PSI - Issue 39

Abhishek Tiwari / Procedia Structural Integrity 39 (2022) 290–300 Abhishek Tiwari/ Structural Integrity Procedia 00 (2019) 000–000

296

7

The material properties used for simulating the plastic to creep transition is listed in Table 2. The element and mesh size in simulation of both types of inhomogeneities are same. The crack driving force in terms of J-integral values are calculated for contours of 1mm, 2mm, 5mm, 10mm and far-field contour as shown in Fig. 1. The configurational forces were calculated by post processing the FE parameters needed for configurational force calculation in python. The details of the post processing are available in Tiwari et al. (2020) and Kolednik et al. (2019). The influence on the crack driving force is calculated in the form of the ratio of the J-integral for a contour closest to the tip which also encompasses the deformed zone (creep or plastic zone), J tip and the far-field J-integral calculated for far contour, J far . Remember that the J -values are time dependent in creep and hence for plastic to creep transition the influence will change with time. The path dependence of the C t integral and J as well as d J /dt has been investigated and compared.

Table 2. Material properties used in finite element simulation of plastic to creep transition.

Elastic Modulus (E, GPa)

Poisson’s ratio (v)

Power law creep coefficient (A, MPa n s -1 )

Power law creep exponent (n)

Plastic properties

Material

Material 1

200

0.3

-

-

σ o = 270MPa σ u = 900MPa ε u pl = 0.23

Material 2

178

0.3

9e-31

10.6

-

5. Results and Discussions To check if the J -integral calculated by configurational force concept and conventional J -integral for contours which are outside the discretization and deformed zones, both are calculated and compared in Fig. 3(a). The results in Fig. 3 belong to the creep inhomogeneity model for L / b o = -0.2 where the crack tip is 10mm away from the interface and the creep zone is small and only at the crack tip.

(a)

(b)

Fig. 3. (a) Comparison of J -integral behaviour obtained from Abaqus with the one calculated using configurational force method with non-linear elastic assumptions and (b) the path dependence of C t in comparison with d J /dt for creep inhomogeneity at a crack tip location L / b o = -0.2.

It can be seen from Fig. 3(a) that the J -integral values obtained using Abaqus default contour integral represented as J VCE and the J-integral calculated by summing the configurational forces in which both elastic and creep strain energy densities are included (represented by J nlel ) have same values.