脆性颗粒材料的应变率效应机理研究

利用分离式Hopkinson压杆（SHPB）,对干燥石英砂进行了被动围压下的动态压缩实验,发现石英砂表现出了明显应变率效应。通过激光粒度分析测量了动静态压缩后的试件的级配曲线,发现同一应力水平下准静态压缩比动态压缩后的试件的颗粒破碎量更大。而通过拟合相对破碎率与外力功之间的关系,发现准静态压缩在颗粒破碎方面能量利用率更高也即破碎效率更高,而这正是脆性颗粒材料应变率效应的本质原因。     

爆炸载荷下脆性颗粒体系破碎特性的数值研究

试验发现,以球形TNT为中心爆源,球形玻璃珠构成的颗粒和球壳中发生破碎的颗粒体积分数随当量比（颗粒球壳的质量与TNT炸药的质量比）的增加呈现指数衰减规律。采用有限元与离散元耦合的连续非连续数值方法,揭示了中心炸药起爆后颗粒环壳内爆炸波的传播衰减和在环壳外界面反射后的稀疏卸载过程。由于爆炸波的短脉冲特性,颗粒内部应力场始终处于应力非均衡状态,采用应力均衡状态下颗粒破碎强度的Weibull分布会得到远高于试验测得的破碎颗粒体积分数。因此采用破坏波传播特征时间内的平均诱导应力而非瞬时诱导应力作为颗粒破碎强度的应力指标,并通过试验结果确定破坏波传播特征时间。考虑了应力传播的非均匀性对于颗粒破碎的影响,得到了平均诱导应力峰值的概率分布随比例距离的变化规律,结合修正后的颗粒破碎强度Weibull分布建立了破碎颗粒体积分数随比例距离的变化模型。     

漂珠颗粒材料静动态力学性能与破碎机理研究

为考察脆性空心颗粒材料冲击载荷下的力学特性,以具有不同粒径分布的粉煤灰漂珠为研究对象,对其静动态力学性能进行实验研究。通过限制颗粒材料压缩应变为50%,分析颗粒破碎率和破碎机理与材料宏观应变率效应的关系。结果表明:（1）不同粒径的漂珠颗粒材料在动态压缩下较准静态压缩下颗粒材料的强度均有明显的增强,在0.001和150 s?1大小颗粒的强度分别提高200%和195%,在150和300 s?1大小颗粒的强度分别提高39%和51.5%,在300和800 s?1大小颗粒的强度并未发生明显的变化;（2）在相同加载速度下粒径较小的颗粒比大粒径颗粒的强度和吸能效果分别提高35%～40%和35%～48%;（3）对破碎后颗粒粒径分布曲线分析可知,随着加载速度的增加,大小颗粒的破碎率和破碎程度都会增大,且在相同加载速度下大颗粒的破碎率较小颗粒的破碎率高;（4）Hardin破碎势分析表明,单位输入能量下颗粒的相对破碎势随冲击速度增大而减小,动态冲击下用于颗粒破碎的能量利用率降低,从而导致材料在相同压缩量下产生更高的能量耗散和应力水平,即表现为宏观的应变率效应。     

颗粒破碎的微观力学模拟

基于颗粒尺度建立了考虑颗粒破碎过程中能量耗散的微观力学模型。为了模拟颗粒体的破碎过程和侧向应力的影响,把胶结在一起的三个等粒径的颗粒体当作颗粒破碎体。基于颗粒破碎准则和热力学原理,考虑了颗粒破碎过程中颗粒接触点之间的塑性滑移和颗粒转动以及侧向应力作用,通过颗粒破碎体内部颗粒之间的接触破碎来模拟颗粒体的破碎。计算结果表明:本文所提出的微观力学模型可以模拟胶结在一起的大颗粒的破碎过程;颗粒之间的微观力学参数对颗粒破碎过程中的力、塑性滑移、颗粒的转动角有不同程度的影响;力-位移关系曲线在破碎前是线性的,而颗粒破碎时竖向力迅速降低到较小值,并伴有颗粒的转动。     

影响冲击载荷下脆性材料碎片尺度的因素

概括回顾近年我们针对脆性材料受冲击拉伸载荷时的断裂及破碎现象的理论分析及数值模拟成果。重点分析碎片尺度对材料参数及加载速率的依赖关系。通过量纲分析,动力学模拟以及数值实验,建立了一个普适性的无量纲关系用以评估碎片尺度。将本研究结果与其他理论及现有实验结果进行的比较表明本模型更为完善合理。     

基于细观力学的矿石颗粒破碎特性研究

为研究矿石颗粒动态破碎过程中内部力学变化和矿石颗粒宏观破碎状态,从细观力学的角度出发,以二维巴西圆盘为研究对象,运用离散元法分析其内部力链变化情况和宏观破碎情况。采用钨矿石作为研究对象,建立了矿石颗粒模型,得到颗粒系统内部粘结键强度的判断依据和冲量函数。仿真计算结果表明:强力链在力链网络中所占的比例较低,且多集中在载荷端和支撑端的接触部位;圆盘内部力链累积冲量随时间的增加而不断增大,并且受到颗粒内部粘结键断裂的影响,粘结键断裂数量越多,颗粒内部力和冲量下降程度越大。     

高应变率加载下材料的损伤破碎规律

对材料损伤破碎规律的分析是研究材料损伤断裂行为的一种有效途径。本文着重介绍了高应变率加载下材料损伤破碎规律的研究进展、基于损伤断裂机理的研究以及材料损伤破碎过程自相似性的分形理论研究,讨论了材料损伤破碎规律与材料自身属性和外部加载条件的相互关系。     

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。     

可破碎颗粒体在动力载荷下的耗能特性

采用离散元的数值方法, 通过连接键将若干小颗粒绑定为一个具有不规则外形的大颗粒体, 设置不同连接键强度模拟了颗粒体在外加动力载荷下破碎过程, 并探讨其中系统能量耗散特性. 计算结果表明, 颗粒体的破碎程度决定了系统能量耗散率, 即内部耗能占外界输入能量的比例. 破碎率越高, 颗粒间相互摩擦和碰撞越剧烈,系统能量耗散率越高. 同时, 在循环载荷下系统内颗粒体破碎绝大部分发生在加载初期, 随着颗粒体的分解破碎速率逐渐减小, 系统耗能能力也随之降低.      

基于连续-非连续单元法的三维脆性颗粒冲击破碎特性分析

通过在连续-非连续单元法(CDEM)中引入考虑应变率效应的断裂能本构以及能量统计算法,实现了球体冲击破碎过程中损伤破裂程度及能量演化的定量分析。计算结果表明,冲击破碎过程分为接触蓄能阶段、损伤破碎阶段和碎块飞散阶段。首先,颗粒的部分动能转化为单元弹性变形能,随后这部分变形能和动能迅速转化为摩擦消耗、阻尼消耗及弹簧断裂能,破碎基本完全后碎块继续飞散。不同冲击速度下,颗粒分别出现了反弹、开裂、破碎和粉碎的现象。随冲击速度的增加,D50的变化速率逐渐放缓,破碎块度逐渐趋于稳定;破裂度、损伤度以及平均损伤因子的变化速率先增加后放缓,颗粒破坏以拉伸破坏为主。以上结论可为脆性材料冲击破碎工艺的优化设计提供依据。     

不同加载速度下脆性颗粒的破坏特性

对直径为8mm的K9玻璃球进行了加载速度为2×10-7和2×10-6m/s的准静态单轴压缩实验以及加载速度为3.4、7.1和10.6m/s的动态单轴压缩实验,研究了K9玻璃单颗粒破碎强度的Weibull分布特性,结合破碎产物的形貌特征,分析了不同加载速度下脆性材料拉伸破坏机制和剪切破坏机制的转变过程,提出了一种拉剪耦合的时序破坏模型,由此揭示了加载速度与3个破坏区的关系。考虑拉伸和剪切失效准则,应用ABAQUS软件进行数值模拟,并初步验证了该破坏模型的冲击过程。研究结果对于认识脆性颗粒材料的动态破坏具有很好的参考意义。     

侧向撞击荷载作用下内八边形空心钢筋混凝土柱的动力响应

相比于实心钢筋混凝土柱,空心钢筋混凝土柱具有自重轻和截面扩展好等优点,被广泛地用作桥墩,由此其不可避免地会受到船舶的撞击。本文中进行6根内八边形空心钢筋混凝土柱和4根内衬八边形钢管空心钢筋混凝土柱的动力响应的实验。在实验中记录了构件破坏形态、撞击力时程曲线和跨中位移时程曲线,并从撞击高度、边界条件和钢板厚度等方面分析了构件的耐撞性能。结果表明:内八边形钢筋混凝土柱和内衬八边形钢管空心钢筋混凝土柱在撞击荷载作用下的破坏形态主要分为两种破坏类型,分别为局部型破坏和整体型破坏;撞击高度越大构件破坏越严重;两端固定对构件的耐撞击性能有提升作用;钢管厚度对构件的耐撞击性能有较明显的提升作用。     

Investigation of dynamic response of brittle materials under high-rate loading

In this paper the dynamic behaviour of brittle materials subjected to high-rate loading is investigated. Taking the effect of damage into account, a direct, explicit and quantitative method is developed to determine the average fragment size generated by crack tension with a constant strain rate. The theoretical predictions of the fragment size are compared with the experimental data, and it is found that the predicted values agree reasonably well with the test results. Furthermore, the dependence of the throw velocity on the strain rate is discussed. The value of the throw velocity increases with the increment of the strain rate. Finally, the properties of the fragmentation in a single borehole blasting experiment are numerically simulated.     

Fracture of brittle geomaterial with a circular hole under biaxial loading

The influence of boundary conditions on the fracture of brittle geomaterial in the stress concentration zone under biaxial loading with account for the size effect is theoretically and experimentally studied. The calculation results are compared with the experimental data.     

Search for conditions of compressive fracture of hard brittle ceramics at impact loading

In this paper we discuss three different experimental configurations to diagnosing the modes of inelastic deformation and to evaluating the failure thresholds at shock compression of hard brittle solids. One of the manifestations of brittle material response is the failure wave phenomenon, which has been previously observed in shock-compressed glasses. However, based on the measurements from our “theory critical” experiments, both alumina and boron carbide did not exhibit this phenomenon. In experiments with free and pre-stressed ceramics, while the Hugoniot elastic limit (HEL) in high-density B₄C ceramic was found to be very sensitive to the transverse stress, it was found relatively less sensitive in Al₂O₃, implying brittle response of the boron carbide and ductile behavior of alumina. To further investigate the effects of stress states on the shock response of brittle materials, a “divergent flow or spherical shock wave” based plate impact experimental technique was employed to vary the ratio of longitudinal and transversal stresses and to probe conditions for compressive fracture thresholds. Two different experimental approaches were considered to generate both longitudinal and shear waves in the target through the impact of convex flyer plates. In the ceramic target plates, the shear wave separates a region of highly divergent flow behind the decaying spherical longitudinal shock wave and a region of low-divergent flow. Experiments with divergent shock loading of alumina and boron carbide ceramic plates coupled with computer simulations demonstrated the validity of these experimental approaches to develop a better understanding of fracture phenomena.     

Three-dimensional elliptic crack under impact loading

The dynamic stress intensity factor of a three-dimensional elliptic crack under impact loading is determined with the finite element method. The computation results can take into account the influence of time and the ratio of the wave speeds on the stress intensity factor. The present method is suitable not only for three-dimensional dynamic crack, but also for three-dimensional dynamic contact. Project supported by the National Natural Science Foundation of China (No. K19672007).     

Analysis of reinforced-concrete strength under impact loading

A mathematical model is proposed to describe deformation and fracture of reinforced concrete under impact loading within the framework of mechanics of continuous media. The problem of the impact of steel cylindrical projectiles on rectangular slabs made of reinforced concrete is solved. The results of mathematical modeling are in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 165–173, November–December, 2006.     

Motion of soil-working tool under impact loading

The cyclic process of penetration of soil by a tool under periodic impact loading was described mathematically. The analysis was based on a piecewise-linear approximation of the dependence of the soil frontal resistance force on tool displacement—an approximation reflecting modern views on the principles of soil-tool interaction.Different intervals in the cycle of steady-state motion of the tool, and different interaction regimes were considered. The mean tool velocity for borehole forming was determined. Conditions for a minimum energy requirement in the cyclic process were formulated, and the influence of frequency on the laws governing the interaction was established.     

Snapping of an elastica under various loading mechanisms

This paper studies the snap-through buckling of a hinged elastica subject to a midpoint force. The focus is placed on how different load models affect the deformation and snapping load. Three different load models are considered. In the first model, the point force is fixed onto a midpoint of the elastica. In the second model, the point force is fixed on a central line in space. In the third model, the external force is applied through a rigid bar, which is allowed to slide along the central line in space. When the loaded elastica deforms symmetrically, as in the case when the magnitude of the point force is small, there is no difference between these three load models. However, when the elastica deforms unsymmetrically, the three load models produce different results. Vibration method is used to determine the stability of the equilibrium configurations. It is found that the elastica may snap via either a sub-critical pitchfork bifurcation or a limit-point bifurcation. If the elastica snaps via a sub-critical pitchfork bifurcation, the pre-snapping deformation is symmetric. If the elastica snaps via a limit-point bifurcation, on the other hand, the pre-snapping deformation is unsymmetric. For a specified initial shape of the elastica, different load models predict different snapping loads and pre-snapping deformations. The theoretical predictions are confirmed by experimental observations.     

Plastic limit state of a thin hollow disk under thermomechanical loading

This paper considers the plastic limit state of a thin hollow axisymmetric disk subjected to thermomechanical loading with a uniform pressure distribution on the inner contour and a temperature increasing during deformation. A semi-analytical solution of the formulated boundary-value problem is obtained. Qualitative features of the behavior of the solution with a loss of the load-carrying capacity of the disk are investigated.