In the present work strain energy release rate as a fracture parameter has been used to evaluate the skin-stiffener debonding in stiffened composite panel with functionally graded (FG) bimodular material property under thermo-mechanical coupled field. The influence of ply lay-up and interaction of residual thermal stresses on the skin-stiffener has been investigated. Stress-dependent elasticity problem of bimodular stiffened panel made up of laminated fiber reinforced polymeric composite is carried out using finite element analysis under various bimodular ratios. The numerical result in terms of compressive load as a function of applied displacement has been compared to the existing literature data to assess the effectiveness of the implemented methodology. Variation of energy release rate along the interface delamination front has been plotted for both mechanical and thermo-mechanical coupled loading with modulus ratio R varying from 1 (unimodular) to 5. Asymmetric variation of energy release rate along the interfacial front has been observed for the bimodular stiffened composite panel.
BhushanAPandaSKKhanDet al.Weibull effective volumes, surfaces, and strength scaling for cylindrical flexure specimens having bi-modularity. J Test Eval2016; 44: 1978–1997.
2.
SunJYZhuHQQinSHet al.A review on the research of mechanical problems with different moduli in tension and compression. J Mech Sci Technol2010; 24: 1845–1854.
3.
JonesRM. Apparent flexural modulus and strength of multimodulus materials. J Compos Mater1976; 10: 342–354.
4.
JonesRM. Stress–strain relations for materials with different moduli in tension and compression. AIAA J1977; 15: 16–23.
5.
O’BrienTK. Characterisation of delamination onset and growth in a composite laminate. Damages Compos Mater1982; 20: 140–167.
6.
WangSSChoiI. The interface crack behavior in dissimilar anisotropic composites under mixed-mode loading. ASME J Appl Mech1983; 50: 179–183.
7.
JohannessonTSjoblomPSeldenR. The detailed structure of delaminated surfaces in graphite/epoxy laminates. J Mater Sci1984; 19: 1171–1177.
Hart-SmithLJ. A peel-type durability test coupon to assess interfaces in bonded, co-bonded, and co-cured composite structures. Int J Adhes Adhes1999; 19: 181–191.
10.
DuongCNHart-SmithLJYuJ. Analytical approach to bonded repair of elliptical dent, corrosion grind-out, and cut-out. Theor Appl Fract Mech2001; 36: 187–193.
11.
ErdoganFGuptaGD. Layered composites with an interface flaws. Int J Solids Struct1971; 7: 1089–1107.
12.
SihGCChenEPHuangSLet al.Material characterization on the fracture of filament-reinforced composites. J Compos Mater1975; 9: 167–186.
13.
RybickiEFSchmueserDWFoxJ. Fracture mechanics of delamination problems in composite materials. J Comp Mater1977; 11: 470–487.
14.
WangSS. An analysis of delamination in angle-ply fiber-reinforced composites. ASME J Appl Mech1980; 47: 64–70.
15.
WangSS. Fracture mechanics of delamination problems in composite materials. J Compos Mater1983; 17: 210–223.
16.
KuriakoseSTalrejaR. Variational solutions to stresses in cracked cross-ply laminates under bending. Int J Solids Struct2004; 41: 2331–2347.
17.
Citarella R and Cricrì G. Three-dimensional BEM and FEM submodelling in a cracked FML full scale aeronautic panel. Appl Compos Mater 2014; 21: 557–577.
18.
Ramkumar RL. Performance of a quantitative study of instability-related delamination growth, NASA CR-166046, 1983.
19.
ArmentaniECitarellaRSepeR. FML full scale aeronautic panel under multiaxial fatigue: experimental test and DBEM simulation. Eng Fract Mech2011; 78: 1717–1728.
20.
ChaiHKnaussWGBabcockCD. Observation of damage growth in compressively loaded laminates. J Exp Mech1983; 23: 329–337.
WhitcombJD. Parametric analytical study of instability-related delamination growth. Compos Sci Technol1986; 25: 18–48.
23.
ChaiHBabcokCDKnaussWG. One delamination modelling of failure in laminated plates by delamination buckling. Int J Solids Struct1981; 17: 1069–1083.
24.
Kim HJ and Hong CS. Buckling and postbuckling behaviour of composite laminates with an embedded delamination. In: Proceedings of ICCM-10, WHISTLER; Vancouver; British Columbia; Canada, 14–18 August 1995.
25.
WhitcombJD. Analysis of a laminate with a postbuckled embedded delamination, including contact effects. Int J Compos Mater1992; 26: 1523–1535.
26.
WhitcombJD. Three dimensional analysis of a postbuckled embedded delamination. Int J Compos Mater1989; 23: 862–889.
27.
SankarBVSonikV. Point-wise energy release rate in delaminated plates. AIAA J1995; 33: 1312–1318.
28.
WangJTRajuIS. Strain energy release rate formulae for skin-stiffener debond modeled with plate elements. Eng Fract Mech1996; 54: 211–228.
29.
KlügJWuXXSunCT. Efficient modeling of postbuckling delamination growth in composite laminates using plate elements. AIAA J1996; 34: 178–184.
30.
BuchholzFGRikardsRWangH. Computational analysis of interlaminar fracture of laminated composites. Int J Fract1997; 86: 37–57.
GaudenziPPeruginiPRiccioA. Post-buckling behaviour of composite panels in the presence of unstable delaminations. Compos Struct2001; 51: 301–309.
33.
RiccioAPeruginiPScaramuzzinoF. Embedded delamination growth in composite panels under compressive load. Compos Part B Eng2001; 32: 209–218.
34.
RiccioAPietropaoliE. Modelling damage propagation in composite plates with embedded delamination under compressive load. J Compos Mater2008; 42: 1309–1335.
35.
De BorstRRemmersJJC. Computational modelling of delamination. Compos Sci Technol2006; 66: 713–722.
36.
RiccioAScaramuzzinoFPeruginiP. Influence of contact phenomena on embedded delamination growth in composites. AIAA J2003; 41: 933–940.
37.
CaputoFDi FeliceGLamannaGet al.Numerical procedures for damage mechanisms analysis in CFRP composites. Key Eng Mater2013; 569–570: 111–118.
38.
GreenhalghEMeeksCClarkeAet al.The effect of defects on the performance of post-buckled CFRP stringer-stiffened panels. Compos Part A Appl Sci Manuf2003; 34: 623–633.
39.
RiccioAGiordanoMZarrelliM. A linear numerical approach to simulate the delamination growth initiation in stiffened composite panels. J Compos Mater2010; 44: 1841–1866.
40.
SuemasuHKuriharaKAraiKet al.Compressive property degradation of composite stiffened panel due to debonding and delaminations. Adv Compos Mater2006; 15: 139–151.
41.
PietropaoliERiccioA. On the robustness of finite element procedures based on virtual crack closure technique and fail release approach for delamination growth phenomena, definition and assessment of a novel methodology. Compos Sci Technol2010; 70: 1288–1300.
42.
PietropaoliERiccioA. Formulation and assessment of an enhanced finite element procedure for the analysis of delamination growth phenomena in composite structures. Compos Sci Technol2011; 71: 836–846.
43.
RiccioARaimondoAScaramuzzinoF. A study on skin delaminations growth in stiffened composite panels by a novel numerical approach. Appl Compos Mater2013; 20: 465–488.
44.
RiccioARaimondoADi CaprioFet al.Delaminations buckling and growth phenomena in stiffened composite panels under compression, Part II: a numerical study. J Compos Mater2013; 48: 2857–2870.
45.
OrificiACThomsonRSHerszbergIet al.An analysis methodology for failure in postbuckling skin–stiffener interfaces. Compos Struct2008; 86: 186–193.
46.
OrificiACHersbergIThomsonRS. Review of methodologies for composite material modelling incorporating failure. Compos Struct2008; 86: 194–210.
47.
OrificiACThomsonRSDegenhardtRet al.Degradation investigation in a postbuckling composite stiffened fuselage panel. Compos Struct2008; 82: 217–224.
48.
RaimondoARiccioA. Inter-laminar and intra-laminar damage evolution in composite panels with skin-stringer debonding under compression. Compos Part B2016; 94: 139–151.
49.
RiccioARaimondoAScaramuzzinoF. A robust numerical approach for the simulation of skin stringer debonding growth in stiffened composite panels under compression. Compos Part B Eng2015; 71: 131–142.
50.
OrificiACDe Zarate AlberdiIOThomsonRSet al.Compression and post-buckling damage growth and collapse analysis of flat composite stiffened panels. Compos Sci Technol2008; 68: 3150–3160.
51.
BertoliniJCastaniéBBarrauJJet al.Multi-level experimental and numerical analysis of composite stiffener debonding, part 1: non-specific specimen level. Compos Struct2009; 90: 381–391.
52.
RiccioARaimondoADi FeliceGet al.A numerical procedure for the simulation of skin–stringer debonding growth in stiffened composite panels. Aerosp Sci Technol2014; 39: 307–314.
53.
XieDeBiggersSBJr. Postbuckling analysis with progressive damage modeling in tailored laminated plates and shells with a cutout. Compos Struct2003; 59: 199–216.
54.
XieDeBiggersSBJr. Progressive damage arrest mechanism in tailored laminated plates with a cutout. Acta Mech Solida Sin2008; 21: 62–72.
55.
XieDeBiggersSBJr. Progressive crack growth analysis using interface element based on the virtual crack closure technique. Finite Elem Anal Des2006; 42: 977–984.
56.
XieDeBiggersSBJr. Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique. Int J Impact Eng2007; 34: 1047–1060.
57.
XieDeBiggersSBJr. Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: formulation and validation. Eng Fract Mech2006; 73: 771–785.
58.
XieDeBiggersSBJr. Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: sensitivity study on modeling details. Eng Fract Mech2006; 73: 786–801.
59.
TayTETanVBCLiuG. A new integrated micro–macro approach to damage and fracture of composites. Mater Sci Eng B2006; 132: 138–142.
60.
FinnSRSpringerGS. Delaminations in composite plates under transverse static or impact loads – a model. Compos Struct1993; 23: 177–190.
61.
LiDHLiuYZhangX. An extended layerwise method for composite laminated beams with multiple delaminations and matrix cracks. Int J Numer Meth Eng2015; 101: 407–434.
LiDHZhangF. Full extended layerwise method for the simulation of laminated composite plates and shells. Comput Struct2017; 187: 101–113.
64.
LiDH. Delamination and transverse crack growth prediction for laminated composite plates and shells. Comput Struct2016; 177: 39–55.
65.
Reeder JR. 3-D mixed mode delamination fracture criteria – an experimentalist’s perspective. Report 20060048260. NASA/Contractor, 2006.
66.
KruegerRMinguetPJ. Analysis of composite skin–stiffener debond specimens using a shell/3D modeling technique. Compos Struct2007; 81: 41–59.
67.
AmbartsumyanSA. Elasticity theory of different moduli, Beijing: China Railway Publishing House, 1986.
68.
JadanDK. Approximate analytical solutions for large flexural and shear deformations of uniformly loaded simply-supported bimodular beam. Iraqi J Civil Eng2011; 8: 1–16.
69.
ANSYS Manual (revision 5). Volume III: Elements DN-R300:50e53.
70.
NimjeSVPanigrahiSK. Interfacial failure analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates. Int J Adhes Adhes2015; 58: 70–79.
71.
ShahSPandaSK. Bimodularity of interface layer and curing stress coupling effects on mixed mode fracture behaviour of functionally graded tee joint. Int J Adhes Adhes2017; 75: 74–87.
