Simulation of Patched Woven Fabric Composite Structures Under Tensile Load

Carbon fi bre-reinforced polymers (CFRP) based on woven or non-crimp fabrics are widely used in various industrial sectors such as automotive, aerospace, and wind energy. The demand for repair concepts for these high performance materials is strongly increasing. A new chemical-physical repair method of CFRPs was developed, based on the local removing of the thermoset matrix by energetically activated oxide semiconductors, and the subsequent patch integration and matrix refi lling. In the scope of this repair method the design of load-adjusted textile repair patches is a major task. In this paper the design of a textile patch to regain the composites performance is analysed by simulation. Therefore, a fi nite element (FE) simulation approach based on the domain superposition technique (DST) is used. This approach enables the modelling of a textile reinforcement structure on the mesoscale, while the matrix is modelled on the macroscale. This leads to a high level of detail by a relatively low computational eff ort.


Introduction
Th e eff orts to reduce CO 2 emissions are driven, among many other things, by lightweight constructions.Th e use of carbon fi bre-reinforced polymers (CFRP) is gaining importance in several fi elds of application due to its excellent mechanical properties at little weight.Th e damage of these composite materials, such as delamination, debonding, fi bre or matrix breakage, is an increasing concern.Th erefore, the demand for appropriate repairing concepts is getting in the focus of investigation.Mostly damaged components are replaced and rarely repaired.A currently applied repair procedure is the scarf method.Th e damaged area is removed by mechanical abrasion (e.g.milling) and a metal sheet or carbon fi bre patch is inserted [1,2].A new chemicalphysical repair method for CFRP by the use of oxide semiconductors (OSC) was previously presented [3].In this method the thermoset matrix is locally removed by applying an OSC in the damaged area.Th e matrix is completely removed by heat-indicated activation of the catalyst.Aft erwards the damaged fi bres are removed and a load-adjusted repair patch is inserted.Th e composite structure is reconstructed by refi lling with the thermoset matrix.Designing the required load and geometry adjusted repair patches based on fi nite element (FE) simulations to regain the composite performance is envisaged due to a reduced trial-and-error design phase.For the simulation the domain superposition technique (DST) off ers many advantages.All reinforcement layers are considered individually and the best geometry for each layer of the repair patch can be designed.Moutoussamy et al. [4] applied the DST for the simulation of steel rebars in concretes.Jiang and Hallet [5,6] presented the DST for the simulation of woven textile reinforcements in composites.Pure mesoscale and microscale models of composites as shown in [7,8] are characterised by complex modelling and high computational eff ort and are particularly useful for unit cell simulations.

Materials
Th e reinforcement structure used for the investigations was a twill woven fabric (KDK-8004 by Carbon Werke Weißgerber GmbH & Co KG) made of 12K (800 tex) carbon fi bres.Th e fabric properties are shown in Table 1.Th e breaking force and elongation at break were determined according to ISO 4606 [9].Th e resin used for the composite production was EPIKOTE Resin MGS RIMR 135 with EPIKURE curing agent MGS RIMH 134 (by HEXION Inc.) with the properties shown in Table 2.For the determination of standard composite properties, the tensile test (according to DIN EN ISO 527-4 [10]) and an inter-laminar shear test (according to DIN EN 2563 [11]) were performed.Th e results are shown in Table 3.

Repair Method
For the local matrix degradation in the damaged area oxide semiconductors (OSC, i. e. Cr 2 O 3 , CeO 2 , NiO, TiO 2 ) were used [3].By utilizing a mask the OSC powder was applied on the composite and activated with an IR-lamp.Th e best results could be achieved with Cr 2 O 3 , where the matrix degradation of a 2 mm thick composite takes about 8-10 min.Figure 1 shows the experimental set up for the local matrix degradation.Aft er locally removing the matrix and the damaged fi bres a reinforcement patch is inserted.Th e geometry and load-adjusted design of the patch is very important to regain the composite performance.In the last step the matrix was refi lled using an epoxy resin and the SCIMP-method (Seeman Composites Resin Infusion Molding Process).

Simulation Method
Th e simulation model for the load-adjusted patch design has to fulfi l crucial requirements, i.e. the representation of the textile reinforcement structure, a  high adaptability for the patch geometry modelling and a reasonable modelling and computational effort.For this, analysis methods which neglect the reinforcement layer stacking cannot predict the required stress-and strain distribution.Th e domain superposition technique (DST) introduced by Jiang et al. [5] is very promising for the modelling of repair patches.Th ereby the textile reinforcement structure is modelled on the mesoscale embedded in a solid element mesh of the matrix, whereby the number of elements and the model size are reduced.

Textile Reinforcement Model
Th e textile reinforcement structure was modelled on the mesoscale, where the yarns were represented by shell elements.In order to achieve a realistic representation of the yarn geometry and to avoid penetrations the shell element thickness was adapted (Figure 2a). Figure 2b shows the geometry model of the twill woven fabric, generated in accordance with the method described in [12] for digital element chains.Th e dimensions were determined by analysing a micro-section.For the mechanical behaviour of the reinforcement yarns a user defi ned material model was used in LS Dyna [13].Furthermore, the low bending stiff ness of the yarns was taken into account by layered shell elements with adjusted material properties of the single layers.Th is mesoscale modelling approach is easily adaptable to various reinforcement structures and can also be used for drape or forming simulations.

Composite model
Th e shown model of the textile reinforcement was embedded in a matrix mesh.By using the DST, the matrix was not modelled explicitly, instead a global mesh was used.Under tensile load of the patched composites the delamination mode I (shear) and mode II (tearing or twist) occur.Th e failure of the matrix was realized in the matrix material model by implementing a tensile and a shear stress based failure criterion.Th e required inter-laminar shear stress parameters are determined according to standard DIN EN 2563:1997.Furthermore, the fi bre pull-out was realised in the model with cohesive elements (nullshells).Th e nullshells were kinematically constrained to the matrix mesh and the elements of the reinforcement structure were coupled to the nullshells with defi ned interface normal and shear failure stresses.Figure 3 shows exemplarily a composite model with two layers of twill woven fabric and the matrix mesh (blue).In a previous simulation step the two textile layers are compacted to get the fi nal composite thickness and to represent the interaction of the yarns.With this kind of simulation approach it became possible to model single layers of the textile reinforcement and the interaction with the matrix.Th us, the optimal geometry and overlap length of the repair patch can be designed to restore the composite performance completely.

Repair Patch Design
For the design of the repair patch a uniform stress distribution and the transferable stresses are most important.Under tensile load the delamination mode I (shear) and mode II (tearing or twist) and thus inter-laminar shear stress occurs.Th us, the transmittable inter-laminar shear stress in the patched area must be at least as high as the tensile strength of the composite.For the design of the repair patches the two layered open-hole specimen was defi ned as a damaged composite.Two diff erent patch designs are discussed.Patch 1 is a "step lap joint" with a ply per ply overlap and patch 2 is an adapted patch with a higher structural integrity (Figure 4).Th erefore, the original structure and the patches were adapted to the tensile load case [14].Th e fi bres oriented perpendicular to the tensile direction were removed from the textile structure.In this case a symmetrical patch design became possible without thickening the composite.Furthermore, the number of load carrying fi bres was increased in the overlapping area.

Model Validation and Composite Simulation
Simulation of the Tensile Test Th e fi rst validation case of the composite model is the simulation of the tensile test without any holes according to DIN EN ISO 527-4.Th e simulation shows excellent agreement with the experiments regarding tensile modulus, breaking force, and elongation at break (Figure 5a). Figure 5b shows the forceelongation curves determined experimentally and numerically under tension load.Th e failure of the composite in the simulation is indicated by the slope of the force curve at about 1.24% elongation at a force of about 23 kN (tensile strength 460 MPa).

Simulation Experiment
Young´s Th e simulation results show the applicability of the selected simulation approach based on the DST.For the investigated composite a very good agreement between experiment and simulation in terms of tensile and failure behaviour was achieved.

Simulation of Patched Composites
For the simulation of the patched composites two models based on the open-hole specimen were created.In a supplementary simulation step the geometric models of the patches are integrated in the existing model of the reinforcement.Figure 7 shows the model of the textile reinforcement of patch design 2. strain profi le across the middle surface of the specimen clearly indicates the local strain/stress peaks.At a total elongation of the specimen of 0.5% already local strains of 1.69% (stress 52.3 MPa) in patch design 1 and 1.32% (stress 48.8 MPa) in patch design 2 occur in the specimen.Th ese stress peaks in the transition area indicate the beginning of the failure.Compared to patch design 1, the stress peaks are reduced signifi cantly with patch design 2. Th is can also be seen in the breaking forces of the specimens.With patch design 1 the specimen breaks at a load of 22.5 kN and with patch design 2 the specimen breaks at 40.8 kN.Th e advantageous stress and strain distribution with patch 2 is caused by the high structural integrity (2.4).In the patched area (between 20-60 mm and 80-120 mm) the fi bre volume fraction is higher, which results in a lower strain (Figure 8b).Th e design of the transition zone between the original structure and the repair patch prevents the stress peaks.With patch design 2 excellent repair results can be achieved, the breaking force under tensile load was about 89% of the undamaged reference specimen.

Conclusion
A novel repair method for CFRPs based on the local matrix degradation was presented.For the design of load-and geometry-adjusted repair patches the FEsimulation was used.To take into account the structure of the textile reinforcement and the patch an adaptable mesoscale model was applied.With the domain superposition technique (DST) the computational eff ort was reduced, whereby the matrix was not explicitly modelled.Th e simulation model also considered the fi bre and matrix failure as well as fibre-matrix debonding.First simulations with diff erent patch geometries showed that about 90% of the composite performance under tensile load can be restored by the integration of a load-adjusted repair patch.Th us, this method is suitable as a repair concept for CFRP structures.

Figure 2 :
Mesoscale model of the textile reinforcement: (a) yarn cross section by adjusting the shell thickness, (b) mesoscale model of twill woven fabric

Figure 3 :
Figure 3: Scheme of the composite model

Figure 4 :
Diff erent repair patch designs: (a) top view (patch is blue), (b) section view: patch 1 and 2

Figure 5 :
Figure 5: Tensile test simulation results: (a) simulation and experimental data, (b) force elongation curve

Figure 8 Figure 8 : 2 Figure 7 :
Figure 8: Strain distribution in diff erent patched specimens (total strain 0.5%): (a) patch design 1, (b) patch design 2 Th e local matrix degradation was successful[3].An optically evaluation shows that the specimen is locally resin free aft er local removing of the matrix.Th e treated area is undamaged and unaff ected by the chemical-physical treatment of the process.Figure 9 shows the rectangular resin free area of the open-hole specimen and a specimen with an integrated repair patch aft er matrix refi lling.Th e general suitability of the chemical-physical local repair procedure was demonstrated.

Figure 9 :
Figure 9: CFRP aft er removing the thermoset matrix and repair procedure: (a) locally removed matrix, (b) integrated patch 2 and refi lled matrix Matthias Hübner, Elias Staiger, Kristin Küchler, Thomas Gereke, Chokri Cherif Technische Universität Dresden, Faculty of Mechanical Science and Engineering, Institute of Textile Machinery and High Performance Material Technology, 01062 Dresden, Germany

Table 1 :
Properties of the reinforcement structure *ISO 4606

Table 2 :
Properties of the resin system