PSI - Issue 39

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

294

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described by the rate of change of J -integral, which is obtained using the concept of configurational forces. The advantage of configurational force concept is that it is independent of materials’ constructive response and therefore it can work for time dependent deformation as well as for crack growth and non-proportional loading condition unlike the conventional J-integral. The conventional method of describing the crack behavior under creep deformation is using the C t integral or C * integral which is similar in nature to the J-integral, except that in C * integral certain parameters are replaced with their rates. For instance, the strain energy density is replaced with the rate of change of strain energy density and the displacement is replaced with the rate of change of displacement. This description of crack driving force may describe the stresses and strains in the in the material at the crack tip, however theoretically it doesn't describe a crack driving force because it is not related to either J or d J /dt. Therefore, a true definition of driving force in creep deformation is not captured by conventional C * or C t integral. Another issue which is associated with the C* or C t integral is that it is path dependent when the creep crack zone is small. C * or C t integral is valid only when the creep zone extends throughout the ligament that is under the extensive creep condition. As the J-integral calculated as summation of configurational forces is independent of material’s constitutive response, it can describe the crack driving force and the rate of change of crack driving force in terms of J and d J /dt. 4. Numerical simulation of material inhomogeneity effect The material inhomogeneity is simulated using 2-dimensional finite element analysis of half symmetric Compact Tension (CT) specimen where a crack transition between two differently creeping materials are modelled. The schematic representation of the two differently creeping material transition is shown in presence of a crack in Fig. 1. To simulate the influence on the crack driving force, the crack tip is modelled at different L / b o ratios of -0.2, -0.16, -0.12 and -0.04. Here, L is the distance of the crack tip from the interface and b o is the initial ligament length which is 50mm. The CT specimen is scaled according to the ASTM E1820 in dimensions for a value of specimen width (W) which is twice of the thickness (B) and initial crack length ( a o = 50mm). Four noded quadrilateral plane strain elements with reduced integration were used for finite element analysis and the creep and other material properties for the creep inhomogeneity are listed in Table 1.

Table 1. Material properties used in finite element simulation of creep inhomogeneity. Material Elastic Modulus (E, GPa)

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

Power law creep exponent (n)

Poisson’s ratio (v)

Material 1 Material 2

200 178

0.3 0.3

9e-31 9e-31

8.0

10.6