Skip to main content
SpringerLink
Log in

Thermo-mechanical-microstructural simulation of double-pass welding process in a TWIP steel by FE formulation and probabilistic model

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This research work developed a decoupled thermo-mechanical-microstructural (TMM) numerical framework to simulate a multi-pass welding process. The numerical framework was applied to evaluate the effect of operating parameters on the weldability of a twinning induced plasticity (TWIP) steel considering metallurgical defects and the weld joint’s mechanical properties. The thermo-mechanical model was solved numerically using a finite element model (FEM). After that, the simulation of the thermo-microstructural field was performed through a combined probabilistic approach Monte Carlo (MC)-Voronoi tessellation. The staggered solution approach and the optimized FE macro-scale mesh further improved the convergence and reduced computing time. The correlation of TMM model estimations with thermal history measurements and mechanical and metallographic characterizations helped explain the variation of post-welding mechanical properties. The nature of residual stresses in the TWIP steel joint was correlated with the heat flux in the critical weld regions. The thermal gradients were also correlated with the weld regions that underwent grain growth and grain size reduction. The grain growth simulation performed by the MC-Voronoi model was in good agreement with the hardness reduction in the heat-affected zone (HAZ). The grain size distribution in the HAZ produced an unexpected tensile elongation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

C P :

Specific heat (J/kg °C)

T :

Temperature (°C)

t :

Time (s)

k :

Thermal conductivity (W/m °C)

q f, r :

Heat source (W/m3)

a, b, cf, cr :

Geometric parameters of double ellipsoidal heat source (m)

Q :

Heat input (J/m)

V :

Voltage (V)

I :

Current intensity (A)

v :

Welding speed (m/s)

ff, fr :

Weight factors (-)

x, y, z :

Global Cartesian coordinates (inertial) (m)

C :

Specific heat matrix (J/kg °C)

\( \dot{T} \) :

Transient temperature (°C)

r p :

Thermal load vector (W/m2)

r q :

Volumetric heat vector (W/m3)

\( {R}_{p_{\mathrm{ext}}} \) :

External forces vector (N)

\( {R}_{p_{\mathrm{int}}} \) :

Internal forces vector (N)

N i :

Vector of shape functions (-)

B :

Vector of derivates of shape functions (-)

V :

Volume (m3)

A :

Area (m2)

h :

Convection coefficient (W/m2 °C)

Δt :

Time increment (s)

Q inf :

Material parameter (MPa)

b c :

Material parameter (-)

{s}:

Deviation stress (MPa)

\( \overrightarrow{u} \) :

Vector of displacements (m)

F :

Yield criterion (MPa)

E :

Young modulus (MPa)

R :

Force residual of FE mechanical model (N)

dT :

Temperature increment vector (°C)

K TH :

Thermal stiffness matrix (MPa/°C)

K T :

Total stiffness matrix (MPa)

K el :

Elastic matrix (MPa)

K pl :

Plastic matrix (MPa)

v r :

Poisson ratio (-)

C M :

Stiffness matrix (MPa)

\( \overrightarrow{\boldsymbol{N}} \) :

Vector of shape functions of six-node rectangular element (-)

a r :

Height of rectangle element (m)

b r :

Base of rectangle element (m)

s, l :

Local coordinates of the six-node rectangular element (m)

tMCS :

Monte Carlo time step (s)

n1, K1 :

EDB model constants (-)

n :

Growth exponent (-)

α :

Thermal expansion coefficient (°C−1)

α r :

Parameter of full Newton-Raphson method (-)

ρ :

Density (kg/m3)

∇:

Gradient operator (m−1)

ξ :

Non-inertial coordinate (m)

η :

Arc efficiency (-)

β :

Environmental heat losses (W/m2)

Ω:

Calculation domain (-)

θ :

Transient integration parameter (-)

σ 0 :

Radius of the yield surface (MPa)

σ 1 :

Yield stress at zero plastic strain (MPa)

ϕ :

Incompatibility (non-linear term) (N/m3)

ε th :

Thermal strain (-)

ε el :

Elastic strain (-)

ε pl :

Plastic strain (-)

ε Total :

Total strain (-)

σ ij :

Stress tensor (MPa)

ρ ij :

Body forces (N/m3)

\( {\overline{\varepsilon}}^{\mathrm{pl}} \) :

Effective plastic strain rate (-)

\( {\dot{\varepsilon}}^{\mathrm{pl}} \) :

Plastic strain rate (-)

L T :

Diagonal matrix (-)

σ :

Incremental stress (MPa)

ε :

Incremental strain (-)

References

  1. Ayesta I, Izquierdo B, Flano O, Sánchez JA, Albizuri J, Aviles R (2016) Influence of the WEDM process on the fatigue behavior of Inconel® 718. Int J Fatigue 92:220–233. https://doi.org/10.1016/j.ijfatigue.2016.07.011

    Article  Google Scholar 

  2. Denkena B, Boehnke D, De Leon L (2008) Machining induced residual stress in structural aluminum parts. Prod Des Eng 2(3):247–253. https://doi.org/10.1007/s11740-008-0097-1

    Article  Google Scholar 

  3. Rashed MG, Ashraf M, Mines RAW, Hazell PJ (2016) Metallic microlattice materials: a current state of the art on manufacturing, mechanical properties and applications. Mater Design 95:518–533. https://doi.org/10.1016/j.matdes.2016.01.146

    Article  Google Scholar 

  4. Lippold JC (2015) Welding metallurgy and weldability. John Wiley & Sons Incorporated, USA

    Book  Google Scholar 

  5. Jeffus L (2020) Welding: principles and applications. Cengage Learning, USA

    Google Scholar 

  6. Weman K (2011) Welding processes handbook, second edn. Woodhead Publishing, USA

  7. Kearns WH (1982) Welding handbook, Vol. 4, Metals and their weldability. American Welding Society, USA

    Google Scholar 

  8. Kumar S, Shahi AS (2011) Effect of heat input on the microstructure and mechanical properties of gas tungsten arc welded AISI 304 stainless steel joints. Mater Design 32(6):3617–3623. https://doi.org/10.1016/j.matdes.2011.02.017

    Article  Google Scholar 

  9. Kumar S, Shahi AS (2016) Studies on metallurgical and impact toughness behavior of variably sensitized weld metal and heat affected zone of AISI 304L welds. Mater Design 89:399–412. https://doi.org/10.1016/j.matdes.2015.09.145

    Article  Google Scholar 

  10. Murugan S, Gill TPS, Kumar PV, Raj B, Bose MSC (2000) Numerical modelling of temperature distribution during multipass welding of plates. Sci Technol Weld Join 5(4):208–214. https://doi.org/10.1179/136217100101538227

    Article  Google Scholar 

  11. Liu C, Zhang JX, Xue CB (2011) Numerical investigation on residual stress distribution and evolution during multipass narrow gap welding of thick-walled stainless steel pipes. Fusion Eng Des 86(4–5):288–295. https://doi.org/10.1016/j.fusengdes.2011.01.116

    Article  Google Scholar 

  12. Murugan S, Rai SK, Kumar PV, Jayakumar T, Raj B (2001) Temperature distribution and residual stresses due to multipass welding in type 304 stainless steel and low carbon steel weld pads. Int J Press Vessel Pip 78(4):307–317. https://doi.org/10.1016/S0308-0161(01)00047-3

    Article  Google Scholar 

  13. De Cooman BC, Kwon O, Chin KG (2012) State-of-the-knowledge on TWIP steel. Mater Sci Technol 28(5):513–527. https://doi.org/10.1179/1743284711Y.0000000095

    Article  Google Scholar 

  14. Dini G, Najafizadeh A, Ueji R, Monir-Vaghefi SM (2010) Improved tensile properties of partially recrystallized submicron grained TWIP steel. Mater Lett 64(1):15–18. https://doi.org/10.1016/j.matlet.2009.09.057

    Article  Google Scholar 

  15. Chen J, Dong FT, Jiang HL, Liu ZY, Wang GD (2018) Influence of final rolling temperature on microstructure and mechanical properties in a hot-rolled TWIP steel for cryogenic application. Mat Sci Eng A 724:330–334. https://doi.org/10.1016/j.msea.2018.03.111

    Article  Google Scholar 

  16. Roncery LM, Weber S, Theisen W (2012) Welding of twinning-induced plasticity steels. Scr Mater 66(12):997–1001. https://doi.org/10.1016/j.scriptamat.2011.11.041

    Article  Google Scholar 

  17. Wei YH, Hou LF, Bin YAN (2014) Microstructure and mechanical properties of TWIP steel joints. J Iron Steel Res Int 21:749–756. https://doi.org/10.1016/S1006-706X(14)60137-0

    Article  Google Scholar 

  18. Yoo J, Kim B, Park Y, Lee C (2015) Microstructural evolution and solidification cracking susceptibility of Fe–18Mn–0.6 C–xAl steel welds. J Mater Sci 50(1):279–286. https://doi.org/10.1007/s10853-014-8586-4

    Article  Google Scholar 

  19. Saha DC, Chang I, Park YD (2014) Heat-affected zone liquation crack on resistance spot welded TWIP steels. Mater Charact 93:40–51. https://doi.org/10.1016/j.matchar.2014.03.016

    Article  Google Scholar 

  20. Nagesh DS, Datta GL (2010) Genetic algorithm for optimization of welding variables for height to width ratio and application of ANN for prediction of bead geometry for TIG welding process. Appl Soft Comput 10(3):897–907. https://doi.org/10.1016/j.asoc.2009.10.007

    Article  Google Scholar 

  21. Chiumenti M, Cervera M, Salmi A, De Saracibar CA, Dialami N, Matsui K (2010) Finite element modeling of multi-pass welding and shaped metal deposition processes. Comput Method Appl M 199(37–40):2343–2359. https://doi.org/10.1016/j.cma.2010.02.018

    Article  MATH  Google Scholar 

  22. Lindgren LE (2006) Numerical modelling of welding. Comput Method Appl M 195(48–49):6710–6736. https://doi.org/10.1016/j.cma.2005.08.018

    Article  MATH  Google Scholar 

  23. Jabbari M, Baran I, Mohanty S, Comminal R, Sonne MR, Nielsen MW, Hattel JH (2018) Multiphysics modelling of manufacturing processes: a review. Adv Mech Eng 10(5):1–30. https://doi.org/10.1177/1687814018766188

    Article  Google Scholar 

  24. Cho WI, Na SJ, Thomy C, Vollertsen F (2012) Numerical simulation of molten pool dynamics in high power disk laser welding. J Mater Process Technol 212(1):262–275. https://doi.org/10.1016/j.jmatprotec.2011.09.011

    Article  Google Scholar 

  25. Lu F, Tang X, Yu H, Yao S (2006) Numerical simulation on interaction between TIG welding arc and weld pool. Comput Mater Sci 35(4):458–465. https://doi.org/10.1016/j.commatsci.2005.03.014

    Article  Google Scholar 

  26. Chakraborty N (2009) The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple. Appl Therm Eng 29(17–18):3618–3631. https://doi.org/10.1016/j.applthermaleng.2009.06.018

    Article  Google Scholar 

  27. Hu Y, He X, Yu G, Ge Z, Zheng C, Ning W (2012) Heat and mass transfer in laser dissimilar welding of stainless steel and nickel. Appl Surf Sci 258(15):5914–5922. https://doi.org/10.1016/j.apsusc.2012.02.143

    Article  Google Scholar 

  28. Zeng Z, Wang L, Wang Y, Zhang H (2009) Numerical and experimental investigation on temperature distribution of the discontinuous welding. Comput Mater Sci 44(4):1153–1162. https://doi.org/10.1016/j.commatsci.2008.07.033

    Article  Google Scholar 

  29. Barroso A, Cañas J, Picón R, París F, Méndez C, Unanue I (2010) Prediction of welding residual stresses and displacements by simplified models. Experimental validation. Mater Design 31(3):1338–1349. https://doi.org/10.1016/j.matdes.2009.09.006

    Article  Google Scholar 

  30. Agelet de Saracibar C, Cervera M, Chiumenti M (2001) On the constitutive modeling of coupled thermomechanical phase-change problems. Int J Plast 17(12):1565–1622. https://doi.org/10.1016/S0749-6419(00)00094-2

    Article  MATH  Google Scholar 

  31. Capriccioli A, Frosi P (2009) Multipurpose ANSYS FE procedure for welding processes simulation. Fusion Eng Des 84(2–6):546–553. https://doi.org/10.1016/j.fusengdes.2009.01.039

    Article  Google Scholar 

  32. Ronda J, Oliver GJ (2000) Consistent thermo-mechano-metallurgical model of welded steel with unified approach to derivation of phase evolution laws and transformation-induced plasticity. Comput Method Appl M 189(2):361–418. https://doi.org/10.1016/S0045-7825(99)00461-2

    Article  MATH  Google Scholar 

  33. Mi G, Xiong L, Wang C, Hu X, Wei Y (2016) A thermal-metallurgical-mechanical model for laser welding Q235 steel. J Mater Process Technol 238:39–48. https://doi.org/10.1016/j.jmatprotec.2016.07.002

    Article  Google Scholar 

  34. Toyoda M, Mochizuki M (2004) Control of mechanical properties in structural steel welds by numerical simulation of coupling among temperature, microstructure, and macro-mechanics. Sci Technol Adv Mater 5(1–2):255–266. https://doi.org/10.1016/j.stam.2003.10.027

    Article  Google Scholar 

  35. Deng D (2009) FEM prediction of welding residual stress and distortion in carbon steel considering phase transformation effects. Mater Design 30(2):359–366. https://doi.org/10.1016/j.matdes.2008.04.052

    Article  Google Scholar 

  36. Raabe D (2002) Cellular automata in materials science with particular reference to recrystallization simulation. Annu Rev Mater Res 32(1):53–76. https://doi.org/10.1146/annurev.matsci.32.090601.152855

    Article  Google Scholar 

  37. Sista S, Yang Z, DebRoy T (2000) Three-dimensional Monte Carlo simulation of grain growth in the heat-affected zone of a 2.25 Cr-1Mo steel weld. Metall Mater Trans B Process Metall Mater Process Sci 31(3):529–536. https://doi.org/10.1007/s11663-000-0158-0

    Article  Google Scholar 

  38. García-García V, Mejía I, Reyes-Calderón F (2019) Improved thermal FE numerical model/DoE based on the Taguchi method to estimate weld penetration/energy and non-metallic inclusions: a case study in Ti-containing TWIP steel butt joints. Int J Adv Manuf Technol 105(1–4):1–20. https://doi.org/10.1007/s00170-019-04169-0

    Article  Google Scholar 

  39. Goldak J, Chakravarti A, Bibby M (1984) A new finite element model for welding heat sources. Metall Trans B 15(2):299–305. https://doi.org/10.1007/BF02667333

    Article  Google Scholar 

  40. Gery D, Long H, Maropoulos P (2005) Effects of welding speed, energy input and heat source distribution on temperature variations in butt joint welding. J Mater Process Technol 167(2–3):393–401. https://doi.org/10.1016/j.jmatprotec.2005.06.018

    Article  Google Scholar 

  41. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures, second edn. John Wiley & Sons, Hoboken

  42. Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics, sixth edn. Elsevier, USA

  43. ANSYS Inc (2009) Theory reference for the mechanical APDL and mechanical applications. ANSYS Inc, USA

    Google Scholar 

  44. Deng D, Murakawa H (2006) Numerical simulation of temperature field and residual stress in multi-pass welds in stainless steel pipe and comparison with experimental measurements. Comput Mater Sci 37(3):269–277. https://doi.org/10.1016/j.commatsci.2005.07.007

    Article  Google Scholar 

  45. Muránsky O, Hamelin CJ, Smith MC, Bendeich PJ, Edwards L (2012) The effect of plasticity theory on predicted residual stress fields in numerical weld analyses. Comput Mater Sci 54:125–134. https://doi.org/10.1016/j.commatsci.2011.10.026

    Article  Google Scholar 

  46. Simo J, Taylor R (1985) Consistent tangent operators for rate-independent elastoplasticity, Comput. Methods Appl Mech Engrg 48:101–118. https://doi.org/10.1016/0045-7825(85)90070-2

    Article  MATH  Google Scholar 

  47. Liang W, Murakawa H, Deng D (2015) Investigation of welding residual stress distribution in a thick-plate joint with an emphasis on the features near weld end-start. Mater Design 67:303–312. https://doi.org/10.1016/j.matdes.2014.11.037

    Article  Google Scholar 

  48. Aarbogh HM, Hamide M, Fjaer HG, Mo A, Bellet M (2010) Experimental validation of finite element codes for welding deformations. J Mater Process Technol 210(13):1681–1689. https://doi.org/10.1016/j.jmatprotec.2010.05.014

    Article  Google Scholar 

  49. Ku FH, McCracken SL (2017) Crack growth evaluation of remnant cracks underneath an excavate and weld repair. In: Pressure Vessels and Piping Conference American Society of Mechanical Engineers, p 57991. https://doi.org/10.1115/PVP2017-66173

    Chapter  Google Scholar 

  50. Mishra S, DebRoy T (2004) Measurements and Monte Carlo simulation of grain growth in the heat-affected zone of Ti–6Al–4V welds. Acta Mater 52(5):1183–1192. https://doi.org/10.1016/j.actamat.2003.11.003

    Article  Google Scholar 

  51. ASTM (2010) Standard test methods for determining average grain size, in ASTM STANDARD E112. ASTM International, West Conshohocken. https://doi.org/10.1520/E0112-10

    Book  Google Scholar 

  52. Gao J, Thompson RG (1996) Real time-temperature models for Monte Carlo simulations of normal grain growth. Acta Mater 44(11):4565–4570. https://doi.org/10.1016/1359-6454(96)00079-1

    Article  Google Scholar 

  53. Sabzi HE, Hanzaki AZ, Abedi HR, Soltani R, Mateo A, Roa J (2016) The effects of bimodal grain size distributions on the work hardening behavior of a TRansformation-TWinning induced plasticity steel. Mater Sci Eng A 678:23–32. https://doi.org/10.1016/j.msea.2016.09.085

    Article  Google Scholar 

  54. García-García V, Mejía I, Reyes-Calderón F (2019) Two-dimensional Monte Carlo–Voronoi simulation of grain growth and nucleation in the heat affected zone of TWIP-Ti welds. Materialia 5:100223. https://doi.org/10.1016/j.mtla.2019.100223

    Article  Google Scholar 

  55. Scott C, Allain S, Faral M, Guelton N (2006) The development of a new Fe-Mn-C austenitic steel for automotive applications. Rev Metal 103(6):293–302. https://doi.org/10.1051/metal:2006142

    Article  Google Scholar 

  56. García-García V, Mejía I, Reyes-Calderón F (2019) Quantitative metallographic characterization of welding microstructures in Ti-containing TWIP steel by means of image processing analysis. Mater Charact 147:1–10. https://doi.org/10.1016/j.matchar.2018.10.012

    Article  Google Scholar 

  57. DuPont JN, Marder AR (1995) Thermal efficiency of arc welding processes. Weld J 74:406–416

    Google Scholar 

  58. Christensen N, Davies V, Gjermundsen K (1965) The distribution of temperature in arc welding. Brit Weld J 12(2):54–75

    Google Scholar 

  59. Zhu XK, Chao YJ (2002) Effects of temperature-dependent material properties on welding simulation. Comput Struct 80(11):967–976. https://doi.org/10.1016/S0045-7949(02)00040-8

    Article  Google Scholar 

  60. Gonçalves CV, Carvalho SR, Guimarães G (2010) Application of optimization techniques and the enthalpy method to solve a 3D-inverse problem during a TIG welding process. Appl Therm Eng 30(16):2396–2402. https://doi.org/10.1016/j.applthermaleng.2010.06.009

    Article  Google Scholar 

  61. Aloraier AS, Joshi S (2012) Residual stresses in flux cored arc welding process in bead-on-plate specimens. Mat Sci Eng A 534:13–21. https://doi.org/10.1016/j.msea.2011.10.107

    Article  Google Scholar 

  62. Anderson MP, Srolovitz DJ, Grest GS, Sahni PS (1984) Computer simulation of grain growth-I, kinetics. Acta Metall Mater 32(5):783–791. https://doi.org/10.1016/0001-6160(84)90151-2

    Article  Google Scholar 

  63. Rae W, Lomas Z, Jackson M, Rahimi S (2017) Measurements of residual stress and microstructural evolution in electron beam welded Ti-6Al-4V using multiple techniques. Mater Charact 132:10–19. https://doi.org/10.1016/j.matchar.2017.07.042sab

    Article  Google Scholar 

Download references

Funding

This study is supported by the National Council on Science and Technology (Consejo Nacional de Ciencia y Tecnología-México) during the project CB-2012-01-0177572. The present research project was also supported by the Coordinación de la Investigación Científica-UMSNH (México) (CIC-1.8). Víctor García’s studies were sponsored by the National Council on Science and Technology (Consejo Nacional de Ciencia y Tecnología-México), N.B. 577720.

Author information

Authors and Affiliations

  1. Instituto de Investigación en Metalurgia y Materiales, Universidad Michoacana de San Nicolás de Hidalgo, Edificio “U-5”, Ciudad Universitaria, 58066, Morelia, Michoacán, Mexico

    V. García-García, I. Mejía & H. Hernández-Belmontes

  2. Departamento de Metal Mecánica, Posgrado en Metalurgía/ Doctorado en Ciencias en Ingeniería, Tecnológico Nacional de México / Instituto Tecnológico de Morelia, Av. Tecnológico 1500, 58120, Morelia, Michoacán, Mexico

    V. García-García & F. Reyes-Calderón

Authors
  1. V. García-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Mejía
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Reyes-Calderón
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Hernández-Belmontes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Mejía.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

García-García, V., Mejía, I., Reyes-Calderón, F. et al. Thermo-mechanical-microstructural simulation of double-pass welding process in a TWIP steel by FE formulation and probabilistic model. Int J Adv Manuf Technol 111, 1115–1134 (2020). https://doi.org/10.1007/s00170-020-06118-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-020-06118-8

Keywords

Search

Navigation