Steady-state Creep Conditions Research Articles

APPLICATION OF THE UMAT SUBROUTINE FOR SOLVING CONTINUUM MECHANICS PROBLEMS (OVERVIEW)

This paper presents an overview of the application of the UMAT subroutine of the SIMULIA Abaqus multifunctional software package in solid mechanics and related areas. This subroutine is used to describe new user materials that are not available in the class of standard materials of the SIMULIA Abaqus package. This overview article provides examples of problems and constitutive equations of materials that are modeled using UMAT / VUMAT procedures. Various types of materials are presented, successfully described by means of user-defined UMAT and VUMAT procedures. A general description and experience of using the UMAT subroutine is given. The results of finite element modeling of the deformation of aplate weakened by a central circular hole under uniform and uniaxial tension with steady-state creep in a damaged medium evolving according to a power law are presented in the coupled formulation of the problem (creep - damage). The distributions of stresses, strains, and damage fields at the tip of the defect under creep conditions are found, and an analysis is made of the effect of the damage accumulation process on the stress fields at the crack tip under steady-state creep conditions. The distributions of stresses and creep strains are demonstrated taking into account the accumulation of damage over time.

A theoretical and computational investigation of mixed mode creep crack growth along an interface

In this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the C^{*}-integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function (C_{k}) is determined in terms of a dimensionless quantity phi _{0} (which is the ratio of geometric and material length scales), mode mixity chi and the deformation and damage coupling parameters. We demonstrate that the form of the C_{k}-function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions.

Dimensional transitions in creeping materials due to nonlinearity and microstructural disorder

Abstract The transition from extremely brittle to very ductile behaviours of creeping materials is discussed, where analogies with power-law hardening materials are pointed out. Considering Norton's Law as a viscous constitutive law, it is possible to define a generalized stress-intensity factor Kc ―characterizing the intermediate asymptotic behaviour under steady-state creep conditions― with physical dimensions depending upon the Norton stress exponent n. In the two limit cases of creep resistant materials (n≅1) and creep sensitive materials (n ≫ 1), Kc assumes respectively the dimensions of an elastic stress-intensity factor ( F L − 3 / 2 ) and of a stress ( F L − 2 ). Such a dimensional transition, with consequent stress-singularity attenuation, is completely analogous to that occurring through the introduction of a fractal stress-intensity factor (Kc)*, when the influence of microstructural disorder is considered.

Установившаяся ползучесть длинной мембраны внутри жесткой матрицы при переменном поперечном давлении

Исследуется задача об установившейся ползучести длинной прямоугольной мембраны в стесненных условиях внутри жесткой матрицы при кусочно-постоянной зависимости величины поперечного давления $q$ от времени $t$. В задаче рассматривается длинная матрица прямоугольного сечения, в которой отношение ее высоты к ширине не меньше 0.5. В качестве примера исследуется ползучесть мембраны при однократном изменении величины поперечного давления во времени. Рассматриваются три варианта условий контакта мембраны и матрицы: идеальное скольжение, прилипание и скольжение с учетом трения. В данной работе исследованы четыре стадии деформирования мембраны. На первой стадии (упругое деформирование) мембрана, плоская в начальном состоянии, под действием давления $q$ мгновенно упруго деформируется, приобретая форму незамкнутой круговой цилиндрической оболочки с центральным углом $2\alpha_1$. На второй стадии мембрана деформируется в условиях установившейся ползучести вплоть до момента касания боковых стенок матрицы. Третья стадия заканчивается в момент касания мембраной поперечной стенки матрицы. На четвертой стадии мембрана контактирует с матрицей по поперечной и боковым сторонам. Анализ проводится до времени практически полного прилегания мембраны к матрице, при котором отношение радиуса мембраны вблизи углов матрицы к начальной ширине мембраны составляет 0.005. Для третьей и четвертой стадий дополнительно учитывается сила трения мембраны о стенки матрицы. Получены зависимости толщины различных частей мембраны от времени, а также интенсивности напряжений в мембране от времени. Применительно к данной постановке задачи рассмотрены отклонения от правила суммирования парциальных времен заполнения матрицы.

A discrete dislocation dynamics model of creeping single crystals

Failure by creep is a design limiting issue for metallic materials used in several high temperature applications. Current theoretical models of creep are phenomenological with little connection to the underlying microscopic mechanisms. In this paper, a bottom-up simulation framework based on the discrete dislocation dynamics method is presented for dislocation creep aided by the diffusion of vacancies, known to be the rate controlling mechanism at high temperature and stress levels. The time evolution of the creep strain and the dislocation microstructure in a periodic unit cell of a nominally infinite single crystal is simulated using the kinetic Monte Carlo method, together with approximate constitutive laws formulated for the rates of thermal activation of dislocations over local pinning obstacles. The deformation of the crystal due to dislocation glide between individual thermal activation events is simulated using a standard dislocation dynamics algorithm, extended to account for constant stress periodic boundary conditions. Steady state creep conditions are obtained in the simulations with the predicted creep rates as a function of stress and temperature in good agreement with experimentally reported values. Arrhenius scaling of the creep rates as a function of temperature and power-law scaling with the applied stress are also reproduced, with the values of the power-law exponents in the high stress regime in good agreement with experiments.

A theoretical and computational framework for studying creep crack growth

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C^*-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity hat{C}_k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity phi _0, which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large phi _0, for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.

Refined Deformation Model for Metal-Composite Plates of Regular Layered Structure in Bending Under Conditions of Steady-State Creep

The problem of the mechanical behavior of metal-composite plates of regular layered structure in bending under conditions of steady-state creep of all phase materials is formulated. Equations describing, with various degrees of accuracy, the stress and viscous creep states of such plates with account of their weakened resistance to transverse shears are obtained. The relations of the classical Kirkhoff theory, the nonclassical Reissner theory results, and the second variant of Timoshenko theory result as special cases of these equations. For asymmetrically loaded annular plates with one edge clamped and statically loaded other one, a simplified variant of the refined theory, whose complexity in practical realization is comparable to that of the Reissner theory, is developed. The bending deformations of such annular plates at different levels of thermal actions are calculated. It is shown that, with increasing temperature, the accuracy of calculations within the framework of the traditional theories decreases sharply and neither of them provides an accuracy for the calculated compliance of the structure even within 20%.

Study of bending deformation of layered metal-composite wall-beams of regular structure under steady-state creep conditions

Study of bending deformation of layered metal-composite wall-beams of regular structure under steady-state creep conditions

Experimental and simulated displacement in cracked specimen of P91 steel under creep conditions

The assessment of crack initiation and propagation under creep conditions is important in the remaining life prediction of pipe components for power generation industry. One of the most successful analytical parameters for describing crack propagation under steady-state creep conditions is the C*-Integral that depends strongly on the material’s creep behavior and the resulting load-line displacement. This study deals with the determination and optimization of a creep model for a P91 grade steel operating at 600 °C. After a good fit provided by the model with uniaxial creep tests was found, the creep behavior of compact type C(T) specimens was modeled to predict creep crack growth (CCG) rates. A modified Cocks and Ashby power law creep controlled cavity growth model was used to compute the creep crack propagation rates. Load-line deflection was found to be strongly dependent on the primary creep strain rate. Lastly, good correlation between the experimental CCG results and the predicted CCG rates from the simulations were found.

Modeling the creep properties of olivine by 2.5-dimensional dislocation dynamics simulations

In this work we performed 2.5-dimensional (2.5D) dislocation dynamics simulations coupling climb with the glide dislocation motion to model the creep behavior of olivine, one of the main component of the Earth's upper mantle. In particular, we present an application of this method to determine the creep strain rate in a material with high lattice resistance, such as olivine. We show that by including the climb mechanism we reach steady state creep conditions. Moreover, we find that a creep power law with a stress exponent close to 3 can be extracted from our simulations and we provide a model based on Orowan's law to predict the creep strain rates in the high temperature and low stress regime. The model presented is relevant to describe the plastic flow of olivine in the Earth's mantle deformation conditions and can be useful to derive the high temperature creep behavior of other materials.

Steady-state creep of bent reinforced metal-composite plates with consideration of their reduced resistance to transverse shear. 1. Deformation model

The problem of deformation of reinforced metal-composite plates is formulated in rectangular Cartesian coordinates using the second version of Timoshenko theory and taking into account the reduced transverse shear resistance of the plates under steady-state creep conditions. A similar model problem of axisymmetric bending of reinforced plates is considered in polar coordinates.

Relationship between Creep Crack Propagation Rates of P92 Steel and Welding HAZ and High Temperature Creep Fracture Parameter C* Based on Reference Stress Method

Uniaxial creep tests on micro-regions of P92 steel base metal and welding HAZ specimens were carried out at 923 K and under different stress levels. The creep equation of index of B and n was obtained from the test data fitted by using least square method. Then, creep crack growth tests based on the reference stress method on P92 steel base metal and welding HAZ compact tensile samples were carried out at 923 K and under stress intensity factor K of 18 MPa·m1/2. From the calculated and experimental data, it was found that a good relationship existed between the creep crack growth rate da/dc and high temperature creep fracture parameter C*. The reference stress method was verified to calculate the C* of compact tension specimens and can predict the creep crack growth rate of the P92 steel base metal and welding HAZ materials under steady state creep conditions. At the same time, high temperature defect evaluation parameters of D0 and Φ were obtained by fitting the linear parts in the relation curves using the log-log method. This study provides tests data on the defects evaluation and life prediction of P92 steel welding materials.

The effects of scoop sampling on the creep behaviour of power plant straight pipes

Small specimen testing techniques are potentially highly useful procedures which could be used to determine many fundamental material properties from relatively small amounts of sample material. Small specimens can be manufactured from scoop samples taken from the surface of a component, allowing for continued operation after sampling. In the past, it has been assumed that, provided the wall thickness dimension around the specimen sample site is greater than the minimum design requirement, the action of scoop sampling will not greatly compromise the future operation of the component. Little study has been completed, however, to verify this assumption or to evaluate the likely reduction in remnant life due to scoop sampling. In the present study, a finite element investigation is made into the effects of scoop sampling on the stress states and failure lives of power plant straight pipes under steady-state creep conditions. Loading conditions considered include an internal pressure load only (assuming closed-end conditions), as well as system loading (in the form of additional axial and in-plane bending moment loading). Typically, the application of system loading increases the likelihood of failure being controlled by the stress states in the vicinity of a scoop excavation. This leads to potentially significant reductions (up to approximately 90%) in creep life of straight piping components. Parametric equations (valid for a range of pipe geometries and scoop cut depths) have been proposed, which can estimate the stress riser effect in the vicinity of an excavation sample under closed-end and additional axial loading conditions.

Simulation of the steady-state creep of crossreinforced metal composites with account of anisotropy of phase materials 2. The case of 2D reinforcement

Iterative models are proposed to describe the mechanical behavior of thin-walled metal-composite structural elements, cross-reinforced in a plane, whose incompressible phase materials operate under the conditions of steady-state anisotropic creep. A comparative analysis of the calculations performed is carried out for different structural models of the mechanical behavior of annular metal-composite plates under the conditions of steadystate creep.

Notch creep rupture strength of 316LN SS and its variation with nitrogen content

Low carbon, nitrogen-alloyed, 316L(N) stainless steel (SS) is a major structural material for high temperature components of sodium cooled fast reactors. With a view to increase the design life from 40 to 60 years and beyond, studies are being carried out to develop 316LN grade austenitic stainless steels with superior high temperature mechanical properties. As a part of this development programme, four laboratory heats of 316LN SS containing 0.07, 0.11, 0.14 and 0.22wt.% nitrogen are being evaluated extensively. Creep tests have been carried out on smooth and notched sample geometries at a nominal stress level of 200MPa and at a temperature of 923K. The notched specimens contained a V-notch at an angle of 60° with root radius of 0.19mm, which provided theoretical stress concentration factor of 4.2. The gauge diameter of the notched specimen at the notch root was 6.4mm and was 10mm for the smooth specimen. It was found that the presence of notch increased the creep life for all the four heats. In the case of smooth specimens, rupture life increased with increase in nitrogen content. In the case of notched specimens, rupture life showed a peak value at 0.14wt.% nitrogen content. The ratio of rupture life of smooth to notched specimens decreased with increase in the nitrogen content from 18 for the material containing 0.07wt.% nitrogen to 3 for the material containing 0.22wt.% nitrogen thereby implying that the notch strengthening effect decreased significantly at high nitrogen levels. The notched specimens showed a lower value of ductility, measured in terms of reduction in area, as compared to the smooth specimens. Finite element analysis of the stress and strain distribution in the notch region was carried out as a function of nitrogen content. The stress concentration factor (Kt) evaluated through stress analysis was found to be 4.2 for the geometry used in this study. The creep analysis was run for a sufficiently long time to achieve the steady state creep condition. The influence of nitrogen content on the values of triaxial stresses under steady state conditions for the given notch geometry was evaluated. The presence of notch with the investigated notch geometry lowered the maximum principal stress and this lead to higher rupture life in all the four heats.

Correlation of creep crack-tip constraint between axially cracked pipelines and test specimens

In this paper, based on the creep constraint parameter R, the creep crack-tip constraints in axially cracked pipelines and various test specimens have been analyzed under conditions of plane strain and steady-state creep, and correlation of the constraint between the cracked pipes and test specimens has been investigated. The creep crack-tip constraint of the single-edge notched tension (SENT) specimen is close to that of axially cracked pipes. The pin-loaded SENT specimen (SENTp) with a/W = 0.35 and 0.05 W loading point offset provides a closely matched creep crack-tip constraint with the axially cracked pipes. It will be more accurate if the creep crack growth rate and creep fracture toughness data measured by the SENTp specimen are used in integrity assessment of axially cracked pipes. The results provide a strong support for use of constraint-designed specimens in creep failure assessments of pressurized pipes at high temperature.

Calculation of the stress-strain state of complex reinforced metal-composite shells under steady-state creep conditions

This paper presents a formulation of the problem of deformation of variable thickness shells reinforced by fibers of constant cross-section. All components of these metal-composite shells operate under steady-state creep conditions. The system of resolution equations together with the appropriate boundary conditions is analyzed. A method for the solution of the problem formulated here is developed. The way to get the approximate solution to the problem at the first stage of unsteady-state creep is proposed. Calculations performed for cylindrical shells indicate that the compliance of such structures under steady-state creep conditions depends strongly on the reinforcement structure.

Steady-state creep of complexly reinforced shallow metal-composite shells

The problem of deformation of shallow shells of variable thickness reinforced with fibers of constant cross section, whose all phases operate under the conditions of steady-state creep, is formulated. The system of resolving equations and the corresponding boundary conditions are analyzed, and the procedure for solving this problem is developed. A way of approximate solution of such problems in the case of transient creep is indicated. The particular calculations performed show that the compliance of thin-walled structures, under the conditions of steady-state creep, greatly depends on the structure of reinforcement.

Analysis of circular cylinder subsidence under creep conditions taking into account and not taking into account barrel distortion

The subsidence of a circular cylinder compressed between rigid stamps under steady-state creep conditions is investigated. We present two solutions, of which one is based on the assumption that all parameters of the stressstrain state of the cylinder are independent of the longitudinal coordinate, and the other suggests barrel distortion (this solution is constructed using the LS-DYNA software package). In both cases, the subsidence of the cylinder is studied for same size and time. Calculations of all principal parameters are performed for two loading regimes: the stamps approach one another at a constant speed, and the applied compression force is constant. It is shown that the compression energy in the first variant is less than in the second variant (difference in the subsidence for specified processes is equal to 8-10%). The subsidence of the cylinder for fixed size and time under the assumption of barrel distortion requires less energy than in the case when the shape of the cylinder remains unchanged.

Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens

In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases.