Influence of Water Uptake on Dynamic Fracture Behavior of Poly(Methyl Methacrylate)

A study was completed to assess the effects of various humidity levels and amount of sorbed water on the fracture behavior of notched poly(methyl methacrylate) (PMMA) samples subjected to stress pulses generated by the impact of a projectile launched from an air gun. Impact experiments were performed on six sets of samples conditioned in different environments: dry samples; samples exposed to three different relative humidity environments (11 %, 60 %, and 98 %) using saturated salt solutions (Lithium Chloride, Sodium Bromide, and Potassium Sulfate, respectively); and distilled water- and seawater-exposed samples. Experiments varied by immersion time and water content, while loading conditions were kept constant. The main goal of this study was to understand the effects of sorbed water on the fracture behavior of PMMA when subjected to high strain rate impacts. It was observed that when PMMA is subjected to strain rates of 10² s ^?1, the effect of water content is not a dominant mechanism on the crack initiation and crack-tip speed of PMMA.     

加载角度对层理页岩裂纹扩展影响的实验研究

采用分离式霍普金森压杆（SHPB）系统对页岩进行冲击实验,研究层理角度对页岩动态断裂过程的影响,在裂尖设置裂纹扩展计,借助高速摄影和数字图像相关（DIC）技术对页岩中心切槽半圆盘弯曲（NSCB）试件断裂的全过程进行研究,得到了不同加载角度下页岩的动态起裂韧度、裂纹扩展速度、断裂过程中应变场和水平位移场的变化规律。实验发现:不同加载角度下,页岩的动态起裂韧度具有显著的各向异性,加载角度与动态起裂韧度呈正相关;加载角度对试样的裂纹扩展速度具有显著影响,与裂纹扩展速度呈负相关;当冲击速度较低时,切槽方向是裂纹扩展的优势方向,而当冲击速度较高时,试样会产生沿层理弱面的次生裂纹,次生裂纹对试样的断裂具有显著影响。     

动载荷作用下裂隙岩体的止裂机理分析

为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC（tunnel with single radial crack）构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。     

Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams

Functionally graded syntactic foam sheets are developed by dispersing microballoons in epoxy for studying dynamic fracture behavior under low velocity impact loading. The volume fraction of microballoons is graded linearly over the width of the sheets. The mode-I crack initiation and growth behaviors are studied using reflection coherent gradient sensing technique and high-speed photography in samples with crack on the compliant and stiff sides and oriented along the compositional gradient. Crack growth along the gradient in each case shows sudden acceleration followed by steady state growth and deceleration during the window of observation. In both cases, the crack accelerations are similar while crack decelerations show differences. The dynamic stress intensity factor history prior to crack initiation in each case shows a rapid increase at different rates with the crack on the compliant side of the graded sheet experiencing higher rate of loading relative to the one with the crack on the stiffer side. Post-crack initiation stress intensity factor histories suggest increasing fracture toughness with crack growth in the graded sample with the crack on the compliant side while a decreasing trend is seen when the crack is on the stiffer side.Optical measurements are supplemented by finite element simulations for studying crack tip constraint effects on fracture behavior of graded foam sheets. Computed plane strain constraints in graded configurations are essentially identical to the homogeneous counterpart and the computed stress intensity factors obtained from plane stress elasto-dynamic analyses of the graded foams correlate well with the experimental measurements prior to crack initiation. The computed T-stress histories however, show an earlier loss of negative crack tip constraint in case of the graded foam sample with a crack on the compliant side. This correlates well with the higher crack tip loading rate and earlier crack initiation suggesting a possible role of in-plane constraint on fracture of graded foam. The coincidence of the time rate of change of in-plane constraint parameter becoming stationary close to experimentally observed crack initiation times are noted.     

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.      

Fracture Characterization of Steels by Means of the Small Punch Test

A hot rolled API X-70 steel plate and its heat-affected zone (the region with the maximum hardness and lowest toughness of the welded joint made using this steel) were employed to obtain the material’s room temperature elasto-plastic fracture toughness, J_Ic, by means of small punch tests (SPTs) using both conventional un-notched samples and longitudinally-notched SPT specimens. In the latter case, the notches were manufactured by micromachining different notch depth-to-thickness ratios (a/t?=?0.3 and 0.4). The representative toughness parameter used with the conventional SPT tests was the maximum strain measured directly in the failed region, while in the case of the notched samples, the consumed energy until the initiation of a crack from the tip of the notch was considered the most useful parameter of choice. The onset of crack initiation was determined directly from the load-displacement plot of each test with the aid of scanning electron microscope observations performed on different samples over which interrupted tests had been conducted. These tests were interrupted at different percentages of the maximum registered load. A simple correlation between the energy consumed until the initiation of crack growth in the notched SPT sample and the critical J value obtained using standard tests (J-R curves) was determined, defining an easy and promising way to derive fracture toughness from miniature SPT tests.     

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。     

爆炸荷载下青砂岩动态起裂韧度的测试方法

为了研究爆炸荷载下青砂岩I型裂纹动态断裂韧度的测试方法,利用内部中心单裂纹圆盘（internal center single crack disc,ICSCD）试样进行了爆炸试验研究。试样由外径为400 mm、内部加载孔径为40 mm、预制裂纹长为60 mm的青砂岩制成。利用同步触发器实现圆盘中心起爆,并同步触发超动态应变仪,通过径向应变片获取爆炸应变曲线、裂纹尖端的环向应变片获取裂纹起裂时刻。以实测爆炸应变曲线为参量,应用Laplace变换推导出试样加载孔壁应力时程曲线表达式,并用数值反演法得出其数值解。利用ANSYS有限元软件,建立数值计算模型,通过相互作用积分法得出了在爆炸荷载作用下砂岩的I型动态应力强度因子曲线。研究结果表明:（1）ICSCD试件能够很好地用来测试岩石的动态起裂韧度;（2）炮孔周边的应力可以通过拉普拉斯变换的数值反演方法得到;（3）通过试验-数值法能稳定计算出ICSCD砂岩构型的动态起裂韧度,其最大误差仅为7%。     

低速冲击下混凝土少筋梁断裂性能

动态加载下,混凝土中钢筋的阻裂性能一直是冲击动力学研究领域的难点之一。利用落锤试验机对含缺口的混凝土少筋梁进行三点弯曲试验,分析了不同加载速率下梁的冲击力、跨中挠度、混凝土起裂应变率和钢筋应变。实验结果表明:在一定加载速率范围内（0.885～1.252 m/s）,混凝土预制裂缝尖端的裂纹起裂应变率、冲击力最大值、跨中挠度峰值与加载速率呈线性增长关系,当加载速率增至1.771 m/s时,增长趋势减弱;冲击力卸载时,钢筋部分弹性变形恢复导致裂纹产生闭合,裂纹嘴张开位移逐渐减小至恒定值,对裂纹嘴张开位移峰值前的部分曲线进行拟合后得到裂纹嘴张开位移率,结果表明裂纹嘴张开位移率随加载速率的提高而线性增大。     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

基于FDM-DEM耦合的冲击损伤大理岩静态断裂力学特征研究

为探究循环冲击损伤后大理岩的静态断裂力学特征,基于有限差分（finite difference method,FDM）-离散元（discrete element method,DEM）耦合的建模技术构建了三维分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）数值模型,其中杆件系统和岩石试件分别采用FLAC3D和PFC3D程序建模。利用该模型对中心直切槽半圆盘（NSCB）试样进行了恒定子弹速度下的循环冲击,随后对受损试样进行静态三点弯曲断裂实验。通过编写Fish程序,提取试样断裂面数据,对断裂面进行重构并定量计算表面粗糙度。通过与相关室内实验结果的对比分析,验证了本文数值分析的合理性与可靠性。模拟结果表明,随着循环冲击次数的增加,试样内部微裂纹、破碎颗粒均增加。连接力场分布混乱,部分力链发生断裂。力链的变化是试样力学性能劣化的根本原因。在静态三点弯曲断裂实验中,冲击5次后试样的静态断裂韧度较天然试样产生一定程度的降低。试样在静载过程中产生的微裂纹和碎块的数量随循环冲击次数的增加而增加,断裂面粗糙度随循环冲击次数的增加而增加。     

On the effect of pulse loads on dynamic rock fracture

The objective of this research was to develop an analytical model which is capable of predicting the fracture pattern in the rock surrounding a wellbore upon which a dynamic loading pulse is applied. The development of the model followed the principle of elastodynamic fracture mechanics. Specifically, inherent cracks are assumed to exist around the edge of the wellbore. Depending on the pulse shape, these cracks are activated to form various fracture patterns. The criterion for initiation of crack growth is determined by the magnitude of the dynamic stress intensity factor associated with the crack. The finite element code HONDO was used to calculate the dynamic stress intensity factors. Analytical predictions were correlated with field experimental data and good agreements were found.     

应力波载荷作用下线弹性断裂过程的动态分析方法研究

利用Hopkinson单压杆实验装置 ,对材料的线弹性动态断裂特性进行了研究 ,建立了应力波载荷作用下动态裂纹起裂及扩展过程的动态分析方法 ,采用该方法可同时测得材料的动态裂纹起裂时间、断裂韧性和裂纹扩展速度。40Cr钢三点弯曲试样的实验结果表明 :该钢的动态裂纹扩展过程主要是减速过程 ,在2 2 5TPam /s的加载速率下 ,起裂时间为 2 8 0 0 s,最大裂纹扩展速度为 478 91m/s ,动态断裂韧性为6 3 12MPam。     

冲击载荷作用下黑砂岩动态断裂参数的分形修正

基于分形理论研究了偏折裂纹扩展路径对动载荷作用下黑砂岩的动态断裂力学参数的测试误差影响作用,采用传统的分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验装置对修正侧开单裂纹半孔板（improved single cleavage semi-circle specimen, ISCSC）试样进行动态冲击实验,随后采用裂纹扩展计进行裂纹起裂时间与裂纹扩展速度等动态断裂力学参数测试,采用分形理论对测试的裂纹扩展速度与动态应力强度因子进行修正,利用实验-数值法对黑砂岩的动态断裂韧度进行计算。研究结果表明,ISCSC构型构件能够有效应用于岩石材料动态裂纹扩展行为的研究,并发生了止裂现象,经分形修正的裂纹扩展速度与动态断裂韧度更接近实际裂纹动态扩展情况,修正前后得到黑砂岩材料的裂纹扩展速度误差为33.51%,动态断裂韧度最大误差为7.68%,说明利用分形理论对动态断裂韧度等动态断裂参数计算更合理。     

冲击载荷作用下圆孔缺陷对裂纹动态扩展行为的影响规律

空腔和裂纹缺陷通常共存于深部地下岩体中,它们共同影响着岩体的结构安全性与稳定性。为了探究动力扰动载荷下圆形空腔对裂隙岩体内裂纹扩展行为的影响规律,提出了不同圆孔倾角的直裂纹空腔圆弧开口试件（circular opening specimen with straight crack cavity, COSSCC）,利用自制大型落锤冲击实验装置进行动态加载实验,同时采用裂纹扩展计系统测试了裂纹的动态起裂时刻与裂纹扩展速度等各种断裂力学参数,随后采用有限差分软件Autodyn进行裂纹扩展路径与圆孔周围应力场的数值分析,并采用有限元软件Abaqus计算裂纹的动态起裂韧度与裂纹扩展过程中的动态扩展韧度。结果表明:（1）当圆孔倾角θ小于10°时,裂纹扩展路径会偏折并穿过圆孔表面;当圆孔倾角θ为20°与30°时,裂纹扩展路径向圆孔方向发生偏折但不会穿过圆孔,圆孔具有明显的裂纹扩展引导作用; 当圆孔倾角θ为40°与50°时,裂纹扩展路径不会发生偏折,圆孔引导作用明显减弱。（2）当裂纹扩展路径达到圆孔空腔附近时,裂纹尖端的拉伸应力区与圆孔边缘的拉伸应力区发生重合,此时裂纹扩展速度显著增大,裂纹动态断裂韧度显著减小。（3）裂纹的偏折方向与裂纹尖端最大周向应力的方向基本一致。（4）裂纹动态断裂韧度始终小于裂纹起裂韧度,且裂纹动态断裂韧度与裂纹动态扩展速度呈负相关关系。裂纹动态扩展速度越大,裂纹动态断裂韧度越小。     

Erratum to: Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.     

Effect of Notch-Tip Radius on Dynamic Brittle Fracture of Polycarbonate

Polycarbonate (PC), which is considered to be a ductile amorphous polymer, is prone to brittle fracture in the presence of sharp notches. In the present work, effect of notch-tip radius on brittle fracture of PC is studied under static and under dynamic loading (high loading rates) conditions. Towards this end, a hybrid experimental and numerical approach is adopted. Dynamic fracture experiments using Hopkinson bar setup are performed on single-edge notched specimen of PC having different notch-tip radii. Ultra-high speed imaging is used for real-time observation of the fracture process. Finite element simulations are simultaneously performed using a well calibrated elastic-viscoplastic constitutive model for polymers. In the presence of a notch, brittle fracture in PC starts with a defect nucleation ahead of it. For each notch-tip radii, we are experimentally able to capture the process of defect initiation and quantify the mean stress required, static as well as dynamic loading. We found that the mean stress required for defect nucleation increases with decreasing notch-tip radius due to increased triaxility at the notch-tip. Defect initiation stresses are also higher for dynamic conditions compared to static loading. Defect initiation toughness for dynamic loading is always higher than those for static loading, but reduction in defect initiation toughness with decreasing notch-tip is severe for dynamic loading.     

综合考虑宏细观缺陷的岩体动态损伤本构模型

针对节理岩体同时含有节理、裂隙等宏观缺陷及微裂隙、微孔洞等细观缺陷的客观事实, 提出了在节理岩体动态损伤本构模型中应同时考虑宏细观缺陷的观点。为此, 首先对基于细观动态断裂机理的经典岩石动态损伤本构模型—TCK(Taylor-Chen-Kuszmaul)模型进行了阐述, 其次基于Lemaitre等效应变假设推导了综合考虑宏细观缺陷的复合损伤变量(张量), 进而在此基础上建立了相应的节理岩体动态损伤本构模型, 并利用该模型讨论了载荷应变率及节理条数对岩体动态力学特性的影响规律。结果表明, 在不同载荷应变率下试件在变形初始阶段是重合的, 而后随着应变的增加, 试件峰值强度、峰值应变及总应变均随载荷应变率的增加而增加; 随着节理条数的增加, 试件峰值强度逐渐降低, 但降低趋势逐渐变缓并趋于某一定值。上述研究结论与目前的理论及实验研究结果的基本规律是一致的, 说明了本模型的合理性。     

Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.     

两套节点格林元嵌入式离散裂缝模型数值模拟方法

对于原始嵌入式离散裂缝模型(EDFM),在计算包含裂缝单元的基质网格内的压力分布时采用了线性分布假设,这导致了油藏开发早期对非稳态窜流量的计算精度不足.因此,本文提出了一种两套节点格林元法的EDFM数值模拟方法.两套节点格林元法的核心思想是将压力节点与流量节点区分开,一套压力节点设置在单元顶点,另一套流量节点设置在网格边的中点,满足局部物质守恒、具有二阶精度的同时,可适用于任意网格类型.本文将两套节点格林元法与EDFM耦合,采用了非稳态渗流控制方程的边界积分形式推导了基质网格与裂缝网格之间传质量的新格式,代替了线性分布假设以提高模拟精度;此外,修正后的EDFM能适应任意形态的基质网格剖分,拓展了原始EDFM仅适用于矩形基质网格、难以考虑复杂油藏边界的局限性.研究表明:通过对比商业模拟软件tNavigator?LGR模块与原始EDFM,验证了本文模型具有较高的早期计算精度;以复杂油藏边界-缝网-SRV分区模型为例,通过对比SFEM-COMSOL商业模拟软件,验证了本文模型处理复杂问题的适应性.本文研究可用于裂缝性油藏开发动态的精确模拟.