CN109446561A - Composite material antisymmetry wraps up square tube crush characteristics analysis method - Google Patents
Composite material antisymmetry wraps up square tube crush characteristics analysis method Download PDFInfo
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Abstract
The invention belongs to research on vehicle passive safety fields, and in particular to a kind of composite material antisymmetry package square tube crush characteristics analysis method.The following steps are included: the description of 1, structure is defined with coordinate；2, the limit stress and elasticity modulus of composite material are calculated；3, surrender membrane forces and unit length plastic limit bending moment are calculated；4, it calculates to surpass in composite material antisymmetry package square tube and folds the energy that unit dissipates；5, final effectively conquassation distance and final folding angles are calculated；6, average crushing force is calculated.The present invention considers that laying angle influences performance, has obtained unit length plastic limit bending moment and has surrendered the theoretical expression of membrane forces.The present invention has derived the average crushing force analytical expression of composite material antisymmetry package square tube, obtains the relationship of structural parameters and disruption properties.Square tube crush characteristics analysis method is wrapped up using composite material antisymmetry of the present invention, can rapidly carry out Top-Down Design, reduces emulation and experiment number, reduces design cost.
Description
Technical field
The invention belongs to research on vehicle passive safety fields, and in particular to a kind of composite material antisymmetry package square tube pressure
Routed characteristic analysis method.
Background technique
Thin walled beam structure is widely used in the industrial circles such as automobile, aerospace and ship, is common carrying and energy-absorbing
Component, axial deformation are stablized, and can efficiently absorb the kinetic energy in impact process, the research and design of thin walled beam are minibus
Research and the important topic in light-weight design.
In the minibus design for carrying out thin walled beam, experimental method is combined with finite element method usually, is passed through
Finite element model is established in large-strain finite element analysis software, and the result of analysis and experiment are compared to prove model
Validity.The method needs to be frequently changed design structure and parameter to obtain ideal design structure.Dynamic method is logical
The deformation characteristics for crossing analysis thin walled beam derive the expression formula of the mean effort under crush loads, illustrate the change in Collapse of Concrete
Shape mechanism inherently discloses the relationship between the energy absorption of thin walled beam and structural parameters, sets for thin walled beam structure
Meter points the direction with parameter designing.Meanwhile initial stage is designed in thin walled beam structure, it is structural according to theoretical expression preresearch estimates
Can, it is rapidly selected suitable material and structural parameters, reduces design cost, reduces trial and error number, shortens design week
Phase.
As the life of the mankind increasingly improves, energy shortage problem is more and more prominent, the light-weight design of product at
For important research topic.Composite material can guarantee crashworthiness energy-absorbing substantially not by higher specific strength and the characteristic of specific modulus
Reach light weight effect under the premise of change, therefore is widely paid close attention to.
When under Axial Loads large deformation occurs for thin walled beam structure, material enters plasticity rank by elastic stage first
Section, crushing force declines rapidly after there is first peak force, and first in Collapse of Concrete fold is formed, and active force exists later
The fluctuation up and down nearby of average crushing force.Therefore averagely crushing force is the important indicator for evaluating thin walled beam crashworthiness.
It is retrieved by domestic and international pertinent literature, finds no the theory analysis side of similar composite material antisymmetry package square tube
Method.
Summary of the invention
The technical problem to be solved by the present invention is to overcome vehicle body minibus conceptual phase due to lacking knot in detail
The geometrical model of structure and be not available the problem of finite element method or test method carry out the analysis of thin walled beam disruption properties, provide
A kind of composite material antisymmetry package square tube thin walled beam crush characteristics analysis method.
In order to solve the above technical problems, the present invention is achieved by the following technical scheme:
A kind of composite material antisymmetry package square tube crush characteristics analysis method, comprising the following steps:
Step 1: structure description is defined with coordinate；
Step 2: the limit stress and elasticity modulus of composite material are calculated；
Step 3: surrender membrane forces and unit length plastic limit bending moment are calculated；
Step 4: it calculates in composite material antisymmetry package square tube and surpasses the energy for folding unit dissipation；
Step 5: final effectively conquassation distance and final folding angles are calculated；
Step 6: average crushing force is calculated.
Structure described in step 1, is the square tube of composite material antisymmetry package, i.e., wraps up outside metal side tube multiple
Condensation material, wherein composite material thickness in monolayer is equal, and the machine direction of composite material is equal with the corner dimension of square tube crest line, just
Minus symbol is opposite；
The coordinate definition refers to that horizontal plastic hinge DA, BC are respectively x, y-axis, and inclination hinge BL is z-axis, and with list
Three reference axis of member deformation constantly change.
Calculating composite material limit stress and elasticity modulus described in step 2, the specific steps are as follows:
Step 1:
Composite material when applying the drawing force that a size is F at the both ends of composite material, under tensional state
Limit stress are as follows:
In formula, σt(θ1) be tensional state under composite material limit stress, XtIndicate that the stretching of composite material principal direction is strong
Degree；YtIndicate the tensile strength perpendicular to composite material principal direction；S is shear strength, θ1For active force and composite fiber
Angle；
Step 2:
Composite material when applying the compression force that a size is F at the both ends of composite material, under compressive state
Limit stress σc(θ1) are as follows:
In formula, σc(θ1) be compressive state under composite material limit stress, XcIndicate the compression of composite material principal direction
Intensity；Yc indicates the compressive strength perpendicular to composite material principal direction；
Step 3:
According to the Formula of Coordinate System Transformation of composite material, the elastic modulus E (θ of draw direction is calculated1)
Wherein, E (θ1) be draw direction elasticity modulus, E1For the elasticity modulus stretched along composite material principal direction；E2For
The elasticity modulus stretched perpendicular to composite material principal direction；G12For modulus of shearing；ν21For Poisson's ratio in face；
Step 4: calculating the limit stress of all directions
The main stretching of composite material and curved direction have: along x, y-axis and z-axis bending, wherein being bent along y-axis and along x
Stress is identical when bending shaft, therefore only analyzes be bent situation along x-axis and z-axis below；Along the stretching of x-axis.
When composite material is along the direction z under tension or compression, θ in formula (1) and formula (2) is taken1=θ, i.e.,
σz,t=σt(θ)σz,c=σc(θ) (4)
Wherein, σz,tThe limit stress of composite material, σ when to stretch in the z-directionz,cComposite material when to compress in the z-direction
Limit stress；θ is the angle that composite material antisymmetry wraps up fiber and square tube axial direction in square tube；
When composite material is stretched or compressed along x-axis, θ in formula (1) and formula (3) is taken1=pi/2-θ, i.e.,
Wherein, σx,tThe limit stress of composite material, E when to stretch in the x-directionxComposite material when to stretch in the x-direction
Elasticity modulus.
Surrender membrane stress and unit length plastic limit bending moment are calculated in step 3, the specific steps are as follows:
Step 1: calculating surrender membrane forces；
(1) the equivalent surrender membrane forces of composite material are calculated according to the conservation of energy
Wherein, YcFor the equivalent surrender membrane forces of composite material, εaFor metal strain；
(2) the surrender membrane forces of composite material antisymmetry package square tube are calculated by the following formula
Nx=σmhm+Ychc (7)
The σ that formula (5) is calculatedx,tWith ExIt substitutes into formula (6) and formula (7), obtains
Wherein, NxThe surrender membrane forces of square tube, σ are wrapped up for composite material antisymmetrymFor metallic equivalent flow stress, hmFor gold
Belong to thickness, hcFor thickness of composite material.
Step 2: unit of account length plastic limit bending moment；
(1) intensity ratio of composite material and metal is calculated
In formula, rz,tWhen to stretch in the z-direction, the intensity ratio of composite material and metal；rz,cWhen to compress in the z-direction,
The intensity ratio of composite material and metal；rx,tWhen to stretch in the x-direction, the intensity ratio of composite material and metal.
(2) when calculating along x, z-axis direction, unit length plastic limit bending moment
Wherein, Mx,tIndicate that fiber stretches under operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mx,c
It indicates under fiber compressive operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mz,tIndicate that fiber stretches operating condition
Under, plastic hinge is around the curved unit length plastic limit bending moment of z-axis；M0For the unit length plastic limit bending moment of metal, pass throughIt is calculated；hrFor relative thickness, i.e. hr=hc/hm。
Surpass in the package square tube of calculating composite material antisymmetry described in step 4 and folds the energy that unit dissipates, particular content
It is as follows:
Analysis when the fiber of composite material and axial load to angle be ± θ when, composite material antisymmetry package square-tube-shaped
At super folding unit energy dissipation；
In the first stage of deformation, folding angles α be crushed to the first stage by 0 ° at the end of folding anglesProcess
In:
(1) material pushes through planar annular from AD and reaches BC, is dissipated by the pulling force effect parallel with x-axis, first part
Energy is
E′1=4NxHbI1 (11)
Wherein: E '1The energy to dissipate for first part；H is super folding unit half-wavelength, and b is annular radius surface, coefficient I1
Calculation formula are as follows:
In formula,ψ0The half of angle between two side rigid plates, for multiple
Condensation material antisymmetry wraps up square tube, ψ0=π/4；Φ is the polar coordinates of annular surface,Folding angles at the end of for the first stage；
(2) energy that horizontal plastic hinge dissipates
Composite material bears compression stress effect and is bent along x-axis in horizontal plastic hinge AD, therefore horizontal plastic hinge AD dissipates
Energy are as follows:
Wherein, EADFor the energy that horizontal plastic hinge AD dissipates, C is square tube side length；
Composite material bears tensile stress effect and is bent along y-axis in horizontal plastic hinge BC, therefore horizontal plastic hinge BC dissipates
Energy are as follows:
In formula, EBCThe energy to dissipate for horizontal plastic hinge BC；
Therefore, the energy that the horizontal plastic hinge of second part dissipates are as follows:
In formula, E'2The energy to dissipate for second part；
(3) inclination plastic hinge LB and BO is bent along the z-axis direction, and composite material bears tensile load, and Part III dissipates
Energy are as follows:
In formula, E '3For the energy that Part III dissipates, coefficient I3It is calculated by following formula:
When deformation be in second stage, i.e. folding angles α byIt is crushed to final folding angles α 'fWhen, composite material package
The energy of the dissipation of square tube are as follows:
(4) tapered zone LDD ' and ODD ' is circumferentially bearing tensile load, the energy that Part IV stretching dissipates are as follows:
E'4=NxH2I4 (16)
Wherein, E'4For the energy coefficient that Part IV dissipates, coefficient I4It is calculated by following formula
(5) horizontal plastic hinge AD and BC dissipates in second stage energy and E2' similar, expression formula are as follows:
Wherein, E '5The energy coefficient to dissipate for Part V；
(6) it migrates hinge to be locked, LBCM and two rigid plate of LDAK relatively rotate, and composite material bears tensile load, rotation
The energy of dissipation are as follows:
E′6=Mz,tHI6 (18)
Wherein, E'6For the energy coefficient that Part VI dissipates, coefficient I6It is calculated by following formula:
Calculating described in step 5 final effectively conquassation distance and final folding angles, the specific steps are as follows:
Step 1: calculate the compacting strain of composite material antisymmetry package square tube:
In formula, εdThe compacting strain of square tube is wrapped up for composite material antisymmetry；
Step 2: calculate final effectively conquassation distance d:
D=2H εd (20)
In formula, d is final effectively conquassation distance；
Step 3: calculate final folding angles:
α′f=arccos (1- εd) (21)
In formula, α 'fFor final folding angles.
Calculating described in step 6 is averaged crushing force, the specific steps are as follows:
Any angle composite material antisymmetry package square tube average crushing force beAnd
In formula,The average crushing force of square tube is wrapped up for composite material antisymmetry, and according to minimum energy principle, is had
Find out H, b andAnd formula (8), (10) are substituted into formula (22) and find out composite material antisymmetry package square tube
Average crushing force.
Compared with prior art, the beneficial effects of the present invention are:
1. the present invention has derived the average crushing force analytical expression of composite material antisymmetry package square tube thin walled beam, obtain
Composite material antisymmetry wraps up square tube thin walled beam structure parameter (sectional dimension, thin walled beam material, fibre reinforced composites laying
Angle) and disruption properties between mechanical relationship, be capable of Accurate Prediction composite material antisymmetry package square tube crush characteristics.
2. the present invention considers fiber laying angle and composite material is anti-under the tension and compression operating condition of composite material in plastic hinge
The unit length plastic limit bending moment of symmetrical package square tube thin walled beam and the theoretical expression of surrender membrane stress, it is long to have obtained unit
Spend plastic limit bending moment and surrender the membrane stress relationship with laying angle respectively.
3. using composite material antisymmetry of the present invention package square tube thin walled beam flexural property analysis method in vehicle body
Minibus conceptual phase is only special according to the material of thin-walled beam section size, thin walled beam and the fibre reinforced composites provided
Property can quickly calculate composite material antisymmetry package square tube thin walled beam disruption properties, compared to finite element stimulation
And the Top-Down Design, it can be achieved that thin walled beam structure is tested, greatly reduce emulation trial and error and experiment number, shorten the development cycle,
Cost is designed and developed in reduction.
Detailed description of the invention
The present invention will be further described below with reference to the drawings:
Fig. 1 is that composite material antisymmetry of the present invention wraps up square tube thin walled beam crush characteristics analysis method flow chart element
Figure.
Fig. 2 a is that composite material antisymmetry of the present invention wraps up rhs-structure schematic diagram.
Fig. 2 b is that super folding unit of the present invention and its coordinate define.
Fig. 3 a is that single layer composite of the present invention bears off-axis simple tension load effect schematic diagram.
Fig. 3 b is that composite material of the present invention is stretched with compression limit stress with laying angle change schematic diagram.
Fig. 4 is the geometry meaning of each symbology in formula.
Fig. 5 is that super folding unit of the present invention is effectively crushed distance and final folding angles schematic diagram.
Fig. 6 is the boundary condition of experiment and the load of emulation of the present invention.
Fig. 7 a is that metal thickness is 1.4mm, and thickness of composite material is that the composite material of 1.2mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 7 b is that metal thickness is 1.6mm, and thickness of composite material is that the composite material of 1.2mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 7 c is that metal thickness is 1.8mm, and thickness of composite material is that the composite material of 1.2mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 7 d is that metal thickness is 2.0mm, and thickness of composite material is that the composite material of 1.2mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 8 a is that metal thickness is 1.4mm, and thickness of composite material is that the composite material of 1.9mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 8 b is that metal thickness is 1.6mm, and thickness of composite material is that the composite material of 1.9mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 8 c is that metal thickness is 1.8mm, and thickness of composite material is that the composite material of 1.9mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 8 d is that metal thickness is 2.0mm, and thickness of composite material is that the composite material of 1.9mm wraps up the theoretical calculation of square tube
The comparison of the average crushing force obtained with analogue simulation.
Fig. 9 is the error between simulation result and theory analysis analysis.
Specific embodiment
The present invention is explained in detail with reference to the accompanying drawing:
The crush characteristics analysis method of composite material antisymmetry package square tube thin walled beam of the present invention considers not first
Influence with ply sequence and winding angle to fibre reinforced composites package square tube deformation pattern obtains crush loads effect
Under energy dissipation mechanism.Using the limit stress of composite material with the variation relation of fiber laying angle, surrender membrane forces are obtained
With unit length plastic limit bending moment and theoretical express；Composite material is in different plasticity hinge and annular in the super folding unit of analysis
The stretching and compressive load operating condition that face is born derive the reason of the average crushing force of composite material package antisymmetry laying package square tube
By expression formula
Composite material antisymmetry wraps up square tube thin walled beam crush characteristics analysis method, and steps are as follows:
The description of I, structure is defined with coordinate
The present invention outside metal side tube for composite material is wrapped up, and wherein composite material thickness in monolayer is equal, fiber side
To equal with the corner dimension of square tube crest line, sign symbol is on the contrary, this structure is known as composite material antisymmetry by the present invention wraps up
Square tube, for example, composite plys are [θ/- θ]2Square tube is wrapped up for a kind of antisymmetry, θ is that composite material antisymmetry wraps up square tube
The angle of middle fiber and square tube axial direction, as shown in Fig. 2-a；
Duplicate super folding unit can be generated in the case where composite material antisymmetry package square tube is by the effect of axial crush loads.
As shown in Fig. 2-b, the super coordinate for folding unit is defined as follows by the present invention: horizontal plastic hinge DA, BC are respectively x, y-axis, are inclined
Tiltedly hinge BL is z-axis, and as three reference axis of element deformation constantly change.According to this definition, composite material antisymmetry package side
Composite fiber direction and coordinate relationship fold unit coordinate and whole coordinate x as shown in Fig. 2-a before pipe deformation occurs0y0z0
It is overlapped.
It is 1. metal side tube in figure, is 2. composite material, is 3. first layer composite fiber, it is 4. compound for the second layer
Material fiber
II, calculates composite material limit stress and elasticity modulus
As shown in Fig. 3-a, θ1For the angle of active force and composite fiber.When in single layer board ends one size of application
For F drawing force when, composite material limit stress under tensional state are as follows:
In formula, σt(θ1) be tensional state under composite material limit stress, XtIndicate that the stretching of composite material principal direction is strong
Degree；YtIndicate the tensile strength perpendicular to composite material principal direction；S is shear strength, θ1For active force and composite fiber
Angle.
Composite material when applying the compression force that a size is F at the both ends of composite material, under compressive state
Limit stress σc(θ1) are as follows:
In formula, σc(θ1) be compressive state under composite material limit stress, XcIndicate the compression of composite material principal direction
Intensity；YcIndicate the compressive strength perpendicular to composite material principal direction.
It is 5. composite fiber in Fig. 3-a.Stretching and composite material limit stress and θ under compressive state1Relationship
As shown in Fig. 3-b.
According to the Formula of Coordinate System Transformation of composite material, the elastic modulus E (θ of draw direction is calculated1)
Wherein, E (θ1) be draw direction elasticity modulus, E1For the elasticity modulus stretched along composite material principal direction；E2For
The elasticity modulus stretched perpendicular to composite material principal direction；G12For modulus of shearing；ν21For Poisson's ratio in face.
Such as Fig. 2-b, the main stretching of composite material and curved direction have: along x, y-axis and z-axis bending, wherein curved along y-axis
It is bent identical as stress when being bent along x-axis, therefore only analyze be bent situation along x-axis and z-axis below；Along the stretching of x-axis.
When composite material is along the direction z under tension or compression, θ in formula (1) and formula (2) is taken1=θ, i.e.,
σz,t=σt(θ)σz,c=σc(θ) (4)
Wherein, σz,tThe limit stress of composite material, σ when to stretch in the z-directionz,cComposite material when to compress in the z-direction
Limit stress；
When composite material is stretched or compressed along x-axis, θ in formula (1) and formula (3) is taken1=pi/2-θ, i.e.,
Wherein, σx,tThe limit stress of composite material, E when to stretch in the x-directionxComposite material when to stretch in the x-direction
Elasticity modulus.
III, calculates surrender membrane stress and unit length plastic limit bending moment
For stretching class energy-absorbing, the equivalent surrender membrane forces of composite material are obtained according to the conservation of energy
Wherein, εaFor metal strain, εx,tFor composite material limiting strain.
By σx,t=Exεx,tSubstitute into the equivalent tensile stress that formula (6) are stretched along the x-axis direction
The equivalent surrender membrane forces of composite material antisymmetry package square tube are calculated by the following formula
Nx=σmhm+Ychc(8)
The σ that formula (5) is calculatedx,tWith ExIt substitutes into formula (7) and formula (8), obtains
Wherein, NxThe equivalent surrender membrane forces of square tube, σ are wrapped up for composite material antisymmetrymFor metallic equivalent flow stress, hm
For metal thickness, hcFor thickness of composite material.
For being bent class energy absorption, the ultimate bending moment of composite material package is
H in formulacFor thickness of composite material, σcIndicate limit stress of the composite material under each operating condition, by formula (1), (4),
(5) formula (10) are substituted into, when obtaining along x, z-axis bending, unit length plastic limit bending moment
Wherein, Mx,tIndicate that fiber stretches under operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mx,c
It indicates under fiber compressive operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mz,tIndicate that fiber stretches operating condition
Under, plastic hinge is around the curved unit length plastic limit bending moment of z-axis；M0For the unit length plastic limit bending moment of metal, pass throughIt is calculated；hrFor relative thickness, i.e. hr=hc/hm。
rz,tWhen to stretch in the z-direction, the intensity ratio of composite material and metal；rz,cWhen to compress in the z-direction, composite wood
The intensity ratio of material and metal；rx,tWhen to stretch in the x-direction, the intensity ratio of composite material and metal can pass through formula
(12) it acquires:
IV, which calculates to surpass in composite material antisymmetry package square tube, folds the energy that unit dissipates
It is stretched based on above-mentioned different directions and obtains different surrender membrane forces and unit length plastic limit bending moment table from bending
Up to formula, in analysis chart 2-b when the fiber of composite material and axial load to angle be ± θ when, composite material antisymmetry package side
The energy that the super folding unit that pipe is formed dissipates.
In the first stage of deformation, folding angles α be crushed to the first stage by 0 ° at the end of folding anglesProcess
In:
(1) material pushes through planar annular from AD and reaches BC, is dissipated by the pulling force effect parallel with x-axis, first part
Energy is
E′1=4NxHbI1 (13)
Wherein: E '1The energy to dissipate for first part；H is super folding unit half-wavelength, and b is annular radius surface, coefficient I1
Calculation formula be
In formula,ψ0The half of angle between two side rigid plates, for multiple
Condensation material antisymmetry wraps up square tube, ψ0=π/4；Φ is the polar coordinates of annular surface,Folding angles at the end of for the first stage；
The geometry meaning of β is as shown in Figure 4.
(2) energy that horizontal plastic hinge dissipates
Composite material bears compression stress effect and is bent along x-axis in horizontal plastic hinge AD, therefore horizontal plastic hinge AD dissipates
Energy be
Wherein, EADFor the energy that horizontal plastic hinge AD dissipates, C is square tube side length；
Composite material bears tensile stress effect and is bent along y-axis in horizontal plastic hinge BC, therefore horizontal plastic hinge BC dissipates
Energy be
In formula, EBCThe energy to dissipate for horizontal plastic hinge BC；
Therefore, the energy of the horizontal plastic hinge dissipation of second part is
In formula, E'2The energy to dissipate for second part；
(3) inclination plastic hinge LB and BO is bent along the z-axis direction, and composite material bears tensile load, and Part III dissipates
Energy be
In formula, E '3For the energy that Part III dissipates, coefficient I3It is calculated by following formula
When deformation be in second stage, i.e. folding angles α byIt is crushed to final folding angles α 'fWhen, composite material package
The energy of the dissipation of square tube are as follows:
(4) in circumferentially receiving tensile load, Part IV stretches the energy to dissipate and is tapered zone LDD ' and ODD '
E'4=NxH2I4 (18)
Wherein, E'4For the energy coefficient that Part IV dissipates, coefficient I4It is calculated by following formula
(5) horizontal plastic hinge AD and BC dissipates in second stage energy and E2' similar, expression formula is
Wherein, E '5The energy coefficient to dissipate for Part V；
(6) it migrates hinge to be locked, LBCM and two rigid plate of LDAK relatively rotate, and composite material bears tensile load, rotation
The energy of dissipation is
E'6=Mz,tHI6 (20)
Wherein, E'6For the energy coefficient that Part VI dissipates, coefficient I6It is calculated by following formula
V, calculates final effectively conquassation distance and final folding angles
Composite material affects the conquassation distance of metal thin-wall beam when wrapping up, due to the heap of material after Failure Analysis of Composite Materials
Product, refering to the geometrical relationship of Fig. 5, final effective distance d is
D=2H εd (21)
In formula, εdThe compacting strain that square tube is wrapped up for composite material antisymmetry, can be found out by formula (22)
Final folding angles
α′f=arccos (1- εd) (23)
VI, calculates average crushing force
Any angle composite material antisymmetry package square tube average crushing force beAnd
According to minimum energy principle, have
Find out H, b andAnd formula (9), (11) substitution formula (24) can be found out into composite material antisymmetry package square tube
Average crushing force.
Embodiment
Next the present invention introduces fibre reinforced composites antisymmetry package square tube proposed by the present invention in conjunction with the embodiments
Crush characteristics analysis method.
The metal material that square tube is wrapped up in embodiment is 6063-T5, side length 25mm, with a thickness of 1.6mm, the flowing of metal
Stress σm=140MPa；The composite material of selection is glass-fiber epoxy-resin composite materials, and composite material is 30 glass of Type
Fiber, matrix are 820 epoxy resin, and the performance parameter of composite material is as shown in table 1.The glass fibre of package is 2 layers, i.e.,
[45/-45], thickness of composite material hc=1.27mm.
Boundary loading condition is refering to Fig. 6,6. to move down the rigid body that speed is V, 7. wraps up metal for composite material
Square tube.
1 galss fiber reinforced resin based composites performance parameter of table
The limit stress and elasticity modulus of I, calculating composite material
The composite property parameter of table 1 and θ=45 ° are substituted into formula (4) and formula (5) available draw direction
Limit stress σx,t=66.20MPa, σz,t=66.20MPa, σz,cThe elastic modulus E that the direction=108.82MPa and x stretchesx=
14.97GPa
II, calculates surrender membrane forces and unit length plastic limit bending moment
The limit stress of obtained composite material calculated above is substituted into formula (9) with elasticity modulus and formula (11) obtains
The surrender membrane stress N of x-axis directionxThe unit length plastic limit bending moment M of=224.00MPamm, x-axis and z-axisx,t=
197.61MPa；Mx,c=253.80MPa；Mz,t=197.61MPa.
III, calculates the average crushing force of composite material antisymmetry package square tube
It is identical as the deformation of pure metal square tube due to deforming, take Ψ0=π/4 can calculate excess of export using MATLAB software
Fold the half-wavelength H=13.75mm of unit.It is answered according to the compacting of the available composite material antisymmetry package square tube of formula (22)
Become εd=0.7913, final effectively conquassation distance d=15.88mm, and substituted into formula (23) and obtain final folding angles αf=
77.95°。
Above-mentioned ultimate bending moment, surrender membrane forces, final conquassation distance and the final folding angles of obtaining substitute into formula (24), lead to
It crosses MATLAB software programming and calculates the average crushing force that can go out above-mentioned composite material antisymmetry package square tube
It is respectively 1.27mm, 1.85mm, 2.87mm and 3.18mm, wing flapping to thickness of composite material using identical step
The composite material antisymmetry that degree is 45 ° wraps up the theoretical calculation that square tube carries out average crushing force.Distance is crushed in experiment to be taken as
The average crushing force comparison that 50mm and 75mm, characteristic research method of the present invention and experiment obtain is as shown in table 2.
The theoretical average crushing force with experiment of table 2 compares
Theoretical calculation and experiment obtain the error of average crushing force within 10%, demonstrate the correct of characteristic analysis method
Property.
The simulation model for establishing above-mentioned experiment simultaneously, takes the thickness of metal to take 1.4mm, 1.6mm, 1.8mm, 2.0mm respectively,
For glass fibre with a thickness of 1.2mm and 1.9mm, the value range of laying angle is 30 °≤θ≤90 °, takes a sub-value every 15 °, obtains
To the average crushing force of analogue simulation.Conquassation analysis method according to the present invention calculates the average value of average crushing force, glass fibers
The theory for tieing up the composite material antisymmetry package square tube with a thickness of 1.2mm and 1.9mm obtains average crushing force result point with emulation
Fig. 7 a, Fig. 7 b, Fig. 7 c, Fig. 7 d and Fig. 8 a, Fig. 8 b, Fig. 8 c, Fig. 8 d are not seen.Error between the two is as shown in Figure 9.It can see
Out, the two has preferable consistency, thus demonstrates the correctness of conquassation analysis method of the invention.
Claims (7)
1. a kind of composite material antisymmetry wraps up square tube crush characteristics analysis method, which comprises the following steps:
Step 1: structure description is defined with coordinate；
Step 2: the limit stress and elasticity modulus of composite material are calculated；
Step 3: surrender membrane forces and unit length plastic limit bending moment are calculated；
Step 4: it calculates in composite material antisymmetry package square tube and surpasses the energy for folding unit dissipation；
Step 5: final effectively conquassation distance and final folding angles are calculated；
Step 6: average crushing force is calculated.
2. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Structure described in step 1 is the square tube of composite material antisymmetry package, i.e., wraps up composite wood outside metal side tube
Material, wherein composite material thickness in monolayer is equal, and the machine direction of composite material is equal with the corner dimension of square tube crest line, positive and negative symbol
It is number opposite；
The coordinate definition refers to that horizontal plastic hinge DA, BC are respectively x, y-axis, and inclination hinge BL is z-axis, and as unit becomes
Three reference axis of shape constantly change.
3. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Calculating composite material limit stress and elasticity modulus described in step 2, the specific steps are as follows:
Step 1:
The composite material limit when applying the drawing force that a size is F at the both ends of composite material, under tensional state
Stress are as follows:
In formula, σt(θ1) be tensional state under composite material limit stress, XtIndicate the tensile strength of composite material principal direction；Yt
Indicate the tensile strength perpendicular to composite material principal direction；S is shear strength, θ1For the folder of active force and composite fiber
Angle；
Step 2:
The composite material limit when applying the compression force that a size is F at the both ends of composite material, under compressive state
Stress σc(θ1) are as follows:
In formula, σc(θ1) be compressive state under composite material limit stress, XcIndicate that the compression of composite material principal direction is strong
Degree；YcIndicate the compressive strength perpendicular to composite material principal direction；
Step 3:
According to the Formula of Coordinate System Transformation of composite material, the elastic modulus E (θ of draw direction is calculated1)
Wherein, E (θ1) be draw direction elasticity modulus, E1For the elasticity modulus stretched along composite material principal direction；E2It is vertical
In the elasticity modulus that composite material principal direction stretches；G12For modulus of shearing；ν21For Poisson's ratio in face；
Step 4: calculating the limit stress of all directions
Composite material it is main stretching and curved direction have: along x, y-axis and z-axis bending, wherein along y-axis bending with it is curved along x-axis
Stress is identical when bent, therefore only analyzes be bent situation along x-axis and z-axis below；Along the stretching of x-axis.
When composite material is along the direction z under tension or compression, θ in formula (1) and formula (2) is taken1=θ, i.e.,
σz,t=σt(θ)σz,c=σc(θ) (4)
Wherein, σz,tThe limit stress of composite material, σ when to stretch in the z-directionz,cThe pole of composite material when to compress in the z-direction
Limit stress；θ is the angle that composite material antisymmetry wraps up fiber and square tube axial direction in square tube；
When composite material is stretched or compressed along x-axis, θ in formula (1) and formula (3) is taken1=pi/2-θ, i.e.,
Wherein, σx,tThe limit stress of composite material, E when to stretch in the x-directionxThe elasticity of composite material when to stretch in the x-direction
Modulus.
4. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Surrender membrane stress and unit length plastic limit bending moment are calculated in step 3, the specific steps are as follows:
Step 1: calculating surrender membrane forces；
(1) the equivalent surrender membrane forces of composite material are calculated according to the conservation of energy
Wherein, YcFor the equivalent surrender membrane forces of composite material, εaFor metal strain；
(2) the surrender membrane forces of composite material antisymmetry package square tube are calculated by the following formula
Nx=σmhm+Ychc (7)
The σ that formula (5) is calculatedx,tWith ExIt substitutes into formula (6) and formula (7), obtains
Wherein, NxThe surrender membrane forces of square tube, σ are wrapped up for composite material antisymmetrymFor metallic equivalent flow stress, hmFor metal thickness
Degree, hcFor thickness of composite material.
Step 2: unit of account length plastic limit bending moment；
(1) intensity ratio of composite material and metal is calculated
In formula, rz,tWhen to stretch in the z-direction, the intensity ratio of composite material and metal；rz,cIt is compound when to compress in the z-direction
The intensity ratio of material and metal；rx,tWhen to stretch in the x-direction, the intensity ratio of composite material and metal.
(2) when calculating along x, z-axis direction, unit length plastic limit bending moment
Wherein, Mx,tIndicate that fiber stretches under operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mx,cIt indicates
Under fiber compressive operating condition, plastic hinge is around the curved unit length plastic limit bending moment of x-axis；Mz,tIndicate that fiber stretches under operating condition, modeling
Property hinge around the curved unit length plastic limit bending moment of z-axis；M0For the unit length plastic limit bending moment of metal, pass throughIt is calculated；hrFor relative thickness, i.e. hr=hc/hm。
5. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Surpass in the package square tube of calculating composite material antisymmetry described in step 4 and fold the energy that unit dissipates, particular content is such as
Under:
Analysis when the fiber of composite material and axial load to angle be ± θ when, composite material antisymmetry wraps up square tube formation
The super energy dissipation for folding unit；
In the first stage of deformation, folding angles α be crushed to the first stage by 0 ° at the end of folding anglesDuring:
(1) material pushes through planar annular from AD and reaches BC, the energy to be dissipated by the pulling force effect parallel with x-axis, first part
For
E′1=4NxHbI1 (11)
Wherein: E '1The energy to dissipate for first part；H is super folding unit half-wavelength, and b is annular radius surface, coefficient I1Meter
Calculate formula are as follows:
In formula,ψ0The half of angle between two side rigid plates, for composite wood
Expect that antisymmetry wraps up square tube, ψ0=π/4；Φ is the polar coordinates of annular surface,Folding angles at the end of for the first stage；
(2) energy that horizontal plastic hinge dissipates
Composite material bears compression stress effect and is bent along x-axis in horizontal plastic hinge AD, therefore the energy that horizontal plastic hinge AD dissipates
Amount are as follows:
Wherein, EADFor the energy that horizontal plastic hinge AD dissipates, C is square tube side length；
Composite material bears tensile stress effect and is bent along y-axis in horizontal plastic hinge BC, therefore the energy that horizontal plastic hinge BC dissipates
Amount are as follows:
In formula, EBCThe energy to dissipate for horizontal plastic hinge BC；
Therefore, the energy that the horizontal plastic hinge of second part dissipates are as follows:
In formula, E'2The energy to dissipate for second part；
(3) inclination plastic hinge LB and BO is bent along the z-axis direction, and composite material bears tensile load, the energy that Part III dissipates
Amount are as follows:
In formula, E '3For the energy that Part III dissipates, coefficient I3It is calculated by following formula:
When deformation be in second stage, i.e. folding angles α byIt is crushed to final folding angles α 'fWhen, composite material wraps up square tube
Dissipation energy are as follows:
(4) tapered zone LDD ' and ODD ' is circumferentially bearing tensile load, the energy that Part IV stretching dissipates are as follows:
E'4=NxH2I4 (16)
Wherein, E'4For the energy coefficient that Part IV dissipates, coefficient I4It is calculated by following formula
(5) horizontal plastic hinge AD and BC dissipates in second stage energy and E '2It is similar, expression formula are as follows:
Wherein, E '5The energy coefficient to dissipate for Part V；
(6) it migrates hinge to be locked, LBCM and two rigid plate of LDAK relatively rotate, and composite material bears tensile load, and rotation dissipates
Energy are as follows:
E'6=Mz,tHI6 (18)
Wherein, E'6For the energy coefficient that Part VI dissipates, coefficient I6It is calculated by following formula:
6. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Calculating described in step 5 final effectively conquassation distance and final folding angles, the specific steps are as follows:
Step 1: calculate the compacting strain of composite material antisymmetry package square tube:
In formula, εdThe compacting strain of square tube is wrapped up for composite material antisymmetry；
Step 2: calculate final effectively conquassation distance d:
D=2H εd (20)
In formula, d is final effectively conquassation distance；
Step 3: calculate final folding angles:
α′f=arccos (1- εd) (21)
In formula, α 'fFor final folding angles.
7. a kind of composite material antisymmetry according to claim 1 wraps up square tube crush characteristics analysis method, feature exists
In:
Calculating described in step 6 is averaged crushing force, the specific steps are as follows:
Any angle composite material antisymmetry package square tube average crushing force beAnd
In formula,The average crushing force of square tube is wrapped up for composite material antisymmetry, and according to minimum energy principle, is had
Find out H, b andAnd formula (8), (10) are substituted into the mean pressure that formula (22) find out composite material antisymmetry package square tube
Routed power.
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