Plastic behavior of a nickel-based alloy under monotonic-tension and low-cycle-fatigue loading

The plastic behavior of an annealed HASTELLOY^® C-22HS™ alloy, a face-centered cubic (FCC), nickel-based superalloy, was examined by in-situ neutron-diffraction measurements at room temperature. Both monotonic-tension and low-cycle-fatigue experiments were conducted. Monotonic-tension straining and cyclic-loading deformation were studied as a function of stress. The plastic behavior during deformation is discussed in light of the relationship between the stress and dislocation-density evolution. The calculated dislocation-density evolution within the alloy reflects the strain hardening and cyclic hardening/softening. Experimentally determined lattice strains are compared to verify the hardening mechanism at selected stress levels for tension and cyclic loadings. Combined with calculations of the dislocation densities, the neutron-diffraction experiments provide direct information about the strain and cyclic hardening of the alloy.     

Quasi-static properties of a photoviscoelastic material

This paper describes the results of mechanical and optical measurements in plasticized polyvinyl chloride under conditions of creep and relaxation at room temperature. It covers one task of a broader investigation aimed at developing experimental methods for viscoelastic stress analysis. The moiré method of strain analysis was found well suited for continuous recording of axial and transversal deformation in creep tests. The material exhibits linear viscoelastic behavior, both mechanical and optical. Strain, stress and birefringence measured from creep and relaxation tests gave straightline plots on log-log scale and, thus simple empirical formulas were possible to derive. The theoretical prediction that birefringence in a linear viscoelastic material not exhibiting flow can be expressed as a linear relationship of stress and strain was satisfactorily substantiated.     

CREEP BEHAVIOR OF Zr-1.5Nb-0.4Sn-0.1Fe-0.1Cu ALLOY

Creep behavior of the Zr-1.5Nb-0.4Sn-0.1Fe-0.1Cu alloy sheet is investigated from 300℃ to 400℃ in the stress range from 50 MPa to 180 MPa along the rolling direction. The measured strain rates range from 8.8 × 10^-10 s^-1 to 4.7 × 10^-7 s^-1. The activation energies are estimated to assess the creep deformation mechanisms in this alloy. The strain rate is slightly different at low stress, while it shows a distinct difference at high stresses. Stress exponents of this alloy increase with increasing applied stress at all testing temperatures. It is concluded that the creep deformation of the Zr-1.5Nb-0.4Sn-0.1Fe-0. 1 Cu alloy is controlled by the diffusion creep at low stress region and by the climbing of dislocations at high stress region.     

Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal

Creep and stress relaxation are known to be interrelated in linearly viscoelastic materials by an exact analytical expression. In this article, analytical interrelations are derived for nonlinearly viscoelastic materials which obey a single integral nonlinear superposition constitutive equation. The kernel is not assumed to be separable as a product of strain and time dependent parts. Superposition is fully taken into account within the single integral formulation used. Specific formulations based on power law time dependence and truncated expansions are developed. These are appropriate for weak stress and strain dependence. The interrelated constitutive formulation is applied to ligaments, in which stiffness increases with strain, stress relaxation proceeds faster than creep, and rate of creep is a function of stress and rate of relaxation is a function of strain. An interrelation was also constructed for a commercial die-cast aluminum alloy currently used in small engine applications.     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Experimental investigation and modeling of non-monotonic creep behavior in polymers

The deformation behavior of two unfilled engineering thermoplastics, ultra high molecular weight polyethylene (UHMWPE) and polycarbonate (PC), has been investigated in creep test conditions. It has been found that a loading history (prior to the creep test) comprising of loading to a maximum stress or strain value followed by partial unloading to arrive at the target stress value can greatly modify the strain-time behavior. Under such a test protocol, while the expected increase in strain during creep (constant tensile load) is observed, at relatively low creep stresses specimens have also demonstrated a monotonic decrease in strain. In an intermediate stress range, specimens have demonstrated time dependent behavior comprising of a transition from decreasing to increasing strain during creep in tension. This paper presents experimental results to delineate these findings and explore the effect of prior strain rate on the qualitative and quantitative changes in the output (strain-time) behavior. Furthermore, modification of the viscoplasticity theory based on overstress (VBO) model into a double element configuration is introduced. These changes confer upon the model the ability to yield non-monotonic behavior in creep, and supporting simulation results have been included. These changes, therefore, allow the model to simulate strain rate sensitivity, creep, relaxation, and recovery behavior, but more importantly address the issue of non-monotonic changes in creep and relaxation when a loading history involves some degree of unloading.     

边坡预应力锚杆蠕变的数值分析

运用非线性蠕变分析理论模型,采用MSC.MARC软件重点研究了锚杆的应力指数、蠕变系数和几何参数的变化对于锚杆应力松弛的影响.通过对预应力锚杆支护的边坡进行数值分析,探讨了锚杆的蠕变规律以及锚杆预应力松弛现象.锚杆的参数取不同数值时,比较数值模拟结果发现:锚杆的轴力和剪力主要分布在锚固段的前端;随着锚杆应力指数及蠕变系数的增加,蠕变应变增大,应力松弛加快.     

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.     

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.     

A non-linear uniaxial integral constitutive equation incorporating rate effects,creep and relaxation

A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.     

Development of viscoplastic constitutive equation through biaxial material testing

Internal-state variables have been used to represent the deformation historyin the recently proposed viscoplastic constitutive equations. In the current study, creep tests under nonproportional loadings were used to study the relative roles played by the internal-state varaibles in the constitutive equation by tracing the strain trajectory in strain space for a given stress trajectory in stress space. An experimental approach to studying the evolution rule for the tensorial state variable is also proposed. The experimental results on 2618-T61 aluminum alloy suggest that the scalarstate variable should play a much more dominant role than the tensorial state varaible in the constitutive modeling of 2618-T61 aluminum alloy.     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

A non-equilibrium thermodynamic geometric structure for thermoviscoplasticity with maximum dissipation

A maximum dissipation principle induces a class of viscoplastic evolution equations within a non-linear, non-equilibrium thermodynamic structure which extends Gibbs thermostatics. The evolution of a relaxation process is determined through non-linear affinities, which generalize the linear Onsager construct, along with the maximum dissipation principle and the long term states. The relaxation modulus is the norm of the plastic strain rate. Forced processes, in which the control variables change with time, are assumed to be relaxation processes at each instant. This class of thermoviscoplastic models includes the three-dimensional Freed–Chaboche–Walker model in which the internal state variables are the back stress, the drag strength and the elastic yield strength for creep initiation.     

High temperature creep behaviour of an FeAl intermetallic strengthened by nanoscale oxide particles

The creep behaviour of an FeAl intermetallic strengthened by nanosized oxide particles has been examined at temperatures of 700–825 °C. For all temperatures the strain rate shows a power law dependence on the applied stress. At the lowest temperature and with the highest stresses there is evidence of a threshold stress produced by the difficulty of overcoming the particle barriers, while for higher temperatures as well as at low stresses there is no threshold stress and creep appears to be controlled by general climb. The fine oxide particles produce good strengthening at low temperatures but are more readily overcome at high temperatures due to their very small size and limited attractive relaxation force. Despite such fall in creep strength, this material remains one of the strongest iron aluminides to the temperature range evaluated.     

Remarks on properties of photoviscoelastic model materials

One of the basic problems of structural-model analysis, model photoelasticity and photoelastic coatings in the problem of mechanical and optical creep, relaxation and related phenomena. It is pointed out that, in spite of creep or relaxation, it is possible to achieve physical similarity between model and object if the model material behaves in a certain range as a linear viscoelastic material. Such a material is called a “momentarily linear material.” Several model materials behave in this way in a certain range of stress and time. Because of creep and relaxation, the common tensile tests are, in general, not quite adequate for evaluation of physical properties of plastics used for models. Also the bending test is not always adequate. It is shown how to obtain sufficiently accurate relations between stress, strain, birefringence and time, using tapered specimens. The problem of biaxial creep of model materials is discussed, and a simple method of evaluating the suitability of a given plastic as a model material is shown. Some conclusions concerning time-dependent factors are formulated, and some possible areas of investigation are shown.     

Anisotropic continuum damage modeling for single crystals at high temperatures

In single crystals, the process of creep damage is generally anisotropic. Indeed, the damage evolution does not only depend on the loading conditions, but also on the lattice orientation. And the current state of damage has an anisotropic influence on the effective stress state, so that it is represented by a tensorial damage variable. Based on the continuum damage mechanics theory, a creep damage model for F.C.C. single crystals has been developed and implemented in a three-dimensional anisotropic creep model. It is shown that the resulting material model is capable of describing the orientation dependence of the creep and damage evolution of nickel-based superalloys in the high temperature regime.     

Deformation and fracture behaviour under combined creep and fatigue

An examination of deformation and fracture has been made for the nickel base superalloy IN597 at 850°C for relatively high stress short life cyclic torsional loading programmes. The cycles combine low cycle fatigue with creep and relaxation dwell from the repeated application of a closed hysteresis loop under strain control. From a consideration of the changing shape of the hysteresis loop throughout cyclic life the effects of dwell stress, inelastic strain range and cycle number on creep deformation are examined together with the variation of peak stress softening with cycle number and relaxation time. Their effects on fracture in a high-temperature oxidising environment are appraised in relation to various predictive techniques; the Coffin-Manson equation, the universal slopes method, the linear damage rule, strain range partitioning and various incremental life prediction laws.Observations made on transgranular and intergranular crack paths are shown to provide the necessary metallographic evidence for the relative contributions to fracture from the repeated action of creep, fatigue and relaxation processes.     

Investigation of the linear flow regime of commercial polymers by numerical conversion of MVM creep measurements

A new experimental and numerical method has been developed to characterize the terminal flow behavior of polydisperse, commercial grade polymer melts over a wide dynamic range of time/frequency scales. Experimentally, an MVM rheometer specifically designed for long time scale (t 10⁴ s) creep measurements is used to measure the creep compliance of three commercial polymers: two high density polyethylenes and one polystyrene. The long time scale MVM creep data are complemented in the short time scale regime by creep data from an industrial plate-plate rheometer. The time-dependent creep data is combined and converted to a discrete retardation spectra using a nonlinear regularization algorithm to address the ill-posed nature of the interconversion. The retardation spectrum is analytically converted to dynamic moduli and compared with independently measured dynamic moduli. In the overlapping frequency region, calculations and measurements show excellent agreement and the combined data span a much larger dynamic range than either independent data set. The calculated and measured dynamic moduli data are combined and a retardation spectrum with a vastly expanded dynamic range is generated. Combining long time scale MVM creep compliance data and dynamic moduli data exploits the intrinsic sensitivities of controlled strain and controlled stress rheological experiments and is a powerful means to greatly expand the experimentally accessible dynamic range of time/frequency. This approach is particularly useful for commercial polymers with broad molecular weight distributions and commensurately large distributions of relaxation times.