PSI - Issue 18

Plekhov O. et al. / Procedia Structural Integrity 18 (2019) 711–718 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

716

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material, which has created effective defect structure for the dissipation of deformation energy. The extension of the area of applicability of the model requests the simulation of nonlocal process of plastic deformation.

0.8

numerical results experimaental results

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1- 

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0.1

0

0.0625

0.1094

0.1562

0.2331

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Fig. 2. Value of 1- β depending on strain. Simulation results.

One of the important applications of the energy balance evaluation is possibility of a calculation of a fatigue crack rate on the base of the energy equations:

 da dN h J J N    1 d d E

(12)

s

,

c

where da dN - fatigue crack rate, d d s E N - the stored energy value per cycle, J - J-integral, c J - critical value of J-integral, h - specimen thickness. The algorithm for a lifetime assessment includes a several steps. First, we chose several stress amplitudes for numerical simulation. For every force, the critical crack length is calculated as:

1/ 2 ( / ) c c K F f a w hw  ,

(13)

where c K - fracture toughness, F - force magnitude, w - width of the specimen, c a - critical length, f - polynomial function depending on the crack size and geometric parameters of the considered sample. Second, for every chosen force, the fatigue crack rate was determined. In order to define crack rate equation (12) well be used. To apply (12) we calculated the value of a stored energy per cycle and the J-integral value. The stored energy value is evaluated according to equation (6). A stationary crack approach for a fatigue crack rate calculation was used. A few loading cycles for every given crack length a are considered and stabilized value of the stored energy per cycle is evaluated. Thus, on the second step of the algorithm the function   d ( ) 1 ( ) ( ) d s c E a l a h J J a N   is length. We will illustrate the abovementioned algorithm by the simulation of the lifetime of the Ti-1Al-1Mn specimen subjected to the cyclic loading. For calibration of the thermodynamical material parameters of the proposed mathematical model, a quasistatic tensile experiment of a Ti-1Al-1Mn dogbone specimen with a strain rate of 1 s -1 was simulated. The constitutive equations were implemented in the finite-element package Simulia Abaqus with the use of UMAT procedure. Following values of the material parameters were obtained as a result of the stress-strain determined. Third, the number of cycles to fracture * N is calculated as 1 a N l a dl    , where * ( ) c o a 0 a - initial crack