PSI - Issue 19

Masahiro Takanashi et al. / Procedia Structural Integrity 19 (2019) 275–283 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4.2. Stress intensity factor

The test was conducted with the strain being constant at the notch root. The upper stress in one cycle was calculated by multiplying the upper strain by the modulus of longitudinal elasticity (206 GPa). Although the lower strain was compressive in all the tests, the lower stress used in the crack growth analysis was assumed to be zero in consideration of crack closure. The equation by Newman and Raju (1981) was employed to calculate the stress intensity factor.

4.3. Crack growth laws

Three types of crack growth laws are used: the crack growth law for ferritic steel of stress ratio R = 0 in JSME S NA1 (2016) and the mean and 95% confidence limit (upper 2 σ ) crack growth laws for SQV2A proposed by Kobayashi et al. (1989). All laws were expressed in the form of Paris ’ law as shown below. The material constants C and m are given in Table 3.

dN da = 

(1)

( ) m C K

Table 3. Material constants in equation (1). Source

C

m

JSME S NA1, Ferritc steel, R = 0

3.78×10 -12 3.80×10 -12 6.88×10 -12

3.07 3.04 3.07

Mean curve for SQV2A by Kobayashi et al. Upper 2 σ curve for SQV2A by Kobayashi et al.

4.4. Crack growth analysis result

Figures 5 to 7 indicate the crack growth analysis results. With respect to the stress intensity factor equations by Newman and Raju (1981), its application limit for a surface crack length is less than half of the plate width. In these figures, the analysis results beyond the limitation ( c ≧ 37.5mm) are shown for reference. It should also be noted that while the fatigue tests were carried out under the displacement control, the crack growth analysis was conducted under constant stress. The testing load relaxed with the crack growth in the final stage of the fatigue test. As a result, the experimental data were always longer than the analysis result in the final stage. In all cases, the mean curve by Kobayashi et al. (1989) gives the slowest crack growth, followed by the JSME curve, and the upper 2 σ curve by Kobayashi et al. (1989). Except for LAS2 test in which only three beach marks were observed, the coalescence of beach marks was observed. In CS1 test, the crack growth in the depth direction substantially agreed with the analysis result by JSME S NA1 until 9×10 4 cycles when macroscopic crack coalesced. However, the crack on the surface was longer than the analysis result by JSME S NA1 at 7.5×10 4 and 8×10 4 cycles. Thereafter, it almost agreed with the analysis result by JSME S NA1 up to 9×10 4 cycles when the cracks coalesced. In LAS1 test, it was the upper 2 σ curve by Kobayashi et al. (1989) that the experimental data of crack depth followed until macroscopic crack coalescence. However, the growth of the surface crack slightly surpassed the analysis results by the upper 2 σ curve. The acceleration of the surface crack in both CS1 and LAS1 tests is considered to be influenced by the presence of microscopic cracks on the notch root. Since the test strain amplitude on the notch root was as high as the yield strain in each test, many micro cracks were initiated on the notch root in the early stage of the fatigue test. Although these micro cracks were not observed as beach marks on the fractured surface, the trace that the cracks grew with coalescence could be confirmed from the small steps appeared on the fractured surface. Such coalescence of micro cracks makes the surface crack growth complex. On the other hand, since the effect of coalescence on the crack growth in the depth direction is small, the crack growth in this direction is within the upper limit of the variation of the crack growth rate.