Concept Of Internal Stress Research Articles

Elastoplastic Flexure of Round Steel Beams. 2. Residual Stress

Residual stress in metals may lead to shaping defects and the failure of metal structures in prolonged operation. It may arise on account of plastic metal flow on shaping (as in forging) or slow irreversible creep at elevated temperature, under the prolonged action of loads. In viscoelastic media, it may be due to ductile strain accumulating when a body is in a deformed state for a long time. Residual stress also affects the microstructure of metals and may be present within and around crystalline grains as residual microstress, sometimes known as latent elastic stress. Residual stress is also described as eigenstress, by analogy with the eigenfunctions introduced by mathematicians to denote functions corresponding to specific parameters (eigenvalues) in a differential equation with specified boundary conditions. The concept of internal stress has been proposed as a general term for stress created by the body itself. Residual stress is then confined to cases in which the internal stress is due to irreversible deformation. Besides the creation of a favorable residual stress system, local increase in strength will be noted in forged metal disks with pronounced strain hardening, as long as the Bauschinger effect does not cancel out such benefits. In the present work, extremal values of the residual stress in a straight cylindrical steel rod (beam) are studied, in the case of flexure.

Using the Internal Stress Concept to Assess the Importance of Moisture Sorption-induced Swelling on the Moisture Transport through the Glassy HPMC Films

The purpose of this research was to elucidate the significance of the changes in the mechanical and the volumetric properties on the moisture diffusivity through the polymer films. The internal stress concept was adapted and applied to estimate the relative impact of these property changes on the total stress experienced by a polymer film during storage. Hydroxypropyl Methylcellulose free films were used as a model material prepared at various conditions and stored at different relative humidities. The changes in the internal stress of these films due to the moisture sorption were studied. It was demonstrated that the stress-relaxation of the films increases at increasing moisture content. At the point when there is a definite loss of stress in the film, which is at moisture content higher than 6%, was shown to correlate with the significant increase of the moisture diffusivity. Further investigations revealed that the loss of stress is especially due to the swelling of the polymer rather than the changes in the inherent strain (the quotient between the tensile strength and the modulus of elasticity) of the HPMC films. This implies that the impact of the moisture sorption on the diffusivity is predominantly via volume addition rather than via altering the mechanical properties. Additionally, the approach presented here also brings up a new application of the internal stress concept, which in essence suggests the possibility to estimate the diffusion coefficient from the sorption isotherm and the mechanical analysis data.

Elasticity and anelasticity of microcrystalline aluminum samples having various deformation and thermal histories

The effect of the amplitude of vibrational deformation on the elastic modulus and internal friction of microcrystalline aluminum samples produced by equal-channel angular pressing was studied. The samples have various deformation and thermal histories. The elastic and inelastic (microplastic) properties of the samples are investigated. As the degree of plastic deformation increases, the Young’s modulus E, the amplitude-independent decrement δi, and the microplastic flow stress σ increase. As the annealing temperature increases, the quantities δi and σ decrease noticeably and the modulus E exhibits a more complex behavior. The experimental data are discussed under the assumption that the dislocation mobility depends on both the spectrum of point defects and the internal stresses, whose level is determined by the degree of plastic deformation and the temperature of subsequent annealing. The concept of internal stresses is also used to analyze the data on the effect of the degree of deformation and annealing on the rupture strength of the samples.

Deformation and life assessment of high temperature materials under creep fatigue loading

AbstractThe knowledge of mechanical long term behaviour under static and cyclic loading for high temperature components requires methodologies for life assessment in order to employ the full potential of materials. A phenomenological life time prediction concept which was developed for multi‐stage creep fatigue loading demonstrates the applicability of rules for synthesis of stress strain path and relaxation including an internal stress concept, as well as mean stress effects. Further, a creep fatigue interaction concept which was also developed covers a wide range of creep dominant loading as well as fatigue dominant loading.Service‐type experiments conducted at different strain rates and hold times for verification purposes demonstrate the acceptability of life prediction method for variation of conventional 1 %Cr‐steels as well as modern high chromium 9‐10 %Cr‐steels. Generally, the service life of components is influenced by multi‐axial behaviour. Multi‐axial experiments with e.g. notched specimens and with cruciform specimens accompanied by advanced methods for calculation of stress strain path and life time prediction stress conditions are of future interest.

Hardening of crystals caused by the dynamic aging of dislocations

A model relating the pronounced effect of mobile impurities on the processes of plastic deformation in crystals to the dynamic aging of dislocations is proposed. The model is based on the concept of internal stresses depending individually on the age of dislocations due to the difference in the impurity environment. The concentration dependence of the impurity contribution to the hardening of materials is calculated. The theory is illustrated by the experimental data for a GeSi solid solution.

Behaviour of heat resistant power plant steels undergoing variable long term loading conditions

High temperature components of power plants are in many cases subjected to variable loading conditions such as cyclic creep or strain cycling. Therefore the cyclic behaviour of important heat resistant steels has been investigated under stress control and to a smaller extent under strain control. The behaviour under cyclic creep rupture conditions was determined in long term experiments covering a wide range of loading conditions. This behaviour can be described with the modified life fraction rule and a factor concept of relative life for single stage cycles and additionally with a multistep hypothesis for multi-stage cycles. The description can be adapted to estimate the life consumption under service type random conditions. The strain cycling behaviour was investigated in regard to the conditions of the heated surface of large components. To simulate this type of loading and to generate long term creep fatigue data, a service type strain cycle was developed. Anisothermal and comparable isothermal cycles were carried out up to 8000 h and delivered similar results. Long term isothermal tests on a bainitic and a martensitic turbine rotor steel could economically be performed up to 70 000 h by means of package type tests combining short term strain cycling and long term creep cycling. Creep fatigue life under single stage and multi-stage conditions can be predicted on the basis of the generalized damage accumulation rule if an internal stress concept and preloading effects are considered. In the long term region governed by viscoelastic deformation, the creep fatigue behaviour can be approximated by the modified life fraction rule concept developed for cyclic creep. Cycle counter programs support the application of the life assessment concepts presented.

Model of Inelastic Response Using Neural Networks.

Inelastic material behavior is usually expressed in terms of constitutive equations. However, it is not easy to estimate parameters included in these equations from the experimental data. This paper describes a model using neural networks for the estimation of material transient responses. To overcome the difficulty for the neural networks to learn the material response curve, two neural networks are independently used to learn the two curves that can be decomposed from the original stress-strain curve based on the internal stress concept. Numerical examples show that the present neural network approach can map the stress-strain curve with good precision.

Recent progress in the modeling of high-temperature creep and its application to alloy development

Recent progress in the understanding of high-temperature creep of alloys is discussed in the context of theoretical modeling and its application to alloy development. Emphasis is placed upon those engineering alloys specifically designed for high-temperature applications, such as precipitation and dispersion-strengthened (DS) alloys and metal-matrix composites (MMCs). Currently, these theoretical models use one of two different approaches, (a) a phenomenological approach, which is used in such models as those based on the internal stress concept, and those based on empirical creep equations; and (b) micromechanical models that are based on dislocation mechanisms and the interactions of dislocations with solute atoms, second-phase particles, and other reinforcements such as fibers. All these theoretical models have a common goal, namely, the understanding of high-temperature strengthening mechanisms and the relationship between high-temperature strength and the micromechanical mechanisms during high-temperature plastic deformation of the alloys. These theoretical studies can provide information that is useful in alloy design and processing, such as the selection of alloy chemistry, and the optimization of phase microstructural features (e.g., reinforcement amount, shape, size, and distribution; matrix grain size; and matrix and reinforcement interfaces) by optimization of processing methods.

Choice of evolution equation for internal stress in creep

The internal stress values in the course of the primary and the steady-state stages of creep in a Fe3wt.%Si alloy were measured by a technique analogical to the strain transient dip test technique. Two types of evolution equation, i.e. phenomenological and derived from dislocation kinetics, were examined by correlating them with the experimental data. In the application of the second group of equations, characteristics of the real dislocation structure were taken into account. The results of structure investigations are discussed in relation to the concept of internal stress in both homogeneous and heterogeneous dislocation structures, in the latter case using the composite model of the dislocation structure.

Activation theory for creep of matrix resin and carbon fibre-reinforced polymer composite

Activation theory used in metals and polymers has been used to model creep of unidirectional composite and resin matrix, using the concept of internal stress. The model fits the experimental creep curves very well for a range of materials. The results obtained for a brittle epoxy and its carbon fibre-reinforced composite with two fibre orientations are reported. The model parameters, such as internal stress, activation volume and activation energy, have been measured experimentally and compared with model-fit values, and their influence on creep is discussed. Finally, an approach to predict the creep rupture of unidirectional composites using internal stress is presented.

The concept of internal stress in the creep of metals and single-phase alloys

The concept of internal stress in the creep of metals and single-phase alloys

Non-linear structural modeling for life predictions: Physical mechanisms and continuum theories

A review of several viscoplastic theories that incorporate isotropic hardening, directional hardening and additional effects due to non-proportional loading is presented. The equations reviewed are generalizations of the internal stress concept and use two internal state variables, namely the drag stress and the back stress variables. Theories that incorporate additional internal variables to model physical phenomena such as strain ageing have also been reviewed. Most of these constitutive equations employ isotropic evolutionary equations for the drag stress and nonlinear hardening rules for the back stress variable. The physical arguments to justify this procedure are given. The similarities between a wide number of formulations of flow and evolutionary equations, as well as the essential differences between them, are presented. Finally, it is shown how a careful examination of experimental behaviors, in conjunction with micromechanical considerations based on the physics of deformation, leads to the formulation of a more general unified framework.

Fatigue life prediction from the viewpoint of internal stress and effective stress

In this study applied stress is separated into two parts: internal stress and effective stress. The concept of internal stress is introduced and discussed, followed by a presentation of its measurement. Experimental results are shown and discussed from this point of view, and the usefulness of this concept is also examined. The main results are: fatigue damage is accumulated on a surface in the form of surface roughness of the material by alternate plastic strain; a material shows increasing ‘fatigue resistivity’ by stress cycling; and the increment of fatigue damage can be monitored in terms of effective stress, which reflects stress history. The fatigue mechanism is discussed on the basis of the behaviour of internal stress and effective stress, and a new cumulative damage model is proposed and discussed.

鋼の疲労における内部応力および有効応力

A new procedure is demonstrated to comprehend fatigue phenomena. The internal stress and the effective stress in a material are defined to analyze the fatigue process. The internal stress is attributed to the dislocation structure developed during fatigue. From this viewpoint, fatigue tests were carried out and some characteristics such as internal stress, effective stress and hysteresis loop were measured. The internal and effective stresses were measured by means of the strain dip test.The main results are as follows:(1) The internal stress increased with the progress of fatigue.(2) The effective stress obtained during fatigue under a maximum stress larger than the fatigue limit (over-stress) was larger than that under or below the fatigue limit (under-stress).(3) During fatigue under manifold multiple-repeated stress in two stress levels (over-stress and under-stress), both the effective stress and the plastic strain range measured at the under-stress increased by the over-stress loading.(4) The effective stress depended on plastic strain rate.From those results, the concept of internal stress is anticipated to contribute not only to the understanding of fatigue mechanism but also to the establishment of a cumulative damage rule.

過小応力のみによる疲れ破壊の考察 内部応力の観点から

The stress applied to a specimen does not fully act to deform material. The effective stress which actually acts on dislocations can be related to the internal stress of material. The origin of internal stress and thus effective stress has been discussed here by means of a dislocation model, concluding that internal stress depends on the dislocation structure. Based on this conclusion, fatigue tests were carried out and the following results were obtained:(1) The behavior of internal stress in the fatigue process showed a clear difference between the over-stressed and the under-stressed conditions.(2) The fatigue failure occurred under many-fold multiple repeated stress in two stress levels below the fatigue limit. Such fracture was attributed to the instability of internal stress.(3) The concept of internal stress and effective stress is useful to the comprehensive understanding of fatigue phenomenon.

Creep and Relaxation Behavior of lnconel-617

The static and dynamic creep behavior of Inconel alloy 617 has been determined in constant load creep tests, relaxation tests, and stress reduction tests in the temperature range 1023 to 1273 K. The results have been interpreted using the internal stress concept: The dependence of the internal stress on the applied stress and test temperature was determined. In a few experiments, the influence of cold deformation prior to the creep test on the magnitude of the internal stress was also investigated.It was found that the experimentally observed relaxation behavior could be more satisfactorily described using the Norton creep equation modified by incorporation of the internal stress than by the conventional Norton creep equation.

On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept

The description of monotonic and cyclic behavior of material is possible by generalizing the internal stress concept by means of a set of internal variables. In this paper the classical isotropic and kinematic hardening rules are briefly discussed, using present plastic strain tensor and cumulated plastic strain as hardening variables. Some additional internal variables are then proposed, giving rise to many possibilities. What is called the “nonlinear kinematic hardening” leads to a natural description of the nonlinear plastic behavior under cyclic loading, but is connected to other concepts such as the Mroz’s model, limited to only two surfaces, and similarities with other approaches are pointed out in the context of a generalization of this rule to viscoplasticity.

Rheological analysis of stress change experiments during high temperature creep

The main results of stress drop experiments during high temperature creep (i.e. the occurrence of zero and sometimes negative creep rates, the existence of two parts with different slopes in the curves of the incubation time Δtr versus the stress decrement Δσ, the zero or positive values of the stress variations in stress relaxation tests) are analysed from a rheological point of view. The basis of the proposed interpretation is the existence of a creep criterion, represented by a limit surface in the stress space, which explains through the usual plastic flow rules the occurrence of zero or negative creep rates. The work hardening splits into a translation (kinematic hardening) and a deformation of this limit surface. The recovery of kinematic hardening is slower than the recovery of deformation. On this basis, the concept of internal stress used either in the activated glide of dislocations or in the Bailey-Orowan relationship and the nature of negative creep rates are discussed.

Stress relaxation and mechanical equation of state in austenitic stainless steels

Stress relaxation experiments have been performed on types 304 and 316 stainless steel at room temperature. The stress-strain rate data show that these materials exhibit the behavior of mechanical equation of state. The experimental results are discussed using the concept of internal stress.

The concept of internal stress in the activated motion of dislocations

The concept of internal stress in the activated motion of dislocations