br The experimental set up and

The experimental set up and geometrical data Fig. 1 shows the set up. A brass tube with constant outside diameter and variable inside diameter is used to control the radial expansion velocity of the steel rings. The steel rings were manufactured from projectile bodies of in-service rounds. The test item is placed such that the expansion of the ring is perpendicular to the axis of a rotating mirror camera that is used to find the expansion velocity. The fragmentation studies were a methysergide of the streak camera studies. However, in this case the fragments were collected in a water tank. To be able to repeat the actual velocity-time conditions, the tubes and rings were allowed to expand first in a thin plastic bag filled with air that was submerged underwater. Thus the expansions and break up occurred in air. The water barrel was then emptied and sieved, and the fragments collected with a magnet. More than 95% of the total mass was collected. The explosive is ignited at time zero at one end of the cylinder. The density of the explosive is 1.87 g/cm3. The total length of the cylinder with explosive is 10.2 cm. The length of the steel ring is 1 cm and the thickness is 0.33 cm. Two different shots (loadings) were studied numerically and experimentally by varying the thickness of the brass cylinder to achieve different expansions velocities of the steel rings. The steady state numerical velocities were found to be 190 m/s and 630 m/s and in good agreement with the measurements (Moxnes et al., 2015 [32]). The parameters of the two different loadings are seen in Table 1. Uniaxial tensile test specimens and two notched tensile specimens were extracted from a heat-treated steel material to establish a J-C strength and fracture model. The steel alloy composition is provided in Table 2. The steel is first casted, then rolled and heat-treated by quenching. Finally it is tempered. The hardness is 530 Vickers which corresponds to 5.2 GPa, or to 5.6 GPa when defined as force per projected contact area of the indenter. The tests were carried out at room temperature in a hydraulic test machine with a strain rate of approximately 5 × 10−4 s−1 (quasi-static condition). The numerical simulations of the mechanical tests were performed, assuming isotropic material properties. The results were compared with the experimental results. The J-C (1983 [24], 1985 [25]) strength model is In the original model, Y(εp) = A + B (Johnson and Cook 1983 [24]), where εp is the plastic strain. In the current work, Y(εp) was set as a piecewise linear function of εp, as shown in Fig. 2. is the plastic strain rate and is the nominal plastic strain rate of 1/s”. mt parameterizes the strength dependency of the temperature. Troom is the reference temperature set to 300 K and Tmelt is the melting temperature set to 1800 K. For the quasi-static tensile tests we set T = Troom. Other properties given for Translocation of a chromosome steel is E = 210 GPa as the elastic modulus, ν = 0.33 as the Poisson ratio and ρ = 7850 kg/m3 as the density. Strain rate parameter c and mt in equation (1) are set to zero for the quasi-static tests and as the baseline values in this article. The J-C (1985 [25]) fracture model is, when not accounting for temperature dependency or strain rate dependency in the fracture strain, given aswhere σ∗ is the triaxiality (negative value of pressure/Mises stress ratio). εf is the fracture strain and D is the damage variable. When D ≥ 1 the strength of the material is set to zero. The experimental results for our steel give D1 = 0.069, D2 = 10.8, and D3 = 4.8 (Moxnes et al., 2014 [31], 2015 [32]). We assume that fracture of the ring is dependent of the subscale microstructure. The fracture strain of the ensemble of elements/particles making up the ring is assumed to be Weibull distributed. Meyer and Brannon (2012) apply randomness to D1 + D2 according to a Weibull distribution. Here we set D1 and D3 as fixed, while D2 is set stochastic to account for subscale microstructure. We set , where D20 = 10.8 is the average value of D2 equal to the experimentally found value. The distribution is a Weibull distribution, to read