Strain incompatibility as a source of residual stress in welding and additive manufacturing. (English) Zbl 1476.74026

Summary: The accumulation of residual stress during welding and additive manufacturing is an important effect that can significantly anticipate the workpiece failure. In this work we exploit the physical and analytical transparency of a 1.5D model to show that the deposition of thermally expanded material onto an elastic substrate leads to the accumulation of strain incompatibility. This field, which is the source of residual stress in the system, introduces memory of the construction history even in the absence of plastic deformations. The model is then applied to describe the onset and the progression of residual stresses during deposition, their evolution upon cooling, and the fundamental role played by the velocity of the moving heat source.


74F05 Thermal effects in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74C99 Plastic materials, materials of stress-rate and internal-variable type
Full Text: DOI arXiv


[1] Agnelli, F.; Constantinescu, A.; Nika, G., Design and testing of 3D-printed micro-architectured polymer materials exhibiting a negative Poisson’s ratio, Contin. Mech. Thermodyn., 32, 433-449 (2020)
[2] Apostol, G.; Solomon, G.; Iordǎchescu, D., Input parameters influence on the residual stress and distortions at laser welding using finite element analysis, UPB Sci. Bull. D, 74, 153-164 (2012)
[3] Archer, R. R., Growth Stresses and Strains in Trees, Springer Series in Wood Science (1987), Springer-Verlag: Springer-Verlag Berlin, Heidelberg
[4] Bentler, J. G.; Labuz, J. F., Performance of a cantilever retaining wall, J. Geotech. Geoenviron. Eng., 132, 1062-1070 (2006)
[5] Boley, B. A.; Weiner, J. H., Theory of Thermal Stresses (1997), Dover Publications · Zbl 1234.74001
[6] Brown, C. B.; Goodman, L. E., Gravitational stresses in accreted bodies, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 276, 1367, 571-576 (1963) · Zbl 0124.40601
[7] Buchbinder, D.; Meiners, W.; Pirch, N.; Wissenbach, K.; Schrage, J., Investigation on reducing distortion by preheating during manufacture of aluminum components using selective laser melting, J. Laser Appl., 26, Article 012004 pp. (2014)
[8] Chen, Y.; Sheng, I. C., Residual stress in weldment, J. Therm. stresses, 15, 1, 53-69 (1992)
[9] Chen, W.; Voisin, T.; Zhang, Y.; Florien, J.-B.; Spadaccini, C. M.; McDowell, D. L.; Zhu, T.; Wang, Y. M., Microscale residual stresses in additively manufactured stainless steel, Nature Comm., 10, 4338 (2019)
[10] Cheng, L.; To, A., Part-scale build orientation optimization for minimizing residual stress and support volume for metal additive manufacturing: Theory and experimental validation, Comput. Aided Des., 113, 1-23 (2019)
[11] Dafalias, Y. F.; Pitouras, Z., Stress field in actin gel growing on spherical substrate, Biomech. Model. Mechanobiol., 8, 9-24 (2009)
[12] Danescu, A.; Chevalier, C.; Grenet, G.; Regreny, Ph.; Letartre, X.; Leclercq, J. L., Spherical curves design for micro-origami using intrinsic stress relaxation, Appl. Phys. Lett., 102, Article 123111 pp. (2013)
[13] Deseri, L.; Piccioni, M.; Zurlo, G., Derivation of a new free energy for biological membranes, Contin. Mech. Thermodyn., 20, 255-273 (2008) · Zbl 1160.74387
[14] Dumais, J.; Kwiatkowska, D., Analysis of surface growth in shoot apices, Plant J., 31, 2, 229-241 (2001)
[15] Elmesalamy, A. S.; Abdolvand, H.; Walsh, J. N.; Francis, J. A.; Suder, W.; Williams, S.; Li, L., Measurement and modelling of the residual stresses in autogenous and narrow gap laser welded AISI grade 316L stainless steel plates, Int. J. Press. Vessels Pip., 147, 64-78 (2016)
[16] Farid, V. T.; Ali, Z. A., Numerical and experimental investigation of T-shape fillet welding of AISI 304 stainless steel plates, Mater. Des., 47, 615-623 (2013)
[17] Fergani, O.; Berto, F.; Welo, T.; Liang, S. Y., Analytical modelling of residual stress in additive manufacturing, Fatigue Fract. Eng. Mater. Struct., 00, 1-8 (2016)
[18] Ferro, P., The influence of phase transformations on the asymptotic residual stress distribution arising near a sharp V-notch tip, Model. Simul. Mater. Sci. Eng., 20, 8, Article 085003 pp. (2012)
[19] Ferro, P.; Porzner, H.; Tiziani, A.; Bonollo, F., The influence of phase transformations on residual stresses induced by the welding process - 3D and 2D numerical models, Model. Simul. Mater. Sci. Eng., 14, 117-136 (2006)
[20] Ge, Q.; Sakhaei, A. H.; Lee, H.; Dunn, C. K.; Fang, N. X.; Dunn, M. L., Multimaterial 4D printing with tailorable shape memory polymers, Sci. Rep., 6, 31110 (2016)
[21] Goodman, L. E.; Brown, C. B., Dead load stresses and the instability of slopes, J. Soil Mech. Found. Div. Proc. ASCE, 89, SM3, 103-134 (1963)
[22] Goodman, L. E.; Brown, C. B., Dead load stresses and the instability of slopes, J. Soil Mech. Found. Div. Proc. ASCE, 89, 103 (1963)
[23] Gumennik, A.; Levy, E. C.; Grena, B.; Hou, C.; Rein, M.; Abouraddy, A. F.; Joannopoulos, J. D.; Fink, Y., Confined in-fiber solidification and structural control of silicon and silicon-germanium microparticles, Proc. Natl. Amer. Soc., 114, 28, 7240-7245 (2017)
[24] John, K.; Caillere, D.; Misbah, C., Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling, Phys. Rev. E, 90, Article 052706 pp. (2014)
[25] Kadish, J.; Barber, J. R.; Washabaugh, P. D., Stresses in rotating spheres grown by accretion, Int. J. Sol. Struct., 42, 5322-5334 (2005) · Zbl 1119.74312
[26] King, W. D.; Fletcher, N. H., Pressure and stresses in freezing water drops, J. Phys. D: Appl. Phys., 6, 192 (1973)
[27] Lai, Y.; Liu, W.; Jibin, Z.; Zhao, Y.; Wang, F.; Han, W., Experimental study on residual stress in titanium alloy laser additive manufacturing, Appl. Mech. Mater., 431, 20-26 (2013)
[28] Leggatt, R. H., Residual stresses in welded structures, Int. J. Press. Vessels Pip., 85, 144-151 (2008)
[29] Liu, S.; Kouadri-Henni, A.; Gavrus, A., DP600 dual phase steel thermo-elasto-plastic constitutive model considering strain rate and temperature influence on FEM residual stress analysis of laser welding, J. Manuf. Processes, 35, 407-419 (2018)
[30] Liu, W.; Ma, J.; Kong, S.; Liu, R.; Kovacevic, F., Numerical modelling and experimental verification of residual stress in autogenous laser welding of high-strength steel, Lasers Manuf. Mater. Process., 2, 24-42 (2015)
[31] Mendes, C. E.; De Melo, L. G.T. C.; Ferreira, R. A.S.; Barros, P. S.; Rolim, T. L.; Yadava, Y. P., The back stress behaviour study analysed in residual stress of welded naval plates in different lamination directions and different thermal contributions, Mater. Res., 20, 2, 722-728 (2017)
[32] Mercelis, P.; Kruth, J., Residual stresses in selective laser sintering and selective laser melting, Rapid Prototyp. J., 12, 5, 254-265 (2006)
[33] Mitra, S.; Arora, K. S.; Bhattacharya, B.; Singh, S. B., Effect of welding speed on the prediction accuracy of residual stress in laser welded 1.2 mm thick dual phase steel, Lasers Manuf. Mater. Process., 7, 74-87 (2020)
[34] Mugwagwa, L.; Yadroitsev, I.; Matope, S., Effect of process parameters on residual stresses, distortions, and porosity in selective laser melting of maraging steel 300, Metals, 9, 10, 1042 (2019)
[35] Mukherjee, T.; Zhang, W.; Debroy, T., An improved prediction of residual stresses and distortion in additive manufacturing, Comput. Mater. Sci., 126, 360-372 (2017)
[36] Promoppatum, P.; Yao, S. C.; Pistorius, P. C.; Rollett, A. D., A comprehensive comparison of the analytical and numerical prediction of the thermal history and solidification microstructure of inconel 718 products made by laser powder-bed fusion, Engineering, 3, 5, 685-694 (2017)
[37] Ravisankar, A.; Velaga, S. K.; Rajput, G.; Venugopal, S., Influence of welding speed and power on residual stress during gas tungsten arc welding (GTAW) of thin sections with constant heat input: a study using numerical simulation and experimental validation, J. Manuf. Process., 16, 2, 200-211 (2014)
[38] Ren, K.; Chew, Y.; Fuh, J. Y.H.; Zhang, Y. F.; Bi, G. J., Thermomechanical analyses for optimized path planning in laser aided additive manufacturing processes, Mater. Des., 162, 80-93 (2019)
[39] Rosenthal, D., The theory of moving sources of heat and its application to metal treatments, Trans. ASME, 43, 849-866 (1946)
[40] Sames, W. J.; List, F. A.; Pannala, S.; Dehoff, R. R.; Babu, S. S., The metallurgy and processing science of metal additive manufacturing, Int. Mater. Rev., 61, 5, 315-360 (2016)
[41] Schwerdtfeger, K.; Sato, M.; Tacke, K. H., Stress formation in solidifying bodies, Metall. Mater. Trans. B, 29, 5, 1057-1068 (1998)
[42] Seang, C.; David, A. K.; Ragneau, E., Laser welding of sheet metal assembly: transformation induced volume strain affect on elastoplastic model, Phys. Procedia, 41, 448-459 (2013)
[43] Shah, K.; Haq, I. U.; Shah, S. A.; Khan, F. U.; Khan, M. T.; Khan, S., Experimental study of direct laser deposition of Ti-6Al-4V and Inconel 718 by using pulsed parameters, Sci. World J., 841549 (2014)
[44] Sudersanan, P. D.; Kempaiah, U. N., The effect of heat input and travel speed on the welding residual stress by finite element method, Int. J. Mech. Prod. Eng. Res. Dev., 2, 4, 43-50 (2012)
[45] Thorat, S. R.; Kharde, Y. R.; Bhosale, K. C.; Kharde, S. B., Effect of welding conditions on residual stresses and heat source distribution on temperature variations on butt welds: a review, Int. J. Eng. Res. Appl., 3, 1, 1434-1439 (2013)
[46] Trincher, V. K., Formulation of the problem of determining the stress-strain state of a growing body, Izv. AN SSSR, Mekh. Tverd. Tela, 19, 2, 119-124 (1984)
[47] Truskinovsky, L.; Zurlo, G., Nonlinear elasticity of incompatible surface growth, Phys. Rev. E, 99, Article 053001 pp. (2019)
[48] Ueda, Y.; Yuan, M. G., Prediction of residual stresses in butt welded plates using inherent strains, J. Eng. Mater. Technol., 115, 417-423 (1993)
[49] Vanel, L.; Howell, D.; Clark, D.; Behringer, R. P.; Clement, E., Memories in sand: Experimental tests of construction history on stress distributions under sandpiles, Phys. Rev. E, 60, R5040(R) (1999)
[50] Wang, X., Chou, K., 2015. Residual stress in metal parts produced by powder-bed additive manufacturing processes. In: 26th International Solid Freeform Fabrication Symposium, pp. 1463-1474.
[51] Wang, X.; Gong, J.; Zhao, Y.; Wang, Y.; Ge, Z., Numerical simulation to study the effect of arc travelling speed and welding sequences on residual stresses in welded sections of new ferritic P92 pipes, High Temp. Mater. Proc., 35, 2, 121-128 (2016)
[52] Wildeman, S.; Sterl, S.; Sun, C.; Loshe, D., Fast dynamics of water droplets freezing from the outside in, Phys. Rev. Lett., 118, Article 084101 pp. (2017)
[53] Yadroitsev, I.; Yadroitsava, I.; Bertrand, Ph.; Smurov, I., Factor analysis of selective laser melting process parameters and geometrical characteristics of synthesized single tracks, Rapid Prototyp. J., 18, 3, 201-208 (2012)
[54] Zurlo, G.; Truskinovsky, L., Printing non-Euclidean solids, Phys. Rev. Lett., 119, Article 048001 pp. (2017)
[55] Zurlo, G.; Truskinovsky, L., Inelastic surface growth, Mech. Res. Commun., 93, 174-179 (2018)
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