where σ is the stress, σΤ is the th

where σ is the stress, σΤ is the threshold value below which no specimen is expected to fail, σ0 is the scalar parameter, and distributionshape parameter, m, is the Weibull modulus. If the threshold value σΤis zero and re-arranging the Eq. (7), the two-parameter Weibull distribution can be plotted as a straight line, as follows:The density of the melt, the metallographic microstructure andmechanical properties taken from cast samples were correlated inorder to verify the accuracy of the simulation results with the experimental results and to predict the most suitable cavity filling pressure–time curve to ensure high castings sanity.4. Results and discussion4.1. Numerical resultsNumerical simulations were conducted for conditions similar tothose of the experiments. The casting parameters, material propertiesand boundary conditions were computed based on equations presentedin the previous sections.Two pressure–time curves were evaluated according to the parameters presented in Table 1. In contrary of the traditional process (LPDC)where after filling the cavity there is a ramping of increase pressure toapplied and held to assist in feeding of the casting [18,19], in pressurecurves studied this ramps was not considered since the sand mould presents a top atmospheric feeder for interdendritic feeding. Moreover, asthe mould cavity is open due to presence of the atmospheric feeder,the final pressure after mould filling was adjusted only to compensatethe metallostatic head pressure of the column of fluid: p(t) = ρgh.Figs. 4 and 5 present the average melt velocity inside the mould cavity registered in sensor S#1 (Fig. 2) for 2 different pressure–time curvesat temperature of 700 and 650 °C, respectively.The mould cavity is filled by applying pressure to the surface of theliquid metal in the crucible placed inside a melting chamber, accordingto Fig. 3. It is notorious that the pressure curve (1) has just two rampswhile in pressure curve (2) an intermediate ramp was introduced. Theintermediate ramp in pressure curve (2) proved to be very importantto slow down the filling of the lateral specimens for velocities lowerthan 0.5 m/s for both melt temperatures.Although the velocity of the fluid cannot be used to simulate defects,it can be used to estimate the chance to occurrence of surface turbulence. It is recognized by the scientific community that turbulent fillingfavours the folding of the metal front leading to the formation ofadditional young oxides as well as their re-incorporation into the bulkof liquid. On this study the use of numerical simulation to establish