PSI - Issue 23

Pejman Shayanfard et al. / Procedia Structural Integrity 23 (2019) 620–625 Pejman Shayanfard et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Therefore a sensitivity analysis was performed in order to understand the influence of these material and geometrical parameters on the stress at the notch-tip. 3.2.1. The Effect of martensite Young’s modulus and transformation strain As explained previously the overloading of the notch-tip is due to transformation strain induced by MT proceeding under stress within NUZ, which has to be accommodated by elastic deformation of martensite induced prematurely within NAZ. This overloading is therefore to some extent proportional to martensite Y oung’s modulus and transformation strain. The effect of Young’s modulus is illustrated in Fig. 4 showing longitudinal -stress-temperature evolution experienced by notch- tip when considering martensite Young’s modulus identical to that of austenite i.e 70 GP a (red dashed curves in Fig. 4) and experimentally measured martensite Young’s modulus of 52 GPa (solid black curves in Fig. 4). Clearly, the higher the martensite Young’s modulus the higher elastic stresses in NAZ induced by MT proceeding in NUZ. Similarly, the higher the transformation strain the higher the elastic stresses induced in NAZ by the MT proceeding in NUZ as shown in Fig. 4. Yellow line in Fig. 4 represents the ultimate case where transformation strain is not considered at all, showing the key role of the transformation strain in amplifying the stress concentration around the notch. In fact, no change in stress concentration is induced by MT when transformation strain is null. In contrary, the higher the transformation strain the higher the stress concentration induced by MT as seen from the comparison of solid-black and solid-blue longitudinal-stress-temperature and longitudinal-stress-longitudinal-strain paths in Fig. 4a and 4b related to transformations strains of 6 % and 3 %, respectively.

Fig. 4 Stress-temperaturature (a) and stress-strain (b) evolutions at the notch tip compared for various transformation strains (TS) and identical (E M =E A =70 GPa) vs. different Young’s moduli of austenite (E A =70 GPa) and martensite (E M =52 GPa) as described in legends.

3.2.2. The effect of notch radius In general, the geometry of the notch drives the extent and gradient of stress concentration in its vicinity and, therefore, the notch radius is one of the key parameters determining the maximum stress at the notch tip as well as the extent of NAZ. The particular case discussed in the previous section is an example of relatively small radius compared to the width of ribbon ( = 0.12 ⁄ . To study the effect of this ratio three additional notch radii were considered, spanning this ratio from 0.12 up to 3.84 while preserving the ligament cross-section (Fig. 1b) i.e. the notch penetration, thus preserving the nominal stress applied by the constant tensile force. As shown in Fig. 5a and 5b, the critical ratio between notch-tip stress and nominal stress ( ℎ− ⁄ ) at the end of cooling drops exponentially when increasing ⁄ ratio and naturally tends to one for a limiting case of notch-free ribbon. The exponential tendencies are related to enlargement of NAZ with increasing ⁄ ratio. The changes in size of NAZ and NUZ can be evaluated by tracking the location of the maximum of transverse stress ahead of the notch-tip. As discussed previously, this maximum is due to Poisson effect induced by longitudinal strains at NAZ that are larger in comparison to strains at NUZ. Fig. 3b1 to 3b4 show colormaps of transverse stresses for considered ⁄ ratios. The vertical cuts represent spatial variations of the stress along the ligament from the notch-tip towards the center (at which the coordinate is equal to 0), while horizontal cuts represent temperature evolutions of the stress at different material points along the ligament. The maxima of transverse stress are reached after the MT is completed i.e. at low temperatures as the Poisson effect is amplified by the transformation strain. These maxima split the ligament into NAZ in vicinity of the notch and NUZ closer to center (coordinate equal to 0 as displayed in Fig. 3). Clearly, with increasing ⁄ ratio NAZ is enlarging at expense of NUZ.