Thermal and mechanical analysis of material response to non-steady ramp and steady shock wave loading

Ramp wave experiments on the Sandia Z accelerator provide a new approach to study the rapid compression response of materials at pressures, temperatures and stress or strain rates not attainable in conventional shock experiments. Due to its shockless nature, the ramp wave experiment is often termed as an isentropic (or quasi-isentropic) compression experiment (ICE). However, in reality there is always some entropy produced when materials are subjected to large amplitude compression even under shockless loading. The entropy production mechanisms that cause deformation to deviate from the isentropic process can be attributed to mechanical and thermal dissipations. The former is due to inelasticity associated with various deformation mechanisms and the rate effect that is inherent in all the deformation processes and the latter is due to irreversible heat conduction. The main purpose of the current study is to gain insights into the effects of ramp and shock loading on the entropy production and thermomechanical responses of materials. Another purpose is to investigate the role of heat conduction in the material response to both the non-steady ramp wave and steady shock.Numerical simulations are used to address the aforementioned research objectives. The thermomechanical response associated with a steady shock wave is investigated first by solving a set of nonlinear ordinary differential equations. Using the steady wave solutions as the reference, the material responses under non-steady ramp waves are then studied with numerical wave propagation simulation. It is demonstrated that the material response to ramp and shock loading is essentially a manifestation of the interaction between the time scale associated with the loading and the intrinsic time scales associated with mechanical deformation and heat transfer. At lower loading rates as encountered in ramp loading, the loading path is closer to an isentrope and results in lower entropy production. The reasonable ramp rate to obtain a quasi-isentropic state depends on the intrinsic time scales of the dissipation mechanisms which are strongly material dependent. Thus shockless loading does not necessarily produce an isentropic response. Between two equilibrium states, heat conduction was shown to have significant effect on the temperature history but it contributes little to the overall temperature change if the specific heat remains constant. It also affects the history of entropy, but only the irreversible part of heat conduction contributes to the net entropy change. The various types of thermomechanical responses of materials would manifest themselves more significantly in terms of the thermal history than the mechanical history. Thus temperature measurement appears to be an important experimental tool in distinguishing the various mechanisms for the thermomechancial responses of the materials.     

基于“钉床型”飞片的斜波加载技术及应用

为了实现斜波加载,设计了一种“钉床型”广义波阻抗梯度飞片,即在基座上密排叠加许多小圆锥,简称“钉床型”飞片。该飞片采用激光选区熔化金属增材制造技术进行制备。利用一级轻气炮加载装置和全光纤激光位移干涉测试系统,开展不同工况下“钉床型”飞片高速击靶压缩实验和层裂实验,重点讨论小圆锥高度和撞击速度对斜波压缩加载波形的影响规律,以及斜波加载对不锈钢靶板层裂特性的影响。实验结果显示:（1）“钉床型”飞片对靶板产生的压缩是逐步的,从自由面速度剖面上观察到压缩波上升前沿时间被显著延长,形成了斜波波阵面,明显不同于冲击压缩的陡峭波阵面;（2）在飞片击靶速度近似恒定条件下,斜波波阵面的上升沿时间、平台速度峰值都明显依赖于“钉床型”飞片上的小圆锥高度,随着小圆锥高度增大,上升沿时间呈线性增大,而平台速度峰值呈线性减小;（3）在“钉床型”飞片的几何尺寸保持不变的条件下,斜波波阵面的上升沿时间随着飞片击靶速度的增大而线性减小,平台速度峰值则线性增大;（4）与冲击加载相比,“钉床型”飞片产生的斜波加载不会对材料的层裂强度产生明显影响,但对材料内部损伤演化速率有一定的影响。     

坚硬岩石在强冲击荷载作用近区的性状研究

根据坚硬岩石的性质,利用力学模型分析了在冲击荷载作用下的岩石破坏过程,经由弹性状态向内摩擦状态的转变,最终达到流体力学状态。通过对内摩擦状态的分析,认为在强冲击荷载区域的变形近似为一维变形状态。冲击荷载作用在岩石中产生的应力波可以看作类似于冲击波的短波,在波阵面附近的某个狭窄区域内将发生参数的急剧变化。根据近区变形状态与质量守恒导出了侵彻近区的速度场表达式。根据短波的研究,给出了近区应力波的衰减规律。     

Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle

The objective of this effort is to develop a computational methodology to capture the side load physics and to anchor the computed aerodynamic side loads with the available data by simulating the startup transient of a regeneratively cooled, high-aspect-ratio nozzle, hot-fired at sea level. The computational methodology is based on an unstructured-grid, pressure-based, reacting flow computational fluid dynamics and heat transfer formulation, and a transient inlet history based on an engine system simulation. Emphases were put on the effects of regenerative cooling on shock formation inside the nozzle, and ramp rate on side load reduction. The results show that three types of asymmetric shock physics incur strong side loads: the generation of combustion wave, shock transitions, and shock pulsations across the nozzle lip, albeit the combustion wave can be avoided with sparklers during hot-firing. Results from both regenerative cooled and adiabatic wall boundary conditions capture the early shock transitions with corresponding side loads matching the measured secondary side load. It is theorized that the first transition from free-shock separation to restricted-shock separation is caused by the Coanda effect. After which the regeneratively cooled wall enhances the Coanda effect such that the supersonic jet stays attached, while the hot adiabatic wall fights off the Coanda effect, and the supersonic jet becomes detached most of the time. As a result, the computed peak side load and dominant frequency due to shock pulsation across the nozzle lip associated with the regeneratively cooled wall boundary condition match those of the test, while those associated with the adiabatic wall boundary condition are much too low. Moreover, shorter ramp time results show that higher ramp rate has the potential in reducing the nozzle side loads.

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Phase transition and dynamics of iron under ramp wave compression

The ramp wave compression experiments of iron with different thicknesses were performed on the magnetically driven ramp loading device CQ-4. Numerical simulations of this process were done with Hayes multi-phase equation of state (H-MEOS) and dynamic equations of phase transition. The calculated results of H-MEOS are in good agreement with those of shock phase transition, but are different from those under ramp wave compression. The reason for this is that the bulk modulus of the material in the Hayes model and the wave velocity are considered constant. Shock compression is a jump from the initial state to the final state, and the sound speed is related to the slope of the Rayleigh line. However, ramp compression is a continuous process, and the bulk modulus is no longer a constant but a function of pressure and temperature. Based on Murnaghan equation of state, the first-order correction of the bulk modulus on pressure in the Hayes model was carried out. The numerical results of the corrected H-MEOS agree well with those of pure iron in both ramp and shock compression phase transition experiments. The calculated results show that the relaxation time of iron is about 30 ns and the phase transition pressure is about 13 GPa. There are obvious differences between the isentropic and adiabatic process in terms of pressure–specific volume and temperature–pressure. The fluctuation of the sound speed after 13 GPa is caused by the phase transition.     

温度对冲击相变波传播的影响

冲击加载下,相界面的传播是一热力耦合过程。相变波阵面不仅是力学和物质间断面,也是温度界面。为考虑温度对相变波传播的影响,本文首先建立了相界面上的热传导方程和热力耦合的相变本构方程,然后采用一维特征线理论和有限差分数值计算相结合的方法,分析了温度界面和相变波的基本相互作用规律,进而给出了连续温度梯度下和绝热冲击下相变波传播规律。结果表明,温度对相变波传播的作用主要体现在两个方面,一方面是作为温度界面将与各类间断面相互作用,另一方面冲击相变波阵面后区域热力学状态变化影响卸载波结构。其原因在于相变方式（可逆、不可逆）和相变阈值应力具有强烈的温度相关性。     

闪长岩单轴加载过程中声发射和弹性波速度变化规律的研究

为研究闪长岩在单轴加载过程中的声发射和各向波速变化规律,在单轴阶段加载和循环阶段加载条件下,对闪长岩岩样破裂过程中的声发射累计数、不同应力水平不同方向的波速、切线模量、轴向应变速率进行了研究。实验结果表明:(1)随着应力水平的增高,声发射事件数不断增加,在高应力水平(约80%峰值强度)时,声发射累计数急剧增多,随后切线模量出现震荡变化。(2)在加载过程中,压密程度及裂纹扩展方向对波速产生了巨大的影响,导致不同方向波速在不同的应力水平呈现出不同的变化规律,由此可以推测破裂面位置和破裂模式。在较高应力水平下(约60%峰值强度),平行于加载方向的波速趋于稳定,而垂直于加载方向的波速则持续下降,故用垂直于加载方向传播的波速预测岩石的破坏更具可靠性。(3)随着应力的增加,应变速率有逐渐减小的趋势,但临近岩石破裂时无异常变化出现,说明利用变形观测难以预测此类岩石的破坏。以上研究表明,根据纵波波速、声发射累计数和切线模量的变化可以有效预测岩石的破坏。     

High-pressure strength of aluminum under quasi-isentropic loading

Under shock loading, metals typically increase in strength with shock pressure initially but at higher stresses will eventually soften due to thermal effects. Under isentropic loading, thermal effects are minimized, so strength should rise to much higher levels. To date, though, study of strength under isentropic loading has been minimal. Here, we report new experimental results for magnetic ramp loading and impact by layered impactors in which the strength of 6061-T6 aluminum is measured under quasi-isentropic loading to stresses as high as 55 GPa. Strength is inferred from measured velocity histories using Lagrangian analysis of the loading and unloading responses; strength is related to the difference of these two responses. A simplified method to infer strength directly from a single velocity history is also presented. Measured strengths are consistent with shock loading and instability growth results to about 30 GPa but are somewhat higher than shock data for higher stresses. The current results also agree reasonably well with the Steinberg–Guinan strength model. Significant relaxation is observed as the peak stress is reached due to rate dependence and perhaps other mechanisms; accounting for this rate dependence is necessary for a valid comparison with other results.     

Computational study of curved shock–vortex interaction

The interaction between a curved shock wave and a compressible vortex is numerically investigated. The investigation concentrates on the local deformation of the shock structure due to the shock–vortex interaction. The essentially non‐oscillatory (ENO) scheme is used to solve the unsteady two‐dimensional Euler equations. A curved shock wave is obtained by the diffraction of an initially planar shock wave around a right‐angled corner and then allowed to interact with a strong compressible vortex superimposed on the flow. The same vortex affects the shock wave differently depending on the placement of the vortex because of the varying strength of the shock wave. This effect could range from a non‐symmetric deformation of the shock wave to a local disruption in the shock structure depending on the strength of the shock wave in the interaction region. This process leading to a local disruption in the shock structure is analyzed in detail. It is shown that such a disruption in the shock structure can be predicted by simple one‐dimensional considerations. Copyright © 1999 John Wiley & Sons, Ltd.     

A holographic interferometric study of shock wave focusing in a circular reflector

A holographic interferometric study was made of the focusing of reflected shock waves from a circular reflector. A diaphragmless shock tube was used for incident shock Mach numbers ranging from 1.03 to 1.74. Hence, the process of reflected shock wave focusing was quantitatively observed. It is found that a converging shock wave along the curved wall undergoes an unsteady evolution of mach reflection and its focusing is, therefore, subject to the evolution of the process of shock wave reflections. The collision of triple points terminates the focusing process at the geometrical focus. In order to interprete quantitatively these interferograms, a numerical simulation using an Eulerian solver combined with adaptive unstructured grids was carried out. It is found numerically that the highest density appears immediately after the triple point collision. This implies that the final stage of focusing is mainly determined by the interaction between shock waves and vortices. The interaction of finite strength shock waves, hence, prevents a curved shock wave from creating the infinite increase of density or pressure at a focal point which is otherwise predicted by the linear acoustic theory.     

Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials

The compressive behavior of open-cell aluminum alloy foam and stainless steel woven textile core materials have been investigated at three different deformation rate regimes. Quasi-static compressive tests were performed using a miniature loading frame, intermediate rates were achieved using a stored energy Kolsky bar, and high strain rate tests were performed using a light gas gun.In agreement with previous studies on foam materials, the strain rate was not found to have a significant effect on the plateau stress of metallic foams. For all the tests, real time imaging of the specimen combined with digital image correlation analysis allowed the determination of local deformation fields and failure modes. For the Kolsky bar tests, the deformations in the foam specimen were found to be more distributed than for the quasi-static test, which is attributed to moderate inertia effects. The differences in failure mode are more dramatic for the gas gun experiments, where a full compaction shock wave is generated at the impact surface. The stresses in front and behind the shock wave front were determined by means of direct and reverse gas gun impact tests, i.e., stationary and launched specimen, respectively. A one-dimensional shock wave model based on an idealized foam behavior is employed to gain insight into the stress history measurements. We show that the predictions of the model are consistent with the experimental observations. Woven textile materials exhibited moderate dependence of strength on the deformation rate in comparison with open-cell foam materials.     

Detonation Initiation by Shock Reflection from an Orifice Plate

Results from an experimental investigation of the interaction of a “non-ideal” shock wave and a single obstacle are reported. The shock wave is produced ahead of an accelerated flame in a 14 cm inner-diameter tube partially filled with orifice plates. The shock wave interacts with a single larger blockage orifice plate placed 15–45 cm after the last orifice plate in the flame acceleration section of the tube. Experiments were performed with stoichiometric ethylene–oxygen mixtures with varying amounts of nitrogen dilution at atmospheric pressure and temperature. The critical nitrogen dilution was found for detonation initiation. It is shown that detonation initiation occurs if the chemical induction time based on the reflected shock state is shorter than the time required for an acoustic wave to traverse the orifice plate upstream surface, from the inner to the outer diameter. The similarity between the present results and those obtained from previous investigators looking at detonation initiation by ideal shock reflection produced in a shock tube indicates that the phenomenon is not sensitive to the detailed structure of the shock front but only on the average shock strength.This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

磁驱动准等熵平面压缩和超高速飞片发射实验技术原理、装置及应用

利用脉冲大电流产生随时间平滑上升的磁压,实现对样品的准等熵平面压缩和超高速飞片发射,是近十年来发展和完善起来的一种新型的强动态斜波加载技术(ramp wave loading).本文简述了其原理、加载装置及数据处理方法等方面的研究进展,同时着重评述利用该技术和方法开展高压物态方程、材料动力学响应方面的研究进展,并对该技术在冲击动力学、天体物理和高能量密度物理等方面的应用前景进行了展望.      

On the influence of elevated surface temperatures on hypersonic shock wave/boundary layer interaction at a heated ramp model

Although important flow parameters as Mach number, Reynolds number and total enthalpy can be reproduced in most hypersonic experiments quite well, due to different surface temperature effects in wind tunnel and flight, scaling as well as specific flow properties of shock wave/boundary layer interactions are different. This especially holds for short-duration facilities like, e.g. shock tunnels where due to short running times the models remain more or less at ambient temperature. To overcome this shortcoming, an experimental study has been conducted using a preheatable ramp model with 15° ramp angle. This allowed us to adjust the surfaces to an arbitrary temperature just before the experiment started. Pressure and heat flux measurements clearly showed the effect of varying surface and free stream temperatures. These results are supported by schlieren pictures and infrared measurements. The comparison of the measurements with theoretical and numerical results shows a good agreement. Separation bubble scaling laws proposed by Katzer and Davis have been applied and partially confirmed using the local conditions of the boundary layer at separation.     

斜波压缩下HMX晶体的弹塑性行为

开展了（010）、（011）晶向HMX晶体的斜波压缩实验,获得了约15 GPa压力下的速度响应剖面。实验结果表明,HMX单晶存在明显弹塑性转变行为,且速度波形有下降趋势,这是材料的黏性效应导致,材料的弹性极限随着样品厚度增加而变化,不同晶向的材料动力学特性存在差异。结合Hobenemser-Prager黏弹塑性本构关系和三阶Birch-Murnaghan物态方程开展了HMX晶体斜波压缩物理过程的数值模拟,计算结果可以很好地描述HMX晶体的弹塑性转变这一物理过程。     

可燃气体中激波聚焦的点火特性

数值模拟了二维平面激波从抛物面上反射在可燃气体中聚焦的过程，研究了形 成爆轰波的点火特性. 对理想化学当量比氢气/空气混合气体，在初始压强20kPa的条件下， 马赫数2.6-2.8的激波聚焦能产生两个点火区：第1个点火区是反射激波会聚引起的，第 2个点火区是由入射激波在抛物面上发生马赫反射引起的. 这种条件下流场中会出现爆燃转 爆轰，起爆点分别分布在管道壁面、抛物反射面和第2点火区附近. 起爆机理分别为激波管 道壁面反射、点火诱导激波的抛物面反射和点火诱导的激波与第2点火区产生的爆燃波的相 互作用. 不同的点火和起爆过程导致了不同的流场波系结构，同时影响了爆轰波传播的波动 力学过程.     

激波与转捩边界层干扰非定常特性数值分析

激波与边界层干扰的非定常问题是高速飞行器气动设计中基础研究内容之一.以往研究主要针对层流和湍流干扰,在分离激波低频振荡及其内在机理方面存在着上游机制和下游机制两类截然不同的理论解释.分析激波与转捩边界层干扰下非定常运动现象有助于进一步加深理解边界层状态以及分离泡结构对低频振荡特性的影响规律,为揭示其产生机理指出新的方向.采用直接数值模拟方法对来流马赫数2.9,24?压缩拐角内激波与转捩边界层干扰下激波的非定常运动特性进行了数值分析.通过在拐角上游平板特定的流向位置添加吹吸扰动激发流动转捩,使得进入拐角的边界层处于转捩初期阶段.在验证了计算程序可靠性的基础上,详细分析了转捩干扰下激波运动的间歇性和振荡特征,着重研究了分离泡展向三维结构对激波振荡特性的影响规律,最后还初步探索了转捩干扰下激波低频振荡产生的物理机制.研究结果表明:分离激波的非定常运动仍存在强间歇性和低频振荡特征,其时间尺度约为上游无干扰区内脉动信号特征尺度的10倍量级;分离泡展向三维结构不会对分离激波的低频振荡特征产生实质影响.依据瞬态脉动流场的低通滤波结果,转捩干扰下激波低频振荡的诱因来源于拐角干扰区下游,与流场中分离泡的收缩/膨胀运动存在一定的关联.     

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

脆性材料动态强度应变率效应

通过求解波动方程,结合有限结构-时间破坏准则,得到了动态载荷下脆性材料单轴拉伸强度应变 率效应的解析表达式。分析结果表明:材料动态强度的应变率效应具有明显的结构响应特征,即材料动态强 度除与应变率和静态参数相关外,还显著地依赖于外载荷结构及其与材料间的相互作用,因而动态强度不是 表征材料动态破坏的内禀材料性质;此外,由于在不同的外载荷条件下材料将表现出不同的动态强度,这是导 致实验结果离散性大的内在因素。