Determination of Bond Strengths in Non-woven Fabrics: a Combined Experimental and Computational Approach

Abstract

Interfiber bonds are important structural components in non-woven fabrics. Bond fracture greatly affects the strength and damage progression in a fiber network structure. Here, we present a novel combined experimental and computational approach to extract bond strengths in non-wovens. In this method, a small specimen is imaged and the obtained 3D geometry of the network is directly modeled in a finite element framework. Bond properties are determined by matching finite element simulation predicted mechanical response to the experimental data. This method is demonstrated by applying it to six specimens of a commercial polypropylene non-woven. A four parameter bi-linear interface law is used with normal stiffness k, shear stiffness βk, separation at the start of damage d ₁, and separation at total loss of bond stiffness d ₂. The determined normal strength (kd ₁)and shear strength (βkd ₁) are (1.3 ± 0.3) × 10² MPa and (1.0 ± 0.2) × 10² MPa, respectively. To show that the obtained bond parameters can be applied to a new specimen, a cross validation is conducted whereby parameters are fit from five specimens and then evaluated on the sixth. Additional validation of the obtained bond strength parameters was conducted with larger size artificial network simulations and peel tests. The proposed method in this work carries the dual advantages of characterizing actual bonds in a non-woven and characterizing hundreds of bonds simultaneously. The method can be applied to a variety of non-woven fabrics that are bonded at fiber-fiber intersections.

Appendices

Appendix A: Fitted Bond Parameters

The bond parameter estimation results of individual fitting and cross validation are shown in Table 4. The obtained values have good consistency among tested specimens. Figure 11 shows the cross validation results. The finite element simulation captures the overall trend of the experimental load-displacement curve, even though the optimization process does not use the experimental data of that specimen. Iterations 2 and 5 have higher simulation force responses than experiments, while the other four iterations show the opposite behavior. This difference is because both specimen 2 and 5 have relatively low bond strength values when fitted independently (Table 3), so they lower the bond strength estimations in the cross validation step when one iteration takes them as part of the training set. As mentioned in the earlier text, specimen 2 and 5 are suspectable of fiber slippage and hence underestimating bond strength values. This may be the reason for the mismatch of simulation and experimental load-displacement curve in this cross validation step.

Table 4 Optimization results for individual fit and cross-validation

Fig. 11

Leave-one-out cross validation results. Bond model parameters obtained from training data sets are tested on the left out test data set. The schematic label shows the partition of each iteration, where “ ×” represents the test data set and “ ∙” represents the training data set. The simulated load-displacement curve, residual and R ² value of each iteration are shown

Appendix B: Peel Test Analysis

Figure 12 shows a simplified loading scenario at the crack tip in a peel test. One bond is connected to four fiber segments and each fiber segment is connected to the rest of non-woven network structure. When a bond is taking up load, two fiber segments are under tension. When a bond is broken, the total energy dissipation (U _total ) comes from the energy to separate bonded interfaces (U _b ) and the relaxation of strain energy in fibers connected to this bond (U _f ).

$$ U_{total} = U_{b}+U_{f} $$

(5)

Fig. 12

The loading approximation of the crack tip in peel tests

Assuming normal bond separation, U _b can be calculated using the cohesive zone model parameters (Table 4):

$$ U_{b} = \frac{1}{2}\times \sigma_{normal}\times A \times d_{1} = (0.10 \pm 0.03)\mu~J $$

(6)

where A is the bond area.

U _f is the strain energy stored in the two stretched fibers and can be calculated as:

$$ U_{f} = \frac{(\sigma_{normal}\times~A)^{2}\times~L_{seg}}{E\times~\pi~R^{2}} = (1.7 \pm 0.8)\mu~J $$

(7)

where L _seg = 0.2mm is the fiber segment length, E = 2400MPa is the fiber modulus and R = 20μ m is the fiber radius.

Summing up eqautions (6) and (7), we have

$$ U_{total} = (1.8 \pm 0.8)\mu~J $$

(8)

as the predicted energy per bond fracture during the static peel test regime.