Failure and damage characterization of (±30°) biaxial braided composites under multiaxial stress states

Accepted Manuscript Failure and Damage Characterization of (±30°) Biaxial Braided Composites Under Multiaxial Stress States Jörg Cichosz, Tobias Wehrkamp-Richter, Hannes Koerber, Roland Hinterhölzl, Pedro P. Camanho PII: DOI: Reference:

S1359-835X(16)30258-5 http://dx.doi.org/10.1016/j.compositesa.2016.08.002 JCOMA 4378

To appear in:

Composites: Part A

Received Date: Revised Date: Accepted Date:

27 December 2015 23 July 2016 1 August 2016

Please cite this article as: Cichosz, J., Wehrkamp-Richter, T., Koerber, H., Hinterhölzl, R., Camanho, P.P., Failure and Damage Characterization of (±30°) Biaxial Braided Composites Under Multiaxial Stress States, Composites: Part A (2016), doi: http://dx.doi.org/10.1016/j.compositesa.2016.08.002

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Failure and Damage Characterization of (±30◦ ) Biaxial Braided Composites Under Multiaxial Stress States J¨ org Cichosza , Tobias Wehrkamp-Richtera , Hannes Koerbera , Roland Hinterh¨ olzla,∗, Pedro P. b Camanho a Institute

for Carbon Composites, Technische Universit¨ at M¨ unchen, Garching b. M¨ unchen, Germany Rua Dr. Roberto Frias, Campus da FEUP, 400 4200-465, Porto, Portugal

b INEGI,

Abstract This paper focuses on the mechanical characterization of (±30◦ ) 2×2 biaxial braided composites under multiaxial stress states. Off-axis experiments in tension and compression were used to introduce multiaxial stresses in the material. The characterization was focused on nonlinear deformation and failure behavior: loading/unloading of the specimen was used to identify the mechanisms for nonlinear deformation and a high-speed-camera is used to record the failure mode of the specimen. It has been found that the failure modes are mainly dominated by shear-induced transverse cracking. A dependency of the failure mode on the transverse yarn stress was observed. The deformation was strongly nonlinear, and dominated by the shear-behavior of the yarns. An equivalent laminate model was employed for failure prediction, showing that the failure of the biaxial braided composites can be predicted accurately, when the knockdown induced by yarn waviness is considered in the material input parameters. Keywords: E: Braiding, D: Mechanical testing, C: Laminate mechanics, Fracture

1. Introduction 1.1. Motivation The growing use of composite materials in high-volume production has raised the need for automated manufacturing processes, which increase material throughput, cost-efficiency and part quality. Textile manufacturing processes, such as the braiding process, can be combined with resin transfer molding infusion technology, yielding a considerable potential for cost-efficient production of composite structures [1]. The overbraiding process, forming a closed network of fibers over ∗ Corresponding

author Email address: [email protected] (Roland Hinterh¨ olzl)

Preprint submitted to Composites Part A

August 2, 2016

a shaped mandrel, enables automated production of near net-shaped preforms for slender and hollow structures; this allows to combine high process quality, low material waste, and a flexibility in mechanical properties. The potential of the braiding process has been demonstrated by the development of the NH90 helicopter main landing gear. The landing gear was manufactured using biaxial braided composites combined with UD reinforcements and could be qualified for a demonstration flight [2]. Further, an improved damage tolerance of braided composites was reported, making them suitable for drive shafts [3]. Other applications for braided composites are given in the automotive industry: the crash-box of the McLaren SLR was produced by triaxial braids, yielding an excellent weight-specific energy absorption [4]; BMW AG also used braiding for the rear bumper beam of the BMW M6 car, which was built in a quantity of 6,000 parts per year [5]. 1.2. Literature review The internal geometry of braided composites comprises two or more sets of interwoven yarns. Yarn waviness introduces a knockdown to the in-plane properties and the fracture and damage behavior can be significantly influenced by the internal geometry [6, 7]. Tsai et al. studied the mechanical behavior of biaxial and triaxial braided composites using pressurized cylinders [8]. Graphite fibers were found to increase the cylinder hoop strength by 25% when compared to glass fibers and biaxial braided composites gave higher strength values attributed to the higher volume fraction of circumferential fibers. Cracking was found to initiate in the yarn directions, oriented along the bias yarns for biaxial braids and along the axial yarns for triaxial braids. Harte and Fleck published an extensive study on the tensile, compressive, and shear behavior of glass/epoxy biaxial braided composite tubes [9, 10]. Tensile and compressive strength of the braided composites decreased and the shear strength increased for bigger braiding angles. The response was explained by the increased matrix influence in tension and compression. This was supported by the stress-strain curves, being linear for small braiding angles and nonlinear for higher ones. The dominant failure modes were fiber failure and neck propagation in tension and fiber microbuckling and diamond-shaped buckling in compression. The failure mode was found to be sensitive to braiding angle and loading, however, matrix properties were controlling failure in most cases. Charlebois et al. presented similar results from experiments using flat coupons of glass/epoxy biaxial braided composites [11]. The tensile strength decreased with the braiding angle, while the compressive strength was nearly constant. Huang and Ramakrishna presented an experimental study on the properties of carbon/epoxy and glass/epoxy reinforced fabrics at low braiding angles

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11◦ − 35◦ [12]. The strength was reported to increase significantly for lower angles: An increase of 50% was obtained with 15◦ compared to 25◦ . Huang and Ramakrishna used specimen with continuous fibers at the edges, and pointed out the significance of the edge condition. This topic was further investigated in various publications: a high dependence of the strength to the edge condition is present for small braiding angles, decreasing for higher braiding angles; 100% strength increase for (±15◦ ) [13] and 13% strength increase for (±45◦ ) [14] when compared to specimen with cut fibers at the edges. However, Kelkar and Whitcomb produced braided specimen with continuous edges from overbraiding and found an increased braiding angle variation due to the flattening of the braided sleeves [15]. They therefore recommended to slit the braided sleeves, which enables to produce specimen with less braiding angle variation. The recommendation was considered in this study, as all coupons were produced by slitted braided preforms. Summarizing the literature published on mechanical testing of braided composites, significant effort has been undertaken for characterization with different constituents, yarn architectures and braiding angles. Only little work is available on the behavior of biaxial braided composites under multiaxial stress states. However, this information becomes indispensable when considering the assessment of macroscopic failure envelope predictions, such as the ones presented by Smith and Swanson for triaxial braided composites [16]. 1.3. Objective The aim of the current study is to provide a failure and damage characterization of biaxial braided composites under multiaxial stress states. A (±30◦ ) carbon/epoxy braided composite is used for the characterization. The multiaxial stress states are achieved by uniaxial loading of offaxis coupons in tension and compression. Special consideration is given to the failure modes, which are evaluated using high-speed camera recordings. Furthermore, the mechanics of the nonlinear deformation –elastic modulus loss and inelastic strains– are evaluated by loading/unloading experiments. Finally, the experimental results are compared to simple equivalent laminate modeling results, assessing the applicability of these models for structural simulation.

2. Material and experimental setup This paper describes the mechanical behavior of (±30◦ ) 2×2 carbon/epoxy biaxial braided composites. The braided preforms were produced on a cylindrical mandrel with 100 mm diameter using a Herzog RF 1-176-100 maypole braiding machine with 176 yarns. Toho Tenax E HTS40 3

F13 12K (800 tex) 0z untwisted yarns, consisting 12,000 filaments, were used. Elastic and strength properties for the HTS40 fiber are given in Table 1. The mandrel diameter was chosen to yield a flat yarn shape with a width of approximately 3.1 mm while keeping the braid closed, avoiding matrix-rich regions. A surface scan of the braided fabric is shown in Fig. 1. [Table 1 about here.] [Figure 1 about here.] The preforms were braided on the cylindrical mandrel, slit along the take-up direction, unrolled to a cutting table and subsequently cut into two rectangular preforms. The first 150 mm and last 50 mm of the braided preform are not used, due to fiber angle deviations in these regions. All cut lines of the braid are taped with a temperature resistant tape prior to cutting, which avoids fiber distortion during cutting. The braided preforms were stacked to five and eight-ply laminates for tensile and compressive experiments, respectively. The laminates were infused using a Hexcel HexFlow RTM6 monocomR ponent epoxy resin in the Vacuum Assisted Process (VAP ). Elastic and strength properties of

RTM6 are given in Table 1 , stress-strain curves can e.g. be found in [17] . Resin and preform were heated to 80◦ C and 120◦ C, respectively, prior to the infusion and the impregnated laminates were cured for 120 minutes at 180◦ C. Several quality inspection steps were conducted over the manufacturing process to ensure a constant quality of the braided composite laminates: braiding angle measurement on the preforms, leakage check of vacuum bagging, thickness measurement of the panels. Additionally, the fiber volume fraction of the panels was measured by digestion according to ASTM D3171 [18] from three specimen evenly distributed over each panel. The mean fiber volume fraction measured was 60.8% and 61.4% for the panels used in tension and compression tests, respectively. Moduli and failure stresses were normalized to a fiber volume content of 60% with the procedure for biaxial braided composites given by Zebdi et al. [19]. The coupons were cut from the laminates using a water-cooled diamond saw. Tensile coupon dimensions were chosen according to ASTM D3039 [20] of length×width×thickness = 250×25×2.5 mm3 . Compression test coupons dimensions were chosen according to ASTM D6641 [21] of length × width × thickness = 140×25×4 mm3 . The off-axis orientation of the specimen was oriented to the longitudinal edge of the panels, representing the take-up direction. Glass/epoxy tabs of 1 mm thickness were used for the experiments. For the tensile experiments, oblique tabs, with the tab angle calculated according to Sun [22], were used to reduce stress 4

concentrations. The oblique angles calculated are given in Table 2. The calculated value for ψ = 30◦ was close to 90◦ , thus, rectangular tabs were used. Due to the small gauge section, no oblique tabs were used in compression. [Table 2 about here.] 2.1. Test Setup The experiments in tension and compression were conducted with a constant machine head speed of 2 mm/s and 1.3 mm/s, respectively. At least six valid experiments were obtained for each test series; all compressive specimen were loaded monotonically up till failure, while two tensile specimen were used for the loading/unloading characterization. A servo-hydraulic gripping system was used for load-introduction in tension (Fig. 2a), while the combined-compression-loading (CLC) test fixture [23], in combination with spherical hinge mounted steel platens was used in compression (Fig. 2c). The CLC test fixture requires using specimen comprising a short free gauge length 14 mm in this study -, which avoids buckling of the specimen. Furthermore the combined load introduction through shear and end load avoids end crushing oh the specimen. [Figure 2 about here.] Two methods for strain measurement on the specimen were used, namely digital image correlation (DIC) and strain gauges. The GOM ARAMIS 4M DIC system with a 2352×1728 pixel2 resolution and two cameras was used for measuring the 3D deformation of the specimen in tension. The measurement area was 65×45 mm2 , placed to the center of the coupon and the acquisition rate of the camera was set to 2 Hz . With the facet size chosen to be 17×17 pixels2 , a resolution of approximately seven measurement points per yarn width was obtained. The specimen strain state was obtained by averaging the strain over the complete measurement area. For the compression tests, linear Tokyo Sokki Kenkyujo FLA-3-11 foil strain gauges, with a gauge size of 3×1.7 mm2 were bonded on both sides of the specimen. Using a strain gauges on both specimen sides allowed to calculate specimen bending according to [21], which was used for validation against specimen buckling for all experiments. For the tensile experiments, a PHOTRON SA5 high-speed camera was used to obtain information about the final failure process. A resolution of 384×1008 pixels2 was used to record the center part of the gauge section in an area of 80×30 mm2 . The maximum acquisition rate, obtainable for this resolution, 17,500 fps, was chosen, which gave a record time of 1.3 s in total. A DEDOLIGHT

5

400 watt flood light provided an adequate lightening for the recordings. In the compression experiments, the high-speed camera could not be used due to the geometric constraints of the test fixture used.

3. Evaluation methodology 3.1. Tangent modulus The tangent modulus of the specimen was evaluated to obtain the initial modulus E 0 at the beginning of the experiment. The common definition of the tangent modulus, using the finite difference quotient of stress and strain is strongly influenced by the signal noise, which introduced considerable errors, especially at low stresses. To reduce the effect of noise, an incremental leastsquares fit of the stress-strain curve was used to calculate the tangent modulus and, thus, obtain the initial modulus. A 2nd dergee polynominal function was fitted to the stress-strain curve in the strain interval εxx = 0%-0.1% and used to calculate the initial modulus E 0 . 3.2. Modulus and inelastic strain The evaluation of the loading/unloading experiments follows the general theory of inelastic strains and damage in composites, given by Ladeveze and Dantec [24]. If damage is introduced, the elastic modulus changes, for each cycle, the elastic modulus (E 1 ) can be calculated from unloading: E1 =

(σ 1 − σ 2 ) . (ε1 − ε2 )

(1)

The superscripts of stress an strain refer to the points in Fig. 3. For comparison, the modulus is usually normalized to the initial value: E  = E 1 /E 0 ,

(2)

where E 0 is the initial elastic modulus, evaluated by a least-squares regression of the stress-strain curve. The inelastic part of the strain (εie ) is calculated from εie = ε1 − σ 1 /E 1 , where ε1 and σ 1 are the strain and stress, respectively, at the unloading point (1, cf. Fig. 3). [Figure 3 about here.]

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(3)

3.3. Equivalent laminate model A (±30◦ ) equivalent laminate model is introduced for three particular purposes: 1) qualitative evaluation of the yarn direction stress components for the off-axis experiments; 2) normalization of the test results according to [19]; 3) macroscopic failure modeling and comparison to the off-axis experiments. The equivalent laminate model is composed from two yarn plies, which are characterized by their in-plane stiffness matrix in the yarn coordinate system F + /F − (cf. Fig. 4): ⎡ ⎤ Q11 Q12 0 ⎢ ⎥ ⎢ ⎥ Q = ⎢Q12 Q22 0 ⎥ ⎣ ⎦ 0 0 Q66

(4)

with Q11 =

E11 1 − ν12 ν21

Q22 =

E22 1 − ν12 ν21

Q12 =

ν12 E22 ν21 E11 = 1 − ν12 ν21 1 − ν12 ν21

Q66 = G12

the yarn ply stiffness matrix can be transformed into the braided composite material coordinate system by ¯ ±θ = T−1 (±θ) · Q · T−T (±θ), Q

(5)

with θ being the braiding angle and T being the transformation matrix ⎡ ⎤ sin2 φ 2 cos φ sin φ cos2 φ ⎢ ⎥ ⎢ ⎥ T(φ) = ⎢ sin2 φ cos2 φ −2 cos φ sin φ ⎥ . ⎣ ⎦ − cos φ sin φ cos φ sin φ cos2 φ − sin2 φ And the equivalent laminate in-plane compliance matrix Seq given as:  −1 1 ¯ +θ ¯ −θ

eq eq −1 S = [Q ] = ; Q +Q 2

(6)

(7)

the elastic constants of the equivalent laminate are: eq = E11

1 eq S11

eq E22 =

1 eq S22

Geq 12 =

1 eq S66

eq ν12 =−

eq S12 eq . S11

(8)

The Young’s modulus of the equivalent laminate in the off-axis direction ψ is calculated from  eq  1 1 1 2ν12 1 2 4 4 2 (9) eq = eq cos (ψ) + eq − eq sin (ψ) cos (ψ) + eq sin (ψ). Eψ E11 G12 E11 E22 Furthermore, the in-plane stress vector in the yarn plies σ F + , σ F − is given by σ F +/− = Q · εF +/− = Q · T(±θ)−T · εeq , 7

(10)

where T is the transformation matrix given in Eq. (6), Q the yarn ply stiffness matrix, and εeq is the in-plane strain vector of the equivalent laminate in the material coordinate system (11/22 cf. Fig. 4).

4. Experimental results The mechanical behavior of a (±30◦ ) biaxial braided composite has been studied using inand off-axis specimen tested under uniaxial load. A total of six off-axis1 (OA) angles, ψ = 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 90◦ (Fig. 4), were tested in tension and compression. The off-axis angle ψ = 75◦ was skipped, as the results were expected to be very similar as for ψ = 90◦ . [Figure 4 about here.] 4.1. Monotonic tension The elastic results from the tensile off-axis experiments are shown in Fig. 5. The modulus in load direction of the specimen was evaluated by two ways: Ex represents the Young’s modulus, evaluated in the strain range from εxx = 0.1%-0.3%, while Ex0 is the initial modulus, evaluated by regression, as described above. In addition to the experimental results, a polar plot from two equivalent laminate models, (±29◦ ) and (±31◦ ), is given. The ply angles of the equivalent laminate models represent the range of braiding angles found in the panels. [Figure 5 about here.] For the off-axis angles 0◦ and 15◦ , the initial modulus is considerable higher than Ex , which is attributed to the nonlinear behavior of the braided composites. The modulus in the fixed strain range deviates less from the initial one, for the higher off-axis angles. The comparison of the experimental results to the equivalent laminate model show that stiffness knockdown due to fiber waviness is mainly prominent for the off-axis angles 0◦ −30◦ , where the stiffness is reduced between 10% and 20% compared to the equivalent laminate. A representative stress-strain curve is given for each off-axis angle in Fig. 6. The stress-strain behavior is nonlinear in all cases except for the load applied in the yarn direction (OA30): this load case is dominated by the axial behavior of the yarn, while the other cases show strong, matrix-induced, nonlinearities. 1 Although,

the experiments with off-axis angles of 0◦ and 90◦ are, strictly speaking, “in-axis”, the term off-axis

will also be used for these experiments throughout this paper.

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[Figure 6 about here.] (sig-eps-PT.csv about here.) A dependence of both failure stress and failure strain on the off-axis angle is observed. From OA00 to OA30, the strength increases, with the failure strain decreasing from 2.3% to 1.2%. The failure strain in yarn direction (OA30) is approximately 30% lower as the one measured for the same material in UD experiments [25], which is attributed to the yarn waviness. Increasing the off-axis angle over 30◦ both failure stress and strain significantly drop: OA45 shows the most brittle response, with a failure strain of 0.5%. For a further increase of the off-axis angle, the failure stress further decreases, while the failure strain increases again. 4.1.1. Failure modes The failure process of the specimen was evaluated using the high-speed camera recordings. Fig. 7 gives three images of the failure process for each off-axis angle. The left picture was recorded prior to final failure, the middle picture during the failure in process and the right one after specimen failure. The failure mechanisms in the specimen were furthermore investigated by post-mortem inspection of the tested specimen. Characteristic failure patterns from each test series are given in Fig. 8. [Figure 7 about here.] For tension in the take-up direction of the braid, OA00, the failure manifests in a broad area of damage, including several transverse cracks over the width of the yarns, and delamination of the plies. The failure process is dominated by the shear stress in the yarns, which can be seen from the transverse displacement of the two parts of the specimen. The failure modes observed for the off-axis angles 15◦ and 30◦ are quite similar. Minor transverse cracking, located at the specimen edges, is observed prior to final failure and the final failure manifests in a discrete crack along the 1F+ direction (oriented for OA15 and OA30 by 45◦ and 60◦ to the load, respectively). Post-mortem inspection of the specimen showed yarn rupture of the 1F− direction as failure mode of the specimen in both cases. For the OA15 case, the yarn rupture is accompanied with transverse cracking and delamination in the area of the major crack. Most of the OA30 specimen showed two main cracks: one of the two was identified as the crack of final failure by the high-speed camera recordings, while the other one was compressive failure introduced by elastic snap-back of the specimen.

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The failure of the specimen changes for the off-axis angles bigger than 30◦ : in the case of OA45, OA60 an OA90, the failure is dominated by transverse tensile cracking. Transverse cracking in the 1F+ direction initiates the failure process, the transverse cracks accumulate, since they spread over the specimen width and, subsequently, a crack along the 1F− yarn direction is forming. The yarns in 1F+ direction are discretely failing, being sheared-off, as they cannot transport the shear stresses over the crack. The 1F+ yarns, failed at the main crack, show various cracks over the yarn width, attributed to the shear type of failure. In the OA90 case, as the yarns are stressed equal, failure localizes along either one of the yarn directions. [Figure 8 about here.] 4.2. Loading/ unloading tension Loading/unloading experiments were conducted to be able to distinguish the underlying mechanics of nonlinear deformation, namely material damage and inelastic deformation. The specimen were unloaded to a small force and instantly reloaded, i.e. viscous effects were not studied, as they were reported to be small for carbon/epoxy (±30◦ ) biaxial braided composites by Kelkar and Whitcomb [15]. Damage is characterized by loss of material stiffness, while other inelastic effects are characterized by permanent strains after unloading. Permanent strains have been reported for composite materials [24, 26, 27] and are commonly attributed to microscopic damage, or viscoelastic and plastic deformation. Two loading/unloading experiments were conducted for each test series, with four load cycles up to approximately 25%, 50%, 80% of the failure load and the last cycle until specimen failure. The results obtained were very similar between the two specimen, and stress-strain behavior as well as failure stress and strain did not differ significantly from the monotonic experiments. No loading/unloading experiments were conducted for the linearly behaving OA30 test series. One representative stress-strain curve for each off-axis angle is shown in Fig. 9 and 10. A significant hysteresis during unloading and reloading is observed within all experiments, which is likely due to frictional forces present at failed fiber/matrix interfaces [14]. Over all off-axis angles, inelastic deformation, manifesting in residual strains after unloading, is present. The highest inelastic strains are visible in the OA00 and OA15 experiments, while the nonlinearity and, thus, the inelastic deformation are smaller for higher off-axis angles. [Figure 9 about here.] [Figure 10 about here.] 10

(sig-eps-cyclic OA00.csv, sig-eps-cyclic OA15.csv, sig-eps-cyclic OA45.csv, sig-eps-cyclic OA60.csv, sig-eps-cyclic OA90.csv about here.) The inelastic strain and normalized modulus (cf. Eq. (2)) evaluated from the unloading cycles according to Eq. (1) and Eq. (3) are presented in Fig. 11. [Figure 11 about here.] The strain given on the x-axis refers to the axial strain of the specimen (εxx ). A nonlinear dependence of the inelastic strain is observed for OA00 and OA15 test series. For the higher off-axis angles, the inelastic strains observed are in general lower and the dependence to the applied strain is linear. An interpretation of the results can be given using an equivalent laminate model: Fig. 12 shows transverse and shear stress in the yarn ply coordinate system for an equal axial strain applied for each off-axis angle. The shear stress, commonly reported as a driver for inelastic deformation of UD plies [27, 28, 24] is nearly constant for the off-axis angle from 45◦ -90◦ . Thus, in these cases, an equal axial strain leads to equal plastic shear deformation, as observed in the experiments. For low off-axis angles, OA00 and OA15, the increased inelastic deformation is primarily attributed to two reasons: higher shear stresses in the yarns and transverse compressive yarn stresses (σ2F +/− < 0), which may also contribute to the inelastic deformation [29]. [Figure 12 about here.] For the normalized modulus, representing damage in the material, the trend is contrary to the inelastic deformation (Fig. 11b): for OA00 and OA15, the progress of the normalized modulus is nonlinear with the slope decreasing for higher strains. For the higher off-axis angles, the moduli decrease linear and of similar magnitudes as for the OA00 and OA15 experiments. It is noted that the high scatter of values for the normalized modulus of the first cycle is attributed to the increased influence of signal noise for small stresses and strains. Summarizing the loading/unloading experiments, a combination of damage and inelastic deformation was found for all off-axis angles. The modulus reduction was found in similar magnitudes for high (OA00) and low (OA90) stressed cases. In opposite, inelastic deformation increased for offaxis angles exhibiting higher stresses, thus, inelastic effects are likely to dominate the behavior for larger strains, which is in accordance with the observations published by Pickett and Fouinneteau for 1×1 carbon/epoxy biaxial braided composites [14].

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4.3. Monotonic compression The combined loading compression test fixture was used for the compression off-axis experiments. All compressive experiments were validated using the criterion of specimen bending being lower than 10%, as given by the standard [21]. Although the criterion was not valid for some of the specimen, no significant difference was found in the strength and failure strain of these specimen. The strain difference between the two specimen sides was attributed to the heterogeneity of the strain field, introduced by the textile yarn architecture. One representative stress-strain curve for each compressive off-axis test series is given in Fig. 13. The curves from the tensile experiments are given for comparison. The elastic properties, i.e. the initial stiffness of the stress-strain curves were similar in tension and compression. An increased stiffness was observed for the OA45 test series in compression. However, the difference was attributed to manufacturing tolerances regarding the off-axis angle, which highly impact the stiffness for this off-axis angle (cf. Fig. 5). For the comparison of the stress-strain curves, compressive stress-strain curves from OA45 were scaled to the initial modulus of the tensile ones. The stress-strain behavior was nonlinear for all off-axis angles. Different to the tensile test, a nonlinear behavior is present for the load applied in the yarn direction (OA30), which is attributed to an increased inelastic deformation of the transverse F+ yarns, oriented 60◦ to the load. Except for the OA30 case, the stress-strain behavior of the (±30◦ ) braided composite in tension and compression was found to be very similar. As in tension, the highest strength is present for the load oriented in the yarn direction. However, the drop of failure stress for off-axis angles increasing 30◦ is less than in tension. The failure stresses of OA15 and OA45, and the ones of OA00 and OA60 are of similar magnitudes. The failure strains for the off axis angles OA00, OA15, and OA30 were found similar of approximately 1%, which is considerably lower than the failure strains measured in tension. Increasing the off-axis angle over 30◦ , the failure strain increases to 1.2% for OA45, and 3.7% and 4.1% for OA60 and OA90, respectively. For all specimen of the PC OA90 test series, the slope of the stress-strain curve started to increase at a strain level of approximately 3.5% (cf. Fig. 13). This behavior was not observed in the force-displacement curves, and, thus, is not believed to be material behavior. It is rather considered that a failure of the foil gauge bond introduced this error. Thus, the actual failure strain of the OA90 test series is believed to be around 5%, as obtained by linear extrapolation. [Figure 13 about here.] 12

(sig-eps-PC.csv about here.) 4.3.1. Failure modes Typical failure modes observed in the compressive experiments are shown in Fig. 8. For the two off-axis angles OA00 and OA15, comparable failure modes have been observed: all specimen failed in a single tensile crack, oriented along the yarn direction. Orientation of the crack was, similar as in tension, along the 1F+ yarn direction for OA15 and along either one of the yarns for OA00. No considerable cracking prior to final failure was observed in the experiments, which correlates with the cracks on the specimen being limited to the final crack. It is noted that the failure of the specimen, although partially being under the tabs, was regarded valid: the crack orientation is given by the yarn architecture, failure modes occurred reproducible and the scatter in measured failure stresses was small. Thus, local effects introduced by the load introduction were considered to be negligible. For the load in yarn direction, compressive kink band failure of the yarns, accompanied with transverse yarn failure and delamination was observed. The cracks, present on the specimen, were as for the tensile experiments oriented along the 1F+ yarn direction, at an angle of 60◦ to the load direction. For OA45, OA60 and OA90, the failure mode observed was compressive transverse cracking of the 1F+ yarns. The failure primarily manifested in inclined transverse cracks, building wedges over the thickness of the laminate, resulting in intra-ply and inter-ply delamination. As for the tensile off-axis experiments, a smooth degradation was observed in the stress-strain curves and the final failure of the specimen was abrupt, without considerable preliminary cracking. 4.4. Comparison of tension and compression Fig. 14a presents a comparison of the Young’s moduli for tensile and compressive experiments. Tensile and compressive moduli follow the same qualitative trend and are very similar in magnitude, only minor differences are observed for OA00 and OA45. For OA00, the difference is attributed to systematical braiding angle deviations observed on all panels (s-shape of the yarns, cf. [30]). Due to the decreased material volume of the gauge section, the effect of the yarn angle and, thus, stiffness variation is less prominent for the compressive specimen. For OA45, the difference is attributed to manufacturing tolerances regarding the off-axis angle. For the failure stresses given in Fig. 14b, a considerable difference between tension and compression exists. For the load applied in the yarn direction (OA30), the tensile failure stress is approximately 30% higher than the compressive one. This particular load case is mainly dom-

13

inated by the yarn longitudinal behavior, thus, the difference is attributed to the fact that the tensile strength of a yarn is higher than the compressive strength. For the other off-axis angles, a clear trend in the strength is observed: the tensile failure stress is higher for the off-axis angles 0◦ and 15◦ , while the compressive failure stresses exceed the tensile ones for the high off-axis angles 45◦ , 60◦ , and 90◦ . The difference in the failure stresses can be attributed to the transverse stress state in the yarns. The qualitative evaluation using the equivalent laminate model (Fig. 12) shows that for a tensile loading, compressive transverse yarn stresses are present for off-axis angles approximately 0◦ − 30◦ , while the transverse stress in both yarn directions is tensile for off-axis angles above 30◦ . The failure modes observed were primarily dominated by shear and transverse cracking. Thus, the equivalent laminate model suggests two explanations for the difference in tensile and compressive strength: • The transverse compressive strength of the yarns is, similar to UD composites, higher than the transverse tensile strength. Thus, tensile yarn transverse failure occurs at lower stresses. • For transverse compressive yarn stresses, shear-initiated cracks in the yarns may be kept closed by the transverse compression, i.e. higher shear stresses in the yarns are possible (described for UD laminates by Sun [31]). Thus, the failure behavior of 2×2 biaxial braided composites can be believed to qualitatively follow the same trends as observed in UD laminates. This is also supported by the failure modes observed in the specimen. Fiber failure is present for the tensile and compressive loads in yarn direction (OA30). However, from the other test series, a broad damaged area including delamination was observed in tensile OA00 and OA15 experiments as well as in the compressive OA45, OA60 and OA90 experiments, comprising transverse compressive stress states. In opposite, discrete tensile failure in a single crack was observed for compression in the OA00 and OA15 case and for tension in the OA45, OA60 and OA90 case (cf. Fig. 8). Furthermore, the comparison of the stress-strain response, being similar in tension and compression, suggests that the in-plane shear behavior is the primary mechanism for the nonlinear deformation. This correlates with the fact that no aggregation of intra-yarn transverse cracking (cf. [32, 33, 34]) was found in the specimen, and, thus, mechanisms at a smaller scale are attributed to introduce the nonlinearity. Microscopic cracking at the scale of the fiber/matrix interface was described to be driving the in-plane shear behavior of UD composites [26, 35, 27], and is likely to be dominant for the stress-strain response of biaxial braided composites. [Figure 14 about here.] 14

5. Equivalent laminate predictions Failure prediction for the biaxial braided composites are based on equivalent laminate predictions. In-plane stresses in the two yarn directions are calculated using Eq. (10). From the experimental data presented in this paper, it is clear that the assumption of linear deformation does not represent the actual material behavior. However, the goal of the current study was not to present a comprehensive constitutive model for biaxial braided composites, but rather to evaluate the predictive capabilities of a simple method for failure prediction. 5.1. Input properties The properties of the equivalent yarn plies need to include the effects of fiber waviness and cannot be measured experimentally. Therefore, two different approaches for input property definition will be used: 1. Material properties measured from UD experiments for the identical fiber/matrix combination used in the braided composites [25] (UD). 2. Material properties calibrated to selected experiments of the test series (UDeq). The elastic UDeq material parameters are calculated from the experiments by application of the inverse CLT approach, presented by Zebdi et al. [19]. The tensile experimental results were used for the elastic definition, with the shear modulus calculated from the ψ = 30◦ off-axis experiment by application of Eq. (9). The UDeq strength parameters are obtained by calibration to distinct off-axis load cases: yarn direction tensile and compressive strength are identified using the OA30 tensile and compressive experiments; in-plane shear strength is identified from the tensile OA00 experiment; and transverse tensile and compressive strength are obtained from the OA90 experiments in tension and compression, respectively. An overview to the material parameters used is given in Table 3. The calibration procedure yields the advantage, that effects of yarn architecture are included in the input property. [Table 3 about here.] 5.2. Failure criteria Failure is analyzed using the maximum stress criterion for fiber failure and the plane-stress version of the Puck criterion (Puck2D), given by Puck and Sch¨ urmann [36], for transverse failure. The relation between stresses and strains is believed to be linear and the first failure predicted is assumed to coincide with the final failure. Sentence deleted here and added to the beginning of Sec. 5 15

5.3. Off-Axis failure curves The results of the failure predictions are compared in Fig. 15 as off-axis-failure-envelopes: the failure stress predicted by the (±30◦ ) equivalent laminate model is given for all off-axis angles for both UD and UDeq material data. The failure curves are given for fiber failure (FF) and transverse failure (TF); only the most critical ply for each failure mode is given, which was F− for fiber failure and F+ for transverse failure in tension and F− for both failure mode in compression. The tensile predictions obtained with UDeq material properties agree well with the experimental results for OA00, OA45, OA60, and OA90. For OA15 and OA30, transverse failure of the F+ ply (oriented 30◦ + ψ to the load) is predicted and the failure stress predicted is 13% and 30% lower as measured in the experiment. The deviation is believed to be due to the assumption of linearity, not considering stress redistribution by plastic deformation of the plies. The off-axis compression predictions for UDeq lie mostly within the scatter of the experimental results. When comparing the UD predictions, based on material propertied not including waviness, the effect of the textile architecture can be evaluated. The predictions for the matrix-dominated properties exhibit only moderate deviations. For most cases, the failure stresses are underpredicted, with the maximal deviations observed for compression in OA60 and OA90, of 22% and 27%, respectively. Considering fiber failure (OA30), the predicted failure stresses are non-conservative: the failure stress is overpredicted in tension and compression, which is attributed to the fiber waviness not being considered. This is especially important for the compressive case, where the fiber failure is the first failure predicted by the equivalent laminate model. [Figure 15 about here.] Summarizing the equivalent laminate modeling results, linear predictions using the Puck2D failure criterion, applied to the equivalent plies yields good accordance to the experimental results. For tensile loading, transverse failure is for all off-axis cases the first failure predicted, which underestimates the failure stresses for fiber-dominated failure modes. In compression, transverse failure is dominant in most cases, except for the yarn directions mainly stressed in longitudinal compression (ψ ≈ 20◦ . . . 40◦ ), where fiber compressive failure is the first and ultimate failure mode. Thus, the effect of yarn waviness on longitudinal yarn properties needs to be accounted for in the model input parameters.

16

6. Conclusions This study presented a failure and damage characterization of (±30◦ ) biaxial braided composites under multiaxial stress states in tension and compression. Multiaxial stress states in the material were achieved by testing off-axis oriented coupons under uniaxial loading. A high-speed camera was used to record and evaluate the final failure of the coupons. Furthermore, cyclic loading/unloading experiments were used to capture the underlying mechanisms of the nonlinear deformation observed in the experiments. The stress-strain behavior was determined to be nonlinear for all cases except for loading in fiber direction. All test series showed a smooth degradation over the complete strain range, which could be attributed to microscopic cracking at the fiber/matrix scale. The loading/unloading experiments showed that a mixture of damage and inelastic behavior was present: inelastic deformation was dominant for larger strains and could be correlated to the shear stress in the yarns. Failure modes in tension and compression were dominated by transverse cracking and shear failure. A simple equivalent laminate model could be used to explain the failure modes: for transverse tension in the yarns, the failure localized to a single crack, while a broad zone of damage was present for a transverse compressive yarn stress. The failure stresses in tension and compression followed an identical trend, being bigger for transverse compressive stresses in the failing yarn direction. Finally, it was shown that equivalent laminate predictions correlate well with the experimental results, if input parameters are calibrated to account for fiber waviness. Experimental results from tension and compression tests in three off-axis angle directions, namely OA00, OA30 and OA90, were sufficient to calibrate this simple failure prediction model, which then provided good correlation with experimental results for all other off-axis angles. The presented results serve as a basis for further research in the field of material modeling of braided composites. Unit cell models need to be developed and validated to being able to predict the influence of fiber waviness for arbitrary internal yarn geometries. In addition, improved macroscopic models for biaxial braided composites need to be developed to account for the damage and the inelastic deformation observed in the experiments.

7. Acknowledgements The authors would like to thank the Austrian competence center program COMET sponsored by the Federal Ministry for Transport, Innovation and Technology and Federal Ministry for Economy, Family and Youth for the support of this research work. The research work was performed at

17

the Technische Universit¨at M¨ unchen (Institute of Carbon Composites) with contributions by the Polymer Competence Center Leoben GmbH (PCCL), Montanuniversitaet Leoben (Chair of Material Science and Testing of Polymers), FACC Operations GmbH and Toho Tenax Europe GmbH. Dr. Markus Wolfahrt (PCCL) is acknowledged for technical support. The authors acknowledge Felix Fr¨ ohlich (Munich Composites GmbH) for providing support during braiding of the preforms.

References [1] Uozumi, T., Kito, A., Yamamoto, T.. CFRP using braided preforms/RTM process for aircraft applications. Adv Compos Mater 2005;14(4):365–383. [2] de Haan, P.. Development of a composite trailing arm for a helicopter main landing gear. In: Proceedings of the International Symposium on Composites Manufacturing for Aircraft Structures. Marknesse, The Netherlands; 2010,. [3] Erber, A., Birkefeld, K., Drechsler, K.. The influence of braiding configuration on damage tolerance of drive shafts. In: SEICO 09, SAMPE Europe 30th. International Jubilee Conference and Forum. Paris, France; 2009,. [4] D¨ olle, N.. FVK-anwendungen bei Daimler - lessons learned. In: CCeV Automotive Forum. Neckarsulm; 2010,. [5] R¨ uger, O.. Preforming: Stand der Technik & Ausblick. http://www.carbon-composites.eu/; 2009. Acessed 24/02/2014. [6] Dadkhah, M., Flintoff, J., Kniveton, T., Cox, B.. Simple models for triaxially braided composites. Composites 1995;26(8):561 – 577. [7] Littell, J.D., Goldberg, R.K., Roberts, G.D., Binienda, W.K.. Full-field strain methods for investigating failure mechanisms in triaxial braided composites. In: Proceedings of the Earth and Space 2008, 11th International Conference on Engineering, Science, Construction, and Operations in Challenging Environments. Long Beach, California; 2008, p. 1–12. [8] Tsai, J.S., Li, S.J., Lee, L.J.. Microstructural analysis of composite tubes made from braided preform and resin transfer molding. J Compos Mater 1998;32(9):829–850. [9] Harte, A.M., Fleck, N.. Deformation and failure mechanisms of braided composite tubes in compression and torsion. Acta Mater 2000;48(6):1259 – 1271.

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[10] Harte, A.M., Fleck, N.A.. On the mechanics of braided composites in tension. Eur J Mech A-Solid 2000;19(2):259 – 275. [11] Charlebois, K.M., Boukhili, R., Zebdi, O., Trochu, F., Gasmi, A.. Evaluation of the physical and mechanical properties of braided fabrics and their composites. J Reinf Plast Compos 2005;24(14):1539–1554. [12] Huang, Z.M., Ramakrishna, S.. Towards automatic designing of 2d biaxial woven and braided fabric reinforced composites. J Compos Mater 2002;36(13):1541–1579. [13] Aggarwal, A., Ramakrishna, S., Ganesh, V.K.. Predicting the strength of diamond braided composites. J Compos Mater 2002;36(5):625–643. [14] Pickett, A., Fouinneteau, M.. Material characterisation and calibration of a meso-mechanical damage model for braid reinforced composites. Composites Part A 2006;37(2):368 – 377. [15] Kelkar, A.D., Whitcomb, J.D.. Characterization and structural behavior of braided composites. Tech. Rep. DOT/FAA/AR-08/52; U.S. Department of Transportation Federal Aviation Administration; January; 2009. [16] Smith, L.V., Swanson, S.R.. Strength design with 2-d triaxial braid textile composites. Compos Sci Technol 1996;56(3):359 – 365. [17] Morelle, X.P., Lani, F., Melchior, M.A., Andr, S., Bailly, C., Pardoen, T.. The elastoviscoplasticity and fracture behaviour of the rtm6 structural epoxy and impact on the response of woven composites. In: ECCM15 - 15TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS. Venice, Italy; 2012,. [18] ASTM D3171, . Standard Test Methods for Constituent Content of Composite Materials. ASTM International; West Conshohocken PA, USA; 1999. [19] Zebdi, O., Boukhili, R., Trochu, F.. An inverse approach based on laminate theory to calculate the mechanical properties of braided composites. J Reinf Plast Compos 2009;28(23):2911– 2930. [20] ASTM D3039, . Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials. ASTM International; West Conshohocken PA, USA; 2000.

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[21] ASTM D6641, . Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials Using a Combined Loading Compression (CLC) Test Fixture. ASTM International; West Conshohocken PA, USA; 2009. [22] Sun, C., Chung, I.. An oblique end-tab design for testing off-axis composite specimens. Composites 1993;24(8):619–623. [23] Wegner, P.M., Adams, D.F.. Verification of the combined load compression (clc) test method. Tech. Rep. DOT/FAA/AR-00/26; U.S. Department of Transportation Federal Aviation Administration; Aug; 2000. [24] Ladeveze, P., LeDantec, E.. Damage modelling of the elementary ply for laminated composites. Compos Sci Technol 1992;43(3):257 – 267. [25] Schubert,

M..

Vergleich eines Resin Transfer Moulding Epoxidharzsystems mit einem

Prepregharzsystem. Tech. Rep.; Toho Tenax Europe GmbH, Wuppertal; 2009. [26] Puck, A., Sch¨ urmann, H.. Failure analysis of FRP laminates by means of physically based phenomenological models. Compos Sci Technol 2002;62(12-13):1633 – 1662. [27] Camanho, P.P., Dvila, C.G., Pinho, S.T., Iannucci, L., Robinson, P.. Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Composites Part A 2006;37(2):165 – 176. CompTest 2004. [28] Puck, A.. Festigkeitsanalyse von Faser-Matrix-Laminaten (Modelle f¨ ur die Praxis). Hanser, M¨ unchen, Wien; 1996. [29] Flatscher,

T., Pettermann,

H.. A constitutive model for fiber-reinforced polymer plies

accounting for plasticity and brittle damage including softening - implementation for implicit FEM. Compos Struct 2011;93(9):2241 – 2249. [30] Birkefeld, K., R¨ oder, M., von Reden, T., Bulat, M., Drechsler, K.. Characterization of biaxial and triaxial braids: Fiber architecture and mechanical properties. Appl Compos Mater 2012;19:259–273. [31] Sun, C., Quinn, B., Oplinger, D.. Comparative evaluation of failure analysis methods for composite laminates. Tech. Rep.; DOT/FAA/AR-95/109; 1996.

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[32] Lomov, S., Ivanov, D., Truong, T., Verpoest, I., Baudry, F., Bosche, K.V., et al. Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test. Compos Sci Technol 2008;68(12):2340 – 2349. [33] Ivanov, D.S., Baudry, F., Van Den Broucke, B., Lomov, S.V., Xie, H., Verpoest, I.. Failure analysis of triaxial braided composite. Compos Sci Technol 2009;69(9):1372 – 1380. [34] Zako, M., Uetsuji, Y., Kurashiki, T.. Finite element analysis of damaged woven fabric composite materials. Compos Sci Technol 2003;63:507 – 516. [35] Ladevze, P., Allix, O., De¨ u, J.F., Lvque, D.. A mesomodel for localisation and damage computation in laminates. Comput Method Appl M 2000;183(1-2):105 – 122. [36] Puck, A., Schuermann, H.. Failure analysis of FRP laminates by means of physically based phenomenological models. Compos Sci Technol 1998;58(7):1045 – 1067. [37] Cichosz, J.. Experimental characterization and numerical modeling of the mechanical response for biaxial braided composites. Ph.D. thesis; Technische Universit¨ at M¨ unchen; 2016. [38] Hexcel, . HexFlow RTM 6 - product datasheet. http://www.hexcel.com/; accessed: 23/07/16.

21

Figure 1: Surface scan of the (±30◦ ) braided fabric.

(a)

(b)

(c)

Figure 2: Test set-up for tension (a), specimen and gripping (b) and compression setup (c).

22

Figure 3: Principle for evaluation of the loading/unloading experiments.

11,x


x

11

x

11

x

x

11

x

1F+

11 2F-

y

22,y

y

y 22

22

2F+

OA00

OA15

OA30

Figure 4: Overview of the fiber orientation of the

(±30◦ )

22

OA45

OA60

x 10

Ex experiments

7

E0 experiments x

UD (±29°) UD (±31°)

6 5 4 3 2 1 0 0

10

20

30

40 50 Off−axis angle [°]

60

70

80

90

Figure 5: Tensile Young’s Moduli Ex and Ex0 over the off-axis angle.

23

22

OA90

experiments (x equals the load direction).

4

8

11,y

y

22

22

Modulus [MPa]

1F-

11

900

PT_OA00 PT_OA15 PT_OA30 PT_OA45 PT_OA60 PT_OA90

800 700

xx [MPa]

600 500 400 300 200 100 0 0

0.005

0.01


xx []

0.015

0.02

0.025

Figure 6: Representative stress-strain curves from the tensile off-axis experiments.

Figure 7: Failure process recorded with a high-speed camera from the tensile off-axis experiments.

24

Figure 8: Failure modes of the specimen observed in the tension (upper) and compression (lower).

25

500 450 400

300 250

σ

xx

[MPa]

350

200 150 100 50 0 0

0.005

0.01

ε [−]

0.015

0.02

0.025

xx

(a) OA00 700 600

σ

xx

[MPa]

500 400 300 200 100 0 0

0.005

0.01 ε [−]

0.015

0.02

xx

(b) OA15 200

100

σ

xx

[MPa]

150

50

0 0

1

2

3 εxx [−]

4

5

6 −3

x 10

(c) OA45 Figure 9: Representative loading/unloading stress-strain curves for OA00, OA15 and OA45.

26

120

100

60

σ

xx

[MPa]

80

40

20

0 0

1

2

3

4 εxx [−]

5

6

7

8 −3

x 10

(a) OA60 100 90 80

60 50

σ

xx

[MPa]

70

40 30 20 10 0 0

0.002

0.004

0.006 ε [−]

0.008

0.01

0.012

xx

(b) OA90 Figure 10: Representative loading/unloading stress-strain curves for OA60 and OA90.

−3

x 10

3 inelastic strain [−]

1 OA00 OA15 OA45 OA60 OA90

3.5

Normalized Modulus [−]

4

2.5 2 1.5 1

OA00 OA15 OA45 OA60 OA90

0.9

0.8

0.7

0.5 0.6

0 0

0.005

0.01 specimen strain ε(1) [−]

0.015

0.02

0

0.005

0.01 specimen strain ε(1) [−]

0.015

0.02

xx

xx

(b)

(a)

Figure 11: Inelastic strains (a) and normalized modulus (b) measured from loading/unloading experiments. Specimen strain refers to the strain at the unloading point (cf. Fig. 3).

27

F- ply

1F11

2F22 F+ ply

Figure 12: Relative yarn ply stresses over off axis angle (loading was adapted to achieve a constant global strain of εxx = 1% for all off-axis angles).

900 PC_OA00 PC_OA15 PC_OA30 PC_OA45 PC_OA60 PC_OA90

800 700

σxx [MPa]

600 500 400 300 200 100 0 0

0.01

0.02

εxx [−]

0.03

0.04

0.05

Figure 13: Representative curves for stress from the compressive off-axis experiments (dotted lines refer to the tensile experiments).

900

600

79±3

204±7

114±4

787±46

605±31

100

581±29

200

420±13

300

198±8

400

441±28

500

468±22

8903±380

17306±744

41253±1377

36510±1858

64841±1589

63755±1204

46982±3137

50466±2136

4

1x10

35420±2505

4

2x10

8989±197

4

3x10

16920±333

4

700

300±22

failure stress [MPa]

4

5x10 4x10

PT PC

800

312±2

PT PC

4

6x10

39819±1067

Young's modulus [MPa]

7x104

0

0 OA00

OA15

OA30

OA45

OA60

OA90

OA00

(a)

OA15

OA30

OA45

OA60

OA90

(b)

Figure 14: Comparison of Young’s modulus (a) and failure stress (b) from tensile (PT) and compressive (PC) off-axis experiments. Error bars correspond to the standard deviation.

28

1500

[MPa]

1000

σxx

UTS

FF F− (UD) TF F+ (UD) FF F− (UDeq) TF F+ (UDeq) 500

0 0

10

20

30 40 50 60 Off−Axis−Angle ψ [°]

70

80

90

(a) 1500

[MPa]

1000

σxx

UCS

FF F− (UD) TF F− (UD) FF F− (UDeq) TF F− (UDeq) 500

0 0

10

20

30 40 50 60 Off−Axis−Angle ψ [°]

70

80

90

(b) Figure 15: BB30 off-axis failure envelopes in tension (a) and compression (b). The points in the curves refer to the experimental results.

29

Table 1: HTS40 fiber and RTM matrix elastic and strength properties extracted from [37] and [38]

HTS 40 elastic Ef 11 [MPa] Ef 22 [MPa] Gf 12 [MPa] νf 12 [-]

HTS 40 strength Xf,T [MPa] Xf,C [MPa]

218400 18100 21800 0.305

3040 1499

RTM6 Em [MPa] νm [-] X [MPa]

2890 0.35 75

Table 2: Calculated oblique tab angles for the (±30◦ ) biaxial braid.

off-axis angle ψ [◦ ] oblique angle φ [◦ ]

0 90

15 -56.3

30 90

45 32.3

60 39.1

90 90

Table 3: Input properties for equivalent laminate model (properties given for 60% fiber volume fraction).

Elastic E11 [MPa] E22 [MPa] G12 [MPa] ν12 [-]

UD

UDeq

134100 7640 4100 0.31

126000 6900 4500 0.22

Strength Xt [MPa] Xc [MPa] Yt [MPa] Yc [MPa] SL [MPa] 1

UD

UDeq

2364 1448 75 1491 70

1475 1134 50 246 88

: values estimated

30