PSI - Issue 13

Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 862–867 Andrzej Neimitz et al. / Structural Integrity Procedia 00 (2018) 000 – 000 crack front. Here: σ m =1/3( σ 11 + σ 22 + σ 33 )= 1/3 I , I is the first invariant of the stress tensor, = √ is the effective stress, and J 2 is the second invariant of the stress tensor deviator; = − − − , = √ ( − + ) , ( ) = ( ) = = , θ is Lode angle, and J 3 is third invariant of stress deviator. It will be shown that the stress distribution in front of the crack assumes unphysical features if a proper calibration of the uniaxial stress strain curve is not performed. 2 Since the stress triaxiality and the Lode parameter change considerably in front of the crack different specimen shapes were designed to provide similar values (Fig.1). Three different materials were tested at three different temperatures: +20ºC, -20ºC, -50ºC. In the preliminary analysis, the uniaxial tensile tests were performed, and the stress – strain curves were recorded. Then, the true stresses and the logarithmic strains were computed using the following formulae: σ true =(1+ ε e ), and for ε =ln(1+ ε e ). a) b) c) 863 2. Calibration of the uniaxial stress-strain curve under condition of large strains and stress triaxiality

Fig.1. Tested specimens. a) two notched cylindrical specimens with R=0.4 mm (   from 0.5 to 1.6; L  from 0.6 to 1) and R=1 mm (   from 0.4 to 1.4; L  from 0.85 to 1) (C04, C1); b) plate with two symmetrical notches, R=1 mm (   0.4; L=0.4) (PN); c) plate with R=10 mm (   0.5; L=0.5) (PR).

Table 1. Heat treatments and tensile properties of the tested S355JR steel.

E [GPa]

R eH [MPa]

R eL [MPa]

R m [MPa]

Symbol

Heat Treatment

Microstructure

N

Normalized at 950 º C

Ferrite-pearlite

197 a) 198 b)

375 380 382 393 412 415

367 378 368 380 406 411

496 614 470 588 511 603

Normalized annealed (600 º C, 150 h)

and

Ferrite containing spheroidized carbide particles Ferrite containing spheroidized carbide particles

NW

210 211 197 198

Quenching in oil and annealed (600 º C, 150 h)

HW

a) in the first line – values obtained from the nominal stress-strain curve; b) in the second line – values obtained from the true stress−logarithmic strain curve.

Since the aim of the research program is the analysis of the failure mechanisms in front of the crack in ductile materials, one can expect large strains. The stress – strain curve must be extrapolated starting from the stress maximum