INFLUENCE OF LOADING RATE ON DYNAMIC FRACTURE BEHAVIOR OF FIBER-REINFORCED COMPOSITES

The effect of loading rate on the dynamic fracture properties and the failure mechanisms of glass fiber-reinforced composite materials under mode I fracture is studied. Dynamic reflective caustic experiments are carried out for two loading rates. By measuring the characteristic dimensions of the shadow spots during the caustic experiments, the dynamic SIFs are calculated for different loading rates. The experimental results indicate that the dynamic fracture toughness Kid increases remarkably with increasing loading rate, and the crack grows faster under the high-velocity impact. Moreover, by examining the crack growth routes and the fracture surfaces, it is shown that the loading rate also greatly affects the failure mechanisms at micro-scale.     

Combined grain size, strain rate and loading condition effects on mechanical behavior of nanocrystalline Cu under high strain rates

Molecular dynamics simulations of nanocrys-talline Cu with average grain sizes of 3.1 nm, 6.2 nm, 12.4 nm and 18.6 nm under uniaxial strain and stress tension at strain rates of 10 8 s 1 , 10 9 s 1 and 10 10 s 1 are performed to study the combined grain size, strain rate and loading condition effects on mechanical properties. It is found that the strength of nanocrystalline Cu increases as grain size increases regardless of loading condition. Both the strength and ductility of nanocrystalline Cu increase with strain rate except that there is no monotonic relation between the strength and strain rate for specimens under uniaxial strain loading. Moreover, the strength and ductility of specimens under uniaxial strain loading are lower than those under uniaxial stress loading. The nucleation of voids at grain boundaries and their subsequent growth characterize the failure of specimens under uniaxial strain loading, while grain boundary sliding and necking dominate the failure of specimens under uniaxial stress loading. The rate dependent strength is mainly caused by the dynamic wave effect that limits dislocation motion, while combined twinning and slipping mechanism makes the material more ductile at higher strain rates.     

DYNAMIC FRACTURE ANALYSIS OF AGED GLASSY POLYCARBONATE BY THE METHOD OF CAUSTICS

The purpose of this work is to investigate the dynamic fracture properties of glassy polycarbonate （PC） with different aging times. The optical method of caustics is adopted in which the shadow spot patterns are recorded by a high speed camera during the dynamic fracture process. Then, the dynamic crack propagation, the stress intensity factor （SIF） and the dynamic fracture toughness of aged PC are obtained through an analysis of the characteristic size of caustic pattern. Moreover, by combining with the investigation of the fracture surface and the energy release rate analysis, the influence of aging time on the dynamic fracture behavior is discussed. Results show that the dynamic fracture toughness and critical energy release rate of PC decreases with aging time for short aging times, whereas they have little change or even increase for longer aging times. Therefore, aging modifies the mechanical properties especially the dynamic fracture properties of PC nonlinearly, not linearly as generally thought of.     

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvature-dominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.     

Experimental study of the blockage boundary for dense-phase pneumatic conveying of powders through a horizontal slit

The estimation of the blockage boundary for pneumatic conveying through a slit is of significant importance.In this paper,we investigate the characteristics for blockage of powder(48 μm average diameter)through a horizontal slit(1.6 m × 0.05 m × 0.002 m).The results show that the required critical solid mass flow rate increases as the superficial air velocity increases superficial air velocity.The solid loading ratio and superficial air velocity displayed a decreasing power law relationship.This finding agrees with existing theory and experimental results.However,a minimum inlet solid loading ratio exists.When the air velocity is greater than the corresponding air velocity of the minimum solid loading ratio,the solid loading ratio exhibits an increasing trend in power law.We also found that when the inlet conveying pressure increased,the critical solid mass flow rate required for blockage,the inlet solid loading ratio,and the minimum inlet solid loading ratio increased.     

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.     

Mechanical behaviors and damage constitutive model of ceramics under shock compression

One-stage light gas gun was utilized to study the dynamic mechanical properties of AD90 alumina subjected to the shock loading. Manganin gauges were adopted to obtain the stress-time histories. The velocity interferometer system for any reflector （VISAR） was used to obtain the free surface velocity profile and determine the Hugoniot elastic limit. The Hugoniot curves were fitted with the experimental data. From Hugoniot curves the compressive behaviors of AD90 alumina were found to change typically from elastic to ＂plastic＂. The dynamic mechanical behaviors for alumina under impact loadings were analyzed by using the path line principle of Lagrange analysis, including the nonlinear characteristics, the strain rate dependence, the dispersion and declination of shock wave in the material. A damage model applicable to ceramics subjected to dynamic compressive loading has been developed. The model was based on the damage micromechanics and wing crack nucleation and growth. The effects of parameters of both the micro-cracks nucleation and the initial crack size on the dynamic fracture strength were discussed. The results of the dynamic damage evolution model were compared with the experimental results and a good agreement was found.     

Size and strain rate effects in tensile strength of penta-twinned Ag nanowires

Penta-twinned Ag nanowires(pt-AgNWs) have recently attracted much attention due to their interesting mechanical and physical properties. Here we perform largescale atomistic simulations to investigate the influence of sample size and strain rate on the tensile strength of pt-AgNWs. The simulation results show an apparent size effect in that the nanowire strength(defined as the critical stress for dislocation nucleation) increases with decreasing wire diameter. To account for such size effect, a theoretical model involving the interaction between an emerging dislocation and the twin boundary has been developed for the surface nucleation of dislocations. It is shown that the model predictions are in quantitative agreement with the results from atomistic simulations and previous experimental studies in the literatures. The simulations also reveal that nanowire strength is strain-rate dependent, which predicts an activation volume for dislocation nucleation in the range of 1–10b~3,where b is the magnitude of the Burgers vector for a full dislocation.     

Effects of bottom shear stresses on the wave-induced dynamic response in a porous seabed：PORO-WSSI （shear） model

When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the wave-seabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot’s dynamic poro-elastic theory.In the model,an "u-p" approximation will be adopted instead of quasi-static model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the wave-induced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model(without shear stresses) and the present model(with shear stresses).As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.     

Hydromagnetic flow between two porous disks rotating about non-coincident axes

Hydromagnetic flow between two porous disks rotating with same angular velocity Ω about two noncoincident axes has been studied in the presence of a uniform transverse magnetic field. An exact solution of the governing equations has been obtained in a closed form. It is found that the primary velocity f/Ωl increases and the secondary velocity g/Ωl decreases with increase in either Reynolds number Re or the Hartman number M. It is also found that the torque at the disk η= 0 increases with increase in either M^2 or K^2. On the other hand there is no torque at the disk η= 1 for large M^2 and K^2. The heat transfer characteristic has also been studied on taking viscous and Joule dissipation into account. It is seen that the temperature increases with increase in either M^2 or K^2. It is found that the rate of heat transfer at the disk η= 0 increases with increase in either M or K. On the other hand the rate of heat transfer at the disk η= 1 increases with increase in K but decreases with increase in M.     

加载速率对40Cr钢Ⅱ型动态断裂特性的影响

采用新型Ⅱ型动态断裂测试技术,对高强钢40Cr在高加载速率下的Ⅱ型动态断裂特性进行了测试研究。基于新设计的Ⅱ型动态断裂试样和分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）技术,通过实验-数值方法确定了裂尖在加载过程中的应力强度因子曲线。采用应变片法确定了试样的起裂时间,最终得到40Cr的Ⅱ型动态断裂韧性值,并对其加载速率相关性和材料的失效机理进行了研究。结果表明,在1.08～5.53 TPa·m1/2/s的加载速率范围内,40Cr的Ⅱ型动态断裂韧性基本表现为与加载速率成正相关的变化趋势。通过对试样断口形貌的分析,确定了材料的失效模式及机理,发现随着加载速率的增加,存在拉伸型失效向绝热剪切型失效模式转变的现象。     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

Dynamic fracture of concrete – compact tension specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 m/s.     

The dependence of crack velocity on the critical stress in fracture

The constant velocity of crack propagation in PMMA is investigated in terms of the fracture stress for both continuously increasing loading (strain rate ?=0.59×10^?4 s^?1) and dynamic loading (strain rate ?=0.35 s^?1). It was found that the constant crack velocity increases with increasing fracture stress and that it depends on the loading conditions (continuously increasing or dynamic loading). In particular, it was found that the increase of the constant velocity for the static loading case is higher than for the dynamic one. However, in both cases, the constant velocity reaches a limiting value for stresses higher than a certain level.     

40Cr材料动态起裂韧性KId（）的实验测试

描述了利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试４０Ｃｒ，材料动态起裂韧性ＫＩｄ（）的试验方法。试样上的动态载荷历程由Ｈｏｐｋｉｎｓｏｎ杆直接测得，并分别代入动态有限元程序及近似公式求得动态应力强度因子历史；由贴在试样裂尖附近的应变片确定起裂时间，最终确定起裂时的动态应力强度因子值，即动态起裂韧性ＫＩｄ（）。试验结果表明:利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试材料动态起裂韧性的方法是可行的，起裂时，动态有限元的位移法、应力法及近似公式法求得的动态应力强度因子值比较吻合；在本文的载荷速率下，４０Ｃｒ材料动态起裂韧性ＫＩｄ（）与准静态裂韧性ＫＩｄ（）相比，降低了约２８％。     

Anomaly in the dynamic strength of austenitic stainless steel 12Cr19Ni10Ti under shock wave loading

Measurement results for the shock wave compression profiles of 12Cr19Ni10Ti steel and its dynamic strength in the strain rate range 10⁵–10⁶ s^?1 are presented. The protracted viscous character of the spall fracture is revealed. With the previously obtained data taken into account, the measurement results are described by a polynomial relation, which can be used to construct the fracture kinetics. On the lower boundary of the range, the resistance to spall fracture is close to the value of the true strength of the material under standard low-rate strain conditions; on the upper boundary, the spall strength is more than twice greater than this quantity. An increase in the temperature results in a decrease in both the dynamic limit of elasticity and the spall fracture strength of steel. The most interesting result is the anomaly in the dependence of the spall fracture strength on the duration of the shock wave compression pulse, which is related to the formation of deformation martensite near the growing discontinuities.     

Ductile–brittle transitions in the fracture of plastically-deforming,adhesively-bonded structures. Part I: Experimental studies

Rate effects for adhesively-bonded joints in steel sheets failing by mode-I fracture and plastic deformation were examined. Three types of test geometries were used to provide a range of crack velocities between 0.1 and 5000 mm/s: a DCB geometry under displacement control, a wedge geometry under displacement control, and a wedge geometry loaded under impact conditions. Two fracture modes were observed: quasi-static crack growth and dynamic crack growth. The quasi-static crack growth was associated with a toughened mode of failure; the dynamic crack growth was associated with a more brittle mode of failure. The experiments indicated that the fracture parameters for the quasi-static crack growth were rate independent, and that quasi-static crack growth could occur even at the highest crack velocities. Effects of rate appeared to be limited to the ease with which a transition to dynamic fracture could be triggered. This transition appeared to be stochastic in nature, it did not appear to be associated with the attainment of any critical value for crack velocity or loading rate. While the mode-I quasi-static fracture behavior appeared to be rate independent, an increase in the tendency for dynamic fracture to be triggered as the crack velocity increased did have the effect of decreasing the average energy dissipated during fracture at higher loading rates.     

准三维针刺C_f/SiC复合材料室温层向动态压缩力学行为的实验研究

为了研究应变率对准三维针刺碳纤维增韧的碳化硅复合材料(Cf/SiC)层向压缩力学性能的影响,本文利用分离式Hopkinson压杆装置对三维针刺Cf/SiC复合材料进行了应变率为10-4至6.5×103s-1的单轴压缩力学性能测试。实验结果表明,由于材料缺陷,其动态压缩强度分布遵循Weibull分布。破坏时,材料并未表现出典型的脆性破坏,而是在应力达到压缩强度后经历了较大的伪塑性变形才最终破坏。这表明三维针刺Cf/SiC复合材料沿厚度方向针刺的碳纤维有助于提高材料的韧性。同时,材料的压缩强度随应变率的升高显著增大,并与对数应变率近似成线性关系。借助光学显微镜和扫描电镜对压缩断口的观察表明:材料的失效模式随着应变率变化而发生改变。在准静态下,材料主要表现为剪切和分层破坏,而在高应变率下,则主要表现为劈裂。     

An experimental method for determining dynamic fracture toughness

The boundary and loading conditions in many dynamic fracture test methods are frequently not well defined and, therefore, introduce a degree of uncertainty in the modeling of the experiment to extract the dynamic fracture resistance for a rapidly propagating crack. A new dynamic fracture test method is presented that overcomes many of these difficulties. In this test, a precracked, three-point bend specimen is loaded by a transmitter bar that is impacted by a striker bar fired from a gas gun. Different levels of energy can be imparted to the specimen by varying the speed and length of the striker to induce different crack growth rates in the material. The specimen is instrumented with a crack ladder gage, crack-opening displacement gage and strain gages to develop requisite data to determine toughness. Typical data for AISI 4340 steel specimen are presented. A simple quasi-dynamic analysis model for deducing the fracture toughness for a running crack from these data is presented, and the results are compared with independent measurements.     

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。