• R Narasimhan

Articles written in Sadhana

• A cohesive finite element formulation for modelling fracture and delamination in solids

In recent years, cohesive zone models have been employed to simulate fracture and delamination in solids. This paper presents in detail the formulation for incorporating cohesive zone models within the framework of a large deformation finite element procedure. A special Ritz-finite element technique is employed to control nodal instabilities that may arise when the cohesive elements experience material softening and lose their stress carrying capacity. A few simple problems are presented to validate the implementation of the cohesive element formulation and to demonstrate the robustness of the Ritz solution method. Finally, quasi-static crack growth along the interface in an adhesively bonded system is simulated employing the cohesive zone model. The crack growth resistance curves obtained from the simulations show trends similar to those observed in experimental studies

• Quasi-static crack tip ﬁelds in rate-sensitive FCC single crystals

In this work, the effects of loading rate, material rate sensitivity and constraint level on quasi-static crack tip ﬁelds in a FCC single crystal are studied. Finite element simulations are performed within a mode I, plane strain modiﬁed boundary layer framework by prescribing the two term $(K −T)$ elastic crack tip ﬁeld as remote boundary conditions. The material is assumed to obey a rate-dependent crystal plasticity theory. The orientation of the single crystal is chosen so that the crack surface coincides with the crystallographic (010) plane and the crack front lies along $[10\bar{1}]$ direction. Solutions corresponding to different stress intensity rates $\dot{K}$, 𝑇-stress values and strain rate exponents 𝑚 are obtained. The results show that the stress levels ahead of the crack tip increase with $\dot{K}$ which is accompanied by gradual shrinking of the plastic zone size. However, the nature of the shear band patterns around the crack tip is not affected by the loading rate. Further, it is found that while positive 𝑇-stress enhances the opening and hydrostatic stress levels ahead of crack tip, they are considerably reduced with imposition of negative 𝑇-stress. Also, negative 𝑇-stress promotes formation of shear bands in the forward sector ahead of the crack tip and suppresses them behind the tip.

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