Principal Strain Difference Research Articles

Determination of the stress and strain fields in porous structures by photoelasticity and digital image correlation techniques

Quantitative visualization of the full-field stress and strain in porous structures is of significance to reveal the mechanism of the damage and failure of engineering materials. To quantitatively characterize the full-field stresses and strains, optical measurement methods, such as photoelasticity for determining the stress fields, moiré and digital image correlation (DIC) methods for measuring the strain fields, have been developed in previous works. However, it is challenging to combine these methods to measure stress and strain fields simultaneously because the speckles and gratings for strain measurement will disturb the interference fringes in the photoelasticity. In this study, a method incorporating photoelasticity and DIC techniques was developed to determine the stress and strain fields simultaneously in different porous structures which were fabricated by three-dimensional (3D) printed technique. The tested models were printed with a highly transparent, colourless material and the speckles on the front surface of the tested models were printed with a translucent, magenta material. Under compressive loads, the stress fields in these models were obtained based on the photoelastic patterns and the strain fields were determined by DIC method. The results indicate the proposed method can simultaneously determine the full-field stresses and strains and the comparison of the distribution of the principal stress and strain difference and the distribution of the shear stress and strain verified its good accuracy. In addition, the stress and strain distribution in different pore structures were compared and found that the optimal design of the pore distribution can greatly change the concentration of the stress and strain fields.

Study of Photoplastic Behaviour of Polycarbonate using Digital Image Correlation

Earlier studies on photoplastic behaviour of polycarbonate are limited to the strain at which the localized yielding (necking) initiates (about 6% strain). In this study, the photoplastic behaviour of polycarbonate is studied using digital image correlation (DIC). Two cases are considered: one in which no localized yielding is observed and the other in which initiation and propagation of the localized yielding is observed. For the first case, a modified dog bone specimen is proposed to evaluate the photoplastic constant. In the second case, a conventional tensile test specimen is used. Both photoplasticity (transmission and reflection) and DIC experiments are performed on the specimens to determine the relation between fringe order and principal strain difference for strains of up to 60%. It is observed that the photoplastic constant is a function of strain. Finally, the behaviour of the tensile test specimen is numerically simulated. The true stress-strain curve of polycarbonate needed for FE simulation is determined using DIC experiments on the standard tensile test specimen. By post-processing the FE results, isochromatic fringes are plotted and compared with experimental results.

Inhomogeneous Creep of Polarization and Strain Around a Circular Hole in Ferroelectrics Under Electric Field: Experiments and Modeling

The simulation of inhomogeneous creep around a circular hole in a solid of anisotropic ferroelectric is presented under various levels of constant electric potential condition from virgin state aiming for understanding the experimental situation by birefringence measurements. Due to the electric field concentration effect presented by the hole, the time dependent fields of stress, strain and polarization can be determined using the finite element method. It is found that the electric field concentration factor by a hole can achieve 6 times of the applied loads and shows slightly time dependence; the creep of polarization and strains process is controlled by the local electric field magnitude, which governs the saturation of remnant polarization and strain. The result of principal strain difference around a hole agrees with the birefringence observation. This confirms the established birefringence-strain correlation by the previous experimental study.

Electrical creep around a circular hole in PLZT 8/65/35

The strain–birefringence correlation was exploited to study the local behaviour near a circular hole in unpoled PLZT 8/65/35 under electric field below than the coercive field. The observed birefringence contours near the hole show a spatial distribution and time dependence. Due to the enhancement of electric field near the hole, the polarization creep rate is greatly increased. The evolution of the local principal strain difference with time and position in the sample is quantified. Overall, an accelerated poling effect is found in comparison with the behaviour under uniform field. This appears to be due to inhomogeneous field distribution which initiates polarization switching in areas of locally enhanced electric field. The presence of the hole promotes a nearly linear growth in average polarization with time, despite the strongly nonlinear response of the parent material. The results indicate that insulating porosity can strongly affect the switching behaviour and coercivity of ferroelectric ceramics.

Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

The paper presents a method to calculate the difference of principal stresses and strains in linear viscoelastic optically sensitive polymeric materials from a time-dependent fringe pattern. The governing equations are derived using the direct and inverse Laplace transforms

Birefringence measurements of creep near an electrode tip in transparent PLZT

Birefringence measurements of time-dependent, creep polarization and strain were made in bulk ceramic samples of PLZT 8/65/35. Two specimen configurations were used: a fixed uniform electric field to measure the creep response and correlate birefringence with strain and polarization, and specimens with a partial surface electrode, to study the local behaviour near the tip of a surface electrode. At low values of electric displacement, the electric displacement depended upon the principal strain difference in a quadratic fashion whereas the birefringence varied linearly with the principal strain difference. Three distinct regimes of switching were identified, corresponding to the nucleation of ferroelectric domains, rapid switching and saturation in the process of domain growth. Finally it is shown that the birefringence measurements near an electrode tip give the spatial evolution of principal strain difference.

New Initiatives on Comparison of Whole‐field Experimental and Numerical Results

Abstract: A simple approach to plot photoelastic fringes in grey scale and also in colour from finite element (FE) results is presented for better recognition and comparison with experiments. This requires proper identification of the plotting variable from FE results. For comparison with transmission photoelasticity, post‐processing of principal stress difference is needed and for reflection photoelasticity the principal strain difference is to be used. The importance of the use of appropriate correction factors for comparison with reflection photoelastic results is emphasised. A newer approach to evaluate Rf for complicated geometries is indicated. Plotting of experimental fringes from finite elements is useful not only for validating the numerical model based on experiments but also for validating the experiments. To illustrate this, the problem of an interfacial crack in a bi‐material Brazilian disc is discussed.

Dielectric response of solids for contactless detection of stresses and strains

The dielectric response of any dielectric material varies with deformations. This effect, called dielectrostriction, can be utilized for monitoring stresses and strains in elastic solids. This article introduces the concept of a planar capacitor sensor and sensor rosettes detecting deformations without mechanical contact with the monitored part. Outputs of two-sensor and four-sensor rosettes attached to isotropic material are directly proportional to the principal directions and the difference of in-plane principal strains or stresses. In this work a linearity of the stress- and strain-dielectric response is experimentally verified for uniaxially loaded specimens. The principal strains and their principal directions are measured using a four-sensor rosette. The agreement between applied and measured values is demonstrated. The developed sensing technology provides a novel approach for stand-alone sensors and a suitable solution for implementation of self-sensing stresses and strains in load-bearing structures.

Elastic-Plastic Behaviour of a Plate with a Central Hole by Photoelastic Coating Method

An application of the elastic-plastic problem by the photoelastic coating method is presented in this paper. A general procedure of this experiment, such as image processing and separation of the difference of principal strain to obtaine stresses from isochromatic fringes is referred. The methodology to extract centre lines of coloured isochromatic fringes is explained. Experiments are conducted with cross-shaped aluminum specimens with a circular hole subjected to uniaxial tension and equi-biaxial tension. Results of image processing are shown, and the distribution of difference of principal strains and separated principal strain are shown in the case of equi-biaxial tension.

A photoelastic clinical study of the static load distributionat the stump/socket interface of PTB sockets

It is recognized that the assessment of prosthetic socket fit is based largely on the subjective clinical judgement of the prosthetist. This study assesses a novel technique, photoelasticity, for use as a tool for the qualitative and quantitative assessment of socket fit. Photoelasticity is a visual technique that produces contours of principal stress or strain differences. The colour and/or distance between the contours can be qualitatively or quantitatively assessed, using a polariscope, to give a full-field analysis of the stresses on the sockets's surface. This paper presents qualitative photoelastic socket surface contour data gathered during several prosthesis fitting sessions for two male trans-tibial amputees. Results are compared with the actual known contact regions at the stump/socket interface to determine if a relationship exists. This comparison of results has then been used to conclude the suitability of photoelasticity as a tool for the assessment of socket fit and recommendations are made as to the future developments of the technique. A direct relationship between the stump/socket contact regions and the qualitative photoelastic contours was demonstrated. Given further development this photoelastic technique may therefore be suitable for qualitative analysis of the interactions between the stump and prosthetic socket.

Strain Measurement on Composites: Errors due to Rosette Misalignment

Abstract: Electrical resistance strain gauges are increasingly used for the determination of the strain field in composite components. The effect of the angular misalignment of a strain gauge rosette on the determination of the strains in a composite material is investigated in this paper. The theoretical analysis shows that the strain error along the principal material directions depends on the difference of principal strains, on the angular misalignment of the rosette and on the angle between the maximum principal strain and the fibre direction. The paper also shows experimental evidence for the theoretical analysis.

Experimental/Numerical Analyses of a Viscoelastic Body under Rolling Contact

In this paper, the authors discuss the first step in theapproach to the fundamental mechanism of small-scale local wear/fracturenear the contact surface between a viscoelastic body and a rigidtraveling roller. A rectangular viscoelastic strip made of epoxy resinwas loaded by a cylindrical hard roller moving along the upper straightedge. A convenient photoviscoelastic method using computer immageprocessing was applied to investigate the time-dependent stress andstrain around a contact region under a typical type of non-proportionalloading conditions. On the other hand, the finite element method (FEM)was used to analyze the viscoelastic stress and strain under the severalconditions. The results obtained from the two methods qualitativelycompared the time variation for the photoviscoelastic fringe patternsand the contour bands of stress/strain distribution patterns. Moreover,the time variation for principal stress differences, principal straindifferences and the directions of principal stress/strain undernon-proportional conditions, were evaluated, at which time the materialshowed remarkable viscoelastic and rubber-like properties.

The Influence of Crystalline Orientation on the Photoelastic Property of {100} Gallium Arsenide Wafer.

We developed an optical birefringence measurement method that uses a photoelastic modulator and a polarized laser. A He-Ne infrared laser was utilized as the light source for measuring the birefringence in gallium arsenide wafers. In this paper we will explain the theory behind this method and the process of measuring the stress in GaAs wafers. The magnitude of the principal stress difference as well as the directions of the principal stresses were obtained simultaneously and quantitatively by using equipment developed for this study. The optical birefringences of stressed GaAs specimens were measured. From the experimental results, it was found that the photoelastic constant depended upon the crystalline orientations. Furthermore, the birefringence direction did not always coincide with the principal stress direction. The relationship between the principal strain difference and the retardation was obtained by the stress-strain analysis of a single GaAs crystal. That relationship was almost independent of the crystalline orientations and the birefringence direction was almost equal to the principal strain direction.

Photoplastic Analysis by Loaded Spherical Indentator Using Strain-Freezing Method.

Hardness test is one of the basic material testings. This investigates strain behavior in polycarbonate plate by loaded spherical indentator using the strain-freezing method to establish a method of evaluating the material properties of high polymer materials which have been widely used as machine parts and structural members because of a high elastic modulus and strength. As a result, the strain-freezing method was found to be effective for analyzing strains in polycarbonate by loaded spherical indentator. Furthermore, the relation between the photoelastic fringe order and principal strain difference is found to be proportional as well as the relation between the total strain.

Determination of Time-Dependent Fringe Order and Principal Birefringence Direction Using Tricolor Photoviscoelasticity.

The authors propose a new method for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using a white incident light with a set of the three primary colors. When using this method, not only fringe order but principal birefringence direction are successfully and easily determined from a single color image through a plane polariscope. Utilizing this method together with photoviscoelastic constitutive equations, timedependent principal stress and strain difference, also their directions are obtained. In this paper, the fundamental of the tricolor photoviscoelastic technique is described briefly, then a successful application of the method to the analysis of an example of viscoelastic problem is shown.

Photoviscoelastic Stress and Strain Analysis around a Surface Groove under Rolling Contact Load

The authors discuss the first step in the approach to the fundamental mechanism of small-scale local fracture near the contact surface between a rigid traveling roller and a viscoelastic plate which has a deep groove on the upper edge of the plate, which simulates pitting or surface cracking around the contact surface. The photoviscoelastic method is applied to investigate the time-dependent stress and strain state under the condition of nonproportional loading, taking a typical case of the interaction of stress fields due to a traveling contact load and a surface groove into account. Complicated variations of the time-dependent photoviscoelastic fringe pattern are observed near the tip of the surface groove. The time variations of not only the principal stress difference and principal strain difference, but also principal directions of stress, strain and birefringence are evaluated using a convenient computer-aided photoviscoelastic technique under the temperature at which the material shows marked viscoelastic behavior. Time variations of stress intensity factors, K I and K II , are also evaluated using the least-squares method following the technique proposed by Sanford and Dally.

Influence of Crystalline Orientation on Photoelastic Property of Si Single Crystal.

We developed an optical birefringence measurement method that uses a photoelastic modulator and a polarized laser. A He-Ne infrared laser was adopted as the light source for measuring the optical birefringence in gallium arsenide wafers. In this paper we explain the theory and the process of measurement of stress in GaAs wafers. The magnitude of principal stress difference and also the directions of the principal stresses were obtained simultaneously and quantitatively using our developed equipment. The optical birefringences of {100} GaAs stressed specimens were measured. From the experimental results, it was found that the photoelastic constant depended on the crystalline orientation and that the birefringence direction did not coincide with the principal stress direction. By stress-strain analysis of the GaAs single crystal, it was found that the birefringence direction coincided with the principal strain direction and that the relationship between the principal strain difference and the birefringence was independent of crystalline orientation.

Elastic-plastic analysis of cracked plates in plane stress: An experimental study

An experimental method is presented for the complete solution of the elastic-plastic plane stress problem of an edge-cracked plate obeying the Mises yield criterion and the Prandtl-Reuss incremental stress-strain flow rule. The material of the plate is assumed as a strain-hardened one with different degrees of hardening. The elastic and plastic components of strain were determined by using the method of birefringent coatings cemented on the surface of the metallic specimens made of the material under study. Normal incidence of circularly polarized light yielded the isolinics and isochromatics of the coating which provided the principal elastic strain differences and strain-directions at the interface. Evaluation of the stress intensity factor at the crack tip, by using the Griffith-Irwin definition, gave the sum of principal stresses at the crack tip. These data were sufficient to separate the components of strain at the coating-plate interface by using the classical shear-difference method.

Calibration of materials for photoelastoplastic models

Photoplasticity is a possible method of analyzing the plastic behavior in a structural member. Various problems attendant with this technique, however, especially those concerning the fundamental relationship between the fringe order and the stress, and the photoelastic material in the plastic range remain to be investigated. A few studies on this relationship in a uniaxial stress state have been presented, but no evaluations have been made in a biaxial stress state, which is considered essential for practical application of the technique. Applying the photoelastic and the moire methods, the relationship is investigated in detail in this paper in both stress states using a tensile specimen with a central hole. It is revealed that in the plate of polycarbonate there is a linear relationship between the fringe order and the difference of principal strains in the plastic range.

A basic study of the strain freezing in photoplastic experiments. Relationship between fringe order and principal strain in biaxial stress state.

Recently, to clarify the mechanism for material deformation during plastic working and to outline the guidelines for plastic design, it is necessary to develop the methods of stress-strain analyses in the elastoplastic and plastic states. In the previous paper, the authors attempted to find a possible strain freezing method in photoplastic experiments, and the results showed that a very fine linear relationship is maintained between the isochromatic fringe order N and principal strain difference (e1-e2) over a very wide range under the uniaxial tensile stress state. In this paper, we discuss the type of relationship between the fringe order and principal strain in the biaxial stress state. The discussions on the results obtained are based on the Moire method and photoplastic method in the use of the strip sheet and cross-type specimens of polycarbonate.