PSI - Issue 28

A.D. Evstifeev et al. / Procedia Structural Integrity 28 (2020) 2261–2266 / Structural Integrity Procedia 00 (2019) 000–000

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guide. Whereas if the circled points do not be neglected the accuracy of the whole experimental test sufficiently decreases. 3. Data analysis 3.1. Incubation time approach The first step to the solution of data analysis problem is to chose a proper fracture criterion which is applicable to the wide range of load rates. The incubation time criterion was used for this purpose since within a framework of the one approach it allows predicting critical stress both in dynamics and quasistatic loading. The form of criterion in particular case that was applied in the present study is follow � � � � � ��� � �� � � � � �� , (1) where is time and ��� describes temporal profile of load stress. The small size of the specimens and relatively great value of the dropping mass allow the assumption about linear dependency of stress � � � � � � , (2) where � � is Heaviside function, is elastic modulus and � is a strain-rate of load. Substitution load function (2) into criterion (1) gives follow analytical function describing strain-rate sensitivity of ultimate fracture stress (M. V. Volkova et al., 2018) ∗ � � � � � � � � � � � � � � � � �� � �� �2 � � � � �� � �� . (3) 3.2. Sign-Perturbed Sums procedure If material response to the load obeys to the incubation time criterion then all data points for certain material can be considered as a results of follow observation model ∗� � � � � � � � � � � 2 � , where � is a random noise of i-th observation and is a number of observation. The SPS-procedure allows to evaluate true value of the incubation time ∗ under only one weak assumption about symmetrical distribution of the random noise. It should be noted that the function � � � obeys to the necessary conditions of SPS-method (M. Volkova et al., 2018). At first it is necessary to set values of algorithm parameters and in order to define the confidence of the result interval as follow � ∗ ∈ � � � � � � . Then at second a table of Bernoulli random signs � �� is generated with a probability equaled to ½ . The third step is to calculate a set of sign-perturbed sums for some value of parameter � � � � � � ∑ �� � ∗� � � � � � �� ���� � �� � �� � � ��� � � � 2 � � � � 2 � � �. Then SPS-Indicator procedure is applied to check whether the current value of � is contained into goal interval or not. The formal steps of SPS-Indicator are follow