PSI - Issue 14

Manish Kumar et al. / Procedia Structural Integrity 14 (2019) 839–848

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Manish Kumar et. al/ Structural Integrity Procedia 00 (2018) 000–000

Keywords: creep; creep crack growth;   C t -integral; relaxation and redistribution; XFEM.

1. Introduction In the era of advanced technology, the efficient and reliable aviation industry has a great impact on the growth of every nation. To make aircraft more efficient and reliable, advance designing techniques has to be adopted in the design phase. The engine of an aircraft is the most important part and its designing is very complex. Therefore, these advance designing techniques must include all complex and non-linear phenomenon occurs in the aircraft engine such as oxidation, rapid change in loading, thermomechanical fatigue, creep, creep-fatigue interaction and the combination of these phenomena. The aero-engine parts operate at high temperature and lead to creep conditions. In creep conditions, excessive deformations and failures can occur at stresses lower than the yield strength of the material. Thus, accurate prediction of deformation and crack growth under creep environment is an important part for the lifetime assessment of aircraft components operating at high temperature. The mathematical modeling of creep deformation is based on the creep laws. The modeling of the different phases of creep depends on the capability of the creep law like power law can model secondary phase while theta projection model can capture all the three phases, more information can be found in Penny and Marriot (1995) and Kumar et al . (2016). In literature, various creep crack characterization parameters were proposed based on fracture mechanics approach to predict the creep crack growth (Landes and Begley, 1976; Bassani and McClintock, 1981; Leung et al ., 1988). The parameter, ( ) C t -integral is best suited parameter to estimate creep crack growth with its ability to capture all the three stages: small-scale creep, transition creep and extensive creep. After the transition time, the ( ) C t -integral approaches to the parameter * C along with its properties of time and path independent. In the recent time, various numerical fracture solving techniques has been developed such as boundary element method (Yan, 2006), meshfree method (Belytschko et al ., 1994; Pant et al ., 2011), extended finite element method (XFEM) (Belytschko and Black, 1999; Patil et al ., 2017) and extended isogeometric analysis (XIGA) (Luycker et al ., 2011; Singh et al. , 2017). XFEM is found most robust and effective method to solve fracture problems due to its advantages over other techniques such as no conformal mesh or remeshing requirement, and number of degrees of freedom remains almost same as of finite element model. Two types of enrichment functions are added to the standard finite element approximation in XFEM to capture the effect of crack i.e. Heaviside and crack tip enrichment function. Heaviside function produces the jump in the displacement at the crack surface while crack tip enrichment function captures the stress singularity at the crack tip. The discontinuity or interface in the continuum is traced by a mathematical function named as level set (Singh et al. , 2018). In the present study, a fully implicit algorithm is developed to simulate creep crack growth using elasto-plastic creep analysis. The creep crack growth is computed in turbine disc of an aero-engine of Inconel 718 at 650 °C using XFEM. The relaxation and redistribution effect of creep is incorporated into in the modeling with the help of creep law and described in Section 2.1. The analysis is divided into two parts: elasto-plastic analysis and creep analysis. Creep analysis is performed after the elasto-plastic analysis using converged elasto-plastic result as the initial state for creep simulation as mentioned in Section 2.2. The creep crack growth characterization parameter ( ) C t -integral is used to estimate the creep crack growth increment after every time step as discussed in Section 2.3 and added to the accumulated crack growth increment. Crack length of the continuum is increased when the accumulated crack growth increment achieves a significant value. The crack growth direction is obtained by maximum principal stress criterion using mode-I and mode-II stress intensity factors (Miranda et al ., 2003) which can be evaluated by various methods such as interaction integral (Rao and Rahman, 2003) and J -integral decomposition (Kumar et al ., 2017). In the present study, the interaction integral approach is used to estimate the stress intensity factors for different modes. During the crack growth number of degrees of freedom increases, therefore an appropriate data transfer scheme is used to transfer the data from old integration point to new integration point. Afterward, a null step analysis is required to restore the equilibrium which is explained in Section 2.4. This data transfer and null step analysis resolved all the issues related to history dependency of plasticity and creep. In Section 3, simulated results of mixed mode creep crack growth in turbine disc of an aero-engine of Inconel 718 at 650 °C are discussed. The main advantage of the proposed scheme over the conventional finite element method is that it does not require a priori crack path for mixed-mode crack growth simulations.