PSI - Issue 12

Lorenzo Bergonzi et al. / Procedia Structural Integrity 12 (2018) 392–403 Lorenzo Bergonzi / Structural Integrity Procedia 00 (2018) 000 – 000

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Figure 4. Outline of equivalent specimen FEM model.

2.3. Results and discussion

The stress values in X direction are extracted and averaged through specimen thickness in correspondence of two significant points, respectively at the end of the radius and on the middle of gage section, obtaining the results listed in Table 2: Table 2. Thickness-averaged stress values at given points of standard ASTM specimen geometry: these will be the reference values used throughout all specimen validation in order to compare the equivalent geometry.

 XX [MPa] 10.01

Extraction point

End of radius Middle section

9.83

In Figure 5 are shown the stress values in correspondence of middle section and at the end of the transition radius, compared to the reference ones. As can be seen, the stress values present an increasing trend up to a connecting radius between 65 - 70 mm, and then decrease: the different shape of the transition region implies a substantial greater rigidity than the standard one. It is therefore necessary to use a smaller radius, to induce a greater compliance or a much higher radius, which causes the load line to be in a section of the specimen with a section equal to that defined by the standard. Between the two solutions the first one is adopted, in order to have a specimen that is as compact as possible. From Figure 5 it is clear how the reference stress is reached in correspondence of a radius amplitude between 50 and 55 mm: in Table 3 the values obtained for a radius equal to 52 mm are shown, which presents the least deviation from reference results.

Table 3. Longitudinal stress in correspondence of the end of radius and on the middle section. ASTM D638 Equivalent

 XX

 XX

Extraction point

[MPa] 10.01

[MPa] 10.07

End of radius Middle section

9.83

9.82

With such a radius, there is a relative difference of 0.61% for stresses at the end of the radius, while a 0.09% error is determined in correspondence of the middle section: Figure 6 reports the definitive size of the equivalent specimen compared to the standard one, while in Figure 7 it is possible to compare the results from the FEM models.