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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Liu DS, Ashcraft JN, Mannarino MM, Silberstein MN, Argun AA, Rutledge GC, Boyce MC, Hammond PT (2013) Spray layer-by-layer electrospun composite proton exchange membranes. Adv Funct Mater 23(24):3087–3095
Russell SJ (2006) Handbook of nonwovens. Woodhead Publishing, Sawston
Yoon K, Hsiao BS, Chu B (2008) Functional nanofibers for environmental applications. J Mater Chem 18(44):5326–5334
Ahmed FE, Lalia BS, Hashaikeh R (2015) A review on electrospinning for membrane fabrication: challenges and applications. Desalination 356:15–30
Ridruejo A, González C, LLorca J (2011) Micromechanisms of deformation and fracture of polypropylene nonwoven fabrics. Int J Solids Struct 48(1):153–162
Silberstein MN, Pai CL, Rutledge GC, Boyce MC (2012) Elastic–plastic behavior of non-woven fibrous mats. J Mech Phys Solids 60(2):295–318
Chen Y, Ridruejo A, González C, Llorca J, Siegmund T (2016) Notch effect in failure of fiberglass non-woven materials. Int J Solids Struct 96:254–264
Isaksson P, Gradin P, Kulachenko A (2006) The onset and progression of damage in isotropic paper sheets. Int J Solids Struct 43(3):713–726
Chen N, Koker MK, Uzun S, Silberstein MN (2016) In-situ x-ray study of the deformation mechanisms of non-woven polypropylene. Int J Solids Struct 97:200–208
Cox H (1952) The elasticity and strength of paper and other fibrous materials. British Journal of Spplied Physics 3(3):72
Åström J, Saarinen S, Niskanen K, Kurkijärvi J (1994) Microscopic mechanics of fiber networks. J Appl Phys 75(5):2383–2392. https://doi.org/10.1063/1.356259
Räisänen V, Alava M, Niskanen K, Nieminen R (1997) Does the shear-lag model apply to random fiber networks? J Mater Res 12(10):2725–2732
Shahsavari A, Picu R (2013) Elasticity of sparsely cross-linked random fibre networks. Philos Mag Lett 93 (6):356–361
Torgnysdotter A, Kulachenko A, Gradin P (2007) The link between the fiber contact zone and the physical properties of paper: a way to control paper properties. J Compos Mater 41(13):1619–1633
Choi SS, Lee SG, Joo CW, Im SS, Kim SH (2004) Formation of interfiber bonding in electrospun poly (etherimide) nanofiber web. J Mater Sci 39(4):1511–1513
Ridruejo A, González C, LLorca J (2012) A constitutive model for the in-plane mechanical behavior of nonwoven fabrics. Int J Solids Struct 49(17):2215–2229
Isaksson P, Hägglund R, Gradin P (2004) Continuum damage mechanics applied to paper. Int J Solids Struct 41(16):4731–4755
Torgnysdotter A, Kulachenko A, Gradin P (2007) Fiber/fiber crosses: finite element modeling and comparison with experiment. J Compos Mater 41(13):1603–1618
Schmied FJ, Teichert C, Kappel L, Hirn U, Schennach R (2012) Joint strength measurements of individual fiber-fiber bonds: an atomic force microscopy based method. Rev Sci Instrum 83(7):073,902
Schmied FJ, Teichert C, Kappel L, Hirn U, Bauer W, Schennach R (2013) What holds paper together: Nanometre scale exploration of bonding between paper fibres. Sci Rep 3:2432
Kulachenko A, Uesaka T (2012) Direct simulations of fiber network deformation and failure. Mech Mater 51:1–14
Koubaa A, Koran Z (1995) Measure of the internal bond strength of paper/board. Tappi J 78(3):103–112
Yousefi Shivyari N, Tajvidi M, Bousfield DW, Gardner DJ (2016) Production and characterization of laminates of paper and cellulose nanofibrils. ACS Appl Mater Interfaces 8(38):25,520–25,528
Berhan L, Sastry A (2003) On modeling bonds in fused, porous networks: 3d simulations of fibrous–particulate joints. J Compos Mater 37(8):715–740
Buell S, Rutledge GC, Vliet KJV (2010) Predicting polymer nanofiber interactions via molecular simulations. ACS Appl Mater Interfaces 2(4):1164–1172
Wernersson EL, Borodulina S, Kulachenko A, Borgefors G (2014) Characterisations of fibre networks in paper using micro computed tomography images. Nord Pulp Pap Res J 29(3):468– 475
Popov V (2010) Contact mechanics and friction: physical principles and applications. Springer Science & Business Media, Berlin
Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(1998):1267–1282
Bower AF (2009) Applied Mechanics of Solids. CRC press, Boca Raton
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313
Financial support for this study was provided by a Cornell Affinito-Stewart grant. We thank Teresa Porri for her assistance in CT experiments and Kintex Industries, LLC for providing material. Xradia/Zeiss Imaging data was acquired in the Cornell BRC-Imaging Facility using the shared, NIH-funded (S10OD012287) Xradia XRM-520 nano-CT. Naigeng Chen is supported by Cornell Higher Energy Synchrotron Source (CHESS), which is supported by the NSF & NIH/NIGMS via NSF award DMR-1332208.
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.
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 ).
Assuming normal bond separation, U b can be calculated using the cohesive zone model parameters (Table 4):
where A is the bond area.
U f is the strain energy stored in the two stretched fibers and can be calculated as:
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
as the predicted energy per bond fracture during the static peel test regime.
Rights and permissions
About this article
Cite this article
Chen, N., Silberstein, M.N. Determination of Bond Strengths in Non-woven Fabrics: a Combined Experimental and Computational Approach. Exp Mech 58, 343–355 (2018). https://doi.org/10.1007/s11340-017-0346-3
- Bond damage
- Micro computed tomography
- Image based modeling