PSI - Issue 17

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 17 (2019) 347–354

350

Konstantinos Kouzoumis / Structural Integrity Procedia 00 (2019) 000 – 000 Table 3: Fracture toughness values , K mat (MPa√m) ‹ƒš‹ƒŽ‹–› ”ƒ–‹‘ k=0, k=1 ȋǦͳͲͲ ‘ Ȍ k=0.5, k=2 ȋǦͳͲͶ ‘ Ȍ ʹͲΨ ƒ•–‡” —”˜‡ ͳ͵ͺǤʹ ͳʹͻǤͺ ͷΨ ƒ•–‡” —”˜‡ ͳͲͲǤͻ ͻͷǤͳ

4

The relationship between fracture toughness and constraint (at -100 o C) was presented in terms of a curve which best fit high and low constraint experimental data in (Hadley and Horn, 2019) and will be used here for the constraint modified Option 3 FALs of both specimens tested at -100 o C and -104 o C. The curve follows equation (2)

(2)

1 ) ] k

c mat K K

1 [1 ( a L  = + −

mat

r

where mat K is the fracture toughness determined from standard high constraint tests, α 1 ,k 1 are material and temperature dependent constants ( α 1 =1.97, k 1 =2.36) and β is the structural constraint parameter, which remains constant throughout the load (load independent), and is calculated as c mat K is the constraint corrected fracture toughness,

T

(3)



=

L

r y 

T denotes the T-stress which was extracted with ABAQUS from the elastic model of each specimen.

4. Assessment of tests

4.1. Option 1 assessments

The basic Option 1 FAL is based on the tensile properties from Table 2 and yielding is taken as discontinuous. The assessments have L r and K r calculated with the use of the handbook solutions included in BS 7910 and R6. From the available solutions the ones used here concern a plate with a through thickness flaw loaded in uniaxial tension. For the calculation of L r , two solutions for the limit load exist, the first one corresponds to failure under plane stress using either the Tresca or Von Mises failure criterion (or plane strain with the use of Tresca). The second solution corresponds to failure under plane strain with the use of the Von Mises criterion. Even though, BS 7910 highlights the first (Mises-plane stress) solution given its more conservative results, the plane strain solution can be invoked from the strength mis-match limit load solutions assuming a plate made wholly out of parent material. Given the thickness of the plates assessed here (50 mm) plane strain conditions are expected in the middle of their thickness and thus the Von Mises plane strain solution is used. The stress intensity factor solutions for the calculation of K r are essentially the same between the two procedures. The difference between them is considered negligible and the stress intensity factor from BS 7910 is used. The fracture toughness values used for the Option 1 assessments were the 5% Master Curve values shown in Table 3. These assessments are designated as assessments “A”. For the biaxially loaded tests, an additional assessment was made, using the lower bound plane strain von Mises limit load solution (given in terms of limit stress) invoked in (Meek and Ainsworth, 2014), shown in equation (4), while K r is calculated as previously. These asses sments are designated as assessments “B”.

2

y 

  

  

1 (1 / ) , | | |1 (1 / ) | a W k k a W − − −

(4)

lb L

m

in

2 ( ) 

=

3

where k is the biaxiality ratio, α is half of the crack length and W is half width of the plate The cruciform specimens were assessed as plates with a width of 500mm and a thickness of 50 mm, whilst the uniaxially loaded specimen ( k=0 ) was treated as a 633mm wide plate of similar thickness. The failure stresses invoked for the assessments were the average stresses that had been calculated from the strain gauge measurements of the original reports.