# The Influence of Friction and Twisting Angle on the Tensile Strength of Polypropylene Baling Twine
## 4 Discussion  
The crucial mechanical characteristic of PP twine, considering its field of application, is tensile strength. The aim of this research is to analyse the possibility of increasing the tensile strength of PP baling twine by changing the helix angle. The stress-strain diagram, Figure 6, shows the change in tensile strength with the change in the number of twists, i.e., the change in the helix angle. The mean stress values indicate a trend of tensile strength growth up to N = 8, i.e., up to an angle of 13.9\({}^{\circ}\), at which the maximum tensile strength values are reached, which is not the case with non-prestressed samples. The change in stress from 213.3 MPa to 283.4 MPa (Figure 7a) represents an increase of approximately 33%. As the number of twists (i.e., the helix angle) rises, the tensile strength decreases (Figure 7a). The influence of the surface helix angle on the relative elongation is shown in Figure 7b. By comparing the diagrams in Figure 7a,b, it can be concluded that the increase in tensile strength is accompanied by an increase in strain and vice versa. Figures 5 and 6 indicate that the behaviour of tested twine samples depends on the helix angle. The tearing of the non-prestressed twine is gradual, and the stress-strain curve resembles a \"sawtooth\". The fibres that suffer the highest stress are ruptured first, after which the stress decreases and elongation increases, while the adjacent undamaged fibres resist the tensile force. The process is repeated until the test sample is ruptured. Due to the complex structure of the material, the plane in which the rupturing occurs has a complex geometry, and its shape and direction cannot be predicted (Figure 9a). With the increase in the surface helix angle of the prestressed sample, the breaking process slows down, i.e., the time interval between the breaking of the first and the last fibre decreases. Thus, at the maximum helix angle, all fibres are broken in a very short time interval (Figure 9b). The tensile strength increases because the fibres change directions, so the tensile force is partially spent on a rising mutual pressure between them. Consequently, the contact area between the fibres increases as well. Due to the complex structure of the twine, the level of prestress in fibres is unequal, so some of them are more tensed than others, especially those that are furthest from the twine's longitudinal axis. Different levels of prestress cause some fibres to deform faster than others. The velocity of fibres' relative motion causes friction between the fibres in contact. So, the increase in tensile strength of the twisted twine is induced by the force of friction between the fibres in relative motion. As fibres are numerous and their orientation is hectic, the effect of friction forces on tensile strength is amplified. Friction forces appear in all directions of the hectically aligned fibres, and their resulting force represents a sum of their projections on the tension axis. Its direction  
Figure 10: Influence of the coefficient of friction between the fibres on the twine’s tensile strength, stress–strain diagram. is opposite that of a tension force, which causes changes in tensile strength. The effect of friction between the fibres in relative motion on the tension strength can be easily discerned from Figure 8. When the mean value of the surface helix angle was 13.9\({}^{\circ}\) (N = 8), prestressed (i.e., twisted) twine samples not immersed in oil had a mean tensile strength of 283.4 MPa, while the mean tensile strength of prestressed samples that were immersed in oil before being tested was 187 MPa. Therefore, the use of oil caused a decrease in tensile strength of 96.4 MPa, or approximately 34%, which proves the assumption that higher friction between the fibres increases the tensile strength of the twine. In non-prestressed samples, the decrease in tensile strength caused by the use of oil was also present but considerably smaller, approximately 6% (Figure 10).