CAD/CAE for stress–strain properties of a wide range of multifilament twisted man-made filament yarns

Abstract

In a previous paper, the computer aided design (CAD)/computer aided engineering (CAE) approach was presented and compared via the stress–strain curves of high-tenacity rayon yarn and the energy method. The maximum stress–extension curves showed very good agreement with experimental results and were more accurate than the previous methods. In this paper, the CAD/CAE method is considered in relation to multifilament yarn, which is equally applicable to a wide range of man-made filament yarns from nine material types. The results of this prediction model were compared with the stress–strain curves of experimental results and the energy method. The maximum stress–extension curves showed very good agreement with the experimental results except for the high-tenacity Terylene and Fortisan. The reasons for the poor agreement between the experimental and predicted curves are discussed. The breaking points obtained with this method are also compared with experimental results and discussed.

Keywords

CAD/CAE multifilament twisted yarns stress–strain properties tensile behavior

This study is an extension of a previous paper which forwarded a computer aided design/computer aided engineering (CAD/CAE) approach for calculating the tensile behavior of a multifilament yarn from the tensile behavior of the individual filaments.¹ The theory uses a CAD/CAE approach to predict the stress–strain curves of a multifilament twist yarn. The yarn structures were based on an idealized helical model with many twist angles. A CAD software package was used to model the yarn structures as an assembly of many filaments by twisting.^2,3 A CAE software package was used for the finite element modeling with large displacements to simulate the stress–strain curves of each filament and yarn. In the earlier paper, experimental results were given for Tenasco yarn (a high-tenacity rayon yarn), and the maximum stress–extension curves showed very good agreement with the experimental results while being more accurate.

In this study, a CAD/CAE approach is considered in relation to multifilament yarns, and could be equally applicable to a wide range of man-made filament yarns. The results from this prediction model for each material were compared with the stress–strain curves of experimental results and the energy method. The breaking point for Super Tenasco, high-tenacity Terylene, and Fortisan in this model for each twist level were compared with experimental results and discussed.

Materials and method

Materials examined

Treloar and Riding⁴ first proposed the energy method to successfully predict the entire stress–strain relationship for a continuous filament of Tenasco yarn. Then, Riding and Wilson⁵ suggested an extension of this theory that calculated the stress–strain curve for other types of materials, such as different types of man-made textiles that are commonly encountered. In addition, an exceptional material (Teflon) was included to examine the effect of a low value of the coefficient of friction between filaments. The materials considered in this work are reported in Table 1.

Table 1.

Comparison of parameters of CAD/CAE model with different materials and twist angles of yarn structures

Material	Twist angle (degrees)	No. fibers	Pitch length	No. elements	No. nodes	Percentage of elements with aspect ratio <3
Super Tenasco	16.74	61	1128.00	910,329	1,585,434	99.0
	23.22	60	790.86	566,347	1,002,252	98.8
	29.92	57	589.57	390,510	696,614	97.6
	36.97	54	450.75	308,562	557,348	98.8
Nylon	16.44	61	1149.85	946,528	1,646,419	99.3
	22.52	60	818.32	590,647	1,043,597	99.2
	35.55	55	474.79	327,187	587,037	98.4
	40.68	53	394.74	313,410	565,902	97.9
Low-tenacity Terylene	14.38	61	1323.37	898,417	1,584,831	99.2
	19.86	60	939.33	657,531	1,157,242	99.2
	31.12	57	562.00	364,536	654,995	95.8
	35.75	54	471.31	316,317	571,765	97.9
Medium-tenacity Terylene	15.44	61	1228.44	955,725	1,669,484	99.2
	21.38	60	866.66	617,239	1,086,342	99.2
	33.16	57	519.28	341,256	613,855	98.1
	37.94	53	435.21	299,972	543,110	98.7
High-tenacity Terylene	15.42	61	1230.11	939,771	1,645,542	99.2
	21.44	60	863.99	612,797	1,079,908	99.1
	33.49	56	512.81	332,661	600,368	97.9
	38.02	53	433.96	294,266	534,418	99.1
Tricel	18.65	60	1003.55	763,285	1,330,829	99.0
	23.71	59	772.56	575,485	1,016,813	98.6
	32.89	57	524.67	330,012	597,403	98.6
	38.28	53	429.93	286,610	523,204	98.9
Acrilan	14.72	61	1291.47	888,895	1,570,772	99.2
	19.96	60	934.23	654,952	1,152,868	99.1
	28.65	58	621.02	432,438	766,682	98.3
	35.71	54	472.00	315,244	569,912	97.7
Teflon	17.07	61	1104.94	910,243	1,580,132	99.1
	22.89	60	803.61	564,676	999,857	98.9
	31.10	57	562.45	367,934	660,072	97.1
	37.63	53	440.10	296,046	536,948	98.5
Fortisan	14.43	61	1318.60	968,885	1,701,425	99.2
	24.15	58	756.70	560,303	990,231	99.0
	32.40	57	534.60	345,826	620,265	98.1
	39.75	53	408.00	294,761	535,730	99.0

The number of twisted yarns in each material type was prepared so it covered a range of twists, with a maximum twist angle of about 40°. The Super Tenasco was twisted on an experimental ring frame and other yarns were twisted on the small-scale laboratory-constructed uptwister, referred to previously⁵. The twist and the retracted length of each yarn were subsequently measured. These results were used to find the value of the yarn’s radius and twist. The stress–strain curve for each yarn was obtained on an Instron Tester (as a mean of 10 specimens) at a constant rate of extension of 50% per minute and with a gauge length of 20 inches.

CAD/CAE approach

A yarn structure model was constructed with the filament assembly model, which presented a new computer modeling approach for 3D yarn structures. The concept of virtual locations with ellipsoid shapes was defined by the yarn-twist level in each ring layer. The geometric information and material information could be directly provided for each distinctive filament. The geometrical parameters of the yarns are shown in Table 1. Each filament diameter was 12 µm and the virtual locations diameter was 12 µm. The number of layers was five and the yarn diameter was 108 µm. The SolidWorks software package⁶ was used to model the yarn structures. SolidWorks Simulation⁷ was used to generate the mesh of the solid elements. When meshing a filament and filament assembly, we used parabolic tetrahedral solid elements (also referred to as second-order elements) that were defined by four corner nodes, six mid-side nodes, and six edges. Based on the results of Sriprateep and Bohez,¹ we chose h_max = 20 µm and h_min = 4 µm for the filament specimen in the following analyses. In the simulation process, one end of the filament specimens was fixed and the other end was extended along the length. In this study, we also used the maximum and average values of the stress for each filament to calculate the stress–extension curves of the yarn and compared them with the experimental results.

Based on the assumption that the friction between the filaments is high, the filament-to-filament interface was assumed to be bonded throughout the model. Global contact conditions were applied for all common areas. The mesh generator bonded the filaments with a compatible mesh option at their interface with all other components. The CAD with the filament assembly model had initial contact and nearly all came into contact during the loading. Any change in contact conditions required re-meshing of the model; the program was re-meshed automatically. When bonding solid faces through the global contact condition, the program generated a compatible mesh on the touching areas and merged the nodes. Bonding was achieved by merging nodes when the mesh was compatible or by using multipoint restraints internally when the mesh was not compatible. Bonding with a compatible mesh gives better results but can cause the meshing to fail for some filament assemblies. Using the re-mesh with the failed parts from incompatible meshes can help mesh such assemblies. Bonding incompatible meshes can generate local stress concentrations in the bonded areas. This study used the CAD/CAE model with compatible mesh option; therefore the stress -strain curves gave better results. The stress distribution of each filament was calculated using the FEM for a large displacement until reaching the target. The percentage of the yarn extension was defined as a geometric constraint. During the simulation process, the results of the stresses and strains can be known directly at each time step of the CAD/CAE model. The parameters of the CAD/CAE model, such as number of elements, number of nodes, and percentage of elements with an aspect ratio less than three with varying twist angles, are shown in Table 1.

Filament–yarn breaking extensions relationship

The stress acting on the filaments after yarn extension can be directly analyzed by the FEM. Therefore, the tensile behavior of the filaments has to be converted to the yarn tensile behavior (the force acting along the yarn axis). The stress acting on the yarn structure (σ_y) was calculated from equation (1) as follows

σ_{y} = \frac{F_{y}}{A_{y}} = \frac{\sum_{j = 1}^{n} σ_{fj} A_{fj} cos α_{j}}{A_{y}}

(1)

where A_y is the cross-sectional area of the yarn; F_y is the yarn tension; n is the number of layers; j is the layer number; σ_fj is the stress acting on the filaments at layer j; A_fj is the cross-sectional area of the filaments along the filament axis at layer j; α_j is the helix angle of the filament at layer j.

For the results of the maximum stress acting on the yarn structure (σ_y_(max)), the maximum stress of the filament in each layer (σ_fj_(max)) is used for the calculation. For the average stress acting on the yarn structure (σ_y_(ave)), the average stress of the filament in each layer (σ_fj_(ave)) is used for the calculation. The tensile behavior of the filaments has to be converted to the yarn tensile behavior. When increasing the percentage of the yarn extension, the stress on the filament in each layer reaches the ultimate strength value, and then the filament breaks. The stress at breaking point in each layer can be expressed in equation (2) as follows

σ_{yb} = \frac{F_{yb}}{A_{y}} = \frac{\sum_{j = 1}^{n} σ_{fj} A_{fj} cos α_{j}}{A_{y}}

(2)

where σ_yb is the stress acting on the yarn structure at the breaking point. In this case, calculating the yarn tension at the breaking point (F_yb) based on all the filaments’ tensions is done by summing all the filament axis tensions. In the case of an ideal twist yarn, the filament in the center of the yarn will break first and then the second and third layers will follow in that order. When the value of the maximum stress of the filament in the layer (σ_fj_(max)) reaches the ultimate strength, then these values are not included in the calculations of the stress of the yarn structure at breaking point (σ_yb_(max)).

Results and discussion

Comparisons with experiment and energy method

The CAD/CAE model with five layers of ideal yarn structures was simulated with a nonlinear material property and large displacement. This work was an extension of a model that calculated the stress–strain curve for nine different types of man-made textiles that are commonly encountered. Four different twist angles of the yarn structures in each type of material were simulated and compared with the stress–strain curves of the experimental results and from the energy method. The relationship of the tensile behavior of the ﬁlaments to the yarn structure can be calculated using equation (2). When the value of the maximum stress of the ﬁlament in the layer (σ_fj_(max)) reached the ultimate strength or breaking point of an individual filament, then it was not included in the calculations of the stress of the yarn structure (σ_yb_(max)). The nonlinear tensile behaviors of the original yarn with nine material types were used from the experimental results of Riding and Wilson.⁵ In general, each type of material has three distinctive regions: linear, yield, and post-yield. Comparisons of the parameters of the CAD/CAE model in each material type, such as number of elements and number of nodes with varying twist angle, are shown in Table 1.

Theoretical stress -strain curves of yarn in each twist angle using CAD/CAE method with breaking point of yarn for five layers of high – tenacity Terylene (Figure 1a) and Fortisan (Figure 1b) is shown in Figure 1. Also the results obtained with each different material are shown in Figures 2 –10, where the stress–extension curves of the yarn at different twist angles are shown in terms of maximum and average stress–extension curves. The results of this prediction model were compared with the stress–strain curves of the experimental results and also from the energy method obtain from Riding and Wilson.⁵ The breaking point of the experimental result is indicated by a cross on each twist angle. It can be seen that there is an agreement between the experimental results and predicted curves with the maximum stress for all the materials except the high-tenacity Terylene and Fortisan (Figures 6 and 10 respectively). A cause for the discrepancy has previously been suggested by Riding and Wilson,⁵ and the reasons for the poor agreement between the experimental and predicted curves for the high-tenacity Terylene and Fortisan could be their relatively small extensibilities. It is probably preferable to compare the results for these two materials with the low-strain portions of the other results. It can be seen that the disagreement in this region is always in the same direction. Another reason for the poor agreement could be due to a possible crimping or buckling of the filaments in the yarn structures. In the case of the high-tenacity Terylene yarn containing the highest twist, expressed as a percentage of the extension until reaching the breaking point, it is about 10%, which is about three times that of the corresponding percentage extension of the low- and medium-tenacity yarns. The amount of buckling in a yarn cannot be measured with our present method to relate the filament buckling with the observed disagreement between the theory and experiment. However, to compare the buckling in two yarns for the ratio of the twisted to untwisted yarn lengths, the values for the most highly twisted medium- and high-tenacity Terylene yarns are 0.8851 and 0.8831, respectively; so, there is little difference in the filament buckling between the yarns. An alternative cause of the discrepancy in the present work could be due to the load–extension properties up to the breaking extension of the filaments, as these can be predicted satisfactorily for medium-tenacity but not for high-tenacity Terylene. The experimental evidence suggested a modification in the basic load–extension behavior of the filaments, and, presumably, this led to the presence of large lateral stresses that might be the primary cause of the discrepancy. This would presumably give rise to greater lateral stresses in a twisted yarn stretched at the high rate of extension than if it were stretched at a normal rate of extension. These results support the premise that large lateral stresses modify the stress–strain behavior of the material.

In general, the CAD/CAE model showed that the maximum stress values were close to the real yarn properties and the average stress–extension curves were lower than the experimental results. However, in the stress–extension curves of the experimental results, each different twist angle was between the maximum and average stress–extension curves of the CAD/CAE model. Figures 2 –10 also illustrate a comparison of the prediction model and energy method. The results showed that the maximum stress values produced were very similar to the energy method, which was in the region of small extensions, and our method was a little lower than the energy method; for the high extensions, our method was a little greater than the energy method. The average stress–extension curves were also lower than the energy method. The reason for the deviations of the maximum stress values at low strains could be due to the packing density of our model compared to real yarn. The filament, initially at a low packing density, would be free to move inwards (migrate) without developing tensile strain until it came into contact with the core of the inner filaments that had already reached a jammed density. For high strains, the maximum stress–extension curves of our CAD/CAE model were a little greater than the energy method. The deviations could be due to the theoretical assumptions concerning the friction between the filaments being so high that the filaments were considered to be bonded to each other when contact between the filaments occurred.

Comparison of breaking extensions with experiment

In Figures 2, 6, and 10, the CAD/CAE method also showed the breaking extensions in each twist level. The results showed that the yarn breaking extensions for the CAD/CAE method in the low-twist yarn was in close agreement with the breaking point of the experimental results. The high-twist yarn had a greater extension to the breaking point than the low-twist yarn. This was due to the CAD/CAE method using the ideal twist yarn with five layers in each yarn structure; the filament in the center of the yarn would break first, and then the second and third layers in that order. The value of the stress of the filament in the outer layer had a greater extension to reach the ultimate strength and then the filament would break. Therefore, the high-twist yarn had more extensions to the breaking point than the low-twist yarn. These results correspond to the yarn breaking extensions of the experimental results, with the exception of Super Tenasco (Figure 2), Acrilan (Figure 8) and Teflon (Figure 9) yarns.⁵ The more highly twisted the yarns, in general, the greater the breaking extensions that exceed those of the individual filaments or yarn at a low twist angle. This could be partly associated with the possible buckling of filaments, which might be expected to increase with the twist. There is a simple assumption that can be made about the tension changes once the break has started. The portion where the fibers have reached their breaking extension may be regarded as no longer contributing to the tension, but the remainder of the yarn may be regarded as still effective. Therefore, the resulting curves would be similar to the CAD/CAE model of the relationship of the tensile behavior of the ﬁlaments to the yarn structure.

The breaking point of the yarn structure in each layer can be calculated using equation (2). For the first example, the breaking extension of the high-tenacity Terylene is shown in Figure 1(a). At a 15.42° twist angle, the yarn structure started to break in the first and second layers at about 9.5% extension and was completely broken at about 11.25% extension, which was the breaking point of the experimental results at about 10.5% (Figure 6(a)). In addition, for the yarn structure at 21.44°, 33.49°, and 38.02° twists, the CAD/CAE method started to break at about 9.5% extension and were completely broken at about 12%, 13.5%, and 15.625%, respectively, and the breaking points of the experimental results were at 11%, 13.5%, and 13.5% extensions (Figures 6(b), (c), and (d) respectively). The second example for Fortisan is shown in Figure 1(b). The yarn structure at a 14.43° twist started to break in the first and second layers at about 6.25% extension and was completely broken at about 7.125% extension, which was nearly the same as the breaking point of the experimental results at about 7%. At 24.15°, 32.4°, and 39.75° twists, the yarn structure started to break at about 6.25% extension and was completely broken at about 7.875%, 8.875%, and 10.5%, respectively, and the breaking points of the experimental results were at 7%, 6.75%, and 7.25% extension (Figure 10(b), (c), and (d) respectively). The results showed that the breaking point for the CAD/CAE method was similar to the experimental results in the low-twist yarn. The high-twist yarn had more extensions to the breaking point than the low-twist yarn, as in the experimental results.

This result was in accordance with the theoretical stress–strain curves of yarn, assuming Hooke’s law, and regarding the broken regions as merely inoperative.⁸ When the portion where the filament breaks has reached its breaking extension, the remainder of the yarn may be regarded as still effective on the stress–strain curves. The results of the stress–strain curves have a form similar to our model. In addition, the mechanics of the failure process and ultimate strength of a twisted yarn structure using a stochastic model were studied by Realff and colleagues.⁹ The model acts to predict the strength and fracture behavior of a blended yarn with continuous components. The features of the blended yarn behavior were simulated and elucidated, including the strength-reinforcing mechanism of the twist yarn, the yarn break propagation pattern, and the effect of the twist on the yarn fracture behavior, as well as the shape effect of the component stress–strain curves. The load versus strain responses corresponding to the various twist levels were quite close to the experimental results. The results showed a decrease in the slope of the load versus the strain curve with an increase in the twist multiple. The filaments reached their breaking extension of a blended yarn, but the remainder of the yarn may be regarded as still effective. Therefore, the resulting curves would be similar to those from the CAD/CAE model.

In this study, the CAD/CAE theory is equally applicable to a wide range of man-made filament yarns. Chudoba and colleagues¹⁰ proposed a study via a multivariate experimental analysis of continuous multifilament glass yarns. The experimental design involved four main factors affecting the yarn tensile behavior, namely twist, fineness, loading rate, and specimen length. In the evaluation, both the main effects and their interactions were considered. The results of the study showed all the main factors and their interactions affecting the yarn stress–strain curves. Therefore, the possibility exists for further work that is capable of adaptation to gauge length, friction, ﬁlament migration, and packing density. The model also could be expanded for more realistic conditions, such as ply, woven, or knit yarns.

Conclusions

The stress–strain properties of a wide range of man-made filament yarns were theoretically modeled using the CAD/CAE method. The results observed from our theory predict satisfactorily the stress–strain properties of varying the yarn twist angle of all the yarns tested except the high-tenacity Terylene and Fortisan. The deviations between the theory and observed results could be due to their relatively small extensibilities. The other reasons for the poor agreement could be due to a possible crimping or buckling of filaments in the yarn structures. An alternative cause of the discrepancy could be the load–extension properties increasing to the breaking extension.

The results illustrated a comparison of the prediction model and the energy method, in which the maximum stress values produced very similar results as the energy method. In our method the region of small extensions was a little lower than the energy method, and for high extensions our method was a little greater than the energy method. The average stress–extension curves were also lower than with the energy method.

The CAD/CAE method also showed the breaking point. The breaking extension for the prediction model was similar to the experimental results in the low-twist yarn. However, the high-twist yarn had a greater extension to the breaking point than the experimental results and the low-twist yarn.

Footnotes

Acknowledgements

The author is thankful to associate Prof. Erik L.J. Bohez (Asian Institute of Technology) and Dr. Naraporn Rungsimuntakul (Thailand Textile Institute) for fruitful discussions on the principles of filament and yarn structure as well as the students in the Manufacturing and Materials Research Unit (MMR), Mahasarakham University.

Declaration of conflicting interests

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

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Faculty of Engineering, Mahasarakham University, Thailand.

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