PSI - Issue 23

Tomáš Babinský et al. / Procedia Structural Integrity 23 (2019) 523–528 Babinský & Polá / Structural Integrity Procedia 00 (2019) 00 – 000 = ( ) = 0 / = [1 + exp ( 0 − )].

525 3

( 2 )

Parameter α characterise the obstacles that can be overcome by thermal activation. Both stress components can be acquired by the analysis of the hysteresis loop during low-cycle fatigue experiment. The shape of the hysteresis loop in relative coordinates is determined by an equation = for ≤ 2 , ( 3 ) = − 2 ( 2 − ) for 2 ≤ ≤ 2 , ( 4 ) where G(x) is second integral function of the PDF ( ) = ∫ (∫ ( ) 0 ) 0 . ( 5 ) Deriving the Eq. (4) twice with respect to relative strain leads to ( 2 − ) = − 2 2 2 2 for 2 ≤ ≤ 2 . ( 6 ) Physically, the second derivative is a synonym for a material hardening velocity. Plotting the second derivative of the half-loop vs. fictive stress ε r E eff /2 enables us to evaluate the probability density function f(σ ic ) as well as saturated effective stress σ es , which is represented by the shift of the probability density function in the plot vs. relative strain or effective stress. In superalloys, the γ’ phase is reported (Petrenec et al. (2013), Šmíd et al. (2011), Polák et al. (2014)) to have much higher effective stress component than the γ matrix as a consequence of short range order in γ’ phase. Thus, matrix is softer and deforms at lower internal critical stress than γ’ phase. The structure of 713LC alloy was fully dendritic with an approximate average grain size of 2.4 mm. The structure consisted of cuboidal γ’ precipitates ordered in thin channels of γ matrix and carbides in interdendritic regions. The specimen cycled with the strain amplitude 8∙10 -3 broke suddenly after 70 cycles. Initial hardening was followed by a slow softening until a sudden fracture. Interdendritic fracture surface shown in Fig 1a indicates premature cracking. Conveniently oriented grains are densely covered with persistent slip markings (PSMs) where persistent slip bands (PSBs) emerge on the surface as shown in Fig.1b. Even though it is apparent that some cracks originated from PSMs, the principal crack probably originated from one of casting defects which were up to 0.5 mm in diameter. The presence of casting defects resulted in a drop of mean stress and apparently influenced the shape of the second derivatives shown in Fig. 2 as well. Second derivatives of the tensile half-loop (Fig. 2a) shows two distinct peaks: the minor peak around 250 MPa corresponds to the deformation of the matrix whereas the major peak around fictive stress 700 MPa corresponds to the deformation of γ’ particles. After few cycles, the minor peak vanished; that could be due to a gradual reduction of plasticity in thin slabs of γ matrix and preferential deformation of γ’ precipitates henceforth. The third smaller peak around 1200 MPa indicates widening of the spectrum of internal critical stresses. The height of peaks decreases and moves to higher fictive stresses with increasing number of cycles, which corresponds to the increase of the internal stress component linked with a localization of dislocation slip into PSBs. However, the comparison of shapes of half loops in the 50th cycle, with respect to the evolution of both tensile and compressive second derivatives, indicates that the crack was already present and could affect the shape of the spectrum. 4. Results and discussion 4.1. Inconel 713LC