A reusable biaxial strain transducer

This paper describles a transducer which is, in effect, a reusable strain-gage rosette. The sensitive member of the instrument is a flat element shaped in the form of a hollow equilateral triangle. At the corners of the triangle are styli mounted perpendicular to the plane of the triangular element. On each side of each arm, an electric-resistance strain gage is centrally mounted parallel to the edges of the arm. The two gages on an arm form a temperature-compensated pair. In operation, the styli are pressed into the test surface, and subsequent straining of the surface induces bending and twisting strains in the arms of the element. The bending strain in an arm is detected by the strain gages mounted thereon and is proportional to the strain in the test surface in the direction parallel to the arm. The bending strain in a particular arm is unaffected by the forces in the other two arms. The theory of the transducer is discussed and experimental evidence which supports the theory is provided.     

A shear stress transducer for molten polymers

Present rheometrical techniques are inadequate for the measurement of viscoelastic properties associated with shearing at high rates. A possible solution to this problem is to use a sliding plate rheometer together with a device for measuring the local wall shear stress away from the ends and edges of the plates. Such a device has been constructed, and the results of preliminary tests are encouraging.     

On the biaxial testing and strength of coated fabrics

In applying coated fabrics as roofing material for lightweight structures like tents, air-inflated structures and convertible roofs, the material is stressed in two dimensions. The different possibilities for biaxial testing of fabrics were examined and a suitable specimen shape was designed which allows the measurement of the true biaxial breaking strength. Experimental results showed that the biaxial strength is equal to the uniaxial strength. Stress-strain relations are given and compared with the uniaxial case.     

An experimental investigation of plastic flow under biaxial stress

Due to the extreme complexity of the problem, it has been necessary to formulate theories of plasticity which grossly simplify the material behavior. While, in many cases, these theories give satisfactory results, there are other cases in which they fail. Therefore an investigation has been initiated with the purpose of evaluating presently used theories and assessing the possibilities for improvement for the cases in which the classical theories are not satisfactory. The present paper describes a system for testing, which includes a data-acquisition system and a computer program for comparisons between test and theory. A few test results are included which verify the adequacy of the system and illustrate some facets of the problem.     

Cyclic stress-strain data analysis under biaxial tensile stress state

A new device was developed to assess fatigue life under biaxial tensile loading at elevated temperatures. It makes use of an annular disk specimen and can be easily mounted onto a standard push-pull machine so that the axial force is converted into radial forces extending across the disk specimen. Therefore, a positive ratio of the tangential to the radial stress can be imposed at the reduced section of the disk specimen; this ratio depends on the specimen configuration and may be fixed to a value ranging from 0.5 to 0.9 by varying the inner diameter of the disk. The proposed device has performed successfully and was used to study the cyclic behavior of Type-304 stainless steel subjected to various biaxial tensile stress states at room temperature and at 200°C. The data obtained from this experimental procedure have been analyzed to evaluate the effectiveness of some correlations already available for treating the biaxial cyclic stress-strain response in terms of the uniaxial behavior. This analysis shows that a successful correlation should account for all the stress components. The authors discuss the concept used in the modeling of the material cyclic behavior and the formulation of a biaxial fatigue damage parameter necessary for an effective analytical life prediction methodology.     

Reproducible time-of-flight measurements with a piezoelectric transducer for acoustoelastic stress evaluation

The acoustic coupling of a piezoelectric transducer to the specimen by means of a viscous couplant proves to be a weak link in performing acoustoelastic experiments. Measurements reveal that an increased coupling layer thickness potentially leads to a more reproducible time-of-flight determination. To assess the consequences of this approach, a model is developed for the pulse-echo configuration. Diffraction in the specimen is taken into account and a viscoelastic model is used to describe wave propagation in shear wave couplant. The results clearly show the advantages of an increased coupling layer thickness. Paper was presented at the 1994 SEM Spring Conference on Experimental Mechanics held in Baltimore, MD on June 8–10.     

A diffraction transducer for vibration analysis

The recently described ditfractographic technique¹, utilizing the diffraction of light passing through an aperture formed by two edges, one fixed as a reference, is used to determine small vibratory displacements. The transducer has little or no inertia, is noncontacting, and has high sensitivity and accuracy. A “time averaged” method is presented whereby peak amplitudes can be obtained with no readout instrumentation and no upper-frequency limit. Alternatively, a photodetector can be used to determine vibration amplitudes with frequency response limited only by the detector circuit.     

A biaxial test specimen for crack arrest studies

A biaxially loaded, single edge notched (SEN) fracture specimen, with mixed modes I and II loading, was used to study the crack arrest capability of a bonded and riveted tear strap without and with simulated multiple site damage (MSD). MSD was modeled by a 50-percent groove without which the running crack would inevitably kink due to K_II loading. A total of thirty-one 2024-T3 aluminum specimens with various crack and MSD configurations were tested. The fracture parameters associated with straight and curved crack paths were determined by using the experimenta results to drive a dynamic finite element model of the specimen in its generation mode. The crack kinking and extension criteria were verified by the excellent agreement between the prediction based on these fracture parameters and the measured crack kinking angles. Comparison between the test results generated by the biaxial stress specimens and by those generated by small- and full-scale pressurized fuselage rupture experiments showed that this specimen can be used to prescreen the effectiveness of tear straps and crack arrestors in an airplane fuselage.     

A biaxial thermomechanical disk test for glassy polymers

Failure criteria for polymers need to include effects from the stress state. For this reason, biaxial test results are of interest. However, biaxial test methods usually require expensive equipment. In the test method presented here, a disk of epoxy is bonded between a steel ring and a steel disk. The temperature is then lowered until fracture is observed. Experiments were performed on three different glassy epoxy polymers. The biaxial stress state was analyzed by finite element analysis and by an approximate analytical model. Experimental observations support the ability of the method to provide material property data. An approximate analytical model was found sufficiently accurate for stress analysis and determination of the stress state at failure.     

A dynamic biaxial testing machine

The development of generalized constitutive equations for materials requires additional experimental data. A testing machine is described which is capable of applying biaxial, tension-torsion loading to thin-walled tubular specimens over a wide range in loading rates. Both components of the load are independently controlled. The objective is to obtain information on the effect of the rate of loading on viscoplastic or viscoelastic behavior of materials. Some preliminary data are given on the effect of loading rate on the yielding of mild steel. Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6. The work presented herein was performed under Contract DA31-124-ARO-D-273 with the Army Research Office, Durham, Durham, N. C.     

A piezoelectric biaxial loading device for interfacial fracture experiments

In this paper we describe the development of a new biaxial loading device for investigating mixed-mode fracture at bimaterial interfaces. The new device makes use of piezoelectric actuators and specially arranged flexures to provide independent displacements normal and tangential to the interface. Capacitive probes and special washer load cells were used for measuring the displacements and reactive loads, respectively. A closed-loop circuit was formed with a personal computer to control the applied displacements to within 10 nm. Preliminary experiments with quartz/epoxy/aluminum sandwich specimens with cracks growing between the quartz and the epoxy found that the intrinsic toughness of this interface was 30% lower than the value for a glass/epoxy interface. Crack opening interferometry measurements having a resolution of 30 nm revealed the presence of a cohesive zone whose size was about 0.5 μm.     

A simple testing technique for fracture under biaxial stresses

Evidence is accumulating to suggest that the fracture toughness of and cyclic crack-propagation rates in a material may be affected by stresses acting parallel to the crack plane. This effect contradicts the justifiable assumption, implicit in fracture-mechanics theory, that only loads causing a stress singularity at the tip of a crack can affect its behavior. More extensive investigation of this important problem involves the development of special testing equipment and specimens. This article offers a simple design for such a system, which has proved in practice to be highly reliable and of adequate accuracy. Preliminary tests on polymethylmethacrylate (PMMA) under biaxial fatigue and ramp loading are described, to demonstrate the technique itself and the phenomena under investigation. The results suggest that, for this material at least, the effects of transverse stresses are indeed slight.     

A procedure for measuring biaxial viscoelastic behavior of thermoplastics

In order to accurately simulate the thermoforming or blowmolding manufacturing processes using finite elements or some other suitable computational procedure, it is necessary to know the constitutive behavior of the material being formed. In this study, an apparatus was developed to measure the large deformation behavior of thermoplastic sheet at elevated temperatures. The specifications of the test apparatus, as well as sample data measurements are presented. Biaxial viscoelastic material properities of ABS sheets were determined at forming temperatures. In particular, the nonlinear stress-strain relationship of the material was experimentally measured at various temperatures above the glass transition temperature and the data correlated to a time and strain separable viscoelastic material model. The results of this study show that it is possible to recover the underlying nonlinear elastic response of heated ABS sheet material, at finite strains, from tests exhibiting significant viscoelastic behavior.     

A new direct biaxial testing machine for anisotropic materials

A screw-driven new biaxial testing machine for the realization of experimental investigations on anisotropic sheet materials, such as composite plates or rolled sheet metals, is presented. The described mechanical concept and servocontrol system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. Moreover, for the proper implementation of biaxial tensile tests, the specific problems linked to the anisotropic properties of the investigated materials are taken into account; therefore, for the first time, the biaxial machine is supplied with the original ‘off-axes testing device,’ consisting of hinged fixtures with knife-edges at each arm of the cruciform specimen. A recently developed optimization method for the optimal design of flat tensile cruciform specimens is shortly reviewed. Numerical simulations illustrate the decisive superiority of the optimized specimen compared with specimen designs proposed in the literature, as well as the necessity to use the ‘off-axes’ testing technique in biaxial tests on anisotropic materials.     

A model for frictional slip in woven fabrics

A continuum model for frictional slip of the yarns of a plain-weave fabric is presented. The model is based on the assumption that the weave is composed of two families of continuously distributed yarns constrained at all times to occupy a common evolving surface in three-dimensional space. The two families may slide relative to one another on the surface, subject to their respective equations of motion, fiber constitutive equations, and frictional slip rules. The theory is intended for the quantitative analysis of deformation, slip and energy dissipation during a ballistic impact event. To cite this article: B. Nadler, D.J. Steigmann, C. R. Mecanique 331 (2003).     

A new method for the biaxial testing of cellular solids

Commercial cellular solids such as metal foams and honeycombs exhibit deformation and failure responses that are dependent on specimen size during testing. For foams, this size dependence originates from the fabrication-induced material and structural inhomogeneities, which cause the uncontrolled localization of deformation during the testing of foam cubes. Different peak loads and failure modes are observed in honeycomb specimens in the plate-shear configuration depending on specimen height. This size dependence causes difficulty in obtaining a more representative constitutive behavior of the material. It has recently been established that the size dependence under uniaxial compression can be eliminated with tapered cellular specimens, which enable controlled deformation at a given region of the specimen. This concept is extended in this paper to the biaxial testing of butterfly-shaped cellular specimens in the Arcan apparatus, which focuses deformation at the central section of the specimen. The Arcan apparatus has been modified such that all displacements at the boundaries of the specimen could be controlled during testing. As a consequence of this fully displacement controlled Arcan apparatus, a force perpendicular to that applied by the standard universal testing machine is generated and becomes significant. Thus, an additional load cell is integrated on the apparatus to measure this load. Example responses of butterfly-shaped specimens composed of aluminum alloy honeycomb, aluminum alloy foam and hybrid stainless-steel assembly are presented to illustrate the capabilities of this new testing method.     

Orientation dependence of stress distributions in polycrystals deforming elastoplastically under biaxial loadings

The influence of biaxiality of the loading on the crystallographic orientation dependence of crystal stress distributions is examined for polycrystalline solids deformed well into the elastoplastic regime. The examination is couched in terms of two decompositions of the stress. The first is a split of the tensor into its hydrostatic and deviatoric components; the second is a spectral decomposition of the deviatoric stress from which we express the relative values of the principal components as a function of the biaxiality of the stress. Using the framework provided by these decompositions, we investigate trends observed in the lattice strains in polycrystals subjected to biaxial loadings, comparing strains measured by neutron diffraction with finite element simulations. We conclude by showing how the orientation dependence of the stress distributions is influenced by the load biaxiality and by connecting features of the distributions to the elastic and plastic properties of the crystals. Implications of the results are discussed relative to the modeling of strain hardening and defect initiation.