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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Global strain is the global displacement u G (relative displacement between the sample ends) divided by a characteristic length of the geometry (the sample diameter D) to get a dimensionless variable:







u G D

 G =



(3)

It is convenient for the sample length to be long enough to have its ends under uniaxial tension. This is achieved when the sample length is four times the diameter (L = 4D). Local and global strain rates are defined, accordingly, as:

u L i 0.01 D ∆t i+1 - u L

d  L /dt =

(4)

i+1 - u

i

u G

G

d  G /dt =

(5)

D ∆t

where indexes i and i+1 are used to designate the value at instants t and t+∆t respectively. The time discretization interval ∆t was chosen to guarantee the convergence of the elastic -plastic finite element computation. Results of such calculations, for L = 4D, are shown in Fig. 2, i.e, the relationship between local and global strain rates for the four geometries, as a function of global strain. In this plot, local strain rate was computed exactly at the notch tip, which corresponds to the sample surface.

Fig. 2. Relationship between local and global strain rates as a function of global strain.

The relationship between local and global strain rates changes with time, as the plastic zone spreads or the global strain (or more properly the dimensionless global displacement) increases. It should be emphasized the influence of the spreading of the plastic zone on the evolution of local strain rate, thus emphasizing the importance of the sample geometry and the constitutive equation of the material. For the wide range of geometries analyzed in this paper, the curve representing the relationship between local and global strain rates vs. global strain (Fig. 2) has always the same general aspect, and three regions can be distinguished, each representing a phase of the process: (i) Region I (Elastic phase): Horizontal. The whole sample is in elastic regime. Plastic deformation has not yet begun.