PECULIARITIES OF IRREVERSIBLE STRAINING IN STEP-WISE LOADING, REVERSE AND INVERSE CREEP

The paper is concerned with the generalization of synthetic theory to the modeling of phenomena such as the Bauschinger negative effect,creep delay,reverse and inverse creep.Detailed calculations of pl...     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Stochastic model of nonisothermal creep and long-term strength of materials

A stochastic model of nonisothermal creep and long-term strength of metallic materials is proposed. Experimental data on the creep of the ZhS6KP alloy at temperatures equal to 900, 950, and 1000°C are stochastically analyzed. These experimental data are used to substantiate the hypotheses applied in constructing the model. The stochastic model is checked for adequacy to the experimental data on the creep of the ZhS6KP alloy under stationary and nonstationary loading conditions. It is shown that the calculated and experimental data are in satisfactory agreement.     

Applied creep theory for bodies with anisotropy due to plastic prestrain

Plastic strains in structures at the stages of manufacturing, testing, and approaching the operation regime cause anisotropic variations in the mechanical properties of materials, including creep strength. We consider the following special but practically important class of loading processes for originally isotropic materials: a simple active plastic strain is followed by a long-term steady-state loading within the elastic limits. To describe the second stage, we present the creep strain deviator in the form of an additive orthogonal decomposition in the directions of the repeated loading and the vector anisotropy. The coefficients in the decomposition are material functions of time, of the intensities of the preliminary and repeated loadings, and of the angle between the directions of these loadings. We obtain conditions on the material functions under which, at any given time instant, there is a one-to-one continuous correspondence between the stress and strain tensors for the model proposed and the boundary-value problem in the generalized statement has a unique solution; we also prove the convergence of the iteration method of elastic solutions used to find this unique solution. The model is identified according to the creep diagrams (under steady-state stresses of different values) determined for the material in the original state and after the plastic prestrain at an angle (zero, extended, and intermediate) to the direction of the repeated loading. We show that our results are in good agreement with the results available in the literature concerning experiments in this class of processes for stainless steel at high temperature. We propose an engineering version of the theory in which only the experimental data for uniaxial tension are used. We discuss the versions of the model for the cases in which the plastic preloading is cyclic (one-dimensional or circular) and the repeated loading is unsteady.     

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.     

Determining the parameters of the fractional exponential heredity kernels of linear viscoelastic materials

The parameters of the fractional exponential creep and relaxation kernels of linear viscoelastic materials are determined. Methods that approximate the kernel by using the Mittag-Leffler function, the Laplace-Carson transform, and direct approximation of the creep function by the original equation are analyzed. The parameters of fractional exponential kernels are determined for aramid fibers, parapolyamide fibers, glass-reinforced plastic, and polymer concrete. It is shown that the kernel parameters calculated through the direct approximation of the creep function provide the best agreement between theory and experiment. The methods are experimentally validated for constant-stress and variable-stress loading in the modes of additional loading and complete unloading Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 12–25, September 2008.     

Nonlinear creep and ductile creep rupture of perfectly elastoplastic rods under tension

The paper is concerned with the problem of predicting nonlinear creep strains and time to ductile rupture of prismatic rods under constant tension. The material of the rod is assumed isotropic, homogeneous, and perfectly plastic. The problem is solved using models that take into account the change in the geometry of the rod during creep, the finiteness of the creep strains, and the effect of the initial and actual elastic strains. The conditions whereby the characteristic dimension of the rod tends to infinity and the accumulated and real strains in the viscous flow are limited are used as a failure criterion. The calculated results are compared with experimental data for a number of steels and alloys to formulate the conditions for the ductile rupture and embrittlement of metallic materials under uniaxial creep __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 120–133, April 2008.     

Asymptotic behavior of creep curves in the Rabotnov nonlinear heredity theory under piecewise constant loadings and memory decay conditions

Some minimal prior constraints are imposed on the two material functions used in the Rabotnov nonlinear constitutive relation. The asymptotic dependence of creep curves on the characteristics of these material functions and on the parameters of loading programs is analytically studied in the case of stepped loadings. Some conditions are obtained for the case when these curves tend to the creep curve under instantaneous loading as t→∞. The importance of the limit value of the creep function derivative at infinity is analyzed for the plastic strain accumulation. A number of distinctions and additional possibilities are found compared to the linear integral relation of viscoelasticity.     

Experimental determination of the natural frequencies of complex-shaped shells

The natural frequencies of a complex-shaped thin elastic shell under loading of two types that cause nonstationary vibrations are experimentally determined. The strains in the shell are recorded with piezoelectric strain gages, followed by the Fourier analysis of the oscillograms     

Fundamental experiments in plasticity and creep of aluminum—Extension of previous results

Paper presents combined stress experiments in plasticity and creep of aluminum 1100-0. The purpose of these experiments was to determine the motion of the yield surface in tension-torsion space for three complicated prestressing paths, to investigate the validity of the normality hypothesis, to investigate the development of creep strains after prestressing, and finally to investigate the validity of the constant volume hypothesis.It is shown that the law of hardening proposed by the author previously [3,5,6] is valid, except possibly when the prestress path intersects the yield surface at a small angle. It is also shown that the normality hypothesis is valid. After prestressing the creep strain vector has in the beginning the same direction as the plastic strain vector but later its direction may change. Finally it is shown that at the level of permanent strains less than 1% the plastic strains follow the constant volume hypothesis but the creep strains do so only when they begin to appear.     

Constitutive relations describing creep deformation for multi-axial time-dependent stress states

A theory of primary and secondary creep deformation in metals is presented, which is based upon the concept of tensor internal state variables and the principles of continuum mechanics and thermodynamics. The theory is able to account for both multi-axial and time-dependent stress and strain states. The wellknown concepts of elastic, anelastic and plastic strains follow naturally from the theory. Homogeneous stress states are considered in detail and a simplified theory is derived by linearizing with respect to the internal state variables. It is demonstrated that the model can be developed in such a way that multi-axial constant-stress creep data can be presented as a single relationship between an equivalent stress and an equivalent strain. It is shown how the theory may be used to describe the multi-axial deformation of metals which are subjected to constant stress states. The multi-axial strain response to a general cyclic stress state is calculated. For uni-axial stress states, square-wave loading and a thermal fatigue stress cycle are analysed.     

Creep deformation at crack tips in elastic-viscoplastic solids

The evaluation of crack growth tests under creep conditions must be based on the stress analysis of a cracked body taking into account elastic, plastic and creep deformation. In addition to the well-known analysis of a cracked body creeping in secondary (steady-state) creep, the stress field at the tip of a stationary crack is calculated for primary (strain-hardening) or tertiary (strain-softening) creep of the whole specimen. For the special hardening creep-law considered, a path-independent integral C¹_h, can be defined which correlates the near-tip field to the applied load.It is also shown how, after sudden load application, creep strains develop in the initially elastic or, for a higher load level, plastic body. Characteristic times are derived to distinguish between short times when the creep-zones, in which creep strains are concentrated, are still small, and long times when the whole specimen creeps extensively in primary and finally in secondary and tertiary creep. Comparing the creep-zone sizes with the specimen dimensions or comparing the characteristic times with the test duration, one can decide which deformation mechanism prevails in the bulk of the specimen and which load parameter enters into the near-tip stress field and determines crack growth behavior. The governing load parameter is the stress intensity factor K₁ if the bulk of the specimen is predominantly elastic and it is the J-integral in a fully-plastic situation when large creep strains are still confined to a small zone. The C¹_h-integral applies if the bulk of the specimen deforms in primary or tertiary creep, and C¹ is the relevant load parameter for predominantly secondary creep of the whole specimen.     

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.     

Nonstationary oscillations of three-layer cylindrical shells under axisymmetric loading

The nonstationary behavior of three-layer cylindrical shells under an axisymmetric loading is considered with the application of hypotheses to each layer. Independent postulations are proposed for the approximation of displacements and transverse strains across the thickness of each layer. Reissner's variational principle for dynamic processes is used to derive the motion equations. The problem of the dynamic deformation of three-layer cylindrical shells under a nonstationary loading is considered in the case where the ends of the shells are rigidly fixed. The values obtained were compared with those predicted from hypotheses relating to the whole packet of the structure (the Timoshenko-type theory of multilayered shells). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 3–9, August, 1999.     

Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers

The inelastic deformation behaviors of metals and polymers are discussed with the aim of finding a common base that would simplify academic and engineering analyses. Only monotonic loading conditions at room temperature are considered. For loading at different rates, nonlinear relations between loading rate and stress level, creep stress level and creep strain, and relaxation rate and stress were common to both type of materials. There are, of course, significant differences in elastic properties, strength levels and the strains involved. Special properties such as relaxation behaviors and creep anomalies can be qualitatively and quantitatively reproduced by the state variable model VBO (viscoplasticity theory based on overstress). Since experimental investigations typically concentrate on one particular aspect of inelastic deformation behavior such as creep or strain-rate dependence, it is often difficult to gather a comprehensive data set for a given material. In spite of this, considerable similitude in the deformation behavior of metals and polymers in various test conditions has nevertheless been established.     

The Thermoviscoelastoplastic Axisymmetric Stress–Strain State of Laminated Flexible Orthotropic Shells

A technique is proposed to determine the thermoviscoelastoplastic axisymmetric stress–strain state of laminated shells made of isotropic and orthotropic materials. The paper deals with processes of shell loading such that both instantaneous elastoplastic and creep strains occur in isotropic materials and elastic and creep strains in orthotropic materials. The technique is developed within the framework of the Kirchhoff–Love hypotheses for a stack of layers with the use of the equations of the geometrically nonlinear theory of shells in a quadratic approximation. The deformation of isotropic materials is described by the equations of the theory of deformation along slightly curved trajectories, while the deformation of orthotropic materials is described by Hooke's law with additional terms allowing for creep. A numerical example is given     

Continuous, large strain, tension/compression testing of sheet material

Modeling sheet metal forming operations requires understanding of the plastic behavior of sheet alloys along non-proportional strain paths. Measurement of hardening under reversed uniaxial loading is of particular interest because of its simplicity of interpretation and its application to material elements drawn over a die radius. However, the compressive strain range attainable with conventional tests of this type is severely limited by buckling. A new method has been developed and optimized employing a simple device, a special specimen geometry, and corrections for friction and off-axis loading. Continuous strain reversal tests have been carried out to compressive strains greater than 0.20 following the guidelines provided for optimizing the test. The breadth of application of the technique has been demonstrated by preliminary tests to reveal the nature of the Bauschinger effect, room-temperature creep, and anelasticity after strain reversals in commercial sheet alloys.     

An experimental study of uniaxial creep,cyclic creep and relaxation of aisi type 304 stainless steel at room temperature

Following previous work (Krempl, 1979), a servocontrolled testing machine and strain measurement at the gage length were used to study the uniaxial rate(time)-dependent behavior of AISI Type 304 stainless steel at room temperature. The test results show that the creep strain accumulated in a given period of time depends strongly on the stress-rate preceding the creep test. In constant stress-rate zero-to-tension loading the creep strain accumulated in a fixed time-period at a given stress level is always higher during loading than during unloading. Continued cycling causes an exhaustion of creep ratchetting which depends on the stress-rate. Periods of creep and relaxation introduced during completely reversed plastic cycling show that the curved portions of the hysteresis loop exhibit most of the inelasticity. In the straight portions, creep and relaxation are small and there exists a region commencing after unloading where the behavior is similar to that at the origin for virgin materials. This region does not extend to zero stress.The results are at variance with creep theory and with viscoplasticity theories which assume that the yield surface expands with the stress. They support the theory of viscoplasticity based on total strain and overstress.     

Effect of creep prestrain on subsequent plastic deformation

The effect of creep prestrain on subsequent plastic deformation is experimentally investigated. The experiments are performed by subjecting thin-walled tubular specimens of stainless steel SUS 304 after creep prestraining to combined axial load and torsion at room temperature to 600°C. The stress-strain relations subsequent to creep prestrain are determined under combined stress state with and without temperature changes in prestraining and subsequent plastic straining. On the experimental results, the plastic hardening effects by creep prestrain are discussed under various temperature conditions. The subsequent stress-strain relations are compared with the calculated results on the equi-plastic strain surfaces.     

An analytical and computational study of crack initiation under transient creep conditions

An analytical method has been developed to predict creep crack initiation (CCI), based on the accumulation of a critical level of damage at a critical distance. The method accounts for the re-distribution of stress from the elastic or elastic–plastic field, experienced on initial loading, to a steady state creep stress distribution, via a transient creep region. The method has been applied to predict CCI times in a fracture specimen of type 316H stainless steel at 550 °C. The failure model has been also been implemented into a finite element (FE) framework. Reasonable and conservative predictions of CCI time can be obtained from the analytical solution relative to FE solutions. Conservative predictions of experimental CCI times are obtained when stress redistribution is taking into account. However, CCI times predicted from a steady state creep model are found to be non-conservative.