Predictive Expressions for Residual Stress and Distortion in Welding and Related Thermal Processes

  • Author / Creator
    Grams, Mitchell R.
  • This work establishes the foundation for the estimation of forces and distortions induced by thermal processes, such as welding, as well as incorporates the effects of departure from idealizations. The Order of Magnitude Scaling (OMS) technique is applied to thermal-mechanical analysis of a moving point heat source. Under typical conditions, the thermal stress field is found to be best characterized by a uniaxial model. The region of plastic behaviour is set by the “first yield temperature”, a material property associated with thermal strain equivalent to the yield strain. The proposed scaling laws are applicable for any parameters that produce a sufficiently elongated first yield isotherm with AR≳17. A survey of single pass welding procedures indicate that this criterion will be met in almost all cases. The resulting uniform residual stress distribution along the heat source trajectory may be separated into a local driving component and a global reaction component. The driving component is expressed as an equivalent concentrated load, termed the tendon force, which is proportional to the linear energy input. A universal estimate of the proportionality factor for any metal with temperature independent properties is obtained as H≈0.23. The temperature dependent behaviour of materials is captured accurately using four independent dimensionless groups and the results are validated for common structural grades of steel, aluminum, and titanium with nonlinear finite element simulations. For some geometries, the section may not be sufficiently rigid to support uniaxial restraint. The concept of compliance is introduced as a simple, accurate, and general measure of the tendency for the geometry to distort at the location of a locally applied force. The effect of compliance is found to depend on a newly defined dimensionless parameter, the Okerblom number (Ok). For symmetric flat plate geometry, this parameter is physically interpreted as the normalized equilibrium temperature rise. The methodology of blended asymptotics is used to obtain explicit compliance correction factors for the yield temperatures and tendon force. The closed-form blended expressions are validated against literature data for flat plates, T-sections, and thin cylinders. The practical utility of the corrected asymptotic methodology is demonstrated with a case study on non-ideal fit-up of circumferential pipeline joints. Angular distortion at the pipe end produces bending across the weld root. The tendon force is used to derive a novel root susceptibility index which relates the welding procedure variables and material properties with the weld cross-section and pipe geometry. The stress concentration associated with non-ideal geometry is considered as a correction factor on the asymptotic case of ideal fit-up. The index presented is a contribution towards an objective criterion for acceptance of high-low offset. Although many of the illustrative examples presented this work relate to welding, the theory and equations presented here are broadly applicable to the fields of thermal cutting, laser processing (cladding and heat treatment), machining, grinding, and additive manufacturing. The simple, general, and accurate formulae presented in this work are well suited for use in procedure development and process design.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • 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.