Internal Stress Components Research Articles

An anomalous cyclic stress evolution in reduced activation ferritic/martensitic steel

An anomalous cyclic stress response characterized by decrease in cyclic stress with increase in strain amplitude is observed in 9Cr–1W reduced activation ferritic/martensitic steel, during low cycle fatigue deformation at 823 K. It is suggested that differences in reduction of internal and effective stress components delineate the nature of cyclic stress response.

The Symmetry-Conforming Theory of Martensite Aging

The Landau theory has been developed for the description of martensite aging. The characteristic features of the theory are: i) the multicomponent non-scalar character of the order parameter describing the slow reconfiguration of lattice defects after martensitic transformation (MT); ii) the complete agreement with Symmetry-Conforming Short-Range-Order principle formulated by X. Ren and K. Otsuka; iii) the applicability to the different MT-s and various defects related to aging phenomena. The physical values interpreted as the components of internal stress, which stabilizes certain variant of martensitic phase, have been composed of the components of slow non-scalar order parameter. An applicability of the developed theory to the description of influence of aging on the MT temperature and yield stress was demonstrated.

Contributions to Internal Stress from Free Dislocations and from Substructure Boundaries in Dislocation Structure Formed in High Temperature Creep

The relation of the internal stress and the parameters of the heterogeneous dislocation structure was suggested in the form of the classical Taylor formula relating the internal stress to the total dislocation density stored in the subgrain interior and in the subgrain boundaries. The other formula combines linearly the stress contribution generated by network dislocations and the stress contribution of the subgrain structure semiempirically related to the subgrain size. The formulas can evaluate the ratio of internal stress components due to sub-boundaries and free dislocations.

Internal Stress Development during Fatigue Cycling of High-Strength Al/SiC Metal Matrix Composites

In this paper, results are presented of the development of internal stresses in 2124 aluminium alloy reinforced with 25% of particulate silicon carbide. Measurements have been made during in situ low-cycle fatigue loading of this composite, using neutron diffraction. The neutron measurements were made using the ENGIN-X diffractometer at the ISIS neutron facility, UK. The results show how the internal stresses evolve with fatigue cycling. Eshelby-based modelling has been used to allow separation of the internal stress components in the MMC.

Analysis of the hysteresis loop in stainless steels I. Austenitic and ferritic steels

In constant amplitude cyclic straining the hysteresis loops of an austenitic and a ferritic steel were recorded and their shape was analysed. The generalised statistical theory of the hysteresis loop based on the Masing hypothesis that considers the effective stress and the distribution of the critical internal stresses of the elementary volumes was employed. The second derivative of the hysteresis half-loop yields information on the effective stress and the probability density function of the critical internal stresses and its evolution in cyclic straining and in dependence on the strain amplitude. The changes of the effective modulus are also reported. The total cyclic stress can be separated into the effective and internal stress components. The high effective stress in ferritic steel is connected with the difficult motion of screw dislocations in the b.c.c. structure. The evolution of the probability density function of the austenitic and ferritic steels during cyclic straining is discussed in terms of changes of the internal dislocation arrangement.

Superposition of external and internal stress components in γ/γ'-microstructures and their effect on γ-channel dislocations

Glide and climb forces on γ-channel dislocations in γ/γ-microstructures are calculated considering a soimplified scenario involving discrete dislocations. The influence of (i) misfit stresses, (ii) volume fraction of γ'-particles, (iii) the density of channel dislocations and (iv) the external stress is considered. In the approach taken in this study we superimpose misfit stresses from thermo-elastic FEM-calculations with applied stresses and with stresses caused by discrete channel dislocations. The calculations are based on previous mechanical and microstructural results where a number of dislocation reactions were observed using TEM and identified as relevant microstructural elements of the overall mechanism of high temperature and low stress creep. Preliminary results show that in a realistic microstructural scenario there is limit to the number of dislocations which can enter a γ-channel by glide (in the absence of recovery processes). This number depends on γ'-volume fraction and on γ/γ'-misfit. Moreover it was found that glide and climb forces depend on the position of the dislocation segment in the channel and that ther is a general tendency to push dislocations out of the channels.

Application of multi-level multi-integration to contact problems Part 1: Non-Hertzian contact in rolling bearings

This paper describes in detail a computer program for the analysis of non-Hertzian contact in rolling bearings using multi-level multi-integration (MLMI), by which any object, i.e. the surface displacement and/or the internal stress component for a given contact pressure distribution, can be obtained in extremely reduced computing time compared with the conventional technique. This paper is composed of three parts: the determination of the values of MLMI parameters so as to make the program adjustable for the wide range of aspect ratios of the mesh rectangle; the development of the numerical procedure solving the contact problem to ensure stable and fast convergence; the application to the contact problems in rolling bearings. By the developed program, the contact analysis can be performed on a personal computer within a few minutes, even if the total number of grid points is more than ten thousand.

State of residual stress induced by cyclic rolling contact loading

The accumulation of plastic microdeformation during cyclic stressing under rolling contact loading conditions results in a complex state of residual stress in the subsurface volume of deep groove ball bearing inner rings. The three-dimensional state of residual stress was analysed experimentally for the first time, employing a combination of methods based on X-ray diffraction. The residual stress field exhibited components of internal stress which were maximal close to the depth at which stresses induced by the external load were at a maximum. From this position the values of the principal components of residual stress decreased with steep gradients towards the surface and to a larger depth. Compressive residual stresses existed in the circumferential and axial directions while in the surface normal direction a tensile residual stress was present. The trends observed by the diffraction analysis were in qualitative agreement with measurements of ring distortion performed upon sectioning.

State of residual stress induced by cyclic rolling contact loading

The accumulation of plastic microdeformation during cyclic stressing under rolling contact loading conditions results in a complex state of residual stress in the subsurface volume of deep groove ball bearing inner rings. The three-dimensional state of residual stress was analysed experimentally for the first time, employing a combination of methods based on X-ray diffraction. The residual stress field exhibited components of internal stress which were maximal close to the depth at which stresses induced by the external load were at a maximum. From this position the values of the principal components of residual stress decreased with steep gradients towards the surface and to a larger depth. Compressive residual stresses existed in the circumferential and axial directions while in the surface normal direction a tensile residual stress was present. The trends observed by the diffraction analysis were in qualitative agreement with measurements of ring distortion performed upon sectioning.

Spiral grain—An adaptation of trees to withstand stem breakage caused by wind-induced torsion

Expressions are derived for the internal mechanical stress components in trees when exposed to bending and torsion by wind forces. The crown is modeled as rectangular, and the stem taper so that the maximum bending stress is equal at all heights. Trees with asymmetric crowns will undergo torsion as well as bending, and the shear stresses associated with torsion are determined and compared to the bending stresses. The results show that shear failure is likely to occur relatively high up on the stem when the crown asymmetry is a few decimeters. The fact that torsion might be critical to the strength of trees towards wind forces, introduces an explanation to spiral grain growth. It is shown that spiral grain in the direction of the wind-induced torque improves the bending strength of the tree. Spiral grain is therefore beneficial for trees with a prevailing external torque.

Effective and internal stresses in cyclic straining of 316 stainless steel

The hysteresis loop of a 316 austenitic stainless steel was recorded and analysed in order to separate the contributions of the effective and internal stresses. The difficulties of application of the Kuhlmann-Wilsdorf-Laird method are discussed and a new method based on the statistical approach to analysis of the hysteresis loop (SAP method) is proposed. In contrast to the Kuhlmann-Wilsdorf-Laird method, this method allows evaluation of the effective elastic moduli and the effective stresses in tension and in compression without ambiguity. The SAP method was applied to cyclic loading of 316 austenitic stainless steel and the effective elastic moduli and effective and internal stress components of the cyclic stress in cyclic loading and their dependence on the number of cycles and on the applied strain amplitude was studied. The effective elastic moduli decrease appreciably with the strain amplitude. The effective stress represents an important fraction of the total stress (approximately 30%) and for most of the life it is constant. The hardening-softening curves and the cyclic stress-strain curve are determined mostly by the internal stress.

Effective and recovery stresses in deformation studies of polyvinyl chloride and polypropylene using the modified strain transient dip test

Partitioning the applied stress into internal stress components (effective and recovery) using the modified strain transient dip test is a useful approach towards a better understanding of the viscoelastic nature of polymers. The internal stresses of polyvinyl chloride (PVC) and polypropylene (PP) were measured successfully using this test on a computer-controlled electro-servo hydraulic tensile testing machine which was designed for rapid step unloading in less than 1 s to avoid memory effects of the polymers. A power-law relationship can be used to describe the variation of the internal stress components with strain. Actual yield strains occurred at smaller values (less than 2%) than those obtained from a conventional stressstrain diagram (which for PVC and PP exceed 3.5% and 7%, respectively). This observation indicated that plastic yielding occurred much earlier and yield strains from conventional stress-strain diagrams may be overestimates. For very ductile material (PP) the activation volumes were comparable in magnitude to that obtained conventionally; whilst for less ductile material (PVC), the activation volume was four times higher. One of the main advantages of stress partitioning is for the detailed definition of the extrapolated yield point which otherwise will be missed out in a conventional plot of applied stress and strain.

A rigid body model and decoupled control architecture for two manipulators holding a complex object

A rigid body dynamical model and control architecture are developed for the closed-chain motion of two manipulators holding an object containing a spherical joint in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the internal stress and strain component of the generalized contract forces. The problem of solving the model for the unknown variables is discussed. A control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the position- and internal stress force-controlled degrees of freedom during motion of the system. The purposed composite controller enables the designer to develop independent, noninteracting control laws for the position- and internal stress force-control of the closed-chain system. Finally, the modeling and control framework is applied to the case of an object containing a revolute joint.

Internal stress and unloading experiments in creep

Internal stresses are developed during deformation and have an important role in determining the mechanical properties and, in particular, the creep properties of crystalline materials. The strain transient dip test is the generally accepted method for the determination of internal stresses developed during creep. The strain transient dip test has been analysed using a number of very general creep models and it is concluded that, for glide-controlled creep, the dip test can only be interpreted if the relation between dislocation velocity and the force on the dislocation is linear. When this is the case it measures not an average internal stress but an average back stress for all the dislocations, mobile and immobile, where the back stress is the resolved component of the internal stress plus the glide component of the line tension force divided by the Burgers vector. The dip test does not allow separation of the back stress into internal stress and line tension components. For recovery models the results of the dip test cannot be simply interpreted because expressions for the creep rate do not define a unique average internal stress or back stress. However, for the recovery model in which strain occurs by athermal or jerky glide there will be a reverse yield stress, i.e. there will be a stress reduction below which there will be “instantaneous” reverse strain followed by reverse creep. By averaging the instability condition for all the dislocations participating in jerky glide it is shown, subject to assumptions, that the sum of the average internal stress experienced by dislocations involved in both forward and reverse creep can be obtained from the reverse yield stress. Separate values for these internal stresses cannot be obtained, however. Determination of the reverse yield stress for recovery creep is the experiment equivalent to the strain transient dip test for glide-controlled creep.

The Bauschinger effect in cyclically deformed niobium single crystals

The Bauschinger effect has been studied in niobium single crystals cyclically deformed to saturation at small strain amplitudes and at different temperatures. The parameters used to characterize the Bauschinger effect have been measured from the saturation hysteresis loops. The fatigued work-hardened crystals have been modelled as a composite consisting of a hard deformable phase (the regions of high dislocation density) embedded in a soft matrix (the regions of low dislocation density). The values of the mean internal stress in the matrix predicted by this simple composite model are in good agreement with those measured experimentally, using a modification of the method originally proposed by Cottrell to separate the lattice friction and internal stress components in reverse deformation.

Time-dependent deformation resistance in unoriented polypropylene

A modified form of the “dip test” which includes a long-term stress relaxation was used to examine the plastic deformation of unoriented polypropylene in the pre-yield region of the tensile stress-strain curve. The results show that the deformation behaviour is consistent with a previously proposed model of a plastically inhomogeneous solid. Such a model predicts that the flow stress may be partitioned into two components and the analysis of the results shows that this is reasonable. A similar model was successfully used to describe deformation in high density polyethylene, but the time dependence of the internal stress component is different from that of polypropylene.

The dynamics of cyclic plastic deformation and fatigue life of low carbon steel at low temperatures

The cyclic plastic stress-strain response and fatigue life of a low carbon steel at low temperatures was studied. The cyclic hardening/softening curves and cyclic stress-strain curves at different temperatures were measured. Two components contributing to the cyclic flow stress were resolved, i.e., the internal stress and the effective stress. The effective stress component was found to be strongly dependent on the temperature and independent of the strain amplitude. The internal stress component was found to be dependent on the plastic strain amplitude and nearly independent of temperature. An analytical form of the cyclic stress-strain curve suitable for the analysis of the temperature and strain rate dependence of the cyclic plastic stress-strain response is proposed. The Manson-Coffin curves were found to be independent of temperature down to 113 K. A tendency to lowering the fatigue life was observed at the lowest temperature and highest strain amplitude only, and was connected with the appearance of brittle fracture, originated from short fatigue cracks.

The role of internal and effective stresses in the plastic flow of iron single crystals

The orientation and temperature dependence of the strain-rate sensitivity of the shear stress in iron single crystals were investigated at temperatures between 295° and 77°K. The results show that the shear stress-shear strain curves can be analyzed by separating the shear stress into internal and effective stress components. At all temperatures and for all orientations, work-hardening is associated with an increasing internal stress. The rapid increase in flow stress with decreasing temperature is a consequence of an increasing effective stress in agreement with implications derived from a thermally activated deformation mechanism. The only exception to this behavior was at 250°K where the work hardening is considerably different from that at 295°K. At 250°K the initial work-hardening rate is associated with both an increasing effective stress and an increasing internal stress.

Stress relaxation, internal stress and work hardening in LiF and NaCl crystals

Stress relaxation is used as an indirect method for determining the velocity-stress exponent for dislocation motion in LiF and NaCl. With the knowledge of this exponent, the applied stress can be separated into its effective stress and internal stress components. The variation of these components with strain is examined and it indicates that work hardening in these crystals is largely due to the development of internal stresses.

The application of strain-rate cycling data to thermally activated deformation

The validity of using strain-rate cycling data to describe low temperature deformation in the b.c.c. alkali metal potassium, was examined using the suggestion by Li (5) that thermally activated deformation should obey the third law of thermodynamics, i.e. ΔS† = 0 at 0°K. In particular, the relations developed by Michalak (3) to separate the applied stress into its effective stress and internal stress components were demonstrated to be completely consistent with the above analysis. By the use of these relations, work hardening in polycrystalline potassium was examined and found to be strongly temperature dependent. At very low temperatures the predominant hardening mechanism appeared to be due to a decreasing mobile dislocation density with strain, leading to an increasing effective stress. At high temperatures, the internal stresses developed by the deformation built up rapidly and for strains in excess of about 5%, they provided the major contribution to the flow stress.