Steady State Creep Stress Research Articles

Characterization of cyclic dynamic and creep responses of pure aluminum by instrumented indentation

<p indent="0mm">Dynamic behavior under cyclic loading conditions and creep behavior under quasi-static loading conditions were investigated by instrumented indentation of pure aluminum to reveal the influence of loading conditions (e.g., load, loading rate, and holding time) on indentation responses. The results of cyclic indentation show that, with the increase in the holding time, load, and loading rate of the pre-cyclic loading segment, the effect of creep on the subsequent cyclic indentation can be weakened, and the measured mechanical properties (e.g., contact depth, indentation hardness, and elastic modulus) can reach constant levels more rapidly with the increase in cycle number. The results of the creep tests show that the elastic modulus and indentation hardness decrease with the increase in holding time, the steady-state creep stress exponent obtained by instrumented indentation is independent of load, and a long holding time is not suggested for the creep tests. Indentation hardness and steady-state creep resistance measured within the inner grains are higher than those measured near the grain boundary regions.

Secondary Creep Analysis of FG Rotating Cylinder with Exponential, Linear and Quadratic Volume Reinforcement.

Creep is an irreversible time-dependent deformation in which a material under constant mechanical stress and elevated temperature for a considerably prolonged period of time, starts to undergo permanent deformation. Creep deformation occurs in three stages namely, primary, secondary and tertiary. Out of these three stages, secondary or steady state creep is particularly an area of engineering interest as it has almost a constant creep rate. Creep deformation plays a significant role in understanding effective service life of an engineering component working under high temperature conditions as such components such as super-heater and re-heater tubes and headers in a boiler, jet engines operating at temperature as high as 1200 C, usually experience a failure or rupture due to creep phenomenon. Design engineers keep a close attention on working stress conditions and elevated temperature under which an engineering component is expected to work as these conditions determine the onset of creep behavior in an engineering component. By recognizing the parameters of material response to creep behavior, engineers can analyse the useful service life and hazardous working conditions for an engineering components. Recognizing the creep phenomenon as high temperature design limitation, ASME Boiler and Pressure Vessel Code have provided guidelines on maximum allowable stresses for materials to be used in creep range. One of the criteria for determination of allowable stresses is 1% creep deformation of material in 100,000 h of service. Thus, the study of creep behavior in engineering components pertaining to high stress and temperature working conditions is very important as it affects the reliability and performance of the engineering components. The aim of our study is to understand the behavior of secondary creep deformation so that an advanced reinforced functionally graded material with better creep resistance, can be designed. In this paper, a secondary creep analysis of functionally graded (FG) thick-walled rotating cylinder under internal and external pressure is conducted. The novelty of the model intends to specify secondary creep stresses and strains by employing exponential, linear and quadratic volume reinforcement for ceramic in metal matrix in radial direction. This will help us to understand the effect of volume reinforcement in FG cylinder under internal/external pressure and rotating centrifugal body force by obtaining secondary creep stresses and strains. The response of the FG cylinder with isotropic material is analyzed and the solution for stress–strain rates in radial and tangential directions are obtained in closed form. Comparison of steady state creep stresses and strains under exponential, linear and quadratic volume reinforcement profiles are discussed and presented graphically.

Analysis of Steady State Creep Behaviour in Spherical Vessels Made of Composite Material

Abstract This study deals with estimation of steady state creep stresses and strain rates in composite spherical vessels subjected to internal and external pressures. The creep behaviour of the material was described by threshold stress based creep law used for composite materials. The well established von-Mises yield criterion has been also used in this analysis. The effect of reinforcement size and reinforcement volume content on the stresses and creep rates in the spherical vessels was studied. The creep stresses in the spherical pressure vessels do not have significant variation except of effective stress. On the other hand, the tangential, radial as well as effective strain rates in the spherical vessel reduced to significant extent by using lesser diameter particles and increasing the quantity of silicon carbide particles.

Creep behavior of the solid acid fuel cell material CsHSO4

Solid acid materials have recently shown great promise as solid-state electrolytes in intermediate temperature fuel cells. However, little is currently known about their mechanical properties, some of which could severely limit their application. In this study, the steady state creep behavior of the prototypical solid acid, CsHSO4, is characterized. In its highly conductive superprotonic state (>141°C), the material creeps at very high rates, as high as 10−2s−1, at stresses in the application design range of only a few MPa. The steady state creep stress exponent n≅3.6 and activation energy Q≅1.02eV=98.8kJ/mol are consistent with a dislocation-based creep mechanism.

Creep Analysis in Functionally Graded Rotating Disc Using Tresca Criterion and Comparison with Von-Mises Criterion

A mathematical model is developed to analyse steady state creep stresses and strain rates in a variable thickness rotating FGM disc that yields according to Tresca criterion. The results obtained are compared with those estimated using Von-Mises criterion. The radial stress (except for region towards the outer disc radius) and tangential stress (except for some portion towards the inner and outer disc radii) estimated using Von-Mises yield criterion are observed to be slightly higher than those obtained using Tresca criterion. The Tresca criterion estimates higher values of effective stress throughout as compared to Von-Mises criterion. The strain rates estimated using Tresca criterion, as compared to Von-Mises criterion, are also higher throughout the disc, with the maximum difference noticed at the inner disc radius. Thus, the design of rotating FGM disc, undergoing creep, based on Tresca yield criterion would be much safer as compared to design based on Von-Mises criterion.

Limit case analysis of the \u201cstable indenter velocity\u201d method for obtaining creep stress exponents from constant load indentation creep tests

This study concerns a commonly-used procedure for evaluating the steady state creep stress exponent, n, from indentation data. The procedure involves monitoring the indenter displacement history under constant load and making the assumption that, once its velocity has stabilised, the system is in a quasi-steady state, with stage II creep dominating the behaviour. The stress and strain fields under the indenter are represented by “equivalent stress” and “equivalent strain rate” values. The estimate of n is then obtained as the gradient of a plot of the logarithm of the equivalent strain rate against the logarithm of the equivalent stress. Concerns have, however, been expressed about the reliability of this procedure, and indeed it has already been shown to be fundamentally flawed. In the present paper, it is demonstrated, using a very simple analysis, that, for a genuinely stable velocity, the procedure always leads to the same, constant value for n (either 1.0 or 0.5, depending on whether the tip shape is spherical or self-similar). This occurs irrespective of the value of the measured velocity, or indeed of any creep characteristic of the material. It is now clear that previously-measured values of n, obtained using this procedure, have varied in a more or less random fashion, depending on the functional form chosen to represent the displacement–time history and the experimental variables (tip shape and size, penetration depth, etc.), with little or no sensitivity to the true value of n.

General estimation equation of transient C(t) under load and displacement control

This paper propose estimation equations of transient C(t)-integrals for general material properties where plastic and creep stress exponent are different under load and displacement control. The new equations are made by modifying the plasticity correction term in the existing equations. The modified plasticity corrections term is expressed in terms of initial elastic-plastic and steady state creep stress fields. For validation, elastic-plastic-creep finite element analysis are performed. FE results are compared with predicted C(t) results using proposed equations. Good agreement with FE results is found even when plastic and creep stress exponents are different.

Steady-State Creep Deformations and Stresses in FGM Rotating Thick Cylindrical Pressure Vessels

AbstractIn the present study, a closed-form analytical solution for the steady-state creep stresses of rotating thick cylindrical pressure vessels made of functionally graded materials (FGMs) is carried out. Norton's law governs the creep response of the material. Exact solutions for stresses and strain rate are obtained under the plane strain condition. How different material parameters involved in Norton's law affect radial and circumferential stresses together with the equivalent strain rate in rotating thick-walled cylindrical vessels under internal pressure is investigated. The result obtained shows that the property of FGMs has a significant influence on the equivalent creep strain rate and stresses distributions along the radial direction.

직관 용접부의 크리프 특성 불균일에 따른 열영향부 정상상태 응력 예측

본 논문은 크리프 파단 수명평가에 주요인자인 정상상태 크리프 응력을 직관 용접부에 대해 정량화한다. 모재와 용접부의 크리프 특성 불균일이 응력에 미치는 영향을 체계적으로 분석하기 위해, 다양한 용접부 불균일에 대해 이차원 유한요소 크리프 탄성해석을 수행하였다. 용접부는 열영향부를 고려하였으며 각각의 재료는 이상화된 탄성-멱 크리프 법칙을 따른다고 가정하였다. 하중에 따른 영향을 보기위해 내압과 인장하중에 대해 연구를 수행하였다. 용접부 크리프 응력의 정량화를 위해 크리프 불균일 지수를 도입하였으며, 무차원화된 단면평균응력과 선형적인 관계를 확인하였다. 불균일 지수로 정량화한 응력과 Type IV 영역을 모사한 용접부의 유한요소해석 결과 및 영국전력의 R5 문헌값의 비교를 통해 연구결과의 유효성을 검증하였다.

Effects of geometry and combined loading on steady-state creep stresses in welded branches

In our previous paper, it was found that the mis-match effect in creep on steady-state stresses within the weld metal for a large bore branch junction could be uniquely quantified by the mis-match factor defined as a function of the creep stress exponent and the ratio of creep constants for the base and weld materials. Furthermore ratios of section-averaged (effective and maximum principal) stresses for the mis-matched case to those for the even-matched case were linearly dependent on the mis-match factor. Above results were obtained for a specific branch geometry under single loading. This paper extends our previous analysis to other branch geometries and to combined loading. It is found that above conclusions can be applied to general branch components under combined loading.

Using the results of creep crack incubation tests on CrMoV steel for predicting long time creep rupture properties

The results of a series of creep crack incubation (CCI) tests have been used to examine the effectiveness of the LICON methodology for predicting long duration uniaxial rupture strength of a CrMoV steel at 550° C. The study has revealed that effective long time predictions can be made, but only with the availability of additional information including: an awareness of the short and long time rupture mechanisms and the associated multi-axial rupture criteria obeyed by the material, the results of uniaxial and multi-axial creep tests, and a knowledge of the steady state creep stress conditions existing in the testpieces (structures) forming part of the evaluation. In order to apply the creep damage enhancement approach to the low alloy creep resistant steel, it has been necessary to establish the steady-state creep stress state in the compact tension testpiece geometry used in the investigation. The new evidence is reviewed.

Exploring the applicability of the LICON methodology for a 1%CrMoV steel

The results of a series of creep crack incubation (CCI) tests have been used to examine the effectiveness of the LICON methodology for predicting long duration uniaxial rupture properties of a 1%CrMoV steel at 550°C. It has been demonstrated that good predictions can be made using this approach but that, for this to be possible, a knowledge of additional information is also required including uniaxial creep strain data, uniaxial and multi-axial rupture time properties and the results of finite element analysis.In order to apply the creep damage enhancement approach to the low alloy creep resistant steel, it has been necessary to establish the steady-state creep stress state in the compact tension testpiece geometry used in the investigation. The new evidence is described.

Optimum design of inhomogeneous rotating discs under secondary creep

Rotating discs commonly used in the aerospace industry often operate under high mechanical stresses due to centrifugal forces, while subject to high temperature gradients. High stresses and temperatures lead to creep in such rotating disc applications. This problem is particularly important in turbine discs under continuous operation. Since such discs are subject to secondary creep effects during most of their useful lives, it is important that they be optimized for minimum weight for the steady-state creep stresses. In this investigation, by considering the variable physical properties of the rotating disc materials under a high temperature gradient, a procedure for weight minimization for the steady-state creep stresses is proposed. The method aims to design the disc thickness profile so as to have minimum weight while the equivalent secondary creep stresses of the rotating disc under a high temperature gradient at all points simultaneously approach but do not exceed an allowable stress. An example is given to illustrate the method.

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.

Internal stress and heterogeneous dislocation structure in creep

The present work deals with the problem of microstructural interpretation of internal stress measured in high-temperature creep by the strain-transient dip-test technique. The development of microstructure in the course of creep is considered a transition from uniformly distributed dislocations to a well-developed substructure. The substructure is supposed to have a composite character that consists of cell or subgrain boundaries with few dislocations in cell or subgrain interiors. Model equations for the relation of internal stress to the parameters of the dislocation structure are discussed and examined with reference to experimental data. The evolution of internal stress in creep, evaluated using different formulae, is compared with the evolution of macroscopically measured internal stress. The use of applied-stress dependences of microstructure parameters permits quite realistic estimates of the values of internal stress in steady-state creep.

Effect of Stress States on Creep Fracture Modes of an Austenitic Steel with High Ductility.

Tensile creep rupture tests using smooth specimens and circumferential U-notched specimens having 4 kinds of notch root radius, and torsional creep rupture tests using smooth and circumferential 60° V-notched specimens of SUS310S austenitic steel with high ductility and high metallographical stability, were conducted at 700°C. In tensile creep rupture tests, it was found that as turning into lower stress level the creep fracture mode of smooth specimens changed from ductile transgranular fracture to brittle intergranular fracture. And irrespective of applied stress and notch geometry, the creep fracture mode of all notched specimens showed brittle intergranular fracture mixed with ductile transgranular fracture. While in torsional creep rupture tests, all smooth and notched specimens in the present test range exhibited a ductile fracture of shear type. These creep fracture modes were discussed on the basis of stress states and steady-state creep stress distributions in notch cross sections calculated by finite element method. The results suggested that mean stress promotes the intergranular creep fracture strongly, and that the equivalent stress promotes the nucleation of intergranular cavities but contributes less to their growth.

Constitutive description of high temperature creep in mechanically alloyed AlCO alloys

Creep curves of four mechanically alloyed aluminum alloys were studied within the range of stresses from 20 to 180 MPa at temperatures of 623 and 723 K. Creep curves of pure aluminum at temperatures of 473–623 K were taken as reference material data. The curves were described by the McVetty equation. The primary and steady-state stages of creep can be interpreted as a result of changes in the internal stress following from competition between work hardening and recovery processes. The analysis makes it possible to divide the internal stress into two components, one being due to stress fields of dislocations and the other to the existence of dispersed particles. The latter component equals the threshold stress in steady-state creep.

Constant structure creep in metals after stress reduction in steady state stage

Constant structure creep in several metals and alloys was investigated in structures corresponding to the steady state creep conditions. Results were interpreted by means of the back stress concept. In accord with postulates of the strain transient dip test technique, the residual effective stress is considered the controlling stress for dislocation glide. The suggested interpretation of constant structure creep data allows to obtain some information about parameters of the dislocation kinetics in the steady state creep. From the interpretation, a pronounced applied stress dependence of the mobile dislocation density as well as a specific relation between the activation area and the effective stress in steady state creep under various creep conditions result.

Role of the phase boundaries in the hot deformation in tension of AL-CuAl 2 single eutectic grains. A deformation model

An attempt is presented to understand globally the steady state creep and stress relaxation behaviours of oriented Al-CuAl 2 single eutectic grains. New and previous observations of the microscopic deformation mechanisms of the lamellar composite are presented in a synthetic manner which includes the role of the phase boundary sliding and the heterogeneity of the deformation. Previous analyses are reconsidered for both mentioned tests. A “unifying” deformation model is presented here, based chiefly 1. (i) on the observation that the measured threshold stress in steady state creep is always practically equal to the measured asymptotic stress in stress relaxation tests; 2. (ii) on the assumption that the contribution of the phase boundary sliding is the leading deformation mechanism. The results show that for both tests, the assumption of diffusion-controlled motion of phase boundary dislocations is sufficient to explain all the preceding measurements with a better accuracy and fewer adjustable parameters than previous models.

Internal stresses in power-law creep

A model based on the flexing of sub-boundaries under stress is proposed for the production of internal stress in steady state creep of pure metals and Class II alloys. The internal stress, computed by considering the bowed-out volume as partially constrained shear transformations, is in good agreement with internal stress measurements by the stress dip technique. The computed internal stress results in a steady state strain rate given by ϵ ̇ ge = A(μΩ/kT)(D/b 2)(χ/μb) 3(σ/μ) m , where m varies between 7 and 4 as σ/μ increases between 2 × 10 −4 to 2 × 10 −3, where χ is the stacking fault energy. The model also predicts correct magnitudes for both the non-linear and linear portions of the anelastic reverse creep that occurs upon stress removal.