Abstract
A combined continuum phase field model for martensitic transformations and fracture is introduced. The positive volume change that accompanies the phase transformation from austenite to martensite leads to an eigenstrain within the martensitic phase, which is considered within the present approach. Since the eigenstrain leads to both tensile and compressive loads, the model accounts for the sign of the local volume change. With aid of this model, the interactions between microcrack propagation and the formation of the martensitic phase are studied in two dimensions. Martensite forms in agreement with experimental observations at the crack tip and thus influences the crack formation. The numerical implementation is performed with finite elements. For the transient terms, an implicit time integration scheme is employed.
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Khan Z., Ahmed M.: Stress-induced martensitic transformation in metastable austenitic stainless steels: effect on fatigue crack growth rate. J. Mater. Eng. Perform. 5(2), 201–208 (1996)
Stolarz J., Baffie N., Magnin T.: Fatigue short crack behaviour in metastable austenitic stainless steels with different grain sizes. Mater. Sci. Eng. A 319–321, 521–526 (2001)
Nebel T., Eifler D.: Cyclic deformation behaviour of austenitic steels at ambient and elevated temperatures. Sadhana 28, 187–208 (2003)
Roth, I., Krupp, U., Kübbeler, J.C.H.M., Fritzen, C.P.: Deformation induced martensite formation in metastable austenitic steel during in situ fatigue loading in a scanning electron microscope. ESOMAT 06030 (2009). doi:10.1051/esomat/200906030
Skorupski R., Smaga M., Eifler D., Schmitt R., Müller R.: Influence of morphology of deformation induced \({\alpha}\)-martensite on stress-strain response in a two phase austeniticmartensitic-steel. Key Eng. Mater. 592–593, 582–585 (2014)
Francfort G., Marigo J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids. J. Mech. Phys. Solids 46, 131942 (1998)
Bourdin, B.: Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound. 9, 411430 (2007). doi:10.4171/IFB/171
Bourdin B., Francfort G., Marigo J.J.: The variational approach to fracture. J. Elast. 91, 5–148 (2008)
Kuhn C., Müller R.: A continuum phase field model for fracture. Eng. Fract. Mech. 77, 3625–3634 (2010)
Chen L.Q., Wang Y., Khachaturyan A.G.: Kintetics of tweed and twin formation during an ordering transition in a substitutional solid solution. Philos. Mag. Lett. 65, 15–23 (1992)
Wang Y., Khachaturyan A.G.: Three-dimensional field model and computer modeling of martensitic transformations. Acta Mater. 2, 759–773 (1997)
Artemev A., Wang Y., Khachaturyan A.G.: Three-dimensional phase field model and simulation of martensitic transformation in multilayer systems under applied stresses. Acta Mater. 48, 2503–2518 (2000)
Jin Y.M., Artemev A., Khachaturyan A.G.: Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of \({{\zeta_{2}^{'}}}\)-martensite in aucd alloys. Acta Mater. 49, 2309–2320 (2001)
Levitas V.I., Lee D.W., Preston D.L.: Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int. J. Plast. 26, 395–422 (2009)
Yamanaka A., Takaki T., Tomita Y.: Elastoplastic phase-field simulation of self- and plastic accommodations in cubic \({\rightarrow}\) tetragonal martensitic transformation. Mater. Sci. Eng. A 491, 378–384 (2008)
Kundin A., Raabe D., Emmerich H.: A phase-field model for incoherent martensitic transformations including plastic accomodation process in the austenite. J. Mech. Phys. Solids 59, 2082–2102 (2011)
Hildebrand F., Miehe C.: Variational phase field modeling of laminate deformation microstructure in finite gradient crystal plasticity. Proc. Appl. Math. Mech. 12, 37–40 (2012)
Gao, L.T., Feng, X.Q., Gao, H.: A phase field method for simulating morphological evolution of vesicles in electric fields. J. Comput. Phys. 228, 41624181 (2009)
Suiker, A.J.S., Turteltaub, S.: Crystalline damage development during martensitic transformations. In: ECOMAS CFD (2006)
Garion C., Skoczen B.: Combined model of strain-induced phase transformation and orthotropic damage in ductile materials at cryogenic temperatures. Int. J. Damage Mech. 12, 331–356 (2003)
Xu B.X., Schrade D., Gross D., Mueller R.: Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable. Int. J. Fract. 166, 163–172 (2010)
Schmitt R., Müller R., Kuhn C., Urbassek H.M.: A phase field approach for multivariant martensitic transformations of stable and metastable phases. Arch. Appl. Mech. 83, 849–859 (2013)
Schmitt R., Wang B., Urbassek H.M., Müller R.: Modeling of martensitic transformations in pure iron by a phase field approach using information from atomistic simulation. Technische Mechanik 33, 119–130 (2013)
Amor H., Marigo J.J., Maurini C.: Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J. Mech. Phys. Solids 57, 1209–1229 (2009)
Kuhn C., Müller R.: Phase field simulation of thermomechanical fracture. Proc. Appl. Math. Mech. 9, 191–192 (2009)
Kuhn C., Schlüter A., Müller R.: A phase field approach for dynamic fracture. Proc. Appl. Math. Mech. 13, 87–88 (2013)
Hofacker M., Miehe C.: Continuum phase field modeling of dynamic fracture: variational principles and staggered fe implementation. Int. J. Fract. 178, 113–129 (2012)
Schrade D., Xu B.X., Müller R., Gross D.: On phase field modeling of ferroelectrics: parameter identification and verification. SMASIS 1, 299–306 (2008)
Schrade D., Mueller R., Xu B., Gross D.: Domain evolution in ferroelectric materials: a continuum phase field model and finite element implementation. Comput. Methods Appl. Mech. Eng. 196, 4365–4374 (2007)
Du Q., Liu C., Wang X.: A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 198, 450468 (2004)
Wechsler, M.S., Lieberman, D.S., Read, T.A.: On the theory of the formation of martensite. J. Metals. Nov. 1503–1515 (1953)
Schmitt R., Kuhn C., Müller R., Bhattacharya K.: Crystal plasticity and martensitic transformations—a phase field approach. Technische Mechanik 34, 23–28 (2014)
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Schmitt, R., Kuhn, C., Skorupski, R. et al. A combined phase field approach for martensitic transformations and damage. Arch Appl Mech 85, 1459–1468 (2015). https://doi.org/10.1007/s00419-014-0945-8
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DOI: https://doi.org/10.1007/s00419-014-0945-8