New equipment for cyclic biaxial testing

Methods of achieving biaxial-stress states in fatigue tests are reviewed. A new design of equipment that produces five distinct biaxial-stress states by simultaneous direct pressurization and axial loading of thinwalled cylindrical specimens is described. Four variations of stress state are obtained by the use of two sizes of specimen and by reversal of the pressurizing connections. The fifth state is obtained by direct pressurization without axial load. The actual magnitudes of stress in the specimen are computed from the output of the load cell in the reaction frame in which the biaxial-testing device is mounted. Additional stress ratios are obtained using standard uniaxial and torsional cyclic-testing arrangements. The initial program using this equipment was to investigate the effects of biaxiality on the cyclic properties and low-cycle fatigue behavior of normalized 1018 mild steel, under fully reversed constant-amplitude strain control. Control was achieved using a servo-controlled, electrohydraulic testing system with one of the two clipon strain transducers, that were mounted on the specimen, providing the controlling electrical signal. The system allowed direct recording of the stress-strain hysteresis loops in both principal directions. The behavior of the equipment and the modes of failure of the specimens are described and some test data are presented. The range of application and limitations of the equipment for further cyclic biaxial testing are discussed.     

An examination of dynamic fracture under biaxial-strain conditions

An experiment to investigate the influence of biaxial strain on the dynamic fracture of metals is outlined. A hollow cylindrical specimen is loaded on the inner diameter by a polyethylene-coated exploding wire which results in a circumferential spallation pattern. Prior to fracture, the spall surface undergoes biaxial deformation with a total hoop strain of the same order of magnitude as the total radial strain. This is in contrast to earlier studies in which fracture induced by stress waves was examined in experiments which are characterized by uniaxial-strain conditions. Comparing the results of the two configurations, it can be shown that the maximum principal-stress history required to cause fracture is the same in both cases, although the stresses normal to the fracture surface are quite different. High-speed photographs of the coated exploding wires and dynamic-flash X-rays of the specimens are included to demonstrate the axisymmetry of both the loading and the spall phenomenon.     

混凝土动态双轴拉压破坏准则细观数值模拟研究

正常服役期内的混凝土结构往往处于复杂应力状态,并且不可避免地会受到偶发动力载荷作用.对于复杂载荷作用下的混凝土力学性能研究,破坏准则是基础.受试验设备等条件限制,现有的动态双轴拉压破坏准则形式复杂、缺乏更高应变率和侧应力比范围且尚未综合考虑应变率和侧应力比的耦合作用.为进一步提出适用范围更高且更准确的混凝土动态双轴拉压...     

Biaxial fracture stresses for filled-epoxy tubes

Strength results for a filled epoxy are reported for biaxial stresses. Three test methods and several specimen configurations were employed. Strength magnitudes were quite dependent upon specimen geometry under compression-compression stresses. For other stress states, this dependence disappeared and the modified Coulomb-Mohr theory fit the data well. Similar data for graphite are cited.     

Low-cycle fatigue of 7075-T651 aluminum alloy in biaxial bending

The uniaxial and biaxial low-cycle-fatigue life of 7075-T651 aluminum alloy in completely reversed bending is investigated. Uniaxial data is obtained from a cantilever specimen, and round and elliptical simply supported plate specimens are used for nominal strain biaxialities of 1∶1, 1∶075 and 1∶0.50 in the plane of the specimen. Experimental data is correlated on the basis of the total octahedral shearing strain range in which the dependent component strains are calculated using the “effective value” of Poisson's ratio for elastic-plastic loading. Good agreement is obtained oetween the uniaxial and biaxial data when the total octahedral shearing-strain range is plotted against the number of cycles to failure in logarithmic coordinates. Also, it is shown that, in anisotropic materials, the directional uniaxial and biaxial low-cycle properties can be predicted from fatigue properties in any one direction if the anisotropy of fracture ductility is known.     

Photoelastic-coating analysis of a thermoplastic,rectangular-parallelepiped pressure vessel

Photoelastic-coating techniques were used to analyze the full-field stress distribution on the critical surface of a cast thermoplastic, rectangular-parallelepiped pressure vessel. Data were presented to illustrate principal-stress magnitudes and directions obtained by the oblique-incidence method. Results obtained from a rectangular-rosette strain gage and from the post-yield residual-fringe pattern were supportive of the experimental techniques employed.     

Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. Part I: experiments

The nonlinear behavior in shear and transverse compression of unidirectional AS4/PEEK and their interaction are investigated experimentally. The composite is rate dependent even at room temperature and its rate exponent is similar to that of neat PEEK. The material is tested under pure shear, pure compression and under biaxial loading histories. The biaxial tests are performed in a custom facility on thin strips of the material. The facility allows freedom to choose the loading path in the biaxial stress and strain spaces of interest. Tests are performed for three biaxial loading paths. In the first, the specimen is sheared then compressed while the shear stress is held constant; in the second, the specimen is compressed then sheared while the compressive stress is held constant; and in the third, the specimen is loaded simultaneously by proportional amounts of compression and shear. It was found that the induced deformation is influenced significantly by the loading history followed. Also, initial loading in shear or compression has only a modest effect on subsequent loading of the other type. An unorthodox yielding behavior for the composite results from this lack of interaction. Finally, the stresses at failure are found to trace an elliptical path in the shear–transverse compression plane, but the failure stress state is not significantly affected by the loading path followed.     

Design of a biaxial extensometer for measuring strains in cruciform specimens

A biaxial extensometer for measuring strains in flat cruciform specimens is presented. This extensometer allows for the use of two displacement or strain transducers to control and measure strains along mutually orthogonal directions in the plane of the specimen. The measurement and control of strains along each direction are completely independent of each other. The resolution and the measurable strain range of the biaxial extensometer depend on the particular displacement transducers employed. Independently adjustable gage lengths are incorporated along the two directions such that different strain ranges can be measured with the same transducer displacement range. The use of the biaxial extensometer with cruciform specimens and other applications, including the possibility for measuring triaxial strains in a plate specimen, are discussed.     

双向加载条件下尼龙6-橡胶复合材料的应力松弛研究

在双向测试系统上进行了不同纵向应变与不同横向应变的双向松弛实验,研究了在双向拉伸载荷作用下单向尼龙6-橡胶复合材料的应力松弛特性．为了预测尼龙6-橡胶复合材料的应力松弛规律,提出了一个松弛型本构模型．当试件承受双向拉伸载荷作用时,将松弛型本构模型获得的理论曲线和实验数据进行了对比,二者取得了较好的一致性．     

Influence of Specimen Geometry on the Estimation of the Planar Biaxial Mechanical Properties of Cruciform Specimens

It is in general challenging to characterize planar mechanical properties of extremely soft tissues such as cell-seeded collagen gels. One of the difficulties is related to premature failure of specimens. This issue may be resolved by employing fillets on stress-concentrated spots of the specimen. The existence of fillets, however, complicates the estimation of stress at the center of the specimen where stiffness data are collected. In this study, cruciform rubber specimens with two types of fillets (general vs. cut-in fillets) at the intersections of perpendicular arms were prepared and subjected to planar biaxial mechanical testing, aiming at investigating how the fillets affect the estimation of mechanical properties of cruciform specimens. Digital image correlation was used to analyze full-field deformation in the central region of the specimens. Finite element analysis with a Neo-Hookean model was performed to simulate the full-field deformation under the same experimental boundary conditions. The strain distribution for each specimen geometry obtained by finite element analysis was found to be in good agreement with that analyzed by digital image correlation, validating the finite element models. Finite element simulation showed that the greatest value of the maximum principal strain decreased with increasing the fillet radius regardless of the fillet type. Increasing the fillet radius, in general, also reduced the strain field uniformity in the central region. Compared with general fillets, however, the use of cut-in fillets provided greater strain field uniformity given the same fillet radius. Finite element analysis was also used to estimate effective transverse length required to convert tensile force at the boundary to local stress at the center. It was found that the effective transverse length for each specimen geometry remained relatively constant if the specimen was not excessively deformed (i.e., global equibiaxial stretch ≤ 1.2). We suggest using cut-in fillets at the intersections of perpendicular arms when preparing cruciform specimens for testing extremely soft tissues.     

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.     

Photoelastic analysis of an orthotropic plate on a nonlinear foundation

Frozen-stress techniques were used to analyze an orthotropic plate on a continuous, nonlinear foundation. A long-range objective of the investigation was to provide experimental results to compare with a future finite-element analysis of the same type problem. Data were presented to illustrate principal stress magnitudes and directions. Close agreement of a static equilibrium check of the nonlinear foundation with the applied load experimentally verified the procedure used for calculation of external pressure on the model-foundation interface. Paper was presented at 1969 Fall Meeting held in Houston, Tex. on October 14–17.     

Composite specimen bearing failure reduction in iosipescu shear tests

ASTM losipescu sheart test fixtures often crush the loaded edges of high shear strength specimens before shear failure occurs between the notches. To alleviate this problem, two new shear test fixtures were designed and built. The first uses a pivoting load surface to track the specimen shape as it changes under load. The second uses a rounded load surface optimized to produce a uniform bearing pressure along the loaded edge of a quasi-isotropic sheet-molding compound (SMC) specimen at shear failure. Finite element analyses and strain gage data are presented that describe the behavior of the baseline ASTM, pivoting load surface and rounded load surface fixtures. A substantial reduction in bearing stress and edge crushing was obtained with the rounded load surface fixture. Additionally, the modified surface optimized to test SMC specimens showed no tendency to change the shear strength measured in other composite specimens.     

Viscoelasticity of brain corpus callosum in biaxial tension

Computational models of the brain rely on accurate constitutive relationships to model the viscoelastic behavior of brain tissue. Current viscoelastic models have been derived from experiments conducted in a single direction at a time and therefore lack information on the effects of multiaxial loading. It is also unclear if the time-dependent behavior of brain tissue is dependent on either strain magnitude or the direction of loading when subjected to tensile stresses. Therefore, biaxial stress relaxation and cyclic experiments were conducted on corpus callosum tissue isolated from fresh ovine brains. Results demonstrated the relaxation behavior to be independent of strain magnitude, and a quasi-linear viscoelastic (QLV) model was able to accurately fit the experimental data. Also, an isotropic reduced relaxation tensor was sufficient to model the stress-relaxation in both the axonal and transverse directions. The QLV model was fitted to the averaged stress relaxation tests at five strain magnitudes while using the measured strain history from the experiments. The resulting model was able to accurately predict the stresses from cyclic tests at two strain magnitudes. In addition to deriving a constitutive model from the averaged experimental data, each specimen was fitted separately and the resulting distributions of the model parameters were reported and used in a probabilistic analysis to determine the probability distribution of model predictions and the sensitivity of the model to the variance of the parameters. These results can be used to improve the viscoelastic constitutive models used in computational studies of the brain.     

Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen

In the current paper, an experimental technique for the evaluation of the in-plane yield loci of sheet metals with the cruciform plate specimen is presented. The measurement system is shown to conform to the optimized design concept proposed by other researchers. Finite element analysis demonstrates a reasonably wide area of uniform stress distribution in the center of the cruciform specimen, which allows the measurement of in-plane strain field by using a stacked strain rosette. Based on the designed apparatus, the yield loci of the 1100-F aluminum sheets corresponding to the as-received condition, and 25% and 50% thickness reductions by further rolling, were constructed, respectively, by applying biaxial loadings along the two principal axes of the cruciform specimen. A set of uniaxial tension tests were also performed to determine the plastic properties of the aluminum sheet along different directions with respect to the rolling direction. Finally, Hill's 1990 yield criterion is examined based on the experimental data from both biaxial and uniaxial tension tests.     

Influence of strain rate on mechanical properties of 6061-T6 aluminum under uniaxial and biaxial states of stress

A technique is presented for determining mechanical properties of materials under dynamic tensile loads. A Dynapak metalworking machine was modified into a test fixture capable of producing the required dynamic loads for uniaxial and certain biaxial tensile tests. Results from uniaxial dynamic tests on 6061-T6 aluminum alloy are presented and compared to “static” data obtained from a universal testing machine. The dependence of tensile strength on strain rate and the augmenting effect of temperature on this dependence can be seen. The results of biaxial tests are described in terms of a modified form of the distortion-energy failure theory.     

Measurement of the shapes of foil bulge-test samples

Accurate measurements of important tensile properties of thin metal foils are often quite difficult to achieve in uniaxial tests because of sample-preparation difficulties and the tensile instability called necking. Consequently, hydraulic bulge tests have been introduced as a successful means of suppressing these problems through the use of a simplified specimen geometry and biaxial rather than uniaxial tensile-stress states. Considerable effort has been made by various investigators to relate such biaxial stress-strain and ductility data to uniaxial data, generally following the assumption that the bulge is shaped like a spherical cap. The present study evaluates this assumption for foils by measuring actual shapes with unprecedented accuracy and detail using the two-source holographic technique and a polynomial-spline computer analysis of the resulting interferograms. These measurements were made on nine specimens of 0.127-mm-thick annealed rolled copper foil which had been deformed into bulges of varying heights up to rupture. A comparison is made between the measured shapes and the spherical-cap shape generally assumed in the interpretation of bulge-test data. The spherical assumption gives results which are reasonably valid for the later stages of deformation. Indeed, the stress-strain curve obtained from bulge testing corresponds closely with the uniaxial tensile curves for this material. The strain at failure (i.e., elongation) was greater in the biaxial bulge test than in the uniaxial test but not nearly as great as the strain expected from a theoretical model proposed by Hill. However, all the specimens measured exhibited localized areas with larger radii of curvature. The presence of these “flats” may be associated with a mode of failure in the bulge test which corresponds to necking instability in the uniaxial test, and thereby account for the limited strain to failure.     

Elastic-plastic analysis of biaxially loaded center-cracked plates

Center-cracked panels loaded in biaxial tension are examined in this paper. Calibration relations for the J integral and the Q constraint factor are presented for a Ramberg–Osgood power law hardening material under plane stress and plane strain loadings. Two cases are examined: an isolated crack and a periodic array of cracks both under biaxial loading conditions. The latter has previously been studied for plane stress conditions. A number of different J estimation schemes are proposed based on the remote load and displacement and their dependence on geometry, biaxiality, and material properties is discussed. The variation of constraint, as characterised by Q, is also presented for plane stress and plane strain conditions. Simple slip line field solutions are derived for perfectly plastic conditions and the resulting limit load solutions are compared with numerically determined values. Implications for failure of cracked plates under biaxial loading are discussed.     

不同尺寸砂岩动态力学性质和应力平衡性的试验研究

采用大直径分离式霍普金森压杆系统获得的不同尺寸试样的实验冲击动态力学参数有差异,因此在直径100 mm压杆上进行了3种直径（50、75和100 mm）和5种长径比（0.4、0.5、0.6、0.8和1.0）的砂岩试样冲击试验,分析了不同尺寸试样应力-应变曲线和应变率曲线随尺寸的变化,提出了用于比较波形对齐重合度的波形叠加系数,并与应力平衡因子共同构建了动态应力平衡性研究体系,由此确定大直径霍普金森压杆试验的试样建议尺寸。同时,利用高速摄影机监测试样的动态破坏状况。结果表明:当长径比相同时,直径75与100 mm岩石试样的动态抗压强度测试值相近,直径50 mm试样具有更明显的长度效应;随着试样直径的增大,应变率曲线从单峰变为双峰;小尺寸试样更易发生轴向劈裂破坏,大尺寸试样受内部应力波叠加影响产生了较大的拉应力,易发生层裂拉伸和轴向劈裂的复合型破坏;对直径75 mm且长径比0.3~0.4的试样,波形对齐后重合度较高,在起始破坏前拥有充足的应力平衡时间,应变率加载效果较好。获得了砂岩试样冲击压缩试验的尺寸效应,可为大直径岩石试样的尺寸选择提供参考。     

Cyclic multiaxial and shear finite deformation response of OFHC: Part I,experimental results

A series of experiments has been conducted on oxygen free high conductivity (OFHC) copper hollow cylinders under cyclic free-end torsion and biaxial tension–torsion at large strains. In addition, equations are developed to account for the finite rotation and strains in electrical resistance strain gages. In free-end cyclic torsion experiments with shear strain range equal to 23%, a significant strain in the axial direction is observed and it accumulates with a constant rate cycle by cycle. In the biaxial tension–torsion (multiaxial ratchetting) experiments, in which the primary (constant) axial stress is larger than the initial yield stress of the material, the loading conditions are varied to determine the influence of primary axial stress, cyclic shear strain range, pre-cyclic hardening and loading sequence on multiaxial ratchetting. Some important experimental features are high-lighted and recommended to help modeling efforts later.