PSI - Issue 71

Arun K. Singh et al. / Procedia Structural Integrity 71 (2025) 90–94

91

E ) GPa & IC ID K K Static and dynamic stress intensity factor ( Elastic modulus of material (

)

MPa m

respectively

Applied stress (

) MPa

0 

Density of steel material (

)

3 . kgm −

s 

Effective static and dynamic surface energy (

)

2 . kJ m −

& s d  

respectively

1. Introduction Fracture is primarily a process of material fragmentation wherein two or more surfaces create owing to crack propagation. Griffith model (1921) traditionally assumes that effective surface energy of solids is independent of rate of rupture. This assumption is found to be quite useful for brittle solids such as glass, ceramics etc (Freund,1998; Melkar,2010). Griffith’s theory also considers slow rate of crack propagation, wherein role of inertia of crack tip is negligible. However, Mott (1948) modified the G riffith’s model after considering the role of crack tip inertia (kinetic energy) on dynamic stress intensity factor (DSIF) ID K in the terms of static stress intensity factor IC K , crack tip velocity v da dt = and, the constant D which is related to inertia of moving crack tip, as following 2 2 K

K

=

IC

ID

2 2   −    1 2 l v v D 

(1)

2 2 s l D k v E   = consists of an additional constant k , limiting velocity l v , elastic

The constant

s  of solid ( Neal-Sturgess, 2012). It is important to note that Eq.1

modulus E and density

ID IC K K = . It is also evident from Eq.1 that ID K

0 D = , that is

reduces to Griffith’s model for

becomes infinite at critical velocity 2 l v D . This observation is attributed to kinetic energy of the crack tip that increases rapidly with crack velocity to result in a singular stress field near the crack tip, hence DSIF as well Freund (1998). Literature survey shows that the effect of crack velocity on dynamic fracture is studied extensively using different numerical methods such as cohesive zone model, phase field model etc. (Landis et al, 2000; Zhou et al., 2005). Nevertheless, rate dependent dynamic crack behaviour is not yet fully understood. Hence, a simple modification in the Motts’ theory of crack (Eq.1) is carried out in view of practical observation that effective surface energy depends on crack velocity or rate of rupture. The proposed model is also validated with the experimental data reported by Rosakis et al. (1984). 2. Results and discussion: Experiments have established that surface energy of solids depends on the rate of rupture process at the crack tip Stampfl and Kolednik (2000). This effective surface energy is attributed to plasticity