vct(虚拟裂纹扩展分析技术)

1、Vcct (Virtual crack closure technique)<Skin-stiffener debond prediction based on computational fracture analysis>Interlaminar fracture mechanics characterizes the onset of delaminations in composites. Shear loading causes the panel to buckle and the resulting out-of-plane deformations initiate

2、 skin/stringer separation at the location of an embeddeddefect.METHOD: Finite Element AnalysisELEMENT: the panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot and the panel in the vicinityof the embeddeddefect weremodeled with a local 3D soil mod

3、el.1. BACKGROUNDAerospaces structures are madeof flat or cured panels with co-cured or adhesively bonded frames and stiffeners computational stress analysis to determine the location of first matrix cracking.An artificial defect was placed at the termination of the center stiffener. The stiffened pa

4、nel is subjected to pure shear loading which causes the panel to buckle.ANALYSIS: nolinear finite element analysisStrain energy release rates and mixed made ratios were computed using the virtual crack closure technique.2. METHODOLOGY 2.1Interlaminar fracture mechanicsThe total strain energy release

5、 rateGTThe mode I component due to interlaminar tensionGIThe mode II component due to interlaminar sliding shear GIIThe modeIII component due to interlaminar scissoring shear GIIIP X Interlaminar tension ModelQ *Iriterlaminar sliding shear Mode IIFigure 2. Fractitre Modes.Interlaminfir scissoring sh

6、ear Mode IIPurpose: to predictdelami natio non set or growth fortwo-dime nsional problems,theses calculatedGcomp onents arecompared to interlaminarfracture toughness propertiesmeasured over a range of modemixities from pure modeI loading to pure mode II load ing.A quasi static mixed-mode fracture cr

7、iterio nis determ ined byplotting the interlaminar fracture toughness,Gc , versus themixed-mode ratio , gii/gt, determ ined from data gen erated using pure Mode I ( Gn /Gt 0) Double Can tilever Bending(DCB) pureMode II ( Gn / Gt 1) four point End Notched Flexure(4ENF), andMixed Mode Bending (MMB) te

8、sts of varying ratio for IM7/8852 carb on epoxy material.GCGICGIIC GICIIGtGic and Giic are the fracture toughness data for mode I and IIis a factor determined by the cure fit. Shownin figure 3 in this article.GII / Gt ,Failure is expected whe n, for a give n mixed mode ratiothe calculated total ener

9、gy release rate, Gt , exceeds theinterlaminar fracture toughness,Gc .2.2. An alysis Tools2.2.1. Virtual Crack Closure Tech niqueVCCT requires force and displaceme ntin put , which is obta inedfrom con ti nuum (2-D) and solid (3-D) fin ite eleme nt an alyses of the cracked (2-D) or delam in ated (3-D

10、) comp onent.Gi and Gii are calculated for four-noded elementsGIZiwlwl*2 aGiiXi ui u aa is the length of the elements at the crack front;Xi and Zi are the forces at the crack tip (nodal pointi);The relativedisplacements behind the crack tip are calculated from the no dal displaces(a): Virtual Crack

11、Closure Technique (VCCT) tbi !bta-nodedelement.For geometric nonlinear analysis where large deformations may occur, both forces and displaceme nts obta ined in the global coord in atesystem n eed to be tran sformedinto a localcoord in ate system (x ,z ) which origi nates at the crack tip.For the two

12、-dime nsio nal eight -no ded quadrilateral eleme nt withquadratic shape fun cti ons this yieldsG|wlwl*GiiUlul*The totalenergy releaserateGtis calculated from thein dividual mode comp onents aslocal crack tip systemdeformed state global systemX.Y.Z: forcesu,v,w： displacementsG,= -Vr/(2Aa )On = - X (-

13、 u'i *) / ()undeformed stateAa(outline)(h):Crack Ciosnre Technique (VCCT) fbi geoiuetncully Honlineur diidlysis.Figure 4: Ct ack Closure Technique for twa-diniensionai analysisIn a finiteelement model made of three-dimensional solideleme nts the delam in ati on of len gth a is represe nted as a

14、two-dimensional discontinuityby two surfaces . (why does it isdisc on ti nu ity?)The model I, mode II, and mode III components of the strainenergy release rate Gi , Gn ,and Gm are calculated asG|Gngiii2 A ZLi wLlwli*2 A XLi uLl uLl*2 A YLiVLlVLl*A a b . Here A is the area virtually closes, a is theb

15、 is thelen gth of the eleme nts at the delam in ati on front, andwidth of the elements.local crack tip i z'1w'1Z, system A辺r/eirdelamination frontintact areaglobal systemdelaminated areaa(b). Top i?tnr &f upper surface怡$ are omitted for davity)Figure 5. Virtual Crack Closure Technique /o

16、r eight noded elemeiirs.A local crack tip coord in ate system is n eeded.2.2.2. A Global/Local Shell 3D Modeling TechniqueComputed mixed mode strain energy release rate components depend on many variables such as element order and shear deformation assumptions, kinematic constraints in the neighborh

17、ood of the delamination front, and continuity of material properties and section stiffness in the vicinity of the debond when delaminations or debonds are modeled with plate or shell finite elements.3. FINITE ELEMENT MODELING3.1. Global Shell Model of Stringer Stiffened PanelThe global model include

18、s the steel load frame and attachments, the panel madeof graphite/epoxy prepreg tape and the stringers made of graphite/epoxy fabric. The outer steel load frame and the attachment bolts were modeled with beamelements available in the element software ABAQUST. he inner steel load frame which overlaps

19、 the panel edge was modeled with standard shell S4 elements.The shell elements ate connected by beam elements designed to enforce plate theory constraints. In the sections containing the artificial defects the beam elements were replaced by gap elements.In preparation for the global/local modeling a

20、pproach shell elements representing the foot of the stiffener and the panel were removed from the original shell model around the center stringer termination as shown in Figure 9. The shell elements used to model the stiffener web and hat were kept in place. At the boundaries shell edges in ABAQUAS

21、were defined as shown which were used to connect the shell model with the local 3D insert model using the shell to solid coupling option in ABAQUS which allows the connection between non-conforming shell and solid models.3.2 Local 3D Insert Model for Solid Modeling of Stringer Foot and Panel SkinThe

22、 local 3D insert model was generated using C3D8I solid brick elements and consisted of an intact section and a delaminated section with a fine mesh around the delamination front. Surfaces were defined on the outer faces of the insert model to provide a connection with the global shell model using th

23、e shell to solid coupling option in ABAQUS. The initial defect is located at the bondline between stringer foot and the panel. This defect was treated as a delamination and modeled as a discrete discontinuity using two unconnected nodes with identical coordinates one on each side of the delamination

24、. A refined mesh was used along the stringer boundary in order to capture edge effects. Using the finite sliding option available in ABAQUScontact was modeled between the delamination surfaces to avoid interpenetration during analysis.3.3. CombinedGlobal/Local Shell/3D Model of Stringer Stiffned Pan

25、elUniform displacements u, v were applied at one corner node to introduce shear as shown in Figure 11a. The inplane displacements u, v were suppressed at the diagonally opposite corner and the out of plane displacement w were suppressed along all four edges across the entire width of the inner and o

26、uter steel load frame.The global shell model was connected to the local 3D insert model using the shell to solid coupling option in ABAQUSwhich allows the connection between non-conforming shell and solid models. For the entire analyses the non-linear solution option was used in ABAQUSA. total of ei

27、ght delamination lengths were modeled. Additional lengths were chosen to study the change in energy release rate distribution across the width (b) of the stringer with increasing delamination length (a).4. ANALYSIS RESULTS 4.1Deformed Panel The longer caused a change in the stiffness which resulted

28、in an altered buckling pattern.Early in the analysis (increment 5) a mode I opening was observed only near one edge. With increasing applied external displacement the deformation changed locally and for increment 15 modeI disappeared completely and the delamination appeared closed over the entire de

29、laminated length. A small scissoring shear (mode III) could be observed. Further increasing the external displacement resulted in a small modeI opening across the entire width of the stringer as observed for increment 20. For the last step of the analysis (increment 41) after the entire external dis

30、placement u=v=6.35mmhad been applied mode I opening was observed across the entire width of the stringer over the entire delaminated length.The figure reveals that not the entire delaminated section opens under mode I. After initial opening, the section below the webtermination closes and the delami

31、nated surfaces contact. This closing is caused by a change in the local buckling pattern, due to stiffness changes caused by the longer delamination, as discussed above. It was observed that the local buckling pattern in the immediate surrounding of the delaminated stringer is dependent on thedelamination length modeled, which made convergence difficult.4.2Calculation of Mixed-Mode Strain Energy Release Rates andFailure IndicesVCCT was used to calculate the mode contributionsGI ， GII andGIII the total ener