Analysis Of Crack Growth Through FractureProcess Zone

Abstract

The strain energy density (SED) criterion is applied for analysing of the crack growth in full range of yielding. A fracture process zone (FPZ) local to the crack tip is defined and discussed in connection with the influence of the constraint effects in fracture. It can be estimated from the uniaxial mechanical properties of the material. Dimensionless constraint parameter is suggested depending on both the local elastic-plastic stress intensity and local fracture stress.According to SEDapproach the above stresses are determined on the distance equal to the fracture process zone size.The relation of connection between the constraint and damage parameters is suggested. It is shown that the damage parameter to describe satisfactory the well known mechanism of ductile-brittle transition for a mild steel at a temperature change taking into account the FPZ-size.Both experimental and analytical results are examined for subcritical crack growth under static loading that depends on the steel structures. Introduction Currently in literature on the fracture mechanics the limitations of the single-parameter theory is discussed. One connects the observed fracture characteristic dependencies on cracked body geometry and its loading conditions with the influence of nonsingular term T at small-scale yielding and in the general case with the constraint parameter Q at full plastic fracture. Thus in [1,2] were computed by the FEM the stress biaxiality factor B expressed over the nonsingular term T for elastic-plastic and elastic state conditions respectively.Then in[3] was developed the Rice's[4] concept on a need of two-parameter description of elasticplastic stress fields in the general yielding conditions. In that work Rice [4] have assumed that have to be correlation between nonsingular parameters T and S connected with the stresses and respectively lying in the normal planes. These stresses caused distinctions 'in the singular stress fields describing by the HRR-model [5-7] and the numerical results based on the FEM and boundary layer formulation.Authors of [8,9] provided the theoretical basis to the distinctions observed in stress fields,by introducing the additional parameter in HRR-model denoted as constraint parameter Q. In the subsequent works [10, 11] both quantitative and qualitative estimates for Q are presented. Some generalizations of twoparameter theory was given in work [12]. The attempt of a taking into account the fracture micromechanisms influence on the cracked body behaviour has required the local fracture stress to be introduced in the computational models [12-14]. Author of [12] suggested the damage function keeping within the range between the brittle and ductile fracture types but did not determine the governing parameter y connected with the fracture micromechanism. Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 944 Localized Damage The object of this work is to analyse and describe the relation between both constraint and damage parameters via the FPZ-size.A more in-depth interpretation of FPZ were given in [ 1 5] by application of the isoenergy density theory that is more general version of the SED-criterion. Constraint Parameter Let the uniaxial stress and strain relation of material is given by Ramberg-Osgood equation. If a , e denote the ultimate stress and ultimate strain, respectively, than the area under the true stress and true strain curve can be obtained as 7 A 4T'-2 on _.+,! (1) -•'•'-{'*•E\?'*- \*' where a and n are strain hardening coefficients while E and are respectively the Young's modulus and yield strength of material. Note that = a^/a^ and the critical value {dW/dV) corresponds to failure of a material element as used in the strain energy density criterion [16]. For a muitiaxial state of stress, (dW/dV) can be expressed in terms of the normalized mean stress o and effective or equivalent stress <ĵ as [5] an +,1 < 'J with v being the Poisson's ratio. Equation (2) may be performed to express the SED into ^ ratio (3) Concept of the strain energy density being the ground of present work proceeds from an assumption that the critical SED value is reached on some distance from the crack tip /•<. where the limiting transition conditions or equality of equations (1) and (2)or (3) are satisfied at fracture