There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Friction stir welding (FSW) is a relatively new solid-state joining process. This joining technique is energy efficient, environment friendly, and versatile. In particular, it can be used to join high-strength aerospace aluminum alloys and other metallic alloys that are hard to weld by conventional fusion welding. FSW is considered to be the most significant development in metal joining in a decade. Recently, friction stir processing (FSP) was developed for microstructural modification of metallic materials. In this review article, the current state of understanding and development of the FSW and FSP are addressed. Particular emphasis has been given to: (a) mechanisms responsible for the formation of welds and microstructural refinement, and (b) effects of FSW/FSP parameters on resultant microstructure and final mechanical properties. While the bulk of the information is related to aluminum alloys, important results are now available for other metals and alloys. At this stage, the technology diffusion has significantly outpaced the fundamental understanding of microstructural evolution and microstructure–property relationships.

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Friction Stir Welding and Processing

An introduction to heat transfer

Recent advances in friction-stir welding : Process, weldment structure and properties

The post-welding stress state, strain history and material conditions of friction stir welded joints are often strongly idealized when used in subsequent modeling analyses, typically by neglecting one or more of the features above. But, it is obvious that the conditions after welding do influence the weld performance. The objective of this paper is to discuss some of the main conflicts that arise when taking both the post-welding material conditions and stress–strain state into account in a subsequent structural analysis. The discussion is here based on a preliminary numerical study of the possible effect of the post-welding conditions when subjecting a friction stir weld to loading transverse to the weld line. The numerical model of the friction stir welded joint, employs a step-wise modeling approach to combine an in-situ weld simulation with a post-welding failure analysis. Using the commercial software ANSYS, a thermo-mechanical model is employed to predict the thermally induced stresses and strains during welding, while an in-house finite element code is used to study the plastic flow localization and failure in a subsequent structural analysis. The coupling between the two models is made by mapping the post-welding stress–strain conditions predicted in ANSYS to the in-house code by using re-meshing techniques. The study indicates a noticeable influence of the post-welding stress–strain condition when subjecting the welded plate to tension. E.g. an increase of the tensile curve prior to plastic flow localization was observed, with a substantial influence on the specimen elongation at the onset of localization and thereby failure. This influence is, however, shown to be strongly affected by the applied boundary conditions. Specimens cut from the welded plate, transverse to the weld line, showed the largest influence of the post-welding conditions, even though significant relaxation of the residual stress state was predicted.

The effect of post-welding conditions in friction stir welds: From weld simulation to ductile failure

Purpose – The purpose of this paper is to determine the magnitude and spatial distribution of the heat transfer coefficient between the workpiece and the backing plate in a friction stir welding process using inverse modelling. Design/methodology/approach – The magnitude and distribution of the heat transfer coefficient are the variables in an optimisation problem. The objective is to minimise the difference between experimentally measured temperatures and temperatures obtained using a 3D finite element model. The optimisation problem is solved using a gradient based optimisation method. This approach yields optimal values for the magnitude and distribution of the heat transfer coefficient. Findings – It is found that the heat transfer coefficient between the workpiece and the backing plate is non-uniform and takes its maximum value in a region below the welding tool. Four different parameterisations of the spatial distribution of the heat transfer coefficient are analysed and a simple, two parameter dist...

Estimating the workpiece-backing plate heat transfer coefficient in friction stirwelding

A holistic approach to strain monitoring in fibre-reinforced polymer composites is presented using embedded fibre Bragg grating sensors. Internal strains are monitored in unidirectional E-glass/epo...

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Life cycle strain monitoring in glass fibre reinforced polymer laminates using embedded fibre Bragg grating sensors from manufacturing to failure

One of the most common processes used in manufacturing of multilayer ceramic packages, multilayer capacitors and large scale integration circuits is tape casting. In this process, the wet tape thickness is one of the single most determining parameters affecting the final properties of the product, and it is therefore of great interest to be able to control it. One way to control the tape thickness is to use a two doctor blade configuration in the tape casting machine. In this case, it becomes important to fix the height of the slurry in front of both doctor blades according to the desired tape thickness and casting speed (belt velocity). In the present work, the flow in both doctor blade regions of a slurry is described with a steady state momentum equation in combination with a Bingham plastic constitutive equation, and this is integrated to a closed form analytical solution for both reservoirs based on the desired wet tape thickness and casting speed. The developed model is used to investigate the impact of different material parameters and machine designs on the required slurry height. The solution is compared with experimental findings from the literature, and good agreement is found.

Bingham plastic fluid flow model in tape casting of ceramics using two doctor blades - analytical approach

The task of finding crucial design interdependencies in the form of mathematical relationships (empirical or otherwise) in an engineering design problem using the Pareto-optimal front is referred to as innovization. Past studies on the subject have limited themselves to a single front. In this paper we introduce the higher-level innovization task through an application of a manufacturing process simulation for the Friction Stir Welding (FSW) process where commonalities among two different Pareto-optimal fronts are analyzed. Multiple design rules are simultaneously deciphered from each front separately and compared. Important design aspects of the FSW problem are revealed in the process. The overall study aims at showing how some design principles can considerably ease the task of optimizing future enhancements to the design.

Jesper Henri Hattel

Papers

The effect of post-welding conditions in friction stir welds: From weld simulation to ductile failure

Estimating the workpiece-backing plate heat transfer coefficient in friction stirwelding

Life cycle strain monitoring in glass fibre reinforced polymer laminates using embedded fibre Bragg grating sensors from manufacturing to failure

Bingham plastic fluid flow model in tape casting of ceramics using two doctor blades - analytical approach

Higher-level innovization: A case study from Friction Stir Welding process optimization