C-shaped specimen plane strain fracture toughness tests

Test equipment, procedures, and data obtained in the evaluation of C-shaped specimens are presented. Observations reported on include: specimen preparation and dimensional measurement; modifications to the standard ASTM E 399 displacement gage, which permit punch mark gage point engagement; and a measurement device for determining the interior and exterior radii of ring segments. Load displacement ratios were determined experimentally which agreed with analytically determined coefficients for three different gage lengths on the inner surfaces of radially-cracked ring segments

Load-displacement measurement and work determination in three-point bend tests of notched or precracked specimens

Suggestions for testing of notched or cracked three-point bend specimens are presented which: (1) correct displacement measurement errors resulting from misalignment between the load applicator and specimen; (2) account for coincidental strains not associated with the work of crack extension; (3) simplify record analysis and processing; and (4) extend displacement gage range without sacrifice of sensitivity or accuracy. These testing details are particularly applicable to procedures in which the crack extension force is determined from the work done on the specimen

Comparison tests and experimental compliance calibration of the proposed standard round compact plane strain fracture toughness specimen

Standard round specimen fracture test results compared satisfactorily with results from standard rectangular compact specimens machined from the same material. The location of the loading pin holes was found to provide adequate strength in the load bearing region for plane strain fracture toughness testing. Excellent agreement was found between the stress intensity coefficient values obtained from compliance measurements and the analytic solution proposed for inclusion in the standard test method. Load displacement measurements were made using long armed displacement gages and hollow loading cylinders. Gage points registered on the loading hole surfaces through small holes in the walls of the loading cylinders

Monitoring crack extension in fracture toughness tests by ultrasonics

An ultrasonic method was used to observe the onset of crack extension and to monitor continued crack growth in fracture toughness specimens during three point bend tests. A 20 MHz transducer was used with commercially available equipment to detect average crack extension less than 0.09 mm. The material tested was a 300-grade maraging steel in the annealed condition. A crack extension resistance curve was developed to demonstrate the usefulness of the ultrasonic method for minimizing the number of tests required to generate such curves

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

Theology, News and Notes - Vol. 35, No. 02

Theology News & Notes was a theological journal published by Fuller Theological Seminary from 1954 through 2014.https://digitalcommons.fuller.edu/tnn/1099/thumbnail.jp

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster