Linear and non-linear elastic and plastic strains in a plate with a large hole loaded axially in its plane

Strain analysis of the ligament of a plate with a large hole indicates that both geometric and material non-linearity may take place. Geometric non-linearity may occur even when the material is strained elastically. This may explain the disagreement in the results obtained recently, for the stress concentration factors, by several investigators. The experimental analyses were conducted on an aluminum plate, using electrical resistance strain gages, and on a polyurethane rubber sheet using photography. The strain concentration factor was found to vary from 1 to 2 depending on the level of deformation.     

Transfer of hydrostatic loading from one boundary to another

If a portion of the surface of a body subjected to uniform pressure is let free, and if that same amount of pressure is applied to the rest of the surface which was originally free, the resultant stress field is the same in both cases but for a sign and a hydrostatic component. Applications may be important especially in experimental work.     

The practical use of the hole method in photoelasticity

A small circular hole has already been used in plane elasto-static photoelasticity to determine the stress tensor for any general loading situation. Originally the idea required the determination of the stress at four points at the free boundary of the hole, then it was found that more precision would be obtained if the measurements were taken at points located at a distance from the center of the hole equal to twice its radius. Later it was suggested that probably still better results would be obtained from points located at 1.4 times the radius. This paper has three objectives: (1) to improve the precision of the measurements by taking them at any point in the vicinity of the hole, which requires that the expressions giving the principal stresses be presented in a different form, as a function of the normalized variable distance from the center of the hole; (2) to show the consistent application of the method, using the values of the birefringence at various arbitrary radial locations, to plane elasto-static loading problems; and, (3) to present the application of this approach in a concise form so that its application is practical.     

Experimental analysis of displacements and shears at surfaces of contact

The displacements which exist at the contact between two loaded bodies depend on the geometry of the surface of contact, the type of the loading and the property of the materials. A method has been developed to determine these displacements experimentally. A grid has been photographically printed on an interior plane of a transparent model of low modulus of elasticity. The displacements were recorded photographically and the analysis was conducted on the photographs of the deformed grids. Shears were determined from the change in angles. The precision of the measurements at the interface is estimated to be plus or minus 0.05 mm. Examples of application are given for the cases of loads applied normally and tangentially to a rigid cylindrical punch resting on a semi-infinite soft plate. Important observations can be made on the zones of friction and of slip. The proposed method is three dimensional and the distributions can be obtained at several interior planes by changing the position of the plane of the grid. The limitations of the method are pointed out. The possibility of using gratings (12 to 40 lpmm) is considered, as well as the advantages of using moiré to analyze the displacements.     

Developments in the optical spatial filtering of superposed crossed gratings

It is shown in this paper how the whole field of displacement components and of their time and space derivatives (isothetics, isotachics and isoparagogics) can be obtained individually, as separate patterns in a simple and precise manner using spatial-filtering techniques. This result can be obtained even when crossed gratings are used on the deformed body. A method for achieving fringe multiplication in moiré patterns produced by superposed, crossed gratings is also demonstrated. It is also shown that displacement components and their time and space derivatives in directions diagonal to the crossed-grating lines can be obtained by proper handling of grating transparencies and spatial-filtering techniques. Hence, the moiré equivalent of a whole field of rosette-strain-gage measurements is obtained from a single photograph of a deformed crossed grating. A disk compressed between two wedges is used as an example. Important applications will be found in the fields of dynamics, nonlinear elasticity and plasticity.