An Analytical Method for Estimating Welding-Induced Plastic Zone Size for Residual Stress Profile Development

Abstract

As demonstrated in a recent comprehensive study on construction of full-field residual stress profiles for fitness-for-service assessment of pressure vessel and piping components, a reasonable estimate of welding-induced plastic zone size is necessary for introducing a shell theory based solution form (Song et al, 2015 [1–2]). This paper presents an analytical method for estimating plastic zone size by first solving an equivalent one dimensional heat transfer problem in which weld zone is represented by a line segment with initial temperature at melting. Thermoplasticity conditions are then imposed by assuming elastic perfectly plastic behaviors. Finally, an analytical expression is obtained to relate plastic zone boundary to maximum temperature field distribution experienced by material points within the whole domain over the entire heating and cooling history. The solution can be further expressed by a rather simple form with the identification of a characteristic length parameter that signifies inflection point of temperature distribution. So estimated plastic zone sizes for various welded joint types have been compared with finite element residual stress analysis results in which sequentially coupled welding heat transfer and thermo-mechanical analysis procedures are used. A good agreement has been achieved for all cases analyzed. Compared with conventional finite element residual stress analysis procedures, this method offers significant simplicity and efficiency, while being reasonably accurate, particularly for applications in residual stress profile estimation and in evaluation of welding induced distortions in complex structures.