Numerical Analysis of VHCF Cruciform Test Specimens with Non-Unitary Biaxiality Ratios

With the development of new materials, it is now known that there is no such thing as a fatigue endurance limit, i.e., materials do not have infinite life when the stress level is such that there is no fracture up to 10 million (1E7) cycles. The problem of testing materials above this number of cycles is that most testing equipment operates well below 150 Hz, making testing up to 1 billion (1E9) cycles or above an impracticality. The recent developments of ultrasonic testing machines where frequencies can go as high as 20 kHz or above enabled tests to be extended to these ranges in just a few days. This is now known as Very High Cycle Fatigue (VHCF). On the other hand, critical components used in Engineering applications are usually subjected to multi-axial loads, as is the case of the fuselage and wings of aircrafts which are subjected to biaxial states of stress. In this paper, VHCF cruciform test specimens purposely designed to develop orthogonal biaxial stresses with different biaxiality ratios will be analysed. The specimens are composed from Aluminium 6082-T651, a medium strength alloy used in many highly stressed engineering applications, including trusses, cranes, bridges and transportation. The specimens work as tuning forks with determined mode shapes at 20±0.5 kHz, where maximum principal stresses are developed at the centre of the specimen. Finite Element Analysis (FEA) is used to assess the dynamic behaviour of the specimens. The framework on how to design and manufacture cruciform specimens with different biaxiality ratios will be explained in a clear way so it can be used by other engineers in the field

A multi-layer 'gas of circles' Markov random field model for the extraction of overlapping near-circular objects.

We propose a multi-layer binary Markov random field (MRF) model that assigns high probability to object configurations in the image domain consisting of an unknown number of possibly touching or overlapping near-circular objects of approximately a given size. Each layer has an associated binary field that specifies a region corresponding to objects. Overlapping objects are represented by regions in different layers. Within each layer, long-range interactions favor connected components of approximately circular shape, while regions in different layers that overlap are penalized. Used as a prior coupled with a suitable data likelihood, the model can be used for object extraction from images, e.g. cells in biological images or densely-packed tree crowns in remote sensing images. We present a theoretical and experimental analysis of the model, and demonstrate its performance on various synthetic and biomedical images