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.     

Propagation of converging spherical deformation waves in a heteromodular elastic medium

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions.     

模型复合材料弹塑性界面应力分析

由纤维增强弹塑性基体所产生的界面具有弹塑性力学行为。考虑到一般材料的塑性变形都遵循幂硬化规律,对模型复合材料的界面进行弹性和应变硬化状态下的变形规律及其应力分析。以纤维拔出试验为研究模型,将界面分成弹性区和塑性区。利用界面应力剪滞理论,分别建立弹性区和塑性区的界面力学基本方程。选择适当的位移函数满足基本方程及埋入纤维的边界条件,再按位移函数求出弹性区和塑性区的界面剪应力。推导出平均界面剪应力与纤维     

受压混凝土的不可逆变形与刚度衰减的研究

本文根据内变量定义，引入表征塑性发展和产生损伤的内变量，根据塑性力学和损伤学方法，结合混凝土单调受压应力一应变全曲线的试验结果，对混凝土不可逆变形和刚度衰减进行了研究，经与反复加卸载试验结果相比，吻合较好，如果将其推广至反复加卸载试验极为困难的复杂受力工况将是方便有效的。     

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock's ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.     

冲击荷载作用下滤波混凝土的动态响应与层裂损伤数值研究

借鉴局域共振材料的工作机制,通过在混凝土基体中嵌入滤波单元,设计出具有应力波衰减特性的滤波混凝土。通过将滤波混凝土结构简化为质量弹簧力学系统来分析滤波混凝土对应力波的衰减机制。采用数值模拟方法,对比研究了冲击荷载作用下普通混凝土模型和滤波混凝土模型中应力波的传播特性和层裂破坏模式。通过参数分析,研究了滤波单元的材料和几何属性对其储能效果的影响。研究结果表明：滤波单元有效降低了混凝土基体中应力波的传播速度和应力峰值;滤波单元的储能机制有效降低了混凝土基体中的能量;金属球的质量越大,滤波单元的储能效果越好,但弹性层的弹性模量和厚度需要通过适当分析进行设计以实现滤波单元的储能最大化;滤波混凝土基体的局部损伤耗散了荷载中的大量能量,有效降低了结构自由面附近的破坏程度。     

饱水对煤层顶板砂岩单轴压缩破坏能量影响的分析

为研究饱水对砂岩力学参数和能量特征的影响,利用RMT-150B岩石力学系统对煤层顶板砂岩自然和饱水试样进行单轴压缩试验。试验结果表明:饱水对砂岩试样的强度和变形参数均有不同程度的影响,软化系数为0.79,弹性模量降幅为5.25%,变形模量降幅为5.92%;饱水后砂岩试样峰值前吸收能量、可释放弹性能和耗散能均有不同程度降低,吸收能量降幅36.8%,可释放弹性能降幅为34.4%,耗散能降幅为57.7%;饱水后砂岩储蓄能量的能力有较大减弱,脆性减弱,塑性明显增强;饱水砂岩试样压缩过程中积蓄可释放能难以使试样滑移破坏,仍需要吸收部分能量使试样逐步失稳破坏;饱水对砂岩试样压缩过程吸收能量、可释放能量比例关系的影响较小,而对耗散能比例关系的影响较大;自然状态下砂岩试样峰值前相同应变条件下吸收能量、可释放能均明显高于饱水试样对应能量值;深部巷道位置确定和支护设计时应充分考虑水对巷道围岩弱化的影响,对于完整坚硬围岩采用高压注水软化可有效防止冲击地压发生和减缓灾害程度。     

Attenuation of shock waves propagating in polyurethane foams

Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities = 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m³. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number.     

Twin-characteristic-parameter solution of axisymmetric dynamic plastic buckling for cylindrical shells under axial compression waves

In the present investigation on the dynamic plastic buckling of cylindrical shells under axial compression waves, the critical axial stress and the exponential parameter of inertia terms in stability equations are treated as a couple of characteristic parameters. The criterion of transformation and conservation of energy in the process of buckling initiation is used to derive the supplementary restraint equation of buckling deformation at the fronts of axial elastic and plastic compression waves. The supplementary restraint equation, stability equations, boundary conditions and continuity conditions constitute the necessary and sufficient conditions of determining the two characteristic parameters. Two characteristic equations are derived for the two characteristic parameters. The critical axial stress or the critical buckling time, the exponential parameter of inertia terms and the initial modes of buckling deformation are calculated quantitatively from the solution of the characteristic equations.     

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

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。     

The elastic–plastic behaviour of foam under shock loading

An experimental investigation of the elastic–plastic nature of shock wave propagation in foams was undertaken. The study involved experimental blast wave and shock tube loading of three foams, two polyurethane open-cell foams and a low-density polyethylene closed-cell foam. Evidence of precursor waves was observed in all three foam samples under various compressive wave loadings. Experiments with an impermeable membrane are used to determine if the precursor wave in an open-cell foam is a result of gas filtration or an elastic response of the foam. The differences between quasi-static and shock compression of foams is discussed in terms of their compressive strain histories and the implications for the energy absorption capacity of foam in both loading scenarios. Through a comparison of shock tube and blast wave loading techniques, suggestions are made concerning the accurate measurements of the principal shock Hugoniot in foams.     

裂隙挤喷流对孔隙介质排水体积模量的影响

实际岩石比如沉积形成的岩石往往是裂隙和孔隙并存的孔隙介质. 由于扁状的裂隙与近似球形或圆管形的孔隙具有不同的可压缩性,当孔隙介质受压时,液体会从易压缩的裂隙中挤出流入不易压缩的孔隙中,这种挤喷流会引起弹性模量的频散和能量的耗散. 着重研究了裂隙挤喷流和液体可压缩性对孔道变形的影响,推导出了动载荷作用下排水体积模量的表达式. 与挤喷流相关的裂隙附加柔度会引起排水体积模量随频率变化,使得孔隙介质呈现黏弹性. 频率越高,模量的实部越大,岩石抵抗变形的能力越强. 而模量的虚部体现了挤喷流对能量的耗散. 裂隙密度主要决定模量频散的幅度以及能量耗散的强度,且裂隙密度越大,模量频散幅度越大,能量耗散也越强. 裂隙的纵横比主要决定模量频散速率最快或能量耗散最强时对应的特征频率. 若孔隙介质中不含有裂隙,即裂隙密度是0时,排水体积模量退化为Biot理论中的排水体积模量.     

An indentation technique for estimating the energy density as fracture toughness with Berkovich indenter for ductile bulk materials

A technique is proposed to estimate the energy density as fracture toughness for ductile bulk materials with an indentation system equipped with a Berkovich indenter based on the theory of plastic deformation energy transforming into the indentation energy of fracture. With progressive increase of penetration loads, the material damage is exhibited on the effective elastic modulus. A quadratic polynomial relationship between the plastic penetration depth and penetration load, and an approximate linear relationship between logarithmic plastic penetration depth and logarithmic effective elastic modulus are exhibited by indentation investigation with Berkovich indenter. The parameter of damage variable is proposed to determine the critical effective elastic modulus at the fracture point. And the strain energy density factor is calculated according to the equations of penetration load, plastic penetration depth and effective elastic modulus. The fracture toughness of aluminum alloy and stainless steel are evaluated by both indentation tests and K_IC fracture toughness tests. The predicted S_cr values of indentation tests are in good agreement with experimental results of CT tests.     

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

Dynamic deformation and failure mechanisms in polycrystalline ceramics are investigated through constitutive modeling and numerical simulation. Two ceramics are studied: silicon carbide (SiC, hexagonal crystal structure) and aluminum oxynitride (AlON, cubic crystal structure). Three dimensional finite element simulations incorporate nonlinear anisotropic elasticity for behavior of single crystals within polycrystalline aggregates, cohesive zone models for intergranular fracture, and contact interactions among fractured interfaces. Boundary conditions considered include uniaxial strain compression, uniaxial stress compression, and shear with varying confinement, all at high loading rates. Results for both materials demonstrate shear-induced dilatation and increasing shear strength with increasing confining pressure. Failure statistics for unconfined loading exhibit a smaller Weibull modulus (corresponding to greater scatter in peak failure strength) in AlON than in SiC, likely a result of lower prescribed cohesive fracture strength and greater elastic anisotropy in the former. In both materials, the predicted Weibull modulus tends to decrease with an increasing number of grains contained in the simulated microstructure.     

平板撞击下C30混凝土中冲击波的传播特性

采用1级气炮加载技术和锰铜应力计多点测试技术,开展了C30混凝土在平板撞击条件下的冲击压缩实验研究。基于锰铜应力计实测的应力波形,研究了混凝土中冲击波的传播特性,结果显示冲击波的应力峰值随传播距离呈现明显的衰减特性,衰减过程可分为2个阶段。在早期阶段,卸载波没有赶上前面传播的冲击波,冲击波应力峰值衰减较慢,主要是混凝土材料的本构粘性效应所引起的;而后期阶段应力峰值的快速衰减则归因于混凝土材料的本构粘性效应、后续的来自飞片自由面的反射波追赶卸载、边侧稀疏波卸载及波传播的几何弥散效应的共同作用;另外,冲击波在混凝土中传播的升时也随着传播距离逐渐增大,即由强间断波逐渐转化为弱间断波。     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

低相变阈值金属高压加载下的相变层裂特性

采用激光速度干涉仪（VISAR）和X光联合测试技术,在冲击压力远高于相变应力加载下,实验研究低相变阈值金属FeMnNi合金的相变层裂特性,结果发现等厚对称碰撞加载下FeMnNi合金出现反常的层裂行为。针对该反常的层裂行为,利用塑性波、相变波、稀疏波和逆相变引发的稀疏冲击波的相互作用过程进行分析,结果表明,该实验状态下FeMnNi合金样品存在相变和逆相变行为,逆相变引发的稀疏冲击波是导致反常层裂行为的主要因素。