A fast and accurate model of explosion fragments to help determine vehicle survivability

  • David Felix

    Student thesis: Doctoral Thesis

    Abstract

    Heat, pressure waves and fragments are the main products of an explosion which is a complex physical event that, in microseconds, converts explosive material into gases and heat and delivers hundreds of fragments with speeds that generally exceed a kilometre per second. Of the three products, fragments travel the furthest and cause the most destruction. For example, fragments from Improvised Explosive Devices (IEDs), bombs or fragmenting devices, can destroy or damage armoured military vehicles as well as injuring or killing troops. This thesis will consider only explosion fragments.

    To protect military vehicles, engineers and designers need to consider how explosions affects their designs. A new vehicle design experiencing an explosion would be destructive, time consuming and costly and so one of the most effective ways, of evaluating a new design, is to employ an accurate computer simulation. Computer methods such as Finite Element Analysis (FEA) provide an accurate simulation, but they are computer intensive and preventatively slow.

    The aim of this thesis is to create a fast and accurate simulation of explosion fragments, as an alternative to FEA.

    The first contribution involves building a model to create fragments on a warhead’s cylindrical casing. The casing is unfurled into a rectangle using templates to define the shape of fragments and two Poisson distributions are used to calculate the fragments’ lengths and widths and determine the number of fragments. To assess the accuracy of the final model the number and weight of created fragments is checked against Mott’s accurate distribution linking the number and weight of fragments. A high correlation coefficient of 0.99 is achieved, showing this new model is accurate. The fast execution time of this model is approximately 0.1 seconds.

    The second contribution involves enhancing the equation that calculates the initial velocity of fragments. Experimental data is used to shape a graph of initial velocity of fragments against the warhead’s length. This information is then used to modify an existing two-dimensional equation that calculates the initial velocity of fragments, through applying the conservation of energy and momentum. The resultant equations are verified against experimental data to reveal the new equations are accurate with correlation coefficients greater than 0.89. The fast execution times of the equations are approximately 35 microseconds.

    The third contribution involves enhancing the equation that calculates the initial angle of projection of fragments. Experimental data is used to shape a graph of initial angle of projection of fragments against the warhead’s length. This information is then used to create a new equation, incorporating the second contribution and published research that indicates how initial angles of projection are affected by the shape of the expanding casing. The new equation is verified against several experimental data sets and achieves correlation coefficients greater than 0.88 which shows the new equation is accurate. An alternative equation, used in some FEA simulations, has a significantly lower correlation coefficient against the same experimental data. The fast execution time of the new equation is approximately 18 microseconds.

    The final contribution involves the creation of an explosion fragment simulation. The simulation uses the equations and models from the first, second and third contributions and includes equations to calculate the flight of fragments and armour penetration. The volume of the target vehicle is divided into cubes and the probability that a cube is hit by fragments is calculated. The resultant simulation is verified by providing test results of the initial impact of fragments, known as witness plates in explosion experiments, and checking them against results produced by FEA simulations and physical experiments. The contribution simulation has similar test results as the FEA simulations except there are fewer hits. This is probably because small fragments are omitted in the contribution simulation. The number of hits in the experimental results is similar to the number of hits in the contribution simulation. The execution time of the simulation is approximately 0.2 seconds, but this can be reduced if the computer code is optimised. An FEA simulation can take many minutes or hours to complete an analysis.
    Date of AwardDec 2020
    Original languageEnglish
    Awarding Institution
    • University of Brighton
    SupervisorPaul Harris (Supervisor) & Ian Colwill (Supervisor)

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