Comparison of isotropic hardening and kinematic hardening in thermoplasticity

Håkansson, Paul; Wallin, Mathias; Ristinmaa, Matti

doi:10.1016/j.ijplas.2004.07.002

Cited by 61 publications

(38 citation statements)

References 28 publications

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“…by Håkansson et al (2005). In order to increase the efficiency of the solution scheme, the number of equations in (66) can be reduced by taking into account the coaxiality between b e , l tr and τ , cf.…”

Section: Ir−1 Imentioning

confidence: 99%

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

Hallberg

Håkansson

Ristinmaa

2007

International Journal of Plasticity

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A constitutive model for diffusionless phase transitions in elastoplastic materials undergoing large deformations has been developed. The model is formulated with starting-point in basic thermodynamic relations and the phase transition is treated through an internal variable (i.e. the phase fractions) approach. The usual yield potential is used together with a transformation potential to describe the evolution of the new phase. A numerical implementation of the model is presented, complete with the derivation of a consistent algorithmic tangent moduli. Simulations based on the presented model are compared to experimental findings with good agreement. The proposed model offers a robust tool, suitable for large-scale simulations of phase transformations in austenitic steels undergoing extensive deformations. This is demonstrated in simulations of the necking of a bar under tensile loading and also in simulations of a cup deep-drawing process.

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Section: Ir−1 Imentioning

confidence: 99%

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

Hallberg

Håkansson

Ristinmaa

2007

International Journal of Plasticity

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“…[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], the problems regarding large thermal and elasto-plastic deformations were considered, appropriate measures to be applied for deformations, additivity of elastic and plastic deformations were established, and problems regarding actual and relative configurations were described. The topics of linear and nonlinear kinematic and isotropic hardening were analysed in papers [30,35,39]. In addition, problems regarding the stability and behaviour under thermomechanical and mechanical loading were analysed, see e.g.…”

Section: Zśloderbach (B)mentioning

confidence: 99%

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

Śloderbach

2016

Continuum Mech. Thermodyn.

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This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337-349, 351-367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.Keywords Bifurcation of the equilibrium state · Conditions and criteria of uniqueness · Boundary-value problem · Generalized coupled thermo-elasto-plasticity · Comparison bodies IntroductionThe incremental boundary-value problem of generalized coupled thermoplasticity is formulated in this paper. This is followed by an interpretation of the uniqueness conditions for the solution of that problem. The necessary and sufficient local uniqueness conditions are deduced together with the global sufficient uniqueness condition. A similar incremental boundary-value problem of coupled generalized thermoplasticity was investigated and discussed [1,3]. In this paper, necessary and sufficient local and global conditions of uniqueness of solution of an incremental boundary-value problem of coupled generalized thermoplasticity for the case of small displacements gradients (small strains) are derived. Uniqueness conditions for the generalized coupled thermoplasticity [1][2][3] and suitable comparison bodies [1][2][3][4][5][6][7] are identified for this purpose. The derived local and global uniqueness conditions are suitable necessary and sufficient conditions excluding occurrence of the bifurcation of equilibrium state in coupled generalized thermoplasticity and for suitable comparison bodies (also in isothermal loading processes).Early papers by Mróz [8,9] defined local conditions of uniqueness for solving an incremental boundary problem for the case of non-associated laws of plastic flow, for isothermal processes and small strains. A similar local condition was obtained by Hueckel and Maier in [10,11]. In their analysis, the stability of the material is defined by means of a condition which states that the half of the product of the stress rate tensor needs to be a positive value. The reported study was confined to the case of the isothermal theory of plasticity (with Communicated by Andreas Öchsner. Z.Śloderbach (B)Faculty of Applications of Chemistry and Mechani...

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“…The final task is to identify R on the basis of experimental data. Taking account of experimental evidence and following Håkansson et al (2005) and Ristinmaa et al (2007) for example, it can first be noted that with use of (4) and (11) the heat equation (5) can be written as…”

Section: Stored Energy Of Cold Workmentioning

confidence: 99%

“…Numerous authors have conducted both experimental and theoretical studies regarding this phenomenon, e.g. Chrysochoos et al (1989); Mason et al (1994); Kapoor and NematNasser (1998); Hodowany et al (2000); Rosakis et al (2000); Håkansson et al (2005); Ristinmaa et al (2007). In particular, the earlier comprehensive review work by Bever et al (1973) in which experimental methods and results regarding the stored energy of cold work are discussed should be mentioned.…”

Section: Introductionmentioning

confidence: 99%

Model Describing Material-Dependent Deformation Behavior in High-Velocity Metal Forming Processes

2009

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A constitutive model for rate dependent and thermomechanically coupled plasticity at finite strains is presented. The plasticity model is based on J 2 plasticity and rate dependent behavior is included by use of a Perzyna-type formulation. Adiabatic heating effects are handled in a consistent way and not, as is a common assumption, through a constant conversion of the internal work rate into rate of heating. The conversion factor is instead derived from thermodynamic considerations. The stored energy is assumed to be a function of a single internal variable which differs from the effective plastic strain. This allows a thermodynamically consistent formulation to be obtained which, as shown, can be calibrated by use of simple procedures. Choosing 100Cr6 steel in two differently heat treated conditions as prototype material, experimental tests are performed enabling the model to be calibrated. Significant differences in deformation behavior are noted as the differently heat treated specimens are compared. In addition, the local stress-updating procedure is reduced to a single scalar equation, permitting a very efficient numerical implementation of the model. The constitutive formulation proposed was employed in an explicit finite element solver, illustrative simulations of a high velocity metal forming process being performed to demonstrate the capabilities of the model and certain characteristic traits of the

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Comparison of isotropic hardening and kinematic hardening in thermoplasticity

Cited by 61 publications

References 28 publications

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

Model Describing Material-Dependent Deformation Behavior in High-Velocity Metal Forming Processes

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