CN106599507B - A method of improving B-K criterion for fibre-bearing bridge joint influences the multidirectional Laminates With Delamination prediction of composite material - Google Patents

A method of improving B-K criterion for fibre-bearing bridge joint influences the multidirectional Laminates With Delamination prediction of composite material Download PDF

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CN106599507B
CN106599507B CN201611214744.9A CN201611214744A CN106599507B CN 106599507 B CN106599507 B CN 106599507B CN 201611214744 A CN201611214744 A CN 201611214744A CN 106599507 B CN106599507 B CN 106599507B
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laminate
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CN106599507A (en
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赵丽滨
龚愉
肖鑫
张建宇
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Chongqing University
Beijing University of Aeronautics and Astronautics
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Beijing University of Aeronautics and Astronautics
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/333Design for testability [DFT], e.g. scan chain or built-in self-test [BIST]

Abstract

The invention discloses a kind of improvement B-K criterion to influence the method for the multidirectional Laminates With Delamination prediction of composite material for fibre-bearing bridge joint, by I/II mixed type static(al) layering test under progress CFRP multi direction laminate I type, II type and different mixing ratios, determine with the I type interlayer faults toughness G for being layered length variationIC(a), II type interlayer faults toughness GIIC(a) and different mixing ratios under interlayer faults toughness GC(a), and the parameter η improved in B-K criterion that the least square fitting acquisition consideration fiber bridge joint of three-dimensional data influences is carried out, then by above-mentioned GIC(a)、GIIC(a) and fitting parameter η value is as the important parameter improved in B-K criterion, it establishes the finite element model based on cohesive force unit and simulates different mixing ratio lower leaf propagation behaviors with the improvement criterion, the accuracy and applicability for improving criterion are proposed by comparative test and numerical value result verification, and then the delamination behavior under any other mixing ratio can be predicted with criterion is improved, to significantly shorten the test period, experimentation cost is reduced.

Description

A kind of improvement B-K criterion influences the multidirectional laminate of composite material point for fibre-bearing bridge joint The method of layer prediction
Technical field
The present invention relates to CFRP multi direction laminate delamination fields, and in particular to a kind of improvement B-K criterion is fine for containing The method that dimension bridge joint influences the multidirectional Laminates With Delamination prediction of composite material, is suitable for the widely used composite woods in fields such as aerospace Expect the research and prediction of multidirectional laying plate I/II Mixed-Mode Delamination propagation behavior.
Background technique
Composite material is gradually applied in aircraft main force support structure because of its good mechanical property.Wherein, carbon fiber tree Resin-based composite has both specific stiffness height while having compared with high specific strength, anticorrosive, fatigue behaviour is good and performance can be set Many advantages, such as meter property and become main a kind of composite material to be used in Modern aircraft structure.With middle modulus high strength carbon fiber The batch production of dimension and the application of toughened resin, this kind of composite material in aircaft configuration application also by secondary load-carrying construction gradually Develop to the main force support structure of force-bearing situation complexity.And the safety of structure of composite material is also increasingly valued by the people.
In the numerous failure modes of laminar composite, fallen off as low velocity impact, synusia, caused by recess or manufacturing defect Layering is most common and crucial one of failure mode.Delamination damage causes veneer structure strength and stiffness to be remarkably decreased, even It may cause external not noticeable catastrophic structure to destroy, this seriously constrains composite material answering in aircraft main structure With.Therefore correct to evaluate and predict composite material in various load and environmental condition lower leaf propagation behavior to multiple in engineering practice The design and analysis of condensation material structure are extremely important, while can also significantly shorten the test period, reduce experimentation cost.
Cohesive zone model (CZM) is widely used to the germinating and extension of simulation layering.Cohesive zone model releases strain energy The standard of rate (SERR) and interlayer faults toughness as assessment delamination is put, prediction I/II Mixed-Mode Delamination extension most makes extensively Criterion is B-K criterion.In traditional B-K criterion, I type and II type interlayer faults toughness be assumed to be with specimen size and point The unrelated intrinsic parameter of material of layer length, it is this to assume it is correct for unidirectional laminate, but multi direction laminate is shown Unworthiness is shown.Traditional B-K criterion of judge delamination in bilinearity CZM, due to not considering the influence of fiber bridge joint, Can not accurate simulation multi direction laminate delamination behavior.
During delamination in the multidirectional laying plate of composite material, fiber bridge joint is a kind of very important crackle screen Cover mechanism.Research shows that the quantity of moderate loss actually depends on layering length, it means that compared with short crack, long crack In more moderate loss will occur, it is therefore desirable to consume more energy to make FRP rebar or cause the fracture of moderate loss Failure.It can be seen that fiber bridge joint significantly suppresses multidirectional laying from the fracture toughness change curve of multidirectional laying plate delamination The delamination of plate, it is therefore desirable to consider the influence that fiber bridges in delamination.The improvement B-K for considering that fiber bridge joint influences is quasi- Then, multidirectional laying plate Mixed-Mode Delamination propagation behavior can just be better anticipated.
Summary of the invention
The technical problem to be solved in the present invention are as follows: overcome the deficiencies of the prior art and provide a kind of improvement B-K criterion for containing The method that fiber bridge joint influences the multidirectional Laminates With Delamination prediction of composite material, is suitable for engineer application, significantly shortening test period, drop Low experimentation cost.The progress of the multidirectional laying plate of composite material any mixing ratio lower leaf propagation behavior is effectively analyzed simultaneously and pre- It surveys, preferably guarantee safety of structure.
The present invention solves the technical solution that above-mentioned technical problem uses are as follows: a kind of improvements B-K criterion is for fibre-bearing bridge joint Influence the method for the multidirectional Laminates With Delamination prediction of composite material, comprising the following steps:
Step 1, pass through double cantilever beam bending (DCB), 4 end edge notch (4ENF) and Mixed Bending (MMB) experiment opening I type, II type and I/II mixed type static(al) the delamination test for opening up the multidirectional laminate of CFRP, obtain corresponding load, are displaced and split The test datas such as line length;
Step 2, data processing is carried out to test data and determines the I type interlayer faults toughness G changed with layering length aIC (a), II type interlayer faults toughness GIIC(a) and different mixing ratios under mixed type interlayer faults toughness GC(a);
Step 3, using the G for considering that the improvement B-K criterion of fiber bridge joint in delamination obtains step 2IC(a)、GIIC (a) and different mixing ratios under GC(a) least square fitting of three-dimensional data is carried out, so that it is determined that it is more to be suitable for studied CRFP To the parameter η value of laminate improved in B-K criterion;
Step 4, establishing the finite element model based on cohesive force unit will be upper by the customized subprogram USDFLD of user State CFRP multi direction laminate I type and II type interlayer faults toughness GIC(a)、GIIC(a) pass through minimum two in expression formula and step 3 The parameter η value multiplied in the improvement B-K criterion that fitting obtains is embedded into improvement B-K criterion as important parameter, using the improvement B-K criterion simulates the delamination behavior under such multi direction laminate difference mixing ratio, and passes through comparative test and numerical result The accuracy for improving B-K criterion is established to verify.
Further, it is (+45/-45/0 that verifying, which improves CFRP multi direction laminate ply stacking-sequence used in criterion,6)S//(-45/+ 45/06)S, the design of this kind of ply stacking-sequence is to reduce bending-torsional coupling effect and the mutual recurvation due to caused by laying asymmetry Qu Xiaoying.
Further, the ply stacking-sequence is (+45/-45/06)S//(-45/+45/06)SCFRP multi direction laminate be It is made using T7009511 carbon fiber/bismaleimide resin system unidirectional pre-immersion material.
Further, the step 2 determines the I type interlayer faults toughness with layering length a variation using amendment beam theory GIC(a) expression formula are as follows:
Wherein: b is specimen width, and F and N' are the modifying factor considered when big displacement and loading blocks influence respectively, due to surveying Amount is to be layered vertical range of the tip away from loaded line and use hinge rather than loading blocks, the two factors are 1.PICWith δICIt is the I type load and displacement applied to sample respectively, | △ | it is the modifying factor for being layered length, for considering that cantilever is splitting point Position additional displacement and rotation due to material anisotropy.
The step 2 determines the II type interlayer faults toughness G with layering length a variation using flexibility methodIIC(a) expression formula Are as follows:
Wherein: PCIt is critical load, C is sample flexibility.
The step 2 determines the I/II mixed type interlayer faults toughness G with layering length a variation according to amendment beam theoryC (a) expression formula are as follows:
GC(a)=GI(a)+GII(a)
Wherein: P is the load applied at the point of application, and c is distance of the point of application to intermediate load roller bearing, PgBe upper beam and It is attached to the weight of wherein loading blocks, cgFor distance of the center of gravity to intermediate load roller bearing of fixture, EfIt is bending modulus, h is that sample is thick That spends is general, and L is fixed span away from as shown in attached drawing 3 (c).
Further, above-mentioned I type is fitted in the step 3 respectively, II type delamination test data obtains with layering The G of length variationIC(a)、GIIC(a) mathematic(al) representation, the G of the CFRP multi direction laminateIC(a) expression formula is segmentation letter Number can be divided into fiber bridge joint sections and stablize expanding section;The G of the CFRP multi direction laminateIIC(a) expression formula passes through linear fit It obtains.
Further, it is based on improving B-K criterion in the step 3 to above-mentioned gained delamination fracture toughness data GIC (a)、GIIC(a) and different mixing ratios under GC(a) least square fitting of three-dimensional data is carried out, wherein GIC(a)、GIIC(a) right The mixing ratio answered is respectively 0 and 1, so that it is determined that it is quasi- to be suitable for the improvement B-K that such CFRP multi direction laminate delamination is judged Parameter η value in then.
Further, the step 4 by interlayer faults toughness data under several mixing ratios of CFRP multi direction laminate into What row least square fitting obtained improves the parameter η value and G in B-K criterionIC(a)、GIIC(a) expression formula is as improvement B-K criterion In important parameter, be embedded into criterion by the customized subprogram USDFLD of finite element user, establish be based on cohesive force unit Finite element model simulate the delamination behavior under such multi direction laminate difference mixing ratio.
Further, the improvement criterion may be used on predicting that the multidirectional laminate of such CFRP expands in any mixing ratio lower leaf Exhibition behavior.For the multidirectional laminate of other materials or other interfaces, which is judging point influenced by fiber bridge joint There is versatility in layer extension.
The advantages of the present invention over the prior art are that:
(1) it cannot achieve the delamination row influenced on multidirectional laying plate by fiber bridge joint for existing delamination criterion Limitation effectively to be simulated proposes a general improvement B-K criterion.
(2) present invention utilizes the I/II mixed type test number under multi direction laminate I type, II type and limited different mixing ratios It obtains improving the η value in B-K criterion according to fitting, such multi direction laminate Mixed-Mode Delamination extension under any mixing ratio can be predicted Behavior, therefore test job amount is significantly shortened, reduce experimentation cost.
(3) prediction result of the invention has been subjected to verification experimental verification, and predicted value and test measured value have preferable consistency, because The precision of this prediction technique of the present invention is higher.
Detailed description of the invention
Fig. 1 is a kind of improvement B-K criterion of the present invention for the multidirectional Laminates With Delamination prediction of fibre-bearing bridge joint influence composite material Method implementation flow chart;
Fig. 2 is the geometric dimension and hinge schematic diagram (in millimeters) of sample;
Fig. 3 is I, II type and I/II type mixed type static(al) layering test loading scheme, wherein Fig. 3 (a) is that the layering of I type is expanded DCB experimental rig schematic diagram is opened up, Fig. 3 (b) is II type delamination 4ENF experimental rig schematic diagram, and Fig. 3 (c) is I/II mixed type Delamination MMB experimental rig schematic diagram, Fig. 3 (d) are I type delamination DCB experimental rig pictorial diagram, and Fig. 3 (e) is II type point Layer extension 4ENF experimental rig pictorial diagram, Fig. 3 (f) are that I/II Mixed-Mode Delamination extends MMB experimental rig pictorial diagram;
Fig. 4 is layering interlayer faults toughness data figure and matched curve, wherein Fig. 4 (a) is that I type layering interlayer faults are tough Datagram and matched curve are spent, Fig. 4 (b) is II type layering interlayer faults toughness data figure and matched curve, and Fig. 4 (c) is mixing ThanWith 0.75 I/II Mixed-Mode Delamination interlayer faults toughness data figure;
Fig. 5 is that least square fitting determines the η value improved in B-K criterion;
Fig. 6 is I/II Mixed-Mode Delamination expanding test load displacement curve and finite element modelling comparative result figure, wherein figure 6 (a) be mixing ratioWith 0.75 I/II Mixed-Mode Delamination expanding test load displacement curve and finite element Analog result comparison diagram, Fig. 6 (b) are mixing ratiosI/II Mixed-Mode Delamination expanding test load displacement curve and limited First analog result comparison diagram.
Specific embodiment
Below with reference to embodiment, invention is further described in detail:
A kind of B-K criterion of improving of the present invention influences the method for the multidirectional Laminates With Delamination prediction of composite material for fibre-bearing bridge joint The specific implementation steps are as follows:
Step 1: sample be made of T700/9511 carbon fiber/bismaleimide resin system unidirectional pre-immersion material, Ply stacking-sequence is (+45/-45/06)S//(-45/+45/06)SCFRP multi direction laminate, in order to ensure displacement load effectively It is applied to the mid-plane of cantilever beam, uses a kind of Fast Installation hinge in DCB and MMB test, as shown in Figure 2;According to ASTM standard D5528-01 carries out I type delamination test (DCB) to CFRP multi direction laminate, using 4ENF experimental rig pair CFRP multi direction laminate carries out the test of II type delamination, is carried out according to ASTM standard D6671M-06 to CFRP multi direction laminate Mixing ratio(MMB) is tested for 0.25,0.4,0.5,0.6 and 0.75 I/II mixed type static(al) delamination, is loaded by adjusting Mixing ratio needed for distance c of the point away from sample middle section realizes test, DCB, 4ENF and MMB experimental rig are as shown in Figure 3.
Step 2: processing test data determines the layering interlayer faults toughness G with layering length a variationIC(a)、GIIC(a) and G under different mixing ratiosC(a).Specific implementation process are as follows: I type interlayer faults toughness GIC(a) expression formula are as follows:
Wherein: b is specimen width, and F and N' are the modifying factor considered when big displacement and loading blocks influence respectively, due to What is measured in present claims is to be layered vertical range of the tip away from loaded line and use hinge rather than loading blocks, the two because Son is 1.PICAnd δICIt is the I type load and displacement applied to sample respectively, | △ | it is the modifying factor for being layered length, is used for Consider that cantilever is splitting sharp position additional displacement and rotation due to material anisotropy.
According to I type delamination test data, the flexibility C with the layering testpieces of a certain determining layering length a is calculated, Then a series of C of linear fit1/3Obtained with crack length a | △ |, further according to GIC(a) expression formula calculates different crack length a Corresponding GIC(a), as a result as shown in Fig. 4 (a).
II type is layered interlayer faults toughness GIIC(a) expression formula are as follows:
Wherein: PCIt is critical load, C is sample flexibility.
According to II type delamination test data, the flexibility with the layering testpieces of a certain determining layering length a is calculated C, then a series of C of linear fit and crack length a are obtainedFurther according to GIICExpression formula calculates a pairs of different crack lengths The G answeredIIC(a), as a result as shown in Fig. 4 (b).
I/II mixed type interlayer faults toughness GC(a) expression formula are as follows:
GC(a)=GI(a)+GII(a)
Wherein: P is the load applied at the point of application, and c is distance of the point of application to intermediate load roller bearing, PgBe upper beam and It is attached to the weight of wherein loading blocks, cgFor distance of the center of gravity to intermediate load roller bearing of fixture, EfIt is bending modulus, h is that sample is thick That spends is general, and L is fixed span away from as shown in attached drawing 3 (c).
According to I/II Mixed-Mode Delamination expanding test data, strain energy release rate I type component G is calculated separatelyI(a) and II Component GII(a), further according to GC(a) expression formula calculates the corresponding G of different crack length aC(a), as shown in Fig. 4 (c).
Step 3: being fitted above-mentioned I type respectively, the layering with layering length variation that II type delamination test data obtains Interlayer faults toughness obtains GIC(a)、GIIC(a) mathematic(al) representation such as Fig. 4 (a) and (b) are shown;Based on improvement B-K criterion to upper State the G of known mixing ratioIC(a)、GIIC(a) and GC(a) least square fitting of three-dimensional data is carried out, so that it is determined that being suitable for institute The parameter η value of the multidirectional laminate of CRFP improved in B-K criterion is studied, as shown in Figure 5.
Step 4: establishing the finite element model based on cohesive force unit will be upper by the customized subprogram USDFLD of user State CFRP multi direction laminate I type and II type interlayer faults toughness GIC(a)、GIIC(a) pass through minimum two in expression formula and step 3 The parameter η value multiplied in the improvement B-K criterion that fitting obtains is embedded into improvement B-K criterion as important parameter, using the improvement B-K criterion simulates the delamination behavior under such multi direction laminate difference mixing ratio, and passes through comparative test and numerical result The accuracy for improving B-K criterion is established to verify.The improvement B-K criterion are as follows:
For mixing ratioI/II Mixed-Mode Delamination with 0.75 extends, and will improve B-K criterion and uses In Abaqus, the finite element model based on cohesive force unit is established, the load displacement relationship and experiment number that numerical simulation obtains According to comparison as shown in Fig. 6 (a).In initial line elastic stage and delamination stage, analog result and test result have well Consistency.
The improvement B-K criterion proposed using the method for the present invention is to for the CFRP multi direction laminate mentioned in above-mentioned steps 1 Carry out mixing ratioI/II mixed type static(al) delamination test bit prediction., mixing ratio be 0.6 I/II mixed type Numerical result and the experimental data comparison of delamination load displacement are as shown in Fig. 6 (b), there it can be seen that in Stiffness Deterioration The initial slope of numerical curve has good consistency with experimental result and remains unchanged before, and the initial damage of prediction carries Lotus and ultimate load and agreement with experimental data are preferable.It can be to the delamination behavior under any mixing ratio using B-K criterion is improved It is predicted well.
Part of that present invention that are not described in detail belong to the well-known technology of those skilled in the art.

Claims (4)

1. a kind of B-K criterion of improving influences the method for the multidirectional Laminates With Delamination prediction of composite material, feature for fibre-bearing bridge joint Be the following steps are included:
Step 1, carried out by double cantilever beam bending (DCB), 4 end edge notch (4ENF) and Mixed Bending (MMB) test I type, II type and the test of I/II mixed type static(al) delamination of the multidirectional laminate of CFRP, obtain corresponding load, displacement and crackle Length test data;
Step 2, data processing is carried out to test data and determines the I type interlayer faults toughness curve G changed with layering length aIC (a), II type interlayer faults toughness curve GIIC(a) and I/II mixed type interlayer faults toughness curve GC(a);
The step 2 determines the I type interlayer faults toughness curve G with layering length a variation using amendment beam theoryIC(a) it expresses Formula are as follows:
Wherein: b is specimen width, and F and N' are the modifying factor considered when big displacement and loading blocks influence respectively, due to measurement It is to be layered vertical range of the tip away from loaded line and use hinge rather than loading blocks, the two factors are 1, PICAnd δICPoint It is not the I type load and displacement applied to sample, | Δ | it is the modifying factor for being layered length, for considering that cantilever is splitting sharp position Additional displacement and rotation due to material anisotropy;
The step 2 determines the II type interlayer faults toughness curve G with layering length a variation using flexibility methodIIC(a) expression formula Are as follows:
Wherein: PCIt is critical load, C is sample flexibility;
The step 2 determines the I/II mixed type interlayer faults toughness curve G with layering length a variation according to amendment beam theoryC (a) expression formula are as follows:
GC(a)=GI(a)+GII(a)
Wherein: P is the load applied at the point of application, and c is distance of the point of application to intermediate load roller bearing, PgIt is upper beam and is attached to The wherein weight of loading blocks, cgFor distance of the center of gravity to intermediate load roller bearing of fixture, EfIt is bending modulus, h is sample thickness, L For fixed span away from;
Step 3, using the G for considering that the improvement B-K criterion of fiber bridge joint in delamination obtains step 2IC(a)、GIIC(a) and GC(a) least square fitting of three-dimensional data is carried out, so that it is determined that being suitable for the improvement B-K criterion of the multidirectional laminate of studied CRFP In parameter η value;
Above-mentioned I type is fitted in the step 3 respectively, the G with layering length variation that II type delamination test data obtainsIC (a)、GIIC(a) mathematic(al) representation, the G of the CFRP multi direction laminateIC(a) expression formula is piecewise function, can be divided into Fiber Bridge It connects section and stablizes expanding section;The G of the CFRP multi direction laminateIIC(a) expression formula is obtained by linear fit;
Step 4, establishing the finite element model based on cohesive force unit will be above-mentioned by the customized subprogram USDFLD of user CFRP multi direction laminate I type and II type interlayer faults toughness GIC(a)、GIIC(a) pass through least square in expression formula and step 3 The parameter η value being fitted in obtained improvement B-K criterion is embedded into as important parameter to be improved in B-K criterion, using improvement B-K Criterion simulates the delamination behavior under such multi direction laminate difference mixing ratio, and is tested by comparative test and numerical result Card establishes the accuracy for improving B-K criterion;
Interlayer faults toughness data under several mixing ratios of CFRP multi direction laminate is carried out least square fitting by the step 4 The obtained parameter η value and G improved in B-K criterionIC(a)、GIIC(a) expression formula as improve B-K criterion in important parameter, Be embedded into criterion by the customized subprogram USDFLD of finite element user, establish the finite element model based on cohesive force unit come Simulate the delamination behavior under such multi direction laminate difference mixing ratio, the improvement B-K criterion are as follows:
Step 5, the static(al) delamination behavior under any other mixing ratio is predicted using the improvement B-K criterion having verified that.
2. a kind of improvement B-K criterion according to claim 1 influences the multidirectional laminate of composite material point for fibre-bearing bridge joint Layer prediction method, it is characterised in that: verifying improve B-K criterion used by CFRP multi direction laminate ply stacking-sequence be (+ 45/-45/06)S//(-45/+45/06)S, the design of this kind of ply stacking-sequence is in order to reduce bending-torsional coupling effect and due to laying Reciprocal curvature effect caused by asymmetry.
3. a kind of improvement B-K criterion according to claim 2 influences the multidirectional laminate of composite material point for fibre-bearing bridge joint The method of layer prediction, it is characterised in that: the ply stacking-sequence is (+45/-45/06)S//(-45/+45/06)SThe multidirectional layer of CFRP Plywood is made of using T700/QY9511 carbon fiber/bismaleimide resin system unidirectional pre-immersion material.
4. a kind of improvement B-K criterion according to claim 1 influences the multidirectional laminate of composite material point for fibre-bearing bridge joint The method of layer prediction, it is characterised in that: the improvement B-K criterion may be used on predicting that the multidirectional laminate of such CFRP is arbitrarily mixing Than lower leaf propagation behavior, for the multidirectional laminate of other materials or other interfaces, improvement B-K criterion is being judged by fiber Bridging has versatility in the delamination influenced.
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