Prediction of Welding Deformation and Residual Stress by Elastic FEM Based on Inherent Strain

Abstract

An elastic finite element method to predict the welding deformation and the residual stress in multipass narrow gap welding is proposed. The proposed method employs the inherent strain as the source of the welding deformation and the residual stress. The inherent strain in welding joint is mainly governed by the maximum heating temperature and the constraint at each material point. In addition to these, the residual stress created during the preceding welding passes is also an influential factor in case of multipass welding. Considering these three factors, the general procedure to compute the inherent strain is shown. Further, the effectiveness of the proposed method is demonstrated through an numerical example. 1. •• OE¾ ‹ß "N‚É‚¨‚¯N‚É‚¨‚¯ ‚é OEvŽZ‹@‚Ì •‚ •« "\ ‰»‚É ‚ae ‚è,‚© ‚È ‚èOE»ŽÀ‚É‹ß ‚¢-n •Ú ‚ÉŠÖ‚· ‚é-â 'è ‚ð"M'e 'Y•« FEM ‚ð-p‚¢ ‚Ä•Ú•× ‚ɉð •Í ‚· ‚é ‚± ‚AE•ã ‰Â "\ ‚AE‚È ‚è ‚Â‚Â‚ ‚é1,2,3)•B ‚µ ‚© ‚µ,'D "• ‚â ŠC-m •\ '¢ •¨ ‚Ì ‚ae ‚¤ ‚É'å OE^‚Å•¡ ŽG‚È•\ '¢ •¨ ‚Ì OEš'¢ ‰ß 'ö ‚ð,"ñ •ü OE`-â 'è ‚AE‚µ ‚Ä'‰ŽÀ‚ɉð •Í ‚· ‚é ‚± ‚AE‚Í,‚Ü ‚¾OE»ŽÀ"I ‚É‚Í •s ‰Â "\ ‚É ‹ß ‚- ,-n •Ú•Ï OE`‚â Žc-¯ ‰ž-Í‚ð •" 'è ‚µ,•H •ì-@‚Ì ‰ü 'P ‚â,Ží •X ‚Ì ‹-"x•] ‰¿‚AE‚¢ ‚¤•HŠw"I-Ú"I ‚ð ‰Ê ‚· ‚½ ‚ß ‚É‚Í,‚ae ‚èŠÈ•Ö ‚È •û-@‚Ì ŠJ "-‚ª-] ‚Ü‚ê ‚é4,5)•Bˆê "Ê ‚É,-n •Ú‚â •Ø'f," ‹È ‚° ‚È ‚Ç‚Ì "M‰Á •H‚É ‚¨‚¯‚¨‚¯ ‚é Žc-¯ ‰ž-Í‚¨‚ae‚ÑÍ‚¨‚ae‚Ñ•Ï OE`‚É ‚‚¢ ‚Ä‚Í,OEÅ-L ‚Ђ¸‚Ý‚ª‚Ђ¸‚Ý‚ª-¼ ŽÒ‚Ì OE´ˆö ‚AE ŠT "O"I ‚É•l ‚¦ ‚é ‚± ‚AE‚ª ‚Å‚« ‚é •B ‚µ ‚½ ‚ª ‚Á‚Ä,-^ ‚¦ ‚ç‚ê ‚½‰Á •H•ð OE•‚É'Î ‚µ ‚ÄOEÅ-L ‚Ђ¸‚݂̂Ђ¸‚Ý‚Ì 'å ‚« ‚³ ‚AE •ª •z ‚ª-\‚ß •ª ‚Á‚Ä‚¨‚ê‚Á‚Ä‚¨‚ê ‚Î,'e •« ‚Ì FEM ‰ð •Í ‚É ‚ae ‚è Žc-¯ ‰ž-Í‚AE •Ï OE`‚ª •" 'è ‚Å ‚« ‚é •B ‚± ‚Ì Žž ‚É-â'è ‚AE‚È ‚é ‚Ì ‚ª,OEÅ-L ‚Ђ¸‚݂̂Ђ¸‚Ý‚Ì OEˆ'è-@‚Å‚ ‚é •B 'ae1•ñ6)‚Å ‚Í,‹÷ "÷-n •Ú‚Ì ‚ae ‚¤ ‚É"ÂOEú‚É'Î ‚µ ‚Ä"ü "M-Ê ‚ª 'Š 'Î "I ‚É•¬ ‚³ ‚¢ •ê • ‡ ‚É‚¨‚¯‚É‚¨‚¯ ‚é ƒr •[ ƒh-n •Ú ‚ð 'Î •Û ‚É3ŽŸ OE³"M 'e 'Y•« FEM ‰ð •Í ‚ð ŽÀ Ž{ ‚µ,•Å •‚ "ž 'B ‰·"x ‚AE•S '© ‚Ì ‹-‚³ ‚Ì ŠÏ "_ ‚© ‚ç OEÅ-L ‚Ђ¸‚݂̂Ђ¸‚Ý‚Ì • ¶ •¬ ‹@•\ ‚¨‚ae‚¨‚ae ‚Ñ•ª •z ‚ð-¾ ‚ç ‚© ‚É ‚µ ‚½•B 'ae2•ñ7)‚Å ‚Í,'½ 'w-n •Ú ‚É ‚¨‚¯‚¨‚¯ ‚é-ÍŠw"I OE»•Û ‚ð-¾‚ç ‚©‚É ‚· ‚é ‚½‚ß ‚Ì 'O'i ŠK‚AE‚µ ‚Ä,•| " ‚É TIG ‚É ‚ae ‚é ƒr •[ ƒh-n •Ú ‚ð OEJ ‚è •Ô ‚µ ŽÀŽ{ ‚µ ‚½Žž ‚Ì •Ï OE`‚¨OE`‚¨‚ae ‚ÑŽc-¯‰ž-Í‚ð,ŽÀ OE±‚AE FEM ‰ð •Í ‚É ‚ae ‚蕪 •Í ‚µ,'½ •d "MƒT ƒCƒNƒ‹ ‚Ì ‰º‚Å‚Ì OEÅ-L ‚Ð ‚¸‚Ý‚Ì‚¸‚Ý‚Ì • ¶ •¬ ‹@•\ ‚ð-¾‚ç ‚©‚É ‚µ ‚½•B-{ ˜_ • ¶ ‚Å ‚Í,'½ 'w-n •Ú ‚Ì ‚Ð ‚AE ‚‚ł ‚é‹· ŠJ•ae '½'w-n •Ú‚Ì-â'è ‚ð,•½-ʂЂ¸‚ÝʂЂ¸‚Ý-â'è ‚¨‚ae‚¨‚ae ‚Ñ3ŽŸ OE³-â'è ‚AE‚µ ‚Ä"M'e 'Y•« FEM ‰ð •Í ‚· ‚é ‚AE‚AE‚à ‚É,'ae1,2•ñ ‚Å‚» ‚ê ‚¼‚ê 'ñ ˆÄ ‚³ ‚ê ‚½ ƒr •[ ƒh-n •Ú‚¨‚ae‚ÑÚ‚¨‚ae‚Ñ'½•d "M-š-ð‚Ì ‰º‚Å‚Ì OEÅ-L ‚Ђ¸‚Ý‚ð‚Ђ¸‚Ý‚ð-p ‚¢ ‚½-n •Ú•Ï OE`OE`•EŽc-¯‰ž-Í‚Ì •" 'è-@‚ð ŽQ•l ‚É ‚µ ‚Ä,'½ 'w-n •Ú ‚É‚¨ ‚¯ ‚é-n •Ú•Ï OE`‚¨OE`‚¨‚ae‚ÑŽc-¯ ‰ž-Í‚ð OEÅ-L ‚Ђ¸‚݂ɂЂ¸‚Ý‚É Šî ‚« •" 'è ‚· ‚é •û-@‚ð 'ñ ˆÄ‚· ‚é •B ‚³ ‚ç ‚É,'ñ ˆÄ ‚³ ‚ê ‚½OEÅ-L ‚Ђ¸‚Ý‚ð‚Ђ¸‚Ý‚ð-p‚¢ ‚½'e •« ‰ð •Í-@‚Ì •HŠw"I-â'è ‚Ö‚Ì "K-p-á ‚Ì ‚Ð ‚AE‚ ‚AE‚µ ‚Ä,‹· ŠJ •ae '½'w-n •Ú ‚ð Žae ‚è•ã ‚°,ŠJ •ae •" ‚Ì •Ï OE`‚¨OE`‚¨‚ae‚ÑŽc-¯‰ž-Í‚Ì-\'ª ‚É'Î ‚· ‚é 'ñ ˆÄ-@‚Ì-L OEø•« ‚ðOEŸ •Ø ‚· ‚é •B * 'å •ã 'å Šw•HŠwOE¤‹ † ‰È ** 'å •ã 'å Šw•Ú• ‡ ‰È ŠwOE¤‹ † •Š *** ‹ß ‹E 'å Šw• ¶ •¨-••HŠw•" OE´•e Žó-• •½•¬10"N1OEŽ9"ú •t ‹G•u ‰‰ ‰ï‚É‚¨‚¢‰ï‚É‚¨‚¢ ‚Ä•u ‰‰ •½•¬10"N5OEŽ14,15"ú