Precursor Decay Research Articles

Role of Crystal Orientation in the Dynamic Strength of Magnesium Alloy AZ31B

The effect of grain orientation distribution on the dynamic strength of highly textured magnesium alloy AZ31B has been studied in a series of plate-impact experiments. Specimens with thicknesses between 0.45 mm and 2 mm were cut parallel and perpendicular to the material extrusion direction and shock loaded to impact stresses between 1.4 GPa and 3.4 GPa. The dynamic strength is found to be highly dependent on the loading direction, with loading along the extrusion direction exhibiting significantly higher Hugoniot elastic limits than the transverse direction, including a much slower precursor decay rate. Application of an orientation-based analysis framework shows that the yield point of the polycrystalline material can be predicted reasonably well from its grain orientation distribution, predicated upon the use of dynamic critical resolved shear stress values from single-crystal data modified by a fitted strengthening factor. It is shown that the strong dependence on loading orientation in Mg AZ31 is caused by the relative differences in slip system activity and the slip anisotropies inherent to the hexagonal close packed crystal structure.

Flowstress and Overstress Approaches to Dynamic Viscoplasticity

Viscoplasticity is mostly modelled by the flowstress approach, where the flowstress (Y) is a function of pressure, temperature, plastic strain and strain rate Y (P, T, ). For dynamic viscoelasticity the flowstress approach is used in hydrocodes together with the radial return algorithm, to determine deviatoric stress components in each computational cell and for each time step. The flowstress approach assumes that during plastic loading, the flowstress in stress space follows the current stress point (current Y). Unloading of a computational cell is therefore always elastic. The overstress approach to dynamic viscoplasticity was used in various versions in the 1950s and early 1960s, before the advent of hydrocodes. By the overstress approach a state point may move out of the quasistatic flow surface upon loading, and hence the term overstress. When this happens, the state point tends to fall back (or relax) onto the quasistatic flow surface through plastic flow, and the rate of this relaxation is an increasing function of the amount of overstress. In this paper we first outline in detail how these two approaches to dynamic viscoplasticity work, and then show an example for which the overstress approach has an advantage over the flowstress approach. The example has to do with elastic precursor decay in planar impact, and with the phenomenon of anomalous thermal strengthening, revealed recently in planar impact tests. The overstress approach has an advantage whenever plastic flow during unloading is of importance.

Understanding the low-energy incomplete fusion reactions

With a motivation to find out the systematics for the low-energy ($\ensuremath{\approx}4$--7 MeV/nucleon) incomplete fusion reactions, the experimentally measured excitation functions for evaporation residues, which were populated during the interactions of $^{18}\mathrm{O}$ with $^{159}\mathrm{Tb}$ target nuclei, have been studied. The analysis clearly exhibits that the $xn/pxn$ channels are populated to a large extent through the complete fusion processes. Although, the production cross-section of the $\ensuremath{\alpha}$-emitting channels, despite of deducting the precursor decay contribution, found to be significantly under-estimated by the statistical model predictions. The observed enhancement, which may be attributed due to the involvement of break-up fusion processes, is found to be get larger with the incident energy. In addition, the present work in light of the literature data imparts the reliance of incomplete fusion processes on various entrance channel parameters, such as the mass-asymmetry of the interacting partners, fissility parameter and also on the ${Z}_{P}{Z}_{T}$ (Coulomb factor). These systematics inarguably indicates the projectile type dependency of the incomplete fusion reactions, and the results may be explained on the basis of the $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value of the projectile. Furthermore, an attempt has been made to explain the trends of incomplete fusion fractions through the total asymmetry parameter and the system parameter, where system parameter seems to explain the data more satisfactorily, as it incorporates the Coulomb factor as well as the masses of the interacting partners.

Understanding the So Called “Anomalous Thermal Strengthening” of Elastic Precursor Decay Tests

Some time ago a Russian shock physics group performed planar impact tests on thin metal targets (1mm or less) at different temperatures. They were able to observe the elastic precursor wave amplitudes at different target thicknesses and for different target temperatures. They concluded from the test results that the elastic precursor wave decay rate was lower for higher test temperatures, or as they phrased it, dynamic strength increases with temperature. Such a behavior is counter intuitive, as we are used to believe from our experience with quasistatic viscoplastic response, that strength should decrease with temperature. Accordingly, these results of the Russian group were referred to by them as "Anomalous Thermal Strengthening". Our purpose here is to reproduce such test results using a hydrocode. To this end we do the following: 1) we change the way our hydrocode computes dynamic viscoplastic response, from the usually used radial return approach to the more appropriate overstress approach; 2) we compute a planar impact example and reproduce an elastic precursor decay behavior; 3) we show how the quasistatic part of the response can be separated from dynamic part; and 4) we make the quasistatic and the dynamic response parts depend separately on temperature, and in this way we’re able to reproduce the elastic precursor wave increase with temperature, as observed in the above mentioned tests. &nbsp

Shock compression of magnesium alloy by ultrashort loads driven by sub-picosecond laser pulses

The shock compression of magnesium (Mg-4Al-2Zn) alloy polycrystalline films on glass under ultrashort loads driven by sub-picosecond laser pulses was investigated. The continuous diagnostics of motion and reflectivity changes of the free rear surface of the samples was carried out in the picosecond range (≤200 ps) in a single pulse mode using ultrafast spectral interferometry. We present the data on elastoplastic shock wave evolution at a propagation distance of several hundreds of nanometers, elastic precursor decay, shear, and tensile strengths at the extreme strain rate of ∼109 s−1.

Assessment of the time-dependent behavior of dislocation multiplication under shock loading

In this study, we proposed a method, which is a combination of qualitative analysis and quantitative analysis, to establish dislocation-based plasticity model, and assessed the time-dependent behavior of dislocation multiplication under shock loading. First, the dimensional analysis method is applied to generate the governing equation of dislocation multiplication rate, and ten potential governing equations are derived. Second, through the theoretical analysis of the mechanical response on the shock front, each time-dependent governing equation is directly integrated on the shock front, and the explicit expression of dislocation density with respect to the applied stress is derived, which is further quantitatively connected to the power scaling characteristics of the plastic front. It's found that only three of the ten equations, including two common equations and one newly derived equation via the dimensional analysis method, can predict the appropriate scaling coefficient of the plastic front. Third, three common equations and the newly derived equation are implemented into a dislocation-based constitutive model, and we compared results, including the velocity profiles and dislocation densities, calculated using the model associated with each equation and experimental results to evaluate the accuracy and efficiency of each equation. Through the comparison of the quantitative relation of the power scaling characteristics of the plastic front, and the elastic precursor decay, it's concluded that the newly derived stress-dependent governing equation is more suitable for shock-loading process than the commonly used equations by previous constitutive models.

Application of model-order reduction of non-linear time-dependent neutronics via POD-Galerkin projection and matrix discrete empirical interpolation

Presented here is an application of model-order reduction to non-linear neutronic transients. The effort described extends previous work (Elzohery and Roberts, 2021b) aimed to develop and assess a Reduced-order model (ROM) framework that can be used for different purposes, such as design optimization and propagating input parameter uncertainties like nuclear data. Here, the target applications is non-linear. The ROM was built with the use of the POD-Galerkin projection method and the matrix version of the Discrete Empirical Interpolation Method (MDEIM) for improved efficiency. Where applications of the ROM to the diffusion equation have been introduced before, this work focuses on treating the non-linearity induced by coupling with different physics. Previous work has used DEIM to approximate non-linear functions resulting from multiphysics coupling such as the temperature and the velocity field (German et al., 2019, 2022). Here, the MDEIM is used to approximate the projection of the problem operator that otherwise must be computed at each non-linear iteration within each time step, which increases the ROM cost. By applying the method to the LRA benchmark, speed ups from 6 to 40 were achieved depending on the full-order model (FOM) spatial fidelity. The maximum relative error in the assemblies power was in the order of 1×10−5%. Moreover, the ROM was parameterized by POD-greedy sampling, and a case study was performed where the kinetic data, i.e., the precursor decay constants and delayed-neutron fraction were assumed to be the model parameters of interest. For the parameterized ROM, the maximum relative error in the assembly power was 1×10−3%, The computational gain from the MDEIM-ROM was compared with that of a direct projection ROM and showed that employing the MDEIM is computationally advantageous, and the advantage grows with dimension of the problem. The method was implemented in the open-source deterministic transport code Detran (Roberts, 2014) where only access to the system operator was needed to construct the ROM, and; hence, the method is trivially invasive and could easily be implemented in many modern deterministic diffusion codes.

Dynamic response of YAG polycrystalline and single‐crystal transparent ceramics: Experiments and mesoscopic simulations

AbstractDue to superior mechanical and optical properties, yttrium–aluminum–garnet (YAG) is emerging as a potential transparent armor material. Its dynamic behavior, however, remains largely unexplored. In this work, both impact experiments and mesoscopic simulations have been performed to better understand the dynamic response of YAG polycrystalline and single‐crystal transparent ceramics. Experimental results demonstrate that the two samples have remarkably different dynamic behaviors with the increasing shock pressure, in which the Hugoniot elastic limit basically keeps unchanged (∼14 GPa) in YAG polycrystalline ceramic, whereas it varies from 11 to 31 GPa in YAG single crystals. Moreover, elastic precursor decay is visible only in single‐crystal samples. Mesoscopic simulations with a lattice‐spring model reveal that the difference arises from the distinct fracture mode in the two samples. Less damage and coarser fragmentations in YAG single crystal also suggest a probability of better ballistic resistance as transparent armor materials.

Evaluating the variations of point kinetics parameters in pressurized heavy water reactor analyses

Since the pressurized heavy water reactor design utilizes natural uranium bundles as its fuel, there is a need to keep replenishing the reactor core with unirradiated fuel bundles in order to keep the reactor critical. This practice causes the fuel inventory in the core to be very dynamic since the changes are not solely due to the depletion of the fuels due to irradiation but also due to the presence of new fuel bundles in the core. An average behaviour of the core after operating in an equilibrium stage for a long time can be captured through the time-average approach. This approach has been extensively used in the pressurized heavy water reactor fuel management, especially during the design phase where the actual data from the operating reactor are not readily available. The time-average core is utilized for many purposes such as to determine the average fueling rate, to determine the average worth of various reactivity control devices, as well as to determine the point kinetics parameters for transient analyses. The objective of this paper is to quantify potential variations in the point kinetics parameters (namely the decay constants and the delayed neutron fractions) as a function of core inventories with respect to the time-average-based values. In particular, 100 core configurations representing various snapshots from an equilibrium operation of the core have been utilized to quantify these potential variations. It should also be noted that the point kinetics equation (PKE) is utilized in this study, instead of full-core space–time model, since the objective of this paper is to bring about the awareness of potential variations and the PKE should be sufficient. The results of this study indicate that, for a point kinetics equations system involving six precursor groups, the variations in precursor decay constants and delayed neutron fractions could be as high as ±0.45% and ±4.85%, respectively. Using the point kinetics parameters in a simple transient involving an insertion of positive reactivity, it is demonstrated that the variation in the trip time for the transient could vary up to approximately ±3.55%, depending on the amount of positive reactivity insertion. These potential variations should be acknowledged since it is an important part of safety analysis. However, it is also important to note that, based on the amount of positive reactivity insertion evaluated in this study, the higher variation corresponds to a lower level of positive reactivity insertion which means that the transient will be slowly developing, could be observed more readily, and, therefore, could be easily terminated.

Effect of small pre-strain on the resistance of molybdenum [100] single crystal to high strain rate deformation and fracture

The evolution of shock compressive pulses and dynamic tensile (spall) strength of pristine and pre-strained (0.6% and 5.4% compression) samples of pure [100]-oriented molybdenum single crystals were studied in a series of planar impact tests accompanied by continuous monitoring of the free surface velocity of the samples by an optic velocimeter. The impact loading of Mo samples of different thicknesses was produced by copper impactors accelerated in the smooth bore gun up to a velocity of about 350 m/s. Analyzing the recorded waveforms showed that pre-straining results in a substantial decrease of the molybdenum Hugoniot elastic limit while the dynamic tensile (spall) strength increases with pre-straining. The spall fracture of all tested (and spalled) samples was found to be brittle and characterized by a weak dependence of spall strength on the tensile strain rate. The obtained results are discussed in the terms of generally accepted theories of elastic precursor decay in ductile and spall fracture in brittle solids.

Atomistic simulation of the shock wave in copper single crystals with pre-existing dislocation network

We present molecular dynamics simulations of shock compression and spall fracture in [111] copper single crystals with pre-existing dislocations. Shock waves are simulated for an impact velocity of 50–900 m/s, which is below the Hugoniot elastic limit for pure [111] crystals. A dislocation network is created by carving out interstitial dislocation loops, followed by their interaction and relaxation to the dislocation network. Samples with different dislocation densities are considered. We find that, behind the shock wave, shear stress is relaxed by multiplication of moving dislocations, which increases with piston velocity. Positively oriented dislocation segments move in the direction of the shock wave, while negatively oriented segments move in the opposite direction. Dislocation segments of different orientation interact with and intersect each other behind the shock wave. The dislocation segments moving at supersonic speeds are observed already at the impact velocity of 300m/s. When the shock pulse ends, the subsequent rarefaction wave creates tensile shear stresses which promote the negatively oriented dislocation segments to move along it. Where incident and reflected rarefaction waves contact, the tensile longitudinal stresses cause dislocation multiplication, which results in an increased dislocation density. The time series of dislocation density and stress along the samples are computed during the shock waves propagation and release. An increase in dislocation density behind the shock wave is found to vary quadratically with shock stress, and does not depend on the initial dislocation density. In the region of tensile stresses, an increase in dislocation density is also approximated by a power function of the maximal tensile stresses. The elastic precursor decay is analyzed for different impact velocities and initial dislocation densities. The decay power increases with the impact velocity and the initial dislocation density in the sample. The plastic strain rate is estimated from the decay of elastic precursor, compared to experimental values, and discussed in terms of dislocation dynamics. Spall fracture is observed in samples of various dislocation density at impact velocities of at least 500m/s, corresponding to tensile stresses of about 12GPa, in agreement with the previously published simulation data. The number of voids, their volumes and distribution are studied using the alpha-shape algorithm for free surface extraction. We show that pre-existing dislocations almost do not affect the spall strength, but significantly slow down the spall process compared to defect-free crystals, resulting in a more ductile fracture.

Shock response of cyclotetramethylene tetranitramine (HMX) single crystal at elevated temperatures

To investigate the shock response of cyclotetramethylene tetranitramine (HMX) single crystals at elevated temperatures (below the phase transition point), plate impact experiments at elevated temperatures were designed and conducted. The HMX/window interface particle velocities at temperatures of 300 K, 373 K, and 423 K were measured by the velocity interferometry system for any reflector (VISAR) technique. To further analyze the related mesoscale deformation mechanisms, a nonlinear thermoelastic-viscoplastic model was developed, which considers thermal activation and phonon drag dislocation slip mechanisms. The proposed model could well reproduce the measured thermal hardening behavior of Hugoniot elastic limit (HEL) of HMX single crystals. At elevated temperatures, the reduced dislocation mobility was observed, which stems from both phonon scattering and radiative damping effects. Comparatively speaking, radiative damping contributes less than phonon scattering to thermal hardening behavior. The calibrated model was further used to predict shock response of HMX single crystals with different thicknesses at different initial temperatures. Both the stress relaxation and elastic precursor decrease with thickness are mainly due to the rapid dislocation generation. These insights shed light on the interplay between dislocation motion and dislocation generation in thermal hardening behavior, stress relaxation, and elastic precursor decay, which serves to reveal the mesoscale deformation mechanisms at elevated temperatures.

Effect of non- α -cluster projectile on incomplete-fusion dynamics: Experimental study of the N14+Ta181 system

In order to study incomplete fusion (ICF) reaction dynamics, the present work manifests the role of a non-$\ensuremath{\alpha}$-cluster $^{14}\mathrm{N}$ projectile on $^{181}\mathrm{Ta}$ target at energies $\ensuremath{\approx}4--7$ MeV/nucleon using the offline $\ensuremath{\gamma}$-ray spectroscopy. The excitation functions for 15 reaction residues populated in $^{14}\mathrm{N}+^{181}\mathrm{Ta}$ system have been measured and analyzed within the framework of statistical model code PACE4. The experimentally measured excitation functions of evaporation residues populated via xn/pxn channels are found to be well reproduced by the predictions of code PACE4, which confirms their production solely via complete fusion process. However, an enhancement in the measured excitation function as compared to PACE4 calculations, particularly in tail portion of $^{192}\mathrm{Hg}$ residue ($3n$ channel) has been observed indicating the presence of precompound emission. A significant contribution from precursor decay in pxn channels has also been observed. An enhancement in the measured excitation functions for $\ensuremath{\alpha}$-emitting channels as compared to the PACE4 predictions has been observed and attributed to the incomplete fusion process. Further, the contribution from incomplete fusion process in the $^{14}\mathrm{N}+^{181}\mathrm{Ta}$ system has also been deduced in terms of strength function (${F}_{\mathrm{ICF}}$). The results have been discussed in terms of the parameters which influence the dynamics of ICF process. The ${F}_{\mathrm{ICF}}$ is found to depend strongly on projectile energies, the product of projectile and target charges, and $\ensuremath{\alpha}\ensuremath{-}Q$ value of the projectile.

Dislocation drag and its influence on elastic precursor decay

Plastic deformation is mediated by the creation and movement of dislocations, and at high stress the latter is dominated by dislocation drag from phonon wind. By simulating a 1-D shock impact problem we analyze the importance of accurately modeling dislocation drag and dislocation density evolution in the high stress regime. Dislocation drag is modeled according to a first-principles derivation as a function of stress and dislocation character, and its temperature and density dependence are approximated to the extent currently known. Much less is known about dislocation density evolution, leading to far greater uncertainty in these model parameters. In studying anisotropic fcc metals with character dependent dislocations, the present work generalizes similar earlier studies by other authors.

Numerical modeling of dynamic response and microcracking in shock-loaded polycrystalline transparent ceramic

Transparent ceramics are promising materials in the fields of high pressure and high temperature. Based on a lattice-spring simulation method, a novel polycrystalline model for shock-wave compression is established to explore the dynamic response and damage evolution of yttrium aluminum garnet (YAG) under shock loading. The macro-response and micro-fracture process under impact loading can be obtained simultaneously, and a correlation between the macroscopic response and mesoscale damage is shown. The process of crack propagation along a grain boundary and through grain-boundary deflection is observed in the simulation. A change in deformation behavior from intergranular fracture to transgranular fracture in the vicinity of grain boundaries, associated with the transition from an elastic response to a plastic response, is observed, as the shock stress increases from below to above the Hugoniot elastic limit. Computational results demonstrate a clear, exponential attenuation of the elastic precursor wave with the propagation of shock waves. The reasons for the elastic precursor decay and the transition from an elastic response to a plastic response are the stress relaxation and energy dissipation caused by internal transgranular fracture. The polycrystalline model will aid in microstructure design and provide a reference for the development of polycrystalline transparent ceramics in the fields of engineering and scientific research.

AT 2020iko: A WZ Sge-type Dwarf Nova Candidate with an Anomalous Precursor Event

Abstract The ongoing Zwicky Transient Facility (ZTF) survey is generating a massive alert rate from a variety of optical transients and variable stars, which are being filtered down to subsets meeting user-specified criteria by broker systems such as the Arizona-NOIRLab Temporal Analysis and Response to Events System (ANTARES). In a beta implementation of the algorithm of Soraisam et al. on ANTARES, we flagged AT 2020iko from the ZTF real-time alert stream as an anomalous source. This source is located close to a red extended Sloan Digital Sky Survey source. In the first few epochs of detection, it exhibited a V-shaped brightness profile, preceded by nondetections both in ZTF and in the All-Sky Automated Survey for Supernovae extending to 2014. Its full light curve shows a precursor event, followed by a main superoutburst and at least two rebrightenings. A low-resolution spectrum of this source points to a dwarf nova (DN) nature. Although some of the features of AT 2020iko indicate an SU UMa-type DN, its large amplitude, presence of rebrightenings, and inferred supercycle period of ≥6 yr are in favor of AT 2020iko being a new WZ Sge-type DN candidate, a subset of rare DNe consisting of extreme mass-ratio (<0.1) binaries with an orbital period around the period minimum. The precusor event of AT 2020iko brightened by 6.5 mag, while its decay spanned 3–5 mag. We speculate this superoutburst is associated with a less expanded accretion disk than in typical superoutbursts in WZ Sge systems, with the large depth of the precursor decay implying an extremely small mass ratio. To the best of our knowledge, such a precursor event has not been recorded for any DN. This result serves to demonstrate the efficacy of our real-time anomaly search algorithm.

Steady plastic wave fronts and scale universality of strain localization in metals and ceramics

Mechanisms of structural relaxation are linked with the metastability of nonequilibrium potential of solid with defects and the generation of collective modes of defects responsible for the plastic strain and damage localization. It is shown that spatial-temporal dynamics of collective modes (auto-solitary and blow-up dissipative structures) provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. These modes have the nature of self-similar solutions of evolution equations for damage parameter (defect-induced strain) and represent the “universality class” providing the four power law for a steady plastic front, splitting of an elastoplastic shock wave front, and elastic precursor decay kinetics. Wide-range constitutive equations reflecting the linkage between defect-induced mechanisms and structural relaxation are used in the numerical simulation for shock wave loading of metals and ceramics in the comparison with experiments.

Elastic Precursor Decay and Spallation in Nonporous Tungsten Carbide Ceramics

To identify the possible contribution of relaxation processes to the resistance against high-rate deformation, evolution of shock-compression waves in tungsten carbide (WC) ceramics manufactured by spark-plasma sintering at a maximum compressive stress of 27 GPa is measured. Strong elastic precursor decay upon changing the thickness of the samples from 0.15 to 4 mm is revealed. At maximum shock compressive stresses twice exceeding the Hugoniot elastic limit, a decrease in the spall strength value by about 30% from its value in the elastic region is recorded.

Затухание упругого предвестника и откол в беспористой керамике карбида вольфрама

AbstractTo identify the possible contribution of relaxation processes to the resistance against high-rate deformation, evolution of shock-compression waves in tungsten carbide (WC) ceramics manufactured by spark-plasma sintering at a maximum compressive stress of 27 GPa is measured. Strong elastic precursor decay upon changing the thickness of the samples from 0.15 to 4 mm is revealed. At maximum shock compressive stresses twice exceeding the Hugoniot elastic limit, a decrease in the spall strength value by about 30% from its value in the elastic region is recorded.

Measurement of excitation functions of evaporation residues in the O16+Sn124 reaction and investigation of the dependence of incomplete fusion dynamics on entrance channel parameters

Excitation functions for the 11 evaporation residues populated through complete and/or incomplete fusion in $^{16}\mathrm{O}+^{124}\mathrm{Sn}$ system at low projectile energies $\ensuremath{\approx}3\ensuremath{-}7\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ have been measured. Recoil catcher activation technique followed by offline $\ensuremath{\gamma}$-ray spectrometry has been employed. Some of the evaporation residues are found to have contributions from precursor decays. The precursor contributions have been separated out from the measured cumulative cross-sections of evaporation residues. Independent cross-sections are compared with statistical model code PACE-4 predictions. The evaporation residues produced through $xn$ and pxn channels are found to be well reproduced with the PACE-4 predictions after subtraction of precursor decay contributions. A substantial enhancement in the measured excitation functions over their theoretical predictions for the evaporation residues produced in $\ensuremath{\alpha}$-emitting channels has been observed, which is attributed to the presence of incomplete fusion of projectile with target at these low energies. The present study shows that the incomplete fusion and the break-up probability of the incident $^{16}\mathrm{O}$ into $\ensuremath{\alpha}$ clusters (i.e., break-up of $^{16}\mathrm{O}$ into $^{12}\mathrm{C}+\ensuremath{\alpha}$ and/or $^{8}\mathrm{Be}+^{8}\mathrm{Be}$) increases with projectile energy. The present data suggests that the deformation of target is highlighting the important role to affect the ICF reactions independently with different projectiles. The comparison of the present study with literature data also shows that the ICF probability depends on various entrance channel parameters, namely, projectile energy, entrance channel mass-asymmetry, $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value, Coulomb factor $({Z}_{\mathrm{P}}{Z}_{\mathrm{T}})$, deformation parameter (${\ensuremath{\beta}}_{2}$), and their combinations. Moreover, the combined parameters ${Z}_{\mathrm{P}}{Z}_{\mathrm{T}}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\beta}}_{2}$ and ${\ensuremath{\mu}}_{\mathrm{EC}}^{\mathrm{AS}}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\beta}}_{2}$ are not found suitable to explain whole ICF characteristics, particularly for spherical and slightly deformed targets. On the other hand, the combined parameter ${Z}_{\mathrm{P}}{Z}_{\mathrm{T}}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\mu}}_{\mathrm{EC}}^{\mathrm{AS}}$ has been found to explain more precisely the ICF dynamics as compared to other single and combined entrance channel parameters.