Limiting conditions for compression testing of flat specimens in the split hopkinson pressure bar

The split Hopkinson pressure bar (SHPB) technique is analyzed during the initial stages of loading by means of axisymmetric finite element simulations of dynamic compression tests. Limiting strains as functions of the test parameters such as the specimen diameterd and heighth were found to ensure a one-dimensional stress state and axial stress homogeneity in specimens of elastic-perfectly plastic material. The one-dimensional stress state is necessary and sufficient for accurate test results for flat specimens (h/d≤0.5) and nonflat specimens, respectively, with diameters up to half of the bar diameter. Only very small values of the Coulomb friction constraint (μ≈0.01) seem to be acceptable. The significance of the determined limiting conditions to the more practical case of a rate dependent material is investigated using an elastic-viscoplastic material for the specimen. The stress and strain rate reconstructed from the calculated bar signals (according to the SHPB analysis) are compared with stresses and strain rates averaged over the cross section of the specimen. Well-known inertia corrections improve the results of the SHPB procedure, but errors remain for small strains and highly time dependent strain rates.     

轴、侧向同卸荷下砂岩力学特性影响的试验研究

本文以实际岩体工程为背景,利用WDT-1500 仪器开展了轴向、侧向同时卸荷条件下砂岩的三轴试验. 结果表明:轴、侧向同卸荷这种卸荷路径下,砂岩试样破坏时并没有出现应力峰值,为了定义试样的破坏强度,将最大与最小主应力差随最小主应力的变化关系曲线上应力跌落的拐点处的应力值定义为破坏强度. 砂岩变形初始段发生应力跌落和轴向应变回弹,破坏前无明显的弹性和屈服阶段;试验的过程中,砂岩的侧向变形明显大于轴向变形,其体积应变一直处于膨胀状态;相对于砂岩的常规三轴试验结果,试样破坏时的强度在轴向、侧向同时卸荷条件下有所降低. 初始轴压和初始围压对试样的力学特征有十分显著的影响,但围压的卸荷速率却并不显著. 砂岩的破坏特征主要是以张-拉为主的混合张剪的破坏.      

软化Mohr-Coulomb材料强度参数的测定方法

为了得到试件的粘聚力和内摩擦角随轴向塑性压应变变化的曲线提出本方法。试件的弹塑性本构关系遵循相关联的Mohr-Coulomb强度准则;对常规三轴试验,试件受力进入塑性状态后,处在棱椎状屈服面的棱上,加载过程遵循Koiter流动法则。按经典塑性力学理论,推导得到轴向塑性压应变与轴向应力与轴向应变的关系;在常规三轴试验机上获得不同围压下试件的全程应力-应变曲线,进而可得到各自围压下轴向塑性压应变随加载过程的变化曲线;把来自不同围压下对应同一轴向塑性压应变的应力分别代入屈服面方程,即可求得对应的粘聚力和内摩擦角。结果表明,Mohr-Coulomb材料的两个强度参数的变化由轴向塑性压应变确定。轴向塑性压应变可以作为塑性变形的状态参数,它和试件的受力过程可以唯一确定试件的变形过程。     

In-situ tensile testing of nano-scale specimens in SEM and TEM

We present a new experimental method for the mechanical characterization of freestanding thin films with thickness on the order of nanometers to micrometers. The method allows, for the first time, in-situ SEM and TEM observation of materials response under uniaxial tension, with measurements of both stresses and strains under a wide variety of environmental conditions such as temperature and humidity. The materials that can be tested include metals, dielectrics, and multi-layer composites that can be deposited/grown on a silicon substrate. The method involves lithography and bulk micromachining techniques to pattern the specimen of desired geometry, release the specimen from the substrate, and co-fabricate a force sensor with the specimen. Co-fabrication provides perfect alignment and gripping. The tensile testing fits an existing TEM straining stage, and a SEM stage. We demonstrate the proposed methodology by fabricating a 200 nm thick, 23.5 μm wide, and 185 μm long freestanding sputter deposited aluminum specimen. The testing was done in-situ inside an environmental SEM chamber. The stress-strain diagram of the specimen shows a linear elastic regime up to the yield stress σ _y MPa, with an elastic modulusE=74.6 GPa.     

Long-term strength of metals in complex stress state (a survey)

An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ _e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ _e on the principal stresses. Statistical methods are used to obtain an expression for σ _e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ _e by using additional material constants are considered.     

Cold-gas experiments to study the flow separation characteristics of a dual-bell nozzle during its transition modes

An experimental investigation has been carried out to study the effect of test environment on transition characteristics and the flow unsteadiness associated with the transition modes of a dual-bell nozzle. Cold-gas tests using gaseous nitrogen were carried out in (i) a horizontal test-rig with nozzle exhausting into atmospheric conditions and, (ii) a high altitude simulation chamber with nozzle operation under self-evacuation mode. Transient tests indicate that increasing δP ₀/δt (the rate of stagnation chamber pressure change) reduces the amplitude of pressure fluctuations of the separation shock at the wall inflection point. This is preferable from the viewpoint of lowering the possible risk of any structural failure during the transition mode. Sea-level tests show 15–17% decrease in the transition nozzle pressure ratio (NPR) during subsequent tests in a single run primarily due to frost formation in the nozzle extension up to the wall inflection location. Frost reduces the wall inflection angle and hence, the transition NPR. However, tests inside the altitude chamber show nearly constant NPR value during subsequent runs primarily due to decrease in back temperature with decrease in back pressure that prevents any frost formation.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.     

Dissolution and Seepage Coupling Effect on Transport and Mechanical Properties of Glauberite Salt Rock

Potential high rates of aqueous dissolution are characteristic of salt rocks, and solute and mass flux through a soluble porous medium are functions of solute concentration gradients and pressure gradients. Due to different dissolution properties for different mineral components in glauberite salt rock, an interaction between mineral dissolution and solvent seepage arises, driven by the hydraulic pressure gradient in the rock. The originally almost impermeable glauberite rock becomes an increasingly permeable porous medium with dissolution, changing the transport and mechanical properties because of the progressive removal of solid sodium sulfate (Na₂SO₄), one of the constitutive components of glauberite salt rock. Glauberite is often found in bedded salt rock deposits, and the mineral glauberite has economic value and has been mined for many years in China. More economic and safe technologies, such as controlled solution mining, are inherently attractive. Thus, investigations into relevant physical and mechanical properties of glauberite in the context of solution mining have value, and to clarify glauberite behaviour, a series of experiments were performed. It is observed through experiments that the permeability of the rock mass during dissolution of glauberite is a function of the dissolution duration and the hydraulic pressure gradient applied to the system. For example, in laboratory tests, after 49, 53 and 70 h of dissolution, the relationships between permeability (k—cm²) and pressure gradient (Δp—MPa across the specimen of length 100 mm) of the glauberite specimens were observed to be k = 0.24 for a Δp of 0.10, k = 0.30 for a Δp of 0.12, and k = 0.41 for a Δp of 0.18, with the empirical functional relationship becoming gradually steeper with pressure. Also, the triaxial compression (mechanical) characteristics of glauberite salt rock change substantially after a period of dissolution: the compressive strength under a confining stress of σ₃ = 2.0 MPa changes initially from 46 to 11 MPa after 70 h of dissolution and seepage. Along with strength degradation, the Young’s modulus (stiffness) changed from 4.6 to 0.5 GPa. Evidently, coupled dissolution and seepage rate greatly impact both transport and mechanical properties of the rock as fabric evolves in a time-dependent manner.     

Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024-T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk.     

A high-strain biaxial-testing rig for thin-walled tubes under axial load and pressure

It is well know that high-strain biaxial testing with axial force and pressure on thin-walled tubes can be interesting from several points of view: capability of testing over the whole range of strain or stress ratios, great versatility of testing. and because of the physical system, the measured strains and stresses are principal. Nevertheless, there are few experimental-biaxial-fatique data due to the complexity of the testing equipment involved. In this paper, an experimental testing rig capable of subjecting thin-walled tubes to combined dynamic loadings in tension-compression with torsion and tension-compression with internal-external pressure is presented. The following components are described: the mechanical and hydraulic system, servohydraulic control, specimen configuration, strain-measuring equipment and data-acquisition system. The computation of stresses and strains, as well as examples of data acquisition, are also shown.     

大埋深粘土三轴高压卸载变形与强度特征

以取自山东巨野矿区埋深近 4 30～ 6 0 0m的深部粘土样为例 ,分析测试了土的常规物理力学性质参数。考虑该埋深土的天然应力水平及其在煤矿建井开挖中的卸载应力变化 ,在三轴伺服仪上 ,进行三向等压分别达 11MPa、12MPa、14MPa下的卸除围压、保持轴压的三轴高压卸载试验 ,分析了深部粘土三轴高压卸载变形和强度特点 ,得到了相关力学参数。成果丰富了土的高压卸载力学性研究 ,并为巨野矿区煤矿立井建设提供了工程地质基础参数     

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...     

Stress-strain relationships for spruce wood: Influence of strain rate,moisture content and loading direction

The influence of strain rate, moisture content and loading direction on the stress-strain relationships for spruce wood has been investigated. The strain rates were approximately 8×10⁻³ s⁻¹, 17s⁻¹ and 1000 s⁻¹, and the states of moisture content were those corresponding to oven dry, fiber saturated and fully saturated. Compressive loads were applied along the principal directions of the stem of the tree, i.e., radially, tangentially and axially. The low and medium strain-rate tests were performed with the aid of a servohydraulic testing machine, while the high strain-rate tests were carried out using the split Hopkinson pressure bar (SHPB) technique. Magnesium or steel bars were used in the different SHPB tests in order to reduce impedance mismatch for the different directions of the wood specimens. The strain rate was found to have large influence on the behavior of the wood, especially under the condition of full saturation, where water transport in the deforming specimen is of major importance.     

冲击速度和轴向静载对红砂岩破碎及能耗的影响

地下岩体工程爆破开挖中,距爆源不同距离处岩体承受的地应力和动载荷大小不同,从动载荷的角度表征岩石动态破坏结果与工程实际更吻合。为研究动载荷和地应力大小对岩体破碎和能量耗散特性的影响,利用动静组合加载试验装置,分别设置7个冲击速度和轴向静应力等级,对红砂岩试件进行冲击试验。根据试件的破碎状况,分析不同静应力工况下冲击速度对岩石破坏模式和机理的影响。计算不同工况下的应力波能量值,研究冲击速度和轴向静应力对岩石能耗特性的影响。对破坏试件进行筛分试验,研究岩石破碎分形维数随冲击速度和轴向静应力的变化关系。结果表明,随着冲击速度的增大,试件的破坏程度逐渐加大。无轴压时岩石试件破坏后整体仍是一个圆柱体,属于张拉破坏;有轴压时岩石试件宏观破坏后呈沙漏状,属于拉剪破坏。岩石耗散能随冲击速度的升高呈二次函数关系递增;轴向静应力越高,递增幅度越小。随着冲击速度的升高,岩石分形维数由零逐渐增加;随着轴向静应力的升高,分形维数由零转为大于零的临界冲击速度先升高后降低。     

Erratum to: Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ ₃ = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.     

A novel impact three-point bend test method for determining dynamic fracture-initiation toughness

A novel impact three-point bend test method has been developed for determining the dynamic fracture-initiation toughness,K _Id, over the range of loading rates . The split-Hopkinson pressure-bar technique is used to measure dynamic loads applied to a bend specimen with a fatigue precrack. The stress-intensity-factor histories for the bend specimen are evaluated by means of a dynamic finite-element technique and the standard formula (ASTM E 399-83) based on the measured dynamic loads. The time of crack initiation is determined using a strain gage mounted near a crack tip. The results for 7075-T6 aluminum alloy and Ti−6A1−2Sn−4Zr−6Mo alloy indicate that the reliableK _Id data can only be obtained by evaluation procedures which take the inertial effects into account. It is shown that the novel impact bend test method in conjunction with dynamic finite-element analysis provides an effective means of characterizing the dynamic fracture-toughness parameterK _Id.     

A Discrete Algorithm of Integrated Photoelasticity for Axisymmetric Problems

By measuring stresses in cylinders with no stress gradient in axial direction, the cross-section of the cylinder may be considered as consisting of concentric rings in each of which the stresses are constant. Axial stress distribution in the cylinder is determined stepwise starting with the outermost ring (the so-called onion-peeling method). This paper generalizes the onion-peeling method for the case of axisymmetric stress distributions when stress gradient in the axial direction is present. Measurement of the integrated isoclinic and optical retardation is carried out in two parallel sections which are perpendicular to the specimen axis, Δz apart from each other. The distributions of the axial stress and shear stress are determined directly from the measurement data, using linear approximation of integrated photoelasticity. Other stress components are determined using the equilibrium equation and the compatibility equation (if stresses are due to external loads) or using the generalized sum rule (if residual stresses in glass are measured). The method is less sensitive to measurement errors than the Abel inversion. In comparison with the polynomial approximation of the stress distributions, the onion-peeling method gives more adequate results if stress distribution is not smooth. The paper is illustrated with several applications.