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Parametric Modeling of Welding Processes Using Numerical-Analytical Basis Functions and Equivalent Source Distributions

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Abstract

A general methodology for inverse thermal analysis of steady-state energy deposition in plate structures, typically welds, is extended with respect to its formulation. This methodology is in terms of numerical-analytical basis functions, which provide parametric representations of weld-temperature histories that can be adopted as input data to various types of computational procedures, such as those for prediction of solid-state phase transformations and mechanical response. The extension of the methodology presented here concerns construction of numerical-analytical basis functions and their associated parameterizations, which permit optimal and convenient parameter optimization with respect to different types of weld-workpiece boundary conditions, energy source characteristics, and experimental measurements adoptable as weld-temperature history constraints. Prototype inverse thermal analyses of a steel weld are presented that provide proof of concept for inverse thermal analysis using these basis functions.

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Acknowledgment

This work was supported by a Naval Research Laboratory (NRL) internal core program.

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    S. G. Lambrakos

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Appendix

Appendix

T :

Temperature of workpiece

T A :

Ambient temperature of workpiece

\(T_{n}^{c}\) :

Constraint condition on temperature field

T M :

Melting temperature

T HE :

Temperature of HAZ-edge as measured (using thermocouples)

κ:

Thermal diffusivity

V :

Welding speed

l 1 :

Thickness of workpiece

l 2 :

Transverse-length parameter or tranverse length of workpiece

l 3 :

Longitudinal-length parameter or longitudinal length of workpiece

\(C\left( {\hat{x}_{k} } \right)\) :

Volumetric source function

Δt :

Time step for specifying average energy deposited during the time Δt

l S :

Length parameter specifying local region of temperature field to be calculated

Δl :

Spatial discretization of the temperature field with respect to l S

Z T :

Value of objective function

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Lambrakos, S.G. Parametric Modeling of Welding Processes Using Numerical-Analytical Basis Functions and Equivalent Source Distributions. J. of Materi Eng and Perform 25, 1360–1375 (2016). https://doi.org/10.1007/s11665-016-1970-2

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  • DOI: https://doi.org/10.1007/s11665-016-1970-2

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