Characterization of Mechanical Behavior of Kevlar 49 Fabrics Deju Zhu1, Barzin Mobasher2, S.D. Rajan3 1
Postdoctoral fellow, Department of Mechanical Engineering, McGill University, Montreal, QC, Canada, E-mail:
[email protected] 2 Professor, Ph.D., P.E., Department of Civil, Environmental and Sustainable Engineering, Arizona State University, Tempe, AZ, 85287, corresponding author, E-mail:
[email protected] 3 Professor, Ph.D., Department of Civil, Environmental and Sustainable Engineering, Arizona State University, Tempe, AZ, 85287, E-mail:
[email protected] ABSTRACT Woven fabrics are used in many applications, including ballistic armors, propulsion engine containment systems and fabric reinforced composites. In order to facilitate the design and improvement of such applications, this paper presents the experimental programs of quasi-static uniaxial tension, biaxial tension and picture frame test to obtain the material properties of Kevlar® 49 fabric. This study discusses the stress-strain response in both the warp and the fill directions of the fabric under uniaxial tension, the effective Poisson’s ratio and the in-plane shear response, and also investigates the possible effect of specimen size on the responses of the fabric. The results show that the fabric exhibits non-linear and orthogonal behavior in tension, and can deform up to 20% before the complete failure. The effective Poisson’s ratio is a nonlinear function of strain. The shear response is nonlinear to the shear angle, but not dependent upon the specimen size after normalization. Images were used to demonstrate the deformation and failure behavior of the fabric. All these results are very important for the numerical modeling of the Kevlar® 49 fabric used in engine fan containment systems and other ballistic protection. Keywords: Woven fabric; Stress-strain response; Poisson’s ratio; Shear behavior 1. Introduction High strength woven fabrics are ideal materials for use in structural systems where large deformations and high energy absorption are required. Their high strength per weight ratio and ability to resist high speed impacts enable them to be very efficient compared to metals. Fabrics are highly anisotropic and the behavior in one direction is coupled to the behavior in the other in a nonlinear manner. Even under uniaxial loading, the response of a fabric is often nonlinear due to its woven structure and to nonlinearities in the material response. In addition, many applications of fabric involve large rotations and deformations. Various deformation mechanisms, i.e. yarn stretch, uncrimping, crimp interchange, locking, trellising and yarn slip, determine the mechanical response of a woven fabric [1]. Research on the mechanics properties of aramid yarns has been reported by some authors, but little on aramid woven fabrics. Schwartz et al. [2] carried out quasi-static tensile tests on single fibers of Kevlar® 29 and 49 taken from various locations within a spool and production lots. An increased strength for fibers at shorter gage lengths, but no increased variability at longer lengths was observed. Amaniampong and Burgoyne [3] studied the effect of gage length and strain rate from 3x10-4 to 0.003 s-1 on the failure stress and failure strain of Kevlar® 49 yarns. Yarn strength decreases slightly as the gage length increases; whereas the failure strain of the Kevlar® 49 yarns was independent of the gage length, however decreased slightly as the strain rate increased. Zhu et al. [4-7] conducted dynamic tensile testing on Kevlar® 49 single yarn and fabrics using a servo-hydraulic high speed machine [8-14] and found that the Young’s modulus, tensile strength, maximum strain and toughness increased with increasing strain rate over a range of 20 to 170 s-1. Naik et al. [15] studied the quasi-static properties of Kevlar® 49 and Zylon fabrics in tension at a strain rate of 1.4x10-4 s-1 and the load-deflection response of single layer and multiple layers in static penetration test.
Determination of biaxial nature of interaction between yarns in two dimensional woven fabrics is among the fundamental characteristics of textile materials. This interaction characterizes important mechanical characteristics for a woven fabric, and affects the response in many applications which incorporate textile fabrics as structural elements. This process is known as crimp interchange which is similar to a Poisson’s effect, although it is nonlinear, so the effective Poisson’s ratio evolves as the fabric is deformed. This mechanism represents an important difference between fabrics and other anisotropic materials because it permits the two families of reinforcing structures to interact in a nonlinear manner [1]. While the significance of the effects of Poisson’s ratios on fabric drape and other behaviors is well recognized, their values were mostly estimated, based on those for ordinary solid materials, for fabric modeling and simulations. Another important material property required for the finite element models of the fabric is the response of the fabric under shear deformation. During shear deformation, the fabric yarns experience large angular variation between warp and fill yarns. Three experimental approaches can be used to characterize the shear properties: the simple shear [16], bias extension test [17] and the picture-frame shear test [18]. The bias extension approach usually brings out a complex combination of shear and tension, which makes it difficult to isolate the shear deformation in the test and hence complicates the characterization of pure shear behavior. In the picture-frame shear test, a fabric sheet is clamped within a square frame hinged at each corner. The two diagonally opposite corners are then displaced using a mechanical testing machine. It can produce a quite uniform shear deformation state in the fabric or composite sheet [19]. In the picture-frame shear test, in-plan shear deformation is limited by local wrinkling, when yarns reach the so-called "locking angle". And corner cut-off is typically needed to allow rotations of the hinges and prevent immediate wrinkling. This paper presents a comprehensive experimental study of Kevlar® 49 fabric subjected to quasi-static uniaxial tension, biaxial tension and in-plane shear. The first section of this paper presents detailed experimental programs to characterize the orthotropic stress-strain relationships by uniaxial tension test, the effective Poisson's ratio by biaxial test, and the shear properties by picture-frame shear test. The second section discusses the results and the possible effects of specimen size and pre-loading on the mechanical properties. Images captured during loading process have been used to study the deformation and failure mechanism of the fabric. The last section summarizes the results and makes some conclusions. It is expected that the results will improve the modeling of the fabric used in aircraft engine fan containment systems [20] and other ballistic protection. 2. Experimental Program The plain-woven Kevlar® 49, a high performance fabric for ballistic protection application, made by EI du Pont de Nemours & Co., is used in this study. It is about five times stronger than steel on an equal weight basis, yet it is more flexible and light weight. The Kevlar® 49 fabric is manufactured using a plain weave of 17x17 yarns (per linear inch) each consisting of hundreds of filaments. The bulk density and linear density are 1.44 g/cm3, 1.656(10-3) g/cm, respectively. The cross-sectional area of each yarn was calculated as 1.15(10-3) cm2 by dividing the linear density of the material by its bulk density [5]. 2.1 Uniaxial Tensile Test The tests were performed in a 90 kN INSTRON machine operated under closed-loop displacement control with the displacement rate of 2.5 mm/min. Digital data acquisition was used to collect data at a sampling rate of 2 Hz. The test was continued until complete failure of the specimen was achieved. The overall specimen deformation was measured by the stroke movement. To create a strip of specimen, the fabric was first cut into rectangular strips, and then a number of yarns along the fabric length are removed from both sides of the fabric width, thereby producing a sample without yarn crossovers along the edges. This step is necessary to ensure that the effects of edge defects are minimized and that the loaded yarns will not slip out of the cross yarns during the test. The fabric was cut into strips with a length of 250 mm and two sets of width-30 mm and 60 mm. In each set, yarns are removed from both sides of the strip such that the samples are left with 17 and 34 longitudinal yarns, respectively. The initial gage length was 200 mm. The total cross-sectional area of a specimen was defined as the crosssectional area per yarn multiplied by the number of yarns per width of the specimen. Five tests were conducted on each specimen size in both the warp and the fill directions, and the deformation and failure behavior of the specimens were recorded by a CCD camera.
2.2 Biaxial Tension Test The test setup comprises of two actuators which are capable of applying displacement velocity and measuring displacement of test specimen in two orthogonal directions independently, two load cells with capacity of 90 and 225 kN which are used force measurement, a grip assembly to hold the specimen, a sliding block (super pillow) on a steel roller which is mounted on ground, and connecting bars and universal joints, as shown in Figure 1(a). The load cell with capacity of 90 kN was used to measure the force in vertical direction, and the other was used to measure the force in horizontal direction. An edge-clamped fabric holding fixture was developed to hold the fabric specimen. The clamping of the fabric edges is accomplished through wrapping with a notch. The grip assembly can hold specimens with size up to 150 mm x 150 mm. The original fabric is 250 mm wide and was cut into different specimen sizes with corner cut-off. The arm parts were clamped to the fixture. Figure 1(b) shows the specimens of 100 mm x 100 mm with corner cut-off. The clamped specimens were pre-loaded in vertical direction for each specimen size at 4.5 N/mm, and keep vertical direction stationary after pre-loading, and then apply displacement in horizontal direction at a loading rate of 5 mm/min. (a)
(b)
Fig. 1 (a) Schematic diagram of biaxial test setup and (b) cruciform specimens of 100 mm x 100 mm 2.3 Picture Frame Test All the tests were conducted in a servo-hydraulic test frame (MTS) operated under closed-loop displacement control. Data were acquired at a sampling rate of 2Hz. A CCD monochrome camera was used to capture the images during loading process. A schematic diagram of the picture frame is shown in Figure 2(a). The frame consists of five basic parts namely bearings, clamping plates, multiplier links, a long plate with a 88.9 mm slot and two connecting fixtures (for connecting to the top and bottom crosshead mount). The side length of the frame (Lframe) is 165 mm, and the side length of the amplifier (La) is 70 mm. The fabric was wound over the circular rod and placed in the circular slot in the top part of the clamping plate. The tightened set screws at the top of the plates kept the assembly intact and prevented the fabric slipping through the application of uniform mechanical pressure. Before the start of the test the multiplier links are orthogonal to each other. The top crosshead mount remains stationary while the stroke moves down at a rate of 5 mm/min. In order to minimize the marginal restriction due to the joints of the fixture, four corners of a square fabric sheet are cut off to generate a test sample with smaller size than clamped in the picture frame. However, the fringe yarns still rotate and make contribution to immediate wrinkling. One way to eliminate the contribution from the edge parts, thus provide an accurate material characterization, is removing some yarns in each arm part. The inner areas of constructed specimens have three different sizes, i.e., 75x75 mm, 100x100 mm and 125x125 mm. Before experiment, four unidirectional-yarn parts are clamped tightly into the two plates on the fixture with screws, as shown in Figure 2(b). When clamped into the fixture, the specimen is kept exactly loose in order to avoid pre-tension in both directions of the fabric.
(a)
(b)
Lframe
La
Fig. 2 (a) Schematic diagram of the picture frame and (b) specimen clamped into fixture The picture frame tests were conducted by following procedure which is similar to the procedure in the reference by Zhu et al. [18]. The shear angle, shear force and shear stress were determined using the same method as discussed by Cao et al. [19]. To compare the results of different specimen sizes or the tests conducted on different fixtures, Harrison et al. [21] proposed a method for normalization which uses the frame length based on an energy method. Their assumption was that the frame length was equal to the fabric length. However, as there is no standard ratio for the length of a test sample to the length of the frame, this method is not the best method for normalization. The investigation continued by comparing the data when normalized by the fabric area as discussed by Peng et al. [22]. Here, the fabric area was defined as the inner square area of the sample, i.e., the arm areas were neglected. The fabric area is directly related to the number of crossovers in the material. A larger sample would have more yarns resulting in more crossovers between the yarns. With an increased number of yarns and crossovers, a larger force is required to shear the sample. The normalization by the inner fabric area is quite straightforward and reasonable if part of the yarns in the arm area is removed so that no shear occurred in the arm area. In the present study, as some of the yarns in the arm area are removed before the tests, it is reasonable to normalize the shear force by the inner fabric area, and normalize the shear stress by the length (width) of the inner area. 3. Experimental Results and Discussion 3.1 Uniaxial Tensile Behavior Figure 3 shows the typical stress versus strain (time) relationship, the fabric deformation and failure mechanism under uniaxial tension. There are four distinct regions in the stress-strain behavior: crimp region, linear pre-peak region, linear post-peak region and non-linear post-peak region. In the undeformed state (t =0 second), the warp and fill yarns are orthogonal to each other and free of any stretch. In the crimp region, the stress increase is relative low due to the straightening of the woven structure of the fabric. As the strain is increased, the yarns in the loading direction are extended and become compacted. When the yarns in the loading directions are fully straightened, or in some cases, until cross yarns wrap around the loaded yarns and thereby prevent them from extending [23], the fabric exhibits a linear response and there is no visible failure of the fabric. The Young’s modulus is defined by the slope of the stress-strain curve in this region. When the stress level reaches the strength of the constituent yarns, the yarns in the loading direction start to fail, resulting in a dramatic decrease in the fabric load-carrying capacity until reaching a transition point which is about 200 MPa (the end of linear postpeak region). After that the stress decreases gradually to almost zero when the strain increases up to about 0.2 mm/mm, representing the nonlinear post-peak region where the failed yarns slip away out of the fabric (t = 200 to 800 second). The strain energy of stretched yarns and the energy dissipated through frictional sliding play key
roles in the energy absorption ability of the fabric. The toughness is defined by the area under the entire stressstrain curve.
t = 100 s
t=0s
t = 200 s
t = 400 s
t = 800 s
Time, s 0
200
400
800
50 mm x 200 mm Specimen Warp Direction
2000
Stress, MPa
600
1500 Linear pre-peak region
1000 Linear post-peak region
500 Nonlinear post-peak region
0
Crimp
0
0.04
0.08
0.12
0.16
0.2
Strain, mm/mm Fig. 3 Typical stress-strain relationship and fabric deformation under uniaxial tension Tables 1 summarizes the tensile properties of both specimen sizes in warp and fill directions. The tensile strength in warp direction is approximately 10-15% lower than that in fill direction, while the ultimate strain in warp direction is approximately 7-12% higher than that in fill direction. The elastic stiffness in pre-peak region of warp direction is almost identical to that of fill direction. Although the tensile strengths of 50 mm wide specimen are slightly lower (2-6%) than those of 25 mm wide specimens in both warp and fill direction, the Young’s modulus, toughness and ultimate strain are almost identical to each other, indicating the tensile properties of the fabric are independent with the width-to-length ratio for the considered range of configuration. Table 1 Summary of Tensile Properties of Kevlar 49 Fabric in Warp and Fill Directions Specimen Size Direction (Width x Length, mm) (Warp/Fill) Warp 50x200 Fill 25x200
Tensile Strength (MPa) 1748 ± 56
Young's Modulus (GPa) 117.2 ± 3.3
Toughness (MPa) 32.4 ± 3.0
Ultimate Strain (mm/mm) 0.0223 ± 0.0012
2013 ± 44
117.1 ± 3.0
33.9 ± 1.3
0.0201 ± 0.0010
Warp
1859 ± 109
117.9 ± 2.5
32.9 ± 1.4
0.0215 ± 0.0015
Fill
2055 ± 72
119.7 ± 4.0
33.2 ± 1.2
0.0200 ± 0.0009
3.2 Effective Poisson’s Ratio Figures 4(a) and 4(b) show the effective Poisson's ratio of the specimens with pre-loading of 4.5 N/mm. The effective Poisson's ratio first increases with increasing strain very quickly at the beginning, then decreases gradually, leveling off before the specimen fails for all the specimen sizes and pre-loading conditions. For the 50 mm x 50 mm specimens, the maximum value of Poisson's ratio varies between 0.35 and 0.57. When the fabric fails at the strain value of 0.025, the effective Poisson's ratio decreases to approximately 0.15 (average value). For the 100 mm x 100 mm specimens, the maximum value of Poisson's ratio is in the ranges of 0.48 to 0.63. And the average Poisson's ratio is also approximately 0.15 when the fabric fails. 0.8
0.8
100 mm x 100 mm Specimens with 450 N (4.5 N/mm) pre-load
0.6
Poisson's Ratio
Poisson's Ratio
50 mm x 50 mm Specimens with 225 N (4.5 N/mm) pre-load
0.4
0.4
0.2
0.2
0
0.6
0
0
0.01
0.02
0.03
0
0.01
0.02
0.03
Strain, mm/mm (b)
Strain, mm/mm (a)
Fig. 4 Effective Poisson’s ratio of (a) 50 mm x 50 mm and (b) 100 mm x 100 mm specimens 3.3 In-plane Shear Behavior The shear response of woven fabric is different from that in metals and other homogeneous material sheets due to the fabric unique woven structure. In particular, the in-plane shear response of fabric is dominated by the relative rotation of the two yarn families. This behavior is responsible for many distinct features observed during shear deformation of woven fabrics. Figure 5 shows the images captured during the shear deformation of the 125 mm x 125 mm specimen. Grid pattern was applied on the specimen surface before the test for image analysis. One should notice that all the specimens undergo fairly uniform shear deformation.
10 degree
20 degree
30 degree
40 degree
Fig. 5 Shear deformation of the 125 mm x 125 mm specimen at different shear angles The initial portion of the Figures 6(a) and 6(b) depicts a linear response corresponding to the elastic rotation, following with a region where the yarns undergo dissipative rotation at the yarn crossover points. In dissipative rotation region (shear angle from 2 to 30 degree), both the shear force and the shear stress slightly increase with shear angle. As the yarns are compressed (shear angle between 30 and 40 degree), shear stiffness in the fabric
0.003
Normalized Shear Stress, MPa/mm
Normalized Shear Force, N/mm2
increases, providing higher shear resistance. The shear force and the shear stress increase much faster in this region. When the yarns cannot be compacted further and the in-plane movements of the yarns are prohibited, the level of shear deformation is commonly referred to as the fabric’s shear locking angle. The last portion of the curves (shear angle above 40 degree) is dominated by shear locking effects.
Specimen Size 75 mm x 75 mm 100 mm x 100 mm 125 mm x 125 mm
0.0025 0.002 0.0015 0.001 0.0005 0
0
10
20
30
40
Shear Angle, Degree (a)
50
0.04
Specimen Size 75 mm x 75 mm 100 mm x 100 mm 125 mm x 125 mm
0.032 0.024 0.016 0.008 0
0
10
20
30
40
50
Shear Angle, Degree (b)
Fig. 6 Normalized (a) shear force and (b) shear stress versus shear angle 4. Conclusions The present study focuses on the experiment and characterization of uniaxial, biaxial tension, and in-plane large shear deformation on the Kevlar 49 fabric, and analyzes the non-linear stress-strain relationship in warp and fills directions, effective Poisson’s ratio as a function of strain, and the shear response. The following conclusions can be reached: (1) The stress-strain response of Kevlar 49 fabric exhibits non-linear and orthogonal behavior in warp and fill directions, and can deform up to 20% before the complete failure. The tensile strength in warp direction is approximately 10-15% lower than that in fill direction, while the ultimate strain in warp direction is approximately 7-12% higher than that in fill direction. The elastic stiffness in pre-peak region of warp direction is almost identical to that of fill direction. (2) The effective Poisson’s ratio is a nonlinear function of strain values. It first increases with increasing strain very quickly at the beginning, then decreases gradually, leveling off before the specimen fails. The maximum value of the effective Poisson’s ratio varies between 0.35 and 0.63, and when the fabric starts to fail it is approximate 0.15. (3) The normalized shear response is independent with the specimen size. The normalized shear force and stress versus shear angle curves consist of several regions: linear elastic rotation region, dissipative rotation region, yarn compression region and shear locking region. Acknowledgements The authors wish to thank William Emmerling, Donald Altobelli and Chip Queitzsch of the Federal Aviation Administration's Aircraft Catastrophic Failure Prevention Research Program for their support and guidance. Funding for this effort was provided by the FAA.
Reference [1]
King MJ. A Continuum constitutive model for the mechanical behavior of woven fabrics including slip and failure. Ph.D. dissertation, Massachusetts Institute of Technology, 2006.
[2] [3] [4]
[5] [6]
[7]
[8]
[9] [10] [11]
[12] [13]
[14]
[15]
[16] [17] [18] [19] [20]
[21]
[22]
[23]
Schwartz P, Wagner HD and Phoenix SL. A study of statistical variability in the strength of single aramid filaments. Journal of Composite Material, 18(4), 312-338, 1984. Amaniampong G and Burgoyne, CJ. Statistical variability in the strength and failure strain of aramid and polyester yarns. Journal of Material Science, 29, 5141-5152, 1994. Zhu D, Mobasher B and Rajan SD. Experimental study of dynamic behavior of Kevlar 49 single yarn. Society for Experimental Mechanics - Annual Conference & Exposition on Experimental and Applied Mechanics, v3, p. 542-547, 2010. Zhu D, Mobasher B and Rajan SD. Dynamic tensile testing of Kevlar 49 fabrics. ASCE Journal of Materials in Civil Engineering, 2010, in press, http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000156. Zhu D, Mobasher B and Rajan SD. High Strain Rate Testing of Kevlar 49 Fabric. Society for Experimental Mechanics - 11th International Congress and Exhibition on Experimental and Applied Mechanics, v1, p.34-35, 2008. Zhu D, Mobasher B and Rajan SD. Image Analysis of Kevlar 49 Fabric at High Strain Rate. Society for Experimental Mechanics - 11th International Congress and Exhibition on Experimental and Applied Mechanics, v2, p.986-991, 2008. Zhu D, Rajan SD, Mobasher B, Peled A and Mignolet M. Modal analysis of a servo-hydraulic high speed testing machine and its application to dynamic tensile testing at an intermediate strain rate. Experimental Mechanics, 2010, in press, http://dx.doi.org/10.1007/s11340-010-9443-2. Zhu D, Mobasher B and Rajan SD. Characterization of dynamic tensile testing using aluminum alloy 6061-T6 at intermediate strain rates. ASCE Journal of Engineering Mechanics 2010 (accepted). Zhu D, Peled A and Mobasher B. Dynamic tensile testing of fabric-cement composites. Construction and Building Materials, 25(1), 385-395, 2011. Zhu D, Mobasher B, Silva FA and Peled A. High Speed Tensile Behavior of Fabric-Cement Composites. International Conference on Material Science and 64th RILEM Annual Week, Proceedings pro075: Material Science - 2nd ICTRC - Textile Reinforced Concrete - theme 1, p. 205-213, 2010. Silva FA, Zhu D, Mobasher B, Soranakom C and Toledo Filho RD. High speed tensile behavior of sisal fiber cement composites. Materials Science and Engineering: A, 527(3), 544-552, 2009. Silva FA, Butler M, Mechtcherine V, Zhu D and Mobasher B. Strain rate effect on the tensile behaviour of textile-reinforced concrete under static and dynamic loading. Materials Science and Engineering: A, 528(3),1727-1734, 2011. Mechtcherine V, Silva FA, Butler M, Zhu D, Mobasher B, Gao S and Mäder E. Behaviour of strainhardening cement-based composites under high strain rates. Journal of Advanced Concrete Technology, 9(1), 51-62, 2011. Naik D, Sankaran S, Mobasher B, Rajan SD and Pereira JM. Development of reliable modeling methodologies for engine fan blade-out containment analysis. Part I: experimental studies. Int J Impact Eng., 36(1), 1-11, 2009. Kothari VK and Tandom SK. Shear behavior of woven fabrics. Textile Research Journal, 59(3),142-150, 1989. Potter KD. The influence of accurate stretch data for reinforcements on the production of complex structural moldings. Part I: deformation of aligned sheets and fabrics. Composites, 10(3), 161-167, 1979. Zhu B, Yu TX and Tao XM. An experimental study of in-plane large shear deformation of woven fabric composite. Composites Science and Technology, 67, 252-261, 2007. Cao J, et al. Characterization of mechanical behavior of woven fabric: experimental methods and benchmark results. Composites Part A, 39, 1037-1053, 2008. Stahlecker Z, Mobasher B, Rajan SD and Pereira, JM. Development of reliable modeling methodologies for engine fan blade-out containment analysis. Part II: finite element analysis. Int J Impact Eng., 36(3), 447-459, 2009. Harrison P, Cliffod MJ and Long AC. Shear characterization of viscous woven textile composites: a comparison between picture frame and bias extension experiments. Composites Science and Technology, 64, 1453-1465, 2004. Peng XQ, Cao J, Chen J, Xue P, Lussier DS and Liu L. Experimental and numerical analysis on normalization of picture frame test for composite materials. Composites Science and Technology, 64, 1121, 2004. Jearanaisilawong P. Investigation of deformation and failure mechanisms in woven and nonwoven fabrics under quasi-static loading conditions. M.S. Thesis, Massachusetts Institute of Technology, 2004.
