Axisymmetric thermoviscoelastoplastic state of thin laminated shells made of a damageable material

A technique for the determination of the axisymmetric thermoviscoelastoplastic state of laminated thin shells made of a damageable material is developed. The technique is based on the kinematic equations of the theory of thin shells that account for transverse shear strains. The thermoviscoplastic equations, which describe the deformation of a shell element along paths of small curvature, are used as the constitutive equations. The equivalent stress that appears in the kinetic equations of damage and creep is determined from a failure criterion that accounts for the stress mode. The thermoviscoplastic deformation of a two-layer shell that models an element of a rocket engine nozzle is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 87–100, April 2008.     

On Approximate Specification of the Functionals of the Thermoviscoplastic Equations for Complex Loading Along Plane Paths

A technique is proposed for approximate specification of the functionals of the thermoviscoplastic equations for complex loading of isotropic materials along arbitrary plane paths. The lag in the vector and scalar properties of the material is taken into account. Instantaneous deformation and creep diagrams plotted in baseline experiments are used. The technique is used to analyze a specific deformation process. The calculated results agree well with experimental data     

一种高聚物银纹损伤演化的实验研究

采用光学显微技术对高聚物蠕变条件下的银纹损伤引发和演化进行了实验观测．通过对银纹面密度的测量,定义一种损伤变量,得到了聚甲基丙烯酸甲酯不同蠕变时间和不同应力水平下的银纹损伤值,并给出了一种损伤演化模型．     

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.     

动力损伤后的脆性岩石静力蠕变断裂模型研究

应力波动力扰动下脆性岩石的静力蠕变特性,对深部地下工程围岩变形的评价有重要的实践意义.动力载荷作用导致的局部细观裂纹损伤严重影响脆性岩石蠕变力学行为.基于细观裂纹扩展与应力关系模型、动力扰动损伤演化函数、静动力载荷演化路径函数与黏弹性本构模型,提出一种应力波动力扰动下脆性岩石蠕变断裂特性的宏细观力学模型.其中动力损伤通过控制岩石内部细观裂纹数量变化实现.模型描述了应力波动力扰动下岩石的应变时间演化曲线,解释了岩石动力扰动下蠕变失效特性.研究了不同应力波幅值及周期影响下的脆性岩石应变-时间关系曲线,并通过试验结果验证了模型的合理性.讨论了动力损伤变化形式,突变发生时刻,突变量的大小对岩石蠕变失效特性的影响.分析了应力波幅值、周期对岩石动态动力损伤效应以及蠕变失效特性的影响.主要研究结果:动力损伤的变化值越大,岩石蠕变失效发生时间越短.冲击载荷扰动期间,动力损伤发生的时刻及增加的形式,对动力扰动后的岩石应变及蠕变破坏时间影响很小.动力损伤变化量随应力波幅值增加、周期减小而加速增大.应力波幅值越大、周期越小,岩石发生蠕变失效时间越短.     

航空涡轮盘多轴蠕变-疲劳寿命预测及对比研究

针对几种经典和新发展的蠕变-疲劳寿命模型开展综述介绍,并建立预测航空涡轮盘在循环热-机蠕变-疲劳载荷谱下蠕变-疲劳行为的数值流程,对某型航空涡轮盘的蠕变-疲劳损伤和寿命进行预测和对比．结果表明：等效应变法与临界平面法得出的疲劳损伤差距较小,等效应变法由于数值计算简单,工程适用性更强．寿命-时间分数(TF)法由于无法考虑应力松弛效应,给出了最为保守的蠕变损伤预测,其对盘体应力三轴度引起的损伤不敏感;延性耗竭法(DE)法仅以蠕变应变率作为损伤因素,虽考虑多轴蠕变因子的影响,但是给出的蠕变损伤过小;修正应变能密度耗竭(MSEDE)法综合考虑蠕变应变与应力松弛,并且考虑多轴蠕变因子与弹性跟随效应的影响,结合疲劳损伤模型可以给出合理的蠕变、疲劳损伤比例,其预测结果更加合理．     

高温环境下纤维复合材料蠕变损伤的细观机理研究

首先利用复合材料纤维断裂单胞模型，编制蠕变损伤子程序，对单胞模型进行蠕变损伤分析。分析了纤维／基体弹性模量比对蠕变变形、蠕变损伤以及应力场的影响。从计算结果发现，蠕变损伤首先在纤维断裂尖端起始，然后沿着一定的角度向基体外围延伸，直至完全损伤，而且纤维／基体模量比对高温环境下的复合材料蠕变损伤产生很大的影响；纤维与基体的模量相差越大，复合材料越容易变形，抵抗蠕变变形的能力就越小，蠕变损伤越严重。经过对不同韧性的基体材料进行研究，发现基体韧性低的复合材料蠕变损伤明显高于高韧性基体复合材料，表明低韧性基体复合材料抵抗蠕变破坏的能力较低。     

Time to Creep Failure of Thin-Walled Cylindrical Pipes under Torsion

The time to creep failure is calculated for rectilinear thin-wall pipes subjected to pure torsion, torsion with uniaxial tension, and torsion with internal pressure. The problem is solved using the concept of equivalent stress. The equivalent stresses are found from the generalized mixed failure criterion whose form depends on the signs of the principal stresses. The criterion relates the maximum normal stress and the intensity of shear stress if the signs coincide, and the maximal shear stress and the octahedral shear stress if the signs are opposite. A technique for determining the material constants is developed. The calculated and experimental data are compared and found to be in satisfactory agreement     

Prediction of creep rupture in 2.25Cr–1Mo notched bars

This paper re-examines the creep life methodology based on the continuum damage mechanics (CDM) of the Kachanov and Rabotnov theory. Uniaxial creep and multiaxial creep rupture formulations are presented taking into account the primary creep effect. The scalar damage parameter is computed up to time-to-rupture as a function of time and stress. The methodology implemented is based on the uniaxial time-to-rupture obtained experimentally. The times-to-rupture for bars with different notches are calculated. It is demonstrated that the use of the damage parameter is vital to indicate the critical damage location where failure occurs. Results are compared to those obtained experimentally. It is shown that the primary creep inclusion has a significant effect on the damage distribution zone.     

A phenomenological model for anisotropic creep in a multipass weld metal

Creep strength of welded joints can be estimated by continuum damage mechanics. In this case constitutive equations are required for different constituents of the welded joint: the weld metal, the heat-affected zone, and the parent material. The objective of this paper is to model the anisotropic creep behavior in a weld metal produced by multipass welding. To explain the origins of anisotropic creep, a mechanical model for a binary structure composed of fine-grained and coarse-grained constituents with different creep properties is introduced. The results illustrate the basic features of the stress redistribution and damage growth in the constituents of the weld metal and agree qualitatively with experimental observations. The structural analysis of a welded joint requires a model of creep for the weld metal under multiaxial stress states. For this purpose the engineering creep theory based on the creep potential hypothesis, the flow rule, and assumption of transverse isotropy is applied. The outcome is a coordinate-free equation for secondary creep formulated in terms of the Norton–Bailey–Odqvist creep potential and three invariants of the stress tensor. The material constants are identified according to the experimental data presented in the literature.     

Failure criteria with unilateral conditions for simulation of plate perforation

Finite element analysis of plate perforation is performed using a thermoelastic–thermoviscoplastic constitutive model and two uncoupled damage criteria with unilateral conditions. The first criterion is based on continuum damage mechanics, while the second is the Cockcroft–Latham criterion. Fracture is assumed to occur at a critical damage, and crack propagation is modelled with element erosion. The identification of the material parameters is based on inverse modelling of a uniaxial tension test. The constitutive model and damage criteria are applied in explicit finite element analysis of the perforation of a 12 mm thick steel plate struck by a blunt projectile in the sub-ordinance velocity regime. The results show the importance of the unilateral conditions in obtaining accurate prediction of the adiabatic shear banding process. The two fracture criteria have comparable dependence on the stress triaxiality and the Lode parameter when the microcrack-closure parameter is set to zero in the criterion based on continuum damage mechanics, and give similar failure mode and ballistic limit in the plate perforation problem.     

Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression

A constitutive model for describing the creep and creep damage in initially isotropic materials with different properties in tension and compression has been applied to the modeling of creep deformation and creep damage growth in thin-walled shells of revolution with the branched meridian. The approach of establishing the basic equations for axisymmetrically loaded branched shells under creep deformation and creep damage conditions has been introduced. To solve the initial/boundary-value problem, the fourth-order Runge–Kutta–Merson’s method of time integration with the combination of the numerically stable Godunov’s method of discrete orthogonalization is used. The solution of the boundary value problem for the branched shell at each time instant is reduced to integration of the series of systems of ordinary differential equations describing the deformation of each branch and the shell with basic meridian. Some numerical examples are considered, and the processes of creep deformation and creep damage growth in a shell with non-branched meridian as well as in a branched shell are analyzed. The influence of the tension–compression asymmetry on the stress–strain state and damage evolution in a shell with non-branched meridian as well as in a branched shell with time are discussed.     

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.     

基于Burgers模型考虑损伤的岩石蠕变全过程研究

岩石蠕变是一个显著的非线性问题，而经典的Burgers 模型是一种线性蠕变模型，必然不能全面地描述岩石蠕变的全过程．当岩石处于高应力水平下的加速蠕变阶段，岩石内部损伤会不断产生和累积，蠕变呈现出明显的非线性特征．为了更好地描述考虑损伤的岩石蠕变全过程，本文假定加速蠕变阶段的损伤演化方程，将损伤引入到Burgers 模型中，提出了一种非线性蠕变损伤模型．然后以乔后盐矿试件蠕变实测数据为分析案例，验证模型在应用于实际工程时的准确性和适用性．最后根据Origin 软件数值拟合的结果，表明本文所提出的非线性蠕变损伤模型能很好地描述岩石蠕变全过程，模型参数取值也在合理范围之内，模型拟合曲线与实验所得数据具有较好的一致性．     

岩体结构面蠕变损伤机理研究

通过对伯格斯模型和西原模型的分析比较,选取西原模型研究岩体结构面的蠕变损伤特性。在τ0<τs情况下,由西原模型推出剪切模量的表达式,以剪切模量为变量定义损伤变量,得到结构面的损伤变量表达式。并以泥岩剪切试验为例,计算了相同正压力作用下的结构面剪切模量和损伤量。结果表明：当τ0<τs时,剪切模量、损伤量均随时间趋于稳定,且结构面蠕变的前两个阶段损伤量较小,而当τ0≥τs时,一段时间后,其损伤量开始突变;剪应力越大,其初始剪切模量越大,随时间降低越快,达到稳定蠕变阶段时降低量也相应越大;剪应力越大,结构面损伤量随时间增长越快,在达到稳定蠕变阶段时,损伤量也越大。     

Stress relaxation and creep of polymer gels in solvent under uniaxial and biaxial deformations

Stress relaxation and creep of polymer gels in solvent under various deformation modes such as uniaxial, strip-biaxial, and equibiaxial were theoretically investigated. The magnitudes of relaxed stress and the creep at equilibrium under each deformation mode were derived by a thermodynamic consideration of gel system. Combining a constitutive equation of gel with the equation of motion of polymer network, the stress and strain under each deformation mode have been formulated. The theory proposed here was applied to the rectangular gels under various deformations to calculate the stress relaxation and creep behavior of polymer networks in solvent. Two methods different in treatment of swelling under the constant strain or stress were employed for the calculation: one is based on the assumption that the swelling proceeds isotropically, and the other considers the anisotropic swelling process. The results obtained by the two methods mainly differ in the diffusion mode determining the swelling behavior. The possibility of undershoot of relative strain in load-free direction in the creep is also expected.     

Axisymmetric thermoviscoelastoplastic state of thin flexible shells with damages

The paper presents a technique to determine the axisymmetric geometrically nonlinear thermoviscoelastoplastic state of thin shells with damages. The technique is based on the geometrically nonlinear equations that incorporate transverse-shear strains. The equations of thermoelasticity that describe the deformation of the body’s element along paths of small curvature are used as equations of state. The equivalent stress in the kinetic equations of damage and creep is determined from a failure criterion that accounts for the stress mode. As an example, the geometrically nonlinear thermoviscoelastoplastic deformation of a corrugated shell is analyzed and the time to its failure is determined __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 49–60, February 2008.     

用电阻量测方法研究蠕变状态下的金属损伤

本文建议一种量测蠕变下金属损伤的方法。与其它方法相比,这个方法可用于进行在蠕变试验过程中的损伤测量,而无需使试件卸载或冷却。用此方法对试验数据进行加工就可得到在蠕变过程中的试验损伤曲线。对这些曲线的分析导致结论:材料破坏时的损伤是所加应力的递减函数。这一结论是以前所得理论结果的试验验证。     

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.     

Non-linear creep damage under one-dimensional variable tensile stress

A non-linear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Non-linear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times.