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.

/pdf/friction-stir-welding-and-processing-3hu3ejo7ub.pdf

Friction Stir Welding and Processing

An introduction to heat transfer

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

The objective of this work is to establish an analytical model for heat generation by friction stir welding (FSW), based on different assumptions of the contact condition between the rotating tool surface and the weld piece. The material flow and heat generation are characterized by the contact conditions at the interface, and are described as sliding, sticking or partial sliding/sticking. Different mechanisms of heat generation are behind each contact condition, making this study important for further understanding of the real FSW process. The analytical expression for the heat generation is a modification of previous analytical models known from the literature and accounts for both conical surfaces and different contact conditions. Experimental results on plunge force and torque are used to determine the contact condition. The sliding condition yields a proportional relationship between the plunge force and heat generation. This is not demonstrated in the experiment, which suggests that the sticking contact condition is present at the tool/matrix interface.

https://iopscience.iop.org/article/10.1088/0965-0393/12/1/013/pdf

An analytical model for the heat generation in friction stir welding

The conditions under which the deposition process in friction stir welding is successful are not fully understood. However, it is known that only under specific thermomechanical conditions does a weld formation occur. If these conditions are not present, void formation will occur leading to a faulty weld. The objective of the present work is to analyse the primary conditions under which the cavity behind the tool is filled. For this, a fully coupled thermomechanical three-dimensional FE model has been developed in ABAQUS/Explicit using the arbitrary Lagrangian–Eulerian formulation and the Johnson–Cook material law. The model accounts for the compressibility by including the elastic response of the aluminium matrix. The contact forces are modelled by Coulomb's Law of friction, making the contact condition highly solution dependent. Furthermore, separation between the workpiece and the tool is allowed. This is often neglected in other models. Once non-recoverable separation is estimated by the model, a void develops. This is suggested as a preliminary criterion for evaluating the success of the deposition process. Of special interest is the contact condition along the tool/matrix interface, which controls the efficiency of the deposition process. In most models presented previously in the literature, the material flow at the tool interface is prescribed as boundary conditions. In all other contact models, the material is forced to keep contact with the tool. Therefore, the models are unable to predict when the suitable thermomechanical conditions and welding parameters are present. In the present work, the quasi-stationary thermomechanical state in the workpiece is established by modelling the dwell and weld periods. The different thermomechanical states in the colder, stiffer far-field matrix and the hotter, softer near-field matrix (under the tool) result in contact at the tool/matrix interface, thus, no void formation is observed. The steady-state model results are compared to the plunge force and heat generation observed in experimental welds in AA2024-T3.

https://iopscience.iop.org/article/10.1088/0965-0393/13/1/006/pdf

A local model for the thermomechanical conditions in friction stir welding

Material flow in butt friction stir welds in AA2024-T3

Thermal modelling of friction stir welding

The increased usage of fiber reinforced polymer composites in load bearing applications requires a detailed understanding of the process induced residual stresses and their effect on the shape distortions. This is utmost necessary in order to have more reliable composite manufacturing since the residual stresses alter the internal stress level of the composite part during the service life and the residual shape distortions may lead to not meeting the desired geometrical tolerances. The occurrence of residual stresses during the manufacturing process inherently contains diverse interactions between the involved physical phenomena mainly related to material flow, heat transfer and polymerization or crystallization. Development of numerical process models is required for virtual design and optimization of the composite manufacturing process which avoids the expensive trial-and-error based approaches. The process models as well as applications focusing on the prediction of residual stresses and shape distortions taking place in composite manufacturing are discussed in this study. The applications on both thermoset and thermoplastic based composites are reviewed in detail.

/pdf/a-review-on-the-mechanical-modeling-of-composite-4qkmjrbd8y.pdf

Jesper Henri Hattel

Papers

An analytical model for the heat generation in friction stir welding

A local model for the thermomechanical conditions in friction stir welding

Material flow in butt friction stir welds in AA2024-T3

Thermal modelling of friction stir welding

A Review on the Mechanical Modeling of Composite Manufacturing Processes