O. Vöhringer

THE ONSET OF TWINNING IN METALS: A CONSTITUTIVE DESCRIPTION

A constitutive approach is developed that predicts the critical stress for twinning as a function of external (temperature, strain rate) and internal (grain size, stacking-fault energy) parameters. Plastic defor- mation by slip and twinning are considered as competitive mechanisms. The twinning stress is equated to the slip stress based on the plastic flow by thermally assisted movement of dislocations over obstacles, which leads to successful prediction of the slip-twinning transition. The model is applied to body centered cubic, face centered cubic, and hexagonal metals and alloys: Fe, Cu, brasses, and Ti, respectively. A constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism. Employing an Eshelby-type analysis, the critical size of twin nucleus and twinning stress are correlated to the twin-boundary energy, which is directly related to the stacking-fault energy (SFE) for FCC metals. The effects of grain size and SFE are examined and the results indicate that the grain-scale pile-ups are not the source of the stress concentrations giving rise to twinning in FCC metals. The constitutive description of the slip-twinning transition are incorporated into the Weertman-Ashby deformation mechanism maps, thereby enabling the introduction of a twinning domain. This is illustrated for titanium with a grain size of 100 µm.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Constitutive description of dynamic deformation: physically-based mechanisms

The response of metals to high-strain-rate deformation is successfully described by physically-based mechanisms which incorporate dislocation dynamics, twinning, displacive (martensitic) phase transformations, grain-size, stacking fault, and solution hardening effects. Several constitutive equations for slip have emerged, the most notable being the Zerilli–Armstrong and MTS. They are based on Becker’s and Seeger’s concepts of dislocations overcoming obstacles through thermal activation. This approach is illustrated for tantalum and it is shown that this highly ductile metal can exhibit shear localization under low temperature and high-strain-rate deformation, as predicted from the Zerilli–Armstrong equation. A constitutive equation is also developed for deformation twinning. The temperature and strain-rate sensitivity for twinning are lower than for slip; on the other hand, its Hall–Petch slope is higher. Thus, the strain rate affects the dominating deformation mechanisms in a significant manner, which can be quantitatively described. Through this constitutive equation it is possible to define a twinning domain in the Weertman– Ashby plot; this is illustrated for titanium. A constitutive description developed earlier and incorporating the grain-size dependence of yield stress is summarized and its extension to the nanocrystalline range is implemented. Computational simulations enable the prediction of work hardening as a function of grain size; the response of polycrystals is successfully modeled for the 50 nm–100 m range. The results of shock compression experiments at pulse durations of 3–10 ns (this is two–three orders less than gas-gun experiments) are presented. They prove that the defect structure is generated at the shock front; the substructures observed are similar to the ones at much larger durations. A mechanism for dislocation generation is presented, providing a constitutive description of plastic deformation. The dislocation densities are calculated which are in agreement with observations. The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle–Grady relationship.

Residual stress relaxation in an AISI 4140 steel due to quasistatic and cyclic loading at higher temperatures

Abstract Residual stresses can be relaxed by supplying sufficiently high amounts of thermal and/or mechanical energy, which converts the residual elastic strains to microplastic strains. In order to better understand this relaxation behavior, shot peening induced residual stresses in normalized condition and in quenched and tempered condition of the steel AISI 4140 (German grade 42 CrMo 4) were investigated in annealing experiments, quasistatic loading experiments and bending fatigue experiments at 25, 250 and 400°C. The residual stress relaxation during alternating bending occurs in different regimes. First, thermal relaxation reduces the residual stresses during specimen heating. The relaxation during the first cycle can be discussed on the basis of the effects due to quasistatic loading, if the inhomogeneous distribution of the loading stress is taken into account. Differences in the behavior after the two heat treatments result from the Bauschinger-effect and effects of dynamic strain ageing. Owing to cyclic creep effects, the interval between the first cycle (N=1) and the number of cycles to crack initiation Ni is characterized by residual stresses which decrease linearly with the logarithm of N. Finally for N>Ni the reduction of residual stresses with the logarithm of N is stronger than linear.

Residual stress measurements by means of neutron diffraction

Abstract A new method for the analysis of multiaxial residual stressstates is presented, which is based on high resolution neutron diffraction. It is analogous to X-ray stress analysis, but the use of neutrons instead of X-rays allows tha analysis of the stress distributions also in the interior of technical components in a non-destructive way. To prove the feasibility of the method, investigations of the loading stress distributions of an aluminium bar subjected to purely elastic bending were performed. Limiting factors due to the volume of the internal probe region and the neutron residual stress analyses were carried out for a plastically deformed bending bar and a transformation-free water-quenched steel cylinder. The results are in fairly good agreement with theoretical expectations and with X-ray control measurements at the surface of the objects.

Effects of warm peening on fatigue life and relaxation behaviour of residual stresses in AISI 4140 steel

A new device has been built which allows shot peening in an air blast machine at elevated temperatures. The effects of conventional shot peening and peening at elevated temperatures on the characteristics of regions close to the surface, on the stability of residual stresses and half widths of X-ray interference lines and on the fatigue strength are presented for a quenched and tempered AISI 4140 steel (German grade 42CrMo4). The alternating bending strength is increased by warm peening compared with conventional shot peening. Additional investigations of samples conventionally peened and then annealed confirm that these effects are due to the stability of the dislocation structure, which is highly affected by strain ageing effects. This causes an additional benefit owing to higher stability of the residual stresses induced.

Depth profiles of macro residual stresses in thin shot peened steel plates determined by X-ray and neutron diffraction

Abstract The aim of the present work is to clarify, whether the near surface residual stresses induced by surface treatments like shot peening are balanced by low-level tensile residual stresses all over the core of the specimen or by relatively high tensile residual stresses in a thin layer adjacent to the surface layer. Therefore X-ray and neutron diffraction analyses were performed and evaluated.

Behaviour of an EB-PVD thermal barrier coating system under thermal–mechanical fatigue loading

Abstract Thermal–mechanical fatigue (TMF) tests were carried out on specimens made of alloy NiCr22Co12Mo9 which were coated with a LPPS CoNiCrAlY bond-coat (BC) and an electron beam-physical vapour deposition zirconia thermal barrier coating (TBC). The TMF tests simulate the thermally induced loadings at the outer surface of TBC-coated cooled gas turbine blades. In the present paper the cyclic deformation behaviour of the samples is analyzed and a quantitative evaluation of the degradation of the TBC system in two heat treatment states under TMF loadings is given. Segmentation cracks within the TBC as well as fatigue cracks in the BC and in the substrate were observed. Both types of cracks occur predominantly perpendicular to the loading direction. The main reason for this degradation of the TBC system are tensile stresses which are formed at low temperatures (

Classification of microstructural changes in laser hardened steel surfaces

Three different steels with C contents of ∼0.2 wt.% and different contents of chromium, molybdenum and vanadium were similarly laser hardened after different preceding heat treatments. The laser-affected zones beneath the surface were characterised by microhardness, dislocation density, carbide type, size and distribution as well as grain size of the austenite. By a systematic study of the changes in microstructure of these laser-affected zones, the effective hardening mechanisms were separated and their influence on the material strength or the microhardness was classified.

Influence of alloying elements on the strain rate and temperature dependence of the flow stress of steels

After a short introduction to the theoretical background of thermally activated glide of dislocations, a constitutive model is presented, which describes the temperature and strain-rate dependence of the flow stress. The properties of this constitutive equation were estimated for several plain carbon steels in normalized conditions, for quenched and tempered low-alloy steels, as well as for some high-strength low-alloy (HSLA) steels based on the temperature dependence and strain-rate sensitivity of the flow stress at temperatures 81 K≤T≤398 K and strain rates 5 · 10−5 s−1≤ε≤1 · 10−2 s−1. The constitutive equation enables the extrapolation of flow-stress data to higher strain rates (ε≲10+4 s−1), which are in good agreement with the results obtained from high strain-rate deformation tests. The influence of solute-alloying elements on the thermal stress, the activation enthalpy, and the constitutive parameters will be discussed.

X-ray diffraction at constant penetration depth – a viable approach for characterizing steep residual stress gradients

The experimental analysis of near-surface residual stresses by X-ray diffraction methods is based on measuring the spacings of lattice planes while the inclination ψ with respect to the surface plane is changed stepwise. A characteristic feature of conventional techniques is that the penetration depth of the X-rays is altered as inclination is varied. By simultaneously varying three different goniometer angles in a particular fashion, both the penetration depth and the measuring direction can be held constant while ψ is varied. Thus the normal and shear stresses can be derived from the sin2ψ plots by means of standard evaluation procedures developed for gradient-free stress states. The depth profile of residual stress is then obtained via Laplace transformation of the results from several stress measurements carried out at different penetration depths. In the present paper, the feasibility of this experimental approach for characterizing the strongly graded, non-equiaxed stress state existing at a machined surface is demonstrated. The results from constant-penetration-depth measurements on the ground surface of an engineering ceramic are compared with those from conventional sin2ψ measurements.