Dynamic Steady-State Stress Field in a Web During Slitting

Based on a dynamic fracture mechanics analysis, the stress field in a continuous film (called a web) during slitting (or cutting) is investigated. For a homogeneous, isotropic and linearly elastic web, the steady-state dynamic stress field surrounding the slitter blade can be related to the interacting traction between the moving web and the blade, and to the far-field tension that is parallel to the slitting direction. The interaction between the moving web and the blade also includes friction that is considered to be a Coulomb type. By solving an integral equation, the normal traction between the web and the blade can be expressed as a function of the blade profile and the web speed. Numerical calculations are performed for an ideal razor blade with the wedge shape. The analysis presented in this study indicates that the contact between the moving web and the blade does not start at the tip of the blade but rather starts at some distance behind the blade tip. Moreover, it is found that the distance from the point where the web begins to separate to the point where the blade and the web start to have contact, is controlled by the toughness of the web material and also by the web speed. Some characteristic nature of the dynamic stress field surrounding the slitter blade is investigated based on the dynamic fracture mechanics analysis results.