional system of coordinatexyzIn, by the yarn in representative volume unit
The translational symmetry that following manner is done in line segment combination operates:
(1)
Wherein,u,v,wFor base vector.
2. according to claim 1 based on the symmetric three-dimensional knitting material of space group p4 it is characterised in that: described representative
Yarn line segment combination in gonosome product unit has z to thicknessh,xoyIn coordinate plane and bundle of planes parallel with it, represent
The section of gonosome product unit is rhombus, and the translation of representative volume unit is along quadrangular z to thicknessh'sTranslate again, three
In dimension braided material, the dot matrix corresponding to representative volume unit is simple tetragonal dot matrix, ultimately forms with space groupRight
A kind of new space continuous yarn of title property intersects geometry.
3. according to claim 2 based on the symmetric three-dimensional knitting material of space group p4 it is characterised in that: each yarn line segment
The representative volume unit of combination includes internal representative volume unit, surface representative volume unit and corner representative volume
Unit, monolayer knitted body representative volume unit sum is:
(2)
Corner representative volume unitNumber and surface representative volume unitNumber be respectively as follows:
,(3)
Internal representative volume unitNumber is
(4)
Wherein, m, n are the representative volume unit number on the adjacent both sides of braided material section tetragon.
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| CN106400295B (en) * | 2016-08-31 | 2018-06-19 | 河南科技大学 | Three-dimensional woven tube and the three dimensional knitting machine and weaving for making the three-dimensional woven tube |
| CN108197398B (en) * | 2018-01-11 | 2020-05-19 | 南京航空航天大学 | Finite element method for predicting failure of three-dimensional braided composite material based on space group P4 |
| CN109440293B (en) * | 2018-12-06 | 2023-09-08 | 河南科技大学 | Three-dimensional two-way angle interlocking fabric based on space group P4mm symmetry |
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| US6439096B1 (en) * | 2000-11-28 | 2002-08-27 | 3Tex, Inc. | Automated 3-D braiding machine and method |
| GB0724044D0 (en) * | 2007-12-08 | 2008-01-16 | Smith & Nephew | Wound packing members |
| CN102041635B (en) * | 2010-12-24 | 2013-09-18 | 河南科技大学 | Three-dimensional woven material based on space group P* |
| CN201908202U (en) * | 2010-12-24 | 2011-07-27 | 河南科技大学 | Three-dimensional knitting material |
| CN102747534B (en) * | 2012-01-15 | 2014-04-02 | 河南科技大学 | Three-dimensional weaving process method based on space group P3* symmetry and apparatus thereof |
| CN102747535B (en) * | 2012-01-15 | 2014-11-12 | 河南科技大学 | Three-dimensional weaving process method based on space group P* symmetry and apparatus thereof |
| CN203333966U (en) * | 2013-06-13 | 2013-12-11 | 宜兴市华恒高性能纤维织造有限公司 | Three-dimensional integral preform for reinforcing beam with T-shaped cross section |
| CN103806219B (en) * | 2014-01-02 | 2015-07-15 | 河南科技大学 | Space group R3 symmetry-based three-dimensional woven material and weaving method thereof |
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