Photoelastic stress analysis of a V-shaped die for plastic work

The stress state in the V-shaped die for plastic compression was investigated by using a photoelastic stress analysis in which an Araldite in a glassy elastic state and a softened celluloid were used as model materials for the die and work specimen, respectively. It was found that the direction of the frictional shear stress is reversed at a certain point on the die surface. Because the frictional shear stress of the die mainly depends on the flow speed of the work material, the popular assumption that the coefficient of friction is a constant over the die surface such as in the case of Coulomb friction appears unrealistic.     

Use of three-dimensional photoelasticity in fracture mechanics

The philosophy of fracture mechanics is reviewed and utilized to formulate a simplified approach to the determination of the stress-intensity factor photoelastically for three-dimensional problems. The method involves a Taylor Series correction for the maximum in-plane shear stress (TSCM) and does not involve stress separation. The results are illustrated by applying the TSCM to surface flaws in bending fields. Other three-dimensional problems solved by the TSCM are cited.     

Deformation of melts of mixtures of incompatible polymers in a uniform shear field and the process of their fibrillation

Fibril formation in mixtures of incompatible polymers, in this case polyethylene and polystyrene, has been studied with their melt being deformed in a uniform shear field. It has been found that when polyethylene is present in a smaller amount, it may form very long fibrils 5 to 8 μm in diameter in the deformed mixture. The formation of such fibrils is determined by the relationship between the viscosity ratio of the mixture components and shear stress. Also, just as in the case of a nonuniform shear field in a flow through a duct, fibril formation in melts of mixtures of incompatible polymers in a uniform shear field takes place upon reaching a certain shear stress. The lower the ratio between the viscosities of the fibril-forming polymer and the other component, the lower this shear stress.     

An electromagnetic shear-stress gage for large-amplitude shear waves

In many materials, especially plastics, ceramics and rocks, large-amplitude shear-wave propagation studies could provide valuable information for the development of constitutive equations. A newly developed electromagnetic-gage configuration provides an output voltage which is directly related to the dynamic shear stress in the material. The electromagnetic shear-stress gage has been used to make direct measurements of shear-wave stresses in PMMA and Solenhofen limestone. Large-amplitude shear waves were obtained with a new plate-impact technique which generates shear waves by a controlled-reflection process. The configuration of the stress gage permits it to be used simultaneously with more conventional electromagnetic velocity gages, thus providing both types of data in one experiment.     

Allowance for the effect of nonisothermicity on heat transfer in channels during the laminar movement of liquids having a linear law of fluidity

Nonisothermal heat exchange during the laminar flow of liquids having a linear law of fluidity in the thermal initial section of channels is analyzed. The calculation for the condition that t_ω =const takes into account the effect of the temperature on the zero-point fluidity and the coefficient of instability of the structure when the thermal conductivity (diffusion) depends on the shear stress.     

The rheological behaviour of HDPE/LDPE blends

The rheological behaviour of three types of HDPE/LDPE blends at several compositions (various weight percentages of LDPE) has been studied with the aid of a capillary rheometer and three different capillaries. In particular, entrance effects and shear viscosities have been determined over a wide shear rate region and at different temperatures. Thus activation energies could also be evaluated. Synergistic effects are evidenced when the relevant properties of the homopolymers parents are not too different from one another.     

Experimental analysis of slow viscous flow using photoviscosity and bubbles

Photoelasticity in solids is a well-developed technique for stress and strain analysis. Less progress has been made in applying a similar effect, photoviscosity, to flow analysis. This paper has three objects: (1) to simplify photoviscous methods; (2) to compare velocity profiles obtained from photoviscosity with those obtained by the double-exposure bubble technique; (3) to determine the principal strain rates and the maximum shear stress from photoviscotity. The problem of slow viscous flow about a cylindrical obstacle in a rectangular channel was selected for the comparison. The fluid was a suspension of milling yellow dye in water. Strain rates and stresses averaged over the path of ligh can be obtained easily using photoviscosity. The bubble technique is shown to be a very powerful tool that permits the determination of the velocity field in three-dimensional problems.     

Determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments

In this paper, theoretical formulations based on the Stroh’s complex function approach were used to find the displacement field and H-integral of a sharp V-notch formed from several anisotropic materials. Displacements from the image-correlation experiments are then substituted into the least-squares formulation to find V-notch stress intensity factors (SIFs) in multi-material anisotropic wedges. Validations using the H-integral indicate that the experimental SIFs evaluated from the proposed method of acceptable accuracy. The major advantage is that the proposed method only requires displacements inside the specimen, and displacements near the notch tip, specimen boundaries, or notch surfaces are not necessary.     

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate.Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the WuCarlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

Stress-concentration factors for semielliptical notches in beams under pure bending

Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical. The graphs herein will enable the designers to find the stress-concentration factors of elliptical notches and to pick out the geometry of the optimum notch which will give the least stress concentration for any given values of 2a/h andd/h. Stresses and the stress-concentration factors at the bottom of the beam opposite the notch are also obtained. These stresses, though smaller in magnitude, are of an opposite sign to the peak stress at the notch. For brittle materials, a smaller tensile stress may be more critical than a large compressive stress; therefore, these stress-concentration factors are also given.     

Photoelastic investigation of a shrink-fit problem

Stress analysis of the components of a shrinkfit assembly has been carried out by the three-dimensional photoelastic technique. Experimental results obtained from the analysis of a typical shrink-fit assembly, wherein a cylindrical wheel is shrink fitted onto a hollow cylindrical hub in an asymmetrical position. Photoelastic models made from hot-setting Araldite B were loaded at the critical temperature in a stress-freezing oven and the meridional and the hoop slices were observed in a transmission polariscope. It is concluded from this investigation that the bending induced in the components due to the asymmetrical placement of the wheel and the contact shear at the interface influences the stress distribution quite considerably. Also, the dimensions of the components in the axial direction have an influence on the mode and contribute to the magnitude of the variation of stress components.     

Crack initiation at the rectangular step notch surface under combined loading

Summary  Under external forces acting on the face of a notch, cracks originate at corners, and the system is liable to fail. An analysis is presented of the stress field in the neighborhood of the notch tips, based on the integral representation of the biharmonic solution and on numerical methods. Computations were performed for constant loading or constant displacement distributed along one face of the notch. The coefficients in the principal terms of the asymptotic formulae for the circumferential and shear stresses depend on the angle and height of the notch face and on the boundary conditions. The maximal values of these coefficients determine the stress intensity factors for the opening and shear modes. The angles corresponding to the maximal values of the intensity factors indicate the directions of initiation of opening and sliding cracks. Received 30 May 2000; accepted for publication 3 April 2001     

The effect of a coupling agent on the viscoelastic properties and internal stresses in high density polyethylene filled with glass spheres

It is shown that covalent bonding between high density polyethylene (HDPE) and glass spheres can have a significant influence on the stress relaxation behaviour and the creep properties of the corresponding composites at room temperature. The bonding is obtained by reacting the glass spheres with an azide functional alkoxysilane which is capable of bonding to the HDPE-chain. The internal stress, evaluated from relaxation experiments, increased markedly as a result of this treatment, and it is suggested that the internal stress level reflects the properties of the interphase region between the filler and the bulk matrix and its effect on the viscoelastic properties.     

A technique for reducing the fringe frequency in large-displacement holography

The analytical method of superposition is combined with the experimental technique of multiple-exposure holography to decrease the sensitivity of holographic measurement by at least an order of magnitude. Moiré fringes of a lower frequency are produced which simultaneously extend the range of measurement to larger displacements. The method is demonstrated for the case of a clamped circular plate subjected to a concentrated load centrally applied.     

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.     

Influence of disperse phase concentration upon the viscoelastic behaviour of emulsions

Rheology of soya oil-water emulsions in the linear region has been studied. The viscoelastic response consisted of three contributions. There was a purely elastic component, a purely viscous component and a contribution due to the retarded compliance. Emulsions became more viscous and elastic with increasing soya oil concentration. Sharp changes in rheology were observed as the concentration approached the random close packed limit. There was also a marked increase in zero-shear viscosity. Breakdown of coagulation structure was observed as the shear stress was increased into the non-linear region. The rheological behaviour of the emulsions in the linear region could be adequately described by the generalized Kelvin-Voigt model.     

Adiabatic shear localization in the impact of edge-notched specimens

Impact experiments are performed on edgenotched specimens in the two-dimensional punch geometry. Materials tested include 18Ni(350) maraging steel; S7 tool steel; 4340, 300M, HP 9-4-20 and D-6ac ultra high-strength steels; and Ti6Al4V alloy. These materials have shown a high susceptibility to dynamic shear failure in previous studies. Impact velocity ranged from 25 m/s to 45 m/s, and shear bands were found to form at the notch tip and at the die corner on the back side of the specimen for all materials tested. Metallurgical analysis confirms the existence of adiabatic shear bands followed by a crack propagating through the fully developed shear band. High-speed photography was used to observe the initiation of adiabatic shear bands shortly after impact. Laser-etched lines on the specimen surfaces allowed the determination of the time of impact and the initiation time of shear failure. The elapsed time between the two was used to estimate the stress intensity factor at the time of shear band initiation. Comparisons of shear band initiation stress intensity factors at the notch tip and die corner are made. It is seen that the shear bands initiate at approximately the same stress intensity factor at both the notch tip and die corner. Finite element simulations support the use of a square root singularity for the stress in the plate near the corners of a deformable punch or die.     

A photoviscoelastic analysis of time-dependent stresses in a polyphase system

The method of photoviscoelastic stress analysis is used to predict time-dependent stress redistributions in a polyphase-material system having a viscoelastic binder and subjected to applied exteernal-loading conditions. The polyphase-material model studied is composed of a photoviscoelastic matrix material and contains rigid inclusions and voids, thus simulating a threephase composite system. In order to perform the study, a photoviscoelastic model material is developed. An epoxy-resin system consisting primarily of Shell Epon 828 and Epon 871, optimized to display the properties desirable for such application, is utilized. The time-dependent stess distributions obtained by the photoviscoelastic analysis are compared with results obtained by applying the “correspondence rule” to a finite-element solution for the elastic stress field of a mathematical model of the three-phase material system. The comparison of results indicates that the technique of photoviscoelastic stress analysis is extremely applicable to complex models such as the one studied. The feasibility of this application to more complex polyphase models with varying loading conditions is indicated.     

<Emphasis Type="Italic">T</Emphasis>-stress estimation by the two-parameter approach for a specimen with a V-shaped notch

In the present research, T-stress solutions are provided for a V-shaped notch in the case of surface defects in a pressurised pipeline. The V-shaped notch is analyzed with the use of the finite element method by the Castem2000 commercial software to determine the stress distribution ahead of the notch tip. The notch aspect ratio is varied. In contrast to a crack, it is found that the T-stress is not constant and depends on the distance from the notch tip. To estimate the T-stress in the case of a notch, a novel method is developed, inspired by the volumetric method approach proposed by Pluvinage. The method is based on averaging the T-stress over the effective distance ahead of the notch tip. The effective distance is determined by the point with the minimum stress gradient in the fracture process zone. This approach is successfully used to quantify the constraints of the notch-tip fields for various geometries and loading conditions. Moreover, the proposed T-stress estimation creates a basis for analyzing the crack path under mixed-mode loading from the viewpoint of the two-parameter fracture mechanics.     

Adaptive control of MEMS gyroscope using global fast terminal sliding mode control and fuzzy-neural-network

An adaptive control of MEMS gyroscope using global fast terminal sliding mode control (GTSMC) and fuzzy-neural-network (FNN) is presented for micro-electro-mechanical systems (MEMS) vibratory gyroscopes in this paper. This approach gives a new global fast terminal sliding surface, which will guarantee that the designed control system can reach the sliding surface and converge to equilibrium point in a shorter finite time from any initial state. In addition, the proposed adaptive global fast terminal sliding mode controller can real-time estimate the angular velocity and the damping and stiffness coefficients. Moreover, the main feature of this scheme is that an adaptive fuzzy-neural-network is employed to learn the upper bound of model uncertainties and external disturbances, so the prior knowledge of the upper bound of the system uncertainties is not required. All adaptive laws in the control system are derived in the same Lyapunov framework, which can guarantee the globally asymptotical stability of the closed-loop system. Numerical simulations for a MEMS gyroscope are investigated to demonstrate the validity of the proposed control approaches.