H Fessler

The Unit Strength Concept in the Interpretation of Beam Test Results for Brittle Materials

SYNOPSISBrittle materials are usually characterised in terms of the “modulus of rupture” obtained from the results of fracture tests on beam specimens. This is not a fundamental quantity. Alternative quantities (the mean strength of unit volume and of unit area) are introduced which are independent of the size of the specimen and the form of test, which allow the correlation of results from different tests, and which may be validly used in design calculations. After an outline of the necessary theory, the derivation of the two “unit strengths” and their use in correlating test results are illustrated using fracture data from a series of reaction-bonded silicon nitride beams. Minimum values obtained are:- mean uniaxial fracture stress of unit volume, 140 N/mm2 per cm3; mean uniaxial fracture stress of unit surface area, 180 N/mm2 per cm2.A means of allowing for the effects of contact friction in the analysis of beam fracture test data is presented. The ignoring of these effects may result in a significant ...

Precision casting of epoxy-resin photoelastic models

Abstract Photoelastic models may be made by four different methods: by machining from fully cured blocks; by machining of oversize simplified castings; by cementing of machined parts; by accurate casting to the same shape as the prototype. A method of casting models to the same proportional accuracy as the prototype and its limitation are described. In this technique a pattern is coated with silicone rubber which is supported by an epoxy-resin casing. Curing shrinkage and differential thermal expansion of the epoxy casing, rubber coating, and Araldite casting are factors which essentially influence the resulting accuracy of the cast models.

Stresses in a bottoming stud assembly with chamfers at the ends of the threads

Abstract Three-dimensional, frozen-stress, photoelastic models of 1 in. BSW studs and tapped blocks have been loaded axially and in torsion. Detailed distributions of axial, principal, and shear stresses show that, as expected, the greatest stresses occur near the front end of engagement, but there are secondary peaks near the back end due to the stresses set up by ‘locking’ the stud at the bottom of the hole. Chamfering the first two turns of the thread of the block eliminates the stress concentration at the front of the block itself but does not reduce the stud stresses significantly. Similarly, the stresses at the back of engagement are reduced if the stud thread is chamfered.

Elasto-plastic and creep behaviour of axially loaded, shouldered tubes

Abstract This paper compares the finite element predictions of elasto-plastic and creep behaviour with experimental data for axially loaded, shouldered tube models. Four shouldered tube models were made of a lead alloy and tested at 61°C, using strain gauges to measure the elasto-plastic and creep strains in the plain tube and fillet regions of the models. Instantaneous stress-strain and creep data were obtained from strain-gauged, uniaxial tensile specimens. The finite element solutions are based on the incremental Prandtl-Reuss equations. The elasto-plastic iterative solutions use a ‘negative gradient’ from the calculated point to the equivalent stress-equivalent strain curve to get the next estimate of the plastic strain increment. A time incremental method is used to obtain the creep solutions. Tests with the mean tube stress below, at and above the yield stress showed very good agreement between prediction and measurement of initial strains in the fillets. Differences between predictions and measurements of creep strains are attributable to cast-to-cast variations.

A micropolariscope for automatic stress analysis

Abstract A micropolariscope has been developed for the automatic analysis of photoelastic data. It will position frozen stress slices mounted on its stage to within ±0.002 mm, and takes readings of isoclinic angles and fractional fringe orders, repeatable to within ±0.08 degrees and ±0.001 fringes. A rectangular grid of up to 3 × 50 points can be read automatically, taking about 1¼ minutes per point; the readings are stored on a floppy disc and printed out. The original slice is itself sliced, and the subslice is viewed again in the orthogonal direction to produce a second set of readings. Software has been devised to analyse the two sets of readings. It makes use of Tesars modification of Frochts Shear Difference method to calculate five cartesian stresses, which may be plotted and printed in tabular form. Flexible facilities are provided for editing, correcting, plotting, and printing intermediate stages in the analysis, and for storing results in data files

Stresses in torispherical drumheads: A photoelastic investigation

The dependence of the elastic stress distribution on the shape and thickness parameters in a wide range of torispherical drumheads has been examined using the photoelastic frozen-stress method. Peak principal stress indices are presented in the form of two contour systems; they have also been studied in terms of mean and bending stresses. An approximate approach to some of the practical problems of non-uniform stress gradients is suggested. Head distortions have been measured. A stress concentration factor based on the Maxwell-von Mises yield criterion is shown to be approximately equal to the conventional one.

Shouldered plates and shats in tension and torsion

Abstract Room-temperature and frozen-stress photoelastic tests have been carried out to determine the magnitude, position, and extent of the stress concentrations which occur in the blending radii at the junctions of sections of different widths in symmetrical plates subjected to direct loads. An empirical equation has been derived from the flat-plate tests which is also applicable to shafts in tension. Other published data are consisent with the predictions of the empirical equations. Stress concentration factors for shafts in torsion are lower than in tension.

Stresses at end-milled keyways in plain shafts subjected to tension, bending, and torsion

Abstract The frozen-stress photoelastic technique has been used to determine the complete surface stress field in empty keyways of British Standard proportions for rectangular keys. A method is included for the photoelastic analysis of general surface stresses in doubly curved surfaces with one small radius. The ratio of measured stress to stress in the same fibre in a shaft without keyway is the same for bending and tension. Stress indices for combined bending and torsion have been calculated for one fillet-radius ratio. A simple method is presented for obtaining a close upper bound for the peak stress in any B.S. keyway for rectangular keys subjected to any combination of bending and torsion.

Multiaxial strength tests for brittle materials

Abstract Matchstick and coin shaped specimens are used to determine the material strength consistency and mean fracture strength under five different stress rations, using Weibull statistics. Many practical loading modes of these simple shapes are assessed. For the best, the necessary experimental work and results of the analyses are presented and illustrated for as-fired reaction-bonded silicon nitride (RBSN) tested at room-temperature.

A 30 ton biaxial tensile testing machine

Abstract The machine is intended for a flat-plate testpiece, one face of which has to be unobstucted throughout the test. Plates up to 36 in long, 27 in wide, and 3/4 in thick can be accommodated. Hydraulic rams actuated by air-hydraulic pumps exert completely independent tensions on cruciform test pieces through spherical bushes. Satisfactory direct-load readings were obtained form pressure gauges.