Simulation of Delamination Growth at CFRPTungsten Aerospace Laminates Using VCCT and CZM Modelling Techniques
Abstract
Delamination analysis in advanced composites is required for the laminate design phase and also during the operation of composite aerospace structures to estimate the criticality of flaws and damage. The virtual crack closure technique (VCCT) and cohesive zone modelling (CZM) have been applied to delamination simulation as numerical tools of crack modelling. VCCT and CZM have their unique advantages and disadvantages per application. This study focuses on the application of VCCT to a brittle delamination in a hybrid tungsten–carbonfibre reinforced composite (CFRPW) and pursues to identify the challenges due to very high internal residual stresses and strain energy as well as unstable crack propagation. The CFRPW composites have application areas in highperformance, lightweight radiation protection enclosures of satellite electronics and ultrahigh frequency (e.g. 5G) systems. In our work, we present the effects of freeedge stress concentrations and interfacial separation prior to nodal release on a combined VCCTCZM model and compare the results to pure VCCT and CZM models of the interfacial crack. Parameter notes are given based on the results to apply the combined method for delamination analyses with interfaces heavily loaded by internal residual strains.
Keywords
Satellite enclosure Finite element simulation Delamination VCCT CZM1 Introduction
Carbonfibrereinforced plastics (CFRPs) have been used in structures and also in electronics housings of satellites due to the weight efficiency achieved in extreme lightweight concepts [1, 2]. Naturally, compositebased housings can be applied to future 5G technologies with highly optimized attenuation windows in otherwise protected enclosures [3, 4].
The main numerical methods for finite element delamination analyses are the Virtual Crack Closure Technique (VCCT) and Cohesive Zone Modelling (CZM). Both methods have their pros and cons in a practical design process since VCCT is primarily applied for structures with an initial flaw [6] and CZM requires fitting parameters other than pure fracture toughness and standardized fitting procedures do not exist. VCCT does not rely on energy dissipation by a cohesive zone after nodal release whereas CZM can be input various models of residual stiffness [7] before full release of the contact. Consequently, VCCT is typically applied for brittle crack propagation [8, 9]. The scientific challenge is to understand the limits of brittle crack propagation for VCCT so that dynamic effects remain insignificant.
The hybrid CFRPmetal laminates utilize steel or tungsten foils [10], which result in extremely high residual stresses during the manufacture [11, 12]. Due to the very high Young’s modulus of the unidirectional CFRP plies and, say, tungsten foils, even the smallest difference in thermal expansion leads to buildup of high interfacial loading between the dissimilar layers. Due to the fact that a separate crack onset phase is typically not simulated, any initial flaw tend to onset unstable crack propagation during a VCCT analysis. What follows is severe convergence problems in the numerical solution iteration or a need to apply artificial damping leading to an unclear error to the solution.
In this paper, we study the application of VCCT in the delamination analysis of CFRPtungsten (CFRPW) laminate. A cracked lapshear (CLS) specimen is 3D modelled using the finite element method and the effects of VCCT and CZM crack models are compared in terms of the crack onset stresses and the cracktip loading. Additionally, a combined analysis with a separate crack nucleation model using a CZMzone along with a VCCT zone is studied.
2 Methods
2.1 Reference Experimental Data
2.2 Finite Element Method
The regions of the specimen that match with the test machine gripping point in reality, were subjected to boundary conditions (BCs). For all the BC surfaces, outofplane (Zcoordinate) displacements were fully set to zero (initial value). The thick end of the specimen (without lap opening) was fixed as regards the longitudinal displacement. In turn, the other end was subjected to enforced displacement to simulate real test machine loading.
 1.
Cohesive zone modelling over the entire straplap interface;
 2.
Virtual crack closure technique applied over the entire straplap interface;
 3.
Combined method where CZM elements are applied at the interface edges and VCCT for the propagation over the rest of the specimen.
Material data for CLS specimen modelling; for directional properties refer to Fig. 3
2.2.1 VCCT Method:
2.2.2 Combined VCCTCZM Method:
CZM techniques for various fracture analyses are versatile and numerous different applications exists. Previously, it has been reported that CZM is needed to simulate the interfacial metalCFRP debonding process in CFRPW laminates under mixed mode fracture conditions [15]. Jokinen and Kanerva formulated a procedure for determining the critical fracture toughness value based on the crack onset during testing and, subsequently, to fit a CZM model with two separate critical traction levels based on crack propagation. This procedure is accurate and reliable, yet is rather element meshdependent due to the CZM zone that covers most of the fracture plane. Therefore, a combined method is considered in this study, where simultaneous application of CZM and VCCT is analysed. In this combined method, CZM is simulating the crack onset process (Fig. 2) and VCCT handles the crack propagation after the process zone of the real crack tip has fully developed.
Input values for the different crack models of crack nucleation and propagation [15]
Parameter  (unit)  Combined method  Pure CZM  Pure VCCT 

τ _{1}  (MPa)  140  140  n/a 
τ_{2}, τ_{3}  (MPa)  240  240  n/a 
G _{ I c}  (J/m^{2})  65  65  65 
G_{IIc}, G_{IIIc}  (J/m^{2})  195  195  195 
3 Results
3.1 Overall Simulation Response
The simulation of a brittle fracture is convenient for methods, which primarily rely on linear elastic fracture mechanics. For example, the CFRPW hybrid laminate involves CFRPW layer interfaces, where mode II dominated fracture has brittle response upon loading and the crack propagates in an unstable manner. Hence, the failure of the interface can be estimated to have linear response. The drawback of brittle failure is that the simulation of crack growth becomes computationally challenging due to convergence problems. Therefore, we pursue to compare different crack modelling methods to assess their capability to simulate unstable crack propagation. The overall strainforce εF response of the three crack models is shown in Fig. 5. It can be seen that the slope \(dF/d\varepsilon \) is essentially linear until the crack onsets and passes the strain measuring point. After passing the strain measuring point, \(dF/d\varepsilon \) increases significantly and the overall strain energy continues to grow in the specimen. This behavior is typical for unstable crack propagation where the crack is unable to extensively release strain energy and the surplus energy speeds up the crack propagation.
3.2 Crack Onset Computation

Simultaneous freeedge stresses and the precrack tip singular stresses are problematic for the VCCT model validated for the CFRPtungsten laminate;

For the real crack, a high stress state without a singularity point does not lead to crack propagation (since it was not observed at edges);

For the real freeedge, already slight deformation (opening along the layer interfaces) release efficiently residual (thermal) strain energy.
4 Discussion
In the current literature, different means have been introduced to simultaneously model both crack nucleation and the crack propagation after full development of the crack. In general, the question of constant materials properties related to fracture (in most cases fracture toughness) depends on the lengthscale of interest [16]. In this study, the process zone is negligible compared to other dimensions of the structure. For this type of simulation case, the development of the crack could be taken into account using a set of fracture toughness values (rising Rcurve method) [17], coupled models of fracture and stress criteria [18], or alternatively by using the traditional CZM [19].
The fundamental challenge of CZM, which also offers possibilities, is the wide variety of parameters included in the damage onset criterion, tractionseparation law, and in the criterion for mode mixity. The crack nucleation process in polymeric materials involves a complex set of micromechanical phenomena, such as crazing, cavitation, shear banding and mechanical interlocking [20, 21, 22], thus, it is expected that a crack nucleation model involves several material parameters. In our previous study, we proposed a method to fit a CZM model for the simulation of CFRPW interfacial delamination for design purposes. In this study, we applied a combined method that uses critical G values for a VCCT zone according to an analysis of a nonpropagating crack at the experimentally determined critical load level (F_{c} in a previous report [5]). The CZM zone of the combined method was given input parameter values according to the fitting procedure presented previously [15]. For the combined method, CZM elements (zero thickness) ahead of the VCCT zone are harnessed by a bilinear tractionseparation law and a power law is applied to account for ERR per fracture mode [23]. Originally, the critical tractions (τ) were validated based on local strain fluctuation at the strap and lap parts of the CLS specimen (due to crackfront propagation over the strain recording point).
The comparison of the three methods revealed that CZM and combined VCCTCZM model can simulate the crack onset correctly. Pure VCCT model results in oversized delamination due to severe propagation from the specimen edges towards the midline—the addition of external tensile load easily shuts down the simulation for reasonable values of control parameters. It should be noted that there are challenges to use the combined VCCTCZM model to compute the entire delamination process through yet it is not necessary for analysing CLS testing. In the event that the simulated process zone is larger or in the order of the spatial size of stress gradients, CZM can dissipate strain energy and halt the crack in a realistic manner. In the combined method, the required process zone size is related also to the length of the transition zone between the methods (length L in Fig. 4). For the CFRPW interface, the need for dissipation exists due to high strain energy induced by internal residual strains. The computational transition, after the crack reaches the VCCT zone in the combined method, tend to speed up the crack propagation because the mode II dominance and residual stresses remain essentially constant after each nodal release. At the VCCT zone, any degree of crack opening is due to the deformation of bulk material elements (CFRP/W) whereas the CZM zone allows crack opening due to the deformation of the interface elements (tractionseparation model) and adjusting its momentary stiffness.
5 Conclusions
This study focused on the analysing of the application of pure VCCT, pure CZM, and a combined VCCTCZM crack model in the simulation of highly brittle and highenergy intensive mode II dominated fracture. As a case study, hybrid CFRPW radiation shielding laminate was simulated in a CLS test setup. It is important to note that the crack onset modelling using VCCTCZM for CFRPW was initially given parameter values based on the procedure defined by Jokinen and Kanerva [15] for a pure CZMbased fitted CLS model. In order to simulate the entire delamination process over wide complex shapes, the effects of CZM element size and the transition zone length must be studied in the future.

Pure VCCT crack model is computationally challenging to apply for the CFRPW laminate with very high internal thermal residual strains;

Combined VCCTCZM model can be used to simulate crack onset at the CFRPW interface of the radiation protection laminate;

Crack onset modelling using VCCTCZM for CFRPW requires a minimum of \(L = \) 1 mm process zone (CZM elements + transition zone).
Notes
Acknowledgements
This investigation was funded by a grant from Business Finland related to the ’LuxTurrim5G’ project and the related subtask (10098/31/2016) carried out by Tampere University of Technology. The authors want to gratefully acknowledge CSC IT Center for Science due to their expertise on computation services.
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