Issue 49

Yu. Bayandin et alii, Frattura ed Integrità Strutturale, 49 (2019) 243-256; DOI: 10.3221/IGF-ESIS.49.24 249 The estimation of the model parameters was carried out by the stress-strain diagrams over a strain rate range of quasi- static and dynamic tests. A modified search method was used for solving the optimization problem. The initial vector of parameter values and the initial step were chosen to calculate the optimizing function at each iteration step. An indicator that has a value   -1, 0,1 allows the determination of the step value. If the point corresponds to the value of the indicator equal zero, then the step decreases, otherwise the current point becomes the minimum. The procedure stops when the step becomes less than the specified accuracy. This method was previously used to determine model parameters for various materials [31]. Fig. 3 shows a comparison for the stress-strain diagrams in the experiment [32] and numerical calculations obtained as a result of identification of model parameters for vanadium at different strain rates. Figure 3: Experimental stress-strain diagrams for vanadium at different strain rates (dotted line − 10 -1 s -1 , dashed line − 10 3 s -1 ) and corresponded numerical simulation (□ − 10 -1 s -1 , ○ − 10 3 s -1 ) It should be noted that the developed model makes it possible to describe stress-strain diagrams for wide-range strain rates (10 -1 −10 3 s -1 ) for the same values of model parameters. The procedure for verification of the model for vanadium was carried out from the shock-wave experiment in the conditions of a plate impact. Fig. 4 presents the results of numerical simulation and experiment [33]. Fig. 4 shows the particle velocity profiles for vanadium sample at different values of the stress amplitude that revealed the correspondence of numerical and experimental tests [33]. The profiles reflect the splitting of the shock wave front into an elastic precursor and the plastic front. The unloading of shock-compressed material behind the shock wave front leads also to the separation of the profile into an elastic wave and a wave of plastic unloading. In this zone, the numerical results do not agree well with the experimental profile, that can be linked with difficulty in recording the unloading wave front in the experiment. The mathematical statement allows the modeling of the behavior of metals under shock wave loading in the presence of damage accumulation to predict the critical state of shocked material (damage localization as spall failure precursor). The spall failure is linked with the final stage of damage kinetics corresponding to the initiation of blow-up localized damage structures [5]. This stage occurs when the value of the bulk component s p of the defect-induced strain reaches the critical value сs p and appropriate distribution over the spatial scale according to blow-up (self-similar) collective modes. The problem of spall failure for the plate impact test was studied numerically for vanadium. The simulation showed a significant dependence of the spall strength on the strain rate and typically (Fig. 5) the increase in spall strength for increasing strain rates [25]. 0 0.02 0.04 0.06 0.08 0.1 0 1 2 3 4 5 6 7 x 10 -3   /2G