Considering the self-similar characteristic of irregular pore network of materials during the damage evolution process, a pore ubiquitiform model (PUM) is developed to characterize the multiscale pore or microcrack network of quasi-brittle materials, and then based on the PUM, the ubiquitiform damage model (UDM) is proposed to describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. The values of porosity and pore specific surface area estimated from the PUM and the stress-deformation curves including the softening curve calculated from the UDM are in good agreement with previous experimental data, respectively. It can be found that, the PUM can be adopted to characterize the self-similar multiscale pore network and estimate the porosity and pore specific surface area, and the UDM can describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. Meanwhile, the UDM can characterize the self-similar characteristic of pore network during the damage evolution process of quasi-brittle materials through the evolving ubiquitiform complexity.

Some explicit analytical expressions of the dynamic shear load-carrying capacity for brittle materials under a quadratic waveform loading are presented on the basis of the incubation time fracture criterion, by which the dynamic shear load-carrying capacity can be determined from the quasi-static material parameters, incubation time and stress wave loading conditions (loading amplitude, loading duration, and waveform). The numerical results are in good agreement with the previous experimental data. It is found that the incubation time fracture criterion can be adopted to describe the time-dependence of the dynamic shear failure of brittle materials and predict shear failure. Meanwhile, the so-called dynamic shear strength should be the dynamic shear load-carrying capacity, which is a computable result rather than a material parameter, and the strain rate enhancement effect on the shear failure strength cannot be considered as a material property but should be a structure response of brittle materials to stress wave loading conditions.

为获得高聚物粘结炸药内部的热点信息,对其内部椭圆形孔洞在激波载荷作用下的坍塌过程进行了研究.通过相似分析和中尺度模拟,分析冲击强度和孔洞几何形状(孔洞尺寸、位置和伸长状态)对热点温度的影响.结果表明:在一定的冲击强度及特定位置和伸长状态下椭圆形孔洞产生的热点温度可高达2990 K,比同面积下圆孔洞产生的热点温度(1946 K)高54％,可使炸药更加敏感;通过使用中间渐近、完全和不完全相似的相似性分析,得到由椭圆形孔洞在激波载荷作用下坍塌所导致的热点温度半经验解析表达,以表征热点温度与冲击强度和孔洞几何形状的关系,热点温度的理论预测结果与数值结果吻合良好.

In recent decades, the incubation time has become a critical parameter to study dynamic failures for materials, but its underlying physical meaning is still vague and the corresponding model remains lacking. In this study, we first established a theoretical framework to evaluate incubation time, wherein a double atomic chain model with atomic thermal vibrations is leveraged. We leveraged three external force loading conditions to analyze incubation time and its associated dynamic load-carrying capacity (DLC). It can be found that the theoretical results for three metal materials (iron, tungsten and aluminum) exhibit reasonable consistencies with the experimental data, thus the model can be used to conduct preliminary studies for incubation time and DLC. The model suggests that, under the ramp loading with a platform amplitude of static strength, the amplitude duration does not remain constant but can quickly reach a constant with increasing ramp or loading rate, which implies that treating incubation time as a constant parameter is reasonable and thus lays a solid foundation for the previous macroscopic models on basis of incubation time. Meanwhile, it also suggests that the rate enhancement effect of failure strength can be obtained from external load and the constant atomic bond parameters without involving microscopic changes in material properties. Therefore, we microscopically unravel the rate enhancement effect of failure strength. Our study indicates that this effect is indeed a structural response, which accords with the previous macroscopical model.

为了探究钝感熔铸含铝炸药的冲击起爆特性,建立化学爆炸加载一维拉格朗日锰铜压阻测试系统,获得了不同加载压力下一典型2,4-二硝基苯甲醚(DNAN)基钝感熔铸含铝炸药的冲击起爆过程压力成长历史.利用熔铸含铝Duan-Zhang-Kim(DZK)细观反应速率模型,确定了该钝感含铝炸药的反应速率模型参数,并对其冲击起爆过程进行了数值模拟研究.结果表明在钝感熔铸含铝炸药的冲击起爆过程中,波阵面附近炸药的反应速率和反应程度均较低,而随着热点点火反应的进行以及化学反应的不断累积,炸药的波后化学反应速率不断增加,并在一段时间后到达峰值.当加载压力越高时,钝感熔铸含铝炸药内部的爆轰成长速率越快.同时,与粒子速度成长历史相比,压力成长历史包含更多的反应速率变化信息,更适用于反应速率模型的验证以及炸药反应流模型参数的确定.

In this study, a ubiquitiform hotspot ignition model with cross-scale characteristics is proposed to describe the ignition stage of PBX, which can account for heterogeneous effects. Firstly, a ubiquitiform model of hotspot intensity is obtained. The model can describe the hotspot information after PBX is impacted. In which, a hotspot distribution model based on the nested ubiquitiform model of explosives is used to characterize geometric properties of hotspot, including the size and location of hotspot; and the Weibull statistical distribution function is used to describe the distribution of hotspot intensity. Then, combining the ubiquitiform model of hotspot intensity with Arrhenius model, the ubiquitiform hotspot ignition model is developed to characterize the ignition stage of PBX. Finally, it is found that the equivalent reaction rate constants calculated by our ignition model are in good agreement with the previous experimental data.

In this study, two general solutions for the dynamic tensile load-carrying capacity of brittle materials subject to an arbitrary incident stress wave in the form of Fourier integrals are derived. In order to verify the general solutions, we reduce them to three particular solutions, respectively, i.e., trapezoidal pulse, quadratic pulse and cubic pulse. It is found that all of them can well capture the experimental trends in the previous studies. In between, the first two particular solutions can exactly accord with the two previous analytical solutions under the same boundary conditions, respectively. Therefore, for arbitrary tensile boundary pulses, the dynamic tensile strength of the brittle materials can be calculated from static parameters and characteristics of external loading. This study improves the credibility of the previous works that working on deriving the dynamic load-carrying capacity through analytical methods, and thus, consolidate their theoretical foundation. Meanwhile, on basis of the general solution, the relation between the dynamic tensile load-carrying capacity and strain rate can be further deduced by combining static parameters, hence, it could be inappropriate to claim the strain rate effect on tensile strength as an intrinsic material property anymore. In addition, we found that the process to obtain an explicit analytical solution becomes increasingly difficult with the increased complexity of waveform for an incident pulse, or even no explicit solution can be obtained.

A melt-cast Duan-Zhang-Kim (DZK) mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism. A series of shock initiation experiments was performed for the Comp B melt-cast explosive to estimate effects of the loading pressure and the particle size of granular explosive component, and the mesoscopic model is validated against the experimental data. Further numerical simulations indicate that the initial density and formula proportion greatly affect the hot-spot ignition of melt-cast explosives.

In this study, similarity analysis and mesoscale simulations were performed to investigate hot spot temperatures in triangular voids inside polymer-bonded explosives (PBXs). We found that there are two different void collapse modes, namely single and double hydrodynamic jet modes. The hot spot temperatures achieved in the double hydrodynamic jet mode are much higher than previous predictions, such as predictions based on circular voids, which agrees with recent experimental observations. Additionally, we verified that void configuration (position and shape) plays a significant role in increasing hot spot temperatures, implying that when establishing a mesoscale reaction rate model, it is insufficient to use void volume alone to characterize the impact sensitivity of PBXs. Finally, two semi-empirical analytical expressions are proposed to represent the dependence of hot spot temperature on both the void configuration and shock intensity. The resulting theoretical predictions are in good agreement with the numerically simulated results. Such mesoscale analytical expressions can be used for establishing theoretical mesoscale hot spot ignition rate models in the future.

Considering the heterogeneity of real materials, a simple statistical model is proposed to describe a ubiquitiformal crack extension in quasi-brittle materials. The complexity of the ubiquitiformal crack is obtained by using the box-counting dimension. In the model, it is assumed that the crack propagates in the direction of the minimum energy dissipation and the heterogeneity of material properties is characterized by the Weibull distribution. The calculated numerical results of the complexity are found to be in good agreement with previous experimental data. Moreover, it is also verified that the complexity is uniquely determined by the Weibull distribution parameters, though the styles of crack extension in each computation are a little bit different from each other, due to the randomness of the spatial distribution of the material properties.

An aluminized melt-cast Duan–Zhang–Kim mesoscopic reaction rate model based on the pore collapse hot-spot ignition mechanism is proposed to characterize the shock initiation behavior as well as size effects of explosive particles on the shock initiation of aluminized melt-cast explosives. For aluminized 2,4-dinitroanisole (DNAN)-based melt-cast R1 explosives [containing 60 wt. % HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine), 30 wt. % DNAN, and 10 wt. % aluminium] with different particle sizes of HMX, both shock initiation experiments and corresponding numerical simulations were performed. The numerical results are found to be in good agreement with the experimental data, by which the mesoscopic reaction rate model is verified and the model parameters for the R1 explosive are determined. It is also found that the smaller the particle size of the granular explosive component, the faster the leading shock wave propagates, and the faster the detonation growth inside the aluminized melt-cast explosive.

A series of shock initiation experiments on the explosive PBXC03 (87 % HMX, 7 % TATB, and 6 % Viton by weight) with different particle sizes and porosities under various shock loadings have been performed, and it is found that the particle size and the porosity of the explosives have much influence on the shock initiation characteristics. That is, the smaller the particle size, the more difficult the explosive to be ignited but the faster the detonation grows once the explosive is ignited. It is also found that the detonation grows the fastest in the explosive with moderate porosity. Moreover, a modified mesoscopic reaction rate model based on the experimental results and the pore collapse hot-spot ignition mechanism is developed, which allows for a separate reaction mechanism evaluation at different reaction stages for the shock initiation and detonation growth processes in the explosives. The calculated pressure-time histories and Pop-Plots for PBXC03 are founded to be all in good agreement with the experimental data. The modified mesoscopic reaction rate model shows its potentiality for quantitatively predicting the effects of the mesostructure of PBXs on the shock initiation and detonation growth processes with a high degree of confidence.

Abstract The crack extension path of concrete materials was simulated numerically based on the non-uniform numerical model of Weibull distribution, and the complexities of various ubiquitiform fracture surfaces were calculated to explore the relationship between complexity and fracture energy. To study the influence of specific crack extension law and fracture mode on the relationship between the complexity and fracture energy, numerical simulation of the crack extension was carried out based on the numerical model with random aggregate distribution, and the reason for the change of the relationship between complexity and fracture energy were discussed.

利用通用显式动力学分析程序LS-DYNA模拟了空客A320与刚性靶体的碰撞过程,获得了飞机以不同速度撞击时的冲击载荷.通过与修正的Riera公式计算的冲击载荷对比,确定了Riera公式和冲击载荷工程模型中修正系数α的取值,并获得了α与撞击速度V0的对应关系.根据飞机的压损载荷冲量与冲击载荷冲量之比,确定了冲击载荷工程模型中冲击载荷系数γ的取值,并获得了γ与撞击速度V0的对应关系.工程模型与数值模拟计算的冲击载荷曲线吻合较好,验证了冲击载荷工程模型的合理性,为空客A320及相似结构飞机的冲击载荷曲线计算提供了依据.

A one-dimensional ubiquitiformal constitutive model for a bimaterial bar is proposed in this paper. An explicit analytical expression for the effective Young modulus is then obtained, which, unlike the fractal one, leads to a continuous displacement distribution along the bar. Moreover, numerical results for concretes are calculated and found to be in agreement with previous experimental data. In addition, some previous empirical and semi-empirical constitutive models are also examined, which shows that each of these models can correspond well to a ubiquitiformal one under a certain complexity.

This paper offers a new method for calculating the reaction rate of the pore collapse hot-spot ignition in multi-component PBX explosives, and proposes a new mesoscopic reaction rate model capable of describing and predicting the shock initiation and detonation behavior of multi-component PBX explosives with any explosive components proportion as well as any explosive particle size. The pressure-time histories in the explosive samples calculated using this mesoscopic reaction rate model are in good agreement with the experimental data. The shock initiation and detonation process of PBX explosives is mainly controlled by both the hot-spot ignition processes and the combustion reaction processes. The PBXC03 explosive with the dominant component of HMX is mainly controlled by the hot-spot ignition and shows the accelerated reaction characteristics. With the dominant component of insensitive TATB, the critical initiation pressure of PBXC10 is high and the shock initiation behavior is controlled by the combustion reaction process, which shows a stable reaction characteristics.

A nesting ubiquitiform (NU) approach was developed to characterize the mesostructural features of polymer-bonded explosives (PBXs), and then used to predicate some equivalent physical properties of PBXs, which can also be expected to be extended to other composites with complicated internal mesostructures. To verify the availability, two NU models for two kinds of PBX with different compositions are presented, which are PBX 9501 and LX-17, based on which, the equivalent thermal conductivities were calculated. Particularly, it is so encouraging that an analytical expression of the equivalent thermal conductivity was obtained only under a simply assumption of homogeneity. Moreover, it was found that the numerical results calculated by both the recursive algorithm and the analytical expression were in good agreement with the experimental data. In addition, it is also shown that such a physical property as the equivalent thermal conductivity is indeed independent of the meso-configuration of the location distribution of the explosive particles and the voids inside the PBX, which seems consistent with the common expectations and lays the foundations for the application of ubiquitiform to investigating some equivalent properties of composites.

An experimental research approach is proposed to investigate the initiation and detonation growth characteristics of polymer bonded explosives (PBXs) under ramp-wave loadings, in which a magnetic compression device and a multichannel photonic Doppler velocimetry are taken as the ramp-wave loading and the measurement systems, respectively. The ramp loadings have a rise time of 530 ns, and the peak pressure P0 varies from 5.4 GPa to 12.4 GPa with the range of the peak ramp loading rate being from 11.6 GPa/μs to 31.3 GPa/μs. Five PBX specimens in different thicknesses were compressed simultaneously until detonation occurs in some of the specimens. All the particle-velocity histories on the reverse side of each sample were measured, which characterizes both the ignition and the detonation growth processes. It is found, under the ramp-wave loadings, that no significant chemical reaction inside the explosive occurs before a strong precursory shock-wave is formed, and the ignition and detonation growth processes are still dominated by the shock-wave induced hot-spots mechanism. Moreover, the experimental data are also found to be basically in good agreement with the numerical results simulated by using the DZK (named Duan-Zhang-Kim) reaction rate model with a pressure threshold, which implies that the ramp-wave loading experimental technique is also practicable for investigating the ramp-induced shock initiation and detonation growth characteristics of PBXs.

A stereological ubiquitiformal softening model for describing the softening behavior of concrete under quasi-static uniaxial tensile loadings is presented in this paper. In the model, both the damage evaluation process of fracture cross-sections and their distribution along the specimens axis are taken into account. The numerical results of a certain kind of full grade concrete made of crushed coarse aggregate are found to be in good agreement with the experimental data. Moreover, an experiental relation between the lower bound to the scale invariance of concrete and its tensile strength is also obtained by data fitting of the experimental data, which provides an effective approach to determine the lower bound to scale invariance of concrete.

To investigate the ubiquitiformal characteristic of the crack extension path in a heterogeneous quasi-brittle material under the dynamic tensile loadings, a ubiquitiformal model is developed in this paper, and the calculated numerical results for the ubiquitiform complexity are in agreement with the previous experiments. It is found that such a crack extension path is indeed of a ubiquitiform, and its complexity decreases with the increase of the loading strain-rate. Moreover, it is also found that the complexity is independent of the randomness of the spatial distribution of the dynamic tensile load-carrying capacity of the material under consideration, and the complexity decreases with increasing shape parameter m of the Weibull distribution. Thus, this work can be taken as a basis for analyzing further the mechanism as well as the ubiquitiformal characteristic of the crack profile in a quasi-brittle material under the dynamic tensile loadings.