Mechanical Response Of A Nylon Woven Fabric With A Cut

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1 Mechanical Response O A Nlon Woven Fabric With A Cut Fu-Pen Chiang and Fernando Cuenca Department o Mechanical Engineering, State Universit o New York at Ston Brook Ston Brook, NY ABSTRACT The understanding o the mechanical response o abrics is important as the range o its applications becomes more signiicant. This paper presents the eperimental results o uniaial tension tests perormed on uncoated nlon abric specimens under the presence o an inclined cut or slit as studied using the white light speckle method. Deormation contours or dierent slit inclinations are presented and the corresponding strain ields eplained. Kewords: Nlon abric; White light speckle method; Uniaial tensile test; Nondestructive evaluation; Inclined cut; Shear bands INTRODUCTION The stud o tear propagation in uncoated woven abrics has been a problem o interest in the past ears given the increasing use o this tpe o materials in inlatable and tension structures, parachute canopies and geotetile-reinorced geotechnical structures [1-3]. The importance o this stud relies on the possibilit o cut or puncture during manipulation or operation o the material. Given the proper conditions this accidental cuts or punctures can be the source o rapidl propagating damage resulting on the catastrophic ailure o the structure. Although work has been done on the understanding o the mechanical behavior o uncoated nlon abrics in pristine condition [4] and the mechanical response under tearing [5], little work has been done on the eects o initial cut geometr on the global response o the material. This tpe o eperimental stud requires non-standard techniques; it requires a technique capable o non-destructive and non-disruptive evaluation o the deormation patterns in the material. This eperimental technique is the white light speckle method The use o the white light speckle method in this stud is to measure the in plane displacements which can de directl linked to corresponding strains. The displacements are deduced rom the comparison o random speckle patterns on the specimen surace generated when it is illuminated with incoherent light ater two consecutive load steps. The technique is a whole ield, high resolution non-destructive one and can be used in man dierent tpes o materials [6]. This paper gives qualitative results on the deormation patterns observed on an uncoated nlon abric with the presence o an embedded sharp cut or slit under the application o uniaial tension and the inluence o the inclination o the slit on the response o the material. THE WHITE LIGHT SPECKLE METHOD The white light speckle method is one o several speckle techniques used in the non-destructive testing ield [7-8]. Basicall what the white light speckle method does is as ollows: First a random speckle pattern must be created on the surace o the specimen, which is the illuminated with an incoherent light beam. As the load steps take place, consequent deormation and rigid bod motion o the specimen correspond to a displacement o the speckle pattern. Instead o ollowing each and ever speckle s movement, the average displacement o a cluster o speckles is obtained as described in the ollowing. A digital camera, speciicall a CCD camera, is used to digitize the speckle patterns beore and ater application o load and consequent deormation. The digitized speckle patterns are then divided in subimages o a certain piel size (e.g piels). The unctions h1() and h2() are the comple amplitudes o the light disturbance o a generic speckle subimage beore and ater deormation. The unction h2() is nothing but the original h1() unction with the added displacements:

2 [ u( ), v( )] h2 ( ) = h1 Where u and v are the displacements in the and directions respectivel. The procedure now is to appl a FFT to both h1 and h2 to ind a numerical intererence between the two speckle patterns in the spectral domain: H1( ) H 2 ( ) F( ) = = ep{ j[ φ1( ) φ2( H (, ) H (, ) 1 2 * )]} where, ) and, ) are the phases o H 1 (, ) and H 2 (, ), respectivel. Finall, a halo unction is obtained b an additional FFT, i.e., G( ξ, η) = I{ F(, )} = G( ξ u, η v) Which is an epanded unction located at (u,v). B determining the peak o this impulse unction, the displacement vector o the speckle cluster in the subimage can be determined uniquel. Once this has been determined, strain distributions can be calculated using displacement/strain relations. EXPERIMENTS AND RESULTS The same uncoated nlon abric used b Hong, Chang and Chiang [4] was used in this stud. Uniaial tension tests were conducted on nlon abric specimens 3 inches wide and 10 inches long, to which a central cut or slit has been introduced a priori. This slit is located at a considerable distance rom the edges o the specimen to avoid boundar eects. The eperiment was displacement controlled, at a rate o 0.2 inches/min. Dierent uniaial tension tests were carried out changing the inclination o the angle φ o the slit, as seen in Figure 1. Figure 1. Eperimental set up or tear stud. The inclination angles used in this stud were 18.45, 33.7, 45 and 56.3 degrees. This angles where chosen given their relative ease to be cut with precision on the abric. Figure 2 shows the vertical displacement contours as obtained b the speckle method, where it can be seen that there is shear strain above and below the slits, especiall near its tips. For this small angle the strain distribution tends to be uniorm on both sides o the slit, with the middle o the band showing normal strains. This will be relected in the tendenc o the slit to open as the load is increased, which was observed eperimentall.

3 Figure 2. Vertical displacement contours or a abric with a central crack inclined degrees as obtained b speckle With the increment o load two phenomena were observed. First the rotation o the slit, which is largel attributed to the Poisson eect eperienced b the material with the increment o load (etension in the load direction combined with compression in the orthogonal direction). Secondl it was observed that at a suicient load, the regions in the vicinit behind o the slit tip will go out o plane and continue to do so until ailure o the undamaged ibers in the vicinit ahead o the slit tip, as shown in the circled areas o Figure 3. Figure 3. Detail o nlon abric specimen with central slit under uniaial loading. As the cut inclination was increased, it could be observed that the shear strain would not be uniorm near the tips o the slit (the ringes are a lot closer to one another on one side o the slit than on the other) and most importantl the width o the normal strain region was reduced signiicantl. The latter is the reason wh at inclinations o more than 45 degrees the slit won t open but retain a sharp elliptical shape. For this latter case the ar ield is also aected b the slit at relativel large loads. This phenomena is illustrated in Figure 4 a, b and c.

4 Figure 4 a) Vertical displacement contours or a abric with a central crack inclined 33.7 degrees as obtained b speckle Figure 4 b) Vertical displacement contours or a abric with a central crack inclined 45 degrees as obtained b speckle

5 CONCLUSIONS Figure 4 c) Vertical displacement contours or a abric with a central crack inclined degrees as obtained b speckle It was observed that the behavior o an uncoated nlon abric with the presence o a sharp slit under uniaial loading depends on the inclination o the cut relative to the horizontal plane. As this inclination increases the shear strain distribution above and below the slit tips becomes non-uniorm when comparing both sides o the slit, reducing the also present normal strain, causing the slit not to open. Failure starts when the undamaged ibers in ront o the slit tip break under tension, as described b Godre and Rossettos. Rotation o the slit is observed and it is attributed to the Poisson eect eperienced b the material. ACKNOWLEDGEMENT The work reported here was supported in part b the Oice o Naval Research Grant # N (Dr. Yapa D.S. Rajapakse: Program Manager) REFERENCES 1. Godre, T. A. and Rossettos, J. H., The onset o tearing at slits in stressed coated plain weave abrics, Journal o Applied Mechanics Transactions o the ASME, Vol.71, No.6, 2004, pp Cavallaro, P., Quigle, C., Johnson, M. E. and Sadegh, A. M., Mechanical Modeling o Inlated Woven Fabrics or Structural Applications, U.S. Arm Smposium on Solid Mechanics, Ma 4-7, 2003, Charlotte, NC (in press). 3. Quigle, C. and Cavallaro, P., Evaluations o Pressure Stiened Air Beam Finite Elements Used in the Design o Highl Mobile Airsupported Structures, U.S. Arm Smposium on Solid Mechanics, Ma 4-7, 2003, Charlotte, NC. 4. Hong, D., Chang, S. and Chiang, F.P., Mechanical Properties o a Nlon Fabric, Proceedings o the American Societ or Composites 18 th Technical Conerence. 5. Godre, T. A. and Rossettos, J. N., The Onset o Tear Propagation at Slits in Stressed Uncoated Plain Weave Fabrics, Journal o Applied Mechanics, Transactions o ASME, Vol. 66, 1999, pp Asundi, A. and Chiang, F. P., Theor and Applications o the White Light Speckle Method or Strain Analsis, Optical Engineering, Vol.21, No.4, 1982, pp Chiang, F. P., Evolution o white light speckle method and its application to micro/nanotechnolog and heart mechanics, Optical Engineering, Vol. 42, No.5, 2003, pp Chen, D.J. and Chiang, F.P., Computer Aided Speckle Intererometr Using Spectral Amplitude Fringes, Applied Optics 3(2), , 1993.

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