Carbon composites based on multiaxial multiply stitched preforms. Part 3: Biaxial tension, picture frame and compression tests of the preforms

Composites: Part A 36 (2005) 1188–1206 www.elsevier.com/locate/compositesa

Carbon composites based on multiaxial multiply stitched preforms. Part 3: Biaxial tension, picture frame and compression tests of the preforms S.V. Lomova,b,*, M. Barburskia,1, Tz. Stoilovaa,2, I. Verpoesta, R. Akkermanc, R. Loenderslootc, R.H.W.ten Thijec a

Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg, 44, B-3001 Leuven, Belgium b On leave of absence from the St. Petersburg State University of Technology and Design, Russia c Department Mechanical Engineering, Universiteit Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Received 1 October 2004

Abstract Deformability of bi- and quadri-axial multi-axial multiply stitched preforms is studied in biaxial tension, shear (picture frame test) and compression. The results complement KES-F measurements in the low load range, reported in the Part 2 of the series (Compos A, 34, 2003, 359–70). The biaxial tension tests reveal a strong interrelation between the two directions of tension in the case of tension in bias direction (relative to the fibres) and independence of deformation in two directions for tension in fibre direction. Non-linearity of the initial part of the tensile diagram due to fibre misalignment is demonstrated. The picture frame test is combined with full-field optical measurements of the shear strain field, allowing true registration of the fabric shear angle (which differs from the shear angle of the frame). Difference between the shear behaviour in different directions relative to the stitching is shown. Thickness is measured for one of the sheared fabrics. Compression tests reveal a high compressibility of the preforms (up to 60%) and a limited nesting effect for compression of the laminates. The compression tests are done also on sheared fabrics. q 2005 Elsevier Ltd. All rights reserved. Keywords: Multi-axial preforms

1. Introduction Multiaxial multiply fabrics (MMF), also called ‘noncrimp fabrics’ (NCF) are a promising class of composite preforms, featuring a low cost and high productivity textile processing technology and mechanical properties close to those of unidirectional laminates. Part 1 in the present series [1] describes the internal geometry of MMF. Deformability of MMFs is studied in Part 2 [2] (measurement with KES-F for low loads) and Part 5 [3] (change of internal geometry under shear); here we continue these studies for a ‘normal’

* Corresponding author. Tel.: C32 16 32 13 00; fax: C32 16 32 19 90. E-mail address: [email protected] (S.V. Lomov). 1 Current address: Technical University of Lodz, Poland. 2 Current addres: Technical University of Sofia, Bulgaria.

1359-835X/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2005.01.015

range of tension, shear and compression loading (with the same fabrics and one more fabric added to the set). The most important deformation mode of a preform in forming is shear. Shear resistance of MMFs was subject of a number of publications [4–6]. An important feature of the MMF shear behaviour is the difference of shear resistance for different directions of the test vis-a`-vis the stitching. We also observed these differences. Comparison of the preforms with different structure, availability of full information of the preform internal geometry and their behaviour at low loads [1,2] allow more insight in the related phenomena. The picture frame test, as has been recently revealed by the international benchmarking round-robin exercise [7], is a difficult test to standardise and interpret the results. Details of the test procedure (frame construction, pretension of the samples) are not readily provided in the previous publications on shear of MMFs. In the present paper the test procedure is presented thoroughly, including full-field optical registration of the strain field of the fabric.

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The latter, apart from assessment of uniformity of the fabric shear, allows relating the measured shear force to the true average shear of the fabric, which differs from the shear angle of the frame. We also demonstrate strong a dependency of the picture frame test results on the fabric pretension. An important aspect of the shear behaviour of a fabric is change of its thickness. The paper presents the measurements of thickness of one of the fabrics in the picture frame test. There are no publications on biaxial tension of MMFs known to the authors, apart from a qualitative discussion in [8]. The tensile behaviour of a preform can seriously influence it’s drapability, as blankholders always introduce tension in the actual forming process. Moreover, this tension is not uniaxial. Apart from a quantitative characterisation of the preform behaviour, the biaxial tensile test must answer two qualitative questions, which are discussed in the paper: – When tested in the direction of fibres, how large is the initial non-linear region of the stress–strain diagram, caused by crimp of the fibres? The lesser this region, the more close to reality will be the assumption of linearity of the preform resistance (which would be advantageous to use to make the draping simulation less computationally demanding). – Do tension deformations in two directions affect one another (as it is the case for woven fabrics)? If yes, then the independent description of the fabric tensile resistance in two directions, adopted in draping codes [9], does not describe the real behaviour and the material models should be made more complex. The compression behaviour of MMFs has been studied just scarcely before [2,10–12]. Knowledge of the compression diagrams is necessary to calculate the thickness of a preform in VARI or RTM-like processes, where it is not defined by the distance between rigid parts of the mould, but by the pressure involved in the process, acting on the flexible part of the mould. It is also interesting to observe and assess the degree of nesting in a MMF laminate (a model of the nesting is presented in [13]). Apart from this, the compression behaviour determines normal forces, acting on a preform during forming, hence friction between the preform and the tool and between the preform layers, which strongly affects the preform formability (friction data are given in Part 2 of the series [2]). In an actual composite forming process a perform is under simultaneous action of compression and shear. No data on compressibility of sheared MMFs are found in the literature. The paper reports results of such a test, which clearly show that the volume of a fabric is changing in the process of shear not only for an uncompressed fabric (as it has been observed in the shear frame test), but also for a fabric under a given pressure.

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The work reported here was done in 2003–2004 in the Department of Metallurgy and Material Engineering, Katholieke Universitait Leuven, and in the Department of Mechanical Engineering, Universiteit Twente. The results were partially reported in conferences [14–18].

2. Materials and test samples Four fabrics are studied in this paper (Fig. 1). The biaxial fabrics B1, B2 and the quadriaxial fabric Q are the same as those used for KES-F characterisation in the part 2 of this series [2]. Fabric B3 is added for this part of the paper series. Their parameters are shown in Table 1. The terminology used for description of the defects in the fibrous layers, induced by the stitching, is explained in Part 1 of the series [1]: We distinguish between ‘channels’, which designate a continuous opening in a fibrous ply (face and back of the fabric B2, face of the fabric Q), and ‘cracks’, which are localised openings of romboidal shape (fabric B1 and B3, back of the fabric Q). Fabric B1 has additional stabilising glass yarns, inserted in 908 direction between its two plies, spaced by 50 mm. Table 2 summarises the tests done for all the fabrics.

3. Shear Only the biaxial fabrics (B1, B2 and B3) were tested in the picture frame tests, as for a quadriaxial fabric the test is impossible because of tension applied to the fibres oriented in the load direction. Shear tests were done in the laboratories of K.U. Leuven (fabrics B1 and B2) and University of Twente (fabric B3) on the identical picture frames. Tests in K.U. Leuven were supported by full-field strain measurements; in the tests in University of Twente, the thickness of the sheared fabric was measured with a special device (see Section 3.7). 3.1. Picture frame test Fig. 2(a) and (b) depicts the picture frame of the Department MTM, K.U. Leuven, and shows the method of gripping the sample. Hinge 1 moves freely in the groove 3. Hinge 2 is connected to the bottom grip of the machine. When the upper plank moves up, pulling at point A, the frame starts closing, its sides rotating in hinges; hinge 1 goes up inside the groove 3. Note that the centres of the hinges collineate with the internal edges of he frame. The maximum stroke of the machine, allowed by the groove 3, is 22 mm, which gives the maximum shear angle of the frame 508. The picture frame of the Department of Mechanical Engineering, Universiteit Twente, has the same dimensions and gripping system. The loading arrangement is, however, different: the load is applied directly to the hinges 1 and 2.

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Fig. 1. Samples of MMF, face and back.

Hence the displacement of the hinges is not restricted, and the test can go on to higher shear angles. The frame was mounted on a Zwick machine, the force is measured with a 1 kN force-cell and a 12 bit AD converter, which results in a step size of 0.2441 N in the force data. In K.U. Leuven, the frame was mounted on an Instron 4467 machine with a 1 kN load cell with the same precision parameters as in Twente. The shear angle of the frame g is related to the displacement of the machine x (displacement of the point A) by: g½8 Z K0:021x2 C 2:689x½mm

(1)

which is an approximation (R2Z0.9999) of a solution of a system of trigonometrical equations describing the movement of the frame. A test speed of 20 mm/min was used in all the tests. First, the load–displacement diagram was registered with an empty frame (Fig. 2(e)), to be subtracted from the load diagram in the test with the fabric, to produce the net force F, acting on the fabric. Lips 4 are pressed by screws in plates 5. The lips and the frame beneath them have a wavy surface, securely gripping a fabric sample (Fig. 2(b)). When the sample is fixed in the frame, it is possible to feel that it is tensed. The deformation

Table 1 Parameters of the multi-axial multi-ply stitched performs Description

Number of plies

Orientation of plies, degrees

Mass of the fabric (g/sq m)

Stitching pattern

Gauge (needles per inch)

Plies

Tow

B1

B2

B3

Q

Bidiagonal carbon fabric Biaxial carbon fabric

2

C45; K45

322G16 Tricot

5

2

0;90

329G14 Tricotchain

5

Bidiagonal carbon fabric Quadriaxal carbon fabric

2

C45; K45

541G12 Chain

5

4

0; K45; 90;C45

629G31 Tricotchain

5

12K Toray T700 50E 24K Toray T700 50E 12K Tenax HTS 5631 12K Toray T700 50E

Stitching

Mass (g/sq m)

Yarn

Defect in fibrous plies

A (mm)

B (mm)

Mass (g/sq m)

Face

Back

Type

Width (mm)

Length (mm)

Type

Width (mm)

Length (mm)

156G8

PES 7.6 tex

4.94

1.71

3

Crack

0.28

5.05

Crack

0.43

7.15

150G8

PES 7.6 tex

5.03

2.64

6

Crack

0.18

4.2

Channel

0.40

n/a

260

PES 5 tex

5.79

2.22

5

Crack

0.28

7.7

Crack

0.29

8.0

156G8

PES 7.6 tex

5.09

2.58

6

Channel

0.66

n/a

Crack

0.48

7.28

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Preform ID

1191

1192

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Table 2 Tests summary Shear

B1 B2 B3 Q

Biaxial tension

Shear diagram

Strain-mapping

Thickness

C C C K

C C K K

K K C

of the pre-tensed fabric cannot exceed a value of 2.8%, given by the geometry of the lips. In practice the pretension is significantly smaller: a very rough estimation by the difference in the distance between the stitching before and after mounting of the fabric gives the range of the pretension as 0.5.1%. In the tests performed in Universiteit Twente, the mounting procedure was different, with the aim of minimising the fabric tension. The grips were loosened to the point where the tension in the fabric disappears (by a feeling of the operator). The effect of this is discussed in Section 3.5. The fabric is firmly gripped in the frame, with the fibres parallel to the frame sides. During the test, the fibres near the gripping are gradually bent, and the shear angle in the central part of the sample is different from the shear angle of the frame. The lesser the bending resistance near the grips, the smaller this deviation. One of the ways to minimise it, is to take out of the fabric the fibres parallel to the frame side near it (Fig. 2(c) and (d)). In the preliminary test it was found that without this measure the test is impossible to perform because of the extensive wrinkling of the material. Therefore the fibres near

Compression

C C K C

Unsheared

Sheared

C C C C

C C C K

the grips were taken out in all the experiments described in this paper. The result of the test is the dependency of the shear force per unit width of the frame side T (the normalisation issues are discussed in [19]) and the shear angle of the frame g. The latter is easily calculated from the displacement on the testing machine (1); the former is calculated as TZ

F ; 2w cos a2

aZ

p Kg 2

(2)

where F is the force applied by the loading machine, w is the width of the gripped side of the sample, a is the frame angle, g is the shear angle. Three loading cycles were performed for each sample. Load diagrams and strain fields during unloading (return of the frame to initial rectangular configuration) were not registered. In some regions of the shear diagrams the force measurements were performed at the limit of the machine precision (difference in tensile force of the frame with fabric and the empty frame about 1 N, which corresponds to the shear force less then 0.01 N/mm). Another factor, which may affect the precision of the measurements, is friction in

Fig. 2. Picture frame (Department MTM, K.U. Leuven): (a) Empty frame: 1,2—hinges, 3—groove, 4—lip, 5—plate with screws ; (b) Grips; Frame with samples of fabrics B1, SC test (c) and B2, SS test (d); (e) Load–displacement diagram of the empty frame.

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Fig. 3. Difference of the shear angle of the fabric B2 and frame shear angle (a), error bars show standard deviation; image of the deformed fabric B2, frame shear angle 148 (b) and distribution of the fabric shear angle (c).

the hinges. In the presence of high fabric pretension this is uncontrollable factor, which might had lead to unsatisfactory results in the first shearing cycle (see Section 3.4). 3.2. Different behaviour: Fabrics B1/B3 and B2, test direction Fabrics B1 and B3 can be mounted in the picture frame with their fibres parallel to the frame sides in two ways: with the stitching parallel to the loading direction and across it. In the former case the stitching, firmly clamped by the frame grips, is in tension. This test direction will be abbreviated as ST (stitching–tension). The shear conditions of the test are therefore violated, and one can expect high resistance to deformation. In the latter case the stitching is in compression, which should not affect the test result very much. This test direction will be abbreviated as SC (stitching – compression). These observations were also made in the previous studies of deformability of MMFs [4–6]. The presence of the glass stabilising yarns introduces another

complication: they are oriented along the tension directions (Fig. 2(c)). Therefore even in the SC tests some ‘parasitic’ tension may be present. To minimise it, the glass yarns were cut near the grips after mounting the sample. In spite of this, the glass yarns are firmly set inside the fabric by the stitching. This leads to irregularities of the fabric shear, shown in the next section. When fabric B2 is mounted with the fibres parallel to the frame sides, the stitching is also parallel to them. Hence there should not be a difference in the test direction. This case will be referred below as SS (stitching-shear). 3.3. Relation between shear of the frame and average shear of the fabric To constitute a true characterisation of the fabric shear behaviour, the test must provide dependency of the shear force on the average shear angle of the fabric. Due to the complications of the gripping discussed above, one cannot be sure that it is the same as the shear angle of the frame.

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(a) 0.4

0.2

T, N/mm

The shear angle of the fabric was measured using the ARAMIS strain-mapping system. The reader is referred to [20] for details of the measurement technique and data processing. Fig. 3 shows results of the full-field registration of the shear field. The curves are the result of averaging data for three samples. There was no statistically significant difference in the average shear angle of the fabric in different shear cycles. Fabric B1 develops a lot of local wrinkling, which prevents resolving the deformation field after the frame shear angle reaches approximately 188, hence results for it are not shown. Fabric B2, in the SS test, behaves in a more stable way, and the strain field can be resolved up to the maximum shear angle of the frame. The local shear angle of the fabric was determined by the angle between the diagonals of initially square facets shown in Fig. 3(b). The measurements show the following:

SC

Shear force, N/mm

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ST

0.1

0.3

0 0

0.2

frame angle 2

1st cycle 2nd cycle 3rd cycle

0.1

0 0

10

20

30

40

Frame shear angle, ˚ (b) 0.3 1st cycle

3.4. Shear diagrams, Fabrics B1 and B2

2nd cycle 3rd cycle

Shear force, N/mm

1. The average shear angle of the fabric is the same as the shear angle of the frame. 2. The scatter of the local shear angle is about G28. The size of the facets is about 15!15 mm. The local shear angle in these measurements is the result of averaging over three unit cells of the fabric, hence local variations within unit cells do not cause the scatter value given above. This value (G28) is quite low, allowing concluding that the shear field is fairly even.

0.2

0.1

0 0

Fabrics B1 and B2 were tested in laboratory of the Department MTM, K.U. Leuven. Fig. 4 shows the results of the picture frame tests on fabrics B1 (SC and ST tests) and B2 (SS test): shear force as a function of the frame shear angle and average fabric shear angle. Three shear cycles are shown. The diagrams for the first shear cycle for both fabrics show an extremely irregular behaviour and evidence tension of the fibres in the frame. This type of behaviour was labelled in [20] as ‘bad tests’, and normally such tests are discarded from the data processing. The cause of ‘bad’ behaviour of a woven fabric has been identified in [20] as deviations of the yarns from directions parallel to the frame sides and variations of the pretension of the different yarns. The arrangement of MMF sample in the frame is much more difficult then mounting of woven fabrics. Fibres, which have to be taken away near the grips, are firmly fixed in the fabric by stitching. Hence the disturbances given to the fibres in the fabric by the process of taking these fibres away are more serious than in a woven fabric. These disturbances are larger for fabric B1, as in this case the fibres are inclined 458 to the stitching, and ‘cracks’ in the fibrous ply do not form continuous fibre bundles between the stitching sites (as ‘channels’ in fabric B2 do). We were not able to make a ‘good’ test (without evidence of the fibre tension) in the first

10

20

30

40

Frame shear angle, ˚ Fig. 4. Shear diagrams of fabric B1, SC (a) and ST (inlet) tests, and fabric B2, SS test (b). Error bars show standard deviation of five tests. Only loading diagrams were registered.

shear cycle. After the first cycle the sample is ‘conditioned’ [19–25] and its behaviour is much more stable. In our measurements the first cycle represent the experimental rig behaviour rather then the material itself, and therefore was not used for the material characterisation. In the second and the third shear cycles some tests also resulted in ‘bad’ diagrams. These were considered as faults in mounting the sample and discarded from the data processing. For the ‘good’ tests the second and the third shear cycles produce very close diagrams for both fabrics. The differences lie well inside experimental scatter, but the third cycle gives shear resistance some 5% less then the second. The scatter is quite large for fabric B1 (up to 50%), and less for fabric B2 (about 20%). On the closer inspection the diagrams for fabric B2 bear evidence of the fibre tension even on the second and the third cycles. The difference in the shear diagrams of the two fabrics, compared in Fig. 5, is not large, but the shear resistance of fabric B2 is definitely lower then that of the fabric B1

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B1, 2nd cycle B2, 2nd cycle B1, KES-F B2, KES-F B3, 2nd cycle

Shear force, N/mm

0.12 0.1 0.08 0.06 0.04 0.02 0 0

10

20

30

40

50

60

Fabric shear angle, ˚ Fig. 5. Comparison of the shear diagrams of fabrics B1 and B2 (picture frame test and on KES-F) and fabric B3 (picture frame test).

(the initial region of the B2 diagram, possibly influenced by the fibre tension, still present in the second cycle, should not be considered). The fabrics having the same areal density, the difference in the shear resistance has to be attributed to the differences in the stitching pattern and direction, since the fabrics have the same areal density. The fibres are tight fixed by the tricot pattern in fabric B1; the 458 direction of the fibres does not connect diagonally the stitching sites (rectangular spacing 4.94!1.71 mm, Table 1). This produces ‘cracks’ in the fibrous ply, without formation of continuous fibre bundles in the plies. The tight fixation of the fibres is evidenced by a significant resistance of the fibres to pulling them out of the fabric (as it was done along the grips). In fabric B2 the fibres are fixed by the tricot-chain stitching much more loosely. There are ‘cracks’ on the face (08) ply and ‘channels’ in the back (908). The latter give fibres freedom to rotate during the shear deformation, behaving like a trellis up to a certain shear angle (about 238, judging by a geometrical estimation of the locking angle glockZarc cos(w/p), where w is the bundle width, p is the bundle spacing). Finally, Fig. 4(a) (inlet) shows results of ST tests of fabric B1, with the stitching in tension. The shear force (which actually represents the tensile resistance of the chain of the stitching loops) is five times higher, then in SC tests, and the shear modulus is 20 times higher; the test had to be stopped at the shear angle of 1.78 because of too high load on the load cell of the machine. 3.5. Shear diagram, fabric B3

To study the influence of the shear rate, the experiments were repeated at the machine speed from 10 to 1000 mm/min. No systematic variation of the shear resistance has been found, the curves changed within the experimental scatter range. The results demonstrate the same difference between the first, on one hand, and the second and the third, on the other, shear cycles. In this test the full cycle has been registered, showing a hysteresis effect. Measurements up to higher shear angles show a sharp increase of the fabric resistance, starting at the frame shear angle of around 458, which is in accordance with the measurements for fabrics B1 and B2 (Fig. 4). When sheared in the ST direction (negative shear angles in Fig. 6), the same increase of the shear resistance is registered, as for fabric B1 (Fig. 4(b)). In spite of the qualitative likeness, the quantitative results of the tests in Universiteit Twente (fabric B3) are quite different with the ones in K.U. Leuven (fabric B1 and B2). The shear resistance of fabric B3 is about 10 times lower then of fabrics B1 and B2 (Fig. 5), in spite of the fact that the areal density of the former is 50% higher then of the latter. This can be explained by the difference of the mounting procedure in two laboratories, which lead to difference in the fabric pretension. Fabric B3, tested with deliberately loosened grips in Universiteit Twente, had much less pretension then fabrics B1 and B2, which were tested in K.U. Leuven without special procedure to minimise the pretension and were subject of a considerable prestrain of about 0.5%. The reader is referred to the discussion and quantitative estimation of the pretension influence on the results of picture frame test in [20,26,27]. 3.6. Comparison with KES-F measurements (fabrics B1 and B2) When compared with KES-F measurements [2], Fig. 5, the picture frame shear diagrams show close values of the diagram slope, i.e. shear modulus of the fabric. However, the values of the shear force in the KES-F measurement are significantly lower then in the picture 0.04 0.03 0.02

st

1 cycle

nd

2

0.01

T, N/mm

0.14

1195

-10

0.00 0 -0.01

10

20

rd

3

30

40

-0.02 -0.03

Fabric B3 was tested in the laboratory of the Department of Mechanical Engineering, Universiteit Twente. Fig. 4 shows the results of the tests: shear force as a function of the frame shear angle. Three shear cycles are shown. The curves are an average of five experiments, which are quite reproducible: coefficient of variation in the range of 20%.

-0.04 -0.05 -0.06

gamma frame, degrees Fig. 6. Shear diagrams of fabric B3.

50

60

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frame test. This is explained by the difference in the level of the fabric pretension in the two tests. In the KES-F measurement [2], a controlled pretension of 0.01 N/mm is given to the fabric. In the picture frame test the pretension is not controlled, but by the values of the prestrain, given above as about 0.5%, and results of the tension tests (see Fig. 11 below), the pretension can be estimated as lying in the range 0.1.1 N/mm, which is by two orders of magnitude higher then in the KES-F test. 3.7. Thickness of the sheared fabric B3 The unit used to measure the thickness of the fabric during the experiment is shown in Fig. 7. The device consists of two circular plates that can slide along a rod. The right plate is blocked at the right side by a conical part. This allows tilting of a few degrees to assure that the right plate is parallel to the left plate. The fabric is locally distorted due to the rod penetrating the fabric. Therefore the inner 10 mm at the centre of the plates is removed. A small spring pushes the plates together. The spring is adjusted to a length where it delivers a pressure of 0.5 kPa on the fabric. The device can measure the thickness within the accuracy of G0.025 mm.

Fig. 7. Measurement of thickness of sheared fabric: (a) measuring unit, (b) typical diagram.

Fig. 8. Thickness of the sheared fabric B3: dependency on the shear angle. Lines: measurement, circles: best fit based on the constant volume assumption. Inlay: Close up of the sheared fabric.

Fig. 7(c) shows the results of a single experiment. The fabric is sheared up to approximately 638 during the experiment. This is the maximum shear angle the trellis frame can obtain due to the size of the measuring device. After that the trellis frame is returned to a 08 shear angle. This cycle is repeated three times. The experiment shows significant hysteresis. The thickness at the same shear angle also decreases after each cycle. This is in line with the observations during the transverse compression tests, as explained in the Section 5.4. Fig. 8 shows the averaged results of the fabric thickness during an increasing shear angle. A total of three experiments were performed and each experiment consists of three cycles. The constant volume fit starts at a shear angle of 08. The increase in thickness of the fabric up to 308 shear is slightly less than the increase expected based on the assumption of a constant volume. The correspondence would be better if the constant volume fit would start at an initial shear angle of 88, but then the deviation at high shear angles would be larger. The error bars in Fig. 8 also indicate a larger deviation in the experimental data at high shear angles. Fig. 8 also shows a phenomenon that could cause this larger deviation. Fibres and stitches start to buckle at high shear angles and can cause an addition increase in thickness. Generally, the experiments demonstrate that the increase in thickness of the fabric during shear deformation can be calculated with the assumption of constant volume for the fabric tested. This conclusion is valid for a low (0.5 kPa) applied pressure, and will be reversed for higher pressures in the compression study, Section 5.4.

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3.8. Validity of simplified models of shear In the forming simulation software [9] fabric shear is uncoupled with tension. Our measurements in this study, as well as results for woven fabrics [7,20,26,27] clearly show that this assumption is far from reality. However, it is not clear, in the absence of comparative simulations, whether

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a full shear diagram is needed for an acceptable simulation of the forming process. If an approximation of zero (negligible) shear resistance up to a certain locking angle of the fabric is enough to simulate a forming process with an acceptable accuracy, then the question of coupling of shear and tension is irrelevant. If, in certain situations, the shear stiffness value before locking has a significant influence on

Fig. 9. Biaxial tensile tester (a), clamping of the sample (b).

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the forming simulation, then the coupling shear-tension should be accounted for and the existing material model should be modified.

4. Biaxial tension Biaxial tension tests were performed for fabrics B1, B2 and Q. 4.1. Equipment and samples The biaxial tester of the Department MTM, K.U. Leuven (Fig. 9) is a tensile machine equipped with four independently controlled axes, developed for the study of deformation of textiles, films and thin sheets. The clamping system consists of freely moveable clamping rigs (mechanical or pneumatic) mounted on each axis. The axes movements are fully computer controlled; the output consists of force–displacement curves in the two principal directions. The apparatus can be used to investigate the constitutive behaviour, anisotropy and limits of deformation of the material. The types of tests that can be performed are: 1. Mono-axial stress tests with clamping in one single direction. 2. Biaxial tests with principal strain ratio’s varying between zero and infinity. 3. Shear tests using a tensile bar clamped over the centreline of the material The biaxial tensile tester has four different axes, which can all be driven separately. The machine has two force transducers in total, one for each direction. They can register a maximum force of about 5 kN, with an accuracy of 0.1%. The axes can be moved at different speeds, reaching from 25 to 175 mm/min, in steps of 25 mm/min. Rigid clamping of the samples is of first importance for the test. It can be ensured by making epoxy tabs, impregnating the fabric in the gripping sites. The ‘grab’ configuration of the samples was used in the tests (Fig. 10). 4.2. Results The fabric behaviour in biaxial tester is determined by the interaction between the yarns or fibres. The theory of the test is well-developed for woven fabrics, where interference between warp and weft is determined by the crimp of the yarns [27–33]. In multiaxial multiply fabrics, the fibres in plies are almost straight and are not interlaced one with another. They are, however, linked by the stitching. The extent of the link is different for different fabrics and different directions of the test. The tests were performed with the following ratios of deformation on the machine axes: ‘1:free’, meaning that only one pair of the clamps is used, ‘1:0’, when one set of

Fig. 10. ‘Grab’ sample for the biaxial test.

the clamps is moving, the other staying fixed, ‘1:1’ (equal deformations in both directions), ‘1:2’ and ‘1:5’ (ratio of deformation in two directions). Practically different speed of the axes was set, corresponding to the chosen ratio of deformations. The tests were performed in the 08/908 and C458/K458 directions relative to the production direction of a fabric. At the end of the diagrams, the apparent stiffness reduces because of the on-set of the slippage in the grips. In the case of 08/908 test of the fabric B1 and the C458/K458 test of the fabric B2 (Fig. 11) the deformation goes in the direction in-between the fibres. Stitching serves as ‘hinges’ between the two fibre systems in the plies. This ensures strong link between the two tension directions. Direction of the stitching in the fabric B1 is different in the tests in 08 and 908. No statistically significant difference was found in these two cases. In the uniaxial tension test in bias direction (Fig. 11(a)) the fabrics are highly extensible (‘bias extension test’). When deformation in the direction perpendicular to load is restricted (biaxial test, Fig. 11(b)), the stiffness of the fabric increases together with the decrease of the deformation ration (loading: perpendicular), shown in Fig. 11(b). This behaviour is caused primarily by the test configuration: fibres gripped in the clamp in one direction, are also gripped in the clamp in the other direction. The results of the tests should be considered as qualitative indication of the fabric behaviour, as the quantitative results depend on the test configuration. The test reflects the combination of shear and tension, which may happen in the actual forming. Comparing the diagrams for fabrics B1 and B2 in Fig. 11, one notices that the diagrams are quite close. Fabric B2,

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(b) 0.007

(a) 0.02

1:free

0.018

0.006

0.016 0.005

0.012

F, kN/mm

F, kN/mm

0.014

0.01 0.008 0.006

0.004

0.003

0.002

B1, 0

0.004 B1 45/45 0.002 0

0.001

B2 0/90 B2, 45 0.1

0

0.2

0

10

eps X, %

(c)

20

30

40

50

eps X, %

0.02 5:1 0.018 2:1 0.016 1:0

1:2

1:5

1:1

0.014

F, kN/mm

0.012

0.01 EpsX:EpsY 0.008

0.006 B1 0/90

0.004

B2 45/45 0.002

0 0

1

2

3

eps X, % Fig. 11. Tension of fabrics B1 and B2: (a) Biaxial and uniaxial in fibre direction (deformation ratios 1:free, 1:0, 1:1, 1:2, 1:5 for each fabric); (b) Uniaxial and (c) biaxial in the bias directions (ratio between deformations in two directions is shown on the curves, first value being the direction of the strain and load shown by the curve). Five tests are averaged for each curve, Cv z 5.10%.

however, offers higher load resistance, with identical areal density of the fabrics (Table 1). This can be attributed to the more straight fibres in the fibre bundles of fabric B2 (compare width of the cracks and channels in the two fabrics, Table 1, which gives the intensity of deviation of the fibres from straight lines).

In the cases of C458/K458 test for B1, 08/908 for B2 (Fig. 11(a)) and both directions for Q fibres lie in the directions of the tension. In this case one may expect non-linearity of the initial stage of deformation, because of waviness of the fibres in the plies. Fibres undergo straightening before receiving full load of the tension.

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Tension diagrams of fabric Q in 0/90 and C45/K45 tests are quite similar to those of fabrics B1 and B2 and not included in the Fig. 11(a). No link between the test directions is revealed by the tests of fabrics B1 and B2. The curves for the different deformation ratios are mixed and are not distinguishable statistically. Fabric B2 exhibits higher tension resistance because of the straighter fibres in it (see above). It is interesting to note that the non-linearity range in strain (about 0.1%) is of the same order as has been registered for woven fabrics [28]. Measurements in the fibre direction are not easy to perform and interpret because of the high rigidity of carbon fibres, which is comparable with the stiffness of the machine. Results presented here are corrected taking in the account this stiffness. In the future work the biaxial tests will be performed on the reconstructed machine with fullfield registration of the strain, which would allow more precise quantitative analysis. 4.3. Validity of simplified models In forming simulation software [9] fabric tension is normally characterised independently for two directions, and it is preferable to have a linear tension diagram of the fabric for the sake of computational effectiveness. Our observations lead to the following conclusions regarding these two assumptions. All the measured diagrams exhibit a nonlinear behaviour. The authors are not aware of studies, where simulation with linear and non-linear diagrams would be compared. Such a study is needed to conclude on the necessity of using true non-linear diagrams instead of the linear approximation. One may argue that, in the absence of comparative simulations it is not clear if incorporation of tensile data is needed at all, and whether the assumption of unstretchable fibres would not be enough for an acceptable simulation. Because of low deformations in the fibre direction this reasoning might be true, but one should take into account interdependence between tension and shear discussed in the Section 3.8. Calculation of the tension forces is of paramount importance for the correct calculation of the shear resistance. Model of unstretchable fibres does not allow such a calculation. Our results show that there is no significant coupling between the tension directions, if they coincide with the fibre directions in the fabric. Hence this assumption in the material models of the existing simulation software can be retained.

5. Compression Compression tests were performed in the laboratory of Department MTM, K.U. Leuven. For biaxial fabrics B1, B2 and B3 relaxed and 308, 458 and 608 sheared configurations

have been measured. For all the unsheared fabrics (B1, B2, B3 and Q) the nesting behaviour was studied in compression of one, two and four layer of the fabric. In addition to the results reported in [2], KES-F measurements on fabric B3 and sheared fabrics were performed in the laboratory of Centexbel, Gent. 5.1. Experimental procedure A flat cylindrical punch with a diameter of 50 mm is mounted in the Instron 4467. A load cell of 1 kN is used. The lowest pressure measured with sufficient accuracy is 1.5 kPa, which is the upper limit of the KES-F pressure range. The fabrics were measured in unsheared and sheared configurations. In the latter case, the sheared state of the fabric was fixed with a specially designed shear frame. Five tests were performed for every sheared configuration. To study the effect of nesting of the layers [13], tests on one, two and four layers of each fabric were performed. In each test three compression cycles were performed, up to the pressure of 200 kPa. 5.2. Summary of the instron measurements. Comparison with KES-F The behaviour of the fabrics in different tests (number of layers, compression cycle, shear angle) exhibits common well-known features of compression, which were already evident in the low range KES-F tests [2]. The initial stiffness is low, fabrics are compressed to about 70.80% of the initial thickness at a pressure of 50 kPa. With the pressure increase to the maximum value of 200 kPa, the thickness of the fabric additionally decreases to about 60.70% of the initial thickness. Actual values depend on the number of layers and compression cycle. Fig. 12 shows typical results of the Instron tests: one layer of fabric B3 for different compression cycles and different shear angles. One sees that the diagrams of the second and the third compression cycles are very close to one another. To make the data more easily overviewed, we do not present below data on the third cycle. As mentioned above, the Instron diagrams do not provide reliable data for the low load range, hence, do not allow determining the initial fabric thickness. These data are provided by the KES-F measurement. The Instron and KESF measurements (fabric B3) are compared in Fig. 13, which shows typical features, common for the fabric behaviour in all the studied cases. For the first cycle KES-F and Instron measurements fairly correspond to one another. A certain jump is evident when passing from KES-F to Instron results for the second cycle. This can be explained by the fact that in contrast with the KES-F measurements in lower pressure range (up to 5 kPa), the first cycle up to 200 kPa cannot be treated as ‘conditioning’, as it gives permanent high deformation to the sample (note that the thickness at the start point of the second cycle of the Instron diagram in

S.V. Lomov et al. / Composites: Part A 36 (2005) 1188–1206

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Fig. 12. Compression diagrams, fabric B3, one layer. Figures in callouts show compression cycles.

 a T0 K T p Z T K Tmin p

(3)

where T is the fabric thickness, mm, p is the pressure, kPa, p* is a parameter, kPa, T0 is a parameter, mm, corresponding to the fabric thickness in the relaxed state (pZ0), Tmin is a parameter, mm, corresponding to the fabric thickness at pZf, a is a dimensionless power parameter.

Approximation (3) was applied to the data set as follows. Consider a set of repetitive measurements for a given test parameters: type of fabric, number of layers, shear angle, number of the compressive cycle. The set of measurements normally consists of five Instron diagrams. These diagrams are processed to produce an averaged diagram. The coefficient of variation of such a set lies within 5.10% for all the measured data. As discussed above, the averaged Instron diagram does not allow to define T0. This is defined by the KES-F measurement in the second cycle, as the first KES-F cycle serves to condition the sample. Hence, the averaged KES-F second cycle diagram was added to

B3, unsheared, one layer 1.4 KES-F, 1st

1.2

Instron, 1st KES-F, 2nd

1

Instron, 2nd

T, mm

Fig. 13 almost coincides with the end point of the first cycle). Based on this, the first cycle of the Instron tests is used below for discussions on the fabric behaviour. Unfortunately, this means that KES-F measurements cannot be used to supplement the Instron data for the second compressive cycle. These observations also mean that the decision, which cycle to use for a fabric characterization purpose, has to be reconsidered in each particular case, depending on the actual loading of the fabric in the manufacturing process under consideration. As stated in the Part 2 of this series, the ‘conditioning’ of the sample by a first cycle of compression is recommended for KES-F measurements at low loads. Hence, the second cycle of KES-F test is adopted as representing the fabric behaviour. Based on this, in the future the correct procedure of testing the fabrics in the high loads range should be as follows: (1) first cycle: condition the sample by applying pressure of 5 kPa; (2) second cycle: measurement up to the desired pressure. To present the considerable amount of data in a concise form, the diagrams were approximated with a power law:

0.8 0.6 0.4 0.2 0 0

5

10

15

20

p, kPa Fig. 13. Compression diagrams: Comparison between Instron and KES-F measurements. Unsheared fabric B3, one layer.

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Table 3 Compression tests: Parameters of the Eq. (3) Fabric

Layers

Shear angle (8)

Cycle

T9, mm

Tmin, mm

p9 (kPa)

a

B1

1

0

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1.153 0.957 1.103 0.944 1.294 1.169 2.082 1.541 4.268 2.972 0.829 0.835 1.263 1.320 1.313 1.312 1.425 1.718 2.673 3.203 0.945 0.870 1.119 1.098 1.400 1.362 1.683 1.530 1.517 1.540 2.826 2.144 2.794 2.893 3.499 3.291 4.103 4.401 5.048 5.020 1.360 1.046 2.410 2.310 4.868 3.972

0.324 0.251 0.240 0.261 0.253 0.309 0.635 0.547 1.245 0.979 0.309 0.246 0.320 0.274 0.224 0.352 0.593 0.527 1.135 1.050 0.396 0.485 0.210 0.462 0.458 0.587 0.602 0.667 0.850 0.834 1.240 1.048 1.178 1.260 1.805 1.669 2.322 2.444 2.137 2.069 0.601 0.515 1.054 0.961 2.072 2.005

1.343 1.097 3.402 1.117 4.777 1.100 1.901 4.824 1.490 4.952 2.660 0.953 2.088 0.153 3.621 0.459 3.845 0.802 6.368 1.346 6.932 3.691 11.688 1.128 4.369 1.562 4.038 3.133 15.231 1.926 3.073 1.335 7.950 0.744 6.309 1.577 20.364 0.887 4.836 0.685 2.652 8.742 5.707 5.297 4.719 14.450

0.631 0.339 0.447 0.386 0.432 0.395 0.624 0.438 0.620 0.393 0.709 0.372 0.761 0.407 0.360 0.450 0.546 0.360 0.476 0.330 0.382 1.013 0.240 0.575 0.392 0.700 0.673 1.353 0.535 0.335 0.962 0.358 0.583 0.468 0.578 0.326 0.491 0.341 0.746 0.474 0.637 0.448 0.484 0.367 0.476 0.452

30 45

B2

2

0

4

0

1

0 30 45

B3

2

0

4

0

1

0 30 45 60

2

0 30 45

4

0 30 45

Q

1

0

2

0

4

0

the averaged Instron first cycle diagram for p!5 kPa. The combined diagram was used via a least square minimisation procedure to determine the best-fit parameters T0, Tmin, p0 and a in (3). In this case T0 represents true initial fabric thickness, and the approximation (3) can be used in the pressure range 0.200 kPa. For the second compressive cycle, KES-F and Instron data do not correspond one to another. Therefore only averaged Instron diagram was used to fit the Eq. (3). Such an approximation is strictly usable only in the range 5.200 kPa, and in this case T0 value has to be considered as an extrapolative estimation of the fabric thickness at the beginning of the second compression cycle.

The results of this processing are summarised in Table 3, which provides the results of the compression tests in full. For the discussion of characteristic features of the behaviour of the fabrics, the data on the first compressive cycle will be used. 5.3. Trends in the compressive behaviour The studied fabrics show quite similar compressive behaviour. Moreover, certain dependency can be established on the areal density of the fabrics. Consider parameters of the compression diagrams for the first compressive cycle of the unsheared fabrics

S.V. Lomov et al. / Composites: Part A 36 (2005) 1188–1206

(a)

1203

(b) 10 p*

B1

One layer, 1st cycle

1.2

B1 approx

a

B2

p*, kPa; a, [-]

B2 approx B3

1 1 300

p*ave= 3.40 kPa

400

B3 approx

areal density, g/sq m

500

600

Q

700

Q approx

0.8

T, mm

aave= 0.590 0.1

0.6

1.6

Thickness, mm

1.4

y = 8.29E-04x + 6.94E-01 R2 = 2.97E-01

0.4

1.2 T0 Tmin Linear (T0) Linear (Tmin)

1 0.8

0.2

0.6 0.4

0

0.2 0 300

0

y = 7.89E-04x + 4.84E-02 2 R = 8.17E-01

400

500

600

100

200

300

400

500

p, kPa 700

areal density, g/m2 Fig. 14. First compressive cycle, unsheared fabrics, one layer: (a) Parameters of the Eq. (3) vs areal density of the fabric; (b) Compression diagrams, points— measured, lines—calculated using (3) with averaged parameters.

(one layer). Fig. 14(a) shows the dependency of these parameters on the areal density of the fabric. Parameters T0 and Tmin increase with the increase of the fabric areal density, as it could be expected. Parameters p* and a do not exhibit a trend—the shape of all the diagrams is very much the same. Hence, the compression diagrams of the studied fabrics can be approximated with Eq. (3), where p* and a are the same for all the fabrics (averaged values, shown in Fig. 14(a)), and T0 and Tmin are calculated using the linear regression formulae, also shown in Fig. 14(a). Fig. 14(b) compares the results of such an approximation with the measurements. The fabrics in question are obtained from different producers and were manufactured using different heavy carbon tows (see Table 1). The similarities of the compression behaviour and the recognisable trend vs areal density of the fabrics reflect similarities of the fibre bundle structure and of the textile manufacturing process. The approximations shown in Fig. 14 could be probably applied to other MMFs.

Table 3, the applicability of this hypothesis can be examined closely. Consider parameters of the compression diagrams for the first compressive cycle of the sheared fabrics (one layer). Shape parameters p* and a do not exhibit a trend on the shear angle. Thickness parameters T0 and Tmin increase with the increasing shear. Fig. 15 plots this dependency for thickness of the fabrics, normalised by the initial thickness of unsheared fabric. Fabric B3 reasonably well conforms to the ‘1/cos’ curves, corresponding to the assumption of the constant volume of the fabric, for initial and minimum thickness, as well as for the thickness at the intermediate pressure 50 kPa. For fabrics B1 and B2 this is the case only for thickness at 50 kPa. Initial and minimum thickness curves considerably deviate from the ‘1/cos’ law, which can be explained by variations of the behaviour of surface of the fabric for initial thickness. For the minimum thickness the deviations are explained by the fact, that it represents infinite pressure, when arrangement of the fibres in tows determines possibility of their compaction, irrespective to the shear of the fabric.

5.4. Shear influence on the compressive behaviour 5.5. Nesting effect in the fabrics Measurements of the thickness of sheared fabric B3 under low pressure (0.5 kPa) demonstrated applicability of the constant volume hypothesis to the calculation of the fabric thickness in this case (Section 3.7). With the data of

As it is discussed in [2,13], nesting of the layers (decrease of the thickness per layer in a laminate) in MMF laminates is of minor importance, being caused by

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1.8 1.6 1.4

T / T0(unsheared)

explained by the fact that when sheared, layers in a laminate tend to buckle because of irregularities of fibre placement in layers and unevenness of tension, applied to different layers.

T0, B1 T0, B2 T0, B3 1/cos Tmin, B1 Tmin, B2 Tmin, B3 1/cos T(50 kPa), B1 T(50 kPa), B2 T(50 kPa), B3 1/cos

2

1.2

6. Conclusions Characterisation of the behaviour of MMFs in tension, shear and compression, together with the KES-F results of Part 2 of this series [2], leads to the following conclusions.

1

0.8

6.1. Shear 0.6 0.4 0.2 0 0

10

20

30

40

50

60

shear angle, degrees Fig. 15. Influence of the fabric shear on the compressibility. Ratio of the sheaed fabric thickness to the initial thickness of the unsheared fabric. One layer, first compressive cycle.

the thin stitching yarn lying on the surface of the fabric and creating the surface roughness of the fabric. Our current measurements show variable nesting for the studied unsheared fabrics. Table 4 gives nesting coefficients z, calculated as 2Z

TðNÞ ; N !Tð1Þ

where N is the number of layers in the laminate, T(N)— thickness of the laminate, T(1)—thickness of one layer. The initially significant nesting decreases with the increase of pressure (nesting coefficient increases), and for sheared fabric gives even opposite effect: increase of the thickness per layer in a laminate. The latter phenomenon can be Table 4 Nesting coefficients Fabric

Shear angle (8)

Number of layers

Nesting coefficient T0

T(10 kPa)

Tmin

B1

0

B2

0

B3

0

2 4 2 4 2 4 2 4 2 4 2 4

0.90 0.93 0.86 0.81 0.80 0.93 0.85 0.92 0.71 0.90 0.89 0.89

1.00 0.97 0.99 1.00 0.94 0.97 1.04 0.92 1.25 0.94 0.99 0.97

0.98 0.96 0.96 0.92 1.07 1.14 1.04 0.92 1.29 1.17 0.88 0.86

30 45 Q

0

1. Shear of biaxial MMFs is characterised by the same phenomena as other bi-directional textiles, when sheared in the direction of compression of the stitching: hysteresis of the diagram, leading to non-zero starting shear resistance, low shear modulus up to approximately 308, when the main shear resistance mode is friction, and rapid increase of the shear modulus with the on-set and intensification of the lateral compression of the fibre bundles. Shear in the direction of tension of the stitching produces high and rapidly increasing resistance in the picture frame test. 2. Shear resistance depends strongly on pretension of the fabric. In the absence of the universally adopted procedure to control and measure the pretension, any reporting of picture frame tests should be supplemented with a thorough description of the gripping procedure and estimations of the pretension. The KES-F and picture frame shear tests coincide in shear modulus with large difference in absolute value of the shear resistance, caused by the difference in pretension. For the same pretension conditions, the shear resistance of the fabrics of 08/908 and C458/K458 construction of the same areal density is close. 3. Average angle of shear of a fabric corresponds to the shear angle of the frame. Variations of the local shear angle of the fabric do not exceed 28. 4. Thickness of a MMF increases with increase of the shear angle. Constant volume assumption is fulfilled for one of the studied fabrics (B3), for others it substitutes a very rough approximation of the real compressive behaviour. 6.2. Tension 1. Tension resistance in two test directions is strongly coupled for a test in a bias direction, and is not significantly coupled for a test in the fibre directions. When two directions are coupled, the resistance in direction X increases with the increase of deformation ratio Y:X. 2. Tension diagrams exhibit a non-linear region. 3. Biaxial tension resistance of fabrics with 08/908 and C 458/K458 construction of the same areal density is close.

S.V. Lomov et al. / Composites: Part A 36 (2005) 1188–1206

6.3. Compression 1. The behaviour of MMFs in compression exhibits common features, which were already evident in the low range KES-F tests. The initial stiffness is low, with reduction of thickness to 70.80% of the initial thickness at a pressure of 50 kPa. With the pressure increase to the maximum value of 200 kPa, the thickness of the fabric additionally decreases to about 60.70% of the initial thickness. The compressive resistance significantly increases after the first compressive cycle, becoming stable in the subsequent cycles. 2. Instron compressive diagrams of the first cycle coincide with KES-F measurements. 3. Compression diagrams of all the studied unsheared fabrics can be estimated by formula (3), with the shape parameters p* and a constant, and thickness parameters T0 and Tmin linearly depending on the areal density of the fabric. 4. The nesting effect, observed earlier for MMF laminates has been confirmed for unsheared fabrics under different pressure levels. For sheared fabrics, an increase of the laminate thickness per layer (negative nesting effect) has been observed.

Acknowledgements The work reported here has been carried out: in K.U. Leuven: in the scope of the projects TECABS (European Commission), ‘Concurrent multi-scale design/ engineering of textile composites’ (K.U. Leuven) and “Predictive tools for permeability, mechanical and electromagnetic properties of fibrous assemblies” (IWT, Flanders), in University of Twente: in the scope of the FALCOM project (European Commission, GRD1-2001-40184). Materials were supplied by Saertex Gmbh and Devold Ltd. Work of M. Barburski, R. Loendersloot and Tz. Stoilova in K.U. Leuven was performed under Marie Curie PhD Fellowships of the European Commission (HPMT-CT-2000-00030). The help of laboratory staff of the Department MTM, K.U. Leuven—Jo Marien, Bart Palgrims, Kris van der Staey and Louis Depre is gratefully acknowledged. KES-F measurements were performed in Centexbel (Gent), with kind help of Dr J. Laperre and Dr W. Vande Wiele. The authors are grateful for Dr Y. Kyosev (T.U. Sofia), Prof. J. Mazajtis (T.U. Lodz) and Prof. N.N. Truevtzev (St-Petersburg State University of Technology and Design) for their support of international collaboration in the field of textile material science.

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