Scholarly article on topic 'Static mechanical properties of hybrid RTM-made composite I- and Π-beams under three-point flexure'

Static mechanical properties of hybrid RTM-made composite I- and Π-beams under three-point flexure Academic research paper on "Materials engineering"

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{Beam / Composites / Experiment / Fabric / Molding / Simulation}

Abstract of research paper on Materials engineering, author of scientific article — Yu Fu, Junjiang Xiong, Chuyang Luo, Xinyao Yun

Abstract This paper deals with three-point flexure tests on hybrid I- and Π-beams, made out of multi-layer carbon fiber/epoxy resin (including twill woven fabric CF3031/5284 and unidirectional cord fabric U3160/5284) reinforced composites, processed using the RTM (resin transfer molding) technique. Static bending properties were determined and failure initiation mechanism was deduced from experimental observations. Failure mode of the tested hybrid RTM-made I-beams can be reckoned to be characteristic of the delamination from the cutout edge within the web and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until local buckling within the curved webs around the conjunction fillet region. In contrast, as distinct from hybrid RTM I-beams subjected to three-point bending loading, hybrid RTM-made Π-beams in three-point flexure tests experienced the resin debonding in the inverted triangular resin-rich zones and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until complete separation of the curved web from the flange. Progressive damage models (PDMs) were presented to predict failure loads and process of hybrid RTM-made I- and Π-beams under three-point flexure. Good correlation was achieved between experimental and numerical results.

Academic research paper on topic "Static mechanical properties of hybrid RTM-made composite I- and Π-beams under three-point flexure"

JOURNAL OF

AERONAUTICS

Chinese Journal of Aeronautics (2015) xxx, xxx-xxx

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics

cja@buaa.edu.cn www.sciencedirect.com

Static mechanical properties of hybrid RTM-made composite I- and n-beams under three-point flexure

Fu Yu, Xiong Junjiang *, Luo Chuyang, Yun Xinyao

School of Transportation Science and Engineering, Beihang University, Beijing 100191, China Received 1 September 2014; revised 9 December 2014; accepted 29 January 2015

KEYWORDS

Composites;

Experiment;

Fabric;

Molding;

Simulation

Abstract This paper deals with three-point flexure tests on hybrid I- and n-beams, made out of multi-layer carbon fiber/epoxy resin (including twill woven fabric CF3031/5284 and unidirectional cord fabric U3160/5284) reinforced composites, processed using the RTM (resin transfer molding) technique. Static bending properties were determined and failure initiation mechanism was deduced from experimental observations. Failure mode of the tested hybrid RTM-made I-beams can be reckoned to be characteristic of the delamination from the cutout edge within the web and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until local buckling within the curved webs around the conjunction fillet region. In contrast, as distinct from hybrid RTM I-beams subjected to three-point bending loading, hybrid RTM-made n-beams in three-point flexure tests experienced the resin debonding in the inverted triangular resin-rich zones and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until complete separation of the curved web from the flange. Progressive damage models (PDMs) were presented to predict failure loads and process of hybrid RTM-made I- and n-beams under three-point flexure. Good correlation was achieved between experimental and numerical results.

© 2015 The Authors. Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

I- or n-beams are commonly used as stiffening structures in aircraft engineering with a typical example as shown in Fig. 1. The loading structures for I- or P-beams are required

to provide enough strength and stiffness with decreased weight and manufacturing cost in operating conditions. Thus integral composite for the advantage of security, amenity and lower cost has received much attention in the aviation industry in recent years.

A significant body of research is available dealing with mechanical behavior and failure mechanism of the I-beams under static loadings using experimental, numerical simulation and analytical methods. Tomblin and Barbero1 experimentally investigated the flange local buckling of pultruded wide-flange FRP (Fiber Reinforced Polymers) I-beams and found that the compressive flange with local buckling exhibited large deformation which could induce material damage. Bank et al.2

* Corresponding author. Tel.: +86 10 82316203. E-mail address: jjxiong@buaa.edu.cn (J. Xiong). Peer review under responsibility of Editorial Committee of CJA.

http://dx.doi.org/10.1016/j.cja.2015.03.004

1000-9361 © 2015 The Authors. Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Fig. 1 I-beam stiffening skin element in aerofoil structure.

carried out four-point bending experiments on pultruded FRP I-beams with different matrix. It was shown that the matrix which governed the failure strength of the I-beams made a great influence on the failure mode. Bank and Yin3 analyzed a common failure mode that the flange locally separated from the web in the pultruded I-beams based on the FEM (Finite Element Method) and found that the transverse tensile normal stress dominated the failure and strength of the junction between the flange and web. As mentioned above, pultruded FRP I-beams with wide flange in bending loading first occurred local buckling within the compression flange and the tearing failure shortly took place at the conjunction between the web and the flange in post buckling stage.

Consequently, analytical solutions were developed based on the CLT (Classical lamination theory)4-6, Vlasov-type linear theory7'8 and Timoshenko beam theory9 to predict static response of composite I-beams under different loading conditions and the effects of several factors were discussed on structural properties of composite I-beams. Barbero et al.4 predicted critical buckling load in the compressive flange of GFRP (Glass Fiber Reinforced Plastic) I-beams subjected to three- and four-point bending loading based on CLT and found that the critical buckling load of the flange was a function of the wavelength. Davalos et al.5 determined the ply stiffness of pultruded FRP I- and box beams by treating the materials as a layer system and obtained the static response of the designed beams according to Timoshenko beam theory. Song et al.6 predicted the static response of composite CUS (Circumferentially Uniform Stiffness) and CAS (Circumferentially Asymmetric Stiffness) I-beams loaded at their free-ends based on the CLT by considering the transverse and warping effects. Chandra et al.7 developed Vlasov-type linear theory to describe the laminated I-beams by introducing transverse deformation to the cross-section of the I-beams and experimentally validate the theory through the result of the static response between the analytical solution and the experiment. Mottram8 presented an analytical modeling to determine the critical local buckling load in the compressive flange of the pultruded composite I-beams under four-point bending configuration based on the Vlasov-type linear theory. Kim and Shin9 performed the deflection analysis of Timoshenko laminated composite beams and showed the influence of the fiber orientation, shear deformation and boundary conditions on the deflection response of the laminated beams.

Actually, there are also some of other factors to significantly influence structural behaviors of composite I-beams. Heredia et al.10 conducted experimental investigations on CMC (Ceramic Matrix Composite) I-beams under axial loads or moments and claimed that manufacturing flaws located in the transition region of the I-beams governed the failure modes and ultimate strength of the members. Khalid et al.11 carried

out the experiments on hand lay-up glass/epoxy composite I-beams and reported that the increase of the lay-ups would promote the first crushing load and energy absorption for the composite I-beams. Gan et al.12 predicted the behavior of pul-truded composite I-beams with various flange-web conjunctions subjected to bending load based on the FE method by introducing a global-local analysis technique. Racher et al.13 investigated the effect of web stiffness on the bending behavior of timber composite I-beams through four-point bending experiments and the FE method. It was shown that the shear stress in the glued joint dominated failure of slender I-beams subjected to bending loading. Gilchrist et al.14 presented the failure mechanism of web- and/or flange-notch carbon-fiber/ epoxy and glass-fiber/epoxy I-beams by means of four-point flexure experiments, fractographic observations and FE method and found that the flange bucking was the dominate failure mode of unnotched I-beams while the failure initiation of notched I-beams was the circular cutout within the web. Hai et al.15 investigated the influence of geometry dimension and material composition on structural static behavior of hybrid FRP composite I-beams by four-point bending experiment and FE method. Ragheb16 established a finite element model to simulate simply-supported I-beams under bending loading by considering the compression flange of the beam to be a hybrid of glass and carbon fibers and gained the optimum hybridization pattern to improve the local buckling capacity of pultruded I-beams.

The previous literature proves that mechanical behaviors of composite I-beams have been studied comprehensively. It is clear that the flanges and web of I-beams respectively exist the normal and shear stresses in the operation conditions, which govern the load-carrying capacity of the I-beams, on the other hand, the flange-web conjunction of I-beams has a significant influence on their ultimate strength and other structural properties.12 In fact, different hybridization schemes and production processes would result in distinct structural properties and failure modes in the I- or n-beams.17 The hybrid RTM-made I- or P-beams are widely used in aerospace engineering owning to the superiority in terms of mechanical properties and impact resistance over the pultruded I-beams. It is important to understand structural behaviors and failure mechanism of hybrid RTM-made I-beams consisting of multi-layer carbon/E-glass (woven fabric and continuous strand mat or roving) located near the flange-web connections. There seems to be a great deal of investigations done on the pultruded I-beams, but few works18,19 on structural behaviors and failure mechanism of the hybrid RTM-made parts from the above review. There is a need for more investigations to provide important information for engineers to have confidence in designing of hybrid RTM-made I- or P-beams in engineering application. In addition, it is well known that the beams in the girder wing mainly bear the bend stresses, while the skins primarily transfer the shear stresses caused by the torque and the wing ribs carry the shear stresses resulted from the shear forces. Thus, in order to understand the mechanical properties of the I- and P-beams, the three-point or four-point flexure is generally adopted to conduct the static tests for determining mechanical properties of the I- and P-

beams.2,4,8,13-15 This

paper, therefore, attempts to provide an insight into failure development in hybrid RTM-made composite I- and P-beams through three-point flexure tests and to achieve new progressive damage models for predicting

structural behaviors of hybrid RTM-made composite I- and n-beams for engineering application.

2. Material and specimens

2.1. Material and lay-up of test specimen

Test specimens for hybrid I- and n-beams were made out of multi-layer carbon fiber/epoxy resin (including TWF CF3031/5284 and UCF U3160/5284) reinforced composites and manufactured using the RTM technique. The specifications and properties of CF3031 and U3160 are listed in Table 1. The 5284 epoxy resin was selected as the matrix of composite I- and n-beams for long-term application at 180 0C in hygrothermal environment.

The hybrid RTM-made box beams were designed and manufactured to allow the test specimens of composite I- and n-beams. Fig. 2 details the geometry and dimension of the box beam with 780 mm length, 100 mm height, 4 mm web thickness, 5 mm flange thickness, 300 mm flange width and 48 mm flange width from the free edge of flange to the web. Stacking sequences of multi-layer box beam are shown in Fig. 3. Representative hybridization pattern for the lay-ups in box beam is indicated in Fig. 3 by dark borders and illustrated in Fig. 4 as proposed by Gan et al.12, which shows the sectional views of sublaminate schemes.

The flanges and the web of the I- or n-beam are respectively simplified to compose of three sublaminates (i.e., sublaminates A, B and C) and two sublaminates (sublaminates C and D) to describe the laminate schemes of the flanges, webs and flange-web conjunction (shown in Figs. 3 and 4). It is well known that 0, 90, 45, —45 degree configuration is widely used in aerospace engineering. Generally, the 00 plies mainly bear the tensile and compressive loadings in the beam flanges, whilst the +450 and —450 layers sustain the shear loads within the web region in this particular overlay design and the ±450 plies overlaid over the outside surface of the parts are used to improve impact resistance. Therefore, 0, 90, 45, —45 degree configuration is chosen for this studies. Sublaminate A is made up of 18 plies with a thickness of 3 mm. 17-ply UCFs of U3160 are stacked following a sequence of [0/45/0/—45/0/45/90/—45/ 0/—45/0/45/0/—45/90/45/0] and a ply TWF of CF3031 is then overlaid over the outside surface of the sublaminate with a ply-angle of ±450, where the 00 direction is defined to be along the axis of the beam. There are 11-ply UCFs of U3160 following a sequence of [0/45/90/—45/0/45/90/—45/45/0/—45] and a ply TWFs of CF3031 is then overlaid over the outface of the sublaminate with a ply-angle of ±450 in sublaminate C with 12 plies and with a thickness of 2 mm. Sublaminates B and D are the layers of 5284 epoxy resin. Obviously, the flange

Table 1 Fabric specifications and properties of U3160 and CF3031.

Geometry parameter CF3031 U3160

Ply thickness (mm) 0.30 0.167

Area density (g-m-2) 220 160

Warp fabric density (bundles-cm-1) 54 80

Weft fabric density (bundles-cm-1) 54 40

(b) Box beam

Fig. 2 Geometry and dimension of box beam.

Fig. 3 Stacking sequence of box beam.

Fig. 4 Hybridization schemes of I-beam.

(composed of sublaminates A, B and C) and the web (composed of sublaminate D and two sublaminates C) are balanced, symmetric and multi-directional combination of ±450, +450, 00, 900 and —450 plies.

The conjunction between the flanges and web is realized by a transition fillet. An 'inverted triangle' resin-rich zone, denoted by the shaded area E in Fig. 4, exists in the connection fillet region between sublaminates A to D. The structural behaviors of flange-web conjunction are governed by the radius of fillet and the mechanical properties of inverted

triangle resin-rich zone. Therefore, the structural behaviors of flange-web conjunction can be improved by choosing an appropriate transition fillet to avoid the excessively high stresses which could be associated with a sharp corner and through filling inverted triangle resin-rich zone with continuous and unconstrained fiber roving.

2.2. Process simulation and profiled molds

The permeability of epoxy resin through fiber architecture has a significant influence on mechanical properties of the RTM products, so it is essential for permeability simulation of epoxy resin to optimize the injection pattern and processing parameters. The FE model for permeability simulation was generated to optimize the injection pattern and process parameters of hybrid RTM-made box beam from the geometry, dimension

(a) Diagrammatic sketch of profiled mould for box beam

(b) RTM mould Fig. 5 Profiled mold for box beam.

(a) Diagrammatic sketch of profiled mould for water-soluble mandrel

and stacking sequence of box beam (Figs. 2 and 3) by using the PAM-RTM code.20 According to the simulated results of resin flowing21, an optimized injection pattern was determined as follows: an injection groove along the bottom margin of an end-cover for infusing resin, twelve vents in the top and bottom dies respectively as well as eight vents in another endcover for discharging air. Under the initial preliminary processing parameters of injection pressure P = 0.1 MPa, resin viscosity o = 0.1 Pa-s, fiber volume fraction V = 55%, fabric permeability k0 = 1.0 x 10-11m2 and permeability of resin-rich zone k1 = 1.0 x 10-11 m2, the processing parameters were optimized as follows: resin viscosity o = 0.1 Pa-s, injection pressure P = 0.4 MPa and injection temperature 60-80 0C.

According to the above simulated results, a profiled mold was fabricated for the RTM process of box beam, consist of a pair of symmetric dies and end-covers, which can be affixed by the locating pins and tightened by the plain shank bolts (shown in Fig. 5). Two matching grooves were respectively cut on the bottom die and both end-covers for sealing mold, and an injection groove was cut along the bottom margin of an end-cover for infusing resin. In addition, three rows of four vents were machined using a 5 mm diameter diamond-coated drill in both the top and bottom dies and two rows of four holes in another end-cover for discharging air, together with two jackscrew holes in the top die and both end-covers for sinking die.

Both steel mandrels with the channel section were fabricated to profile both the left and right channel-sections of box beam, while a water-soluble mandrel with symmetric closed-section for the central closed-section of box beam. Similarly, a profiled mold was manufactured to attain the water-soluble mandrel, consist of a pair of symmetric dies, side covers and end-covers with two steel skeletons, which can be tightened by the locating pins and bolts (shown in Fig. 6).

2.3. Test specimens of RTM-made I- and n-beams

Fig. 7(a)-(f) show the production procedure of water-soluble mandrel. Water-soluble resin was first mixed with water and acetone to become the solvent mixture, and a certain alumina

(b) Profiled mould for water-soluble mandrel

(c) Steel skeleton for locating water-soluble mandrel (d) Steel skeleton and end-covers

Fig. 6 Profiled mold for water-soluble mandrel.

(d) Die sinking (e) Drying (f) Product

Fig. 7 Production process of water-soluble mandrel.

(a) Lay-ups over water-soluble mandrel (b) Filling in inverted triangle resin-rich zone (c) Resin injection and cure (d) Product

Fig. 8 RTM process of box beam.

ceramics, kaolin clay and solidified agent was then put into the solvent mixture and mixed into uniform ceramics slurry. After this, the water-soluble ceramics slurry was infused in the closed mold and the curing was then conducted. Finally, a water-soluble mandrel was produced. During curing, the mold was first heated up to 60 0C at a rate of 5 0C/min and held for 10 h at this temperature. The mold was then heated up again at the same rate (5 0C/min) to the desired temperatures of 60, 80, 100, 120 0C and 130 0C and held for 10 h at each temperature. Next, the mold was cooled to room temperature and the curing was completed.

The RTM process of box beam is illustrated in Fig. 8(a)-(d). According to the stacking sequence shown in Fig. 3, multi-layer TWFs of CF3031and UCFs of U3160 were first stacked up one over the other in the profiled mold to yield preformed profiles of the top and bottom flange caps, and then overlaid over the outfaces of closed-sectional water-soluble mandrel and channel-sectional steel mandrels to achieve preformed profiles of the webs of box beam. Subsequently, the 5284 epoxy was then injected into the mold as a matrix following the above optimized process parameters in Section 2.2. After this, the curing was conducted and the hybrid RTM-made box beam was produced. During curing, the composite

preformed prepreg in the RTM mold was first heated up to 80 0C at a rate of 5 0C/min and held for 1 h at this temperature, at the same time, the injection pressure was first set as 0.05 MPa and then increased to 0.4 MPa slowly. The mold was heated up again at the same rate (5 0C/min) to the desired temperature 180 0C and held for 2 h at this temperature. Next, the mold was cooled to room temperature and the curing was completed. Finally, the quality of curing box beams was ascertained through the CT scanning.

Three I-beams and five n-beams for three-point bending tests were respectively cut from two box beams in longitudinal and transverse direction. The geometry and dimension of both types of test specimens are respectively shown in Figs. 9 and 10. In order to understand the effect of notched web on failure mechanism of the I-beam, a circular cutout was cut with a diamond-coated circular saw and centrally situated in the web region of the beam. The hole diameter was selected to be 50 mm about 56% of the internal web depth. The web cutout stands for lightening holes or access ports within an I-section component, although it is worth nothing that the web notch would not exceed about 40% of the internal web depth in common engineering practice.

(b) I-beam

Fig. 9 Hybrid RTM-made I-beam. 3. Static bending experiments

All three-point flexure tests of hybrid RTM-made I- and P-beams were conducted on MTS880-100kN servo-hydraulic machine in a dry state at room temperature as shown in Fig. 11(a) and (b) respectively. F in Fig. 11(a) and (b) stands for the bending load applied on the hybrid RTM-made I- and P-beams. The specimens were supported on two cylindrical rollers to simulate simply supported boundary conditions and the bending loads were applied at the midspan by a remotely controlled hydraulic jack at a displacement rate of 1 mm/min and 2 mm/min respectively. The levels of applied load were monitored with a load cell and the deflections were measured by dial gauges of tester. It is worth pointing out that the types and location of the electrical strain gauges have a significant influence on the reliability and precise of measured strains on composite beams22,23, whereas it is reliable to measure the load-displacement P — d curves from the tester. As a result, the experimental analysis is mainly dependent on the load-displacement P — d curves. The load-displacement

P — d curves of 3 tests on the I-beam and 5 tests on the P-beam were respectively shown in Fig. 12(a) and (b). It is apparent that the P — d curves of the tested RTM-made specimens are almost identical in the linear elastic region. An existence of more than one peak on the P — d curves of all specimens marks the damage initiation and propagation, which causes load drops on the P — d curves. In order to discuss failure initiation mechanism, the failure initiation load is defined as the initial load drop, which is obtained from the P — d curves determined by the tests or from the noise emitted during the loading process. Note that there exists an error for failure initiation load determined from the noise emitted during the loading process because of the delay record of noise. Failure initiation loads for the I- and P-beams are listed in Table 2. The mean values of failure initiation load and failure load for the I- and P-beams are 26000 N, 37500 N, 1189 N and 2504 N respectively, in other words, failure initiation load of the I-beams is approximately 69% of failure load, whilst that of the P-beams is about 47% of final failure load.

From experimental observation on the I-beams, a slight noise was emitted from the I-beams when the load increased to about 26000 N. The crack first occurred near top edge of circular cutout within the web as the load increasing (Fig. 13(a)) and there was a small load drop on the P — d curve (Fig. 12(a)). The crack subsequently propagated to the inverted triangular resin-rich zone followed by the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web as shown in Fig. 9(b)). During the debonding propagation process, local buckling dis-continuously appeared within the curved web around the conjunction fillet region and the I-beam continued to carry load until the delamination within the flange as shown in Fig. 9(c). Hence, the failure mode of the tested hybrid RTM-made I-beams in three-point bending tests can be reckoned to be characteristic of the delamination from the circular cutout edge within the web and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until the local buckling within the curved webs around the conjunction fillet region. These results are consistent with the research closures of previous works.14

Experimental observation on the P-beams shows that the resin debonding firstly appeared at the interface between the

(b) n-beam

Fig. 10 Hybrid RTM-made n-beam.

Fig. 11 Boundary condition and load direction in three-point flexure.

Fig. 12 Load-displacement P — d curves of I- and P-beams.

Table 2 Experimental results of failure initiation load and failure load.

Specimen no. Failure initiation load (N) Failure load (N)

I-beam P-beam I-beam P-beam

1 24000 1229 40000 2505

2 26000 1185 37500 2493

3 28000 1272 35000 2577

4 1063 2480

5 1195 2465

Mean 26000 1189 37500 2504

inverted triangular resin-rich zone and the adjacent curved web (Fig. 14(a)) with a small load drop on the P — d curve (Fig. 12(b)) in three-point flexure tests at a bending load of about 1189 N. The resin debonding subsequently propagated along the interface until the delamination in the top flange as shown in Fig. 14(b). During the debonding propagation process, the P-beams also continued to carry load until the delam-ination in the top flange as shown in Fig. 8(b). The delamination finally propagated until complete separation of the curved web from the top flange (Fig. 14(c)) following by load drops on the P — d curves as shown in Fig. 8(b). Therefore, as distinct from the I-beams, the P-beams in three-point flexure tests experienced the resin debonding in the inverted triangular resin-rich zones and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until complete separation of the curved web from the flange. These efforts have a good agreement with those in literature.24,25

As mentioned above, it is evident that all notched I-beams showed failure initiation in the delamination from the cutout of the shear-loaded web and finally failed in local buckling within the curved webs, while the P-beams exhibited failure initiation in the resin debonding in the inverted triangular resin-rich zones and finally failed in complete delamination in compressive flange.

4. Progressive damage analysis

4.1. Progressive damage model

The progressive damage model (PDM) has been proven to be an effective method in predicting the failure strength and failure

(c) Local buckling within curved web Fig 13 Failure process of I-beam.

process of composite structures in recent years. It is necessary for a numerical strength-based progressive damage approach and damage criteria used in composite structures under representative boundary and loading conditions. The numerical response is evaluated using non-linear finite element analysis with a special routine to define the failure modes and the progressive degradation of elastic properties with increasing damage levels. The I- and P-beams (shown in Figs. 9(a) and 10(a)) are chosen to be modeled and local coordinate systems are then set up to ensure fibers correctly 3D oriented in order to provide numerical analysis to validate the experimental results. Fig. 11 illustrates the definitions of three axial directions 1-3 of the coordinate system and three normal stresses c1 to r3 both for the planes and curved overlaminate parts of the plain weave fabric, where the coordinate axes 1-3 denote the longitudinal, transverse and through-thickness directions of the overlaminate respectively. The definitions of three shear stress components s12, s13 and s23 can be obtained based on the definitions of three normal stresses r1 to r3. Geometrically inverted triangular resin-rich zones are bordered by both curved webs and the flange on both I- and P-beams as shown in Fig. 15. Since the experiments of I- and P-beams showed that the critical areas of the beams are at triangular zones, in order to well suit to model triangular zones, the higher order 3D, 8-node SOLID45 element of ANSYS code26 with quadratic displacement behavior is implemented to model the

(c) Complete separation of curved web from flange Fig. 14 Failure process of P-beams.

(b) FE model for n-beam Fig. 15 3D FE models for I- and P-beams.

zone to attain a high accuracy of simulation. Moreover, 3D, 8-node layered solid element SOLID46 with three degrees of freedom per node is employed to model the composite layup and each layer of the composite layup is modeled with one element through the thickness to obtain the higher accuracy of interlaminar stress. The mesh of the FE model was refined iteratively until the mesh subdivision had almost no effect on the prediction of the PDM according to sensitivity analysis. The isotropic 5284 resin is used for the inverted triangular zone, while the orthotropic CF3031/5284 and U3160/5284 composites are used for the surface and inner part of the web, curved web and flange. 3D FE models of the I- and P-beams are respectively generated to predict failure loads and failure process in

association with relevant material properties listed in Table 3. The resin debonding between the laminate and the resin-rich zone has been assumed to have the same properties as the resin debonding of the ply.18'19 The loading and boundary conditions in three-point flexure tests on both the I- and n-beams are defined as the simply supports as shown in Fig. 11(a) and (b).

As it considers the interaction between longitudinal, transverse and through-thickness strengths of material, the Tsai-Wu criterion27 seems more appropriate and effective for predicting the failure of E-glass/epoxy composites in contrast to the maximum stress or strain rule. However, Tsai-Wu is not suitable for isolating individual damage modes and has fallen out of favor over the years for this reason and for its history in metal failure theories. In fact, the Hashin criterion28 is proven to be more apt in identifying damage modes, but not in the delami-nation mode, whereas the Tong-Norris criterion29 has widely used for isolating the delamination failure. Thus the mixed damage criterion incorporating the Hashin criterion and Tong-Norris rule is adopted in this work to respectively identify the matrix, fiber and delamination failures.

In order to define the progressive degradation of elastic properties with increasing damage levels, the method for stiffness reduction is simple but effective and the reduction of stiffness depends on the failure mode in action.30 For fiber failure, the material is deemed to have lost complete stiffness at the material point, whereas for matrix failure zero stiffness are assigned for the failed lamina in the transverse direction (i.e., the transverse modulus E2 and Poisson's ratios u12 and u23 are reduced to zero) and the elastic modulus E1, E3, G12, G13, G23 and Poisson's ratio u13 remain unchanged. When the fiber/matrix shear is predicted at a material point, the shear modulus G12 and Poisson's ratio u12 are reduced to zero, however the longitudinal modulus E1 and the transverse modulus E2 remain unchanged. For delamination failure, through-thickness stiffness E3 and Poisson's ratios u13 and u23 are degraded to zero.

From the FE model, mixed damage criterion and stiffness reduction method mentioned above, the scheme flowchart of progressive damage analysis for I- and P-beams subjected to displacement loading is established (shown in Fig. 12). From Fig. 16, it can be seen that the stress patterns of I- and P-beams are simulated by means of the non-linear FE model, and the damage elements and failure modes are identified from the mixed damage criterion, and the elastic properties of damage elements are then degraded by using the method for stiffness reduction. With such-and-such iterative interpolation calculation, the progressive damage analysis for the I- and P-beams is performed. In order to verify the non-linear FE model, damage criteria and stiffness reduction method, the load-displacement curves of both I- and P-beams are numerically simulated from the above scheme flowchart of progressive damage analysis and compared with the experiments (shown in Fig. 12). Fig. 12 demonstrates that the predicted values to construct the P — d curve from progressive damage analysis are in good agreement with those from the experiments. The experimental results appear relatively less stiff as against the numerical results. This is probably due to the significant changes in experimental structural stiffness. In fact, even non-observable amounts of slipping and lack of true clamp conditions can change experimental structural stiffness significantly, however, the numerical model applies perfect

Table 3 Properties of U3160/5284 and CF3031/5284.

Property U3160/5284 CF3031/5284

Longitudinal elasticity modulus E1 (GPa) 116.32 6.28

Transverse elasticity modulus E2 (GPa) 8.4 6.12

Through-thickness elasticity modulus E3 (GPa) 8.4 8.4

Poisson's ratio v12 0.296 0.0459

Poisson's ratio v13 0.15 0.15

Poisson's ratio v23 0.15 0.15

In-plane shear modulus G12 (GPa) 4.1 4.09

Inter-laminar shear modulus G13 (GPa) 3 3

Inter-laminar shear modulus G23 (GPa) 3 3

Longitudinal tensile strength X1t (MPa) 1415 556

Transverse tensile strength X2t (MPa) 43 601

Though-thickness tensile strength X3t (MPa) 23 601

Longitudinal compressive strength X1c (MPa) 993 673

Transverse compressive strength X2c (MPa) 184 651

Through-thickness compressive strength X3c (MPa) 184 651

In-plane shear strength X12 (MPa) 88.3 83.2

Interlaminar shear strength X13 (MPa) 86 80

Interlaminar shear strength X23 (MPa) 86 80

Fiber volume fraction (%) 55 55

boundary conditions. This results in the curves of calculated results being stiffer than those shown in the experimental ones. Table 4 shows the results of initial and ultimate failure loads between experiments and progressive damage analysis. From Table 4, it can be observed that all predictions are insignificantly greater than the experiments and the maximum relative deviation between predictions and experiments is less than 13%. Thus it is argued that the progressive damage model presented in this paper has better precise than the ply discount model with a deviation of 26% in Literature.31 Actually, based on the degradation rules of ply discount model, all elastic modulus in failure ply were completely degraded to be zero and the residual load-carrying capacity was entirely neglected. This resulted in a greater deviation of predicted results by the ply discount model from the experiments than that by using new progressive damage model presented in this paper.

4.2. Failure prediction

From the above scheme flowchart of progressive damage analysis, the progressive damage process of hybrid RTM-made I-and P-beams can be numerically simulated. Fig. 17 shows the progressive damage process on section A-A of I-beam (see Fig. 13). From Fig. 17, it can be seen that the matrix cracking occurs near the top edge of circular cutout within the web (shown in Fig. 17(a)). As the load increased, the matrix cracking propagates upwards to the inverted triangular resin-rich zone (shown in Fig. 17(b)) and then along the interface between the inverted triangular resin-rich zone and the adjacent curved web until matrix cracking appears in the top flange (see Fig. 17(c)). Finally, a combination of matrix cracking in the resin-rich zone and the top flange causes the delam-ination initiation and propagation along the interface between curved web and top flange (shown in Fig. 7(d)). The delamina-tion initiation and propagation lead to several load drops on the P — d curves. This is exactly consistent with the findings about the failure process and mode in experiments.

Stress analysis

Stiffness reduction

Fig. 16 Scheme flowchart of progressive damage analysis.

Similarly, Fig. 18 shows the progressive damage process of P-beams subject to three-point flexure. From Fig. 18, it can be observed that the matrix cracking first occurs at the interface between the triangular resin-rich zone and the curved web (shown in Fig. 18(a)) and then propagates along this interface up to the top flange (see Fig. 18(b)). Finally, the delamination initiates and propagates along the interface between the curved web and top flange until catastrophic failure of the P-beam (shown in Fig. 18(c)). The predictions correlate well with the findings in experiments. Note that based on the delamination failure criterion and the stress results of the FE analysis, the delamination failure element is identified and the elastic moduli E3, t13 and t23 of failure element are degraded to zero. With the increasing load, more delamination failure elements are further identified until final failure and the delamination propagation is thus simulated.

Table 4 Failure loads of I- and П-beams.

Method Failure initiation Ultimate failure

load (N) load (N)

I-beam П-beam I-beam П-beam

Experiment 26000 1189 37500 2504

Prediction 29227 1319 40351 2728

Relative deviation (%) 12.41 10.93 7.6 8.96

From the above progressive damage analysis, it is clear that the PDMs can effectively simulated the progressive damage process and accurately predict failure loads of the tested hybrid RTM-made I- and n-beams made of multi-layer TWF U3160/5284 and UCF CF3031/5284 reinforced composites under three-point flexure.

5. Conclusions

The mechanical behaviors of hybrid RTM-made I- and P-beams made of multi-layer TWF U3160/5284 and UCF CF3031/5284 reinforced composites were investigated. The static response and failure mechanism under three-point

flexure were described and analyzed. The significant results emerging from the studies are as follows.

(1) Failure process and mode of hybrid RTM-made I-beams are different from that of П-beams. Failure mode of the tested hybrid RTM-made I-beams in three-point flexure tests can be reckoned to be characteristic of the delamination from the circular cutout edge within the web and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until local buckling within the curved webs around the conjunction fillet region. In contrast, the hybrid RTM-made П-beams in three-point flexure tests experienced the resin debonding in the inverted triangular resin-rich zones and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until complete separation of the curved web from the top flange. These efforts have a good agreement with previous works in literature.

(2) The PDMs can effectively simulated the progressive damage process and accurately predict failure loads of the tested hybrid RTM-made I- and П-beams made of multi-layer TWF U3160/5284 and UCF CF3031/5284

(c) Matrix cracking propagation in the triangular resin-rich zone (d) Delamiation failure

Fig. 17 Progressive damage process of I-beams.

Fig. 18 Progressive damage process of П-beams.

reinforced composites under three-point flexure. Good correlation was achieved between experimental and numerical results.

Acknowledgment

This project was supported by the National Natural Science

Foundation of China (No. 51375033).

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Fu Yu is a Ph.D. student at School of Transportation Science and Engineering, Beihang University. He received his B.S. degree from Beihang University in 2010. His area of research includes composite materials and corrosion fatigue.

Xiong Junjiang is a professor and Ph.D. supervisor at School of Transportation Science and Engineering, Beihang University. He received the Ph.D. degree from the same university in 1995. His current research interest is fatigue and fracture reliability engineering, aircraft structural airworthiness.