T. Antretter

A new view on transformation induced plasticity (TRIP)

Abstract The phenomenon of transformation induced plasticity (TRIP) in steel is reinvestigated both experimentally and theoretically. The irreversible length change (TRIP strain) consists not only of a plastic contribution (“Greenwood–Johnson” effect) but also of a contribution due to the length change caused by the transformation shear component of the martensitic variants (orientation effect or “Magee” effect). This orientation effect, which is fully accepted for shape memory alloys, is explained for steels. Micromechanical investigations help to quantify the orientation effect. Finally a proposal for a modified constitutive law for elastic plastic phase changing materials is presented.

First-principles study of elastic and thermal properties of refractory carbides and nitrides

Abstract The elastic properties and thermal expansion of TiC, TiN, VC and VN are calculated by means of a precise first-principles electronic structure method. The single-crystal elastic constants are derived from the total energies of distorted structures. For the thermal expansion, the contribution of electronic states is determined within a free-electron model utilizing the density of states at the Fermi energy of the actual materials. The contribution of lattice vibrations to the thermal properties is modelled by Debyes approximation for phonon dispersion. Anharmonic effects are included via Gruneisens theory requiring the volume dependence of the Debye temperature. For the calculation of the Gruneisen parameter, volume- and pressure-dependent single-crystal elastic constants are needed. Since in reality refractory compounds always contain vacancies, the influence of vacancies is studied for vanadium carbides by a supercell of composition VC0.75. It is found that vacancies significantly increase the...

Mechanical properties of a Cr–Ni–Mo–Al–Ti maraging steel in the process of martensitic transformation

Abstract Mechanical properties of a Cr–Ni–Mo–Al–Ti maraging steel are studied experimentally in the process of martensitic transformation. The transformation-start and -finish temperatures are determined from the dilatometric curves under a tensile, compressive or shear hold stress. An anomalous temperature-dependence of the yield stress is investigated. By checking the closing of the dilatometric loop in a full heating–annealing–cooling thermal cycle under the applied hold stress, a back stress is confirmed to exist in both the axial and radial directions in the thin-walled tubular specimen, and its initial value is identified. The annealing condition is proved to have a marked effect on the initial value of the back stress. The back stress is shown to evolve in the progress of transformation. The evolution of the TRIP strain is evaluated under the hold stress in both the axial and shear direction. Especially when the hold stress is removed in the process of transformation, a backflow, due to the Magee effect, is observed.

Effect of back stress evolution due to martensitic transformation on iso-volume fraction lines in a Cr–Ni–Mo–Al–Ti maraging steel

Abstract The effect of the back stress evolution on the iso-martensite volume fraction lines (the iso- ξ lines) is experimentally investigated in a Cr–Ni–Mo–Al–Ti maraging steel in the process of martensitic transformation by identifying the iso- ξ lines inside the transformation zone bounded by the martensite-start and -finish lines. Each iso- ξ line is composed of a tensile-branch and a compressive-branch, which are parallel to the tensile- and compressive-branches of the martensite-start line, respectively. When the back stress evolves due to martensitic transformation, the iso- ξ line translates as a whole into the direction of the back stress evolution with its slope unchanged. The ordinate of the intersection point of both branches stands for the value of the back stress. The back stress evolution identified in the present tests well supplements the evolution response determined in a quite different way in the unloading tests described in [Mater. Sci. Eng. A (2002) in press].

Diffusional phase transformation and deformation in steels

Abstract During diffusional phase transformations at high temperatures (e.g. γ–α transformation in low-alloy steels) the interface migrates due to a chemical and/or mechanical driving force. A low solubility in the product phase forces the solute atoms (C in α) to move by diffusion, and, therefore, the mole fraction of the solute depends on time and spatial position. In order to evaluate the transformation kinetics numerically, carbon diffusion and interface migration, coupled by appropriate boundary conditions, are simulated. The grain size, the mobility, and the diffusion coefficient determine the growth kinetics. A micromechanical study has been performed in order to investigate the influence of an external uniaxially applied load on the transformation kinetics.

Back stress evolution and iso-volume fraction lines in a Cr–Ni–Mo–Al–Ti maraging steel in the process of martensitic transformation

Abstract The quantitative identification of the back stress evolution is carried out for a Cr–Ni–Mo–Al–Ti maraging steel in the process of martensitic transformation under thermomechanical loading conditions. The evolution depends on the direction of the applied stress: tensile, compressive or shear. The iso-volume fraction lines (the iso- ξ lines) are determined between the transformation-start and -finish lines on the applied stress–temperature plane. The iso- ξ lines are composed of a tensile-branch and a compressive-branch, each of which is parallel to the martensite-start line. The interaction point of the tensile- and compressive-branches of the iso- ξ line shifts to the direction of the back stress evolution. The almost hold stress-independent martensite-finish line, identified in a previous paper (Mater. Sci. Eng. A308 (2001) 25) is proved to be attributed to the back stress evolution.

Hierarchical models for simulating the mechanical behavior of heterogeneous materials: an approach to high speed tool steel

A hierarchical modeling strategy is presented which allows the computational simulation of the thermo-mechanical behavior of materials exhibiting different morphological characteristics at different length scales. As a typical example of such materials high speed tool steel is considered as some sort of in-situ metal matrix composite containing, at the micro level, carbidic inclusions in a martensitic steel matrix, and, at the meso level, clusters or stringers of inclusion rich areas. The macroscopic stiffness and strength behavior depends on the morphology at both levels which can be taken into account simultaneously by the proposed hierarchical concepts.

Simulation of the Damping of a Shape Memory Alloy Rod by Using the Likhachev Model

In this paper vibration damping of a shape memory alloy rod is studied. The mathematical model includes the heat conduction equation, the stress wave equation, a kinetic law and a constitutive law. As kinetic law the Likhachev model is used, which describes the one-way effect, pseudoelasticity properties and thermal loading cycles. It is observed that the vibration amplitude of the rod decreases in this model very quickly. Results are in good agreement with earlier investigations, where other kinetic laws have been used.

Measurement of all Six Components of X-Ray Elastic Factors

A method is presented by which all components of Fij(ϕ, ψ, hkl) belonging to the same measurement direction and reflection can be determined. The neutron measurements are to be done with a single specimen, shaped as a cuboctahedron. An apparatus for producing a compressive stress state in the specimen is needed. It must be small enough to fit into the neutron goniometer and to allow movement of the goniometer to all Eulerian angles. Using this set-up the tensors F(ϕ, ψ, hkl) can be measured for any ϕ, ψ and (hkl).

The thermo-mechanical response to a general loading path of a martensitically transforming steel

An extensive experimental program on a 9% Ni, 12% Cr, 2% Mo steel is introduced. This material transforms from the austenitic (γ) phase into the martensitic (α′) phase at a low temperature level around 150°C upon cooling on air only, thus making it especially suitable for testing purposes since it exhibits practically no creep effects during and after transformation (Fischer et al., 1996). Dilatometric tests are carried out for two types of specimens (longitudinal specimens (LSs) with a rolling texture and radial specimens (RSs)). Interestingly, the dilatation loops do not close after cooling down to room temperature. For an increasing annealing temperature the gap becomes smaller and closes for RSs. It turns out that the dilatometric loops close for preloaded specimens, pointing to an initial backstress in the material in the same order of magnitude as the load stress so it must not be neglected. Monitoring the martensite start (Ms ) and finish temperature (Mf ) for different loading conditions and stress levels reveals a strong influence of the type of loading (tension, shear, compression) on Ms . The overall yield stress as a function of temperature is noticeably disturbed immediately after transformation starts. As the temperature approaches Mf the composite effect in the α′-γ region prevails. Experiments including mixed, nonproportional loading paths for cooling as well as at constant temperature have been performed. The orientations of the martensitic variants account for the different deformation behavior for different loading types but equal global equivalent stresses (see also Fischer et al., 2000a). A comprehensive micromechanical modeling concept is presented based on the numerical implementation of a transformation condition (Fischer and Reisner, 1998) governing the variant selection into a finite element algorithm (see Reisner et al., 1998). Finally, the issue of an improved constitutive law for the TRIP strain rate has been tackled. A novel approach for an evolution law including the backstress has first been presented by Videau et al. (1996) and has later been refined by Fischer et al. (2000b).