V. J. Parks

Strain Measurement Using Grids

Determining strain with grids is one of the oldest and simplest methods of experimental stress analysis. Here, the method is reviewed. Various techniques that are used to print, record, and analyze grids are discussed, and the types of problems to which the grid method has been applied are presented.

Various forms of the strain-displacement relations applied to experimental strain analysis

AbstractThe purpose of this paper is to present the strain-displacement relations in a general way and to develop modified forms for three special cases which have application in experimental strain analysis:1.Small rotations—large strains2.Small strains—large rotations3.Small strains—small rotations The development will be made for two definitions of strain: (a) ratio of change of length to initial length (Lagrangian description), and (b) ratio of change of length to final length (Eulerian description).An example of the error introduced when each of the modified expressions is used is analyzed and graphically represented. Applications to several experimental strain-analysis methods are reviewed. The general relation and each of the modified forms are illustrated with the moiré pattern of a uniform strain field subjected to the conditions of the three special cases.

The range of speckle metrology

The range of four methods of speckle metrology as applied to in-plane displacement analysis is studied, in terms of the number of fringes that can be generated. Both quality and quantity of fringes are treated insofar as they affect the range and precision of the method. Some 20 variables are seen to influence the fringe range. A number of these are analyzed parametrically. The most serious restriction on the range seems to be the strain in the plane of analysis. This restriction severely limits application of the method.

The grid method

Determining strain with grids is one of the oldest and simplest methods of experimental stress analysis. Here, the method is reviewed. Various techniques that have been developed to print, record and analyze grids are discussed, and the types of problems to which the grid method has been applied are presented.

A method for directly determining surface strain fields using diffraction gratings

This paper describes a new method for determining the strain distribution at the surface of solid bodies. The method is purely optical; it uses the diffraction phenomena generated by a copy of a grating that is applied to the specimen. A suitable mask performs filtering of the diffraction pattern; the image that is reconstructed from this filtered pattern shows light and dark areas; it is shown that the boundary line of those areas is the locus of points exhibiting the same value of strain, measured along a certain direction.

Moiré-fringe interpolation and multiplication by fringe shifting

A simple technique of shifting the master grating to increase the sensitivity of moiré measurements is proposed. Details of the technique are described and an application of multiplication by three of a 1000-lines/in. grating is given. It is believed that multiplication by five should be obtainable.

Moiré fringes as parametric curves

Advantage is taken in this paper of the parametric properties of families of curves to express in a simple manner several fundamental properties of moiré fringes. Attention is called, in particular, to the necessary limitations on the angle of rotation of two gratings, and on the magnitude of their difference in pitch, to obtain an easily interpretable moiré-fringe pattern.

Photoelasticity methods to determine stresses in propellant-grain models

Two- and three-dimensional photoelasticity methods to stress and strain analyze propellant-grain models are reviewed. Pressure, restrained shrinkage and transient thermal loadings are considered. The advantages and limitations of two-dimensional simulations of the three-dimensional problems are studied in detail.

New method to determine restrained-shrinkage stresses in propellant-grain models

This paper deals with the photoelastic determination of restrained-shrinkage stresses which may be produced by curing or by thermal effects in models of solid propellant grains bonded to the case. Use is made of the birefringence exhibited in the curing process of a restrained polyurethane rubber. The techniques developed to take advantage of this property are shown in detail. The method can also be applied to the determination of the residual stresses produced in the curing process of a propellant cast around a rigid insert. An example of this application is also given. The extension of the method, using epoxies, to three-dimensional analyses is pointed out.

On the definitions of strain and their use in large-strain analysis

It is pointed out that when strains are computed from a displacement field, the engineering definition of strain(lf−li)/li has advantages in respect to other definitions used in finite-strain theory. Tensorial transformations can still be used easily by means of Mohrs circle. Illustrations for the case of Eulerian and Lagrangian strains are shown. The comments may be of particular interest to experimental analysts.