The EIFS-based fatigue life prediction approach of nickel-based single crystals with film cooling holes at elevated temperature

Highlights

• A comprehensive surface integrity assessment method for FCHs.

• Quantitative evaluation of surface integrity of two different drilling processes with any characterization technologies.

• Mechanism of crack nucleation and propagation in nickel base single crystal alloy flat plate specimen with FCHs.

• The ultimate defect length is proposed to guide the engineering practices.

• A novel total fatigue life prediction method considering initial manufacturing defects.

Abstract

In this study, a new framework for the fatigue life prediction of nickel-base single crystal (SX) superalloys with different drilling film cooling holes (FCHs) at high temperatures (900 ℃ and 980 ℃) is investigated based on surface integrity quantification and fracture mechanics. For all the tested SX superalloys with anisotropy (smooth and FCHs specimens), the initial damage state is regarded as the equivalent initial flaw size (EIFS) that is independent of the specimens and hole geometry in the same drilling, and the rationality of EIFS is verified for the first time by conducting numerous fatigue tests and comprehensive surface integrity analysis. Subsequently, the fatigue crack path and microstructure of different specimens at different temperatures are analyzed to reveal the crack initiation mechanism and propagation modes, and a new equivalent stress intensity factor, $\mathrm{\Delta }{\mathrm{K}}_{\mathrm{e}\mathrm{q}}$, is proposed to describe the crack propagation driving force. The EIFS and $\mathrm{\Delta }{\mathrm{K}}_{\mathrm{e}\mathrm{q}}$ are combined, and a fatigue crack growth rate (FCGR) with better fit is obtained to comprehensively reflect the different fracture modes (the mixture of Stage I and Mode I). Finally, based on the experimental observation and FCGR description, the fatigue life of the FCHs structure at room and high temperature is predicted to be 3–5 times the dispersion zone of the total fatigue life, and the ultimate defect length is proposed to guide the engineering practices.

Introduction

With the increasing performance requirements of modern aeroengines, turbine blades, which are their most critical components, are subjected to extremely high temperatures, necessitating the accurate prediction of the service life of the film cooling holes (FCHs) structure. Predicting the strength life of the different manufacturing and casting of nickel-base single crystal (SX) has always been an urgent problem to be solved in the engineering field [1], [2].

In the past few decades, researchers have focused on the study of material constitutive and the simple fatigue and creep of SX materials, such as the kinetic-constitutive approach [3] and crystallographic time-dependent damage models [4], [5], to characterize the evolution of damage-rates related to current physical quantities, such as stress, strain, strain rate, and material defects [6]. These models were studied prior to the occurrence of cracks. Crack propagation based on these mechanical mechanisms (such as energy density) has also been studied, but it has not been involved in structural parts [7], [8]. Leidermark et al. [9] and Bourbita et al. [10] used the critical distances method to predict the low-cycle fatigue life of SX-notched specimens, and achieved satisfactory results. However, two key problems for SX superalloys have not yet been solved: that is, the inaccurate anisotropic constitutive model and complicated fatigue damage mechanism and accumulation criterion of FCHs.

From another perspective, fatigue failure is historically characterized by crack initiation followed by crack propagation analysis, and the current prediction methods of fatigue life does not separate these two stages, because their boundaries are very difficult to determine. Although some scholars [11] regard different scale lengths of crack propagation as their boundaries, this is not accepted by most researchers. In addition, the crack growth path and growth rate of SX superalloys have obvious differences at different crack lengths [12], as shown in Fig. 1(a). Previous short-crack growth studies [13], [14] on SX superalloys reported that the nucleation and growth of cracks are closely related to the crystal orientation, loading, and temperature. The driving force of crack growth cannot simply be determined based on the stress intensity determined by $\mathrm{\Delta }K$ using the conventional linear elastic fracture mechanics (LEFM), even though the crack growth life can capture the FCGR on the basis of $\mathrm{\Delta }K$, in conjunction with the Paris law [15], [16]. These models are often described by damage parameters, such as maximum plastic strain and maximum resolved shear stress [15], [17]; however, these studies can only explain the result of single factor or limited factor coupling, and the actual fatigue failure mostly starts from micro-defects, such as micro-cracks in the recast layer, micro-pores (∼10⁻⁶ m) of materials, etc. Furthermore, SX materials show different fracture modes at different temperatures and crystal orientations, usually mode I perpendicular to the loading axis and mixed crack propagation along the crystal surface [18], which further increases the difficulty of description.

An effective approach for estimating the fatigue life is the concept of equivalent initial flaw size (EIFS), which bypasses the above difficulties. The EIFS is not an actual defect size, but an “imaginary” defect size. The same fatigue life can be obtained by integrating the FCGR of long cracks (or approximate long cracks) at a point, as shown in Fig. 1(b). Once inferred, other similar structures under similar load conditions provide accurate estimates to avoid overengineering of the structure using EIFS values, comparable to a probabilistic fatigue life prediction model [22]. At present, the calculation of EIFS mainly focuses on the back-extrapolation theories, such as the TTCI theory [23], EPS method [24], and Bayesian updating [25], which are mainly calculated according to the recorded test data (such as fracture analysis, a-N curve) or the finite element (FE) method. Their calculation results have been proven in steel, aluminum alloys, titanium alloys, and other materials for standard smooth or notched specimens [26], [27], [28]. Unfortunately, their research mainly focuses on isotropic materials that the crack-growth morphology and path of these materials are significantly different from those of anisotropic materials. In addition, most of the calculated results of EIFS value are deduced according to the real fatigue life. A typical approach involves selecting a series of EIFS values and numerically evaluating their corresponding fatigue life, which are which are then compared with the experimental results; the most appropriate value amongst those in the series is the designated EIFS value [29]. The inferred EIFS value is closely related to the structure and test environment; therefore, it is impossible to further predict the fatigue life in other environments.

In recent years, the research teams have adopted purely deterministic methods to estimate EIFS in anisotropic materials, including the previously mentioned back-extrapolation method [30] and Kitagawa-Takahashi (K-T) diagram method [31], [32]. This method was first applied to isotropic smooth specimens and then transferred to notched specimens [33], [34], Li et al. [35], [36] further developed the EIFS into an SX FCHs structure. There was no doubt that the single EIFS value determined by the conventional K-T diagram was not sufficient. It was necessary to obtain the EIFS distribution (EIFSD) representing the uncertainty of EIFS that can reflect the original quality of a batch of samples or even other similar structures. Salemi et al. [25] proposed a method combining Bayesian and FE to estimate EIFSD with uncertainty and predict the fatigue life. Aliabadi et al. [37], [38] devoted themselves to solving for EIFSD using the double boundary element method combined with Bayesian. However, the accuracy of their results at high temperatures needs to be further verified, and the description of the FCGR for SX materials also needs to be further improved, because simple crack simulation modeling has a higher uncertainty than that of more traditional isotropic materials. Therefore, this study aims to expand the author's previous work through numerous tests, and develop an EIFS analysis method for the structure of SX FCHs at elevated temperatures, and predict the entire fatigue life on this basis.

The aims of this article are threefold: (i) to present a properties-driven probabilistic framework to predict the EIFS; (ii) to propose a crack initiation mechanism and propagation driving force for SX superalloy FCGR based on EIFS; and (iii) to verify the correctness of EIFS through surface integrity analysis and predict the total fatigue life. The remainder of this paper is organized as follows. Section 2 outlines a new EIFS determination method and life prediction framework for SX FCHs structures. Subsequently, the test results are analyzed to determine the crack initiation mechanism and develop a crack driving force considering the crack growth path in Section 4. Finally, Section 5 compares the EIFS results calculated using different methods, and performs surface integrity verification for EIFS and fatigue life prediction.