Micromechanics of hydroentangled nonwoven fabrics

Abstract

The mechanics of nonwoven fabrics is largely dependent on fiber properties, and other physical factors such as structural arrangement and degree of entanglement of the fibers. In this study, modeled and experimental stress–strain behaviors of uniaxially loaded hydroentangled nonwoven fabrics have been analyzed and compared. The theoretical values from the model were deduced from the measured properties of micro-samples, namely, fiber volume faction, orientation distribution and mechanical properties. Testing of the micro-samples was performed on a Deben Microtest Module fitted in the FEI Quanta 200 Scanning Electron Microscope. The experimental stress–strain results show that the structure is in the linear region when the modeled results approach the highest specific stress. Also, the theoretical models highly overestimate the specific stress of the hydroentangled nonwoven fabrics. The results show that the application of the model was limited in predicting tensile stress. Furthermore, a trapezoid method was used to quantify the actual deformation energy from the stress–strain graphs up to the ultimate tensile strength. The theoretical deformation energy was estimated and compared to the experimental values. The model was subsequently modified to improve its predictive capability.

Keywords

hydroentanglement scanning electron microscopy microstructure fiber element deformation energy micromechanics

Many studies on micromechanics of nonwoven fabrics have been published on adhesive, thermal and spunbonded fabrics, but limited on hydroentangled structures.^1–5 The microstructure of thermally bonded nonwoven fabrics consists of both continuous and discontinuous regions, whereas hydroentangled nonwoven structures are predominantly discontinuous.² Therefore, their micromechanics would be expected to be different and further research is required as their application areas have been expanded. In thermobond nonwoven fabrics the bonding points are fused and hence have limited movement when responding to tensile strain, whereas hydroentangled fabrics rely only on inter-fiber friction like needlepunched structures but they are more compact.² In hydroentanglement bonding, high-pressure collimated waterjets are directed to loose fiber-webs that entangle fibers to produce nonwoven fabrics without using any chemical binder. The integrity of the hydroentangled fabric structure is attributed to inter-fiber friction of tight cohesive groupings of fiber bundles.^6,7 Therefore, the micromechanics of hydroentangled nonwoven fabrics would be expected to be different. The uses of hydroentangled fabric are extensive because it resembles a woven fabric. The uses of hydroentangled fabrics are in reinforcement of polymer matrices in composites, geotextiles, medical textiles and many other such technical applications.⁶ Some models have not been verified for predicting the mechanical characteristics of hydroentangled fabrics; hence, further research is necessary.

Stress–strain properties of nonwoven structures

The mechanical properties of nonwoven fabrics, such as tensile strength and tensile modulus, are due to resistance to deformation under applied loads. The constituent fibers act as the load-bearing elements. Hence, the response to deformation of the nonwoven fabrics is largely influenced by fiber properties, structural arrangement and degree of entanglement of constituent fibers.^4,8,9 The most influential fiber properties are fiber length, curl, strength and elongation. The bonds formed between fibers allow the transfer of load.^9–11 The fiber arrangement in the structure determines the number of fiber–fiber bonds, bonds-per-fiber and preferential alignment of fibers, which impacts the fabric mechanics. Thus, the tensile strength and tensile modulus of the nonwoven fabric are maximum in the direction of fiber alignment where the ability of fibers to bear load is the highest.^3,12 As such, the fiber-orientation distribution (FOD) provides a numerical parameter that is required for predicting the mechanical performance of the nonwoven fabric.^1,13–15 In this study, we use semi-empirical micromechanical analysis to explore stress–strain behavior of hydroentangled nonwoven fabrics.

Stress–strain models of nonwoven fabrics

The main purpose of developing theoretical models is to predict the variations in tensile strength in load-bearing structures, such as nonwoven fabrics and composite materials. In these models, for example discrete models, the mechanical behavior of the constituent fibers is translated to the macro-structural behavior. Therefore, it is critical to determine fiber-to-fiber contacts, fiber orientation, fiber properties and the predominant modes of deformation.^4,9,16 Hearle and Stevenson¹⁷ developed a theoretical model to predict the strength of nonwoven fabrics based on the fiber network theory. Here, the fabric stress, $σ fc$ , was calculated from the product of fiber stresses, $σ f$ , and their respective relative frequencies. This, and other similar models, ignored the curl factor and assumed that fibers lay parallel to the surface of the sheet.¹³ Rawal et al.³ modified the models and included the effects of both fiber reorientation and curl. Bais-Singh and Goswami¹⁸ proposed a tensile model for spun-bonded nonwoven fabrics based on the classical laminar theory. There have been several other models, such as the continuum models¹⁹ and finite-element models;^5,9 however, little specific work has been reported on micromechanics of fibrous assemblies, such as hydroentangled nonwoven fabrics.

In the small-strain range, where the Hookean behavior is assumed, the elongation of fiber elements is the predominant mode of structural deformation. Each fiber element undergoes stress–strain behavior, as expressed in Equation (1):

σ f = E ɛ f

(1)

where E is the Young’s modulus or initial modulus.^2,20 For small strains under uniaxial loading, the Small Strain Theory is used and the effect of the lateral contraction is assumed to be negligible. Where the strain is large, the Large Strain Theory is applied and the Poisson’s ratio of the fabric is factored into the strain equation. Farukh et al.² discussed the theory in their model and expressed the total number of fibers, N_f, using Equation (2):

N f = \frac{F A . ρ fc}{ρ f . l f . C A}

(2)

where F_A is cross-sectional area of the fabric,

ρ fc

is fabric density,

ρ f

is fiber density, l_f is fiber length and C_A is the cross-sectional area of the fiber. The N_f contributing to the fabric stress is dependent on the relative frequency of fibers oriented at the testing angle, β_i. If the FOD is

ϕ (β i)

, the number of fibers, N_f, is

ϕ (β i) cos β i

. Then the fabric stress,

σ fc

, can be calculated from the fiber stress components,

σ f cos β

, from Equation (3):

σ fc = \sum_{i = 1}^{n} (σ f cos β) {ϕ (β) cos β}

(3)

This model was derived by Hearle and Stevenson²⁰ to predict macro-tensile behavior of fibrous structures. Alternatively, according to Bais-Singh and Goswami,¹⁸ during loading each layer experiences the same strain as the strain applied to the fabric. Therefore, the layer strain, $ɛ l$ , and the total stress, $σ fc$ , in the fiber direction, θ, can be calculated from Equations (4) and (5), respectively. This model also included the lateral changes, $θ γ LT$ , in the dimensions of the nonwoven fabrics experiencing axial loading:

ɛ l = \cos 2 θ ɛ L + \sin 2 θ ɛ T + \sin θ \cos θ γ LT

(4)

σ fc = \int_{- 90}^{90} \int_{k = 1}^{NF} σ f \cos 2 θ φ k f (ɛ f) . \partial θ

(5)

where

φ fk

is the fiber volume fraction in the fabric layer.

Rawal et al.⁴ considered a meso-domain and calculated the fabric stress, $σ fc$ , from Equation (6):

σ fc = \sum_{i = 1}^{n} mK α (β f) \cos β fj ϕ (β fj) σ f (β f, \bar{ɛ})

(6)

and

K α (β f) = \int_{- π / 2 - α}^{π / 2 - α} | cos (β f) | ϕ (β f) δ β f

(7)

where m is mass per unit area,

β f

is the final fiber orientation,

K α

is the directional parameter and

\bar{ɛ}

is the fabric strain. The concept in the above models is to transform fiber strain to fabric stress.^4,18,21

Linking deformation energy and stress–strain behavior of fibrous material

Wilbrink et al.²² analyzed the strain energy to model the mechanics of fibrous material. Here, fibers were considered as discrete elements of a spring network model governing the mechanical deformation of the dissipative system. That is, for a network under loading, stress is determined from the strain of elements. Fiber strain defines the anisotropic behavior of nonwoven fabrics better than fiber reorientation, which is negligible in comparison.² Since axial loading is associated with elongation and fabric stiffness, Young’s modulus of the fabric, E, can be evaluated from strain energy as given by Equation (8):¹⁶

U s = \frac{E . C A}{L} (Δ L) 2

(8)

where U_s is the strain energy, E is the Young’s modulus, C_A is the cross-sectional area of the fabric, L is the initial length of the sample and

Δ L

is the elongation. The product,

E . C A

expresses the resistance to tension. The total strain energy is the area under the stress–strain curve resulting from axial deformation and shearing of fibers. By the principle of conservation of energy, the work done on the specimen during loading is equivalent to energy changes in individual elements.¹ That is, deformation energy is the sum of strain energies of microelements in the network assuming elastic deformation. The derivative of this total energy with respect to applied strain provides the corresponding initial modulus of the material. Therefore, for a network under loading, the system energy,

E (u, s)

, is expressed by Equation (9):

E (u, s) = \sum_{e = 1}^{n e} \frac{1}{2} k e ω_{e}^{2}

(9)

where n_e is the number of elastic springs, k_e is the stiffness constant and

ω e

is equivalent elongation. We used this model to develop a semi-empirical model for the deformation energy of the fiber network of hydroentangled nonwoven fabrics.

In the current study, the main objective was to verify available theoretical models and ascertain their applicability to hydroentangled nonwoven fabrics when subjected to uniaxial loading.

Methodology

Nonwoven fabric production

The fiber type and process parameters used to make different nonwoven fabric samples are listed in Table 1. The pilot hydroentanglement machine employed to produce the samples was capable of producing 60-cm wide fabric, operating at a maximum machine speed of 20 m/min and waterjet pressure (WJP) of 250 bar. It had three manifolds fitted with jet-strips of 0.10-mm diameter holes. The machine bonded the top and bottom sides of the cross-lapped batt successively in a single pass.²³ Nonwoven fabrics produced from two different fiber types, cotton (C) and viscose (V), were hydroentangled at different WJPs of 80 bar (P₁), 100 bar (P₂) and 120 bar (P₃).

Table 1.

Process parameters for different samples

Processing parameter	Sample
Processing parameter	CP₁	CP₂	CP₃	VP₁	VP₂	VP₃
Constituent fiber type	Cotton	Cotton	Cotton	Viscose	Viscose	Viscose
Waterjet pressure (bars)	80	100	120	80	100	120
Machine speed (m/min)	3	3	3	3	3	3

The fibers and nonwoven fabrics were conditioned in standard laboratory atmosphere of 20 ± 2℃ temperature and relative humidity of 65 ± 2% for 24 hours prior to testing.

Fiber properties

An Instron tensile testing machine fitted with a 5-N load cell was used to measure the stress–strain characteristics of the individual fibers. The ASTM D 3822-96 test method was followed to characterize cotton and viscose fibers used in producing the hydroentangled fabric samples. The Young’s modulus was determined from the initial slope of the fiber stress–strain graphs within the Hookean region. An Optical Fiber Diameter Analyzer (OFDA) was used to measure the average fiber diameter.

Sample preparation

Square samples of 100 mm × 100 mm were cut and weighed using a balance. The rectangular specimens measuring 20 mm × 5 mm in length and width, respectively, were cut in machine-direction (MD) and cross-machine direction (CD) from the same 100 mm × 100 mm square sample. As such, the physical properties of the specimens cut in MD and CD are similar to those given in Table 2. Then small rectangular strips measuring 20 mm × 5 mm in length and width, respectively, were cut. Three strips were cut in each principal direction, that is, the MD and CD. The strips were then coated with gold using an SPI-MODULE© Sputter Coater for 120 seconds to prevent the accumulation of charge on the surface, which leads to the deterioration of scanning electron microscope (SEM) images.

Table 2.

Properties of hydroentangled nonwoven fabrics.

Specimen	Areal weight (g/m²)	Fabric thickness (mm)	Fabric Density (Kg/m³)	Fiber volume fraction
CP1.CD	115.5	0.585	197.426	0.128
CP2.CD	133.7	0.689	194.049	0.127
CP3.CD	133.6	0.666	200.691	0.130
CP1.MD	115.5	0.585	197.426	0.128
CP2.MD	133.7	0.689	194.049	0.127
CP3.MD	133.6	0.666	200.691	0.130
VP1.CD	115.5	0.585	197.426	0.128
VP2.CD	148.1	0.714	207.282	0.136
VP3.CD	148.0	0.668	221.781	0.146
VP1.MD	115.5	0.585	197.426	0.128
VP2.MD	148.1	0.714	207.282	0.136
VP3.MD	148.0	0.668	221.781	0.146

Fabric thickness

The fabric thickness was measured according to the ISO 9073-2: 1995 Standard Test Method on a Mitutoyo Elastocon EV06 Electronic Thickness gauge, with a presser foot of 50.5 mm in diameter and exerting pressure of 1 kPa on the fabric specimen. The sample density, ρ, was calculated from the weight, area and thickness measurement.

Stress–strain measurement of micro-samples

A Deben Microtest module, shown in Figure 1, fitted with a 660 N load cell was used to test the stress–strain behavior of the micro-sample. The module settings were stage gauge length of 10 mm, maximum extension of 10 mm and motor speed of 0.5 mm/min. For the test, a sputter coated specimen strip of 20 mm × 5 mm dimensions was clamped in the test module jaws, as shown in Figure 1. The module was fitted in the FEI Quanta 200 SEM chamber and testing was conducted in situ. The in situ fit enabled recording of dynamic deformation during the uniaxial loading of the specimen. Simultaneously, the stress–strain behavior was captured on a computer interfaced with the Deben Microtest software. Three specimens cut in each direction were tested and the average reported.

Figure 1.

Deben Microtest module in the scanning electron microscope (SEM) chamber.

The micro-samples of hydroentangled nonwoven in the current work were tested in two principal axes of symmetry, that is, MD (0° or 180°) and CD (90°), respectively.

Fiber-orientation distribution function

A Direct Tracking Analysis method was used to estimate the FOD function of the nonwoven network. Images from five specimens, measuring 10 cm × 10 cm, were observed under an Olympus light microscope interfaced with an Olympus CX 31 Image Analyzer. Digital images were captured by the digitization software and the fiber-orientation angles were estimated. About 1000 fiber-segments per sample were imaged and their orientation angles relative to MD as the reference axis were measured. The frequency of fibers in each 10-degree angle interval of the orientation angle class between 0° to180° was quantified. A trigonometric function was fitted to the data to model the FOD by following the method described elsewhere.^17,24

Model analysis

Some basic assumptions made in the analysis were that the fiber diameter and Young’s modulus, E_f, remained constant as loading increased. The fiber curvature was not measured due to another assumption that fibers only provide resistance to stress when they are straight and not still curved.²⁵ In the numerical calculations and modeling, the objective was to transform fiber strain, $ɛ f$ , to fabric stress, $σ fc$ , for different specimens in CD and MD at different fabric strain, $ɛ fc$ . As $ɛ fc$ is an independent variable, it is used to evaluate $ɛ f$ . The $ɛ fc$ was set at $ɛ fc = 0, 0.005; 0.010; 0.015 \dots 0.800$ , where at the limit most of the specimens failed completely. The $ɛ f$ is calculated from the Large Strain Theory using Equation (10):²⁰

ɛ f = [(1 + ɛ fc) 2 \cos 2 β + (1 - v ɛ fc) 2 \sin 2 β] 2 - 1

(10)

where v is the average Poisson’s ratio in MD or CD for modeling MD and CD

σ fc

, respectively. The v was determined using the SEM micrographs of the specimen before and after loading to failure. The

ɛ f

was determined at β at each class interval of 5° between 0° and 180°. Of note, as the fabric stretches, not all fibers experience the same

ɛ f

because they lie at different angles, β, to the test direction. If the

ɛ f

at β was higher than the maximum fiber strain,

\bar{ɛ f}

, at set

ɛ fc

, those fibers in that initial orientation were excluded from subsequent numerical analysis because it meant they would have failed. Therefore, for fibers to contribute to

σ fc

, the criteria was for their

ɛ f \leq \bar{ɛ f}

. The second quantity determined was the total number of fibers, n_f, lying at angle β. To calculate n_f, the relative frequency of fibers at angle β obtained from FOD was used, as given in Equation (11):

n f lyingat β = (rel . frequencyoffibersorientedatangle β) \times N f

(11)

The n_f was determined at β at each class interval of 5° between 0° and 180°. With n_f and $ɛ f$ , the $σ f$ is determined according to Equations (3) and (6), giving the total contribution of all fibers by adding the $σ f$ at angle β to give $σ fc$ .^4,20 The specific $σ fc$ is calculated by dividing $σ fc$ by the fiber linear density. The specific $σ fc$ predicted by Hearle and Stevenson²⁰ and Rawal et al.’s⁴ models were identified by suffixes −1 and −2, respectively. The experimental specific $σ fc$ was calculated using Equation (12):

Experimentalspecific, σ fc = \frac{measuredtensilestrength (N)}{width (m)} \times \frac{1}{fabricdensity (g . m - 2)} .

(12)

Results and discussion

Fiber characterization

Figures 2(a) and (b) show SEM micrographs of cotton and viscose fibers, respectively. The surface of cotton fiber is convoluted with a flattened and collapsed cross-section. The shape of the viscose fiber, shown in Figure 2(b), appears circular with serrations on its surface. A summary of the important properties of these constituent fibers used in this study is shown in Table 3.

Figure 2.

Scanning electron micrographs of (a) cotton and (b) viscose fibers.

Table 3.

Properties of cotton and viscose fibers

	Fiber characteristics
Fiber type	Density, ρ_f (g/cm³)	Fiber size (dtex)	Length (mm)	Diameter (µm)	Cross-section area (10⁻¹²m²)	Tensile stress at max load, σ_f (MPa)	Strain, ɛ_f (%)	Initial modulus, E (10³N/mm²)
Cotton	1.54	1.8	25	12.9 ± 3.8 ^a6.3 ± 1.4	130.7 ± 11.3 (81.3 ± 5.3)	229 ± 48	6.8 ± 2.3	5.65 ± 1.37
Viscose	1.52	1.7	38	13.4 ± 3.2	141.0 ± 8.0	263 ± 45	9.5 ± 1.3	9.85 ± 1.82

Thickness of the flattened surface.

Nonwoven fabric characterization

The measured and calculated properties of the nonwoven fabrics are summarized in Table 2. It was not possible to produce nonwoven fabrics with the same areal weight due to inherent variations in constituent fiber properties, web densities and other processing factors.

It is evident from Table 2 that the fabric density and fiber volume fraction increased with the increase in WJP. This was expected, as at higher WJPs more energy is transferred to fibers so as to entangle and compact fibers to a higher degree.

Fiber-orientation density function

The fiber frequency at different orientation angles was analyzed and fitted for each sample following the method proposed by Hearle and Ozsanlav¹. The following empirical equations were obtained:

f (x) VP 2 = 7.273 - 4.595 \cos 4 β R 2 = 0.90

f (x) VP 1 = 7.632 - 5.537 \cos 4 β R 2 = 0.91

f (x) CP 1 = 7.588 - 5.79 \cos 4 β R 2 = 0.85

f (x) CP 2 = 8.098 - 6.776 \cos 4 β R 2 = 0.93

The graphs representing the calculated FOD are shown in Figure 3.

Figure 3.

Graphs of relative fiber frequency at different orientation angles.

The FOD profiles in Figure 3 show the predominance of fiber orientation in CD since the webs were produced by the cross-lapping technique. The high impact force of the waterjets caused displacement of the fibers during the entanglement process, as evidenced by the shift in FOD profiles with respect to change in WJP. At high WJP of 100 bar, the FOD profile becomes broader with a reduced proportion of fibers oriented to CD than that at WJP of 80 bar. Furthermore, the FOD profile peaks are relatively higher at WJP of 80 bar than that at WJP of 100 bar, indicating reorientation of more fibers from the CD to MD at higher WJP.

Model and experimental micro-mechanical behavior at fabric strain of 10%

Figures 4(a)–(d) show the calculated specific stress of the hydroentangled fabrics in MD and CD. The graphs show initial linearity up to about 5% strain. This is typical of most stress–strain graphs for fibrous assemblies, such as nonwoven fabrics. They are characterized by initial linear zones followed by nonlinear regions.²¹ In MD, as shown in Figures 4(a) and (c), the specific stress predicted by Model 1 is lower than that of Model 2. However, in CD the results obtained for Model 2 are higher. Both the models correctly predicted the specific stress in CD when compared to that in MD. Figures 4(e) and (f) show measured specific stresses of different samples and are almost five times lower than that of the predicted values. When modeling stress–strain behavior, the fabric responds instantly to the added load because fiber elements are assumed to behave as elements that are fixed at both ends. Therefore, the initial modulus of fibers is a huge contributor to the monolithic microstructural behavior. Practically, fiber elements initially rearrange, straighten and slip in response to increasing load. These events result in reducing specific stress of the structure achieved experimentally, as shown in Figures 4(e) and (f) compared to the model. Also, from Figure 4(f), it is evident that high fabric area weight and high WJP produce hydroentangled nonwoven fabrics with high specific stress in CD. For example, the areal weight of specimen VP2.CD is higher than that for VP1.CD and CP2.CD by about 30% and 10%, respectively. In Figure 4(f), the graphs of CP1.CD and CP2.CD achieved similar specific stresses up to strain of 10%. This can be attributed to use of optimum WJP of 80 and 100 bar to form the two nonwoven fabrics as their areal weights are similar. Moyo et al.²³ showed that for hydroentangled nonwoven fabrics, there is an optimum processing WJP beyond which the structural integrity of the fibers is adversely affected.

Figure 4.

Modeled and experimental specific stress–strain curves of cotton and viscose nonwoven fabrics up to fabric strain of 10%.

Model and experimental micro-mechanical behavior at fabric strain of 50%

Stress–strain graphs were obtained for both cotton and viscose fabrics, as shown in Figure 5. In Figures 5(a)–(d), the maximum specific stress of the nonwoven fabrics is achieved below the fabric strain of 10%. Also, the graphs obtained from theoretical results are narrower with higher peaks showing high stiffness. Experimentally, Figures 5(e) and (f) show peaks at about 45% in MD and 35% in CD. These graphs are relatively broader than those in Figures 5(a)–(d). Relatively, as shown in Figures 5(b), (d) and (f), higher specific stress is observed in CD than that in corresponding MD due to preferential orientation of fibers in CD. This further confirms that higher tensile strength of the fabric is directly dependent on the fiber orientation. With further increase in load beyond the peak, the specific stress of the nonwoven fabrics in CD was reduced abruptly due to localized fabric damage and fiber breakage. In MD, this decrease was gradual, possibly due to the dominance of fiber slippage and reorientation of the fibers from the CD.²¹ The nonwoven fabrics produced from cotton fibers experienced higher strain than those produced from viscose fibers. The cotton fiber is convoluted and has more crimp, which is removed or straightened out before the fiber element can experience any stress, thus achieving higher strain.¹ The heterogeneous microstructure of the samples caused the anisotropic behavior, as shown in Figure 5. Also, there is evidence of differences in fiber movements within the structure that are fiber dependent. In Figure 5(e), the experimental specific stresses of CP1 is higher than that for VP1 in MD and the results are opposite when considering the same in CD of the two fabrics. This indicates that more cotton fibers were displaced and reoriented from the predominant CD on the cross-laid web towards the MD in the fabric than viscose fibers. With fewer fibers lying in MD, the viscose fabric is weak and cannot resist the axial tension in MD. Fibers offer resistance or bear forces acting along their axes.^3,12 As such, the strength of VP1 is relatively higher than that for CP1. In Figure 5, the maximum fabric stress is obtained at about 5% and 7.5% strain for cotton and viscose fabrics, respectively. However, the experimental stress–strain curves show that the structure is in the linear region and it has not approached the highest specific stress point. The experimental curves in MD are more flat and the maximum specific strain is attained at about 50% fabric strain. That of the model is narrower and similar to CD only with fabric showing lower specific stress. This indicates that the theoretical model is limited at small strain. Also, as shown in Figure 5, the theoretical results in comparison to experimental results are limited at large tensile strain. This difference can be attributed to bonding in hydroentangled nonwoven fabrics, which depends on the inter-fiber friction. As such, the contribution of individual fibers is overestimated, which in turn overestimates the fabric stress. The peak of the theoretical results is attained at a much lower fabric strain and it appears to be largely dependent on individual fiber strain. However, empirical results suggest that the majority of fiber reorientation and rearrangement take place before enough pressure is generated. It is the pressure that results in an increase in both the inter-fiber friction and resistance to the axial forces.

Figure 5.

Modeled and experimental specific stress–strain curves of cotton and viscose nonwoven fabrics up to fabric strain of 50%.

Comparison between experimental and theoretical deformation energy

The area under the stress–strain curve up to the ultimate tensile strength (UTS) was calculated to represent deformation energy using the Trapezoidal Rule.²⁶ Owing to the high measuring frequency of the Deben microtensile tester, the value is expected to be a good approximation. The deformation energy was then used to determine the initial modulus, E, from Equation (8). As shown in Figure 6, steady increases in the stiffness of the cotton nonwoven fabric, both in CD and MD, were observed with the increase in WJP. This could be explained by increased values of V_f and ρ_fc (Table 2)_. Figures 4(e) and (f) and Figures 5(e) and (f) show hydroentangled nonwoven fabrics produced at WJPs of 80 and 100 bar, respectively. The values of their initial modulus, E, are much closer. However, Figure 6 includes results from a fabric produced at WJP of 120 bar, and it is evident that the comparative values of E increase with the increase in WJP. Also, the values of E for viscose nonwoven fabrics are higher than that of cotton fabrics. This could be attributed to higher fiber length and initial modulus of individual viscose fibers, as shown in Table 3. Also, hydroentangled viscose nonwoven fabrics achieve much higher V_f_. and ρ_fc with viscose fibers. Therefore, it is relatively easier to process viscose fibers than cotton fibers.

Figure 6.

Initial moduli of the hydroentangled nonwoven fabrics.

In verifying the latest model, as proposed by Wilbrink et al.²² and given by Equation (9), we considered deformation energy up to the UTS. We substituted the stiffness constant, elongation and number of spring elements by Young’s modulus of fibers, E_f, fiber strain, $ɛ f$ , and total number of fibers, N_f, respectively as shown in Equation (13):

E (T) = \sum_{e = 1}^{NF} \frac{1}{2} E f ɛ_{f}^{2}

(13)

where

E (T)

is total deformation energy of the nonwoven fabric. We then modified Equation (13) and introduced

\cos 2 β

to account for components of fiber responses with respect to test direction and to account for fiber orientation in the structure. This accounted for the random fiber arrangement in the structure, as shown in Equation (14):

E (T) = \int_{i = 1}^{NF} \int_{0}^{π / 2} \frac{1}{2} E fi ɛ_{fi}^{2} \cos 2 β δ β

(14)

where

i = 1, \dots, NF

and β is the orientation angle of component fibers. The results obtained from Equations (13) and (14) were compared with experimental results, as shown in Figure 7. The predicted deformation energy is higher in both MD and CD. It is evident from Figure 7 that the spring-model by Wilbrink et al.,²² applied as is, overestimates the micro-deformation energy of hydroentangled nonwoven fabric. The difference between measured and predicted results can partly be attributed to the absence of a factor that represents fiber orientation in the estimation. The proposed modification of the model given in Equation (14) performs better. With improved modeling of fiber orientation, the fit would be expected to improve further. Further work would include the effect of WJP in the model.

Figure 7.

Experimental and modeled deformation energy of nonwoven fabrics.

The values predicted by the model proposed by Farukh et al.² were higher than those of the experimental results. The difference can be attributed to assumptions and inherent variations in fiber mechanical properties and fiber dimensions, such as diameter and length. Also, these models were formulated and verified for thermal bonded nonwoven fabrics where bonding points are continuous. The measurement of fiber orientation is based on only surface fibers, which may not be a correct representation as FOD is critical in most theoretical predictions.

Conclusions

Some existing stress–strain models developed for nonwoven fabrics have been applied to hydroentangled nonwoven fabrics. The theoretical specific stress and deformation energy differed with the experimental results. The model to predict deformation energy was improved by including the orientation distribution in the calculation. The maximum fabric stress is obtained at about 5% and 7.5% strain for cotton and viscose fabric, respectively. However, the experimental stress–strain curves show that the structure is in the linear region when the modeled results approached their highest specific stress point. The theoretical models highly overestimate the specific stress of the hydroentangled nonwoven fabrics. Therefore, the theoretical results in comparison with experimental results are limited for both small and large tensile strains. An increase in sample stiffness was observed with the increase in WJP, in both CD and MD_. Also, the initial modulus of viscose nonwoven fabrics was comparatively higher than that of cotton fabrics. The models for predicting fabric stress need improvements to accommodate the behavior of hydroentangled nonwoven fabrics.

Footnotes

Future work

Further work is under way for investigating the dominant failure mechanism in hydroentangled nonwoven fabric. The research includes observing the individual fiber migration influenced by the impact of high-pressure waterjets to develop a more comprehensive model.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is based on the research supported in part by the National Research Foundation of South Africa (Grant specific unique reference number (UID) 90326). The authors acknowledge that opinions, findings, and conclusions expressed in any publication generated by the supported research are those of the authors, and that the sponsors accept no liability whatsoever in this regard.

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