A Model for Fracture Probability as a Function of Stress and Strain

Abstract

Distributions of ultimate stress (σ m) and strain (ε m) are obtained by Monte-Carlo simulations with a chain-of-bundles (COB) model. The COB contains linear-elastic elements, for which the fracture probability distribution of stress and strain is varied. Various entities describing the combined distribution of σ m and ε m for the COB are calculated. Simulated σ m - ε m distributions resemble those observed experimentally for various materials. Experimental trends for the combined σ m - ε m distributions, which are observed when, e.g., changing material parameters or processing conditions, can be interpreted in terms of changes in critical substructures, and simulations like those presented here may be useful in such studies.

Statistical Aspects of Tensile Fracture of Isotactic Polypropylene

“…However, there are major difficulties in characterizing the fracture behavior of these materials under tensile deformation as a result of the wide and inconsistent scatter in fracture strain and stress [4]. This scattering is always observed, even though tensile experiments are performed under identical test conditions and specimens are selected to be as nearly identical as possible.…”

“…In ductile fracture, extensive plastic deformation, such as yielding and necking, takes place before fracture. To our knowledge, very little data has been published concerning the statistical analysis of ductile fracture behavior in typical tensile tests ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 4 for commodity plastics [13,14].…”

Gaussian and Non-Gaussian Distributions of Fracture Properties in Tensile Stretching of High-Density Polyethylene

“…Nevertheless, there exist some difficulties in characterizing fracture features during tensile deformation of semicrystalline polymers, one of which comes from the scattered behavior of fracture properties. 19 When a large number of uniaxial tensile tests are performed under identical conditions, materials always exhibit scattered stress−strain curves, thus presenting a distribution of the tensile strength, elongation at break, and fracture toughness. These scattered phenomena arise from the inherent randomness of the fracture position within the aligned chain bundles.…”

“…Tensile stretching is one of the robust methods to investigate the fracture behavior of materials. Nevertheless, there exist some difficulties in characterizing fracture features during tensile deformation of semicrystalline polymers, one of which comes from the scattered behavior of fracture properties . When a large number of uniaxial tensile tests are performed under identical conditions, materials always exhibit scattered stress–strain curves, thus presenting a distribution of the tensile strength, elongation at break, and fracture toughness.…”

“…Meanwhile, most of the energy is dissipated by the yield process and thus ductile samples possess a relatively high fracture energy . The statistical fracture behavior of brittle materials, such as ceramic, fibers, and composites, has been investigated extensively. ,− Weibull analyzed the scattered behavior of brittle fracture utilizing a distribution function that came to bear his name . Phoenix and co-workers , put forward the chain-of-bundles (COB) model to predict the fracture behavior of fibrous materials.…”