PSI - Issue 23

W. Teraud et al. / Procedia Structural Integrity 23 (2019) 390–395 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.1. Definition of the localization time

To determine the point in time in an experiment in which a neck is formed in a sample, it is necessary to have an appropriate criterion, which by some parameters of the deformable sample, available from the experiment, gives an answer about the presence or absence of the neck. Let the criterion for the appearance of the neck is the function  ( t ), taking the values 0 or 1, the value 0 indicating the absence, and the value 1 indicating the occurrence of localization of deformations in the sample at the corresponding time t =  . Let us introduce into consideration a uniformly deformable specimen with the dimensions of the working area w 0 ( t ),  0 ( t ), l 0 ( t ), i.e. a virtual sample that is deformed according to the same law of variation of l ( t ) as the real sample under consideration l 0 ( t )  l ( t ), for which it is necessary to calculate  ( t ), but preserving the uniform deformation of the entire working area during the entire stretching . For a flat specimen, necking determination presents a dual problem compared with cylindrical specimens of Lokoshchenko and Teraud (2013), since development of the neck in width and thickness develops in parallel. As a simple solution to the problem, we assume that the creep deformations across the thickness p h and the width p w are equal to:  p p w  . (1) For a real sample, taking into account (1), the transverse tensile stress is    . Constructing the criterion  ( t ) by the difference between the actual value of the current voltage  2 ( t , y ) and the corresponding uniform voltage ( ) 0 t  calculated by condition (2), we obtain the criterion  4 ( t ), hereafter we follow the original indexation described in Teraud (2017):           4 0 2 4 ( ) ( , ) max ( ) t k t y t H y   , (3) where H […] is the Heviside function. The localization time  4 (neck formation time) was determined from the condition  4 (  4 ) = 1. It should be noted that assumption (1) is not fully confirmed by experimental data, but it is the simplest to calculate. As a result of the experiments, a database was obtained on the high-temperature deformation of a titanium alloy with the additional effect of implanted hydrogen in the metal structure and without this effect. The dependence of longitudinal creep deformation on time for values of the initial tensile stress of 352 MPa (experiments nos. 10, 12, 13, and 14) and 552 MPa (experiments nos. 7, 8, 9, 15) is shown in Fig. 1. For experiment No. 15, the curve is not shown until the moment of destruction. You can see that hydrogen significantly reduces the time to destruction, and the more, the higher the level of hydrogen concentration in the sample. In parentheses are the concentration of hydrogen C H . According to the expression (3) when the value of the parameter k 4 = 1.0 MPa was calculated the point in time at which the deformations were localized, this point in time is shown in dots in the graphs, numerical values 1,0  are given in table 1. Evaluating the relative position of the points on the curves, you can see that For samples with hydrogen embedded, strain localization occurs earlier. / ( , ) w w t y    , 2 t y 2 2 0 0 3. Results Therefore, since the expression  ( t, y, r ) =  0 ( t ) is satisfied, there is no distorting effect of the neck, then for the virtual sample: / ( ) / ( ), ( ) 0 t ( ) w t w l l t  0 0 0 0 0 l l t    , 0 0 0 t     ( ) ( ) l t l . (2)