Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

Effect of strain rate on the tension–compression asymmetric responses of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si

An experimental investigation is performed to explore the tension–compression asymmetry of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si alloy over a wide range of strain rates. A split Hopkinson bar technique is used to obtain the dynamic stress–strain responses under uniaxial tension and compression loading conditions. Experimental results indicate that the alloy is a rate sensitive material. Both tension yield strength and compression yield strength increase with increasing strain rate. The mechanical responses of the alloy have the tension–compression asymmetry. The values of yield strength and subsequent flow stress in compression are much higher than that in tension. The yield strength is more sensitive to change with strain rate in tension than compression. The difference of the yield strength between tension and compression increases with the increase of strain rate. The tensile specimen is broken in a manner of ductile fracture presenting characteristic dimples, while the compressive specimen fails in a manner of localized shearing failure.     

Strain rate effects on dynamic fracture and strength

An experimental procedure and accompanying theoretical analysis is presented to produce a well-characterized technique for quantifying dynamic fracture properties of quasi-brittle materials. An analytical and experimental investigation of mode I fracture of concrete was conducted under the dynamic loading of a split Hopkinson pressure bar. Fracture specimens in the form of notched-cavity splitting tension cylinders were subjected to stress wave loading that produced strain rates nearing 10/s. Fracture parameters were extracted by the application of the two-parameter fracture model, a nonlinear fracture model for quasi-brittle materials. Finite element analysis verified the experimental configuration and addressed inertial contributions within the dynamic environment. Ultra-high-speed digital photography was synchronized with the fracture process to provide additional validation and insight to the experimental technique. Results show that the effective fracture toughness and specimen strength both increase significantly with loading rate. The numeric and photographic results validate the experimental technique as a new tool in determining rate dependent material properties.     

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material under thermo-mechanical loading

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material (FGM) is investigated using a three point bend specimen. The modified split Hopkinson pressure bar (SHPB) apparatus in conjunction with induction coil heating system is used during elevated temperature dynamic loading experiments. A simple and accurate technique has been developed to identify the time corresponding to the load at which the fracture initiates. A series of experiments are conducted at different temperatures ranging from room temperature to 800 °C, and the effect of temperature and loading rate on the fracture initiation toughness is investigated. The material fracture toughness is found to be sensitive to temperature and the fracture initiation toughness increases as the temperature increases. Furthermore, the fracture initiation toughness is strain rate sensitive and is higher for dynamic loading as compared to quasi-static loading.     

Zr-W多功能含能结构材料的制备及动态压缩特性

利用材料试验机和分离式霍普金森压杆（SHPB）系统对加压烧结制备的Zr-W多功能含能结构材料在不同应变率下的压缩行为进行测试。通过在试样上直接贴应变片与波形整形技术相结合,实现了恒应变率动态加载。试验结果表明:该材料在准静态和动态加载下均呈现良好的线弹性,弹性模量对应变率效应不敏感,约为186 GPa。烧结生成的W₂Zr相显著提高了Zr-W材料的强度和脆性,试样在强冲击载荷作用下发生破碎反应并释放大量的热量,表现出很高的含能特性,动态破坏应变和破坏强度表现出一定的正应变率效应。      

被动围压条件下岩石材料冲击压缩试验研究

为研究煤矿岩石材料被动围压条件下动态力学性能和变形破坏规律,利用Ø50mm变截面分离式Hopkinson压杆(SHPB)试验装置,对45#钢质套筒环向约束状态下煤矿岩石试件进行了不同加载速率冲击压缩试验。试验结果表明：被动围压条件下SHPB试验中,岩石试件的材料延性和抗破坏能力均得到增强,试件轴向应力是采用同种加载条件无围压SHPB试验时的1.2倍,破坏应变比无围压SHPB试验提高2～3倍,且径向应力随轴向应变增大总体呈上升趋势,试件破坏为压剪破坏模式,与无围压SHPB试验有所不同。     

Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Thin Aluminum Sheets

An experimental investigation was undertaken to characterize the dynamic fracture characteristics of 2024-T3 aluminum thin sheets ranging in thickness from 1.63–2.54 mm. Specifically, the critical dynamic stress intensity factor Kdc was determined over a wide range of loading rates ( expressed as the time rate of change of the stress intensity factor KdI ) using both a servo- hydraulic loading frame and a split Hopkinson bar in tension. In addition, the dynamic crack propagation toughness, KD, was measured as a function of crack tip speed using high sensitivity strain gages. A dramatic increase in both Kdc and KD was observed with increasing loading rate and crack tip speed, respectively. These relations were found to be independent of specimen thickness over the range of 1.5 to 2.5 mm.     

有机玻璃纯Ⅰ型和纯Ⅱ型动态断裂行为的实验研究

采用尖槽式中心切口圆盘试件,在分离式霍布金森压杆试验装置上对有机玻璃纯Ⅰ型和纯Ⅱ型加载条件下的动态断裂行为进行了实验研究。结果表明,加载速率对有机玻璃的断裂行为有显著的影响,有机玻璃纯Ⅰ型和纯Ⅱ型断裂韧度的测试结果均表现出明显的加载速率相关性,且随着加载速率的增加而增大。     

Dynamic compressive behavior of unidirectional E-glass/vinylester composites

Results from an experimental investigation on the mechanical behavior of unidirectional fiber reinforced polymer composites (E-glass/vinylester) with 30%, 50% fiber volume fraction under dynamic uniaxial compression are presented. Specimens are loaded in the fiber direction using a servo-hydraulic material testing system for low strain rates and a Kolsky (split Hopkinson) pressure bar for high strain rates, up to 3000/s. The results indicate that the compressive strength of the composite increases with increasing strain rate. Post-test scanning electron microscopy is used to identify the failure modes. In uniaxial compression the specimens are split axially (followed by fiber kink band formation). Based on the experimental results and observations, an energy-based analytic model for studying axial splitting phenomenon in unidirectional fiber reinforced composites is extended to predict the compressive strength of these composites under dynamic uniaxial loading condition.     

Study on energy properties and failure behaviors of heat-treated granite under static and dynamic compression

Abstract

The material testing machine and the split Hopkinson pressure bar (SHPB) were adopted, respectively, to conduct the static and dynamic compression tests on granite specimens heat treated by different temperatures. The effects of strain rate and heat-treatment temperature on the mechanism of energy evolution of the specimen during deformation and failure process were studied. The results show a significant strain rate effect on the granite, with the energy dissipation density increasing with increasing impact velocity (or strain rate), regardless of the treatment temperature. The specimens heat treated at 300?°C and 700?°C have the minimum and maximum energy dissipation densities, respectively. The specimen in the SHPB tests easily broke into pieces or even powder; while under static compression, only macroscopic fracture surfaces and spalling phenomenon on the specimen were detected. The energy dissipation density is inversely proportional to the compressive strength of the specimen. The rate of energy dissipation change is defined, which can be used to identify the stages in the deformation process of rock and to determine the position of the failure point in the stress-strain curve. For both the dynamic and static compression tests, the value of energy utilization ratio is relatively low, with a maximum value of about 35%.     

基于键基近场动力学理论的单裂纹圆孔板冲击破坏研究

基于键基近场动力学理论,建立分离式霍普金森杆冲击单裂纹圆孔板动力学模型,其中霍普金森杆用一维PD模型、单裂纹圆孔板用二维PD模型描述,采用短程斥力模型描述碰撞过程,模拟冲击压缩条件下单裂纹圆孔板动态破坏行为。通过试样端面受力分析得到端面载荷的V形分布规律,解决了传统实验-数值研究法在端面加载上的局限性。研究不同入射速度下试件裂纹的扩展过程和破坏模式,准确捕获了裂纹起裂、止裂及二次起裂时间。根据键基近场动力学理论下材料动态应力强度因子计算方法,求得裂纹的起裂韧度,为材料动态断裂韧度计算提供了新的途径。     

Experimental and numerical study on dynamic fracture behaviour of AISI 1045 steel for compressor crankshaft

Dynamic fracture behaviour of AISI 1045 steel for compressor crankshaft was studied by experimental and numerical methods. True stress–strain relations of the material under different strain rates were measured, and dynamic constitutive model with consideration to strain‐hardening and strain‐rate hardening was proposed. Dynamic fracture tests loaded by Hopkinson pressure bar were carried out, and fracture toughness was determined using a finite element method with the combination of ABAQUS and Zencrack software. Loading states of the specimen and determination methods of the dynamic fracture toughness were discussed. By comparing the fracture behaviours under quasi‐static and dynamic conditions, it was found that the fracture modes exhibited a transition from ductile to brittle fracture with the increasing loading rate, and the dynamic fracture toughness value was less than the quasi‐static one.     

灰岩和白云岩动态压缩力学性能的SHPB实验

为了得到爆破荷载作用下岩石的破坏特性及爆破振动波的传播特性,利用RMT-150C多功能实验机和改进后的ф50mm的分离式Hopkinson压杆装置,分别研究灰岩和白云岩试件的静态力学特性和在5种不同应变率等级下的动态力学性能。实验结果表明,随着平均应变率的增加,灰岩和白云岩试件的动态抗压强度、峰值应变、吸收能、比能量吸收值以及破碎程度都明显增加,表现出显著的应变率效应,而初始弹性模量对应变率的相关性不敏感。从岩石的动态抗压强度和能量吸收两个方面,对比分析灰岩和白云岩动态力学性能的共性和差异性,更合理地解释了岩石在动态冲击荷载下的破坏本质。     

Rate dependent deformation of carbon fibre reinforced Al–Li metal matrix composite

Abstract

The dynamic deformation characteristics and failure behaviour of laminated carbon fibre reinforced Al–Li metal matrix composite has been studied experimentally with the objective of investigating the dependence of mechanical properties on the applied strain rate and fibre volume fraction. A vacuum melting/casting process was used for manufacturing the tested composite. Impact testing was performed using a Saginomiya 100 metal forming machine and a compressive split Hopkinson bar over a strain rate range of 10^-1 s^-1 to 3×10³ s^-1. It is shown that the flow stress of the composite increases with strain rate and fibre volume fraction. The highest elongation to fracture values were found at low rate loading conditions, although a significant increase in ductility is obtained in the dynamic range. The composite appears to exhibit a lower rate of work hardening during dynamic deformation. Strain rate sensitivity and activation volume are strongly dependent on strain rate and fibre volume fraction. Fractographic analysis using scanning electron microscopy reveals that there is a distinct difference in the morphologies of the fractures, with corresponding different damage mechanisms, between specimens tested at low and high strain rates. Both strain rate and fibre volume fraction are important in controlling fibre fragment length and the density of the Al–Li debris. The relationships between mechanical response and fracture characteristics are also discussed.     

软材料的霍普金森压杆测试新技术

提出了一种用于软材料动态压缩性能测试的霍普金森压杆改进方案。该方案采用了长杆直接撞击试件的加载方式并在透射杆中使用半导体应变片。通过对测试过程中试件内应力波传播的分析,提出了实现软材料动态性能测试时试件内应力尽快均匀的最佳加载方式以及实现此种加载的加载整形技术。该方案能解决由于杆-试件之间波阻抗失配导致的应变信号微弱而测试困难的问题,与高聚物霍普金森压杆相比则具有更高的可靠性。该方案能实现对软材料的大变形、近似恒应变率及大应变率范围动态压缩测试。最后给出了一个试验性装置的测试结果。     

Determination of dynamic rock Mode-I fracture parameters using cracked chevron notched semi-circular bend specimen

Rock dynamic fractures are common in many geophysical processes and engineering applications. Characterization of rock dynamic fracture properties such as the initiation fracture toughness, the fracture energy, and the fracture velocity, is thus of great importance in rock mechanics. A novel method is proposed in this work to measure dynamic Mode-I rock fracture parameters using a cracked chevron notched semi-circular bend (CCNSCB) specimen loaded by a split Hopkinson pressure bar (SHPB) apparatus. A strain gauge is mounted on the sample surface near the chevron notch to detect the fracture onset, and a laser gap gauge (LGG) is used to monitor the crack surface opening distance (CSOD) during the dynamic test. With dynamic force balance achieved in the tests, the stable–unstable transition of the crack propagation crack is observed and the initiation fracture toughness is calculated from the dynamic peak load. The average dynamic fracture energy as well as the fracture propagation toughness are calculated based on the first law of thermodynamics. The measured dynamic fracture properties of Laurentian granite using CCNSCB method are consistent with those reported in the literature using other methods.     

SiC颗粒增强6061Al基复合材料的动态拉伸性能Ⅰ应变硬化

利用拉伸split Hopkinson bar实验装置研究了SiCp/6061Al复合材料及其基体合金的动态拉伸性能及应变硬化行为。结果表明，与静态加载类似，在动态加载条件下，SiCp/6061Al复合材料的强度高于基体合金的强度，其断裂延伸率低于基体合金的断裂延伸率，在低应变动态拉伸时，复合材料的应变硬化指数高于Al合金材料的应变硬化指数，随着应变的增加，复合材料的应变硬化指数迅速下降，以至低于基体合金的应变硬化指数。     

二维C/SiC复合材料准静态和动态拉伸力学性能

采用分离式Hopkinson拉杆装置和电子万能试验机研究了二维C/SiC复合材料在4种应变率（0.001、0.010、90.000和350.000 s-1）下的拉伸力学性能,计算并验证了动态试验中的应力平衡状态;采用SEM分析了复合材料在不同应变率下的破坏断口和失效机制;建立了复合材料包含损伤和应变率相关的本构方程。结果表明:二维C/SiC复合材料的应力-应变曲线都表现出非线性的特征。随着应变率的增加,二维C/SiC复合材料的拉伸强度从204 MPa增加到270 MPa,增加了33%,这表明复合材料的拉伸强度具有较强的应变率敏感性。复合材料在准静态和动态加载下表现出不同的破坏模式是由材料内部界面行为的应变率效应造成的。      

Stress–strain behavior of composites under high strain rate compression along thickness direction: Effect of loading condition

Investigations are carried out on the behavior of typical plain weave E-glass/epoxy; plain weave carbon/epoxy; satin weave carbon/epoxy; and satin weave carbon – plain weave E-glass and epoxy hybrid composites under high strain rate compressive loading along thickness direction. Compressive split Hopkinson pressure bar apparatus was used for the studies. Two loading cases, namely, specimen not failed and specimen failed during loading are investigated. The special characteristics of specimen not failed case are presented. For this case, the specimens are under compressive strain initially and are under tensile strain during the later part of loading. The induced tensile strain is higher than the induced compressive strain. This could lead to failure of specimen/structure under tensile strain even though the applied load is compressive.     

三轴SHPB加载下砂岩力学特性和破坏模式的试验研究

利用改造的三轴SHPB动静组合加载实验装置,对均质砂岩进行了不同围压和不同应变率下的三轴冲击压缩试验,作为对比利用RMT-150C试验机也进行了部分准静态下的三轴压缩实验。根据实验结果,分析了围压对砂岩动态冲击性能的影响,并重点讨论了冲击过程中岩石的破坏模式。研究结果表明,在围压一定的情况下,岩石的动态压缩强度随应变率的提高而提高;在应变率相同的情况下,岩石的动态压缩强度和弹性模量会随着围压的增大而增大。岩石发生破坏的临界入射能,随着围压的增大而增大。岩石单位体积吸收能与应变率之间呈线性递增关系,而且递增的程度随着围压的增加而增加。三轴冲击加载下,应变率较低时岩石内部形成压剪破裂面但整体不失稳,应变率很大时岩石破碎形成锥形块体形式。