| Abstract Scope |
The mechanical effects of thermal fabrication processes such as welding, cutting, heat treatment, and additive manufacturing are a fundamental consideration for design with modern engineering materials. Industrial operators often rely on the experience of skilled tradespeople and equipment operators to achieve desired outcomes through a process of trial-and-error. Although adequate for minor deviations from existing practice, this approach is costly, inefficient, and may not be suitable for all cases. This is a particular concern for new material systems and advanced processes, such as additive manufacturing, where existing intuition is often insufficient to identify even a good starting point of proposed parameters and operating conditions. There is thus a strong and growing need for improved predictive expressions that may be employed quickly and easily by industrial practitioners.
The current state of the art in prediction of thermal-mechanical welding phenomena are computational algorithms that incorporate coupled numerical heat transfer, fluid mechanics, and solid mechanics; these models are capable of simulating transient stress development with temperature dependent elastic-plastic material models. Although it is possible to achieve high accuracy for a specific application, there is often limited or unknown applicability outside the specific parameters used. Exploring behaviour of even a small range of parameters or materials requires a significant investment of time and cost, in addition to the high-level of expertise required to develop and interpret the results of the computational models.
Analytical formulae offer a promising alternative to purely empirical methods. Although not yet widely applied to welding, fundamental analytical solutions form the basis of essential tools used in complex real-world engineering applications ranging from design of heat exchangers to gear trains. In this work, the mathematical techniques of dimensional analysis, asymptotic approximation, and scaling are used to derive a general model for the development of welding residual stress and distortion. The complex interactions between various thermal-mechanical phenomena are distilled into simple engineering equations suitable for use in procedure development and process design. This novel methodology has two key advantages over competing experimental and numerical techniques: (1) there is a clear understanding of the relationship and dependency between input parameters and output characteristic values; and (2) it may be readily adapted to consider the effect of changing heat source properties, new materials, or variations of any other essential input parameters.
The engineering expressions presented in this work begin with a minimal representation considering only the dominant underlying physical phenomena. Correction factors are then incorporated, as necessary to account for relevant secondary phenomena. Limited rigidity of finite section geometry is identified as a key secondary consideration under typical conditions for procedure development. The concept of compliance is introduced as a measure of the tendency for less rigid sections to considerably deform during fabrication in reaction to the development of internal plastic strains. Correction for the compliance effect is found to be fundamentally dependent on a novel dimensionless parameter, the Okerblom number (Ok). For symmetric flat plate geometry, this parameter has a physical interpretation as the normalized equilibrium temperature rise. For all other geometries, this parameter may be calculated as the product of the equilibrium temperature rise and the normalized compliance. Closed-form expressions for the compliance correction factor are derived from fundamental principles without the need for calibration or fitting to previous experiments and requiring input of only the component geometry and tabulated material properties. The proposed expressions are validated by comparison to published literature data for the plastic zone size and tendon force in a selection of geometries, including butt welded flat plates, T-sections, and circumferential joints.
Practical applications for these new predictive tools extend to a variety of welding processes, as well as many other fabrication methods which utilize moving heat sources, such as thermal cutting, laser processing (cladding and heat treatment), machining, grinding, and additive manufacturing. This fundamental work provides a strong foundation for future consideration of additional effects, including consecutive thermal cycles, phase transformations, and pre-existing residual stress fields. Because of their closed form, these expressions are ideally suited for use in metamodels, engineering design calculations, as well as codes and standards. |