Radiation effects on creep rupture and fatigue strength of pure aluminum

Paper describes an experimental investigation on the effect of nuclear radiation on the creep rupture and fatigue strength of pure aluminum for the ratios of alternating stress to mean stress ranging from zero to infinity. It was found that not only was the strength of the material tested affected by radiation over a range of ratios of stresses, but also the brittle-ductile transition was influenced.Based upon the experimental results obtained, an analytical model was developed to correlate creep rupture, fatigue strength and radiation effect for various ratios of stresses. This information may prove to be valuable in dealing with the stress analysis of nuclear reactors.Paper was presented at 1966 SESA Annual Meeting held in Pittsburgh, Pa., on November 6–9.     

Interaction of a growing crack with the boundary in a bicrystal

Dynamic photoelasticity has been used in conjunction with selective etching on lithium fluoride bicrystals to examine the interaction of a growing crack with inclined boundaries; it is found that the stresses at the head of the crack alter as the boundary is approached. The speed of the crack is related to the angle of incidence on the boundary and the angular disorientation of the latter. The change in crack speed is related to the change in state of stress at the vertex. Analytical and experimental distributions are presented for the stresses ahead of a growing crack.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 138–143, July–August, 1973.     

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

This paper describes the effect of thermal exposure (high-temperature exposure) (T = 675?C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675?C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress–strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.     

Direct measurement of static yield properties of cohesive suspensions

A technique of yield stress investigation based upon the combined use of two devices (an applied stress rheometer and an instrument for measuring the propagation velocity of small amplitude, torsional shear waves) is described. Investigations into the low shear rate rheological properties of illitic suspensions are reported for shear rates, typically, in the range 10^–4— 10^–1 s^–1 under applied stresses in the range 0.01 — 10 Nm^–2 and involving shear strains between 10^–1 and 10^–4. Results are presented which demonstrate that the technique does not invoke the excessive structural disruption of material associated with applied shear rate based methods (direct and otherwise) and the widely encountered problem of wall slip at the surface of rotational measuring devices is avoided using miniature vane geometries. Results are compared with those obtained using smooth-walled cyclindrical measuring devices in both applied stress and applied shear rate instruments.Yield measurements are considered in relation to the structural properties of the undisturbed material state and shear moduli obtained by studying the propagation of small amplitude (10^–5 rad), high frequency (~ 300 Hz) torsional shear waves through the test materials are reported. Experimental techniques and instrument modifications to permit these measurements are described.     

Boundary element approach to creep deformation of edge notched and cracked specimens

A direct formulation of the boundary element method using a complex variable numerical approach is presented for the time-dependent inelastic stresses in edge notched and cracked creeping metallic structural components subject to high temperature gradients. Particular attention is focused on the numerical evaluation of energy rate contour integrals in single edge cracked specimens in tension. The constitutive models used in the numerical calculation are internal state variable creep–plasticity or elastic power law creep model. Numerical results are compared with solution obtained from other methods for different loading rates.     

Investigations into cyclic creep of materials (review)

Conclusions In this review, we analyzed the studies known to the author on cyclic creep of structural materials published since 1936. Some of the studies could not be examined but references to these studies and a brief analysis of the results can be found in [3, 54–56, 115]. The classification of these studies and interpretation of the results presented by the author and also the terminology used do not pretend to be unambiguous and universal. Slghtly different approaches to solving this problem were proposed in, for example, [7, 55, 66].It is important to continue investigations in the cyclic creep area in the following directions:generalization of the unidimensional models of cyclic creep for the multiaxial stress states;experimental examination and construction of the theory of cyclic creep for nonstationary loading conditions;examination of the development of cyclic creep in heterogeneous and anisotropic materials;development of the method of calculating the stress-strain state and endurance of structural members in the creep conditions in cyclic loading.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev, Translated from Prikladnaya Mekhanika, Vol. 23, No. 12, pp. 3–19, December, 1987.     

The Stress State of a Rectangular Piezoceramic Plate with Transverse–Longitudinal Polarization

Longitudinal mechanical stresses in the exciting and generating sections of a planar piezoelectric transverse–longitudinal transformer are analyzed. It is shown that the longitudinal stresses in both sections are axisymmetric about the boundary line. The results obtained in experimental studies of the stress state in the exciting section by using piezotransformer transducers are presented     

Vibrocreep of metals in uniaxial and complex stress states

The results of the creep tests with extension and torsion of tubular specimens made of D16AT and AD1 aluminum alloys, which were earlier obtained at the Institute of Mechanics, Lomonosov State University, were analyzed theoretically. Experimental data obtained with the author’s participation imply that a sharp increase in creep rate is observed under certain conditions when a vibration stress of small amplitude is added to the static stress. This effect (vibrocreep effect) is manifested only if the form of the stress state under the common action of static and dynamic stresses differs from the form of the static stress state. In this case, as the duration of the applied vibration stress increases, the vibrocreep effect gradually weakens. In this paper, we propose a model for describing the obtained experimental data containing the kinetic parameter; this parameter is nonzero only in the case of a complex stress state in the tubular specimens. As a positive measure of this parameter, we use the angle of rotation of the maximum principal stress vector when small vibrations are added to the basic stress state. The obtained experimental and theoretical creep curves are in a good agreement for different types of the stress states.     

A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ_o/J=18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of K, gives a fair estimate of the crack opening stress near the crack front at a distance of order 10⁻² in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

The creep deformation of vibrating structures

In a recent paper [1] it was shown that the evaluation of certain bounding solutions for a structure subjected to cyclic loading was equivalent to assuming that the cycle time Δt was short compared with a stress redistribution time. Comparisons between values which are likely to occur in creep design situations indicated that Δt may often be assumed to be small and the bounding solution may be expected to closely approximate the actual stress history. In this paper the solution for the limiting case when Δt → 0 is evaluated for a class of constitutive relationships which may be expressed in terms of a finite number of state variables. Strain-hardening viscous, visco-elastic and Bailey-Orowan equations are discussed and particular solutions for which the residual stresses remain constant in time are derived. The solution for a non-linear visco-elastic model indicates that, for the stationary cyclic state, the constitutive equation need only predict the creep strain over a discrete number of cycles and need not predict the strains during a cycle. This observation should considerably simplify creep analysis.The solution of a simple example demonstrates the similarity between the predicting of the various constitutive relationships for isothermal problems. In fact they provide virtually identical solutions when expressed in terms of reference stress histories. The finite element solution of a plate containing a hole and subjected to variable edge loading is also presented for a viscous material. The solutions show behaviour which is similar to that of the two bar structure.     

Modeling deformation behavior of polymers with viscoplasticity theory based on overstress

The nonlinear strain rate sensitivity, multiple creep and recovery behavior of polyphenylene oxide (PPO), which were explored through strain rate-controlled experiments at ambient temperature by Khan [The deformation behavior of solid polymers and modeling with the viscoplasticity theory based overstress, Ph.D. Thesis, Rensselaer Polytechnic Institute, New York], are modeled using the modified viscoplasticity theory based on overstress (VBO). In addition, VBO used by Krempl and Ho [An overstress model for solid polymer deformation behavior applied to Nylon 66, ASTM STP 1357, 2000, p. 118] and the classical VBO are used to demonstrate the improved modeling capabilities of VBO for solid polymer deformation. The unified model (VBO) has two tensor valued state variables, the equilibrium and kinematic stresses and two scalar valued states variables, drag and isotropic stresses. The simulations include monotonic loading and unloading at various strain rates, multiple creep and recovery at zero stress. Since creep behavior has been found to be profoundly influenced by the level of the stress, the tests are performed at different stresses above and below the yield point. Numerical results are compared to experimental data. It is shown that nonlinear rate sensitivity, nonlinear unloading, creep and recovery at zero stress can be reproduced using the modified viscoplasticity theory based on overstress.     

Deformation of lead disks under impact

The effect of relatively low-velocity (1–3 m/sec) impact on a thin disk of imcompressible viscoplastic material placed in the gap between parallel rough surfaces is considered. The state of stress of the interlayer is assumed nearly hydrostatic during impact, the duration of which is limited by the elastic deformation of the elements of the striker system. The mathematical problem of determining the distributions of stresses, velocities, and temperatures for the axisymmetric deformation of a disk is reduced to the integration of an ordinary second-order differential equation. Numerical calculations for certain cases of impact are compared with the results of experiments on lead samples. Plane strain of an interlayer of viscoplastic material between rigid plates moving with a constant velocity is discussed in [1]. The state of stress of the interlayer for the same conditions of motion of the plates was studied in [2] for axial symmetry. In the present paper we take account of the impact nature of the loading and the elastic compression of the elements of the striker system, factors on which the deformation and the pressure developed in the impact depend.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 153–158, September–October, 1975.     

On rupture attributable to creep

The results of creep rupture tests carried out in a plane-stressed state are presented; the experiments confirm the validity of an earlier energy approach as regards the time to rupture under creep conditions [1],Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 140–143, November–December, 1973.     

Theory of creep of initially strain-hardening isotropic materials

Conclusions We analyzed the status of the problem of developing governing equations of isotropic creep within the framework of a mechanical equation of state. The feasibility of using equations of the hereditary type to describe the third stage of creep was evaluated.We also constructed a creep theory based on a refinement of the principle of the similarity of isochronic curves. This can be regarded as an attempt to generalize the concepts of mechanical equation of state and nonlinear heredity. The theory makes it possible to consider the initial strain-hardening of the medium, evaluate the third stage of creep, and take into account the history and cyclicity of loading.It was shown that nonsteady creep develops in media which exhibit linear strain-hardening, while the development of all three stages of creep is possible in media characterized by exponential strain-hardening. It was discovered that there is a sudden increase in the rate of nonsteady creep under constant stress. The creep of certain structural materials under steady, stepped, and cyclic loading was calculated and satisfactory agreement was obtained with experimental results.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 2, pp. 90–100, February, 1989.     

Solution of a contact problem for a prestressed layer and punch

Conclusions On the basis of the analysis of the analytical solution and of the numerical computations, we can draw the following conclusions.the initial stresses in the layer affect significantly the distribution law of the contact stresses and displacements in the layer and in the cylinder (Figs. 1–5). This influence is noted in the cylinder for the sections <1 (Figs. 1, 2) and in the domain of the contact of the punch and the layer (Figs. 3–5).The initial stresses affect in an essential manner the character of the distribution of u₃, and depend on the quantity .For h>15, for the determination of the stress-strain state in the punch and in the layer, with a sufficient accuracy for engineering applications, one can use the solution for the semispace. Thus in this paper one obtains the analytic and graphical dependences, reflecting the influence of the initial stresses on the stress-strain state of the elastic punchlayer system with initial stresses. This influence is essential (Fig. 1–5) for both compressible and incompressible bodies and has to be taken into account at the calculations of machine components and constructions.Hmelnickii Institute of Light Industrial Technology, Translated from Prikladnaya Mekhanika, Vol. 23, No. 3, pp. 14–22, March 1987.     

An application of a damage constitutive model to concrete at high temperature and prediction of spalling

A characteristic feature of concrete under uniaxial compression is the development of cracks parallel to the loading direction. A damage constitutive model proposed by Ortiz [Ortiz, M., 1985. A constitutive theory for the inelastic behaviour of concrete. Mech. Mater. 4, 67–93] can predict the transverse tensile stress responsible for these cracks by considering the interaction between the aggregate and the mortar and the development of damage in the latter. When concrete is exposed to high temperature, as is the case during fire, the failure mode is thermal spalling. In order to improve the prediction of the stresses involved in this failure Ortiz’s model is extended to account for the effects of high temperature. Published experimental results for uniaxial and biaxial compression at high temperatures are used to calibrate the temperature dependence of some of the material properties. The transient creep strain is accounted for by modifying the constrained thermal strain. The stress analysis is coupled with hygro-thermal analysis of heat, mass transfer and pore pressure build-up. The effect of pore pressure on the damage evolution is modeled by applying a body force in the stress analysis module proportional to the pressure gradient. A numerical example of concrete under fire is solved and the computed results are discussed. Spalling is predicted when the damage variable reaches its maximum value of unity. The predicted depth and time of spalling for a range of variation of permeability and initial liquid water content are presented. They are in good agreement with published experimental results.     

Long-term strength of metals in complex stress state (a survey)

An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ _e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ _e on the principal stresses. Statistical methods are used to obtain an expression for σ _e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ _e by using additional material constants are considered.     

Modification of critical state models by Mohr–Coulomb criterion

In order to combine the Mohr–Coulomb criterion and the critical state models for soils, a transformed stress tensor based on the Mohr–Coulomb criterion is proposed. The new stress tensor is determined by a transformation that makes the Mohr–Coulomb criterion become a cone having an axis as the space diagonal in transformed principal stress space, and is applied to the Cam-clay and Sekiguchi–Ohta models, which are two typical isotropic and anisotropic hardening critical state models for soils, for improving modelling capability of describing soil behaviour in general stresses. The revised models give more accurately predicted results than the original ones.