Issue 7

S.K. Kudari et alii, Frattura ed Integrità Strutturale, 7 (2009) 57-64; DOI: 10.3221/IGF-ESIS.07.04 61 Figure 2 : True stress vs . true strain curve for investigated IF steel. Figure 3 : Typical plot of the variations of microhardness values ahead of a crack-tip. The microhardness values in the saturation plateau were found to fluctuate within some definite limits for the IF steel. The fluctuation of microhardness values of a material is an intrinsic phenomenon; never the less this was examined in the following way. The average microhardness values of these steels were separately determined on unloaded samples. These experiments yielded average microhardness of IF steel 147 ± 5 VH. When the mean value was marked on the microhardness-distance plots, the saturation plateau could be delineated, but the point, which demarcates the elastic- plastic boundary, could not be ascertained with certainty. Next, each set of data was subjected to polynomial fit with polynomial equations of different degrees. It was found that as the degree of the polynomial increases, the magnitudes of the regression coefficients also increase. But while carrying out this exercise, it was found that the improvement in the magnitude of the regression co-efficient was marginal for fitted polynomials with degrees greater than six. Hence, a sixth degree polynomial was selected to describe the obtained variation of micro-hardness with distance. Typically, such best-fit curve is also shown in Fig.3. The first intersection of the sixth degree polynomial with mean value of the saturation plateau was located. The distance between the crack-tip and this point was considered as the extent of plastic zone size (r p ) in a specimen as shown in Fig.3. The degree of scatter associated with micro-hardness values measured in plastic zone was found to be ± 5%. This scatter of microhardness is in close agreement with the scatter reported b y Ray and Mondal [20]. In order to study the effect of specimen geometry and a/W ratio on plastic zone size a few experiments were carried out to reveal the microhardness variation ahead of crack-tip up to the end of ligament. A typical such plot for CT specimen with a/W=0.5 is shown in Fig.4. It is noted from this figure that microhardness first decreases to a plateau and again increases up to the end of the ligament. The increase of microhardness near the ligament end of the specimen is due to the existence of compressive plastic zone [21] d ue to bend loading. Because of development of compressive plastic zone in specimens with higher a/W ratio, the growth of crack-tip plastic zone size gets hindered. The development of compressive plastic zone depends on the specimen geometry and loading. Thus it can be concluded that the magnitude of PZS in a material is significantly influenced by the type and the geometry of the specimen selected for the investigation. The shape of plastic enclaves using FEA has been obtained at different load steps and the extent of plastic zone size, r p , at θ =0 o have been estimated. The method of to estimate the value of r p by using FEA outputs of the plastic enclave is discussed elsewhere [5]. The magnitudes of r p estimated by microhardness technique in CT and SENT specimens (a/W=0.50) of IF steel were compared with the theoretically estimated magnitudes of r p i n Fig.5. This plot helps to infer that the experimental results of PZS are in good agreement with the results estimated by elastic- plastic FEA. Commonly, experimentally determined plastic zone sizes are compared with those derived from the existing analytical models [7, 8, 9]. These analytical models use normalized applied stress ( σ / σ y ) as a reference parameter. The