Photoelastic Investigations Research Articles

Stress distributions around the interference fit between a round pin and a perforated finite plate

Interference fit couplings between a perforated finite plate and a round pin are widely used mechanical systems in several industrial applications. Only a few works in the literature investigate the coupling contact pressure due to interference in the absence of an external load, and these works are limited to a few specific configurations. To overcome this limitation, this work performs a numerical systematic investigation of the pin-plate coupling for a wide range of configurations that can be encountered in practice. Three are the variables investigated: the pin diameter, the plate length, and the pin offset in the longitudinal direction, all of them normalized over plate width, for a total of 18 configurations. The work provides a detailed prediction of the contact pressure and equivalent von Mises stress along the contact surface and compares the results with photoelastic investigations retrieved from the literature. For design purposes, the results are synthesized through two stress concentration factors, one referring to the peak contact pressure, and the second one to the peak von Mises stress.

Interfacial shear strength studies of experimental carbon fibres, novel thermosetting polyurethane and epoxy matrices and bespoke sizing agents

The strength and nature of the fibre-matrix connection affects many of the key mechanical characteristics of composite parts. The complex interplay of fibre surface, sizing agent and matrix material has been a longstanding problem and receives substantial attention when new ingredients are introduced. For the first time, this study investigated a novel thermosetting polyurethane resin together with a set of experimental carbon fibres. The fibres were manufactured using a unique facility that closely models a commercial production line. This equipment allowed extracting fibres after carbonisation, after electrochemical surface treatment and after coating with epoxy, polyurethane and polyamide based sizing agents. A commercial carbon fibre and a state of the art epoxy resin were selected as reference materials. The single fibre fragmentation test was used to measure the interfacial shear strength (IFSS) of the resulting combinations. The results show the enormous importance of etching away the relatively inert outer layer during surface treatment as the IFSS increased by factor 2.6. The newly developed polyurethane resin showed for unsized fibres up to 50% higher values for the IFSS than corresponding combinations employing epoxy resin. This superiority melted down to 5–21% when looking at the sized fibres, showing the need for developing sizing agents that facilitate adhesion to polyurethane matrices. A relative advantage of identical sizing and matrix polymer could be found when looking at sized fibres. Photoelastic investigations of the fragmented specimens supported the measured values for the IFSS. There was a close correlation between high IFSS results and strong photoelastic stress patterns.

A CAE approach for the stress analysis of gear models by 3D digital photoelasticity

The use of numerical and experimental methods to determine the stress field of mechanical components is well known. In particular, 3D photoelasticity can be considered the only experimental technique for the complete stress state evaluation of 3D components. The advent of rapid prototyping techniques has allowed the manufacturing of complex models in a matter of hours by using birifrangent materials. The present paper is focused on the description of a Computer Aided Engineering (CAE) approach which combines Finite Element (FE) simulations and automatic photoelastic investigations for the stress analysis of face gear drives, made by stereolithography. Computer Aided Design (CAD) geometries, used to manufacture the stereolithographic models, are directly used to perform FE analyses, thus allowing the stress analysis process to become simpler and easier. The substantial agreement observed between experimental and numerical results proved the potentialities of the adopted approach and the usefulness of FE simulations to optimize photoelastic analyses through cost- and time-effective experiments even for complex 3D shapes.

Tibiofibular screw fixation for syndesmotic ruptures: a biomechanical analysis

The mechanisms of injuries to the tibiofibular syndesmosis include isolated rupture and rupture in combination with ankle fractures. Current concepts of surgical treatment are fixation using bioabsorbable screws, syndesmotic stapling, syndesmotic hooks, and the widely used screw fixation. Postoperative care utilises passive motion of the ankle joint either with or without axial weight-bearing. The aim of our investigation was to quantify the motion of the mortise during axial load. Therefore, photoelastic tests, on the one hand, and biomechanical tests of cadaveric specimens, on the other, using axial loads of up to 2,000 N were used. Our photoelastic investigations showed force distribution through the screw into the cranial and caudal parts of the distal fibula. Biomechanical testing showed a progressive dehiscence in both ruptured and fixated specimens up to 2.89 (ruptured) and 2.42 mm (despite screw). Our findings strongly suggest a concept of partial weight-bearing at most to support regeneration of scar tissue and to prevent the appearance of instability in the ankle joint.

On the use of stereolithography built photoelastic models for stress analysis investigations

When designing mechanical components, it is essential to investigate and provide crucial information for mechanical failure due to stress generation. Photoelasticity and numerical methods are well known for stress determination and design evaluation purposes. The rapid-prototyping technique of stereolithography allows complex models of components to be built, in a matter of hours, out of photoelastic resins. The objective of this study was to evaluate the feasibility of a commercially available epoxy-based photopolymer for photoelastic investigations. A number of experiments were undertaken to address critical material and fabrication issues related to stereolithography built photoelastic specimens. The data gathered from photoelastic model testing was compared to the ones generated by numerical analysis. The good correlation between them in terms of measured and calculated magnitudes of stress provide increased confidence in the investigated photopolymer for photoelastic stress analysis purposes, and consequently for validation of computer-based models, utilizing thus stereolithography models as complementary design tools.

Automatic Plotting of Principal Stress Trajectories by Direction Function Contouring.

We propose a new algorithm to plot principal stress trajectories in plane systems. Much time and labor with experience are required in order to draw trajectories from the result of the photoelastic investigations. The possibility of branching or joining of trajectories cannot be disregarded, when the method of tracking principal stress direction from element to element is used. Our algorithm, on the contrary, plots the principal stress trajectories as the contours of the direction function which is evaluated from the result of FEM using the constant strain triangular elements. Direction function is a two dimensional scalar field whose value is constant along principal stress trajectories. Two function values for the first and the second principal stress of each node are computed by solving the simultaneous liner equations with rectangular sparse matrix. The unit direction vectors of principal stress given by FEM determine the matrix. When the scalar field forms a spiral surface, the unique value of the direction potential of each node is obtained by putting the discontinuity along a polygonal line in the finite element mesh. The line density of the trajectories with broken line pattern in the output figure is read as the magnitude of the principal stress declining toward the free boundary.

Advanced digital photoelastic investigations on the tooth-bone interface.

The purpose of this study was to investigate the behavior of the tooth-bone interface on the nature of stress distribution in the tooth and its supporting alveolar bone for various occlusal loads using an advanced digital photoelastic technique. A digital image processing system coupled with a circular polariscope was used for the stress analysis. The phase shift technique and a phase unwrapping algorithm was utilized for fringe processing. This aids in obtaining qualitative and quantitative information on the nature of stress distribution within the dento-osseous structures. The experiments revealed bending stresses within dento-osseous structures. However, the compressive stress magnitude was larger than the tensile stress. Zero stress regions were also identified within the dento-osseous structures. The results suggest that the geometry of the dento-osseous structures and the structural gradients at the tooth-bone interface play a significant role in the distribution of stresses without stress concentrations. Further, the application of an advanced image-processing system with the circular polariscope showed notable advantages and could be applied in other biomechanical investigations.

Fixation of three-dimensional states of deformation in polymers by ionizing radiation — III. Experimental results and implementation

Photoelastic investigations using transparent polymeric materials are still a potential tool in mechanical engineering, in civil engineering and more recently in biomechanics. They allow the analysis of deformations or stresses even in complex three-dimensional bodies. In order to extend the application of such plastic models at ambient temperature it was necessary to improve the fixation of deformations in the loaded state. This could be realized by the study and proper modification of some radiation-curable polymer systems (Schaudy et al., 1995, 1996). The experimental results reveal a broad variety of properties due to the type of the polymer system and to the degree of crosslinking caused by the radiation dose applied. Simple spatial models are as well discussed as the industrial and scientific implementation of the new materials.

Application of a birefringent lens in photoelastic studies using a coherent moiré technique

Abstract In photoelastic investigations, one uses the property of stress induced birefringence for stress analysis. Normal polariscopes are used for such studies. However, the accuracy of the methods is low. For better accuracy, interferometric and holographic methods are generally used. Holography, along with a shearing technique, is also used to obtain partial derivatives of displacement with respect to spatial co-ordinates. In these methods, the resultant fringe pattern is obtained from the mutually shifted holograms and the generation of such patterns requires four exposures altogether. The present paper represents a method based on a coherent moire technique for studying the first derivative of a stress pattern using birefringence properties. The analysis seems to be very similar to holographic techniques as both produce second order fringes. The advantage of this method is that it requires only one exposure. The basic principle as well as some experimental results are presented.

Simulation of three-dimensional waves for crack detection

The numerical solution of transient dynamic problems with a broad frequency range needs large systems with many degrees of freedom and time steps. This is the domain of today's powerful supercomputers. Fast algorithms and programs for dynamic problems have to be developed to make effective use of vector computers and parallel computers to get high accuracy of the numerical system with short computational time. The FD-program TransDyn, developed at the CRI, uses a fast vectorized explicit algorithm for the solution of two- and three-dimensional transient dynamic problems on supercomputers and workstations with graphic visualizations. As an example of application the vectorized program is used for realistic simulations of mechanical waves for crack detection on a Siemens S400 40 . The numerical results are compared with results from photoelastic investigations.

Irradiation of polymers for photoelastic investigations

The photoelastic behaviour of transparent polymers is studied with the objective to learn more about the correlations between molecular structure, mechanical properties, and stress-optical sensitivity on the one hand and to improve the fixation process by radiation at room temperature for practical purposes on the other hand. The fixation of three dimensional states of deformation allows the analysis of special states of elastic stresses even in the interior of complex constructional units and machine parts. As a continuation of former work, the polymeric system consisting of well-known epoxy resin and maleic anhydride has been modified by the addition of mono- and polyfunctional acrylates and of an inhibitor to protect the reactive double bonds. Preliminary results are presented. This work is part of the Austrian contribution to an international co-operation between scientists from Hungary, Croatia and Austria.

Mixed-mode stress intensity factors for arbitrarily oriented cracks in cylindrical shells under axial pull and torsion

Results of photoelastic investigations conducted on cylindrical tubes (made of Araldite material) containing cracks oriented at 0°, 30°, 45°, 60° and 90° to the axis of the tube and subjected to axial and torsional loads are reported. The stress-intensity factors (SIFs) were determined by analysing the crack-tip stress fields. Smith and Smith's method [ Engng Fracture Mech. 4, 357–366 (1972)] and a new method developed by the authors by modifying Rakesh et al.'s method [Proc. 26th Congress of ISTAM, India (1981)] were employed to evaluate the mixed-mode SIFs.

Thermoelastic and photoelastic properties of crosslinked liquid‐crystalline side chain polymers

AbstractMeasurements of stress and birefringence of crosslinked liquid‐crystalline side chain polymers are reported. The results are compared with those obtained for conventional elastomers. It is found that the thermoelastic behaviour in the nematic state completely differs from that observed for common polymer networks due to the anistropic ordering of the mesogenic side chains. The retractive force in the nematic state is found to be independent of path, indicating that the nematic phase is a homogeneous phase. Photoelastic investigations prove the propotionality of stress and birefringence above the clearing temperature Tc which is similar to common elastomers. The stress‐optical coefficient, however, strongly depends on temperature in the pretransformation region. X‐ray measurements show a uniform orientation of the mesogenic side groups in the nematic state. The diffraction patterns observed contain many more reflexes than observed for common nematics.

Elastic and photoelastic properties of polyisoprene networks — applicability and bounds of theories

AbstractMeasurements of stress and birefringence of networks of natural rubber and cis‐1,4‐polyisoprene deformed by simple elongation are reported. The experimental results are compared with theoretical calculations. It is found that the stress‐strain relation is in accordance with the empirical Mooney‐Rivlin equation. The constants 2 C1 and 2 C2 increase linearly with temperature indicating that both reflect essentially entropic elasticity. From theories dealing with the origin of the Mooney‐Rivlin behaviour, neither the entanglement concept nor the fluctuation or packing concept alone may account for the elastic behaviour observed. The photoelastic investigations prove the well‐known proportionality of stress and birefringence.

Photoelastic parametric studies of mode I stress intensity factors

Results of photoelastic investigations on single edge-notch tension specimens of varying notch angle and crack length are reported. The experimental results of Mode I stress intensity factors are compared with analytical results.

Effect of specimen thickness on mode I stress intensity factor in photoelastic investigations

The determination of the Mode I stress intensity factor (SIF) in the case of cracks and geometrical discontinuities in three-dimensional photoelastic models involves usually an approach in which the stresses in the model are frozen or locked, and a slice containing the region of interest is cut from the model for analysis. Questions arise related to the acceptable thickness of the slice, taking into account the requirement to obtain a satisfactory or consistent value for SIF from photoelastic data. Other questions are concerned with the domain within which the observed photoelastic data give reasonably consistent values for SIF. The present investigation provides some findings pertaining to these questions.

The Effect of Notches at the Tooth Root Fillet on the Endurance Strength of Gears

Notches at the tooth root fillet can be caused by shaving or grinding. The influence of different notches at the root fillet on the endurance strength of case hardened spur gears was investigated in back-to-back tests and pulsator tests. Data of the test gears: MnCr and CrNi Steels, module 3 (8 DP) and module 8 (3 DP). Besides the a.m. tests photo elastic investigations were performed. On the basis of some characteristic parameters, it was possible, to find a calculation procedure, to determine the loss of endurance strength due to the effect of various kinds of notches. Moreover it was investigated to what extent the endurance strength of notched gears could be increased by regrinding or shot peening the root fillet. It is known that notches at the tooth root fillet can essentially reduce the endurance strength of gears. This is of special importance for case hardened gears. It is desirable that such notches should be avoided, but sometimes notches are produced by shaving or grinding due to inadequacy of tooling or non-uniform heat distortion. Therefore the influence of geometry and position of notches at the root fillet on the endurance of case hardened spur gears was investigated in back-to-back and pulsator tests. Additionally the extent the endurance strength of notched gears could be increased by regrinding or shot peening the root fillets was studied.

Influence of Flank Wear on the Stresses in a Cutting Tool

The present paper is devoted to the study of the influence of flank wear upon the contact and internal stresses in a single-point tool. A comprehensive model for the distribution of contact stresses along the wear land is proposed and compared with experimental results obtained from photoelastic investigations. For this purpose orthogonal machining of lead was carried out at low speed and constant depth of cut, making use of a transparent epoxy tool provided with a pre-honed wear flat along the flank surface. Wear level and rake angle seem to have influence on both the tool-chip and tool-work contact stresses in differing degrees. The elastic stress field in the tool wedge is evaluated analytically for given mixed boundary loading conditions. These results, on comparison with the experimental data obtained from photoelastic investigation and actual cutting test, indicate noticeable influence of wear level upon contact stress redistribution and stress field reorientation. Based on this, the role of flank wear upon the brittle strength of the tool is clarified.

Photoelasticity for stress analysis under high hydrostatic pressure

Experimental research relative to pressure effects on the mechanical behavior of materials is frequently handicapped by the difficulties associated with making load and deformation measurements in a hostile environment. The application of photoelasticity in high-pressure experiments provides a means for studying the effect of hydrostatic stress on varying stress fields. The purpose of this paper is to examine the feasibility of using the photoelastic method of stress analysis in a high-pressure environment. The unusual feature of this application is the finite elastic deformations suffered by the photoelastic model under high pressure. As a result, the mechanical and stress-optical properties of the model materials are functions of pressure. Another important feature in this study is the selection of a suitable model material. Since the model must come into contact with the liquid pressure media, chemical and absorption resistance are essential considerations. Although it was found that photoelastic investigations can be carried out at high pressure, limitations are imposed by the presence of the optical vessel and pressurized fluid.

Photoelastic investigations on initial plastic straining

Photoelasticity has been used for an investigation of the stress distribution in billets forged on flat dies. The flat models of the billet were made of birefringent material which were loaded to a state approaching the elastic limit. The authors' experiments were based on Nadai's hypothesis that in the first stages of plastic straining the stresses and strains are commensurate with the corresponding extremal values in the elastic range. The stresses were analysed for different values of feed ratio, i.e. relation of (actual) width of contact area between the die and the billet to its height. The experiments showed that if the feed ratio is less than 1·3, tensile stresses are present in the central zone of the billet under the die centre. There are no unfavourable tensile stresses in the central zone of the billet if the feed ratio is more than 1·3. However, for all values of feed ratio at points on the billet axis at a distance of 0·2 of the height of the billet from the die edge, tensile stresses are present. These conclusions lead to practical recommendations, concerning the forging of ingots and bars of complex brittle alloys at a maximum feed ratio.