Technical NoteNumerical models to determine the effect of soft and hard inclusions on different plastic zones of a fatigue crack in a C(T) specimen
Introduction
Many researchers were correlated the fatigue crack growth rates with the elastic stress intensity factor range under small scale yielding conditions for decades with significant success [1], [2]. However, the cyclic plastic damage progression in the cyclic plastic zone (also known as reverse plastic zone) is the primary mechanical driving force for the growth of fatigue crack under cyclic loading [3], [4], [5]. Therefore, it is extremely important to know the exact size and shape of crack tip plastic zones when assessing the safety state of a cracked component in practice. Typically three zones (cyclic plastic, monotonic plastic and elastic zones) are observed at the fatigue crack tip. Cyclic plastic deformation and damage progression take place only in the cyclic plastic zone. Therefore, size and shape of the cyclic plastic zone play a key role in fatigue crack growth investigation.
Several researchers were attempted to determine the size of plastic zones. Irwin [6] and Dugdale [7] were proposed different analytical models to estimate the plastic zone size ahead of a fatigue crack tip for an infinite plate. Paul and Tarafder [8] and Paul [9] were reported that the size of monotonic plastic zone depends upon the maximum stress intensity factor (i.e. R ratio (ratio of minimum and maximum stress intensity factor) and δK (amplitude of stress intensity factor)) while the size of cyclic plastic zone depends upon the δK. The cyclic plastic deformation mode in the cyclic plastic zone is normally controlled by R ratio. Normally, low cycle fatigue (LCF) is observed for R ratio = −1 (symmetric loading) and ratcheting is observed for R ratio ≠ −1 (asymmetric loading) [9]. Ratcheting deformation at the fatigue crack tip is also reported by Tong et al. [10]. Flouriot et al. [11] were also reported strain ratchetting primarily in some of the localised slip bands during elasto(visco)-plastic simulation. Many experimental techniques are available to determine the plastic zone size (specifically monotonic plastic zone size) in literatures [12], [13], [14], [15]. However, experimentally measurement of cyclic plastic zone is extremely difficult with available technologies because of its scale and multiaxiality. As a consequence researchers were extensively used finite element simulation technique to determine the sizes of cyclic and monotonic plastic zones. In the present investigation, finite element simulation technique with advanced material model is adopted to determine the cyclic plastic zones at the fatigue crack tip.
The mechanism of fatigue crack growth is fundamentally influenced by the presence of micro-defects that are inherent to the materials such as micro-cavities and inclusions. Number of researchers were investigated the effect of micro-cavities on size and shape of plastic zones [16], [17], [18], [19]. However, Bouiadjra et al. [18], [19] were adopted isotropic hardening law to model the cyclic plastic deformation process, and the isotropic hardening law is unable to address even simple Bauschinger effect. Kinematic hardening model is the most suitable to represent the cyclic plastic deformation behaviour of materials [20], [21], because it is able to address the key issues of cyclic plasticity phenomena like Bauschinger effect, ratcheting and mean stress relaxation. Paul [22] was recently used kinematic hardening model to determine the effect of micro-cavities on size and shape of plastic zones. However, literatures regarding the effect of inclusions on plastic zones are not available till date. Therefore, the effect of soft and hard inclusions on size and shape of plastic zones are investigated in the present work by an advanced kinematic hardening model to understand it properly.
Section snippets
Finite element analysis
A full compact tension (C(T)) specimen (width (W) = 62.5 mm, height = 60 mm and thickness (B) 20 mm) is selected for the present investigation. A stationary fatigue crack with length of 25 mm (notch length 20 mm and 5 mm stationary crack) is considered for the current study (Fig. 1(a)). Two dimensional plane strain finite element simulation is conducted on that full C(T) specimen. Semicircular crack tip (Fig. 1(b)) is adopted to model the crack tip, as adopted by other researchers [23], [24], [25]. Four
Results and discussion
The size and shape of monotonic and cyclic plastic zones for different positions, size and shape of hard and soft inclusions are investigated in the present work. In depth implicit plane strain analysis is conducted on a full CT specimen with a stationary crack length of 25 mm at δK (amplitude of stress intensity factor) 18 MP√mm and R (ratio of maximum and minimum stress intensity factor) −0.5. The Kmax (maximum stress intensity factor) is 24 MP√mm for δK of 18 MP√mm and R of −0.5. The monotonic
Conclusions
Effect on size and shape of monotonic and cyclic plastic zones at fatigue crack tip in the presence of soft and hard inclusions are analysed under selected cyclic loading conditions in a plane strain finite element model. The Chaboche non-linear kinematic hardening model, von-Mises yield criterion and associated flow rule were employed for this work. Finite element simulation results show that the presence of soft inclusion (MnS) has significant effect on the size and shape of monotonic and
Acknowledgements
Author likes to acknowledge Dr. Soumitra Tarafder, National Metallurgical Laboratory, Jamshedpur, India for his valuable suggestions.
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