First order reaction kinetics for transient creep in NiAl hardened austenitic steel

Abstract

Transient creep of an NiAl hardened austenitic steel was analysed in the temperature range of 823 to 923 K at stresses ranging from 150 to 450 MPa in the frame work of first order reaction kinetics. The present analysis is aimed: to correlate various transient creep parameters with steady state creep rate following first order reaction rate theory to obtain correlation constants; and to arrive at a unified equation to describe primary and steady state regimes of the creep curves in terms of correlation coefficients thus derived. Good correlation of transient creep parameters with steady state creep rate has been obtained over the test conditions studied indicating that the basic mechanism of deformation is the same for all the three stages of creep. Unified equation that fits the experimental creep strain time data for different test conditions over transient and steady state regimes has been obtained in terms of correlation coefficients.     

Characteristics of steady state deformation of an Al–0.1 Mg alloy at low temperatures

The present work aims to address the characteristics of steady state deformation, which determines the limit of grain refinement for a given material by severe plastic deformation. The focus is on low temperatures at which most deformation processing is conducted. Submicron grained Al–0.1 Mg alloy prepared by equal channel angular pressing was deformed by plane strain compression in a channel-die and rolling at a constant strain rate of 10^?2 s^?1 and at a range of temperatures from 77 to 473 K to various strains. Microstructures were characterized by electron backscatter imaging and EBSD in a FEGSEM. Grain refinement to the ECAP submicron structure occurred during deformation at cryogenic temperatures of 77–213 K, whereas coarsening took place during deformation at elevated temperatures. A steady state deformation was observed at all temperatures where a constant grain structure was developed and maintained upon further straining. The microstructural characteristics of steady state deformation and mechanism responsible for the establishment of the steady state are discussed.     

A periodic array of cracks in functionally graded materials subjected to transient loading

A periodic array of cracks in an infinite functionally graded material under transient mechanical loading is investigated. In-plane normal (mode I) and shear (mode II) loading conditions are considered. For each individual loading mode, a singular integral equation is derived, in which the crack surface displacements are unknown functions. Numerical results are obtained to illustrate the variation of the stress intensity factors as a function of the crack periodicity for different values of material inhomogeneity, either at the transient state or steady state. The material inhomogeneity can increase or decrease the mode I and mode II stress intensity factors. Compared with the single crack solution, it is also shown that multiple cracking may decrease the mode I stress intensity factors, but enhance the mode II stress intensity factors significantly.     

S30408奥氏体不锈钢高温力学性能试验研究

不锈钢材料高温力学性能是不锈钢结构抗火设计与数值模拟分析的重要参数。相对于碳素钢,不锈钢材料具有强非线性、比例极限低、无明显屈服平台、各向异性、应变硬化显著等特点,高温下两种材料的力学性能存在着较大的差异。该文利用MTS810试验系统对S30408奥氏体不锈钢进行了常温、高温稳态和高温瞬态试验研究,并将试验结果与《欧洲规范》以及已有的研究结果进行了对比分析。利用稳态试验结果,对影响高温下不锈钢材料力学性能的硬化指数n_θ和m_θ进行了修正,提出高温下不锈钢材料本构关系表达式,并给出了高温下不锈钢材料的初始弹性模量、屈服强度和极限强度的折减系数。对比分析了稳态试验结果与瞬态试验结果,结果表明：通过两种试验方法获得的高温下不锈钢材料应力-应变曲线存在一定的差异;在温度600℃范围内,差异不明显,当温度超过600℃时,两者差异随温度升高而逐渐增大。     

Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply

Numerical solutions obtained by the meshless local Petrov–Galerkin (MLPG) method are presented for transient thermoelastic deformations of functionally graded (FG) beams. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. In this study, the MLPG weak formulations associated with the governing equations of the transient-state thermal equilibrium and quasi-static mechanical equilibrium are given. The penalty method is adopted to efficiently enforce the essential boundary conditions, and the test function is chosen to equal the weight function of the moving least squares approximation. An example is demonstrated for an FG beam with thermoelastic moduli varying exponentially through the thickness direction under a nonuniformly convective heat supply. Results obtained from the MLPG method are found to agree well with those by the analytical solution. The nonhomogeneity of the material properties on the thermo-mechanical response of the FG beam is investigated. It is shown that temperature and deformation fields of FG beams in a transient state differ substantially from those at the steady state. Besides that, the rate of change of the heat supply on the transient responses is also delineated.     

轴心受压H形截面不锈钢柱抗火性能分析

基于国产奥氏体S30408不锈钢材料,针对轴心受压H形截面不锈钢柱,采用高温稳态分析和瞬态分析两种方法对其抗火性能开展了有限元数值模拟分析,揭示了不锈钢柱高温下受力性能与破坏模式。通过高温稳态分析,给出了不同温度下不锈钢柱的荷载-位移曲线及极限承载力-温度曲线;通过高温瞬态分析,研究了特定火灾升温模式下不锈钢柱表面温度的变化规律,给出了不同荷载比下不锈钢柱的临界温度;并将两种方法的计算结果与《欧洲规范》(EN1993-1-2)的计算结果进行对比分析。在此基础上,分别采用高温稳态分析和瞬态分析方法,对不锈钢柱的抗火性能开展了参数化分析,着重考察了构件初始缺陷、荷载比、截面尺寸以及长细比对高温下极限承载力和临界温度的影响。研究结果表明:构件的长细比和截面尺寸为轴心受压H形截面不锈钢柱高温极限承载力的主要影响因素,荷载比为不锈钢柱临界温度的关键因素,初始缺陷对不锈钢柱的抗火性能影响不明显。     

Creep deformation of metal—matrix composites

Various models of creep deformation of composite materials are reviewed and their predictions compared with available experimental data. The implications of rule-of-mixtures strengthening when (a) both matrix and reinforcing phase are subject to creep deformation and (b) the reinforcement extends elastically in a creeping matrix for the establishment of steady state creep and for the representation of creep data for composites are discussed.Evidence of deviation from rule-of-mixtures behaviour is given, particularly where the dispersed phase can lead to either strengthening or weakening of the matrix. The value of analysing transient creep following stress changes to elucidate the creep mechanisms will be discussed. It will be shown that the reinforcement can influence matrix creep by (i) introducing a threshold stress and (ii) altering the deformation kinetics. In some nickel-base alloys, the latter factor can lead to significant strain softening that prevents the establishment of steady state creep.     

Thermo-Chemical Modelling Strategies for the Pultrusion Process

In the present study, three dimensional (3D) numerical modeling strategies of a thermosetting pultrusion process are investigated considering both transient and steady state approaches. For the transient solution, an unconditionally stable alternating direction implicit Douglas-Gunn (ADI-DG) scheme is implemented as a first contribution of its kind in this specific field of application. The corresponding results are compared with the results obtained from the transient fully implicit scheme, the straightforward extension of the 2D ADI and the steady state approach. The implementation of the proposed approach is described in detail. The calculated temperature and cure degree profiles at steady state are found to agree well with results obtained from similar analyses in the literature. Detailed case studies are carried out investigating the computational accuracy and the efficiency of the 3D ADI-DG solver. It is found that the steady state approach is much faster than the transient approach in terms of the computational time and the number of iteration loops to obtain converged results for reaching the steady state. Hence, it is highly suitable for automatic process optimization which often involves many design evaluations. On the other hand sometimes the transient regime may be of interest and here the proposed ADI-DG method shows to be considerably faster than the transient fully implicit method which is generally used by the general purpose commercial finite element solvers. Finally, using the proposed steady-state approach, a design of experiments is carried out for the curing characteristic of the product based on pulling speed and part thickness.     

Steady state flow of cohesive and non-cohesive powders

Steady state flow of powders is a crucial concept to investigate the powders’ strength and flow properties. This state is defined as a continuous deformation of the material without volume change while the stresses at the specimen’s boundaries remain constant. Recent investigations have shown that this state, especially for cohesive powders, is not always as constant as it should be by definition. This paper presents experimental and numerical work, both for cohesive and non-cohesive powders. The experimental part focuses on the use of different control strategies, leading to steady state flow of different quality. Differences between steady state flow for cohesive and non-cohesive powders are shown.     

The effect of cryogenic deformation on the limiting grain size in an SMG Al-alloy

The minimum grain size obtainable in an Al–0.1%Mg submicron grained (SMG) alloy, subjected to cryogenic plane strain deformation, and its subsequent stability during room temperature deformation have been investigated. A decreasing steady state grain size was obtained with reducing deformation temperature. However, a true nanocrystalline grain structure was not obtained even at 77 K with the high angle boundary spacing only approaching the nanoscale in the sample normal direction. The cryogenically deformed material was unstable on subsequent deformation at room temperature and underwent rapid dynamic grain growth. Dynamic grain coarsening is shown to limit the minimum grain size achievable in an SPD process, even under cryogenic conditions.     

A creep model with damage based on internal variable theory and its fundamental properties

The creep damage is discussed within Rice irreversible internal state variable (ISV) thermodynamic theory. An ISV small-strain unified creep model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The proposed model can describe viscoelasticity and, preferably, three phases of creep deformation. Creep strain results from internal structural adjustment, and different creep stages accompany different thermodynamic properties in terms of flow potential function and energy dissipation rate. During the viscoelastic process, the thermodynamic state of the material system tends to equilibrate spontaneously. The thermodynamic state of the material system without damage tends to equilibrate or achieve steady state after loading. Kinetic equations of ISVs can be derived by one single flow potential function, and the energy dissipation rate decreases monotonically over time. In the entire creep damage process, multiple potentials are needed to characterise evolution of ISVs, rotational fluxes are presented in affinity space, and the thermodynamic state of material system tends to depart from the steady or equilibrium state. The energy dissipation rate can be a measure of the distance between the current thermodynamic state and the equilibrium state. The time derivative of the rate can characterise the development trend of the material, and the integral value in the domain may be regarded as indices to evaluate the long-term stability of the structure.     

Cyclic indentation in aluminum

Cyclic indentation was used to evaluate the dynamic deformation of aluminum. Under the load-controlled cyclic indentation, the indenter continuously penetrated into the material and reached a steady state at which the penetration speed (per cycle) was a constant. The amplitude of the cyclic indentation depth was basically controlled by the amplitude of the cyclic indentation load, independent of the mean indentation load and the indentation frequency. The steady state penetration speed decreased with increasing the amplitude of the cyclic indentation load due to the increase in the size of plastic zone. It also decreased with the increase in the mean indentation load due to local strain hardening, while it increased with the increase of the indentation frequency.     

A2017合金半固态压缩的变形机制和成形性能

利用Gleeble-1500热学-力学模拟机,对A2017半固态合金进行半固态压缩变形实验,分析了应力-应变曲线和组织变化,研究了压缩变形机制及成形性能结果表明,用单辊搅拌冷却(SCR)技术制备的A2017半固态合金的组织为细小均匀的非枝晶等轴晶,二次加热后可转化为均匀的球形晶和共晶液相组成的半固态组织;A2017合金半固态压缩变形的塑性好、变形抗力低;随着变形温度的升高或者变形速率的降低,变形的抗力降低.在稳定的流动变形阶段,A2017合金的半固态变形机制主要由液相流动和固相颗粒的转动与滑动组成,触变性能稳定,最大半固态加工变形范围为60%左右.     

Transient scattering of elastic waves by three dimensional non-axisymmetric dipping layers

Scattering of elastic plane waves by three dimensional non-axisymmetric multiple dipping layers embedded in an elastic half-space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square sense at points on the layer interfaces and on the surface of the half-space. The transient response is constructed from the steady state solution by using Fourier synthesis. Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non-axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.     

SiCw／6061A1复合材料温度循环拉伸变形行为

本文采用热循环拉伸试验方法研究了ＳｉＣｗ／６０６１Ａ１复合材料的变形行为．结果表明，ＳｉＣｗ／６０６１Ａ１复合材料温度循环拉伸变形行为与蠕变类似分为初始变形阶段、稳态变形阶段和快速断裂三个阶段；温度循环拉伸变形稳态流变速率明显提高；温度循环拉伸变形的应力指数低于恒温蠕变的应力指数．     

Transient free convection about a vertical flat plate embedded in a porous medium

The problems of transient free convection in a porous medium adjacent to a vertical semi-infinite flat plate with a step increase in wall temperature and surface heat flux are considered in this paper. By assuming a temperature profile in each case, the governing equation for the boundary layer thickness is obtained by an integral method. These governing equations are first-order partial differential equations of the hyperbolic type that can be solved exactly by the method of characteristics and approximately by the method of integral relations. The results based on the method of characteristics clearly indicate that during the initial stage when the leading edge effect is not being felt, heat is transferred as if by transient 1-dimensional heat conduction. At a later time, depending on the vertical location, the heat transfer characteristics change from transient 1-dimensional heat conduction to steady 2-dimensional convection. The thickness of the boundary layer is shown to be increasing with time until it reaches steady state where its value remains constant thereafter. The growth rate of the boundary layer thickness exhibits a discontinuity at the end of the transient period and the beginning of the steady state period. On the other hand, the results based on the method of integral relations show that the boundary layer thickness grows continuously with time and approaches the steady state value asymptotically; the growth rate of the boundary layer thickness decreases from a finite value to zero continuously as the steady state is approached. Except between the end of the transient period and the beginning of the steady state period, the results based on the method of integral relations are in good agreement with those based on the method of characteristics.     

Transient Current Behaviour for Iron in 3.5%NaCl and 3.5%NaCl+ 1%NaNO_2 Solutions during Corrosion Fatigue

The transient current behaviour for Iron in 3.5%NaCl and 3.5%NaCl +1%NaNO2 solutions during corrosion fatigue (CF) process has been investigated at different given strain amplitudes and strain rates. The results show that elastic strain has little contribution to material dissolution. The elastic tension strain results in the decrease in the transient current, while the elastic compression strain increases the transient current. Compared to the elastic deformation, plastic deformation affects material dissolution evidently For iron in 3.5%NaCl solution, the strain amplitude plays a dominant role in the dissolution process accelerated by the plastic strain, while in 3.5%NaCl+1%NaNO2 solution, both the strain amplitude and strain rate play an important role in this process. In this paper, the effect of the elastic deformation on the material dissolution and the relation between the tension and compression current peak values under the plastic cycle deformation are discussed     

Some recent developments in numerical modelling of fracture toughness in brittle matrix composites

Finite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near-tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached. The toughening effect of a crack-bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.     

Transient piezothermoelastic problem for a laminated composite strip composed of angle-ply and piezoelectric laminae

This paper is concerned with the theoretical treatment of transient piezothermoelastic problem which is developed for a laminated composite strip composed of angle-ply laminae and a piezoelectric material of crystal class mm2, subject to nonuniform heat supply in the width direction. We obtain the exact solution for the two-dimensional temperature change in a transient state and the transient piezothermoelastic response of a simple supported composite strip under the state of generalized plane deformation. As an example, numerical calculations are carried out for a angle-ply laminated composite strip made of an alumina fiber reinforced aluminum composite, associated with a piezoelectric layer of a cadmium selenide solid. Some numerical results for temperature change, displacement, stress and electric potential distributions in a transient state are shown in figures. Furthermore, the influence of the thickness of the piezoelectric layer on the thermal stress or electric field is investigated.