PSI - Issue 59

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

27

4

L/2

x = a - r

R

r

a

A

D/2

Fig. 1. Axisymmetric notched geometries used in the calculations.

Table 1. Dimensions of the samples. Sample

R/D 0.03 0.05 0.36 0.40

A/D 0.10 0.39 0.10 0.39

A B C D

The material selected for the computations was a high-strength eutectoid pearlitic steel whose stress-strain curve fits the following Ramberg-Osgood equation:

n

   P

 E +  

(1)

 =

where E = 199 GPa is the elastic modulus, and P and n the Ramberg-Osgood parameters (P = 2100 MPa, n = 4.9). Calculations were performed using the finite element method and an elastic-plastic code on the basis of the incremental plasticity theory. Tensile tests were simulated by displacement control at sample ends, introducing in the computer program an incremental displacement step by step. Since the numerical results are node displacements, strains are defined by dividing such displacements by a suitable length. For local strain at the notch tip (  L ) a local reference length B = 0.01 D was selected, after checking that it was small enough for numerical results (the relationship between local and global strain rate) to be independent of the chosen size and also much higher than relevant microstructural parameters of the material (the average size of the pearlite colony for the selected steel).

u L B =

u L 0.01 D

 L =

(2)

where u L is the relative displacement between the ends of the local reference length B, which is 0.01 times the sample diameter.