PSI - Issue 59

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

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However, the displacement rate is not the most suitable variable and it allows the establishment of only qualitative phenomenological relations. To obtain quantitative relations and objective results one needs to know the local strain rate at the crack or notch tip, because at that point the environmental attack is localized, and the crack (or notch) tip strain rate controls the EAF process (Scully and Moran, 1988; Rieck et al., 1989). As a consequence, the local strain rate – and not the global or applied displacement rate – has to be compared with the dissolution (or film rupture) and passivation rates, or with the hydrogen diffusion rate, depending on the specific considered process. 4. Local strain rate at a crack or notch tip Previous research on this subject refers to the computation of (local) strain rate at a crack tip. Many difficulties arise in determining the strain distribution and the spreading of the plastic zone in the close vicinity of a crack tip (Patel and Jarman, 1985). Lidbury (1983) states that the crack-tip (or effective) strain rate under conditions of monotonic loading and general yielding can be 10 to 20 times the nominal or applied strain rate. References by Maiya (1987) and Maiya and Shack (1985) provide a definition of the crack-tip strain rate associated with the J integral. In the article by Congleton et al. (1985) an estimation of the strain rate at a crack tip is made for an ideally plastic solid under plane strain and fully plastic conditions (Rice and Sorensen, 1978) and this solution was used by Parkins (1987, 1989, 1990) to study the kinetics of stress corrosion cracking. Finally, and emphasizing the difficulty of a correct determination of the local strain rate at a crack tip, Andresen and Ford (1988) propose a simply empirical value of the crack-tip strain rate. An inherent limitation of all these expressions for the local strain rate at the crack tip is that they do not take into account the constitutive equation of the material, whose incidence in the local strain rate is not negligible, as is demonstrated by Toribio (1997a, 1997b) for cracks and by Toribio (1998) and Toribio and Elices (1992) for notches. The main consequence of that oversimplification is the prediction of a constant local strain rate at the crack tip if the typical condition of constant extension rate is achieved during a SCC test. Another important fault of previous models is the lack of proper definition of the reference length for evaluating the crack tip strain rate (CTSR). This issue is properly solved in the new attempts to evaluate the local strain rate at a crack or notch tip or its vicinity ( crack tip strain rate CTSR and notch tip strain rate NTSR) with a quite rigorous definition of the global and local reference lengths to calculate the global and local strains, as described in previous research by the author, cf. Toribio and Elices (1992), Toribio (1997a), Toribio (1997b), Toribio (1998). This paper deals with the concept of local strain rate at a notch tip as a function of the global strain rate or, more precisely, the displacement rate. The first – local or effective strain rate – is associated with a reference length short enough to guarantee the convergence of the mathematical method, although greater than the grain size of the material (to preserve the congruence of the continuum mechanics approach with the physical reality of the material); the latter – global, nominal or applied strain rate – is associated with a reference length long enough to permit uniaxial stress state at its ends. It can be controlled during the test, using the appropriate experimental device, and it is related to the crosshead speed of the testing machine. 5. Definition and evaluation of the local strain rate at a notch tip ( notch tip strain rate NTSR) The local strain at the notch tip – or notch tip strain – (  L or  NT ) is defined as the strain associated with the local reference length – or notch tip reference length – (B or L NT ) placed at the notch tip or its vicinity (small enough to guarantee the convergence of the mathematical or numerical procedure, although greater than the material grain size or characteristic microstructural unit of the material to preserve the congruence of the continuum mechanics model to reproduce the physical reality). To analyze very different levels of notch tip strain (and thus quite distinct values of NTSR), four axisymmetric round-notched specimens of very different notch geometries were considered (Fig. 1). The dimensions of the samples were chosen as follows in Table 1, where R is the notch radius, A the notch depth and D the sample diameter. Cylindrical coordinates r,  and z were used. The radius of the net section was called a (therefore a = D/2-A), and the distances from the notch tip were measured through the auxiliary coordinate x (with x = a-r).