PSI - Issue 14

L.R. Botvina / Procedia Structural Integrity 14 (2019) 26–33

29

L.R.Botvina/ Structural Integrity Procedia 00 (2018) 000 – 000

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To analyze the process of fatigue and creep from the standpoint of the theory of phase transitions, the dependences of fatigue crack lengths in notched specimens from aluminum alloys on the number of cycles and creep curves of heat-resistant steel at an elevated temperature were plotted for different stresses. As the order parameters, the number of cycles at the stable stage of crack growth ( N ) under cyclic loading, and the lifetime at the second stage of creep (τ) were used. As a result of such an analysis, power-law dependences of the normalized values of the order parameters under cyclic loading (relation (2) and creep (relation (3) on the normalized stress values were obtained by Botvina (1994, 1997): |( − ) ⁄ | = |[( − )/ ] | (2) | ( − с ) ⁄ | = 1 |[( − ⁄ )] | , (3) where σ and σ c are the amplitudes of the current and critical stress, respectively. The critical index for fatigue failure of the investigated aluminum alloy is equal to 7; an increase in the frequency of cyclic loading leads to decreasing the critical exponent. In the case of creep, the critical exponent γ varies from 1.9 to 4 as a function of the testing temperature: the lower the temperature, the lower the critical exponent. For the creep close to the critical point, as for the fatigue, the sensitivity of the deformation values to the stress variation increases and the fracture mechanism changes. We considered crystallization of semi-solid materials studied in detail by Flemings (1991). Semi-solid materials include those containing 50-60% already crystallized phase and are used to obtained composite materials or for other final shaping processes. The major factors determining the mechanism of crystallization in such materials are the cooling rate and the rate of shear of the liquid metal. Shearing the liquid metal during the early stages of solidification promotes a breakdown of the dendritic structure, and as a result the viscosity decreases and a spheroidal structure forms (Fig. 2a). Thus, the phase transition at the critical point is connected with transition (under decreasing the shear rate) from a spheroidal structure to a dendritic one.

Fig. 2. (a) viscosity of the alloy Al-4,5%Cu-1,5%Mg for constant cooling rate (0.03 C/sec) and different shear rates ( ̇ ) of the melt according to Flemings (1991), (b) the relation between the normalized values of the order parameter and the shear rate of the melt: ̇ = 90 1/sec (1), ̇ = 180 1/sec (2), ̇ = 330 1/sec (3), ̇ = 560 1/sec (4) and (c) diagrams of crystallization in ordinary and in universal (d) coordinates. As we see from Fig. 2b, the crystallization process of the alloy Al-4,5%Cu-1,5%Mg is characterized by a significantly smaller critical exponent compared with the exponents characterizing the fracture processes but the relation for the order parameter is similar to the preceding relation: | ( − ⁄ |= |[ ̇– ̇ ̇ ⁄ ] | (4)