An XFEM-based methodology for fatigue delamination and permeability of composites
Introduction
Fibre-reinforced composites are candidate materials for the next generation of reusable space launch vehicles (RSLVs). The drive to replace conventional metal alloys with alternative materials stems from the need to reduce the cost of transporting a payload to orbit, which currently stands at around $20,000 per kg [1]. The high specific strength, specific stiffness, toughness and chemical resistance of composites such as carbon fibre reinforced polymers (CFRP) make them ideal for many structural components of RSLVs, in particular the fuel tanks which are used to store liquid hydrogen and liquid oxygen at cryogenic temperatures. Unlike current designs, the fuel tanks for RSLVs are anticipated to undergo numerous fuelling/refuelling and take-off/landing cycles, with the inner walls of the tank being exposed to temperatures as low as −250 °C. The extreme thermo-mechanical cycling resulting from such a regime can lead to severe damage accumulation in the CFRP in the form of microcracking and delamination, possibly resulting in permeation of the cryogen through the tank wall due to interaction between these damage modes as shown in Fig. 1.
The ability to model and predict the degradation of composites under thermal/mechanical fatigue loading is a key step in the design of efficient and safe cryogenic fuel tanks, as well as aerospace components in general. The effect of microcracking on the properties of composites as well as its role in the development of other laminate failure modes, such as delamination, has been well documented [2]. Zhang et al. [3] took a theoretical approach to investigating delaminations induced by transverse microcracking in composite laminates, using first-order shear laminate theory in their analysis. Roy and Benjamin [4], [5] built on this work to predict the opening displacement of transverse cracks, based on prescribed thermal and mechanical loads, as well as ply crack density and adjoining delamination length. They also predicted the through-thickness delaminated crack opening displacement (DCOD) distribution for a composite, subjected to thermal and mechanical loading, using both a mathematical model and a 2D FE model of a composite laminate. These models were used to predict laminate permeability based on the existence of overlap areas between transverse cracks and delaminations in the aforementioned leakage paths. Nair and Roy [6] went further and compared the permeability predicted by the FE models, which used crack densities taken from Bechel et al. [7] and an estimation of the variation of delamination length with thermal cycles as input, with experimental data from the same source with reasonable success.
The above studies rely on assuming a delamination length for a given number of thermal cycles. This is, in part, due to the difficulties in monitoring delamination growth in composite laminates [8], [9], where unlike transverse cracks, the delaminations are typically closed and difficult to locate and measure. However, the delamination length at the tips of transverse cracks has been shown to affect the magnitude of DCOD and hence laminate permeability [4], [5], [6], [10]. A method of predicting the growth of delaminations at overlap areas under thermal/mechanical loading is required to give more accurate and efficient modelling of damage progression in composite laminates, for permeability predictions.
Previous work on composite failure simulation includes a number of delamination growth prediction models. Analytical and numerical solutions for modelling of interlaminar failure typically involves a pre-defined interface [11], [12], [13], [14], [15], [16], as well as the use of specially devised constitutive equations and finite elements to simulate delamination growth and interaction between various damage modes [17], [18], [19]. A key objective of the present work is the meso-modelling of delamination growth in a CFRP laminate under cryogenic fatigue loading, to predict the DCOD of transverse microcracks and hence laminate permeability. This is achieved through the Virtual Crack Closure Technique (VCCT), in conjunction with the extended finite element method (XFEM), in order to predict the variation in DCOD with increasing delamination length. The use of XFEM leads to significant savings in computational cost in terms of both analysis set-up and run-times and does not require a priori definition of either crack length or crack path. The technique also allows simulation of both inter- and intralaminar crack growth, as well as three-dimensional growth and damage. This methodology is also used to predict the influence of existing interlaminar defects on subsequent fatigue delamination growth under cryogenic loading. Although XFEM is a relatively novel technique in the area of composite fracture mechanics, some recent work [20], [21] uses this technique for static and fatigue delamination modelling, but without consideration of thermal delamination, and for development of bimaterial orthotropic enrichment functions for use with XFEM [22]. The context of the present work is application to cryogenic fatigue of three-dimensional fuel tanks fabricated from multi-ply composite laminates. Hence a key driver for the methodology presented here is the requirement for application to complex geometries and loading histories. Thus, the XFEM approach is developed within a general-purpose, non-linear finite element code.
The novel XFEM-based methodology for prediction of DCOD and delamination growth trends under thermal fatigue loading was validated using recognised test cases, involving thermal and mechanical loads, in both static and fatigue loading regimes. Static double cantilever beam (DCB) and end notch flexure (ENF) tests were used as a starting point for the study, with predicted crack growth from these models being compared with experimental test data for CF/PEEK specimens. Sub-critical loading scenarios, in the form of mechanical and thermal fatigue loading of composite laminates, were validated against analytical and experimental data from the literature. Subsequently, the modelling of delamination growth in a quasi-isotropic laminate under cryogenic fatigue loading was conducted in order to predict DCOD and hence composite laminate permeability.
Section snippets
Delamination modelling methodology
The extended finite element method is an extension of the classical finite element method, based on the concept of partition of unity [23], which allows modelling of discontinuities through the use of special enrichment functions which are incorporated into the finite element approximation. XFEM was introduced by Belytschko and Black [24] as an alternative to modelling crack growth problems, but is useful in modelling material abstractions in general, such as voids, grain boundaries and
Static results
The output from the experimental tests was in the form of load-displacement plots and Mode I and Mode II fracture toughness values. Due to the fact that the mean fracture toughness from each test was used as input for the models, the load-displacement graphs were used to compare the performance of the finite element models with the experiments.
Conclusion
A novel crack growth methodology is presented for the prediction of thermal fatigue delamination, DCOD and composite laminate permeability. The XFEM-based crack growth methodology was validated against measurements from standardised static and fatigue delamination tests.
XFEM models of Mode I DCB and Mode II ENF tests were developed to validate the static delamination prediction capability against experimental test data for CF/PEEK. The 2D models accurately predicted the measured
Acknowledgements
This research is funded by the European Space Agency Network Partnering Initiative and the Irish Research Council (IRC) Enterprise Partnership Scheme (EPS). Research collaborators include ÉireComposites Teo, the Irish Centre for Composites Research (ICOMP) and Astrium Space Transportation.
References (48)
- et al.
Modelling of permeation and damage ingraphite/epoxy laminates for cryogenic fuel storage
Compos Sci Technol
(2004) - et al.
Modelling of permeation and damage in graphite/epoxy laminates for cryogenic tanks in the presence of delaminations and stitch cracks
Compos Sci Technol
(2007) - et al.
Limiting the permeability of composites for cryogenic applications
Compos Sci Technol
(2006) - et al.
Delamination monitoring of graphite/epoxy laminated composite plate of electric resistance change method
Compos Sci Technol
(2002) - et al.
Interlaminar interface modelling for the prediction of delamination
Compos Struct
(1992) - et al.
Damage analysis of interlaminar fracture specimens
Compos Struct
(1995) - et al.
A mesomodel for localisation and damage computation in laminates
Compos Methods Appl Mech Eng
(2000) - et al.
Geometrical and interfacial non-linearities in the analysis of delamination in composites
Int J Solids Struct
(1999) - et al.
A damage model for the simulation of delamination in advanced composites under variable-mode loading
Mech Mater
(2006) - et al.
Mesh-independent modeling of both distributed and discrete matrix cracking in interaction with delamination in composites
Eng Fract Mech
(2010)
A level set model for delamination – modeling crack growth without cohesive zone or stress singularity
Eng Fract Mech
Delamination modelling of GLARE using the extended finite element method
Compos Sci Technol
The partition of unity finite element method: basic theory and applications
Comput Meth Appl Mech Eng
A survey of the extended finite element
Compos Amp Struct
Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions
Eng Fract Mech
Effects of fibre bridging on GIC of a unidirectional glass/epoxy composite
Compos Sci Technol
Interlaminar fatigue crack growth of cross-ply composites under thermal cycles
Compos Struct
Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus
Compos Sci Technol
Hybrid composites for LH2 fuel tank structure
Delaminations induced by constrained transverse cracking in symmetric composite laminates
Int J Solids Struct
Modelling of opening displacement of transverse cracks in graphite-epoxy laminates using shear lag analysis
Monitoring of laminated composites delamination based on electro-mechanical impedance measurement
Int Mater Syst Struct
Prediction of cryogen leak rate through damaged composite laminates
Compos Mater
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