Issue 47

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 47 (2019) 348-366; DOI: 10.3221/IGF-ESIS.47.26

with material type. In particular, the location of the most damaged point in the structure shifts in accordance to the degree by which material is sensitive to the hydrostatic stress value.

auto-PSDs

cross-PSDs

G G G

Re{G Re{G Re{G

}

xx

xx,yy

10 4

10 4

}

yy

xx,xy

}

10 2

10 2

xy

yy,xy

10 -2 stress PSD [(Pa 2 )/Hz] 10 0

10 -2 stress PSD [(Pa 2 )/Hz] 10 0

10 -4

10 -4

0

50

100

150

200

0

50

100

150

200

frequency, f [Hz]

frequency, f [Hz]

Figure 7 : Auto- and cross-PSD (one-sided) in a node close to the round notch.

A

C

.41E‐16      .18E‐04      .36E‐04      .54E‐04      .72E‐04      .90E‐04      .11E‐03      .13E‐03      .14E‐03      .16E‐03      .18E‐03      .20E‐03      .22E‐03      .23E‐03      .25E‐03      .27E‐03     

‐16.38       ‐15.53       ‐14.68       ‐13.82       ‐12.97       ‐12.11       ‐11.26       ‐10.4        ‐9.55        ‐8.7         ‐7.84        ‐6.99        ‐6.13        ‐5.28        ‐4.42        ‐3.57       

Material 1

D

B

.10E‐15      .82E‐04      .16E‐03      .25E‐03      .33E‐03      .41E‐03      .49E‐03      .57E‐03      .66E‐03      .74E‐03      .82E‐03      .90E‐03      .98E‐03      .11E‐02      .11E‐02      .12E‐02     

‐15.99      ‐15.12      ‐14.25      ‐13.38      ‐12.51      ‐11.63      ‐10.76      ‐9.89        ‐9.02        ‐8.14        ‐7.27        ‐6.4         ‐5.53        ‐4.65        ‐3.78        ‐2.91       

Material 2

(a)

(b)

Figure 8 : Comparison of damage maps for Material 1 vs. Material 2. Figs. (b) plots of log 10

(D) from Figs. (a) .

Indeed, in a FE model the stress ratio ρ ref

may vary over a range of values, which depend on the variation of the local

multiaxial state of stress among nodes. Fig. 9(a) illustrates the distribution of ρ ref

values obtained in numerical simulations.

This distribution holds for both materials, being ρ ref only a function of the local stress, not of material. The figure also marks the values at which the multiaxial stress is close to uniaxial tension or torsion, and the regions A, B, C, D identified in Fig. 8(a) (top). The values of ρ ref then measure if the stress in a point is more tension-like or torsion-like.

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