Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading

D V Babich

doi:10.11648/j.ajmp.20170606.11

Abstract

A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.

Highlights

A large body of studies reviewed in monographs [1]-[5], a.o. shows that fatigue failure of materials is a complex multiple-stage process which includes dispersed microfailure of structural elements
The prediction methods are based on various models that are outlined in [8]-[15] and involve the weakest link model, the linear damage accumulation rule, as well as such representations as the stress-life, Coffin-Manson, ParisErdogan ones
In the last case the fracture mechanics is used with a power law relationship between the crack growth rate and stress intensity factor

Summary

Introduction

A large body of studies reviewed in monographs [1]-[5], a.o. shows that fatigue failure of materials is a complex multiple-stage process which includes dispersed microfailure of structural elements. This is attributed to the fact that engineering materials contain randomly scattered over a volume microdefects, which under cyclic loading initiate microcracks. Later on these microdefects coalescence, that leads to formation of macrocracks and to the loss of the body integrity. It is assumed that the macrofailure occurs by forming macrocracks due to accumulation of microdefects in the form of flat microcracks randomly dispersed over a volume ([19])

Model of Microcrack Accumulation

Statistical Strength Criterion

Modeling the Fatigue Failure

Numerical Example

Conclusions