Cracking During Nanoindentation and its Use in the Measurement of Fracture Toughness

Results of an investigation aimed at developing a technique by which the fracture toughness of a thin film or small volume can be determined in nanoindentation experiments are reported. The method is based on the radial cracking which occurs when brittle materials are deformed by a sharp indenter such as a Vickers or Berkovich diamond. In microindentation experiments, the lengths of radial cracks have been found to correlate reasonably well with fracture toughness, and a simple semi-empirical method has been developed to compute the toughness from the crack lengths. However, a problem is encountered in extending this method into the nanoindentation regime with the standard Berkovich indenter in that there are well defined loads, called cracking thresholds, below which indentation cracking does not occur in most brittle materials. We have recently found that the problems imposed by the cracking threshold can be largely overcome by using an indenter with the geometry of the comer of a cube. For the cube-corner indenter, cracking thresholds in most brittle materials are as small as 1 mN ({approximately}0.1 grams). In addition, the simple, well-developed relation between toughness and crack length used for the Vickers indenter in the microindentation regime can be used for the cube-corner indenter in the nanoindentation regime provided a different empirical constant is used

Cracking during nanoindentation and its use in the measurement of fracture toughness

Results of an investigation aimed at developing a technique by which the fracture toughness of a thin film or small volume can be determined in nanoindentation experiments are reported. The method is based on the radial cracking which occurs when brittle materials are deformed by a sharp indenter such as a Vickers or Berkovich diamond. In microindentation experiments, the lengths of radial cracks have been found to correlate reasonably well with fracture toughness, and a simple semi-empirical method has been developed to compute the toughness from the crack lengths. However, a problem is encountered in extending this method into the nanoindentation regime with the standard Berkovich indenter in that there are well defined loads, called cracking thresholds, below which indentation cracking does not occur in most brittle materials. We have recently found that the problems imposed by the cracking threshold can be largely overcome by using an indenter with the geometry of the comer of a cube. For the cube-corner indenter, cracking thresholds in most brittle materials are as small as 1 mN ({approximately}0.1 grams). In addition, the simple, well-developed relation between toughness and crack length used for the Vickers indenter in the microindentation regime can be used for the cube-corner indenter in the nanoindentation regime provided a different empirical constant is used

Intelligent sampling for the measurement of structured surfaces

Uniform sampling in metrology has known drawbacks such as coherent spectral aliasing and a lack of efficiency in terms of measuring time and data storage. The requirement for intelligent sampling strategies has been outlined over recent years, particularly where the measurement of structured surfaces is concerned. Most of the present research on intelligent sampling has focused on dimensional metrology using coordinate-measuring machines with little reported on the area of surface metrology. In the research reported here, potential intelligent sampling strategies for surface topography measurement of structured surfaces are investigated by using numerical simulation and experimental verification. The methods include the jittered uniform method, low-discrepancy pattern sampling and several adaptive methods which originate from computer graphics, coordinate metrology and previous research by the authors. By combining the use of advanced reconstruction methods and feature-based characterization techniques, the measurement performance of the sampling methods is studied using case studies. The advantages, stability and feasibility of these techniques for practical measurements are discussed

TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial orders for analytic and cross-code test cases

Decoupling algorithms from schedules for easy optimization of image processing pipelines

Using existing programming tools, writing high-performance image processing code requires sacrificing readability, portability, and modularity. We argue that this is a consequence of conflating what computations define the algorithm, with decisions about storage and the order of computation. We refer to these latter two concerns as the schedule, including choices of tiling, fusion, recomputation vs. storage, vectorization, and parallelism. We propose a representation for feed-forward imaging pipelines that separates the algorithm from its schedule, enabling high-performance without sacrificing code clarity. This decoupling simplifies the algorithm specification: images and intermediate buffers become functions over an infinite integer domain, with no explicit storage or boundary conditions. Imaging pipelines are compositions of functions. Programmers separately specify scheduling strategies for the various functions composing the algorithm, which allows them to efficiently explore different optimizations without changing the algorithmic code. We demonstrate the power of this representation by expressing a range of recent image processing applications in an embedded domain specific language called Halide, and compiling them for ARM, x86, and GPUs. Our compiler targets SIMD units, multiple cores, and complex memory hierarchies. We demonstrate that it can handle algorithms such as a camera raw pipeline, the bilateral grid, fast local Laplacian filtering, and image segmentation. The algorithms expressed in our language are both shorter and faster than state-of-the-art implementations.National Science Foundation (U.S.) (Grant 0964004)National Science Foundation (U.S.) (Grant 0964218)National Science Foundation (U.S.) (Grant 0832997)United States. Dept. of Energy (Award DE-SC0005288)Cognex CorporationAdobe System