Long-range Internal Stresses Research Articles

Internal stresses induced by tensile deformation of a co-based metallic glass

Deformation-induced internal stresses in metallic glasses (MG) is one of the most important questions in the problem of adequate plastic flow description of these materials. Internal stresses arising at deformation define a strong worsening of MG soft magnetic properties after cold working. TEM-investigations of partially crystallized MG show long-range interaction of crystallites with shear band switch indicates the presence of long-range internal stress fields connected with shear bands. An analogous conclusion was drawn from the analysis of domain structure in deformed ferromagnetic MG. Deformation-induced internal stresses are particularly manifested in the anomalous stress relaxation, in the Bauschinger effect and in the strain recovery of predeformed samples. The present paper is devoted to determination of effective internal stresses arising at tension of a Co-based MG and to investigation of their temperature dependence.

Dislocation Motion in λ Tial Studied by in situ Straining Experiments in the Hvem

AbstractMicro-tensile specimens of coarse-grained Ti52at%Al crystals have been deformed in situ in a high voltage electron microscope at room temperature. In addition to some twinning, “simple” 1/2〈110] dislocations as well as superdislocations were moving, with the simple dislocations prevailing even if their orientation factor is lower than that of the superdislocations. Both types of dislocations are pinned, probably by small precipitates having a distance along the dislocations of about 100 nm. The precipitates consist most probably of Al2O3. Under stress, the dislocations bow out between the obstacles. The bowing is stronger for 1/2〈110] dislocations. An effective stress of about 41 MPa is estimated from their curvature. The kinematic behaviour of the dislocations is in accord with precipitation hardening. The dislocations are generated by the double-cross slip mechanism. Their density within the slip bands corresponds to a long-range internal stress of about 40 MPa. These data are consistent with the flow stress of PST crystals in the easy orientation, taken from the literature.

Low cycle fatigue behavior of an α + β titanium alloy: Ti6246

The present study focused on the cyclic behavior of an α + β titanium alloy, Ti6246. Low cycle fatigue tests were carried out between 20°C and 500°C under plastic strain control. The experimental results show that the 6246 alloy exhibits cyclic softening irrespective of the imposed temperature of strain. Nevertheless, careful analysis of the stress-strain hysteresis loops revealed that the physical origins and the underlying physical mechanisms of the softening are strongly temperature dependent. At room temperature, the softening appears to proceed from a decrease in the kinematic component of stress: it is governed by the gradual homogenization of the initially heterogeneous distribution of dislocations (localized slip bands) in the α phase in relation to the long-range internal stress field. In contrast, at high temperatures, the second phase shearing process due to the homogeneously distributed dislocations, and the occurrence of cross-slip, lower the isotropic contribution and lead to the observed cyclic softening. The mechanical results and the microstructural observations are therefore fairly consistent with one another.

Local variations of lattice parameter and long-range internal stresses during cyclic deformation of polycrystalline copper

X-ray line profiles and line positions were measured on single grains of cyclically deformed polycrystalline copper specimens unloaded from characteristic points of the stress-strain hysteresis loop. A high-resolution double crystal diffractometer was used to obtain local lattice parameter changes, from which long-range internal stresses and mean stresses were evaluated. In the case of samples unloaded from the load-reversal points the asymmetry of the characteristically broadened X-ray line profiles indicated forward and backward internal stresses prevailing in the dislocation cell wals and cell interiors of the dislocation cell structure, respectively. The changes of the long-range internal stresses after unloading from different points of the stress-strain hysteresis loop can be explained in terms of the composite model. In addition, mean strains and stresses, varying from grain, could be determined from the shifts of the Bragg reflections. A detailed microstructure-based discussion of the elastic stored energy, evaluated from the analysis of the stress-strain hysteresis loop, is given.

Mean Stresses and Long-Range Internal Stresses in Cyclically Deformed Polycrystalline Copper Studied by High Resolution X-Ray Line Profile Analysis

Mean Stresses and Long-Range Internal Stresses in Cyclically Deformed Polycrystalline Copper Studied by High Resolution X-Ray Line Profile Analysis

A constitutive model for creep-plasticity interaction based on dislocation dynamics

A glide-plus-climb micromechanism of dislocation evolution with the formation of subgrains is proposed for modelling of the creep-plasticity interaction (CPI). The long-range internal stress can be divided into the resistance for dislocation climb in subgrain boundaries and that for dislocation glide within grains or subgrains. Their evolution equations are then derived based on dislocation dynamics. Furthermore, a unified constitutuve model for CPI is developed from Orowan's formula. Theoretical calculations on the basis of this model show a very good agreement between the model prediction and experimental results of benchmark tests for 2 1/4 Cr-1 Mo steel at 600°C.

Long-range internal stresses in steady-state subgrain structures

Long-range internal stresses in steady-state subgrain structures

Local lattice parameter measurements in cyclically deformed copper by convergent-beam electron diffraction

Convergent-beam electron diffraction was used to characterize local lattice distortions associated with a heterogeneous dislocation arrangement in cyclically deformed polycrystalline copper. The results indicated the presence of a distorted lattice within the interior of the dislocation cells formed during cyclic deformation. The lattice distortion exhibited a dependence on external deformation conditions. Local lattice parameters were evaluated using computer-simulated patterns based on a kinematical approximation. From these measurements local strains and stresses are estimated. The lattice distortions measured are interpreted in terms of a model predicting substantial long-range internal stresses arising from glide dislocations of opposite sign accumulated on either side of the dislocation cell walls at the interfaces between the walls and the cell interiors.

Dislocation distributions as seen by X-ray line profiles

Asymmetric X-ray line broadening is direct evidence for the existence of residual long-range internal stresses in plastically deformed metals containing heterogeneously distributed dislocations, especially dislocation cell structures. Asymmetric line profiles and concomitant long-range internal stresses were found after various types of deformation, such as tensile deformation, fatigue, compression and wire drawing over a wide range of strains from 2 × 10 −3 to 1.52. As a general result, it is found that the long-range internal stresses increase monotonically up to about 15% strain and level off into saturation at larger strains.

Effects of magnetic fields on the dislocation unlocking from paramagnetic centers in non-magnetic crystals

Displacements of dislocations as a result of exposing the specimens to a static magnetic field ( B=0.1−2 T) in the absence of mechanical loading in the temperature interval T=4.2−293 K were found and investigated for NaCl, CsI, LiF, Zn and Al single crystals. This effect is characterized by the following properties: the mean dislocation path l increases linearly with the time t of the magnetic treatment; the mean dislocation velocity ν is proportional to the square of the magnetic magnetic induction ( ν∝ B 2) and inversely proportional to the square root of the concentration of paramagnetic impurities ( ν∝1 √C ); the effect is temperature independent in the range T = 4.2–77 K and it grows only by 20%–30% with a further increase in T up to room temperature; l( t) and l( B) saturate at large values of t and B at a level corresponding to an average distance between “forest” dislocations; an abrupt decrease in the effect is found when the frequency ν of an alternating magnetic field exceeds some critical value ν c ∝ B 2 ( ν c ≈ 15 Hz at B = 0.3 T). The phenomenon is interpreted as a result of unlocking of dislocations from paramagnetic centers under the action of an external magnetic field and motion of dislocations in the long-range internal stress field.

An estimate of internal stress evolution in the primary creep based on the composite model of dislocation structure

Abstract The paper gives an estimate of the average internal stress which can be measured by the strain transient dip test technique in the heterogeneous dislocation structure consisting of cells or subgrains bounded by low-angle subboundaries. The structure is described by the two-component model of hard and soft regions and the process of creep is considered an iso-strain rate deformation process. An evolution of the internal stress is derived from the evolution of dislocation structure characteristics in the normal primary creep and is evaluated for alpha iron from experimental data which were published earlier by the present author ( Philos. Mag., 25 (1972) 865; 28 (1973) 891, 1099). As an illustration of local conditions, local stresses and local strain rates are evaluated. The results document a growth of the mean internal stress in creep and changes of local stresses in the hard and the soft region. The internal stress values are relatively low and do not approach the value found experimentally in the steady-state creep which reaches the value of long-range internal stress in the soft region. A suggested interpretation of this discrepancy is based on an assumption that the actual steady-state creep has not yet been reached in the region of constant creep rate.

About the internal stress measurements during sigmoidal transient creep in Cu-16at.%Al

It is well established that during steady power law creep, the main sources of long-range internal stress σ i are the cell wall dislocations. However, the physical source of σ i for sigmoidal transient creep is not so well established. From literature on the subject, the pioneer work due to Hasegawa, Karashima and Ikeuchi was taken for a deep analysis. According to our analysis the mobile dislocation must be taken into account in order to explain σ i during sigmoidal transient creep. An experimental technique for determining σ i during the primary stage of creep, based on previous ideas from Qian and Reed-Hill, is proposed.

Thermal activation model of endurance limit

A thermal activation model of the endurance limit is proposed in the present study. It can quantitatively explain the effects of temperature and frequency on the endurance limit of metals at or below room temperature. Theoretical analysis indicates that the endurance limit, σac, which is considered as a parameter characterizing the resistance of metals to cyclic microplastic deformation, has the same thermally activated nature as the plastic flow stress has and it can be resolved into two independent components: the long-range internal stress (the athermal component), μ(eapc), and the short-range effective stress (the thermal component), σa *(T, ep). The former is considered as a material constant insensitive to temperature and strain rate (or frequency). The latter, the temperature- and strain rate-dependent part of the endurance limit, is approximately identical with the effective stress component of plastic flow stress (or cyclic yielding stress). In light of the thermal activation model, the temperature and strain-rate dependence of monotonic and cyclic flow stresses in a low alloy steel (16Mn) and a precipitation-hardening aluminum alloy (LY12CZ) were experimentally investigated. The results indicate that the effective stress components of monotonic and cyclic flow stresses are identical, if the temperature and strain rate are held unchanged, and that both of them are approximately independent of the magnitude of plastic strain. On the basis of the thermal activation model, an expression predicting the endurance limit below room temperature is offered. The predicted values of the endurance limit agree with the test data of steels and aluminum alloys available in literature.

Inelastic torsion and strain recovery of metallic glasses

Heating-induced strain recovery of metallic glasses Ni 60Nb 40, Fe 81B 14Si 5 and Co 87Nb 5Zr 8 inelastically predeformed by torsion at various temperatures is investigated. It is determined that strain recovery measurements are a fine indicator of deformation mode. Inhomogeneous deformation results in formation of long-range internal stress fields and always leads to partial strain recovery on heating. Homogeneous deformation is accompanied by formation of local internal microstresses which are the reason of complete strain recovery. The transition from inhomogeneous to homogeneous deformation mode is determined mainly not by homologous testing temperature but by preliminary heat treatment.

Work-hardening behavior of mild steel under stress reversal at large strains

Abstract A physically based modeling and experimental investigation of the work-hardening behavior of AK-mild steel under stress reversal at large strains is presented. Internal variables describing the polarity of persistent dislocation structures, a “capacitor-like” behavior, and long-range internal stresses were introduced. By considering the evolution of dislocation substructures during reversed deformation, the model explains the strain-hardening stagnation, the type II recovery and the influence of the amount of prestress. The strain-hardening behavior at large strains (up to an amount of shear of 90%) has been investigated. A satisfactory quantitative agreement has been achieved between model predictions and experimental results.

Internal stresses and elastic energy in ferroelectric and ferroelastic ceramics: Calculations by the dislocation method

A method is proposed for calculating the internal stresses in ferroelectric and ferroelastic ceramics which is based on the modelling of the mechanical sources of stress by fictitious dislocations continuously distributed on the grain and twin boundaries. For tetragonal and orthorhombic ceramics with a lamellar twin structure, the dislocation models of representative grain boundaries are worked out. On this basis the elastic energy is calculated which is associated with highly inhomogeneous stress fields concentrated near the boundaries of twinned grains. The part of the energy of long-range internal stress fields, which depends on the twin structure, is also estimated with the aid of the dislocation method. The results obtained are used to calculate the equilibrium parameters of the lamellar twin structures in ferroelectric BaTiO3 ceramic and ferroelastic high-Tc superconducting YBa2Cu3O7-δ ceramic.

Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-oriented copper single crystals: The correction of an erratum

Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-oriented copper single crystals: The correction of an erratum

Temperature dependence of cyclic saturation in low amplitude fatigue of copper single crystals

Single slip oriented copper single crystals were cyclically saturated in tension-compression at constant amplitudes of plastic strain at a temperature of 77 K. The cyclic stress-strain curve for the crystals displays a plateau associated with persistent slip bands (PSBs), whose volume fraction increases when the plastic strain amplitude is increased. By comparison with the room-temperature behaviour it appears that although the plateau stress and the length of the plateau are highly sensitive to the temperature, their ratio is temperature-independent, unless secondary cyclic hardening intervenes to shorten the plateau. Existing models based on cross-slip of screw dislocations are consistent with this result. Electron microscopy revealed significant deviations from the regularity usually assumed for the structure of PSBs. The deviations allow the Eshelby model to account for the plateau stress as the sum of long-range internal stress carried by tilted PSB walls and the stresses required for dislocation bowing or passing.

Large-strain Bauschinger effects in fcc metals and alloys

We have performed Bauschinger experiments on a variety of fcc metals and alloys, after large amounts of prestrain, using torsion and a short thin-walled tube geometry. The materials we studied were 99.99 pct Al, OFE copper, 70:30 brass, Al-1 pct Mg, Al-2 pct Mg, Al-0.17 pct Fe-0.07 pct Si, Al-0.8 pct Mn, and two Al-Cu alloys (Al-2.6 pct Cu and Al-4 pct Cu) given different heat treatments. For the material systems other than the Al-Cu alloys, the stress reversal was after a prestrain in shear of ≈3.0. Two stress reversals were performed on the Al-Cu alloys. The first was at γ = 0.3 and the second at γ = 1.2. Thus, for the Al-Cu, the prestrain and the final increment of deformation were in the same direction. The Bauschinger yield stress in these experiments was characterized by a very large offset shear strain of 0.05. This definition of reverse yield minimizes the effects of heterogeneous deformation and long-range internal elastic stresses that arise mainly from second-phase particles. We attributed the effects we observed to “isotropic hardening” associated with the dislocation substructures that developed in the different materials. We found that the behavior of these materials could be divided into two categories: those which deform by planar slip and those that form a “cell” structure and are characterized as having wavy slip. When the deformation was wavy in nature, we attributed the observed Bauschinger effects to be a result of the untangling of the “cells” formed during the prestrain. Different morphologies of cells had different behaviors when the stress was reversed. The behavior of the planar slip alloys depended on whether or not the barriers to dislocation activity were rigid or shearable. The θ′ precipitates in the Al-Cu alloys and the twin boundaries in the 70:30 brass constituted rigid barriers to dislocation motion, and a very large Bauschinger effect was observed. The solid solution Al-Cu material and that containing Guinier-Preston (GP) zones and θ″ had almost no Bauschinger effect when the yield stress in reverse deformation was considered. After yield, these materials hardened very rapidly and the flow stress in the reverse direction exceeded that for the equivalent amount of monotonie deformation.

Asymmetric X-ray line broadening of plastically deformed crystals. II. Evaluation procedure and application to [001]-Cu crystals

In paper I [Groma, Ungár & Wilkens (1988). J. Appl. Cryst. 21, 47–53] a theory was developed to interpret the asymmetric X-ray line broadening of plastically deformed crystals. It was shown that the dislocation structure can be described by five distinct parameters, namely the dislocation density, the mean quadratic spatial fluctuation of the dislocation density, the effective outer cut-off radius, the dipole polarization and the spatial fluctuation of the dipole polarization of the dislocation structure. In this paper a procedure is developed to evaluate these parameters from the Fourier transform of the line profiles. The theory and this procedure are tested by applying it to the asymmetric line profiles of tensile-deformed Cu single crystals orientated for ideal multiple slip. The asymmetry of these profiles is assigned to the dipole polarization of the dislocation cell structure and is directly correlated to residual long-range internal stresses. It is shown that the data can be interpreted in terms of the quasi-composite model of the dislocation cell structure developed earlier for the same material.