Studies of Different Criteria for Crack Growth Instability in Ductile Materials

Abstract

A general instability condition of solid mechanics, valid for a nonlinear structural component in an otherwise elastic system, is shown to be inherent in the T-modulus concept of instability. This condition involves the slope of the descending part of the load-displacement curve of the nonlinear component. It is shown that this slope can be used to evaluate T appl at instability; Tappl can then be used to give a simple estimation of Tmat without the need for exact crack length determination. In this paper such evaluations for large panel specimens and smaller bend and CT specimens are reported for three structural steels. The obtained data are in good agreement with conventionally determined data. However T-evaluations for tension-type specimens give values which are higher by a factor of two than those calculated for bendtype specimens. This indicates that T is not geometry independent, but that T from bend and CT specimens gives a lower bound. A method is discussed of analyzing the instability of a large structure with a cracked, ductile component using the slope of the load-displacement curve and the general instability criteria of mechanics without recourse to fracture parameters.

On the Relation Between Stable Crack Growth and Fatigue

“…[ S ] and by Kaiser and Carlsson [3], that the two following expressions are equivalent at instability.…”

“…Values of JIC and T,,, are determined by standard stable crack-growth tests according to ASTM E813, more details of these tests are given in ref. [2] and [3]. The definition of T,,, is:…”

“…The specimen geometries used were: Two sizes of CT-specimens with W = 40 mm and W = 100 mm respectively, both with thickness B = 20 mm, and one type of bend specimen with W = 40mm and B = 20mm. All three specimen sizes were used both in this study and in [2] and [3]. To obtain the fatigue data only the small CT-specimens were used.…”

“…A structure could be modelled as a cracked component in series with a spring with compliance C,,,. If the total deflection is kept constant a general expression for the applied d J/da could look like [ 3 ] :…”

“…It is therefore possible, as is done in [3], to take the slope of the P-A curve, insert this value into an expression for Tapp, and thus get an estimation of T,,,,,. For a C T specimen under limit load conditions Tapp takes the form [3] To test this relation some CT-specimens of OX812 were run under displacement control with constant increments, as described earlier. At certain intervals, however, a large increase in displacement was made to simulate unstable behaviour.…”