Abstract
Material models in the framework of continuum mechanics cover the experimentally observed phenomena with a mathematical representation and a correspondingsetofmaterialparameters,whichneedtobeestablishedandvalidated. The theory of viscoplasticity plays an important role to describe the material behaviour of polymers and metals for a conventional as well as an additive manufacturing process. Naturally, the manufacturing process influences the microstructure and is to be reflected in the analysis and the characterisation of the material. The geometry reconstruction of microscopic images supports the extension of well-known material models and motivates the investigation of the interaction in bicontinuous composites. A universal measurement method as the contactfree thermography can be applied to validate the analytical assumption by an extended set of characteristics.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Abaqus (2014) Documentation 6.14. Dassault Systèmes, Providence Road, Rhode Island, USA
Agius, D., et al.: Sensitivity and optimisation of the chaboche plasticity model parameters in strain-life fatigue predictions. Mater. Des. 118, 107–121 (2017). https://doi.org/10.1016/j.matdes.2017.01.027
Arndt, C., et al.: Microengineered hollow graphene tube systems generate conductive hydrogels with extremely low filler concentration. Nano Lett. 21(8), 3690–3697 (2021). https://doi.org/10.1021/acs.nanolett.0c04375,pMID:33724848
Bodner SR, Partom Y (1975) Constitutive equations for elastic-viscoplastic strain-hardening materials. Transaction ASME Journal of Applied Mechanics 42(2):385–389, DOI https://doi.org/10.1115/1.3423586, https://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/42/2/385/5118618/385_1.pdf
Bodner, S.R., Lindenfeld, A.: Constitutive modelling of the stored energy of cold work under cyclic loading. Eur. J. Mech. a. Solids 14(3), 333–348 (1995)
Bodner SR (2000) Unified plasticity - an engineering approach. Final Report for Period 01 AFRL-ML-WP-TR-2001–4019, Technion-Israel Institute of Technology, Haifa 32000, Israel
Bröcker, C., Matzenmiller, A.: An enhanced concept of rheological models to represent nonlinear thermoviscoplasticity and its energy storage behavior. Continuum Mech. Thermodyn. 25(6), 749–778 (2013). https://doi.org/10.1007/s00161-012-0268-3
Carolan, D., Chong, H., Ivankovic, A., Kinloch, A., Taylor, A.: Co-continuous polymer systems: A numerical investigation. Comput. Mater. Sci. 98, 24–33 (2015). https://doi.org/10.1016/j.commatsci.2014.10.039
Chaboche, J.L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast 5(3), 247–302 (1989). https://doi.org/10.1016/0749-6419(89)90015-6
Chrysochoos, A.: Infrared thermography applied to the analysis of material behavior: a brief overview. Quantitative InfraRed Thermography Journal 9(2), 193–208 (2012). https://doi.org/10.1080/17686733.2012.746069
Chrysochoos, A., Maisonneuve, O., Martin, G., Caumon, H., Chezeaux, J.: Plastic and dissipated work and stored energy. Nucl. Eng. Des. 114(3), 323–333 (1989). https://doi.org/10.1016/0029-5493(89)90110-6
Cook G, Cook W (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the Seventh International Symposium on Ballistics, The Hague pp 541–547
DIN Deutsches Institut für Normung eV (2012) DIN EN ISO 527–2: Kunststoffe – Bestimmung der Zugeigenschaften: Teil 2: Prüfbedingungen für Form- und Extrusionsmassen
Dupin, S., Lame, O., Barrès, C., Charmeau, J.Y.: Microstructural origin of physical and mechanical properties of polyamide 12 processed by laser sintering. Eur. Polymer J. 48(9), 1611–1621 (2012). https://doi.org/10.1016/j.eurpolymj.2012.06.007
ElGhezalM, D.: Porousplasticity: Predictivesecondmomenthomogenizationmodels coupled with Gurson’s single cavity stress-strain solution. Int. J. Plast 108, 201–221 (2018). https://doi.org/10.1016/j.ijplas.2018.05.006
Forster AM (2015) Materials testing standards for additive manufacturing of polymer materials: State of the art and standards applicability. Nist interagency/internal report (nistir), National Institute of Standards and Technology, Gaithersburg, MD, DOI https://doi.org/10.6028/NIST.IR.8059
Franke R, Schob D, Ziegenhorn M (2017) Prüfverfahren und numerische Simulation von mechanischen Eigenschaften 3D-gedruckter thermoplastischer Kunststoffe, Springer Fachmedien Wiesbaden, pp 137–158. DOI https://doi.org/10.1007/978-3-658-17780-5_9
Gong, Y.P., Hyde, C.J., Sun, W., Hyde, T.H.: Determination of material properties in the chaboche unified viscoplasticity model. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 224(1), 19–29 (2010). https://doi.org/10.1243/14644207JMDA273
Goodridge, R.D., Tuck, C.J., Hague, R.J.M.: Laser sintering of polyamides and other polymers. Prog. Mater Sci. 57(2), 229–267 (2012). https://doi.org/10.1016/j.pmatsci.2011.04.001
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth - Part I. Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology 99(1):2–15
Haupt P (2002) Continuum Mechanics and Theory of Materials, 2nd edn. Springer-Verlag, DOI https://doi.org/10.1007/978-3-662-04775-0
Huber, N., Viswanath, R., Mameka, N., Markmann, J., Weißmüller, J.: Scaling laws of nanoporous metals under uniaxial compression. Acta Mater. 67, 252–265 (2014). https://doi.org/10.1016/j.actamat.2013.12.003
Kachanov, M.: Continuum model of medium with cracks. J .eng. Mech. Div. 106(5), 1039–1051 (1980). https://doi.org/10.1061/JMCEA3.0002642
Kamlah, M., Haupt, P.: On the macroscopic description of stored energy and self heating during plastic deformation. Int. J. Plast 13(10), 893–911 (1998). https://doi.org/10.1016/S0749-6419(97)00063-6
Khdir, Y., Kanit, T., Zaïri, F., Naït-Abdelaziz, M.: Computational homogenization of elastic–plastic composites. Int. J. Solids Struct. 50(18), 2829–2835 (2013). https://doi.org/10.1016/j.ijsolstr.2013.03.019
Krempl, E.: Models of viscoplasticity some comments on equilibrium (back) stress and drag stress. Acta Mech. 69(1), 25–42 (1987). https://doi.org/10.1007/BF01175712
Lee, T., Kashyap, R., Chu, C.: Building skeleton models via 3-d medial surface axis thinning algorithms. Graphical Models and Image Processing 56(6), 462–478 (1994). https://doi.org/10.1006/cgip.1994.1042
Lemaître J, Desmorat R (2005) Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin and New York
Oldyrev, P.P., Tamuzh, V.P.: Energy dissipation in a glass-reinforced plastic during prolonged cyclic deformation. Strength Mater. 1(3), 244–248 (1969). https://doi.org/10.1007/BF01543209
Olschewski, J.: Viskoplastische Materialmodellierung und Anwendung im Gasturbinenbau. Tech. Mech. 16(1), 39–50 (1996)
Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (2018). https://doi.org/10.1109/TSMC.1979.4310076
Perzyna, P.: The constitutive equations for rate sensitive plastic materials. Q. Appl. Math. 20, 321–332 (1963). https://doi.org/10.1090/qam/144536
Reese, S.: Multiplicative thermo-viscoplasticity: A thermodynamic model and its finite element implementation. Tech. Mech. 18(3), 209–216 (1998)
Rice, J., Tracey, D.: On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17(3), 201–217 (1969). https://doi.org/10.1016/0022-5096(69)90033-7
Richert, C., Huber, N.: Skeletonization, geometrical analysis, and finite element modeling of nanoporous gold based on 3d tomography data. Metals 8(282), 1–20 (2018). https://doi.org/10.3390/met8040282
Rosakis, P., Rosakis, A., Ravichandran, G., Hodowany, J.: A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids 48(3), 581–607 (2000). https://doi.org/10.1016/S0022-5096(99)00048-4
Roschning, B., Huber, N.: Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction, elastic poisson’s ratio, young’s modulus and yield strength. J. Mech. Phys. Solids 92, 55–71 (2016). https://doi.org/10.1016/j.jmps.2016.02.018
Schindelin, J., Argenda-CarrerasI, F.E.: Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012). https://doi.org/10.1038/nmeth.2019
Schob, D., et al.: Experimental and numerical simulation of material and damage behaviour of 3D printed polyamide 12 under quasi-static loading. Archives of Mechanics 71(4–5), 507–526 (2019). https://doi.org/10.24423/aom.3162
Schob D, Sagradov I, Roszak R, Sparr H, Ziegenhorn M, Kupsch A, Léonard F, Müller B, Bruno G (2020) Experimental determination and numerical simulation of material and damage behaviour of 3D printed polyamide 12 under cyclic loading. Engineering Fracture Mechanics 229(106841), DOI https://doi.org/10.1016/j.engfracmech.2019.106841
Shutov, A.V., Ihlemann, J.: On the simulation of plastic forming under consideration of thermal effects. Materialwiss. Werkstofftech. 42(7), 632–638 (2011). https://doi.org/10.1002/mawe.201100821
Soyarslan, C., Pradas, M., Bargmann, S.: Effective elastic properties of 3d stochastic bicontinuous composites. Mech. Mater. 137(103), 098 (2019). https://doi.org/10.1016/j.mechmat.2019.103098
Sparr, H., Roszak, R., Sagradov, I., Schob, D., Ziegenhorn, M.: Thermo-viscoplasticmaterial modelling for self-heating loads and its experimental verification. Tech. Mech. 40(1), 66–76 (2020). https://doi.org/10.24352/UB.OVGU-2020-015
Stichel, T., et al.: A round robin study for selective laser sintering of polyamide 12: Microstructural origin of the mechanical properties. Opt. Laser Technol. 89, 31–40 (2017). https://doi.org/10.1016/j.optlastec.2016.09.042
Taylor, G., Quinney, H.: The latent energy remaining in a metal after cold working. Proceedings of the Royal Society of London Series a, Containing Papers of a Mathematical and Physical Character 143(849), 307–326 (1934)
Truesdell C, Noll W (1992) The Non-Linear Field Theories of Mechanics, 3rd edn. Springer-Verlag, Berlin, DOI https://doi.org/10.1007/978-3-662-10388-3
Tvergaard, V., Needleman, A.: Analysis of the cup cone fracture in a round tensile bar. Acta Metallurgia 32(1), 157–169 (1984). https://doi.org/10.1016/0001-6160(84)90213-X
van Hooreweder, B., de Coninck, F., Moens, B.R., Sas, P.: Microstructural characterization of SLS-PA12 specimens under dynamic tension/compression excitation. Polym. Testing 29(3), 319–326 (2010). https://doi.org/10.1016/j.polymertesting.2009.12.006
Yanase, K., Chatterjee, H., Ghosh, S.K.: On numerical evaluation of eshelby tensor for superspherical and superellipsoidal inclusions in isotropic elastic material. Compos. B 192(107), 964 (2020). https://doi.org/10.1016/j.compositesb.2020.107964
Zaïri, F., Naït-Abdelaziz, M., Woznica, K., Gloaguen, J.M.: Constitutive equations for the viscoplastic-damage behaviour of a rubber-modified polymer. Eur. J. Mech. a. Solids 24(1), 169–182 (2005). https://doi.org/10.1016/j.euromechsol.2004.11.003
Acknowledgements
The financial support of the BMWi and AiF Projekt GmbH is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ziegenhorn, M. et al. (2022). Applications of Viscoplasticity and Damage Models, the Thermomechanical Consistency and the Prospect of a Microstructural Representation. In: Altenbach, H., Beitelschmidt, M., Kästner, M., Naumenko, K., Wallmersperger, T. (eds) Material Modeling and Structural Mechanics . Advanced Structured Materials, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-97675-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-97675-0_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-97674-3
Online ISBN: 978-3-030-97675-0
eBook Packages: EngineeringEngineering (R0)