RD-E: 2603 Forming

Failure criteria defined with failure model /FAIL/FLD.

In Radioss it is possible to simulate failure with a failure model. FLD failure models are most commonly used for forming, which describe material failure in strain space. Here, one shell element and circular plate model are used to demonstrate the failure behavior with FLD failure model.

Options and Keywords Used

Input Files

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

FLD Failure Model (Forming Limit Diagram)

This failure model uses the generic forming limit diagram (FLD), defined for the given material. The curve is expressed in the area of principal strains (major and minor strains).


Figure 1.
The above FLD diagram shows:
  • In uniaxial test (by d ε minor d ε major =−v=−0.33 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai aadsgacqaH1oqzdaWgaaWcbaGaamyBaiaadMgacaWGUbGaam4Baiaa dkhaaeqaaaGcbaGaamizaiabew7aLnaaBaaaleaacaWGTbGaamyyai aadQgacaWGVbGaamOCaaqabaaaaOGaeyypa0JaeyOeI0IaamODaiab g2da9iabgkHiTiaaicdacaGGUaGaaG4maiaaiodaaaa@4E3B@ ) once point P1 (-0.0374,0.1133) is reached, the element fails
  • In eqibiaxial test (by d ε minor d ε major =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai aadsgacqaH1oqzdaWgaaWcbaGaamyBaiaadMgacaWGUbGaam4Baiaa dkhaaeqaaaGcbaGaamizaiabew7aLnaaBaaaleaacaWGTbGaamyyai aadQgacaWGVbGaamOCaaqabaaaaOGaeyypa0JaaGymaaaa@4835@ ) once point P2(0.26,0.26) is reached, the element fails


Figure 2.
The damage will print either with /ANIM/SHELL/DAMA or /ANIM/SHELL/FLDF in the Engine file. Both define damage as:(1) D= ε major ε lim MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebGaey ypa0ZaaSaaaeaacqaH1oqzdaWgaaWcbaGaamyBaiaadggacaWGQbGa am4BaiaadkhaaeqaaaGcbaGaeqyTdu2aaSbaaSqaaiGacYgacaGGPb GaaiyBaaqabaaaaaaa@4479@
It compares the current ε m a j o r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda WgaaWcbaGaamyBaiaadggacaWGQbGaam4Baiaadkhaaeqaaaaa@3DED@ with ε lim MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda WgaaWcbaGaciiBaiaacMgacaGGTbaabeaaaaa@3C0B@ , which is from the FLD curve by the same ε m i n o r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda WgaaWcbaGaamyBaiaadggacaWGQbGaam4Baiaadkhaaeqaaaaa@3DED@ .


Figure 3.

Only with /ANIM/SHELL/FLDF and Ifail_sh=4 is it possible to compute just the damage and not delete the element. It used to have a better vision of dangerous zones.

Results

Use the above FLD curve in the plate example and failure printed in animation with /ANIM/SHELL/FLDF and /ANIM/SHELL/DAMA like:


Figure 4.
/ANIM/SHELL/FLDZ can also be used to print the failure zone.


Figure 5. Failure zone
FLDZ=6
Failure
ε m a j o r > ε lim MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaad2gacaWGHbGaamOAaiaad+gacaWGYbaabeaakiabg6da +iabew7aLnaaBaaaleaaciGGSbGaaiyAaiaac2gaaeqaaaaa@4231@
FLDZ=5
Marginal
ε lim > ε m a j o r > ε m arg i n a l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiGacYgacaGGPbGaaiyBaaqabaGccqGH+aGpcqaH1oqzdaWg aaWcbaGaamyBaiaadggacaWGQbGaam4BaiaadkhaaeqaaOGaeyOpa4 JaeqyTdu2aaSbaaSqaaiaad2gaciGGHbGaaiOCaiaacEgacaWGPbGa amOBaiaadggacaWGSbaabeaaaaa@4C88@
FLDZ=4
Safe
ε m arg i n a l > ε m a j o r > | ε m i n o r | MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaad2gaciGGHbGaaiOCaiaacEgacaWGPbGaamOBaiaadgga caWGSbaabeaakiabg6da+iabew7aLnaaBaaaleaacaWGTbGaamyyai aadQgacaWGVbGaamOCaaqabaGccqGH+aGpdaabdaqaaiabew7aLnaa BaaaleaacaWGTbGaamyAaiaad6gacaWGVbGaamOCaaqabaaakiaawE a7caGLiWoaaaa@51A2@
FLDZ=3
Compression
− ε m i n o r > ε m a j o r > − ε m i n o r ⋅ R a n i 1 + R a n i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaeq yTdu2aaSbaaSqaaiaad2gacaWGPbGaamOBaiaad+gacaWGYbaabeaa kiabg6da+iabew7aLnaaBaaaleaacaWGTbGaamyyaiaadQgacaWGVb GaamOCaaqabaGccqGH+aGpcqGHsislcqaH1oqzdaWgaaWcbaGaamyB aiaadMgacaWGUbGaam4BaiaadkhaaeqaaOGaeyyXIC9aaSaaaeaaca WGsbWaaSbaaSqaaiaadggacaWGUbGaamyAaaqabaaakeaacaaIXaGa ey4kaSIaamOuamaaBaaaleaacaWGHbGaamOBaiaadMgaaeqaaaaaaa a@593B@
FLDZ=2
High wrinkle
− ε m i n o r ⋅ R a n i 1 + R a n i > ε m a j o r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaeq yTdu2aaSbaaSqaaiaad2gacaWGPbGaamOBaiaad+gacaWGYbaabeaa kiabgwSixpaalaaabaGaamOuamaaBaaaleaacaWGHbGaamOBaiaadM gaaeqaaaGcbaGaaGymaiabgUcaRiaadkfadaWgaaWcbaGaamyyaiaa d6gacaWGPbaabeaaaaGccqGH+aGpcqaH1oqzdaWgaaWcbaGaamyBai aadggacaWGQbGaam4Baiaadkhaaeqaaaaa@50AB@
FLDZ=1
Loose metal
ε m a j o r 2 + ε m i n o r 2 > F a c t o r _ L o o s e m e t a l 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaad2gacaWGHbGaamOAaiaad+gacaWGYbaabeaakmaaCaaa leqabaGaaGOmaaaakiabgUcaRiabew7aLnaaBaaaleaacaWGTbGaam yAaiaad6gacaWGVbGaamOCaaqabaGcdaahaaWcbeqaaiaaikdaaaGc cqGH+aGpcaWGgbGaamyyaiaadogacaWG0bGaam4BaiaadkhacaGGFb Gaamitaiaad+gacaWGVbGaam4CaiaadwgacaWGTbGaamyzaiaadsha caWGHbGaamiBamaaCaaaleqabaGaaGOmaaaaaaa@5781@


Figure 6. Failure zone in plate test

Conclusion

Failure model /FAIL/FLD used principal strain ratio to describe the material failure behavior which is suitable to describe material failure in forming.