Residual stress measurement for injection molded components

Residual stress induced during manufacturing of injection molded components such as polymethyl methacrylate （PMMA） affects the mechanical and optical properties of these components. These residual stresses can be visualized and quantified by measuring their birefringence. In this paper, a low birefringence polariscope （LBP） is used to measure the whole-field residual stress distribution of these injection molded specimens. Detailed analytical and experimental study is conducted to quantify the residual stress measurement in these materials. A commercial birefringence measurement system was used to validate the results obtained to our measurement system. This study can help in material diagnosis for quality and manufacturing purpose and be useful for understanding of residual stress in imaging or other anolications.

Comparative study of various internal fixation methods for treating patellar fractures by three-dimensional photoelasticity

Objective: To compare the biomechanical basis of 3 different internal fixation methods: nitinol patellar concentrator (NT-PC), tension band and wire circle in treating patellar fractures. Methods: The epoxy resin three dimensional photoelasticity patellar models were made by precise moulding, and were fixated by nitinol patellar concentrator (NT-PC), tension band and wire circle respectively. The patellar models with frozen stress stripes were put into the polarized light field and the stress distributions were compared. As for the model fixated by NT-PC, by dividing layer, photographing and tracing, we used the iterative method to calculate the stress value of every internal node of the epoxy resin patellar model, and the character of stress was analyzed. Results: An overall stress field was yielded when the patellar model was fixated by NT-PC, and the stripes were more than that of tension band model and wire circle model, which have only few stress stripes in the fixated layers. Further analysis indicated that there were continuous fixated stresses in the facies articularis and distal pole of patella, and the character of stresses produced by NT-PC were mainly in longitudinal direction, then in transverse direction. The shearing stresses were small. Conclusion: The initiative and continuous memorial stress of NT-PC and its overall stress distribution character are the essence of NT-PC distinguished with tension band and wire circle in treating patellar fractures. The stress character produced by NT-PC is good for the stability of fracture site and prompts fracture healing.

Three-dimensional photoelasticity analysis of Nitinol Patellar Concentrator for treating patellar fractures

Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.

Hybrid Method to Analyze Contact Stress Distribution on Dry Friction Interfaces

A hybrid method is established by combining photoelastic experiment and finite element analysis.The method is used to evaluate contact stress distribution on dry friction interfaces,such as the contact interfaces between shrouds of fan blades and turbine blades.The photoelastic stress frozen experiment method is used to decide the displacement boundary conditions of numerical calculation.Higher accuracy and efficiency of solving problems are improved by the method.Technical difficulty and high cost of experiment are also avoided by the method.Good agreement of the stress distribution by using the hybrid method and experiment is obtained.

High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.

Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leakage of second-order symmetric backward wave mode S2b in contrast to third-order anti-symmetric backward mode A3b is shown by the dispersion curve of a plate immersed in water, and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S2b and A3b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

EXPERIMENTAL STUDY ON CRACK CURVING PROPAGATION IN BENDING BEAMS UNDER IMPULSIVE LOAD

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave.

UTILIZING PHASE RETARD INTEGRATION METHOD OF FLOW BIREFRINGENCE TO ANALYSE THE FLOW WITH SYMMETRIC PLANE

The formulas which are suitable to birefringent medium with symmetric plane are derived by means of phase retard integration.We have adopted this concept to the axisymmetric problems and deduced some useful formulas for these cases.As a practical application,the strain rate analysis of flow in a diverging or a converging vessel is illustrated at the end of this paper.

THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY

This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.

The Mathematical Foundations of Elasticity and Electromagnetism Revisited

The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.

Analysis of the Stress Distribution Pattern of Anatomic and Non-Anatomic Tooth Forms on Maxillary and Mandibular Edentulous Ridges—A Photoelastic Study

Aim: To compare the type of stress distribution pattern occurring with anatomic and non-anatomic tooth forms beneath a complete denture in both maxillary and mandibular arch. Methodology: A photoelastic model of the edentulous maxillary and mandibular ridge was prepared meticulously to simulate the human mandible and maxilla. Two sets of acrylic teeth with anatomic and non-anatomic occlusal forms were used to fabricate upper and lower dentures. A vertical static load of 100 N was applied through the mandibular model to the maxillary model. After load application on the dentures the photoelastic model as well as the upper and lower complete dentures were sectioned in the midline. The sectioned photoelastic model was viewed through a polariscope to observe the fringe pattern indicating varying amounts of stress distribution. In this study, a two-dimensional photoelastic stress analysis technique was utilized. Results: Force per unit area was observed more in anatomic teeth than the non-anatomic counterpart. Hence anatomic tooth forms may increase the possibility of bone resorption rate over a period of time. However, in non-anatomic lower teeth, a decrease in value was observed from posterior to anterior region. Conclusion: Stress of greater magnitude was observed with cuspal teeth whereas non-anatomic (0°) showed slightly less magnitude of stress. Depending upon the clinical situation the clinician needs to choose the type of occlusal tooth forms for edentulous patients.

Stress Concentrations for Slotted Plates in Bi-Axial Stress

The photo-elastic method has been employed to determine stress concentration factor (SCF) for square plates containing holes and inclined slots when the plate edges are subjected to in-plane tension combined with compression. Analyses given of the isochromatic fringe pattern surrounding the hole provides the SCF conveniently. The model material is calibrated from the known solution to the stress raiser arising from a small circular hole in a plate placed under biaxial tension-compression. These results also compare well with a plane stress FE analysis. Consequently, photo-elasticity has enabled SCF’s to be determined experimentally for a biaxial stress ratio, nominally equal to –4, in plates containing a long, thin slot arranged to be in alignment with each stress axis. The two, principal stresses lying along axes of symmetry in the region surrounding the notch are separated within each isochromatic fringe by the Kuske method [1]. FE provides a comparable full-field view in which contours of maximum shear stress may be identified with the isochromatic fringe pattern directly. The principal stress distributions referred to the plate axes show their maximum concentrations at the notch boundary. Here up to a fourfold magnification occurs in the greater of the two nominal stresses under loads applied to the plate edges. Thus, it is of importance to establish the manner in which the tangential stress is distributed around the slot boundary. Conveniently, it is shown how this distribution is also revealed from an isochro-matic fringe pattern, within which lie the points of maximum tension and maximum compression.

A SIMPLE METHOD OF DETERMINING STRESS INTENSITY FACTOR K Ⅰ FROM ISOCHROMATIC FRINGE LOOPS *

A new photoelastic method of obtaining mode I stress intensity factor(SIF) is presented. The method considers the influence of far field stress, σ ox , on the value of SIF. The only information needed for K Ⅰ calculation is the area between isochromatic fringe loops. The method is examined by two kinds of specimen in different load cases.Experimental results show that it is quite simple and of high precision.

New Methods of Determining the Mixed Mode Stress Intensity Factors for V-Shaped Notch

In this paper, on the basis of the stress field given by D.H.Chen, three new photoelastic methods are developed for determining the stress intensity factors K1 and K2 of V-shaped notch. Some photoelastic experiments are performed on a skew -symmetric 45° notch. Measurements of the coordinates components of r,θand fringe order N are made for progressively smaller fringes and used in the proposed methods to solve K1 and K2.Plots of apparent K vs. r/l are made and extrapolated to the notch tip to yield the true values of K1 and K2.The results obtained by the three methods are very close to each other. When the notch problem is simplified as a crack problem, the corresponding equation is identical to the one proposed by D.G. Smith, which shows that the proposed methods are applicable for both notch and crack problems.

SEPARATION OF PRINCIPAL STRESSES IN DYNAMIC PHOTOELASTICITY

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved.

DDGS HIGH SPEED CAMERA WITH SOME APPLICATIONS

DDGS high speed camera is an improved version of the multispark system. In this system the time delay and the frame interval can be set arbitrarily from 5 mu s to 10000 mu s, and the intervals may be equal or not. The modified spark gaps can provide point flashes that are small enough in size and strong enough in light for both dynamic caustics and dynamic photo-elasticity. In addition, this system can be changed easily to observe the Bow by schlieren method, Thus, this optical system is suitable to investigate many dynamic problems in the fields of solid and fluid mechanics.

Photoeiastic-Stress Analysis of The Effect of Various Clasps on An Abutment Tooth

It is reported in this article that the mandibular unilateral distal-extension remova-ble partial dentures with wrvught wtre retentive clasp arm,cast circumferential retentive arm andI-bar retentive arm were tested under vertical loading,and the stresses around the root of thetooth adjacent to the extension base were ovserved by means of photoeiastic stress analysis.The results showed that the retentive clasp arm or reciprocal clasp arm in distal-extension remov-able partial denture does not affect the magnitude and direction of the abutment tooth force,that there is no obvious difference among the wrought wire clasp arm,cast circumferential clasparm and I-bar clasp on the abutment tooth force,and that the force created due to loading of re-movable partial denture is transmitted to the primary abutment tooth mainly through theocclusal rest.

A method for visualizing sound propagation in solids and liquids

A new method for visualizing sound propagation in solids and liquids is described in this paper. The method can show the sound propagation process dynamically in two dimensions. Compared with Schlieren method and dynamic photo-elastic method, this method cannot only show the sound field distribution in liquid and solid at different time moments, but also can be applied to non-transparent solid. In addition, it does not strictly require small residual stress of the sample. The sample can, therefore, be easily made. Because the acoustic field is obtained by indirect measurements, the recording can be affected by the after-shock of the receiving sensor and is prone to the influence of the direct wave of the liquid. Putting an aluminum plate into a liquid, we recorded the compression wave, shear wave and surface wave in the aluminum and, in the liquid we also recorded the direct wave and three head waves, which are directly coupled with the compression wave, shear wave and surface wave respectively. The recording clearly depicts the coupling relationship of the sound waves through the interface between the aluminum and the liquid. Putting a plexiglass into a liquid, we also recorded the sound waves in the plexiglass and the coupling relationship between the sound waves in the two mediums.

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

A MIXED METHOD OF SOLUTION FOR CONTACT STRESSES ON ROLLER

A mixed method of solution for contact stresses on rollers was suggested by the combina- tion of similitude principle.photoelastic method,Hertz's contact theory and numerical calculation.Thus,not only the distribution regularity of axial contact pressure on roller of limited length,but also the three-dimensional solution of stresses in the contact po- sitions may be obtained.An actual example is presented in the paper.It shows that the practical damaged phenomenon in real roller is in agreement with the result of the analysis