PSI - Issue 14

Ashok Saxena / Procedia Structural Integrity 14 (2019) 774–781 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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ductile materials only for that reason. Standard test methods for creep-brittle materials are not available. Similarly, for creep-fatigue conditions, there is an ASTM standard. E2760-16 [2016], available to guide testing of metals. This standard does include creep-brittle materials because under cyclic loading when small-scale-creep conditions can be assured, the cyclic crack growth rate, da/dN, has been repeatedly shown to correlate with the cyclic stress intensity parameter, ∆K, provided the load ratio, frequency of loading, and the waveform can be held constant. as seen in Fig. 4 for Inconel 718 at several loading frequencies [Floreen and Kane, 1979].

Fig.3- Creep crack growth rate as a function of C t parameter in 1Cr 1Mo-0.25V steel at 538 0 C under small-scale creep to widespread creep in large C(T) specimens [Saxena, Yagi, and Tabuchi, 1994]. VAH1 and VAH 2 refer to two specimens tested at different load levels and the arrows point to crack growth rates from the beginning of the test going forward in time.

3. Crack Growth During Thermal-Mechanical Fatigue Conditions

High transient stresses during start-up and the period immediately following start-up, cause thermal-mechanical fatigue (TMF) conditions in thick-section components such as turbine discs that operate at elevated temperatures. Often, the stresses are high enough to cause plastic deformation [Saxena et al. 1986 ] so the ∆J parameter of Dowli ng and Begley [1976, 1977] is attractive for describing the fatigue crack growth behavior. However, there are important limitations in using ∆J because it is based on deformation theory of plasticity that requires the loading to be proportional and the relationship between cyclic stress and cyclic strain to be unique. In other words, for every value of stress range, there is a single unique value of strain range in the entire cracked body. Neither of these conditions can be assured during TMF conditions, where the ratio of principal stresses vary with increasing primary loads, and due to temperature gradients in the body, the basic plastic properties such as strength and strain hardening vary from point-to-point in the cracked body. Also, non-saturated cyclic deformations can occur that further lead to conditions of multi- valued relationship between cyclic stress, and strain ranges. Thus, ∆J loses its property of path independence, and the ability to uniquely relate to crack tip stress, and strain range via the Hutchinson-Rice Rosengren (HHR) type equations [Hutchinson, 1968, Rice and Rosengren, 1968 ]. The limits in the use of ∆J for such applications have not been explored [Yoon, 1991] but not established. Alternate parameters for predicting crack growth rate s under TMF conditions must be identified where ∆J is not applicable.