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

Branching principles of animal and plant networks identified by combining extensive data, machine learning, and modeling

Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi, and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks--mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii--which dictate essential biologic functions related to resource transport and supply--are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.Comment: 55 pages, 8 figures, 8 table

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

Toward a theory for diversity gradients: the abundance–adaptation hypothesis

The abundance–adaptation hypothesis argues that taxa with more individuals and faster generation times will have more evolutionary ‘experiments’ allowing expansion into, and diversification within, novel habitats. Thus, as older taxa have produced more individuals over time, and smaller taxa have higher population sizes and faster generation times, the Latitudinal Diversity Gradients (LDGs) of these clades should show shallower slopes. We describe the LDGs for archaea, bacteria, fungi, invertebrates and trees from six North American forests. For three focal groups – bacteria, ants, and trees – older taxa had shallower LDG slopes than the more recent, terminal taxa. Across 12 orders of magnitude of body mass, LDG slopes were steeper in larger taxa. The slopes of LDGs vary systematically with body size and clade age, underscoring the non-canonical nature of LDGs. The steepest LDG slopes were found for the largest organisms while the smallest, from bacteria to small litter-soil invertebrates, have shallower- to zero-slope LDGs. If tropical niche conservatism is the failure of clades to adapt to, and diversify in temperate habitats, then the steep LDGs of chordates and plants likely arise from the decreased ability of clades with large individuals to adapt to the multiple challenges of extra-tropical life