Developments in the Application of the Grid Method to Dynamic Problems

1959 ◽  
Vol 26 (4) ◽  
pp. 629-634
Author(s):  
A. J. Durelli ◽  
J. W. Dally ◽  
W. F. Riley
Keyword(s):  
Dynamic Stress ◽  
Grid Method ◽  
Circular Disk ◽  
Model Material ◽  
Dynamic Problems ◽  
Principal Stresses ◽  
Stress Studies ◽  
Low Modulus ◽  
Fringe Patterns ◽  
Dynamic Loading Conditions

Abstract The objective of the research reported in this paper was to develop the grid method further for use in dynamic-stress studies. A rubber-thread grid network in a low-modulus model material (a urethane rubber known as Hysol 8705) was used in conjunction with a microflash light source to record grid distortions and photoelastic fringe patterns in a model subjected to dynamic-loading conditions. By considering a strut subjected to axial impact it was possible to establish that the static and dynamic values of Poisson’s ratio were identical, and the strain-fringe value of the material varied with strain rate. In addition, stresses in the axial and transverse directions were determined along the center line of the strut. Finally, the methods established were applied to the problem of a circular disk subjected to diametrical impact and both principal stresses were determined along a vertical diameter at one instant during impact.

New analysis of holophotoelastic patterns and their application

1976 ◽  
Vol 11 (1) ◽  
pp. 11-17 ◽  
Author(s):  
J Ebbeni ◽  
J Coenen ◽  
A Hermanne
Keyword(s):  
Numerical Methods ◽  
Dynamic Problems ◽  
Principal Stresses ◽  
Optical Elements ◽  
New Type ◽  
The Difference ◽  
Fringe Patterns

This paper shows that by the use of a new type of diffuser it is possible in photo-holoelasticimetry, without any addition of optical elements or particular preparation of the specimen, to record simultaneously but separately fringe patterns respectively related to the sum and the difference of the principal stresses. The value of intensity of the interfering light reaching the hologram plate is established and hence the equations of the recorded pseudoisopachic fringe patterns are given. Used successfully for the study of particular static problems, where numerical methods are very difficult or impossible, the present interferometer is also suited for dynamic problems.

Application of Moire Methods to the Determination of Transient Stress and Strain Distributions

1962 ◽  
Vol 29 (1) ◽  
pp. 23-29 ◽  
Author(s):  
W. F. Riley ◽  
A. J. Durelli
Keyword(s):  
Strain Distribution ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Distribution Problem ◽  
Principal Stresses ◽  
Transient Stress ◽  
Optical Phenomenon ◽  
Moiré Effect ◽  
Fringe Patterns

When two arrays of lines are superimposed an optical phenomenon known as the moire effect is observed under certain conditions. This moire effect is used by the authors to determine the distribution of transient strains on the surface of two-dimensional bodies. The method can be used to solve completely the strain-distribution problem or it can be used in combination with photoelasticity to separate the principal stresses. The methods used in interpreting the moire fringe patterns and the techniques used to produce the patterns are described in the paper. Two applications are discussed.

scholarly journals Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

2020 ◽  
pp. 237-249
Author(s):  
L. V Stepanova
Keyword(s):  
Series Expansion ◽  
Digital Image ◽  
Power Series Expansion ◽  
Crack Tip ◽  
Higher Order ◽  
Accurate Estimation ◽  
Principal Stresses ◽  
Isochromatic Fringe ◽  
Higher Order Terms ◽  
Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

scholarly journals Tactile Whole-Field Imaging Sensor on Photoelasticity

2007 ◽  
Author(s):  
Venketesh N. Dubey ◽  
Gurtej S. Grewal
Keyword(s):  
Phase Shifting ◽  
Sensing Applications ◽  
Shear Loads ◽  
Photoelastic Effect ◽  
Low Modulus ◽  
Fringe Patterns ◽  
Imaging Sensor ◽  
Field Imaging ◽  
New Strategies

The paper describes a whole-field imaging sensor developed on the principles of photoelasticity. The sensor produces colored fringe patterns when load is applied on the contacting surface. These fringes can be analyzed using conventional photoelastic techniques, however, as the loading in the present case is not conventional some new strategies need to be devised to analyze the load imprint. The loading is unconventional in the sense that low modulus photoelastic material is deformed under vertical load in the direction of light travel to induce the photoelastic effect. The paper discusses the efficacy of both RGB calibration and phase shifting techniques in sensing applications. The characteristics of fringe patterns obtained under vertical and shear loads have been studied and the results obtained under these conditions are discussed with their limitations specifically when this is applied for sensing applications. Finally a case study has been conducted to analyze a foot image and conclusions drawn from this have been presented.

A Photoelastic Approach to Transient Stress Problems Employing Low-Modulus Materials

1959 ◽  
Vol 26 (4) ◽  
pp. 613-620
Author(s):  
J. W. Dally ◽  
W. F. Riley ◽  
A. J. Durelli
Keyword(s):  
Wave Theory ◽  
Stress Distributions ◽  
Specific Energy Loss ◽  
Elementary Wave ◽  
Dynamic Loadings ◽  
Complete Study ◽  
Low Modulus ◽  
Fringe Patterns ◽  
Fixed End ◽  
Rate Of Loading

Abstract The objective of the program discussed in this paper was to develop a method, using photoelasticity and low-modulus materials, for studying dynamic stress distributions. Early in the program a number of low-modulus materials were studied and Hysol 8705 (a urethane-rubber compound) was selected as the most promising. A complete study of its mechanical and optical properties was made under static and dynamic loadings. It was established, that Poisson’s ratio ν is independent of rate of loading, the stress fringe value fσ is independent of rate of loading for strain rates greater than 8 in/in/ sec, and both the modulus of elasticity E and the strain fringe value fϵ were dependent oil the rate of loading. The specific energy loss for the material was about 10 per cent for the stress ranges associated with photoelastic determinations. Experimental observations of photoelastic fringe patterns in a rectangular strut subjected to axial impact were made to illustrate the potential of the method. Three different end conditions were imposed on the unloaded end of the strut: (a) A free end normal to the axis; (b) a fixed end normal to the axis; and (c) a free end inclined 45 deg to the axis. For the cases where the ends were normal to the axis it was found that the fringes followed the same law of reflection as the law for stresses given by elementary wave theory.

scholarly journals Analysis of Rock Dynamic Stresses During the Drilling by Polycrystalline Diamond Compact Bits

2020 ◽  
Vol 19 (4) ◽  
pp. 607-618
Author(s):  
J. P. Yu ◽  
D. Y. Zou ◽  
Y. Zhang
Keyword(s):  
Axial Force ◽  
Dynamic Stress ◽  
Tangential Force ◽  
Polycrystalline Diamond ◽  
Rock Breaking ◽  
The Finite Element Method ◽  
Principal Stresses ◽  
Dynamic Stresses ◽  
Polycrystalline Diamond Compact ◽  
Initial Rock

In view of shortening the development period of polycrystalline diamond compact (PDC) bits, the finite element method was adopted to simulate the dynamic stress of rocks. By employing drilling related theories, the three dynamic principal stresses of rock were analysed and the dynamic rock-breaking criterion was established. Second, the drilling model of PDC core bit was constructed, and the stress was simulated and calculated. Finally, laboratory tests were carried out to verify the simulation results. The analytical results demonstrate that the two obvious stages in the rock-breaking process are the initial rock-breaking stage and the normal one. The dynamic rock-breaking stress in the normal drilling stage varies from 66.3 to 99.6 MPa, which is lower than 278.4 MPa in the initial rock-breaking stage. During spud drilling, the axial force and the tangential force are 1.85 and 1.60 kN, respectively. During normal drilling, the axial force ranges from 0.2 to 0.9 kN, and the tangential force from 0.15 to 0.6 kN. The load of normal drilling is lower than the spudding load, and the bit is more likely to be damaged during spudding. The bit is normally worn during normal drilling.

Experiments for the Determination of Transient Stress and Strain Distributions in Two-Dimensional Problems

1957 ◽  
Vol 24 (1) ◽  
pp. 69-76
Author(s):  
A. J. Durelli ◽  
W. F. Riley
Keyword(s):  
Wave Propagation ◽  
Modulus Of Elasticity ◽  
Impact Load ◽  
Dynamic Properties ◽  
Circular Disk ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Low Velocity ◽  
Transient Stress ◽  
Fringe Patterns

Abstract The object of this investigation was to develop a method utilizing photoelasticity for determining transient stress and strain distributions in two-dimensional problems. Numerous investigators have approached this problem using the common photoelastic materials which have a relatively high modulus of elasticity and correspondingly high velocity of wave propagation. However, many difficulties were encountered in photographically recording data, and only a few reliable stress patterns were obtained. In order to avoid these difficulties, a material with a low modulus of elasticity and a correspondingly low velocity of wave propagation was developed. As a result the 8-mm. Fastax camera is capable of recording precise fringe patterns. The material used was a member of the epoxy-resin family, modified to give the desired properties. Both its static and dynamic properties were determined as accurately as possible. It was found that the strain-fringe value of the material is approximately constant, but the modulus of elasticity and stress-fringe value are different for static and dynamic loadings. Preliminary studies were conducted to develop the method using a circular disk under a radially applied concentrated impact load as the model. A simply supported beam under central impact was then studied, and deflection curves obtained were compared with curves theoretically predicted by Saint Venant and Flamant. The comparisons showed good agreement. An analysis of the formation of the fringe pattern for various times after impact also was made.

scholarly journals Investigation of the influence of the method of fixing the cut-off tool inserts on its stress state

2021 ◽  
Vol 24 (1) ◽  
pp. 7-13
Author(s):  
Pavlo Zabrodskyi ◽  
Bohdan Sheludchenko ◽  
Savelіі Kukharets
Keyword(s):  
Stress State ◽  
Cross Sections ◽  
Stress Reduction ◽  
Cutting Tools ◽  
Complex Model ◽  
Principal Stresses ◽  
Sensitive Material ◽  
Stress Studies ◽  
Carbide Inserts ◽  
Carbide Insert

Cut-off tools equipped with carbide inserts are commonly used in turning operations. Due to the very heavy conditions in which such blades work, they fail, as a rule, not as a result of their operation, but due to the breakage of carbide inserts. This study investigates the causes of such failures and methods to prevent such phenomena. A thorough analysis of the current state and research methods of stress state in cutting tools, including turning cutters, was carried out. Methods of stress reduction in carbide inserts were also analysed. This paper focuses on the study of the stress state in cut-off tools with brazed carbide inserts. The stress state in the carbide inserts and the influence of different fixation methods of carbide insert to the holder were considered. The main approach to stress studies was the photoelasticity method, which allows quickly and clearly obtaining and evaluating the results. Models of carbide inserts were made of optically sensitive material. It as a part of a complex model of a cut-off tool with a carbide insert with three different methods of fixation were loaded with a force by means of a specially designed stand simulating the cutting force. The study was carried out on a PPU-7 polarisation-projection unit. Isochromatic and isocline patterns were obtained. The estimation of the principal stresses was performed by the difference of shearing stresses for three cross sections of the insert: at the surface, in the middle and at the base. It was found that the best result is given by the method in which the insert on the side far from the cutting edge has a bevel made at an angle of 10°

scholarly journals Photoelastic Stress Analysis Under Unconventional Loading

2007 ◽  
Author(s):  
Venketesh N. Dubey ◽  
Gurtej S. Grewal
Keyword(s):  
Stress Analysis ◽  
Phase Shifting ◽  
Vertical Load ◽  
Sensing Applications ◽  
Shear Loads ◽  
Photoelastic Effect ◽  
Low Modulus ◽  
Photoelastic Stress ◽  
Fringe Patterns

This paper presents use of conventional photoelastic techniques under unconventional loading situations to evaluate their efficacy in sensing applications. The loading is unconventional in the sense that low modulus photoelastic material is deformed under vertical load in the direction of light travel to induce the photoelastic effect. This is atypical of conventional methods where loading is across the light travel. Both RGB calibration and phase shifting techniques have been used to study the characteristics of fringe patterns obtained under vertical and shear loads. The results obtained under these conditions are discussed with their limitations specially when this is applied for sensing applications. Finally a case study has been conducted to analyze the foot image and conclusions drawn from this have been presented.

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