Gradient theory from the thermomechanics point of view

This work demonstrates how gradients of internal state variables can be used in a set of internal variables when the thermomechanics of internal state variables is utilised. This is done by introducing a thermal internal variable called specific dissipative entropy. The gradient term in a material model can be used to avoid localisation. A material model showing Hookean deformation and creep is evaluated. Damage affects the Hookean response. The damage evolution equation contains a Laplacian of damage being introduced to avoid localisation of damage and mesh-dependence of a finite element solution. The material model satisfies the Clausius–Duhem inequality.     

Activation theory for creep of matrix resin and carbon fibre-reinforced polymer composite

Activation theory used in metals and polymers has been used to model creep of unidirectional composite and resin matrix, using the concept of internal stress. The model fits the experimental creep curves very well for a range of materials. The results obtained for a brittle epoxy and its carbon fibre-reinforced composite with two fibre orientations are reported. The model parameters, such as internal stress, activation volume and activation energy, have been measured experimentally and compared with model-fit values, and their influence on creep is discussed. Finally, an approach to predict the creep rupture of unidirectional composites using internal stress is presented.     

复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

复合固体推进剂黏弹性微裂纹损伤本构模型

为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量。在Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式。该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载。其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程。该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致。数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力。     

Elasto-plastic stress analysis and burst strength evaluation of Al-carbon fiber/epoxy composite cylindrical laminates

This paper concentrates on the elastic–plastic stress analysis and damage evolution of the Al-carbon fiber/epoxy composite cylindrical laminates under internal pressure and thermal residual stress. Firstly, the elastic stress analysis of the composite laminates is performed by using the classical laminate theory. Secondly, the elasto-plastic stress analysis of the liner layer is further conducted by employing the power hardening theory and the Hencky equation in the plastic theory. Finally, an universal solution algorithm based on the last-ply failure criterion is proposed to explore the damage evolution and the burst strength of the composite laminates. Effects of the winding angle and number of the composite layers as well as the thermal residual stress are addressed. The calculated burst strengths are also compared with the experimental results.     

Constitutive equations of ageing polymeric materials

In a previous paper, a constitutive equation of relaxation behaviour of time-dependent chemically unstable materials has been developed by employing the irreversible thermodynamics of internal variables and Eyring's absolute reaction theory. In that paper, a theoretical expression for the effect of chemical crosslink density,v, on the relaxation rate has been developed. In this paper the creep behaviour of a network polymer undergoing a scission process has been developed. The temperature effect using the WLF equation on the coupled chemomechanical behaviour has also been incorporated into the equation.     

On the creep crack growth prediction by a local approach

Classical methods to predict crack growth in structures are generally based on fracture mechanics concepts. For high-temperature applications, where creep (monotonic or cyclic) or thermal stresses are present, such classical approaches lead to large difficulties. An alternative method is to calculate as accurately as possible the actual local behaviour including viscoplasticity and creep damage effects. The different levels of the possible “local approaches” are briefly reviewed and discussed; the case of creep crack growth is then studied in detail, through the use of viscoplastic constitutive equations including creep damage effect. Both the creep damage and the hardening of the metal are supposed to be isotropic, characterized respectively by the following scalar internal variables: the Kachanov's damage variable D and the cumulated viscoplastic strain p. The evolution equation of creep damage is a differential non-linear one with non-linear cumulative effect. The local states of different mechanical fields ((σ, , D) and their redistribution, due to damage effect, are accurately investigated and illustrated by various numerical examples. Finally the approach is applied to the creep of initially cracked CT specimen.     

Transient creep behavior of a metal matrix composite with a dilute concentration of randomly oriented spheroidal inclusions

The transient creep behavior of a metal matrix composite containing a dilute concentration of randomly oriented spheroidal inclusions is derived explicitly from the constitutive equation of the matrix. This theory can account for the influence of inclusion shape, elastic inhomogeneity between both phases, and the volume fraction of inclusions. The micro-macro transition is carried out by considering the mechanics of incremental creep, which discloses the nature of stress relaxation in the ductile matrix and the connection between the micro and macro creep strains. The transient creep curves of the composite are displayed with several inclusion shapes. Consistent with the known elastic behavior, spherical inclusions are found to provide the weakest reinforcing effect, whereas thin, circular discs possess the most effective strengthening shape. According to this theory and in line with the experimental data, the creep resistance of cobalt at 500°C can improve by more than 80% after adding a mere 5% of rutile particles into it.     

复合材料蠕变本构关系及实验测定 Ⅱ实验测定

在前一部分,本文得到复合材料蠕变的本构关系,在此基础上,本文进一步分析了复合材料蠕变本构关系的具体形式,实验测得了长纤维增强复合材料在蠕变、恢复两个阶段的应变,以用来确定本构关系中的待定参数,考虑到本构关系为复杂的非线性方程,本文提出了用离散变量和最小二乘法联合的方法确定参数,进而拟合蠕变本构关系的理论公式,分离出了蠕变过程中的弹性变形、粘弹性变形和粘塑性变形,对本构关系中的几个参函数,本文根据有限的实验数据拟合了其函数.     

复合材料蠕变本构关系及实验测定Ⅱ实验测定

在前一部分,本文得到复合材料蠕变的本构关系,在此基础上,本文进一步分析了复合材料蠕变本构关系的具体形式,实验测得了长纤维增强复合材料在蠕变、恢复两个阶段的应变,以用来确定本构关系中的待定参数,考虑到本构关系为复杂的非线性方程,本文提出了用离散变量和最小二乘法联合的方法确定参数,进而拟合蠕变本构关系的理论公式,分离出了蠕变过程中的弹性变形、粘弹性变形和粘塑性变形,对本构关系中的几个参函数,本文根据有限的实验数据拟合了其函数。      

基于微观组织演化的P91钢长时蠕变寿命预测

通过对P91耐热钢在高温长时蠕变过程中微观组织演化行为的综合考察,探讨了影响其长时蠕变寿命的主要因素,其中包括强化相(M_(23)C_6、MX)与析出相(Laves、Z相)的粗化现象以及和位错间的交互作用等。在此基础上,通过对蠕变幂率本构方程中耦合相应内应力参量,并结合Monkman-Grant方程,从微观组织演化的角度建立了P91耐热钢长时蠕变寿命预测模型。最后利用该模型对873K(600℃)时的P91耐热钢的相关蠕变寿命进行了预测,结果显示其计算数值与实验数据吻合较好,从而进一步表明基于微观组织演化的预测模型在P91耐热钢长时蠕变寿命的研究中具有重要意义。     

基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。     

几何非线性结构的徐变效应分析

主要研究了几何非线性结构的徐变效应问题。在大变形理论的基础上,给出了空间梁单元的非线性几何方程,阐述了几何非线性结构进行徐变效应分析的原理和方法,并建立了相应的平衡方程。考虑徐变效应的内力重分布的影响,得到了按施工阶段进行几何非线性结构的徐变分析的增量形式和分析步骤。最后通过与试验结果进行比较,验证了程序的正确性。     

非均匀温度场压杆蠕变屈曲分析

本文分析了受短时热冲击压杆在非均匀温度场下的蠕变屈曲问题。控制方程考虑了几何非线性以及横截面上应力分布非线性，以内力和位移为基本未知量，在空间上以样条配点法离散，而对时间以初应力法求蠕变变形。计算结果得到了蠕变屈曲破坏的典型模式。     

原位合成TiB2/ ZL109 复合材料的高温蠕变行为

采用原位合成方法制备了TiB₂ 超细颗粒增强ZL109 复合材料, 对材料进行了高温拉伸蠕变实验。实验结果表明, 复合材料在高温恒应力条件下, 表现出高的名义应力指数和高的名义蠕变激活能, 优于纯Al 和ZL109 合金, 而且比常规外加颗粒复合材料具有更好的高温蠕变性能。引入门槛应力概念, 复合材料的蠕变实验结果能够用微观结构不变模型来解释, 说明复合材料的蠕变受到基体点阵扩散的控制。复合材料的蠕变断裂行为可以用Monkman2Grant 经验公式来描述, 蠕变断裂特征为延性断裂。     

Analysis of the coupled effect of plastic damage and creep damage in nimonic 80A at finite deformation

The coupled effect and the anisotropic feature of plastic damage and creep damage in Nimonic 80A are analysed with special emphasis on the finite deformation and the material spin of the damaged material. In view of that both the plastic and the creep damage are governed by the formation of grain boundary cavities, it is first assumed that the states of plastic damage and creep damage are represented in terms of symmetric second-rank damage tensors Ω^P and Ω^C, the sum of these tensors Ω = Ω^P + Ω^C represents the damage state of the material. The evolution equations of these variables are established on the basis of the experimental observations on the nucleation and growth of microscopic cavities. The creep constitutive equation of the material, on the other hand, is formulated by taking account of the acceleration due to material damage as well as the material softening caused by the formation of the dislocation network at particle interfaces. Finally, creep damage process at finite deformation of Nimonic 80A at 750°C subjected to prior plastic damage brought about by the plastic prestrain at room temperature is analysed. The numerical results are compared with the corresponding experimental results to discuss the validity of the proposed theory. Though considerable rotation of principal damage direction was observed in the process of torsional creep, its effect on the creep damage process was found to be rather small.     

On the Prediction of Creep Damage by Bending of Thin-Walled Structures

Analysis of thin-walled structures operating at elevated temperaturesneeds a consideration of time-dependent creep-damage behaviour. Within theframework of the creep theory and the CDM the irreversible deformations ofthe structural elements can be described by constitutive equations withinternal state variables. The paper deals with an application ofphysically based creep-damage constitutive model with two damageparameters, proposed by Hayhurst, to the stress analysis of thin-walledplates and shallow shells. The governing equations of the shell theory areformulated by the consideration of geometrical nonlinearities associatedwith time-dependent finite deflections. Numerical examples show aninfluence of the finite deflections on the life-time predictions in platesas well as illustrate a dependence of damage evolution on the stress statemode. The results for creep damage evolution in plates are compared withresults based on the classical Kachanov–Rabotnov creep-damageconstitutive model.