RESEARCH ON FAILURE CRITERION FOR COMPOSITE MATERIALS IN OPTIMIZATION

Transcription

1 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES RESEARCH ON FAILURE CRITERION FOR COMPOSITE MATERIALS IN OPTIMIZATION PhD. Cheng Wenyuan *, Prof. Cui Degang ** BEIHANG Universiy,*Aviaion Indusry Developmen Research Cener of China, ** China Aviaion Indusry Corporaion II (AVIC II) Keywords: Failure crierion, grid echnology, geneic algorihm Absrac China Aviaion Indusry is face o seriously challenge and good opporuniy in high performance compuing fields, such as CFD compuing, muli-objecive opimizaion for composie srucures under muliple consrains, ec. A remoe muli-cluser grid opimizaion sysem (RMGOS) is developed in our previous research o solve he ime-consuming aircraf design problems and proved o be efficien. On he oher hand, he failure crierion for composie maerials has is limiaion in applicaion for solve he srengh problem in engineering design. In his paper, he four classic failure crierions have been discussed wih respec o he enveloping range and an Equivalen Srain crierion is suggesed as an alernaive mehod. The Finie Elemen Analysis (FEA) model for he sandwich honeycomb composie srucure has been esablished and opimized under various failure crierions hrough he grid opimizaion sysem. The opimizaion resuls have been verified wih he experimen resuls. The resuls show ha he RMGOS can solve he composie srucure opimizaion problem efficienly and he crierion is he bes in applicaion. Background The applicaion of grid echnology in high performance compuing fields as he ool o solve resource share and effeciveness problem, such as aeronauics, asronauics, meeorology, medicine, ec, has become more and more maure wih he developmen of basic knowledge in grid echnology [,]. Especially in aircraf srucure design, he simulaion plaform for srucure opimizaion has been developed by inegraing Geneic Algorihm (GA) [] wih Grid Technology, which has become one of he new developmen direcions in aircraf srucure design. In previous research, he RMGOS has been developed o offer he way o solve composie srucure opimizaion problem wih consrained of various differen condiions. In his paper, he difference beween various failure crierions for composie maerial has been analyzed and a new failure crierion based on Equivalen Srain has been suggesed. Through he RMGOS, he FEA model for sandwich honeycomb composie srucure has been esablished and opimized for he minimum weigh under consrains of siffness in each failure crierion. The opimizaion resuls also have been verified wih experimens. Failure Crierions for Composie Srucure. Tradiional Failure Crierions The four radiional failure crierions for composie maerials in plane sress sae include [,5] :.. Crierion σ σ σ σ τ + + Y S = ().. Crierion σ σ σ σ c + + σ c c YYc c () Yc Y τ + σ + = Y Y S c

2 CHENG WENYUAN, CUI DEGANG.. Crierion F σ + F σ σ + F σ + F σ + F σ + F σ = () Table The properies of T7/QY9 Modulus E L E T G LT v ρ(g/cm ) /GPa Applicaion Range for Failure Crierions The applicaion range for four failure crierions is shown in Fig. The enveloping surface of crierion is fully in he coverage range of maximum sress. The enveloping surface of crierion exceeds he coverage range of maximum sress in he hird and fourh quadrans. The ransverse compression sress in G posiion of he ellipse is grea han F posiion, however he longiudinal compression sress has made an increase of %, which has exceeded he longiudinal compression srengh value. And he value in D posiion is also greaer han E posiion of %. In he hird quadran, he coverage range of crierion is surpassing he oher crierions. Especially in B posiion, he ransverse compression sress is greaer han C posiion of %, however he longiudinal compression sress is 5MPa, which exceeds he longiudinal compression srengh value. The same, he ransverse compression sress in A posiion is 5MPa, however he longiudinal compression sress is greaer han F posiion of 5%, which is abnormal. Hence, in he hird quadran, he Max-Sress crierion is suggesed. 5 MaxSress F E σ /MPa A G B C σ /MPa Fig Comparison of enveloping surface for various failure crierions in he sae of σ -σ In his paper, he T7/ QY9 has been chosen as he composie maerials, and he above curves in Fig are drawn according o he following properies shown in Table. D Srengh c Y Y c S /MPa Equivalen Srain Failure Crierion In engineering design, he failure crierion is usually based on srain, bu less considering of he coupling beween all he srain componens. On he oher hand, he above four classic failure crierions are based on he phenomenological heory, which usually deals wih he sress insead of srain. In his paper, a new failure srain crierion is suggesed by using Equivalen Srain ε von for engineering design, and in his crierion, he coupling effec of srain componens has been considered. The Equivalen Srain crierion is described as follows: ε von /[ε von ]= () The working srain ε von can be calculaed by he flowing equaion: [( ε ε ) + ε + ε ] γ ε = + (5) von Here, [ε von ] is allowable srain calculaed by he allowable srain componens wih he above equaion. Composie Srucure Opimizaion based on Grid Plaform. Remoe Muli-cluser Grid Opimizaion Sysem (RMGOS) [] In his paper, RMGOS is developed by inegraing he grid echnology and commercial FEA sofware o he GA. The commercial FEA sofware is uilized as he analysis ool o achieve he accuracy for he engineering requiremen. The sysem is applied o solve muli-objecive composie srucure opimizaion problem. The flow char of he opimizaion process is shown in Fig. In he flow, he neural-nework is uilizing for predicing he search zone of nex opimizaion loop o reduce he opimizaion ime.

3 RESEARCH ON FAILURE CRITERION FOR COMPOSITE MATERIALS IN OPTIMIZATION The algorihm of RMGOS includes (Fig ): inpu he iniial informaion including FE model, variables and consrains, ec; in GA module A, he objecive funcion informaion is deal wih by Pareo GA, and he populaion chromosomes are generaed randomly or from he informaion of he previous generaion; he daum files (feasible projec se) for FEA are formed from he chromosome informaion; in he grid compuaion environmen, he feasible projec se are divided ino some job unis and dispached o local/remoe compuaion nodes hrough he grid Job Schedule Server; he numerical resuls are sen back o he Server afer parallel compuaions; afer having colleced he resuls of all job unis, he nex generaion will be generaed by he GA operaions in GA module B which performs he operaions of selecion, crossover and muaion and obains he useful informaion, hen he resuls of model B will reurn o GA module A. Therefore, he compuaion could be compleed and he saisfacory soluions can be obained afer necessary or cerain loops. FE model No No GA module A Feasible projec se Job Schedule Server Complee Objecives and consrains Yes Evaluaion oupu GA module B Saisfy Yes Cluser Cluser Cluser n- Cluser n FE analysis Oupu Fig Flow char of he opimizaion process. Opimizaion for Honeycomb Sandwich Composie Srucures To verify he RMGOS and Equivalen Srain Failure Crierion, a FEA model has been esablished o opimize he minimum weigh under consrain of siffness. The problem is described as follows: Min W s.. η < 9 α 9 () x min Where W represens he weigh for composie srucure, a is adding angle, x is adding layer posiion, and min are he skin hickness, he minimum skin hickness respecively. In he flow process, he opimizaion sars from he iniial panel skin wih a minimum hickness, such as mm. The opimizaion is sep by sep o develop iself. In each sep, % composie weigh is dispersed and added in he opimum posiion wih bes lay-up angle. The opimizaion process keep running unil reach he convergence, including reach preassigned sep or judging if he failure efficiency η is less han zero. In he opimizaion, four failure crierions including Tsaihill,, Tsaiwu, Equivalen Srain, are chosen as deerminan condiions. The Numerical Resuls Afer he opimizaions, four honeycomb sandwich composie srucures have been designed relaed o he four failure crierions. Each srucure has me he design requiremen, bu he skin layous are differen. The failure indexes and design variables in various crierions are shown in Fig. In he iniial sae, Weigh Added (%) Equivalen Srain in Srain sae) Fig Opimizaion process in four failure crierions

4 CHENG WENYUAN, CUI DEGANG he difference beween failure indexes in all failure crierions is grea, however, wih he opimizaion process, when adding -% weigh, he maximum failure index in model are all less han., which mee he design requiremen. In his circumsance, he srucure is safe. Equivalen Srain (Opimized by Crierion) The failure indexes of he four ses of opimizaion resuls under four differen failure crierions are shown in Fig. In he iniial sae, he failure index for is maximizing, and he one for Equivalen Srain is minimize. The oher wo is similar. When adding some cerain percen weigh, failure index in each crierion reach.. Especially using crierion, he consisency is bes and he resuls opimized by Equivalen Srain crierion has some error. Equivalen Srain (Opimized by Crierion) Weigh Added (%) Weigh Added (%) Equivalen Srain (Opimized by Equivalen Srain Crierion) Equivalen Srain (Opimized by Crierion) Weigh Added (%) Weigh Added (%). Equivalen of Raw Opimizaion Resuls In he raw opimizaion resuls obained afer he RMGOS calculaion, each lay-up has differen hickness and differen angles, which needs o be ransferred o sandard lay-up for engineering applicaion by using he equivalen equaion of hree direcions siffness... The Equivalen of Three Direcion Siffness The mechanical derive can proof ha, no maer how choose he lay-up angle, he oal hickness remain he same, when he siffness in he longiudinal, ransverse and shear direcions has been deermined. Hence, in he iniial design for Fig Flow char of he opimizaion process laminae, he hree direcion siffness can be calculaed according o he srucure design, hen he lay-up angle and hickness can be calculaed consequenly. The longiudinal, ransverse and shear siffness is he basic characerisic for laminae. When designing one symmeric laminae, he lay-up number in every se of angle can be calculaed, if he wo axial rigidiy Eδ, Eδ and shear rigidiy Gδ has been given. The following is he equaion: A A E δ = A ; Eδ = A ; Gδ = A (7) A A Assume ha he hree lay-up angleα, β, θ are o, 5 o, 9 o respecively. The corresponding lay-up number is N, N, N. When he hree

5 RESEARCH ON FAILURE CRITERION FOR COMPOSITE MATERIALS IN OPTIMIZATION direcion siffness is given, he lay-up number can be calculaed ou by he following equaion: α β θ α β θ ( QN + QN + QN) TB Eδ = ( QN + QN + QN) TB α β θ Q N + Q N + Q N α β θ α β θ ( QN + QN + QN) TB Eδ = ( QN + QN + QN) TB α β θ Q N + Q N + Q N α β θ Gδ = ( Q N + Q N + Q N ) TB () Here, TB represens he hickness in each lamina. The experimen samples are a group of symmeric imbalance honeycomb sandwich composie srucure, as shown in Fig 7. The samples skin is composie maerial wih opimized lay-up for four crierions. The core is paper honeycomb. There are 5 groups of samples wih wo same samples in each group. Fig 5 D siffness sae in composie panel.. The Equivalen of Three Direcion Siffness By using he ool Equivalen Equaion of Three Direcions Siffness, he raw opimized resuls has been ransferred o he sandard lay-up laminae me he manufacory requiremen, as shown in Fig. The differen color area represens differen lay-up hickness and angles. Fig 7 Experimen design. The Experimen Resuls Loading poin.. The Failure Load The experimen daa of he samples is shown in Table and Fig, including he loading and failure process for each sample. When he sample - reaches failure condiion, i is far away from he design srengh value wihou consideraion of he release force beween he aluminum reinforcemen in roo and panel. Hence self-plugging rives are used o srengh he srucure in each sample in order o avoiding he failure resul from he release force. Afer reach he maximum loading, he curve drop sharply. Table The failure load of samples Value/N EquSrain Srandard Design Exp Samp Fig Skin lay-up afer opimizaion for four crierions. The Experimen for Opimizaion Resuls Exp Samp Load/N The Experimen Design Time 5

6 CHENG WENYUAN, CUI DEGANG Fig Flow char of he opimizaion process.. The Failure Mode There are hree kinds of failure mode, including: The sample - failed because of he release srengh beween he aluminum and he composie panel (op fig in Fig 9). In his mode, he insufficien of adhere release srengh resul in he failure when adding 7% design load. Fig 9 The failure modes of experimen samples The sample - failed resul from he collapse of honeycomb under he buckling loading (middle fig in Fig 9). In his mode, he reinforcemen from he self-plugging rive improved he bearing capaciy of he composie panel, so he failure load is greaer han he design load. On he oher hand, he design srengh of honeycomb is very lower, so he failure always focused on he honeycomb srucure. The sample 5- failed because of he crack in composie panel. In his mode, he sandard wihou opimizaion failed in he middle par resul from he insufficien srengh in he relevan posiion. In all samples, - is he s failure mode (lower fig in Fig 9). The sample 5- and 5- are he rd failure mode. The oher samples are also he nd failure mode... The Failure Srain The comparison beween experimen and compuaion value in es poin is shown in Fig and Fig, here, he five figures represen lay-up opimized wih he sandard,, Equivalen Srain,, crierion respecively. The curve is made wih he es number as abscissa and srain value as verical coordinae. The heory curve describes he compuaion srain in all es posiion under design loading. The es and es curve show he acual experimen srain. The loadcase and loadcase curve represen he srain recalculaed by adding he acual failure load in he FEA model. The experimen srain is less han compuaion srain in each crierion. The reason is ha he reinforcemen in roo posiion is insufficien o offer enough suppor o he whole srucure. Hence, he honeycomb srucure has collapsed when he composie panel is far away from he failure. There exis some wave in each crierion; i means he design hasn realized he equal srain sae. The difficul o close agreemen on he design wih he manufacure process is he main reason. Anoher reason is ha he sepped shape change of he lay-up resuls in he disconinuous srain disribuion. The es posiion in sandard lay-up wave more sharply han he oher lay-up. I means

7 RESEARCH ON FAILURE CRITERION FOR COMPOSITE MATERIALS IN OPTIMIZATION Srain Srain Srain Srain Srain ha i s difficul o obain good lay-up by arbirary design wihou opimizaion. heory loadcase loadcase es es -Non-Crierion - -VonEquSrain Srain Fig The es srain value in samples crierion, and he Equivalen Srain crierion is wors. The srain disribuion in roo posiion is even and he wave in loading secion is sharp. I shows ha he equal srain design is very successful in roo posiion. 5. Conclusion The resuls opimized by RMGOS have been verified hrough he experimen. I shows ha using he disribuion compuing plaform inegraes maure FEA sofware and grid echnology wih GA, he complicaed aircraf srucure design problem can be solved efficienly, especially in solving he composie srucure opimizaion wih muliple consrains. From he compuaion and experimen resuls, crierion is bes in effeciveness and he Equivalen Srain crierion may be as one evaluaion mehod only as reference. References [] CHENG Wen-yuan, CHANG Yan, CUI De-gang, e al. Opimizaion Design Sysem for Composie Srucures based on Grid Technology. Chinese Journal of Aeronauics. Vol., No., pp 55-59, 7. [] Yan,Chang, Wenyuan, Cheng, u,liu, e al. Applicaion of Grid Technology in Muli-Objecive Aircraf Opimizaion Sysem. h Inernaional Conference on Compuer Suppored Cooperaive Work In Design, Proceedings, Vols and, pp 9-9,. [] Ming Zhou, Shudong Sun, Geneic Algorihms: Theory and Applicaion, s ediion, Defence indusry publishing company,. [] Maohong Yu. Advance in srengh heories for maerials under complex sress sae in he h cenrury. Advance in Mechanics, Vol., No., pp 59-5,. [5] Chinese Insiue of Aeronauics. Design manual for composie. s ediion, Aviaion Indusry,. Fig The es srain in ransverse secion The wave in crierion is he bes and he disribuion of srain is he mos even, which means he effeciveness is bes. crierion is beer han Copyrigh Saemen The auhors confirm ha hey, and/or heir company or insiuion, hold copyrigh on all of he original maerial included in heir paper. They also confirm hey have obained permission, from he copyrigh holder of any hird pary maerial included in heir paper, o publish i as par of heir paper. The auhors gran full permission for he publicaion and disribuion of heir paper as par of 7

8 CHENG WENYUAN, CUI DEGANG he ICAS proceedings or as individual off-prins from he proceedings.