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Yarn/Yarn Friction Analysis Considering the Weaving Process of Textile Fabrics: Analytical Model and Experimental Validation

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Abstract

The friction between twisted yarns during the process of manufacturing textile reinforcements has been considered an important issue that can strongly influence the mechanical properties of the preform, which deteriorate the mechanical characteristics of fiber-reinforced composites if the friction is excessive. Based on Hertzian contact theory, a novel analytical model has been developed in this research to describe the friction behavior between the twisted yarns in orthogonal and non-orthogonal contact. The realistic contact area was modeled under micro/meso scales taking into account the contact angle between the yarns and the orientation of the fibers influenced by the twist. The efficacy of the developed model was confirmed by the experimental approach. Through the developed model, the yarn/yarn friction behaviors were characterized under different conditions considering the weaving process, such as orthogonal and non-orthogonal contact, same/different twist level, and same/different twist direction, which is essential for optimizing the textile preform forming process and enhancing the mechanical properties of the composites.

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Data Availability

The raw and experimental data required to reproduce these studies can be shared on request.

Abbreviations

F f :

Friction force (N)

COF :

Coefficient of friction

A r/yarn :

Realistic contact area of yarn (m2)

A r/fiber :

Realistic contact area of fiber (m2)

F n :

Normal load in \(\overrightarrow{n}\) (N)

F t :

Tangential load of yarn (N)

α :

Angle between fiber axes (°)

β :

Angle between yarn axes (°)

γ :

Twist angle of yarn (°)

θ :

Angle between z \(\left(\overrightarrow{z}\right)\) and normal \(\left(\overrightarrow{n}\right)\) directions (°)

r f :

Radius of fiber (m)

R :

Radius of yarn (m)

R * :

Equivalent radius of fiber (m)

E * :

Equivalent Young’s modulus of fiber (Pa)

E :

Young’s modulus of fiber (Pa)

ν :

Poisson’s ratio of fiber

R’ :

Major relative radius of curvature of the contact surface

R’’ :

Minor relative radius of curvature of the contact surface

τ :

Shear strength (Pa)

H :

Displacement under the action of F

f N :

Normal load of fiber (N)

n :

Number of contact fibers in width of upper yarn

m :

Number of contact fibers in width of lower yarn

T t :

Twist of yarn (tpm)

h i :

Distance between the fibers (m)

b :

Half-width of the contact (m)

E l :

Longitudinal modulus of yarn (Pa)

E t :

Transverse modulus of yarn (Pa)

v 12 :

Poisson’s ratio of yarn

F :

Applied normal force in \(\overrightarrow{z}\) (N)

F p :

Pre-tension of yarn (N)

l :

Length of twisted yarn sample (m)

k :

Fitting coefficient

a :

Span of sample (m)

u :

Distance between contact point and center of span (m)

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Acknowledgements

The authors gratefully acknowledge: the financial support from the China Scholarship Council (CSC 202108120054).

Author information

Authors and Affiliations

  1. Ministry of Education Key Laboratory of Advanced Textile Composite Materials, Tiangong University, Tianjin, 300387, China

    Yu Wang & Yanan Jiao

  2. School of Textile Science and Engineering, Tiangong University, Tianjin, 300387, China

    Yu Wang & Yanan Jiao

  3. Lpmt, Ensisa, University of Haute-Alsace, 68000, Mulhouse, France

    Yu Wang & Peng Wang

  4. University of Strasbourg, Strasbourg, France

    Yu Wang & Peng Wang

Authors
  1. Yu Wang
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  2. Yanan Jiao
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Contributions

YW: investigation, methodology, theoretical analysis, experimental analysis, validation, visualization and writing—original draft. YJ: project administration, supervision, validation and review & editing. PW: project administration, supervision, methodology, formal analysis, validation and writing—review & editing.

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Correspondence to Peng Wang.

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Appendix A

Appendix A

The changing relationships between θ and displacement H under the action of F are detailed in this appendix. All parameters are shown in Fig. 15. The applied normal force F in the kinematic friction process can be further calculated by tension acting on the lower yarn T through the following equations:

$$T = E_{l} S\left( {\frac{H}{{\sin \theta_{1} }} + \frac{H}{{\sin \theta_{2} }} - 1} \right) + F_{p},$$
(17)

where El is the longitudinal modulus of yarn, S is the area of yarn’s cross section, and Fp is the initial pre-tension applied to yarn.

$$\sqrt {(\frac{a}{2} - u)^{2} + H^{2} } + \sqrt {(\frac{a}{2} + u)^{2} + H^{2} } = l,$$
(18)

where l is the length of the yarn sample involved in friction which is obtained from the experiment. Moreover, θ1 and θ2 are given as

$$\theta_{1} = \arctan \frac{2H}{{a - l\sqrt {\frac{{a^{2} + 4H^{2} - l^{2} }}{{a^{2} - l^{2} }}} }},$$
(19)
$$\theta_{2} = \arctan \frac{2H}{{a + l\sqrt {\frac{{a^{2} + 4H^{2} - l^{2} }}{{a^{2} - l^{2} }}} }},$$
(20)

where H is displacement under the action of F, which can have a relationship using θ1 and θ2 see Eq. (14):

Fig. 15
figure 15

The description of dimensional parameters during the friction process based on Fig. 5

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Wang, Y., Jiao, Y. & Wang, P. Yarn/Yarn Friction Analysis Considering the Weaving Process of Textile Fabrics: Analytical Model and Experimental Validation. Tribol Lett 71, 91 (2023). https://doi.org/10.1007/s11249-023-01755-y

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