Calculation of Stresses and Strains in Four‐Point Bending Creep Tests

TLDR

Creep compliance depends on temperature, grain size, and other factors but not stress, and the elastic relation between load‑point deflection and outer‑fiber strain is valid for viscous creep and approximately for nonviscous creep when the support‑to‑load distance ratio is not large. A general equation linking load‑point deflection, applied load, creep exponent N, and geometry was derived, and measuring deflection‑rate versus load in ceramic systems enables direct determination of the creep exponent and steady‑state compliance.

Abstract

An analysis of strains and stresses in four‐point bending creep tests in the limit of small beam deflections resulted in a general equation which relates the load‐point deflection, the applied load, the creep exponent ( N ), and the geometrical parameters of the loading system. Measurements of load‐point deflection rates, which are experimentally easy to accomplish in ceramic systems, vs the applied load lead to the direct determination of the creep exponent and the creep compliance in a steady‐state creep test. The creep compliance is a function of the temperature, grain size, and all other factors except stress. The elastic equation relating the load‐point deflection and the outer fiber strain is strictly valid for viscous creep and approximately valid for nonviscous creep (i.e. N >1) if the ratio of the distance between the support points to the distance between the load points is not very large.