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D. R. PETTERSON Research Division, Chicopee Manufacturing Corp., Milltown, N. J.
Mechanics of Nonwoven Fabrics
THE
TEXTILE and paper industries for centuries have had two distinct processes, using different raw materials (length and type of fibers) and producing different end products. Recent developments of synthetic resins allowed the papermaker to use noncellulosic fibers. Also, new resins have aided the textile manufacturer to by-pass processes of spinning and weaving and to form self-supporting webs of fibers other than wool. The two materials began to have more similarities than differences. Nonwoven structure refers to product o either process. Nonwoven fabric is two-dimensional assemblage of textile-type fibers, held together with some additive bonding material, and resulting in a self-supporting weblike structure. The problems of translating fiber properties to yarn properties, and yarn properties to woven fabric properties, have received much study. One major problem has been the three-dimensional nature of a woven fabric us. two-dimensions of a nonwoven structure which lends itself to two-dimensional stress analysis. A study made by M.I.T. provided a method for predicting general mechanical properties of final nonwoven material from fiber properties, the bonding agent, and their geometric arrangement in the structure (7). The experimental and theoretical determination of gross engineering properties of an orthotropic nonwoven bonded fabric was the first step. The load-bearing structure of a nonwoven fabric (tensile and compressive loads) is described by its engineering constants.
1. Modulus of elasticity, E, is the ratio of stress to elongation or slope of stress-strain curve up to limit of proportionality. Most mechanical engineering materials have linear or Hookean stressstrain response, at least in early stages of deformation. 2. Poisson's ratio is the ratio of strain contraction in the direction perpendicular to the loading to positive strain in the direction of loading, when material is under a single tensile load. 3. The modulus of rigidity is a function similar to that for modulus of elasticity, relating shear stress to shear or angular distortion of the material.
rolled sheet steel, paper, and wood do not have this characteristic and are anisotropic. One type of anisotropy occurs when the two-dimensional material possesses two definite axes of symmetry at right angles to each other. This material is orthotropic and engineering properties are specified for both axes of symmetry. Paper, wood, and woven fabrics are orthotropic, as are many nonwoven fabrics. An analytical theory has been developed to predict the behavior of orthotropic materials (wood and plywood) (7-5) when principal stresses are not along axes of symmetry. Although it is valid only in the initial Hookean region of the material, predicted data can De, in practice, very satisfactory for certain nonlinear materials or nonwoven fabrics. Generally, nonwoven fabrics are divided into two groups-oriented (produced by carding and drafting) and isotropic (produced either by careful formation on a wet process or by commercial random fiber machines). Isotropic behavior represents a special case in the orthotropic theory, The mathematical theory can be reviewed (5,6).
Experimental Procedure All tests were carried out on an Instron tensile tester. Preliminary work
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Orthotropic Theory In many engineering applications, the stress carrying material is isotropic, or the engineering properties (or stressstrain curves) are the same in all directions. Many materials such as wire,
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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was done to eliminate wrinkling of fabric. A short fiber rayon web weighing ounce per square yard and bonded with regenerated viscose was used in these particular tests. A photographic procedure was used to measure the strain in both y and x directions. The fabric was strained a t a rate of 6.25 to 8% per minute giving rupture times from 20 to 40 seconds. Measurement of negatives and correlation of time intervals on Instron chart gave longitudinal and transverse strain at various levels with an observational error of 0.10 to 0.209& Orthotropic equations are derived in terms of stresses defined as force per unit area. Textile fiber strengths and stresses are in terms of force per weight per particular length. The weight of a unit width of rayon nonwoven fabric 9000 meters long is its equivalent denier. Thus dividing the force per unit width by this equivalent denier gives specific stress for fabric in grams per denier. From Figure 1. the initial modulus E L is 45 grams per denier, the proportional limit taken at 0.25y0strain offset is 0.42 gram per denier and the rupture stress is 0.56 gram per denier at a rupture strain of 3.8%. Figure 2 shows average results of the tests carried out at seven different anglts from 0 to 90".
N a N W O V E N FABRICS Ratios of E L and eT obtained from photographic measurements are used to determine Poisson’s ratio. The slope of resulting curve is Poisson’s ratio V L T (Figure 3). I n most cases the Poisson’s ratio is practically constant up to specific proportional limit stress and continually increases thereafter. I n using orthotropic theory, calculations are restricted to the region of constant modulus or Hookean portion of the stress-strain curve.
Predicted Values The experimental method has given directly four material constants-namely, EL, ET,v L T , and v T L . They are related by EL/ET = V L T ~ V T L Of these measured values, V T L is the least accurate, involving the largest experimental errors. Because this relationship has been used in simplifying the original equations (5, 6)) the calculated value of V T L is used. G L T calculated by the equation for the modulus when 8 is 45” gives 9 grams per denier. After determining the four independent constants, values of E, a t any test angle can be calculated (Figure 4). Except for angles of 60 to 75’) experimental values obtained with photographic method and Instron data show good agreement. Calculated values of v z y show satisfactory agreement between measured and predicted data. Two additional calculations can be made-for the specific proportional limit stress at any angle e; and for the specific rupture stress at any angle e. Cafculations for proportional limit and failure are based on certain additional assumptions of behavior and are not as exact as the expressions for moduli and Poisson’s ratio (5). However, the experimental and predicted values agree very well.
Conclusion The orthotropic theory developed for rigid materials appears to predict well the behavior of this particular flexible fibrous nonwoven structure. The material tested was selected for its low binder content and the corresponding existence of a large proportion of free unsupported fiber length between bonds. Presumably as the amount of binder is increased, the predicted and measured properties agree even more closely. A problem exists concerning the importance of straight or curved fiber segments between bonding points; for the analysis is inherently dependent upon the assumption that the fibers in the structure can take compressive loads. I n a second material tested where this assumption was not valid, the prediction of elastic modulus, proportional limit, and rupture stress were found to be reasonably good but for that of Poisson’s ratio
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was in large error. This is easily explained, because Poisson’s ratio depends upon the balance between compressive and tensile components transverse to the direction of loading. If the compressive modulus of this structure is greatly reduced, large Poisson’s ratios result without true regard to the actual fiber orientation of the fabric. The difference between predicted and experimental properties is reasonable and is perhaps twice that experienced in applying the same equations to the analysis of plywood and multilayer glass fabric laminates. Although it does not offer a final design system for nonwoven fabrics, this procedure is an attempt to characterize the nonwoven structure as a mechanical engineering material. Such information may lead to a more efficient and intelligent application of nonwoven fabrics, and may assist the manufacturer and converter in designing and creating more efficient mechanical structures for the particular end use applications desired.
Acknowledgment The author wishes to thank the Union Carbide Chemicals Co. for supporting the research, and for permitting publication of the results.
Literature Cited (1) Forest Products Laboratory, Madison, Wis., Forest Products Laboratory Repts., “Compression, Tension, and Shear Tests on Yellow Poplar Plywood Panels,” No. 1328 (1946). (2) Zbid., “Stress-Strain Relations in Wood and Plywood Considered as Orthotropic Materials,” No. 1503 (1946).
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Figure 4. Predicted and experimental specific moduli at various angles of test show satisfactory agreement in most cases
(3) Zbid., “Directional Properties of GlassFabric-Base Plastic Laminates Panels,” No. 1803 (1949). (4) Zbid., “Mechanical Properties of Plastic Laminates,” No. 1820 (1951). (5) Zbzd., “Tensile Properties of GlassFabric Laminates with Laminates,” No. 1853 (1955). (6) Love, A. E. H., “A Treatise on the Mathematical Theory of Elasticity,” Dover Publ., New York, 1944. ( 7 ) Petterson, D. R., “On the Mechanics of Nonwoven Fabrics,” Sc.D. thesis, M.I.T., 1958. RECEIVED for review February 18, 1959 ACCEPTEDMay 1, 1959 Division of Industrial and Engineering Chemistry, Symposium of Nonwoven Fabrics, 135th Meeting, ACS, Boston, Mass., April 1959. VOL. 51, NO. 8
AUGUST 1959
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