High strain-rate testing: Tension and compression

Details of the split Hopkinson pressure-bar method for obtaining complete stress-strain curves at strain rates on the order of 1000 sec^?1 in either tension or compression are presented. In compression, a gage for measuring radial strain and, therefore, Poisson's ratio is also described. Some typical results are presented for aluminum, and various factors pertaining to the accuracy of the results are discussed.     

On the uniaxial compression behavior of regular shaped cellular metals

The numerical simulation of random cellular metals is still connected to many unsolved problems due to their stochastic structure. Therefore, a periodic model of a cellular metal is developed for fundamental studies of the mechanical behavior and is numerically investigated under uniaxial compression. The influence of differing hardening behaviors and differing boundary conditions on the characteristics of the material is investigated. Recommendations for the numerical simulation are derived. In contrast to common models, experimental samples of the same geometry are easy to manufacture and the results of the experiments show good agreement with the finite element calculations. Based on the proposed concept of a unit cell with periodic boundary conditions, it is possible to derive constitutive equations of cellular materials under complex loading conditions.     

An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression

Strength and deformability characteristics of rock with pre-existing fissures are governed by cracking behavior. To further research the effects of pre-existing fissures on the mechanical properties and crack coalescence process, a series of uniaxial compression tests were carried out for rock-like material with two unparallel fissures.In the present study, cement, quartz sand, and water were used to fabricate a kind of brittle rock-like material cylindrical model specimen. The mechanical properties of rock-like material specimen used in this research were all in good agreement with the brittle rock materials. Two unparallel fissures(a horizontal fissure and an inclined fissure) were created by inserting steel during molding the model specimen.Then all the pre-fissured rock-like specimens were tested under uniaxial compression by a rock mechanics servocontrolled testing system. The peak strength and Young's modulus of pre-fissured specimen all first decreased and then increased when the fissure angle increased from 0?to 75?.In order to investigate the crack initiation, propagation and coalescence process, photographic monitoring was adopted to capture images during the entire deformation process.Moreover, acoustic emission(AE) monitoring technique was also used to obtain the AE evolution characteristic of prefissured specimen. The relationship between axial stress, AE events, and the crack coalescence process was set up: when a new crack was initiated or a crack coalescence occurred, thecorresponding axial stress dropped in the axial stress–time curve and a big AE event could be observed simultaneously.Finally, the mechanism of crack propagation under microscopic observation was discussed. These experimental results are expected to increase the understanding of the strength failure behavior and the cracking mechanism of rock containing unparallel fissures.     

Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression

Based on experimental results of brittle, intact sandstone under uniaxial compression, the micro-parameters were firstly confirmed by adopting particle flow code(PFC2D). Then, the validation of the simulated models were cross checked with the experimental results of brittle sandstone containing three parallel fissures under uniaxial compression. The simulated results agreed very well with the experimental results, including the peak strength, peak axial strain, and ultimate failure mode. Using the same microparameters, the numerical models containing a new geometry of three fissures are constructed to investigate the fissure angle on the fracture mechanical behavior of brittle sandstone under uniaxial compression. The strength and deformation parameters of brittle sandstone containing new three fissures are dependent to the fissure angle. With the increase of the fissure angle, the elastic modulus, the crack damage threshold,and the peak strength of brittle sandstone containing three fissures firstly increase and secondly decrease. But the peak axial strain is nonlinearly related to the fissure angle. In the entire process of deformation, the crack initiation and propagation behavior of brittle sandstone containing three fissures under uniaxial compression are investigated with respect tothe fissure angle. Six different crack coalescence modes are identified for brittle sandstone containing three fissures under uniaxial compression. The influence of the fissure angle on the length of crack propagation and crack coalescence stress is evaluated. These investigated conclusions are very important for ensuring the stability and safety of rock engineering with intermittent structures.     

A statistical model of microcracking of concrete under uniaxial compression

At increasing external load, numerous microcracks propagate in discrete and successive stages within a body of concrete material according to the hierarchy of their tensile fracture strengths. Each microcrack propagation is conditional upon the statistical encounter of its associated fracture criterion. This paper shows the development of a statistical model for the progressive microcrack growth process within a body of concrete material at monotonic uniaxial loading in compression to ultimate failure. This model is formulated by using the Weibull's statistical theory of the strength of materials. The body of heterogeneous concrete material is simulated as a continuum comprising a large population of microscopic “weakest-link” isoenergy elements, each of which contains a unit-volume of representative micro-structural material which is linearly elastic, homogeneous and isotropic. The statistical modelling is derived from the stochastic evaluation of the tensile micro-fracture probabilities of these isoenergy elements at increasing global uniaxial compressive strains.     

单轴压缩下微纳晶镍的孔洞演化模型

在含孔隙微纳晶材料受单轴压缩载荷下的大塑性变形中,由于孔洞与基体变形的不匹配,在孔洞周围将产生大量的几何必需位错,本文假设这些位错均匀地从孔洞表面向其内部发射,促使孔洞周围先产生局部非均匀变形,从而导致微纳晶镍试样内孔隙率的变化。基于这种假设本文首先建立了单轴压缩载荷下孔洞的演化发展模型,并用此模型预测了孔隙率的变化,将其与实验测定值进行了比较,结果表明孔洞演化发展模型具有一定合理性。在此基础上,讨论了固定孔隙率和演化发展的孔隙率对不同晶粒尺寸和不同应变速率下的纳晶镍试样力学行为的影响。     

The strain-rate behavior of ductile polymers

The stress-strain-strain-rate behavior of polycarbonate is presented. It is demonstrated that the material does not exhibit a double-yield-point phenomenon, as others have reported, if true stress is plotted against actual strain. Also, the behavior of polycarbonate is presented under constant strain rate and relaxation conditions. The observed behavior of the material is discussed in relation to elements of recent theories of viscoelasto-plasticity due to Nagdi and Murch and Crochet. Simple mechanical models of the Bingham type are presented and are discussed with respect to the constitutive equation characterization of polycarbonte. The advantages and disadvantages of more general models are mentioned. Finally, the strain-rate behavior of PMMA (Polymethylmethacrylate) and a poylester given by others is presented and discussed, relative to polycarbonate and the characterization procedures used.     

含预置损伤复合材料加筋板的单轴压缩屈曲分析

通过试验和有限元方法分析了单轴压缩下加筋板的失效模式.研究了三种预置损伤位置及四种损伤尺寸的复合材料T型加筋板的线性及非线性屈曲行为,比较了损伤对临界屈曲载荷和最大失效载荷的影响.研究结果表明:损伤位置在桁条间蒙皮时,损伤的尺寸对其临界屈曲载荷和最大失效载荷影响较小;损伤位置在桁条区蒙皮时,加筋板的临界屈曲载荷随损伤尺寸的增加而明显降低,最大降低50%;损伤位置在桁条边凸缘处蒙皮时,加筋板最大失效载荷所受影响随损伤尺寸的增加而明显降低,最大降低25%.从而得到了复合材料加筋板临界屈曲载荷比和最大失效载荷比与损伤位置及尺寸的关系图.     

Numerical analysis of edge effects in laminated composites under uniaxial compression

Edge effects in a laminated composite with two isotropic components under uniaxial compression are studied. Grid equations are derived using a modified variational difference method. Numerical results are analyzed     

Statistics of particle interactions in dense granular material under uniaxial compression

Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local relative motion and the macroscopic motion. The validity of the Voigt and Reuss assumptions is examined, and extensions to these assumptions are proposed. Effects of history in the dense granular material are investigated. Statistical samples used in this paper are obtained using three-dimensional numerical simulations of dense granular media under uniaxial cyclical compression. The results show that stresses arise mostly from normal forces between particles, and direct contributions from frictional tangential forces between particles are small. Tangential friction, however, significantly increases the particle contact time, and thus reduces the rate of contact breakage. The contact breakage rate is demonstrated to be a stress relaxation rate. Therefore, stress increases significantly with friction between particles as a result of prolonged relaxation time.     

Postbuckling of rectangular plates under uniaxial compression combined with lateral pressure

Based on the nonlinear large deflection equations of von Kármán plates, the lateral pressure is first converted into an initial deflection by Galerkin method, the postbuckling behavior of simply supported rectangular plates under uniaxial compression combined with lateral pressure is then studied applying perturbation method by taking deflection as perturbation parameter. Two types of in-plane boundary conditions and the effects of initial geometric imperfection are also considered. It is found that the theoretical results are in good accordance with experiments.     

单轴压缩下页岩类脆性材料细观损伤演化的离散元分析

了解广泛存在的类似页岩的脆性材料各向异性对工程安全具有重要意义。本研究将页岩视为粘结颗粒材料,基于离散单元方法研究了横观各向同性脆性页岩的损伤演化。再现了不同层理角的页岩试样的破坏模式,并对比了实验和数值模拟的抗压强度和弹性模量。引入微裂纹的概念,通过定义裂纹密度函数,系统地研究了单轴压缩条件下,页岩层理角对细观结构的影响。此外基于平均配位数建立了配位数变化与细观损伤的联系,并根据配位数的变化与裂纹数量将加载过程分为三个阶段,分析了不同阶段配位数与裂纹数量的对应变化关系。研究表明,页岩的裂纹密度随着层理角的增加而增加,而试样的平均配位数在加载过程中先上升后剧烈下降,颗粒集合体在单轴压缩条件下的应力应变及裂纹数量曲线与平均配位数曲线有良好的一致性。该研究揭示了横观各向同性脆性岩石的破坏过程和内在机理,将为页岩类脆性材料的工程应用提供理论指导。     

Stress and strain-rate formulations for fabric evolution in polar ice

Re-orientation of individual crystal glide planes, as isotropic surface ice is deformed during its passage to depth in an ice sheet, creates a fabric and associated anisotropy. We re-examine an orthotropic viscous law which was developed to reflect the induced anisotropy arising from the mean rotation of crystal axes during deformation. This expresses the deviatoric stress, the stress formulation, in terms of the strain-rate, strain, and three structure tensors based on the principal stretch axes, and involves two fabric response coefficient functions which determine the strength of the anisotropy. A validity condition implicitly relates the two response functions, so the model law has only one independent fabric response function. A modified formulation is now presented in which the two fabric response coefficients are expressed as functions of different invariant arguments, and the validity condition becomes an explicit algebraic relation between the two functions. The response can therefore be described explicitly in terms of a single fabric response function. An analogous orthotropic viscous law for the strain-rate, the strain-rate formulation, akin to the conventional “flow law” for isotropic ice, expressed in terms of the deviatoric stresss, strain and the three structure tensors, is also constructed. Correlations with complete (idealised) uni-axial compression and shearing responses are made for the stress formulation, to determine the fabric response function which would yield these responses. Received January 30, 2002 / Published online October 15, 2002 RID="*" ID="*" On leave from the Institute of Hydroengineering, Polish Academy of Sciences, ul. Waryńskiego 17, 71-310 Szczecin, Poland Communicated by Kolumban Hutter, Darmstadt     

Elasto-plastic analysis for the buckling and postbuckling of rectangular plates under uniaxial compression

Full-range analysis for the buckling and postbuckling of rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as itsperturbation parameter.In this paper the effects of initial geometric imperfection on the postbuckling behaviorof plates have been discussed.It is seen that the effect of initial imperfection on the inelasticpostbuckling of plates is sensitive.By comparison,it is found that the theoretical results ofthis paper are in good agreement with experiments.     

Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression

In this paper, applving perturbation method to von Kármán nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments. The method suggested in this paper which has not been found in previous papers is rather simple and easy for the postbuckling analysis of rectangular plates.     

Numerical modeling of ice behavior under high velocity impacts

In this work a constitutive relation for ice at high strain rates and an algorithm for its numerical integration are developed. This model is based on the Drucker–Prager plasticity criteria, which allows a different behavior in tension and in compression. In addition a failure criteria, based on pressure cut-offs, is implemented to describe the ice damage. In order to validate the constitutive model, numerical simulations were compared with experimental results, in which ice cylinders were impacted against a steel plate, allowing the measurement of the contact load. Three different numerical solvers are used in order to analyze its performance to appropriately modeling the ice behavior.     

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar (SHPB) method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of −3^?C, −8^?C, −13^?C, −17^?C, −23^?C, and −28^?C and with the strain rates from 900 s⁻¹ to 1 500 s⁻¹. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain rate sensitivity. The strength of the frozen soil under the nearly uniaxial strain is greater than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.     

Postbuckling behavior of circular cylindrical shells under compression

Applying the Galerkin procedure to the Donnell basic equations, reasonably accurate solutions are obtained for the postbuckling behavior of clamped circular cylindrical shells under axial compression. To make a distinct comparison with the previous experimental results, calculations are carried out for shells with the same elastic and geometric parameters and the relations between the waveform, axial shortening and maximum deflections with applied loads are clarified. The results here obtained are found to be in reasonable agreement with experimental ones throughout the regions with fairly large deformations.     

单轴压缩下断续节理岩体动态损伤本构模型

断续节理将对工程岩体的强度及变形等力学特性产生显著影响,损伤力学中视节理为岩体的一种宏观损伤,因而采用损伤张量来刻画其对岩体的影响。目前学术界提出了用节理的几何、强度及变形等3类参数来描述节理的物理力学性质,而目前的岩体损伤张量计算方法都只涉及前2类参数,均没有涉及其变形参数即法向及切向刚度。为此,在前人研究的基础上,基于断裂及损伤理论提出了考虑节理法向及切向刚度的单轴压缩下单条断续节理引起的损伤张量计算公式,进而通过考虑节理间相互作用给出了单组单排或多排节理岩体损伤张量计算公式。其次,以岩石细观动态损伤模型为基础,结合宏细观损伤耦合观点提出了一个能够同时考虑节理几何、强度及变形参数的断续节理岩体动态损伤本构模型。最后,利用该模型讨论了节理参数及载荷应变率等对岩体动态力学特性的影响,认为节理长度减小及摩擦角增大将导致岩体动态峰值强度及弹性模量增大;岩体动态峰值强度及弹性模量则随着节理法向及切向刚度的增大分别减小或增大;而当节理法向及切向刚度按照同一比例增大时,岩体动态峰值强度及弹性模量则是增大的。岩体动态峰值强度与载荷应变率呈正相关。     

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006.