Textile Testing

Yarn irregularity index (CV%)

Yarn irregularity is usually expressed as the coefficient of variation of mass per unit length, CV\% = (s/\bar{m}) \times 100, where s is the standard deviation and \bar{m} is the mean mass per unit length. A capacitance evenness tester senses the dielectric response of the fibre mass in its sensing zone, and its standard output is this CV%, not the absolute mass per unit length or the standard deviation.

For a yarn with n fibres in its cross-section, random fibre placement sets a theoretical minimum irregularity of CV_{theor} = 1/\sqrt{n}. The index of irregularity is the ratio I = CV_{measured}/CV_{theor}, so a perfectly random yarn has I = 1 and larger values indicate additional non-random variation. The fibre count is the yarn linear density divided by the fibre linear density, and denier is converted to tex by dividing by 9. For example, a yarn of 40 tex made from 3 denier fibres has n = 40/(3/9) = 120 fibres, so CV_{theor} = 1/\sqrt{120} = 9.13\%; a measured CV of 11% then gives I \approx 1.20.

The variability of a yarn sample is also tested statistically. The F-value is the ratio of the sample variance to the nominal variance, F = s^2/\sigma^2, so a sample standard deviation twice the nominal value gives F = 4.

A spectrogram, produced by Uster-type analysers, plots the spectral content of mass variation against wavelength. Periodic variations appear as distinct peaks at characteristic wavelengths, and since each wavelength corresponds to a machine element with a fixed cycle, the peak position helps to locate the faulty machine part such as a roller or gear. Random variation appears as a flat background. Single imperfections such as thick places and neps are not identified from the spectrogram but from the imperfection diagram.

Work of rupture from load–elongation

The work of rupture is the energy absorbed by a specimen up to break and equals the area under its load–elongation curve, W = \int_0^{e_b} F\,de. If force is in newtons and elongation in metres, the result is in N·m (joules). If elongation is recorded in centimetres, the result in N·cm must be divided by 100 to obtain N·m. For a load F = a\,e, for example, the work up to a breaking elongation e_b is a e_b^2/2.

The work factor compares the actual work with that of an ideal rectangular load–elongation curve having the same breaking load and breaking elongation: WF = WR/(F_b e_b). Because F_b and e_b are fixed in the comparison, WR is directly proportional to WF. A yarn with WF = 0.3 therefore absorbs less work at rupture than a yarn with WF = 0.5.

If the specimen breaks within the Hookean region, the load–elongation curve is a straight line from the origin to the breaking point. The area is then a triangle, \tfrac{1}{2}F_b e_b, so WF is exactly 0.5. A curve that rises more steeply near break (convex) gives WF below 0.5, and a curve that rises quickly and then flattens (concave) gives WF above 0.5.

For a power-law stress–strain curve \sigma = k\varepsilon^{n}, the work to rupture is k\varepsilon_b^{n+1}/(n+1) and the rectangular reference is k\varepsilon_b^{n+1}, so WF = 1/(n+1), independent of k and \varepsilon_b. For \sigma \propto \varepsilon^{1/2} the work factor is 2/3, and for \sigma \propto \varepsilon^{2} it is 1/3. Students should remember this shortcut for quick calculations.

Fabric drape coefficient

The drape coefficient describes how a circular fabric specimen hangs under its own weight when it is supported on a small central disc. In the Cusick drape meter it is the ratio of the projected (shadow) area of the draped specimen to the total annular area around the support. In practice it is measured as the ratio of the mass of the paper cut to the shadow area to the mass of the whole paper ring of the same size, F = W_{shadow}/W_{total}.

If the total paper ring mass is known, the shadow mass follows as W_{shadow} = F \times W_{total}. For example, a drape coefficient of 0.5 with a ring of 4 g gives a shadow mass of 2 g.

A high drape coefficient means the fabric forms fewer but larger, stiffer folds and has a large projected area, so the fabric is stiff and has poor drapability. A low drape coefficient means the fabric conforms closely to the support and is limp and flexible. The drape coefficient therefore indicates stiffness and does not measure strength, compressibility or surface smoothness.

HVI cotton fibre testing

The High Volume Instrument (HVI) tests cotton in bulk, and its strength test is carried out on a bundle of fibres clamped between jaws, as in Stelometer-type testing. Single-fibre strength is a different test that uses single-fibre testers, so HVI strength should not be described as a single-fibre measurement.

Fineness in HVI is determined by the micronaire test, which uses the airflow principle. A fixed mass of cotton is compressed to a fixed volume, air is drawn through the plug, and the resulting pressure drop is related to the specific surface of the fibres, that is, to fineness and maturity. Fineness is therefore not measured by directly measuring fibre diameter.

The micronaire reading depends on the sample mass. If more cotton than specified is loaded, the plug is denser, the resistance to airflow rises, and the air flow falls. The pressure reading is then lower, so the micronaire value is reported lower for fibres of any fineness.

HVI detects trash by image processing of the sample surface. Nep count, however, is measured by AFIS, which senses individual fibres, and AFIS does not use the airflow principle for fineness.

Tensile modulus calculation

The tensile modulus E is the ratio of stress to strain in the Hookean (linear) region of the stress–strain curve, E = \sigma/\varepsilon. Strain is dimensionless, so the modulus has the same units as stress. For example, a filament with stress 0.9 GPa at a strain of 0.03 has E = 0.9/0.03 = 30 GPa. The modulus should be taken only from the linear portion of the curve, since it is not constant beyond the Hookean region.

A load–elongation curve can be converted to a stress–strain curve only when two dimensions are known. Stress (tenacity) is the force divided by the initial linear density, \sigma = F/T_0, and strain is the elongation divided by the gauge length, \varepsilon = \Delta L/L_0. Thus the initial linear density and the gauge length are required, while the linear density and the length at break are not needed, because stress and strain are defined on the initial dimensions.

Fabric tensile strength (strip test)

In the strip test, a fabric strip of standard width is clamped over a fixed gauge length and pulled to break. Since a fabric does not have a single linear density, its tenacity in cN/tex is found by converting the strip to an equivalent linear density. The mass per unit length of the strip is the areal density multiplied by the strip width, and since 1 tex equals 1 g per 1000 m, the linear density in tex is T = \rho_A \, w \times 1000, where \rho_A is in g/m^2 and w is in m. The tenacity is then the breaking force in cN divided by T in tex.

For example, a fabric of 200 g/m^2 tested in a 4 cm strip has a linear density of 200 \times 0.04 \times 1000 = 8000 tex. The gauge length does not enter the tenacity calculation, so it affects only the elongation measurement.

Tear strength of a woven fabric depends on how the load is shared among yarns as the tear propagates. Tear resistance is higher when the thread density is lower, because fewer yarns are restrained in the tear zone. It is also higher when the float length is longer, because more yarn length can be drawn into the tear and carry load.

Elastic recovery and permanent set

When a textile is stretched and then released, the total extension BD is divided into an elastic part CD, which is recovered, and a permanent set BC, which remains. The permanent set is the difference between the final length after release and the original length.

Elastic recovery (%) is the recovered extension divided by the extension at the maximum load, multiplied by 100. The recovered extension is the extension at maximum load minus the permanent set. For example, a 200 mm specimen stretched to 210 mm and then relaxed to 204 mm has a permanent set of 4 mm, a recovered extension of 6 mm, and an elastic recovery of 6/10 \times 100 = 60\%.

A perfectly elastic material recovers all its extension, so the permanent set is zero and the elastic extension equals the total extension. A perfectly plastic material recovers nothing, so the elastic extension is zero and the permanent set equals the total extension. Real textile materials lie between these two limits.

KES-FB and FAST low-stress properties

The Kawabata Evaluation System for Fabric (KES-FB) and the FAST (Fabric Assurance by Simple Testing) system both characterise fabric behaviour at low stress. In KES-FB, FB1 measures tensile and shear properties, FB2 measures pure bending, FB3 measures compression, and FB4 measures surface properties. In FAST, FAST-1 measures compression, FAST-2 measures bending and FAST-3 measures extensibility. The same low-stress property is therefore measured by KES-FB2 and FAST-2 for bending, and by KES-FB3 and FAST-1 for compression.

In the KES-FB1 tensile tester, the specimen is held on a rotating drum. The tensile strain is determined from the angle through which the drum rotates, and the tensile force is determined by a torque sensor that measures the torque transmitted through the drum. The system does not use a tensile load cell, and crosshead movement is not the strain measure.

Guarded hot plate heat loss

The guarded hot plate measures the thermal resistance of a fabric by metering the power that flows from a heated test plate of known area A held at a temperature difference \Delta T. The thermal resistance is R = A\,\Delta T/P, where P is the power supplied to the plate in W, A in m^2, and \Delta T in K.

To isolate the fabric, the power is first measured without the specimen, giving R_0 for the air layer alone, and then with the specimen, giving R_1. The fabric resistance is R_f = R_1 - R_0, and the intrinsic transmittance is U_f = 1/R_f in W/(m^2K). A specimen that reduces the heat loss from the plate has a larger resistance and a lower transmittance.

The guard ring and the bottom plate are kept at the same temperature as the test plate. This removes the lateral temperature gradient, so the heat flow through the specimen is one-dimensional. Only the heat flow from the central test plate is metered and used in the calculation, and the heat flow from the guard ring is excluded.

Fabric bending length (Shirley stiffness)

In the Shirley fabric stiffness tester, a fabric strip is slid off the edge of a platform until its free tip touches a plane inclined at the standard angle of 41.5°. The length of the strip that projects beyond the platform edge at this point is the overhanging length L. The bending length C is defined as half of this overhang at the standard angle, so C = L/2.

It follows that the overhanging length is twice the bending length, L = 2C. A strip with a bending length of 3 cm therefore has an overhang of 6 cm. A stiffer fabric projects less far before reaching the inclined plane, so it has a shorter overhang and a smaller bending length.

Fibre count in tuft

The number of fibres in a tuft is the total tuft mass divided by the mass of one fibre. Fineness in tex is the mass in grams of 1000 m of fibre, so 1 tex equals 1 mg/m. A fibre of fineness T tex and length L metres therefore has a mass of T \times L mg, and the fibre count is n = m_{tuft}/(T\,L), with m_{tuft} in mg.

For example, a tuft of 12 mg made of fibres of 0.2 tex and 30 mm length contains 12/(0.2 \times 0.03) = 2000 fibres. Care must be taken to convert the fibre length from mm to m before applying the formula.

Yarn count (Ne) calculation

The English cotton count N_e is the number of 840-yard hanks per pound of yarn. It is given by N_e = (L/840)/W, where L is the length in yards and W is the mass in pounds. Since 1 lb equals 453.59 g, a mass in grams must be divided by 453.59 before use.

For example, 240 yards of yarn weighing 4 g has 240/840 = 0.2857 hank and 4/453.59 = 0.008818 lb, so N_e = 0.2857/0.008818 = 32.4. The count is inversely proportional to the mass of a fixed length, so a heavier sample gives a lower count.