Solution
Kshitij answered on
Apr 06 2021
Methods
Various methods and approaches are being taken into account by the researchers to estimate and determine the best suitable method from the available alternatives, for the best suitable results and efficient outcomes. as in the past years, it has been noticed that the demand for accurate and reliable estimation and determination of the various low and high values of the performance of the various objects. The major objective of the same was to have a theoretical implication of the present practical methods. Here are the several methods undertaken to test the ballistic limitation of the machinery, they are as follows:
Lagrangian method
To understand the loss caused and the destruction occu
ed by the deformation of the aluminum sheets in the testing procedure is significant for ensuring the safety of the operations in the process of determination of the ballistic limit and checking the thickness and quality of the aluminum sheet against the factors creating pressure on the sheet, threes separate methodologies were used for simulation purpose. In the various industries, it has been noticed that the practice of implementing the Johnson cook model is common and is incorporated into the most optimized fine material available with them. At the first and foremost stage of analysis, a 3D model was created in the system to check the ballistic limit of the sheet while applying the same level of pressure and force on the sheet as it will be facing practically. The presented model based on geometry shows that there consist an aluminum sheet as a target and the force of stanag is applied on the same with 37.62 * 54R AP ammunition. Before the core, a cap made up of lead-antimony was placed in front of the same. The major objective behind placing the cap was to stabilize the projectile at the time of flight and the very initial and starting stage of the penetration procedure.
The total mass applied on the sheet is approximately 10.04g. The velocity of the ammunition was noticed to be 854 m/s as stated in the stanag 4569. The simulation will make the use of the Lagrange method for the purpose of ammunition and to target the shield. At the time of generating the solution, two different types of appropriations were applied. In the first approach though the force applied was comparatively more but a small radius was generated in the shield to soften the same and to improve the ability of the sheet to bear the attacks and text the ballistic ability of the same. In the second model approach, the model was prepared in such a manner using the geometric approach for its presentation and preparation. Although, the prepared model of sine mesh was not that successful as per the expectations of the researchers, in the type first the domain of solution has not attained good co
elation when compared to the results of the test. In the second type, because of the tetragonal mesh, and termination in the e
or, all this resulted in the distortion of the element. In order to eliminate the problems, the model was dismantled and redesigned with new features. The already generated model was optimized and modified in such a manner to maintain the stability of the results and to get the accurate and appropriate results for better performance. As in the conventional models, the numerical factor in the simulation was ignored by the researchers and only the accuracy and reliability of the same was taken as the significant areas for the study. The aluminum shield was divided into three major areas i.e. inner area middle area and outer area. The area is coarsening starting from the inner to the outer region. The transition among the different regions are good prominent enough to prevent the level of stress and will waive the reflections at the boundary area. The shield has meshed with constant hexagonal stress with various solid elements of numerous sizes ranging from 0.2 mm and 1 mm under total observe elements is approximately 734 in number. The projectile also reflects a very fine mess. The aluminum sheet includes 947 elements and 207 elements for the force applied to the same. Apart from the front and rear antimony caps, the properties of the JC model were being assigned to all the material present in the model. The antimony caps included in the model of various materials like ISOTROPIC etc. The algorithms that were implemented to simulate the connection among the surface at the time penetration. The option of erosion, static friction and dynamic and bucket frequency are investigated for an appropriate and accurate result. The parameters for control were also put to use to control hourglass, and for the purpose of terminating the solution. One of the most prominent and important tools for controlling the impact of the problem is the time step scale factor (TSSF). TSSF is the best available tool used for the purpose of providing optimum steps in time for the accuracy and confirmation of the numerical and geometrical stability (Fa
e, Bonnet, et.al.,2017).
SPH method
In the year of 1983, Johnson and cook the most famous personalities of that period invented a model commonly known as Johnson cook model which created a mathematical equation which includes numerous phenomena like hardening the material, rate of hardening the same, and the process of thermal softening. However the same has t be clarified that their integrated effect is not taken into consideration. With the recent and constant level of developments, the SPH method has proved to be a reliable and efficient tool for the reason of providing accuracy and stability in the outcomes for the great problems like deformation and will result in successful implementation in the various hydro codes. One of the most common FE code which involves SPH is Ls-Dyna. In the recent studies because of the high cost in computation in SPH an alternative substitute for the numerical solutions the technique of combining FEM/SPH is being put to use. Since in the SPH method the use of the lagrangian formula is being implemented, integration of the SPH and lagrangian is possible with the help of defined interfaces in connecting the same. A similar kind of approach has been followed by various researchers in their study. The study of compatibility among the two different approaches i.e. SPF and Lagrangian solver in the process of Ls-Dyna is to ensure by permitting the use of the classical keywords and making the use of fixed approach comparatively convenient and easy. For resolving the issue, the section of large deformation of the objective id modeled along the SPH and where the deformation takes place in small sections of the society with the hexagonal lagrangian in the solid elements. Such combining and coupling should be optimistically a
anged for the purpose of the simulate transition of the various propagation of the wave at the interface of SPH –Lagrange. It has been observed that the stress of wave propagation after the impact of force and pressure applied on the sheet it was plotted at different time steps. As shown there was no reflection of the transition at the mesh boundaries. For the purpose of the simulation, the Lagrange method was used for the hardened aluminum projectile, SPH, and discretization of an aluminum target.
The various layers of the aluminum sheet were divided into numerous regions. In the SPH section, an equispaced discretization was put to use. After the application of various substances and material also the result was not being able to improve the accuracy and effectiveness of the system and hence were removed and omitted. The geometrical details of the model as generated from the above sources were used for detailed analyses of the system. The core target of the model was SPH having the size of the particle as 0.2 mm and are su
ounded by a Lagrange region with an element size of 0.5 mm and 1 mm. the connection between SPH and the Lagrange element was developed with the help of tide notes to surface the connection was being able to build even at the time of penetration through the applied force. In SPH simulation the bulk of viscosity was ignored. In the model FE, the state rule required at least four notes of SPH. Reduction in the number of SPH notes or particles will result in earlier or premature penetration of the particles of the sheet into FE mesh without having any properties of the material. Even in the integrated approach, the cost of computation of the SPH is superior as comparative lagrangian analysis (Liu, Zhang, et.al., 2017).
Kneubuehl method
The Johnson cook model is a pre model of empirical study and is the most common and widely used model among all. This deals with the theory of continuum mechanics that defines the dependent rates and inelastic and low flexible behavior of the solids especially the layers of aluminum sheets. This method works on the theory of probabilities and statistics. It has been considered from his point that the response of armor P (Vi) is the cumulative distribution function (CDF) of the impact of the pressure in the velocity which is just a random variable, which causes the perforation of the target. Though the general velocity Vi is just a continuous randomly opted variable. This particular method helps in the implementation of the previously discussed methods and strategies and with the help of such strategies and planning a successful experiment is being ca
ied for testing the ballistic limit of the various layers of the aluminum shield used for making automobiles. The same level of pressure is applied on such shields to check the point at which the sheet will
eak down or get damaged so that the cures and solution for the same could be found and implemented. Therefore, for the purpose of estimation of the central tendency and perforation dispersion, methods opted to solve the issue were statistical mean (Vm) along with standard deviation (σ), the applicable formulae for the same are
Vm =
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