PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 24–30 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

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(ii) Region II (Transition phase): Steeped. Plastic deformation starts just at the notch tip and later spreads progressively. (iii) Region III (Plastic phase): Slightly increasing or quasi-horizontal. Plastic deformation has reached the sample axis. Regarding the influence of the specimen geometry, notch depth directly influences the length of the transition phase (II). Both notch depth and radius influence the numerical value of the relationship between local and global strain rates during elastic (I) and plastic (III) phases. The more severe the notch (the lower the radius and the greater the depth), the higher the stress concentration and, therefore, the local strain rate. In all cases the elastic phase is a small percentage of the loading process. The length of the elastic region is a function of the yield strength of the material, which increases with yield strength. From dimensional analysis, the relationship between the local strain rate at the notch tip and the global strain rate at the sample ends is: (d  L /dt) / (d  G /dt)= f (  , n, P/E; R/D, A/D, L/D;  G ) (6) where  is the Poisson Coefficient, n, P and E are defined in equation (1); R, A, D and L are geometrical parameters (Fig. 1) and  G the global displacement that increases as the sample becomes more loaded and the plastic zone spreads; f is therefore a function of seven dimensionless variables referring to material properties (  , n, P/E), geometry (R/D, A/D, L/D) and level of loading (  G ). Consideration should be given to the influence of external action  G , which makes the local strain rate d  L /dt change as the test proceeds, even keeping constant the global strain rate, as usually occurs in SSRT, in which a constant displacement rate is externally applied on the sample. Such results obviously should be reflected in the experimental results. 6. Conclusions 1. Local strain rate at a notch tip ( notch tip strain rate NTSR) is numerically computed as a function of global strain rate (or testing displacement rate) for a wide range of notch geometries. It is shown that local strain rate may be one order of magnitude greater than global strain rate. 2. Yielding development is relevant for the evolution of the local strain rate at the notch tip. The NTSR is markedly increased as a consequence of the spreading of the plastic zone. The importance of the sample geometry and the constitutive equation of the material is thus emphasized. 3. Local strain rate at the notch tip depends not only on the material properties and sample geometry, but also on the loading process, that is, on the global strain externally applied on the sample ends. Therefore, the relationship between local and global strain rates is not constant, but increases with time, even for constant global strain rate. 4. Notch tip strain rate (NTSR) results are directly applicable to environmentally assisted fracture (EAF). Usual fracture criteria under aggressive environments can be improved by replacing global strain rates by local ones. For hydrogen embrittlement, space-time averages of the NTSR are representative. References Andresen, P.L., Ford, F.P., 1988. Life prediction by mechanistic modeling and system monitoring of environmental cracking of iron and nickel alloys in aqueous systems. Materials Science and Engineering A103, 167-184. Ayas, C., Deshpande, V.S., Fleck, N.A., 2014. A fracture criterion for the notch strength of high strength steels in the presence of hydrogen. Journal of the Mechanics and Physics of Solids 63, 80-93. Burnell, G., Hardie, D., Parkins, R.N., 1987. Stress corrosion and hydrogen embrittlement of two precipitation hardening stainless steels. British Corrosion Journal 22, 229-237. Congleton, J., Shoji, T., Parkins, R.N., 1985. The stress corrosion cracking of reactor pressure vessel steel in high temperature water. Corrosion Science 25, 633-650. Ford, F.P., Silverman, M., 1980. Effect of loading rate on environmentally controlled cracking of sensitized 304 stainless steel in high purity water. Corrosion 36, 597-603.