PSI - Issue 32

N.V. Boychenko et al. / Procedia Structural Integrity 32 (2021) 326–333 Boychenko N.V./ Structural Integrity Procedia 00 (2019) 000 – 000

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4.2. CMSG plasticity dominated zone

The size of the CMSG plasticity dominated zone was determined as radial coordinate where the HRR and CMSG hoop or equivalent stress become equal. The boundaries of the CMSG plasticity dominated zone are listed in Table 1.

Table 1. The boundaries of the CMSG plasticity dominated zone

(r/a) max

σ θ

σ e

  

N =0.075

N =0.4

N =0.075

N =0.4

ij

ij

HRR

CMSG

3∙10 -5

3∙10 -5

1.5∙10 -4

1.5∙10 -4

l =1 μm

CMSG

6 ∙ 10 -4

6 ∙ 10 -4

2∙10 -4

2∙10 -4

l =5μm

The size of the CMSG plasticity dominated zone is sensitive to intrinsic material length parameter, wherein does not depend on the strain hardening exponent. The boundary of the CMSG plasticity dominated zone is varied within dimensionless coordinate 3∙10 -5 < r/a <6∙10 -4 depending on the intrinsic material length. Fig. 5 shows the boundary of the CMSG plasticity dominated zone as a function of the intrinsic material length parameter. The size of the dominated zone increases with increasing of l .

Fig. 5. The boundaries of the CMSG plasticity dominated zone

By fitting the numerical calculations, the values of the boundary of CMSG plasticity dominated zone of intrinsic material length were represented in the form of the approximation equations in following forms: Hoop stresses σ θ : r/a = 0.00001419e 0.74893307∙ l (9) Equivalent stresses σ e : r/a = 0.00000785e 0.64756679∙ l (10) The size of the CMSG plasticity dominated zone can be determined for any value of the intrinsic material length parameter from the considered range using equations (9) and (10).