Fragment Total Kinetic Energy Research Articles

Effects of structural configuration on perforation/spalling damage and secondary fragment velocity of reinforced concrete slabs subjected to close-in explosion

Reinforced concrete (RC) slabs are vulnerable to localized damage from close-in TNT explosions, suffering perforation and extensive spalling damages that generate high-velocity secondary fragments posing severe risks to nearby facilities and personnel. Current numerical methods such as the Finite Element Method (FEM) face challenges in accurately predicting fragmentation due to mesh distortion caused by large deformations and discontinuities, underscoring the need for enhanced modelling techniques. As a result, although numerous studies have numerically investigated how structural configurations influence RC slab damage under blast loads, the issue of mesh distortion and element erosion in FEM has led to the inability in reliably predicting the associated threats from high-velocity fragments. This study numerically investigates the influences of structural configuration (e.g., concrete strength, reinforcement ratio and layout, dimensions of slabs, and concrete cover depth) on the perforation/spalling area and fragment ejecting velocity of one-way RC slabs subjected to close-in explosions through an ALE-FEM-SPH numerical model, which has been demonstrated effective and reliable in the authors’ previous studies. The results indicate that concrete strength and slab thickness most significantly affect both the damage and fragment characteristics, while the slab's width-to-height ratio, reinforcement ratio, and layout, have less influence, particularly on fragment velocity. Empirical equations derived from extensive numerical data are provided to help engineers and security personnel quickly evaluate the blast effects on RC slabs. The accuracy and robustness of the proposed formulae, which can be straightforwardly used to predict blast fragments of reinforced concrete slabs, have been statistically evaluated and the proposed formulae demonstrate satisfactory precision, with less than 20 % error in estimating damage area, maximum fragment velocity, and total kinetic energy of fragments.

Calculation of the energy dependence of fission fragments yields and kinetic energy distributions for neutron-induced 235U fission* *Supported by the National Natural Science Foundation of China (12075105), the NSFC-Nuclear Technology Innovation Joint Fund (U2167203), the Major Science and Technology Projects of Gansu Province (22ZD6GB020), the Fundamental Research Funds for the Central Universities of China (lzujbky-2022-ey14, lzujbky-2022- kb07)

Fission fragments yields and average total kinetic energy are fundamental nuclear data for nuclear energy applications and the study of nuclear devices. Certain fission products, such as 95Zr, 99Mo, 140Ba, 144Ce, and 147Nd, serve as burnup monitors, assessing the number of fissions induced by neutrons on 235U. However, current experimental data for these fission products worldwide are inconsistent, introducing significant uncertainty into related scientific research. In this study, we employed the Potential-driving Model to calculate the independent yields of 235U and evaluate its advantages in such calculations. Additionally, we investigated the energy dependence of independent yields to select important products. Furthermore, we calculated the cumulative yields of 95Zr, 99Mo, 140Ba, 144Ce, and 147Nd, and compared them with existing literature data to explore the energy dependence of fission products for 235U. Given the lack of fission product yield data above 14.8 MeV, we extended our calculated incident neutron energy to 20 MeV, aiming to support future scientific research. The Geant4 physical model does not consider the influence of incident neutron energy on the average total kinetic energy of fission fragments; thus, we introduced the excitation function of the total kinetic energy of fission fragments recommended by Madland et al., which effectively describes the experimental data of the average total kinetic energy of fragments formed in 235U fission. In this paper, we comprehensively discuss the energy dependence of fission product yields and average total kinetic energy.

Study of various ground state decay mechanisms of Actinide nuclei* *Financial support from the Department of Science and Technology (DST), New Delhi, India in the form of a research project grant (CRG/2021/001144) is gratefully acknowledged.

The special property of the actinide mass region is that nuclei belonging to this group are radioactive and undergo different ground state processes, such as alpha decay, cluster radioactivity (CR), heavy particle radioactivity (HPR), and spontaneous fission (SF). In this study, the probable radioactive decay modes of the heavy mass region (Z = 89−102) are studied within the framework of the preformed cluster model (PCM). In the PCM, the radioactive decay modes are explored in terms of the preformation probability () and penetration probability (P) at the turning point , where the penetration of fragments is initiated [R = R (touching state) + (neck length parameter)]. First, the alpha decay half-lives are calculated for light and heavy nuclei, and points are obtained by optimizing the neck length parameter. These points are further employed to fix the Q-value dependent turning point ((Q)). Then, using the ((Q)) relation, the decay half-lives are computed, and the calculated results are compared with the available theoretical and experimental data. The isotopical trend of and P is studied with respect to the mass number of the parent and daughter nucleus, respectively. The CR and HPR channels are also explored, and a comparison of calculated data is conducted with the available literature. Comparative analysis of the fragmentation potential and preformation probability is carried out for alpha decay and SF. The mass distribution of the nuclei is studied as a function of fragment mass (A ) by considering the spherical and hot-compact deformation of the decaying fragments. Finally, the most probable fission fragments are identified using the fragmentation structure, and the corresponding fission fragment total kinetic energy of the identified fragments is calculated and compared with available data, wherever applicable.

Fragmentation analysis of Z=112 –116 nuclei using a Skyrme energy density formalism within the collective clusterization approach

The Skyrme energy density formalism is applied to address the capture cross sections of $_{112}^{286}\mathrm{Cn}^{*}$, $_{114}^{292}\mathrm{Fl}^{*}$, and $_{116}^{296}\mathrm{Lv}^{*}$ superheavy nuclei formed in $^{48}\mathrm{Ca}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U},^{244}\mathrm{Pu},^{248}\mathrm{Cm}$ reactions. The dynamics of $^{48}\mathrm{Ca}$-induced reactions is investigated by including GSkI and SSk forces for the hot-optimum configurations of decay fragments. The neutron evaporation $(3n \mathrm{and} 4n)$, compound nucleus fission (CN fission) and quasifission (QF) cross sections are calculated with the application of both forces, but the GSkI force seems to be appropriate only for the neutron evaporation channels. However, by including SSk force various decay processes can be handled by including the only parameter of the model, called the neck length parameter $(\mathrm{\ensuremath{\Delta}}R)$. The fragment mass distribution of $Z=112$--116 nuclei shows considerable modifications in the fission, symmetric quasifission $({\mathrm{QF}}_{\mathrm{sym}.})$ and asymmetric quasifission $({\mathrm{QF}}_{\mathrm{asym}.})$ regions with the inclusion of the SSk force as compared to analysis based on the density independent potentials. In addition to this, the role of ${\ensuremath{\beta}}_{2}$ deformations and magic shell effects (around the Pb isotope) is scrutinized through the fragmentation behavior and preformation probability of $_{112}^{286}\mathrm{Cn}^{*}$, $_{114}^{292}\mathrm{Fl}^{*}$, and $_{116}^{296}\mathrm{Lv}^{*}$ nuclei. Finally, the distribution of the average total kinetic energy of fragments is calculated with the density dependent SSk force and compared with experimental data and earlier work based on the proximity potential.

Super-short fission mode in fermium isotopes

The so-called super-short fission mode, in which a nucleus divides nearly symmetrically into two unusually energetic fragments, competes favorably with the standard asymmetric fission mode for spontaneous fission of a limited number of nuclei near $^{264}\mathrm{Fm}$ but it quickly fades away at finite excitations. We investigate the energy-dependent competition between those two fission modes for even fermium isotopes from $^{254}\mathrm{Fm}$ to $^{268}\mathrm{Fm}$, using the Metropolis method to simulate the strongly damped fission dynamics being driven by shape- and energy-dependent level densities. The origin of the super-short mode is discussed and its effects on the fragment mass distribution, the total fragment kinetic energy, and the neutron multiplicity are calculated. Generally good agreement with the available data is obtained.

Dependence of average total kinetic energy of fission fragments on excitation energy of fissioning nucleus

The expression of dependence of the average total kinetic energy of fission fragments on the excitation energy of the fissioning system is obtained in a simple model, which takes into account the statistical and quantum properties. The experimental data of the average total kinetic energy of fragments formed in the fission of nuclei 234,236,239U and 240Pu are well described using the obtained expression in the wide range of the excitation energy of these nuclei. The origin of the energy dependence of the average total kinetic energy is discussed in details.

Examination of different features of fission fragments of the excited compound nucleus Np236 produced in the p+U235 reaction at 10.3≤Ep≤30.0MeV within a stochastic approach

A stochastic approach based on four-dimensional Langevin equations has been used to estimate the mass distributions of fission fragments, the average masses of heavy fragments, the average total kinetic energies of fragments, and the average number of neutrons emitted per fission of $^{236}\mathrm{Np}$ produced in the $p+^{235}\mathrm{U}$ reaction at $10.3\ensuremath{\le}{E}_{p}\ensuremath{\le}30.0\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. Three collective shape coordinates plus the projection of total spin of the compound nucleus to the symmetry axis $K$ were considered in the four-dimensional dynamical model. The effects of shell corrections and dissipation coefficient of $K {\ensuremath{\gamma}}_{K}$ were considered in the dynamical calculations. Comparison of the theoretical results for the mass distributions of fission fragments, the average masses of heavy fragments, and the average number of neutrons emitted per fission with the experimental data showed that the results of calculations were in good agreement with the experimental data, although the results of calculations for the average total kinetic energies of fission fragments were slightly higher than the experimental data. It was also shown that the number of fission events increased with time, and almost all of the fission events occurred dynamically until $t=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ and that the number of fission events became saturated. Furthermore, it was also shown that the average masses of heavy fragments and the average total kinetic energies of fission fragments of $^{236}\mathrm{Np}$ decreased with increasing projectile energy.

Correlation studies of fission-fragment neutron multiplicities

We calculate neutron multiplicities from fission fragments with specified mass numbers for events having a specified total fragment kinetic energy. The shape evolution from the initial compound nucleus to the scission configurations is obtained with the Metropolis walk method on the five-dimensional potential-energy landscape, calculated with the macroscopic-microscopic method for the three-quadratic-surface shape family. Shape-dependent microscopic level densities are used to guide the random walk, to partition the intrinsic excitation energy between the two proto-fragments at scission, and to determine the spectrum of the neutrons evaporated from the fragments. The contributions to the total excitation energy of the resulting fragments from statistical excitation and shape distortion at scission is studied. Good agreement is obtained with available experimental data on neutron multiplicities in correlation with fission fragments from $^{235}$U(n$_{\rm th}$,f). At higher neutron energies a superlong fission mode appears which affects the dependence of the observables on the total fragment kinetic energy.

Angular momentum effects in fission

Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify. Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations. Methods: We employ the fission simulation model $\mathtt{FREYA}$ which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in $\mathtt{FREYA}$ and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of $^{235}$U relative to the ground state. Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, $^{235 {\rm m}}$U($n_{\rm th}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energy.

Kinetic Energy Distribution for Neutron-Induced Fission of Thorium Isotopes

The fission fragment total kinetic energy TKE(A) was calculated for neutron-induced fission of 229,232Th using the scission point model. The calculated results were compared with the available experimental data to obtain the parameters of the scission point model. With these parameters, the total kinetic energy distribution was evaluated for neutron-induced fission of Thorium isotopes. The deformation parameters of the Thorium isotopes were discussed at the scission point.

Parameter Optimization and Sensitivity Studies of Spontaneous Fission with FREYA

For many years, the state of the art for simulating fission in transport codes amounted to sampling from average distributions. However, such "average" fission models have limited capabilities. Energy is not explicitly conserved and no correlations are available because all particles are emitted independently. However, in a true fission event, the emitted particles are correlated. Recently, Monte Carlo codes generating complete fission events have been developed, thus allowing the use of event-by-event analysis techniques. Such techniques are particularly useful because the complete kinematic information is available for the fission products and the emitted neutrons and photons. It is therefore possible to extract any desired observables, including correlations. The fast event-by-event fission code FREYA (Fission Reaction Event Yield Algorithm) generates large samples of complete fission events, employing only a few physics-based parameters. A recent optimization of these parameters for the isotopes in FREYA that undergo spontaneous fission is described and results are presented. The sensitivity of neutron observables in FREYA to the input yield functions is also discussed and the correlation between the average neutron multiplicity and fragment total kinetic energy is quantified.

Sensitivity of neutron observables to the model input in simulations of 252Cf(sf)

Within the framework of $\mathtt{FREYA}$ event-by-event fission simulations, we study the sensitivity of various neutron observables to the input yield function $Y(A,Z,\mathrm{TKE})$ on which the fission event sampling is based. We first perform a statistical analysis of the available fission data in order to determine the distribution of possible yield functions $Y(A,Z,\mathrm{TKE})$ and we then construct a sample of 15 000 such yield functions. For each of these, $\mathtt{FREYA}$ is used to generate one million fission events, leading to a corresponding ensemble of fission observables, including the neutron multiplicity distribution and its factorial moments, the neutron energy spectrum, and the neutron-neutron angular correlation. This procedure allows us to study the sensitivity of those neutron observables to the uncertainty in the experimental data. Particular attention is given to the pronounced anticorrelation between the mean neutron multiplicity $\overline{\ensuremath{\nu}}$ and the mean total fragment kinetic energy $\overline{\mathrm{TKE}}$. Because the former observable is very well determined experimentally, it is possible to exploit that inherent anticorrelation to derive a significantly stricter tolerance on $\overline{\mathrm{TKE}}$. In addition, we study the sensitivity to the various $\mathtt{FREYA}$ parameters and we introduce a method for determining a $A$-dependent $x$ parameter, $x(A)$, based on the measured $A$-dependent neutron multiplicity, $\overline{\ensuremath{\nu}}(A)$.

Spontaneous fission of rutherfordium isotopes - total kinetic energies

The isotopes 255,256,258Rf were produced in the fusion-evaporation reactions 50Ti + 207,208Pb and 50Ti + 209Bi at GSI Darmstadt, using the velocity filter SHIP. Total kinetic energies of fragments from spontaneous fission for these isotopes were evaluated with a correction to pulse-height defect.

Sensitivity of the 252Cf(sf) neutron observables to the FREYA input yield functions Y(A, Z, TKE)

Within the framework of the fission event generator FREYA, we are studying the sensitivity of various neutron observables to the yield distribution Y (A ,Z ,TKE) used as input to the code. Concentrating on spontaneous fission of 252 Cf, we have sampled a large number of different input yield functions based on χ2 fits to the experimental data on Y (A ) and Y (TKE|A ). For each of these input yield distributions, we then use FREYA to generate a large sample of complete fission events from which we extract a variety of neutron observables, including the multiplicity distribution, the associated correlation coefficients, and its factorial moments, the dependence of the mean neutron multiplicity on the total fragment kinetic energy TKE and on the fragment mass number A , the neutron energy spectrum, and the two-neutron angular correlation function. In this way, we can determine the variation of these observables resulting from the uncertainties in the experimental mesurements. The imposition of a constraint on the resulting mean neutron multiplicity reduces the variation of the calculated neutron observables and provides a means for shrinking the uncertainties associated with the measured data.

Prompt particle emission in correlation with fission fragments

The de-excitation process of primary fission fragments can be simulated with the FIFRELIN Monte Carlo code leading to an estimation of prompt fission observables such as neutron/gamma multiplicities and spectra in correlation with fission fragments. De-excitation cascades are simulated using the notion of nuclear realization following Becvar terminology generalized to neutron/gamma coupled emission. A nuclear realization is a random set of nuclear levels (energy, spin, parity) in association with partial widths for neutron, gamma or electron emission. Experimental data related to electromagnetic transitions in the discrete level region are taken from RIPL-3 database. When nuclear level structure is completely unknown (in the continuum region), level density and strength function models are used. In between these regions, our partial knowledge of nuclear structure is completed by models up to a fixed maximum level density. In this way the whole available experimental information is accounted for. FIFRELIN is ruled by five free input parameters driving the excitation energy sharing, the rotational energy and the spin distribution of primary fission fragments. These five free parameters are determined to match a target observable such as the average total prompt neutron multiplicity (ν). Once this procedure is completed, the whole set of fission observables can be compared with experimental results. Obviously the number of observables obtained within this code is higher than what is available from measurements. This code can therefore provide useful insights into the compatibility between models and a whole set of fission observables. In the present work the influence of shell corrections is reported on level densities and prompt fission neutron spectra (PFNS). The impact of the input data such as primary fission fragment total kinetic energy (TKE) is also addressed. Average prompt neutron multiplicity as a function of TKE is also estimated for each mass split and compared to recent measurements. The presence of structures in the calculations (especially for light nuclei) is clearly related to the nuclear level scheme. Various situations occur and an overestimation (or underestimation) of the calculated number of emitted neutrons can be correlated to the light or heavy fragment of a pair and to a restricted energy range. In addition prompt fission gamma spectra (PFGS) are estimated for selected fragment mass ranges and compared to recent measurements. In this way the presence of specific gamma-ray transitions can be established.

Numerical simulation of steel plates subjected to the impact of both impact waves and fragments

The main objective of this study is to explore the deformation feature and damage pattern of a steel plate under the synergetic effects of blast and fragments loading. The combined blast and fragments loading effects under the condition of cast TNT and prefabricated fragments acting on a steel plate, are sim-ulated using the finite element program ANSYS/LS -DYNA. The flight of fragments driven by the charge is predicted, and the blast loading and fragments loading are analyzed respectively, while the deformation and damage characteristic under the combined loading are compared with experiment results. The simulation re-sults agree relatively well with the experimental results. Meanwhile, it is seen that the fragment at the cen-ter of the charge bottom has the highest velocity and the lowest velocity occurs at the edge. Under the exper-imental condition, blast reaches the structure first and fragments impact subsequently, and the total kinetic energy of fragments is much larger than that of blast wave and explosion products transmitted to the struc-ture. The punched hole appearing in the central region of the steel plate is mainly caused by the dense frag-ment cluster, which should be treated as the main target load for protective structures.

An analytical approach for quantification of glazing hazard in buildings subject to external explosive blasts

This paper describes a conservative analytical approach for quantification of glazing hazard in terms of number of casualties among building occupiers from flying glass fragments produced by shattered windows due to external explosive blast. Three main stages are discussed in the proposed analytical approach: modelling nonlinear transient–dynamic response of monolithic windows subjected to conventional explosions, conservative estimation of glass fragment trajectories influenced by additional aerodynamic forces due to vented blast pressures and estimation of casualties. Four injury severity levels are considered, ranging from minor cuts and bruises to multiple serious injuries with significant blood loss. The total kinetic energy of fragments at impact on occupiers is estimated and used to predict the severity level of injuries, with calculation based on available injury data from archive events. Comparison studies presented in this paper highlight the lack of robustness of existing methods towards quantification of glazing hazard due to explosive blasts. The proposed analytical method will be of direct importance to both engineers and practitioners involved with planning glazing retrofits for existing buildings and identifying cost-effective combinations of protection measures for new buildings.

Energy Dependence of Plutonium and Uranium Average Fragment Total Kinetic Energies

A simple method has been developed to extrapolate measured first-chance fission-product average fragment total kinetic energies to higher energies where second-, third-, and fourth-chance fission are of importance. A prediction is made for the average total kinetic energy of 239Pu(n,f) and 235U(n,f) fission fragments up to a neutron energy of 20 MeV. These predictions will be tested over the next few years by the SPIDER collaboration at Los Alamos National Laboratory.

Point-by-Point model description of average prompt neutron data as a function of total kinetic energy of fission fragments

The experimental data of average prompt neutron multiplicity as a function of total kinetic energy of fragments (TKE) exhibit, especially in the case of 252 Cf(SF), different slopes dTKE/dν and different behaviours at low TKE values. The Point-by-Point (PbP) model can describe these different behaviours. The higher slope dTKE/dν and the flattening of at low TKE exhibited by a part of experimental data sets is very well reproduced when the PbP multi-parametric matrix ν(A,TKE) is averaged over a double distribution Y(A,TKE). The lower slope and the almost linear behaviour over the entire TKE range exhibited by other data sets is well described when the same matrix ν(A,TKE) is averaged over a single distribution Y(A). In the case of average prompt neutron energy in SCM as a function of TKE, different dTKE/de slopes are also obtained by averaging the same PbP matrix e(A,TKE) over Y(A,TKE) and over Y(A). The results are exemplified for three fissioning systems benefiting of experimental data as a function of TKE: 252 Cf(SF), 235 U(nth,f) and 239 Pu(nth,f). In the case of 234 U(n,f) for the first time it was possible to calculate (TKE) and (TKE) at many incident energies by averaging the PbP multi-parametric matrices over the experimental Y(A,TKE) distributions recently measured at IRMM for 14 incident energies in the range 0.3- 5 MeV. The results revealed that the slope dTKE/dν does not vary with the incident energy and the flattening of at low TKE values is more pronounced at low incident energies. The average model parameters dependences on TKE resulted from the PbP treatment allow the use of the most probable fragmentation approach, having the great advantage to provide results at many TKE values in a very short computing time compared to PbP and Monte Carlo treatments.

Neutron induced fission of234U

The fission fragment properties of 234 U(n,f) were investigated as a function of incident neutron energy from 0.2 MeV up to 5 MeV. The fission fragment mass, angular distribution and kinetic energy were measured with a double Frisch-grid ionization chamber using both analogue and digital data acquisition techniques. The reaction 234 U(n,f) is relevant, since it involves the same compound nucleus as formed after neutron evaporation from highly excited 236 U*, the so-called second-chance fission of 235 U. Experimental data on fission fragment properties like fission fragment mass and total kinetic energy (TKE) as a function of incident neutron energy are rather scarce for this reaction. For the theoretical modelling of the reaction cross sections for Uranium isotopes this information is a crucial input parameter. In addition, 234 U is also an important isotope in the Thorium-based fuel cycle. The strong anisotropy of the angular distribution around the vibrational resonance at En = 0.77 MeV could be confirmed using the full angular range. Fluctuations in the fragment TKE have been observed in the threshold region around the strong vibrational resonance at En = 0.77 MeV. The present results are in contradiction with corresponding literature values. Changes in the mass yield around the vibrational resonance and at En = 5 MeV relative to En = 2 MeV show a different signature. The drop in mean TKE around 2.5 to 3 MeV points to pair breaking as also observed in 235,238 U(n,f). The measured two-dimensional mass yield and TKE distribution have been described in terms of fission modes. The yield of the standard 1 (S1) mode shows fluctuations in the threshold of the fission cross section due to the influence of the resonance and levels off at about 20% yield for higher incident neutron energies. The S2 mode shows the respective opposite behaviour. The mean TKE of both modes decreases with En . The decrease in mean TKE overrules the increase in S1 yield, so the mean TKE is dropping as a function of En above 2.5 MeV.