A Microstructure-Based Time-Dependent Crack Growth Model for Life and Reliability Prediction of Turbopropulsion Systems

Abstract

The objective of this investigation was to develop an innovative methodology for life and reliability prediction of hot-section components in advanced turbopropulsion systems. A set of generic microstructure-based time-dependent crack growth (TDCG) models was developed and used to assess the sources of material variability due to microstructure and material parameters such as grain size, activation energy, and crack growth threshold for TDCG. A comparison of model predictions and experimental data obtained in air and in vacuum suggests that oxidation is responsible for higher crack growth rates at high temperatures, low frequencies, and long dwell times, but oxidation can also induce higher crack growth thresholds (ΔK _th or K _th) under certain conditions. Using the enhanced risk analysis tool and material constants calibrated to IN 718 data, the effect of TDCG on the risk of fracture in turboengine components was demonstrated for a generic rotor design and a realistic mission profile using the DARWIN^® probabilistic life-prediction code. The results of this investigation confirmed that TDCG and cycle-dependent crack growth in IN 718 can be treated by a simple summation of the crack increments over a mission. For the temperatures considered, TDCG in IN 718 can be considered as a K-controlled or a diffusion-controlled oxidation-induced degradation process. This methodology provides a pathway for evaluating microstructural effects on multiple damage modes in hot-section components.

Appendix

Oxidation at the crack tip is considered to occur within the damage zone, which is represented schematically by a crack-tip element of height d and width s in Figure 2. The plastic strain within the crack-tip element can be related to the crack-tip opening displacement, CTOD, and is approximated as[68]

$$ \varepsilon_{\text{tip}}^{\text{p}} = \frac{\text{CTOD}}{d} $$

(A1)

For small-scale yielding, CTOD is given by Reference 69

$$ {\text{CTOD}} = \frac{{K^{2} }}{{2\sigma_{y} E}} $$

(A2)

which can be combined with Eq. [A1] to give

$$ \varepsilon_{\text{tip}}^{\text{p}} = \frac{{K^{2} }}{{2\sigma_{y} E\;d}} $$

(A3)

Rearranging the terms in Eq. [2] leads one to

$$ \frac{1}{{t_{f} }} = \frac{1}{{t_{o} }}\left( {\frac{{\varepsilon_{\text{P} } }}{{\varepsilon_{\text{f} }^{ \ast } }}} \right)^{1/b} $$

(A4)

which is substituted into Eq. [1] to give

$$ \frac{da}{dt} = \frac{s}{{t_{\text{o}} }}\left( {\frac{{\varepsilon_{\text{P}} }}{{\varepsilon_{\text{f}}^{ \ast } }}} \right)^{1/b} $$

(A5)

which becomes

$$ \frac{da}{dt} = \frac{s}{{t_{\text{o}} }}\left[ {\frac{1}{{2\sigma_{y} E\varepsilon_{\text{f}}^{ \ast } d}}} \right]^{\frac{m}{2}} K^{m} $$

(A6)

upon substituting Eqs. [A3] into [A5] and setting m = 1/b. The crack-tip element height d is assumed to be a function of the grain size, D, according to the expression given by Reference 70

$$ d = d_{\text{o}} \;\left( {\frac{D}{{D_{\text{o}} }}} \right)^{\gamma } $$

(A7)

where D _o is a reference grain size, d _o is the crack-tip element height at the reference grain size D _o, and γ is an empirical constant. The crack-tip element width, s, is assumed to be related to the diffusive flow of oxygen atoms from the crack tip and is expressed as

$$ s = s_{\text{o}} \;\exp \;\left( { - \frac{Q}{RT}} \right) $$

(A8)

substituting Eqs. [A7] and [A8] into Eq. [4]. The proposed model, Eq. [4], is fairly complex and contains a large number of material constants including the yield stress (σ _y ), critical fracture strain (ε _f), Young’s modulus (E), grain size (D), and activation energy for grain-boundary diffusion (Q). There are also several empirical constants such as m, γ, s _o, t _o, and d _o. All of these parameters appear in the parameter B _o in Eqs. [6] and [7]. For evaluating material constants and applying the model, only the B _o parameter needs to be evaluated and individual contributors to B _o need not be evaluated if experimental data are not readily available. Table AI presents the model constants for IN 718 for various Q values. It is noted that the value for s _o/t _o was adjusted for a given Q value so that the computed B _o value matched the experimental B _o. The s _o/t _o value is correlated to the Q value and s _o/t _o cannot be predicted at this time.

Table AI Model Constants for IN 718 at 923 K (650 °C) for Two Q Values