PSI - Issue 14

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

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1. Introduction Various techniques are available for numerical simulation of crack growth in a plant component; some of these are node-release-technique by Brocks (2017), Gurson-Tvergaard-Needleman damage model by Needleman et al. (1992), Cohesive-zone-model, etc. The cohesive zone model introduced by Barenblatt (1962) and Dugdale (1960) is a damage mechanics methodology used to simulate the initiation and propagation of cracks in solids using finite element technique. In this model, a narrow band of vanishing thickness lies ahead of crack tip to represent the fracture process zone. The upper and lower surfaces, as shown in Fig. 1a, are called the cohesive surfaces. Both the surfaces are subjected to cohesive tractions during the loading of the component. The cohesive tractions follow a constitutive law called the Traction Separation Law (TSL), which relates the cohesive traction with the distance of separation. A typical TSL is shown in Fig. 1b. Three parameters which are generally used to define a TSL are cohesive energy, peak stress and the distance of separation.

Fig. 1. (a) Cohesive zone model;(b) Exponential traction separation law

In the present work, an exponential traction separation law (TSL) is used to simulate the crack growth. Finite element code WARP3D available in open literature is used for this purpose by Healy et al. (2016). An exponential TSL combining normal and shear tractions into a single effective traction ( t ) is available in WARP3D. The model thus has a single traction separation curve and a single energy of separation (G). The shape of the exponential law is dependent on user specified values of peak stress (T) and displacement at peak stress during the analysis (δ p ). The effective opening displacement is given by where δ t and δ n are tangential and normal displacements and β is a user defined weight parameter which assigns different weights to tangential and normal displacements. The relationship t - δ follows from

(1)

The work of separation per unit area of the cohesive surface is given by

(2)

The cohesive parameters are not material constants but vary with crack length, size & geometry of the component. This is because the fracture process depends on the state of stress triaxiality at the location of the crack as discussed by Chen et al. (2005), Mahler et al. (2015) and Anuradha & Manivasagam (2009). Among several methods to measure crack tip constraint, the J-h approach is one widely used method to incorporate triaxial state of