Isotropic Specimens Research Articles

Development of a Hybrid Method of Reflection Photoelasticity for Crack Problems in Anisotropic Plates

Reflection type photoelastic experiment can be used more effectively than a transmission type photoelastic experiment especially in industrial fields. Moreover, composite materials have been widely used in engineering applications and structures because of their outstanding advantages which individual isotropic components do not have. The development of these materials requires a promising technique such as reflection photoelasticity to analyze their behaviors in service. Unfortunately, there are few experimental studies based on this technique. Therefore, a hybrid method based on this technique was developed in this research to analyze the fracture behavior of opaque anisotropic materials. The application of this method will help to understand the fracture behaviors of anisotropic materials used in engineering components and structures. The validity of this method was verified by comparison of the results obtained from this method with ones obtained from the hybrid methods for isotropic material on the same isotropic specimen. The reflection type photoelastic experiment for orthotropic materials was then applied to orthotropic plates with a central crack of various inclination angles. Using this hybrid method for anisotropic materials, stress intensity factors and separated stress components were obtained at the vicinity of the crack-tip in orthotropic plates from only the isochromatic fringe patterns of the isotropic coating material.

Magnetic flux leakage measurement setup for defect detection

This paper describes a potential technique to detect medium size defects in ferromagnetic specimen by using rather inexpensive but highly sensitive sensors based on the giant magneto resistive effect (GMR) [1]. The sensor effect is used very effectively in ultra high density magnetic recording devices and might thus prove effective in the material testing business, too. These sensors measure the magnetic flux leakage near the surface of a magneto-conductive object. In order to test their potential initial tests were performed and their results evaluated. For this survey some test specimen were made by intentionally causing some imperfections (actually small drilled holes, or some surface scratches, etc.) in an otherwise homogeneous and isotropic ferromagnetic specimen. In order to obtain the distribution of the magnetic flux leakage, the surface of the test specimen was mechanically scanned. Preliminary results are very encouraging since we could show that even small blemishes can easily be detected this way.

Full elastic tensor of a crystal of the superhard compound ReB 2

The search for superhard materials, driven by their widespread use in industrial applications, highlights one of the most difficult problems in the field of materials science: the accurate characterization of a material’s intrinsic physical properties. This paper reports on the full elastic tensor of two polycrystalline isotropic specimens and one specimen of ReB 2 consisting of highly oriented grains. The high-monocrystal bulk modulus value extracted from the grain-oriented specimen, measured by resonant ultrasound spectroscopy, validates the ultra-incompressibility of ReB 2. An observed hardness of 40 GPa and a Debye temperature of 731 K were calculated for the ReB 2 crystal, confirming its superhard and super-stiff properties. All the measured moduli of the ReB 2 grain-oriented crystal exceed the comparable ones for the polycrystal by amounts that cannot be explained by averaging over direction, which may reveal why recent measurements reported on ReB 2 containing excess boron yield values that are not as hard or incompressible as the crystal.

Description of anisotropically microstrain-broadened line profiles by Edgeworth series

Abstract The diffraction effects within the Stokes-Wilson approximation of a non-Gaussian microstrain distribution in a macroscopically isotropic specimen are described by anisotropic Edgeworth series. This Edgeworth series can for each reflection hkl be quantified by the 3rd, 4th ... N th cumulants of the microstrain distribution projected on the reflection´s diffraction vector. The diffraction-vector (hkl) dependence of these N th cumulants can be described by 2N th-rank tensors which characterise the microstrain distribution in the crystal´s frame of reference. The situation considerably simplifies in the special case of univariateness of the microstrain distribution, leading to equal (or inverted) shapes of the line-broadening contribution due to microstrain for all different hkl reflections. The Edgeworth description of microstrain was applied to X-ray powder diffraction data of two slightly inhomogeneous hexagonal ε-iron-nitride powders, ε-FeN0.433 and ε-FeN0.407. The microstrain-like line-broadening data was evaluated in terms of the probability-density functions described by Edgeworth series for the composition of these two powders.

A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing

This paper presents a hybrid procedure for mechanical characterization of hyper-elastic materials based on moiré, finite element analysis and global optimization. The characterization process is absolutely general because does not require any assumption on specimen geometry, loading or/and boundary conditions. The novel experimental approach followed in this research relies on a proper combination of intrinsic moiré and projection moiré which allows 3D displacement components to be measured simultaneously and independently using always the same experimental setup and just one single camera. In order to properly compare experimental data and finite element predictions, 3D displacement information encoded in moiré patterns which are relative to the deformed configuration taken by the specimen are expressed in the reference system of the unloaded state. A global optimization algorithm based on multi-level and multi-point simulated annealing which keeps memory of all best records generated in the optimization is used in order to find the unknown material properties through the minimization of the Ω functional built by summing over the differences between displacements measured experimentally and those predicted numerically. Feasibility, efficiency and robustness of the proposed methodology are demonstrated for both isotropic and anisotropic specimens subject to increasing pressure loads: a natural rubber membrane and a glutaraldehyde treated bovine pericardium patch, respectively. Remarkably, the results of the characterization process are in very good agreement with target data independently determined. For the isotropic specimen, the maximum error on hyper-elastic constants is less than 1% and the residual error on displacements is less than 3.5%. For the anisotropic specimen, the maximum error on material properties is about 3.5% while the residual error on displacements is less than 3%. The identification process fails or becomes less reliable if “local” displacement values are considered.

Influence of Anisotropic Properties Upon Stress Intensity Factors under Biaxial Stress

In this study, stress intensity factors were investigated and determined by photoelastic and caustics methods to clarify the mechanical behavior of crack tips under various biaxiality ratios. Polycarbonate (PC) plates with isotropic and anisotropic properties were used as specimens. The results confirmed that regardless of biaxiality ratio or the material’s property only ‘KI’ was generated in cases of a crack angle θ = 0º. It was also confirmed that only KI was generated in the isotropic PC plate with crack angle θ = 45º under a biaxial load (1:1). When the biaxiality ratio is more than 1:1 with a crack angle θ = 45º, both KI and KII are simultaneously generated in the isotropic specimen. Furthermore, KI, and KII values are influenced most by the extrusion direction in the anisotropic specimens as the biaxiality load ratios increase.

On the concept of a fully bonded coupon gauge for stress separation from thermoelastic data

Several forms of gauge can be used for the determination of individual stresses from thermoelastic data alone. A particularly useful form of gauge is the ‘coupon gauge’, consisting of a thin coupon of material which is bonded to the stressed specimen (or substrate). A novel formulation of the thermoelastic response of the fully bonded thermoelastic coupon gauge is used as the basis for the appraisal of the four possible gauge—specimen material combinations. The validity of the principal assumptions underlying the performance of these gauges is demonstrated and it is shown experimentally that the behaviour of samples of the orthotropic gauge—isotropic specimen material combination conforms to theory.

Application of a single-reflection collimating multilayer optic for X-ray diffraction experiments employing parallel-beam geometry

Instrumental aberrations of a parallel-beam diffractometer equipped with a rotating anode X-ray source, a single-reflection collimating multilayer optic and a parallel-plate collimator in front of the detector have been investigated on the basis of standard measurements (i.e.employing stress- and texture-free isotropic powder specimens exhibiting small or negligible structural diffraction line broadening). It has been shown that a defocusing correction, which is a major instrumental aberration for diffraction patterns collected with divergent-beam (focusing) geometries, is unnecessary for this diffractometer. The performance of the diffractometer equipped with the single-reflection collimating multilayer optic (single-reflection mirror) is compared with the performance of the diffractometer equipped with a Kirkpatrick–Baez optic (cross-coupled Göbel mirror) on the basis of experimental standard measurements and ray-tracing calculations. The results indicate that the use of the single-reflection mirror provides a significant gain in photon flux and brilliance. A high photon flux, high brilliance and minimal divergence of the incident beam make the setup based on the single-reflection mirror particularly suitable for grazing-incidence diffraction, and thus for the investigation of very thin films (yielding low diffracted intensities) and of stress and texture (requiring the acquisition of large measured data sets, corresponding to the variation of the orientation of the diffraction vector with respect to the specimen frame of reference). A comparative discussion of primary optics which can be used to realise parallel-beam geometry shows the range of possible applications of parallel-beam diffractometers and indicates the virtues and disadvantages of the different optics.

Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.

Toughening of immiscible PPE/SAN blends by triblock terpolymers

The mechanical performance of immiscible blends of poly(2,6-dimethyl-1,4-phenylene ether) (PPE) and poly(styrene- co-acrylonitrile) (SAN) and the subsequent influence of compatibilisation by tailored polystyrene- block-polybutadiene- block-poly(methyl methacrylate) triblock terpolymers (SBM) on the mechanical performance under static and dynamic loads is analysed in detail. A PPE/SAN 60/40 blend was selected as a base system for the compatibilisation experiments. The observed static tensile behaviour is described by micromechanical models and correlated to the blend microstructures as observed by transmission electron microscopy. In most cases, the addition of the SBM triblock terpolymers further enhances the ductility of the blend while only leading to a minor reduction of modulus and strength. Triblock terpolymers with symmetric end blocks, mainly located at the interface between PPE and SAN, led to nearly isotropic specimens. In contrast, SBM materials with a longer polystyrene block predominantly formed micelles in the PPE phase and the blends revealed a highly anisotropic morphology. Comparative investigations of the fatigue crack growth behaviour parallel to the direction of injection also reflected this variation in mechanical anisotropy of the compatibilised blends. A poor toughness and a predominant interfacial failure were observed in the case of the SBM with a long polystyrene block. In contrast, a considerable improvement in properties as a result of pronounced plastic deformations was observed for blends compatibilised by triblock terpolymers with symmetric end blocks. The systematic correlation between morphology and mechanical performance of compatibilised PPE/SAN blends established in this study provides an efficient way for the desired selection of suitable and effective compatibilising agents, ensuring both a superior multiaxial toughness as well as a high strength and modulus of the overall system.

A higher order scheme for two-dimensional quasi-static crack growth simulations

An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree, n. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to x 3/2. We therefore allow the crack extensions to contain such a term in addition to the monomial terms. The discontinuity in the crack growth direction at a kink, the kink angle, is determined by requiring that the mode II stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack. To implement the scheme, accurate values of the stress intensity factors and T-stress are needed in each step of the simulation. These fracture parameters are computed using a previously developed integral equation of the second kind.

Strengthening Concrete Slabs for Punching Shear with Carbon Fiber-Reinforced Polymer Laminates

Although research into the application of externally bonded fiber-reinforced polymers (FRPs) to reinforce concrete slabs has concentrated on improving flexural capacity, FRP laminates also offer the potential to improve the shear capacity of reinforced concrete slabs. This paper describes an innovative approach for increasing the two-way shear strength of concrete slabs with carbon FRP laminates. A process analogous to stitching is used to retrofit concrete slabs with FRP strands. An experimental study was carried out on 28 square, isotropic two-way slab specimens simulating conditions in the vicinity of an interior square column in a continuous flat plate structure. Parameters such as the concrete strength, flexural capacity, and shear reinforcement arrangement were investigated, and the applicability of existing CSA A23.3-04 and ACI 318-05 standard specifications for punching shear resistance were examined. Results from the tests show that marked increases in the punching shear capacity and ductility (over 80 and 700%, respectively) can be achieved with CFRP retrofitting of slabs. The proposed procedure appears to be technically superior, easier to implement and produces more durable structures that traditional strengthening techniques. Although the procedure was tested for retrofitting of existing slabs, the results are equally applicable to new structures.

In search of the mixed derivative ∂2 M/∂P∂T (M = G, K): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg3Al2Si3O12) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) P = −19.3(4); (∂G/∂T) P = −10.4(2) MPa K−1] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂2 G/∂P∂T = [0.07(12), 0.20(14)] × 10−3 K−1 and ∂2 K S /∂P∂T = [−0.20(24), 0.22(26)] × 10−3 K−1, both of order 10−4 K−1 and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.

Compression of homogeneous and graded SiC/EP rings: experimental results and FE modelling

Functionally graded rings based on an epoxy matrix and SiC fillers were prepared and subjected to a compression test. For comparison, rings with homogeneous filler concentration and neat epoxy were also tested. The homogeneous and the graded rings showed the tendency to break at different locations. In order to have accurate information about the material properties, tension and compression tests were performed on isotropic specimens having various SiC volume fractions. The FE simulations of the compressed rings verified the experimental data, as the stress/strain components in the representing locations were able to predict the failure.

Linear pressurization method for determining hydraulic permeability and specific storage of a rock sample

SUMMARY We studied the methodology and applicability of linear pressurization for determining simultaneously hydraulic permeability and specific storage of a rock sample. We analytically solved the governing equation for 1-D pressure diffusion through a homogenous, isotropic cylindrical rock specimen located between a downstream and an upstream reservoir considering linear pressurization of the upstream fluid as the boundary condition. The solution consists of a transient and a steady state for which both differential pressure between the two reservoirs and injection rate at the upstream reservoir assume constant values. Since the steady-state differential pressure is linearly proportional to the compressive storage of the downstream reservoir, tests conducted with a systematic variation of the size of the downstream reservoir permit determining permeability and specific storage from the intercept and slope of the linear relationship. Alternatively, simultaneous measurement of differential pressure and fluid injection rate at steady-state conditions provides a basis for calculation of the hydraulic properties as previously presented for linear injection. Experiments were performed on Fontainebleau sandstone samples to document the feasibility of the method. The determined storage capacity value is used to calculate various poroelastic parameters, such as bulk and pore-space compressibility, Skempton and the effective pressure coefficient.

Influences of Isotropic and Anisotropic Material Properties on Stress Intensity Factors of the Crack Tip under Biaxial Stress

In order to clarify the effect of anisotropy on local deformation and the stress intensity factors in the vicinity of the crack tip under complicated stress states, biaxial loading tests were carried out on isotropic (Photoelastic sheet: PSM-1, Measurements Group, Inc) and anisotropic (LEXAN 9030, General Electric Company) polycarbonate materials. The biaxial dynamic loading device, which was developed by the authors, was fully utilized in the experiments. We carried out the experiments using isotropic and anisotropic specimens with a pre-processed 0°, 15°, 30°, 45°, 60°, 75° or 90° crack angle. We applied the equal biaxial stress, that is, the loads for both the Y- and X-axis as 0N : 0N-3920N : 3920N (1 : 1). We determined the stress intensity factors of specimens using both photoelasticity and caustics method. The results of the experiments were compared. As a result, when the materials with anisotropic property are used as machine or structural members, it is important to consider the extrusion direction of the material in their design.

Stresses in a thin, circular aeolotropic plate subjected to uniform lateral load

Closed form, approximate stress solutions for simply supported cubic and orthotropic plates subjected to a lateral pressure are presented and compared with a series solution. The accuracy of the approximate solutions depends on the degree of anisotropy. For cubic plates exhibiting significant anisotropy, the approximate solution is within ∼10% of the series solution. For a graphite–epoxy composite plate of orthotropic symmetry, the approximate solution is within 10% of the series solution for the maximum stress at the plate centre and within 23% for the minimum stress at the plate centre. Single crystal plates tend to exhibit a large tangential stress where the stiff directions intersect the plate edges, implying that the edges of brittle single crystal test specimens must either be prepared better than those of isotropic specimens or have more of the plate overhanging the support.

Anisotropy and its Relation to Liquefaction Resistance of Granular Material

ABSTRACT This research establishes quantitative relationships between soil's anisotropy and liquefaction resistance for granular materials. Uniform medium density (Dr = 50%) sand specimens were prepared using three different sample preparation techniques (air pluviated (AP), moist tamped (MT), and moist vibrated (MV) to create different initial soil fabrics. Undrained cyclic triaxial tests were then performed to determine the liquefaction resistance of each soil specimen. On the same specimens in the triaxial cell, vertical and horizontal compression wave velocities and vertical shear wave velocity (Vs) were measured using piezoelectric bender elements. Anisotropic (transversely isotropic) elastic constants of the soil specimens were determined from the elastic wave measurements and additional consolidation test data. With the aid of additional data from earlier discrete element model (DEM) simulations, anisotropic parameters, which influence the liquefaction resistance, were examine. It was found that when liquefaction resistance is divided by G12/(E1/E2)3, by Gaverage/(E1/E2)3, or by V5.0s, liquefaction resistance curves converge to a unique curve regardless of the sample preparation techniques. Liquefaction Stress Ratio Reduction Factor (LSRRF) was introduced to estimate the reduction of liquefaction cyclic stress ratio of an anisotropic specimen from the isotropic specimen as simple functions of (E1/E2)-5.0 or (Vs/Vs(iso.))5.0.

In situdetermination of stresses from time-of-flight neutron transmission spectra

The pulsed neutron transmission diffraction technique exploits the sharp steps in intensity (Bragg edges) appearing in the transmitted spectra of thermal neutrons through polycrystalline materials. In this paper the positions of these edges acquired by the time-of-flight (TOF) technique are used to measure accurately the interplanar lattice distances to a resolution of Δd/d≃ 10−4of specimens subjected toin situuniaxial tensile loading. The sensitivity of the method is assessed for elastically isotropic (b.c.c. ferritic) and anisotropic (f.c.c. austenitic) polycrystalline specimens of negligible and moderately textured steels. For the more anisotropic austenitic steel, the elastic anisotropy is studied with regard to a Pawley refinement, and compared with previous results from conventional neutron diffraction experiments on the same material. It is shown that the method can be used to determine anisotropic strains, diffraction elastic constants, the residual and applied stress state as well as the unstrained lattice parameter by recording transmission spectra at different specimen inclinations, by complete analogy with the sin2ψ technique frequently used in X-ray diffraction. The technique is shown to deliver reliable measures of strain even in the case of moderate texture and elastic anisotropy.

Diffraction stress analysis of macroscopically elastically anisotropic specimens: On the concepts of diffraction elastic constants and stress factors

A unifying, rigorous treatment has been given for the diffraction stress analysis of both macroscopically elastically isotropic specimens and macroscopically elastically anisotropic specimens. The applicability ranges of so-called diffraction elastic constants and diffraction stress factors have been discussed. It has been shown that the diffraction stress factors, originally introduced for the diffraction stress analysis of textured specimens, can be generally used in the diffraction stress analysis of macroscopically elastically anisotropic specimens exhibiting direction-dependent grain interaction, independently of the presence of texture. The grain-interaction tensor has been introduced and investigated for various grain interaction models. The notion surface anisotropy of bulk specimens has been revisited as a special case of direction-dependent grain interaction.