# Mathematical Treatment of Phase Transformation and Analytical Calculation Method of Restraint Stress-Strain(Welding Mechanics, Strength & Design)

## Abstract

In this paper, in order to develop the model of mathematical treatment of metal during transformation, a series of experiments and theoretical analyses were conducted. Thermal elastic-plastic analysis was performed using the variously idealized mechanical properties in the region of phase transformation. The validity of the idealization was examined by comparing with the residual stresses produced in RRC-test and slit weld specimen and clarify the production mechanism of restraint stresses. The main results are as follows. (1) When restraint stresses before transformation acts on occurring or developing transformation, the transformation superplasticity phenomenon appears. Thus the formerly produced restraint stresses are relaxed for a time. At the same time, compressive stresses are produced by transformation expansion. Restraint stresses stagnate until welding heat transfers out of the restraint length. Afterwards, restraint stress rapidly increase to be residual stress at room temperature. Therefore, if the detailed information on the production process of restraint stress is necessary, the analysis needs to take into accounts the above-mentioned phenomenon in addition to transformation expansion. (2) In consideration of the above-mentioned phenomenon, the most accurate model (model M2) assumes that the material which is cooled to the starting temperature of phase transformation does not possess rigidity for a time while rigidity gradually recovers and transformation expansion occurs in the region of phase transformation. The simplified model (model M3) which assumes that the material does not possess rigidity until it is cooled to the starting temperature of phase transformation is also accurate. If only welding residual stress is necessary, the analysis on the assumption that the weld metal and HAZ do not possess rigidity until the material is cooled to the terminating temperature of phase transformation is adequate enough that its result roughly coincides with the experimental one (model M4). (3) Based on the above outcomes, the already developed analytical calculation theory for estimation of restraint stress-strain perpendicular to the weld line of the weld metal due to slit weld is extended so as to apply to the material (HT-80) in which the effect of phase transformation is remarkable.

## Journal

• Transactions of JWRI

Transactions of JWRI 14(1), 153-162, 1985-07

Osaka University

## Codes

• NII Article ID (NAID)
110006486606
• NII NACSIS-CAT ID (NCID)
AA00867058
• Text Lang
ENG
• ISSN
03874508
• Data Source
NII-ELS

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