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Design Rules for Characteristics of Heat Flow in Welding on Thick Plates using Asymptotics and Blending

  • Author / Creator
    Wang, Ying
  • The problem of moving heat sources is central to a wide range of industrial fields, including welding, surface heat treatment and additive manufacturing. However, there are few general and easily applicable solutions to predict critical thermal characteristics of heat flow such as the cooling rate and dimensions of the heat affected zone, which have a decisive effect on the metallurgical and mechanical properties of the workpiece. Design rules in the form of asymptotes and correction factors have been obtained for the first time to predict critical thermal characteristics in welding and other moving heat source processes.

    Design rules are presented for 13 critical thermal characteristics based on Rosenthal's point heat source model. Related thermal characteristics are: maximum isotherm width and its location, leading and trailing lengths of isotherm, centerline heating rate and cooling rate, peak temperature and its gradient at the maximum width, aspect ratio of isotherms, melting efficiency, cooling time from 800C to 500C, solidification time, thickness of the heat affected zone, and modification criteria to account for the effect of joint preparation. Dimensional analysis suggests that all dimensionless characteristics depend on a single dimensionless parameter that captures all possible cases. This dimensionless number is the Rykalin number (Ry), except for the dimensionless maximum temperature, which depends on the distance from the centerline. Ry can be interpreted as a Peclet number, and it reflects the effect of advection relative to conduction. The obtained design rules are accurate to within 7% of the exact analytical solutions.

    Although the point heat source model captures isotherm characteristics for all values of Ry, it cannot provide reliable estimations in the vicinity of the heat source because of the singularity at the origin, which is intrinsic to the assumption of point heat source. For the first time, design rules for the peak temperature and the penetration depth have been obtained based on a moving Gaussian surface heat source on a thick substrate. In dimensionless form, peak temperature depends on the dimensionless distribution parameter. Penetration depth depends on two dimensionless quantities: Ry and the dimensionless heat distribution parameter. Conventional blending techniques are extended to multiple dimensionless groups. Correction factors associated with the heat distribution parameter have been developed to improve the accuracy of point heat source solutions. The maximum error of estimation from the exact solution is below 0.19% for the peak temperature and 9.7% for the penetration depth. Prediction of peak temperature and the penetration depth is accurate within the range of validity of the assumptions in the moving Gaussian surface source model. The obtained design rules have an excellent agreement with published measurements and simulation data for various processes and material systems.

    This research has addressed the problems associated with applying sophisticated numerical simulations that are often challenging for practitioners to use and empirical expressions that can hardly be generalized to other processes due to the lack of theoretical foundation. Derived from the first principles, the obtained design rules are general and capable of reflecting quantitative effects of operating parameters (e.g., power and velocity of the heat source) on resulting thermal characteristics. They are simple enough to be calculated with a calculator or spreadsheet and can also verify numerical models. The systematic methodology of asymptotic analysis and blending can be extended to other disciplines besides welding.

  • Subjects / Keywords
  • Graduation date
    Spring 2021
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-0ep4-gw27
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.