PSI - Issue 17

M. Carrera et al. / Procedia Structural Integrity 17 (2019) 872–877 M. Carrera, P. Lopez-Crespo, P.J. Withers / StructuralIntegrity Procedia 00 (2019) 000 – 000

875

4

2.2. Post-processing. Plastic zone estimation method

Figure 1 shows the procedure designed to obtain the plastic zone. From the XRD test, the strain fields are obtained. The strain results acquired in the crack opening and crack growing direction can be observed in Figure 2. The shear strain maps γ xy were estimated numerically with the help of Ansys finite element modelling software. In conjunction with previous experimental fields around the crack tip, an elastic equivalent strain field can be obtained, under plain strain conditions. The equivalent strain was computed as follows (Bannantine, Comer and Handrock (1990):

2                           2 2 2 2 2 xy yz zx    + +

(

) ( 2

) ( 2

)

2 6

    =

yy yy   − + − + − + zz zz   xx

(1)

eq

xx

The stress fields were then obtained, by applying Hooke’s law. Plastic zone is obtained from the stress field by differentiating values higher than yield stress, highlighting the plastic zone.

Figure 2: LHS figure, crack opening strain field. Central figure, crack growing strain field. Both are obtained through XRD. RHS figure, shear strain field, obtained from FEM.

3. Results. Plastic zones

Result of plastic zone obtained at 30.000 cycles can be observed in Figure 3. The shape of the plastic zones obtained is similar to the plain strain theoretical model analysed, which represent the classical shape of an “8” observed in literature (e.g. Broek, (1982)). One remarkable feature of the plastic zone results is the symmetry. The plastic zone estimation exhibits a high degree of symmetry along the x axis ( y =0). Such symmetry is expected given that we are analysing a CT specimen where the crack propagates under pure mode I loading. Figure 3 also illustrates that the size of the plastic zone obtained is noticeably smaller than the plain strain solution and of course much smaller than the plane stress solution. Table 2 shows a comparison of theoretical models and experimental plastic zone area. This difference might be due to each strain data point being measured over a gauge volume of with length ~1.4 mm along the thickness direction. This produces a smearing of the strain results which in turn generates smaller plastic zone.

Table 2. Area comparison between theoretical models and experimental result [mm 2 ]. Experimental result Plain strain model Plain stress model Area obtained 0.0750 0.4640 1.5976