The Effect of Notches on the Failure of Two-Dimensional Nonwoven Fiber Networks

The tearing response of sheets of nonwoven fiber material is investigated. It addresses the question on how notch length and notch geometry is related to the tearing strength and tearing processes. The system considered consists of elastic-brittle fibers connected by strong interfiber bonds. Fiber fracture is the only failure mechanism. For a random fiber orientation case, deformation of the unnotched specimen occurs by long-range fiber chains connecting the load inducing boundaries, and failure is by tearing the cross section. The strength of the notched random fiber sheets is well described by a net section criterion, independent of the notch geometry. For a fiber orientation with symmetry relative to the loading direction, tensile loading is transferred by formation of the X-shaped fiber chains centered in the specimen. The subsequent failure occurs along the fiber chain by shear. Thus, the tearing strength is independent of the notch depth in double-edge notched and single-edge notched specimens, when the presence of shallow notch does not disrupt the force chains in the model. As the notch disturbs the fiber chains, alternative shear failure path forms near the notch tip, leading to a dependence of failure strength on the notch geometry. Then, the failure strength of notched nonwoven networks is described by a shear strength and a notch geometry term.

Hypothesis of Plastic Adaptation in Metal Fatigue: Physical Bases, Mechanisms and Application to Data Analyses

Author has proposed a new idea of an equivalent stress ratio as the parameter for correspondence between cyclic stress conditions of a notched and unnotched specimen. The equivalent stress ratio is formulated as a function of a nominal stress ratio and a theoretical stress concentration factor of a notched specimen. Derivation of the equivalent stress ratio is based on the hypothesis of plastic adaptation in metal fatigue. In the present paper, physical bases of the hypothesis of plastic adaptation and its mechanisms are discussed from a viewpoint of micromechanics. As a result, it is found that the hypothesis is applicable to analyses of metal fatigue characteristics themselve as well as notch problems. The fatigue strength diagrams of ferrous metals are rearranged from JSMS database and other literature by using the equivalent stress ratios (REQ-parameter method). Fatigue strength is discriminated into the two types: critical stresses to form and propagate mode I fatigue cracks, i.e., σw1 and σw2. According to the critical stresses, the fatigue strength diagrams are categorized into three groups, i.e., (1) σw1/σw2-transition types, (2) σw2-dominant types and (3) σw1/σw2-mixed types. Such discrimination depends on kinds of metals, especially, conditions of dispersed precipitates.