The influence of non-linear elasticity on the determination of Weibull parameters using the fibre bundle tensile test

Abstract

We address the influence of individual fibre stress-strain non-linearity on the extraction of Weibull-parameters from fibre bundle tensile tests. We extend the statistical theory of fibre bundle strength to include the non-linear elastic behaviour observed in many technically important fibres, e.g. glass-, carbon-, and alumina-fibres. It is shown that neglecting this non-linearity may lead to significant errors in determining the shape and scale parameters of the fibre fracture strength Weibull-distribution. A refinement of the existing extraction technique, accounting for this effect, is presented. The error resulting from neglecting the non-linear behaviour is assessed through a parametric study of the Weibull parameters for different levels of non-linearity. Explicit calculations are performed for two fibres of technical importance, namely Nextel 610e a-alumina fibre and a T300 carbon fibre. q

Non-Hookean Elastic Behavior and Crystallite Orientation in Carbon Fibers

“…In such a state, stressstrain curves are convex downwards particularly. More recent papers [8,9], especially those using more sophisticated methods for the strain measurements, confirm the agreement between experiments and Ishikawa's constitutive equation for nonlinear elasticity. They also confirm the suitability of E À e square polynomial (Equation ( 3)) for adequate description of nonlinear elasticity of carbon fibers and unidirectional carbon fiber composites.…”

“…However, it is suitable for description of nonlinear elasticity due to its simplicity and because it includes the coefficient that can be accepted as a measure of nonlinear elasticity degree. The Ishikawa's fractional E À r constitutive equations for nonlinear elasticity of unidirectional carbon/polymer composites [7] and other theoretical approaches [8,9] suggest square polynomial expression for description of nonlinear elasticity of carbon fibers/epoxy resin unidirectional composites.…”

Fracture Strength Distribution in E-Glass Fiber Using Acoustic Emission

“…One common method of characterizing the strength of fibers is using the two-parameter distribution given by Weibull. Weibull statistics have been applied to study flaw distributions in bundles of glass fibers under tensile loadings [3,6,7].…”

“…Single fiber tests are time consuming and prone to errors caused by a sampling problem such as failing weak fiber during handling and fiber bending. These problems can affect in calculation of Weibull parameters [3]. In contrast, fiber BTTs include a greater number of fibers (usually hundreds or thousands) evaluated in a single test.…”