PSI - Issue 14

Viswa Teja Vanapalli et al. / Procedia Structural Integrity 14 (2019) 521–528 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

523

3

stress in fracture mechanics, where J is the applied J integral and ‘ h ’ is the triaxiality factor which is defined as ratio of hydrostatic stress (σ h ) to the von Mises equivalent stress (σ v ).

(3)

where

, with σ 1 , σ 2 and σ 3 being the

and

principal stresses. The multiaxiality quotient ‘q’ is given by,

(4)

The ‘q’ parameter varies with the increase in applied load. In order to compare ‘q’ for different cracked specimens, the variation of q is plotted along the crack-line with the increase in applied J integral. The minimum value of ‘q’, which is generally obtained at a distance from crack tip, is taken as the value of ‘q’ for that geometry. The applied J-integral value at any load step may be calculated using the closed form formula given in ASTM E 1820-15a (2015) or numerically using domain integral technique by Healy et al. (2016). The primary objectives of the present work are a) to determine appropriate cohesive parameters (i.e. cohesive energy and peak stress) for fracture specimens made of SA333 Grade 6 steel by using the experimental results, b) to ascertain variation of cohesive parameters as a function of crack tip stress triaxiality and c) to assess variation of cohesive zone parameters for a particular value of stress triaxiality due to possible microstructural changes near the crack tip within the material.

2. Fracture analyses of TPBB specimens and Straight pipes with through-wall flaws

2.1. Material properties & Experimental data

The experimental results of TPBB specimens and piping components made of SA333 Grade 6 steel used for the present analyses are taken from literature CIEP/98/0055 (2000). This material is widely used in Indian nuclear reactors piping& elbows. The material properties of SA333 Grade 6 steel are tabulated in Table 1. J-initiation value for this material is found to be close to 220 kJ/m 2 determined using stretch zone width at crack initiation (J SZW ) (CSIR, 2014). The experimental results of TPBB specimens used in the present analysis are of 8 mm, 12 mm and 25 mm thickness. The 8mm thick specimens are prepared from 8” diameter pipes while 12mm and 25mm thick specimens are prepared from 16” diameter pipes.

Table 1. Mechanical properties of SA333 Grade-6 Steel (CIEP/98/0055, 2000) 8” diameter pipe

16” diameter pipe

Young’s Modulus, E Yield Strength, σ y Ultimate Strength, σ u

203000 MPa

203000 MPa

285 MPa 420 MPa

307 MPa 463 MPa

Ramberg Osgood parameters α n

10.759 4.301

10.249 4.23

2.2. Finite element model

Fig. 2a. shows the schematic diagram of TPBB specimen. In the present analysis, 3D finite element model (Fig. 2b.) of a quarter specimen is used making use of symmetric boundary conditions. The finite element model (FEM) of the specimen is prepared using 8-noded solid brick elements while cohesive zone is modelled using 8-noded cohesive interface elements. The true stress strain curve as reported in (CIEP/98/0055, 2000) is used in the analysis. Cohesive elements are located at the crack plane from initial crack tip up to a distance of 4 mm in the direction of