Issue 7

S. K. Kudari et alii, Frattura ed Integrità Strutturale, 7 (2009) 57-64 ; DOI: 10.3221/IGF-ESIS.07.04 60 The sequential developments of plastic zone in the selected specimens were evaluated at different applied loads corresponding to stress ratio ( σ/σ y ) ranging between 0.1 and 0.85. The boundary separating the plastic enclave from the elastic bulk was obtained from the iso-stress contours of effective stress ( σ eff ) estimated using von Mises yield criterion following the procedure adopted by Gdoutos and Papakaliatakis [13]. The elastic-plastic FE analysis is performed considering the material behavior to be multilinear kinematic hardening pertaining to IF steel. The Newton-Rapson procedure in which stiffness matrix is updated for every equilibrium iterations was used for the nonlinear convergence. In these analyses the elastic modulus and Poisson’s ratio of the material has been taken as 194 GPa and 0.3, whereas the yield strength and the true stress-strain curve were taken from experimental results of tensile test. The plastic part of the true stress-strain curve (Fig.2) was divided into twenty segments for the multilinear hardening model. The magnitude of J-integral was evaluated for a path at a specific loading condition and for a particular specimen geometry using the expression proposed by Rice [14] ∫ Γ       ∂ ∂ − = ds x u T Wdy J i i (1) W= ∫ ε ε σ 0 ij ij d ; j ij i n T σ = where W = strain energy density, T i = traction vector, u i = displacement vector, s = element of arc length along contour Γ The contour around the crack-tip was defined by four corner nodes in this analysis domain. The average value of J at a particular loading magnitude was estimated by considering four different paths around the crack-tip. R ESULTS AND DISCUSSION he estimated magnitudes of the tensile properties and hardness of the investigated steels are summarized in Tab. 2. The estimated 2% yield strength, ultimate tensile strength and percentage of elongation of the investigated steels as indicated in Tab. 2 are in close agreement with some earlier reported results [15, 16] f or IF steel. The true stress ( σ ) – true strain ( ε ) curve for the investigated material up to a maximum load is shown i n Fig.2, which is used for elastic-plastic FE analysis. The experimental determination of plastic zone has been carried out by examining the variation of microhardness with distance ahead of crack-tip along θ =0 o plane. A typical plot obtained for SENT specimen with a/W=0.25 and σ / σ y = 0.60 is shown in Fig.3 in which the average microhardness of the material with its upper and lower bounds are also indicated. The result in this figure indicates that the values of micro-hardness (Vickers hardness, VH) continuously decrease with increase in distance ahead of a crack-tip to a saturation plateau. The extent of plastic zone ahead of a crack-tip is considered to be the distance between the location of the crack-tip and the point where microhardness of the material reaches the saturation plateau in microhardness vs . distance curve. σ ys (MPa) σ uts (MPa) %El VHN 125.40 273.10 51.12 147 Table.2 Mechanical properties of the interstitial free steel used in the analyses. ( σ ys - yield strength, σ uts - ultimate tensile strength, %El- percentage elongation, VHN Vickers hardness number) A few earlier investigators [17, 18, 19] have employed graphical method to locate the boundary of the plastic zone from the microhardness-distance plots. The obtained experimental data of microhardness vs . distance (Fig.3) exhibit considerable scatter, and as a consequence application of the graphical method to demarcate the plastic zone boundary in an unambiguous manner is difficult. A simple analytical procedure was thus developed to locate the boundary of the plastically deformed regimes to overcome the above problem.