Why Impacted Yarns Break at Lower Speed Than Classical Theory Predicts

Fabrics are an extremely important element of body armors and other armors. Understanding fabrics requires understanding how yarns deform. Classical theory has shown very good agreement with the deformation of a single yarn when impacted. However, the speed at which a yarn would break based on this classical theory is not correct; it has been experimentally noted that yarns break when impacted at a lower velocity. This paper explores the mechanism of yarn breakage. The problem of the strike of a yarn by a flat-faced projectile is analytically solved for early times. It is rigorously demonstrated that when a flat-faced projectile strikes a yarn, the breaking speed will always be at least 11% less than the classical-theory result. It is further shown that when the yarn material in front of the projectile is “bounced” off the front surface due to the impact, that the breaking speed is further reduced. If the yarn bounces elastically off the surface due to the impact at twice the impact velocity (the theoretical maximum), there is a 40% reduction in the breaking speed of a yarn. A beautiful theory of yarn deformation under an applied boundary condition was developed by Smith [1,2]. This theory was developed in the context of impact on yarns. There has been extensive experimental work showing that the wave propagation speeds of the longitudinal and transverse waves and the subsequent deflections are well modeled by the theory. However, numerous researchers have realized that the yarn breaking speed inferred from the classical theory is larger than what is observed in experiment. Why are the impacted yarns breaking at lower speeds than the theory predicts? Most often yarns are impacted by fragment simulating projectiles or right circular cylinders. These projectiles have flat impact faces. In our computational investigation of this phenomenon, we have noticed that the flat face impact leads to a “bounce” of the yarn off the impact surface (Fig. 1). A longitudinal and transverse wave are produced in the yarn, originating at the impactor edges, traveling both outward away from the impactor and inward where the waves from opposing impactor edges. The waves meet at the geometric center of the yarn in front of the projectile; the stress and strain in the yarn double, leading to higher stresses. After this first wave effect, we also see, during more complicated wave interactions a small increase in stress until the material is relieved to the classical (Smith) solution stress at later time.