PSI - Issue 37

Cheng Qian et al. / Procedia Structural Integrity 37 (2022) 926–933 Cheng Qian et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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unified constraint parameter. Simha (2020) recently re-evaluated and re-interpreted C p using 3-D FEA. Yang et al. (2014) proposed an alternative unified constraint parameter A p , which was defined on the basis of the area surrounded by an equivalent plastic strain isoline ahead of the crack tip. In this study, A PEEQ was calculated as the area surrounded by the  p = 0.2 isoline at mid-plane of the given model. A ref was calculated from a standard deeply-cracked SE(B) model. Similar to A p , V p in Tonge et al. (2020) was defined as the ratio between the volume of the plastic zone in a given component and that in a standard high constraint specimen. Again,  p = 0.2 isoline was adopted in this study. The 11 constraint parameters are summarized in Table 1 with their definitions, source references, and calculation equations.

Table 1. Summary of constraint parameters.

Constraint parameter

Definition

Reference

Equation

O’Dowd et al. (1991 and 1992) = − 0 for = 0 and 0 = 2 = − 0 for = 0 and 0 = 2 = [ 0 0 ] − 1 +1 O’Dowd et al. (1994) Zhu et al. (2001) Zhu et al. (2007)

Difference between reference and actual stress fields Alternative of Q HRR based on modified boundary layer analysis

Q HRR

Q SSY

Loading modified Q HRR

Q LM

= [ 0 0 ] − 1 +1 × [ ( ,0)− ( ,0) 0 + 0 3 ] 0 = 1 [( ) 1 ̃ ( 1) ( , ) + 2 ( ) 2 ̃ ( 2) ( , ) + 2 2 ( ) 3 ̃ ( 3) ( , )] for = 0 and 0 = 2 0 = 1 [( ) 1 ̃ ( 1) ( , ) + 2 ( ) 2 ̃ ( 2) ( , ) + 2 2 ( ) 3 ̃ ( 3) ( , )] + 0 3 for = 0 and 0 = 2

Bending modified Q HRR

Q BM

Yang et al. (1993); Chao et al. (1997)

Second parameter in the three-term asymptotic stress field

A 2

Chao et al. (2004)

Bending modified A 2

A 2 BM

ℎ = = 33 11 + 22 = √ = √ 3

Ratio between hydrostatic stress and von Mises stress

Hancock et al. (1993) Guo (1993 and 1995)

h

for = 0 and 0 = 2

Out-of-plane constraint

T z

He et al. (2019); Simha (2020) = √ 2 +1 0 0 0 √

Equivalent plastic zone radius

C p

Ratio between the area of the equivalent plastic zone in a given component and that in a standard high constraint specimen Ratio between the volume of the equivalent plastic zone in a given component and that in a standard high constraint specimen

Yang et al. (2014)

A p

Tonge et al. (2020)

V p

4. Results and discussion 4.1. Experimental results

Figures 2 (a), (b) and (c) showed  J -conversion - R ,  ExxonMobil - R , and J - R curves of all tested specimens, respectively. Although there were some differences between the duplicates tests these data were averaged and fitted in the power law form according to ASTM E1820-18a, ASTM (2018). In general, the results showed the expected trends of higher resistance curves for both shallow-cracked versus deeply-cracked specimen types and tension versus bending loading modes for  a values greater then 0.20 mm. In addition, it was seen that the shallow-cracked SE(B) specimens exhibited similarly high fracture toughness values as the intrinsically low-constraint deeply-cracked SE(T) specimens. It was also seen that the geometric CTODs from the ExxonMobil method were always larger than the J -conversion ones based on ASTM E1820 or CanmetMATERIALS methods (exhibiting up to 30-40% differences based on the last value measurements, which is consistent with previous observations in Park et al. (2015).