Issue 52

A.V. Tumanov et alii, Frattura ed Integrità Strutturale, 52 (2020) 299-309; DOI: 10.3221/IGF-ESIS.52.23 300 The Hayhurst model [1] one of the generalized models for the creep damage accumulation. The main disadvantage of this model is necessity to use six parameters as material properties in order to describe the damage accumulation behavior. Moreover, the parameters determination methods are mainly indirect. According to this, the Rabotnov-Kachanov model is used due to the direct method of material constants determination. The Lemaitre model [2] is the one of the most frequently used for the fatigue damage accumulation behavior. In similar phenomenological models using the tensor damage parameter leads to considerable difficulties for material constants determination. For the different creep and fatigue laws if the stress state is unchanged the scalar, vector, and tensor damage parameters give almost identical results. In this regard, models with a scalar damage parameter as a simplified alternative can be considered [3-6]. The main problem of the residual life prediction under the creep-fatigue loading conditions is the complex character of their interaction [7-10]. Statistical approximations of experimental results by the polynomial functions are most common approach of the creep-fatigue interaction behavior. In present study, continuum damage mechanics is applied to assess the creep-fatigue interaction and the crack growth rate prediction, considering the complete sequence of formulations. F ATIGUE DAMAGE ACCUMULATION RATE he variable critical distance is one of important parameter in modern fracture mechanics, denoted to as the fracture process zone size. A general assumption regarding the distance criterion under elastic–plastic and creep loading conditions is that a crack increment occurs when the fracture resistance parameter (stress, strain, or energy) reaches a critical value at a characteristic distance from the crack tip. In creep–fatigue interaction both the fatigue and the creep crack growth rate can be obtained from damage accumulation rule independently. The crack size is assumed to increase when the local strain energy density at the crack tip reaches the critical value. Hence, a material point initially at a characteristic distance, c r , ahead of the crack tip, 0 r  , moves to the tip both in time t  after an increment in the crack growth for creep and in number of cycles N  , in case of fatigue. It is assumed that the crack length increment equal to the fracture process zone size, f a r   , and the crack growth rate, a  , becomes [11-12]:   0 f r f f f a r dr      (1) where   f r   is the damage accumulation rate. Eqn. (1) for creep conditions was proposed initially, however the analogy between the creep time t  and the number of cycles N  makes possible to use this dependence for low cycle fatigue. Usually, the one of the main characteristic in models with a scalar damage parameter is the number of cycles before fracture f N at the stress amplitude a  . In the simplest case of uniaxial tension-compression, the fatigue life can be obtained from: 1 2 ' c a f f N          (2) where ' f  and c are fatigue constants. The damage parameter at constant stress amplitude according to [13] 1 ln 1 ln N f f f f N N N              (3) where 1 N f   - the critical value of the damage parameter in the penultimate cycle and it is associated with static toughness 0 T U by the following relationship: T