Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

This paper describes the effect of thermal exposure (high-temperature exposure) (T = 675?C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675?C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress–strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.     

Creep constitutive modeling of an aluminum alloy under multiaxial and cyclic loading

A constitutive model is developed to characterize creep response of polycrystalline metals. The model is based on the effective stress concept and back stress is utilized as an internal variable. A memory aspect is incorporated in the model to account for the previous maximal stress as a result of dislocation related micromechanisms. The model is used to predict the creep potential of an aluminum alloy under multiaxial and cyclic loading. The predicted results are compared with the available experimental results on an aluminum alloy (2618-T61). The associated six basic model parameters are evaluated by using an optimization technique, called ‘Box Algorithm’. These model parameters are then used to predict some unoptimized experimental data sets. The influence of multiaxial and cyclic loadings is investigated in detail for the selected aluminum alloy. Overall, excellent correlations are observed.     

Mathematical modelling of the superplastic forming of a long rectangular sheet

Standard finite element software (ANSYS FEM-code) is used to model the superplastic forming of a superplastic sheet alloy into a rectangular die. As distinct from other known approaches the boundary value problem is stated in the present study in terms of the theory of creep. The results of finite element calculations are found to be in a good agreement with corresponding analytical solutions and experimental data for titanium sheet alloy Ti-6Al-4V. The approach suggested can be used in practice for estimating the current geometry and the thickness of the dome and the time intervals both for the constant gas pressure forming and for the constant strain rate forming.     

尼龙6/蒙脱土复合材料蠕变行为研究

针对经典黏弹性模型不能很好分析黏弹性材料的蠕变行为问题,运用分数阶导数的类标准线性体模型与Prony级数模型研究了黏弹性材料尼龙6/蒙脱土复合材料的蠕变行为.采用原位聚合法制备了尼龙6/蒙脱土复合材料,在室温环境下对其进行蠕变实验.然后运用分数阶导数的类标准线性体模型和Prony级数模型对复合材料的蠕变实验数据进行分析...     

Creep characterization of transversely-isotropic metallic materials

A constitutive equation for modelling secondary creep in directionally-solidified eutectic alloys is proposed, based on a generalization of the Bailey-Norton law to transversely-isotropic materials. In addition to the power-law index, it is found that three material parameters are required to characterize secondary-creep behaviour and their experimental determination is discussed. The theory is compared with creep data obtained on a Co-Cr-C eutectic alloy.     

Creep of a heat-resistant aluminum alloy in a complex state of stress

The article gives the results of experimental investigations of the creep of heat-resistant aluminum alloy AK4-1 with constant and variable loads, at a temperature of 175 °C and a duration of the tests equal to 100 h. Based on the experimental data, a verification of the theory of creep is adduced, based on the following hypotheses: 1) the change in the volume is elastic; 2) the deviator of the creep rates is proportional to the deviator of the stresses; 3) the intensities of the stresses, of the creep deformations, and their rates are connected by a relationship which does not depend on the type of the state of stress. It should be pointed out that the results of investigation of creep, under a complex state of stress, in carbon, low-alloy, austenitic steels, copper, and certain light alloys, are given in [1–6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 83–86, March–April, 1971.     

Identification of material parameters for inelastic constitutive models: Stochastic simulations for the analysis of deviations

For parameter identification a distance function between the measured and the simulated data has to be minimized. Therefore, the influence of three different norms used in the definition of such a distance function is investigated. The nonlinear optimization problem is solved using a modified random search algorithm originally proposed by Price (1978). Next a stochastic model for the generation of artificial test data is presented. This model is used for a stochastic simulation of test data (constant strain rate tension with relaxation and creep). From these artificial data the material parameters of the model of Chan, Bodner and Lindholm are identified. To measure the quality of the identified material parameters their mean values and empirical standard deviations are computed. Furthermore, the coefficients of the empirical correlation matrix for the material parameters are computed. The model responses for tensile tests with the parameter vector generated from all tests and with the estimated parameters (from stochastic simulations) differ not considerably. However, for the creep tests the different parameter estimations lead to quite different model responses. Received October 22, 1999     

岩石蠕变模型的比较和修正

对三种岩石在不同的应力下进行了蠕变实验,对蠕变实验曲线用粘弹模型进行了模型参数的反演,结果认为标准线性体、伯格斯和对数模型都是实验曲线的很好近似.为了进一步了解蠕变实验时间对模型参数的影响,研究了蠕变模型的预测功能.将实验蠕变曲线分成二部分,第一部分用于模型参数的反演,第二部分用于模型预测数据的检验.时间外延所得的模型的预测曲线都明显偏离了实测曲线,伯格斯和对数模型的预测曲线比实测曲线偏高,而标准线性体模型则偏低.根据不同时间的蠕变实验数据的比较和分析,认为实验时间对蠕变模型参数的反演有较为明显的影响,但只要对标准线性体模型作适当修正,引入与时间尺度有关的函数C(t),则该模型的预测能力就有较大的提高.     

沉淀相的尺寸与形态对镍基合金蠕变行为的影响

镍基合金具有优良的高温力学性能,广泛应用于涡轮叶片等热端部件。沉淀相的尺寸和形态是影响镍基合金力学性能的重要因素。本文在考虑应变梯度的镍基合金晶体塑性本构模型的基础上,引入了各向异性损伤张量,研究了包含两种不同尺寸和三种不同长细比的沉淀相形态的镍基合金蠕变行为。结果表明,该模型能够很好地反映沉淀相的尺寸对镍基合金蠕变行为的影响,与实验结果符合较好。同时,沉淀相的形态也对镍基合金的力学性能产生重要影响,随着沉淀相长细比的增加,镍基合金的蠕变寿命延长,这体现了粗化和形态对镍基合金蠕变行为影响的一种竞争的机制。     

Multiaxial creep and cyclic plasticity in nickel-base superalloy C263

Physically-based constitutive equations for uniaxial creep deformation in nickel alloy C263 [Acta Mater. 50 (2002) 2917] have been generalised for multiaxial stress states using conventional von Mises type assumptions. A range of biaxial creep tests have been carried out on nickel alloy C263 in order to investigate the stress state sensitivity of creep damage evolution. The sensitivity has been quantified in C263 and embodied within the creep constitutive equations for this material. The equations have been implemented into finite element code. The resulting computed creep behaviour for a range of stress state compares well with experimental results. Creep tests have been carried out on double notched bar specimens over a range of nominal stress. The effect of the notches is to introduce multiaxial stress states local to the notches which influences creep damage evolution. Finite element models of the double notch bar specimens have been developed and used to test the ability of the model to predict correctly, or otherwise, the creep rupture lifetimes of components in which multiaxial stress states exist. Reasonable comparisons with experimental results are achieved. The γ^′ solvus temperature of C263 is about 925 °C, so that thermo-mechanical fatigue (TMF) loading in which the temperature exceeds the solvus leads to the dissolution of the γ^′ precipitate, and a resulting solution treated material. The cyclic plasticity and creep behaviour of the solution treated material is quite different to that of the material with standard heat treatment. A time-independent cyclic plasticity model with kinematic and isotropic hardening has been developed for solution treated and standard heat treated nickel-base superalloy C263. It has been combined with the physically-based creep model to provide constitutive equations for TMF in C263 over the temperature range 20–950 °C, capable of predicting deformation and life in creep cavitation-dominated TMF failure.     

An Extension of the Monkman-Grant Model for the Prediction of the Creep Rupture Time Using Small Punch Tests

Creep tests on a small scale have the potential to be used without significant removal of material or in areas where the available material is limited. In this paper an extension of the modified Monkman-Grant model for the prediction of the creep rupture time using Small Punch Creep Tests (SPCT) is investigated. This test basically consists of punching, under constant load, a small size specimen (10×10×0.5 mm) with the ends fixed. For this purpose an AZ31B magnesium alloy, taking a test temperature of 150?ºC, has been selected. The Monkman-Grant relation is a predictive model, initially developed for uniaxial creep tests, which can be used to predict the rupture time of tests which have been interrupted once secondary stage of creep has been reached. The proposed extension of the Monkman-Grant model for SPCT is based on the definition of the Minimum Relative Punch Displacement Rate. The experimental techniques and data analysis, involving small punch testing, are explained in detail. The proposed predictive model allows the test times of small punch testing to be reduced and it can be directly applied to predict the failure time from an interrupted test at the time when the Minimum Relative Punch Displacement Rate is reached. Good correlations are obtained by comparing the failure time from the proposed Monkman-Grant extension with the experimental failure time.     

基于时序参数法的BFRP蠕变行为预测

本文研究了基于时序参数法的玄武岩纤维增强复合材料(BFRP)板弯曲蠕变行为．为了提高模型理论预测的精度,文中将整个实验时长的数据进行了合理的细化分组,且每组时长尽可能相同,然后对细化分组的数据组分别进行直接外推法拟合,得到各数据组对应的拟合方程参数,最后获得了BFRP板弯曲蠕变行为的理论预测模型．对比模型预测值和实验值可以发现：模型预测值随着时间的增长,越来越接近于实验值,最后二者的相对误差几乎为零．该结果表明：文中建立的蠕变预测模型具有足够高的精度,可以应用于BFRP的蠕变行为的预测．     

岩石蠕变特性试验研究

针对大安山煤矿+550水平西二石门围岩蠕变变形严重的问题,采用室内蠕变试验与理论分析相结合的方法研究岩石蠕变特性。选取泥质粉砂岩作为软岩试样,通过自制三轴蠕变仪对所取岩样进行恒围压分级增轴压的三轴压缩蠕变试验,结果表明:随应力水平的提高,起始蠕变速率增大,进入稳态蠕变阶段用时延长,稳态蠕变速率从0h-1增大到3.12e-4·h-1,瞬时应变以线性关系增加,围压9MPa条件下的起始蠕变应力阈值为6MPa,当应力水平超过岩石长期强度时出现加速蠕变。基于蠕变试验规律,考虑起始蠕变应力阈值,将一种可用阶跃函数表示的开关元件与广义K体并联,并引入损伤元件对CVISC蠕变模型进行改进。采用1st-Opt中的Levenberg-Marquardt+通用全局优化法计算蠕变参数并进行反演。反演结果表明理论曲线与试验曲线的吻合效果较好,证明了所建模型的合理性。上述研究成果可为岩石工程的长期稳定性分析提供试验和理论依据。     

Experimental and Numerical Analysis of Initial Plasticity in P91 Steel Small Punch Creep Samples

To date, the complex behaviour of small punch creep test (SPCT) specimens has not been completely understood, making the test hard to numerically model and the data difficult to interpret. This paper presents a novel numerical model able to generate results that match the experimental findings. For the first time, pre-strained uniaxial creep test data of a P91 steel at 600 ^°C have been implemented in a conveniently modified Liu and Murakami creep damage model in order to simulate the effects of the initial localised plasticity on the subsequent creep response of a small punch creep test specimen. Finite element (FE) results, in terms of creep displacement rate and time to failure, obtained by the modified Liu and Murakami model are in good agreement with experimental small punch creep test data. The rupture times obtained by the FE calculations which make use of the non-modified creep damage model are one order of magnitude shorter than those obtained by using the modified constitutive model. Although further investigation is needed, this novel approach has confirmed that the effects of initial localised plasticity, taking place in the early stages of small punch creep test, cannot be neglected. The new results, obtained by using the modified constitutive model, show a significant improvement with respect to those obtained by a ’state of the art’ creep damage constitutive model (the Liu and Murakami constitutive model) both in terms of minimum load-line displacement rate and time to rupture. The new modelling method will potentially lead to improved capability for SPCT data interpretation.     

含水状态下油页岩非线性损伤蠕变特性研究

为研究水对油页岩蠕变规律的影响,以不同含水状态下油页岩三轴压缩蠕变实验数据为依据,对水作用下油页岩蠕变3个阶段各自的力学特征进行了分析。作者认为,在衰减蠕变和稳态蠕变阶段岩石内部损伤程度较小;当岩石处于加速蠕变阶段时,岩石内部不断产生损伤,呈现出明显非线性特征,同时水作用进一步加剧了岩石蠕变损伤程度。本文将非线性损伤演化方程引入到改进的Burgers模型中,将含水率变化引起的蠕变参数的变化引入到方程中,建立了不同含水率下油页岩非线性损伤蠕变模型。采用非线性最小二乘法反演蠕变参数,将蠕变方程计算结果与实验结果进行拟合,效果良好。     

钢-混凝土组合梁收缩徐变效应的随机分析

钢-混凝土组合梁是由混凝土板和钢梁通过剪力键连接而成的组合结构。由于混凝土的收缩徐变,将引起结构内力和应力重分布。混凝土收缩徐变具有离散性大的特点,进而导致结构长期响应表现出随机性。本文综合考虑徐变模型、收缩模型、混凝土抗压强度、混凝土弹性模量、环境湿度、钢材弹性模量、荷载以及剪力键刚度的随机性对钢-混凝土组合梁结构响应的影响。利用拉丁超立方抽样技术和基于响应面方法的蒙特卡洛抽样,研究了钢-混凝土组合梁挠度和应力时变效应的概率问题。     

海相沉积软土蠕变BP神经网络本构模型

海相沉积软土具有很强的蠕变特性,传统分级构建蠕变本构模型方法不实用,且很难真正反映岩土流变的非线性特性。为此,本文引入具有超强非线性映射和容错能力的BP神经网络模型,通过改进BP算法,根据江门软土的室内直剪蠕变试验结果,建立了海相沉积软土BP神经网络蠕变本构模型,避免了传统方法为满足试验曲线变化规律和蠕变特性而需要建立复杂的本构数学表达式。最后,利用上海地区软土蠕变实验结果对本文提出的方法进行了验证,并对BP神经网络蠕变模型在描述软土流变方面的特点进行了讨论。结果表明,本文建模方法简单,并能很好地描述软土的非线性蠕变问题。     

A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.