CDM predictions of creep damage initiation and growth in ferritic steel weldments in a medium-bore branched pipe under constant pressure at 590° C using a four-material weld model

The paper reports the use of three-dimensional creep continuum damage mechanics techniques to study the creep failure of a medium-bore low-alloy ferritic-steel cylinder–cylinder branched pressure vessel welded connection, tested at a constant pressure of 4 MPa, at a uniform temperature of 590°C. The development of computational techniques is reported to analyse this problem with a four-material model of the welded connection which includes: parent, type IV, heat-affected zone (HAZ) and weld materials. The results of analyses are presented for two sets of creep damage constitutive equations. For both equation sets, lifetimes are conservatively, yet accurately predicted; however, the results of metallographic examinations of a tested vessel are not accurately predicted. To overcome this deficiency further analyses of the vessel are recommended which include: a coarse-grained HAZ (CGHAZ), adjacent to the weld material; and, more-refined finite element modelling.     

On a finite-strain viscoplastic law coupled with anisotropic damage: theoretical formulations and numerical applications

Based on a dissipation inequality at finite strains and the effective stress concept, a Chaboche-type infinitesimal viscoplastic theory is extended to finite-strain cases coupled with anisotropic damage. The anisotropic damage is described by a rank-two symmetric tensor. The constitutive law is formulated in the corotational material coordinate system. Thus, the evolution equations of all internal variables can be expressed in terms of their material time derivatives. The numerical algorithm for implementing the material model in a finite element programme is also formulated, and several numerical examples are shown. Comparing the numerical simulations with experimental observations indicates that the present material model can describe well the primary, secondary and tertiary creep. It can also predict the anisotropic damage modes observed in experiments correctly.     

Approximate creep rupture lifetimes for butt welded ferritic steel pressurised pipes

The creep rupture of butt welded ferritic steel pipes composed of a range of weld and heat affected zone materials has been previously analysed in detail (Leckie and Hayhurst, 1994). These analyses required substantial computational resources which cannot be justified during the preliminary phases of the design process. To reduce cost and improve speed an approximate method for the analysis of kinematically determinate structures, known as the modal method (Leckie and Hayhurst, 1974), has been developed to compute creep rupture lifetimes. This paper reports an extension of the method for the analysis of multi-material structures, such as weldments, and its implementation as a post processor to a stationary state finite element creep analysis. Histories of stress and damage have been determined using the modal method for weldments with a range of heat affected zone and weld material combinations. The lifetimes determined in this way are compared with those determined using complete continuum damage mechanics analyses, and are shown to be conservative; in addition the regions of intense damage have been shown to be accurately predicted. The modal method is also shown to be superior to more approximate reference stress methods.     

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.     

An anisotropic fibre-network model for mechano-sorptive creep in paper

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.     

Mechano-sorptive creep under compressive loading – A micromechanical model

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. It has also been observed that the mechano-sorptive effects are larger in compression than in tension. In this paper a simplified network model for mechano-sorptive creep is presented. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre–fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys constitutive laws that are non-linear in stress. Geometrical fibre effects are included in the model in order to capture experimental observations of the differences between paper loaded in tension and compression. Theoretical predictions based on the developed model are compared to experimental results for paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model, i.e. the creep is accelerated by the moisture cycling and the mechano-sorptive effects are larger in compression than in tension.     

Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part I – Material properties

In order to evaluate the macroscopic performance of friction stir welded automotive tailor-welded blank (TWB) sheets, the hardening behavior, anisotropic yielding properties and forming limit diagram were characterized both for base (material) and weld zones. In order to describe the Bauschinger and transient hardening behaviors as well as permanent softening during reverse loading, the modified Chaboche type combined isotropic–kinematic hardening law was applied. As for anisotropic yielding, the non-quadratic anisotropic yield function, Yld2000-2d, was utilized for base material zones, while isotropy was assumed for weld zones for simplicity. As for weld zones, hardening properties were obtained using the rule of mixture and selectively by direct measurement using sub-sized specimens. Forming limit diagrams were measured for base materials but calculated for weld zones based on Hill’s bifurcation and M–K theories. In this work, four automotive sheets were considered: aluminum alloy 6111-T4, 5083-H18, 5083-O and dual-phase steel DP590 sheets, each having one or two thicknesses. Base sheets with the same and different thicknesses were friction-stir welded for tailor-welded blank (TWB) samples.     

两种热处理钢轨焊接接头冲击磨损与损伤性能研究

研究了过共析钢轨焊接接头淬火和正火后不同区域的硬度与微观组织,利用冲击磨损试验机对不同区域进行冲击试验,分析了各区域冲击磨损与损伤特性. 结果表明:钢轨焊接接头分为母材区、焊缝区和热影响区. 母材区微观组织为片层状珠光体,焊缝区为珠光体与先共析铁素体且正火后铁素体含量较多,热影响区淬火后为粒状珠光体而正火后存在少量片层状珠光体. 焊接接头不同区域硬度大小为母材区>淬火焊缝区>正火焊缝区>正火热影响区>淬火热影响区. 硬度越低的区域,冲击深度和磨损体积越大. 母材区冲击损伤轻微,表面呈轻微剥落;焊缝区损伤较严重,出现明显裂纹且正火后损伤较淬火后严重;热影响区损伤最为严重且正火后损伤较淬火后略轻微.      

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。     

High temperature fracture parameter for a weld interface crack

A fracture parameter is introduced to characterize crack growth at elevated temperature for a weld interface crack. Finite element analyses are made for a compact tension (CT) specimen under constant load where an interface is modeled along the crack plane to simulate the dividing line of the weld metal (WM) and base metal (BM). A constitutive relation for an elastic-creeping material is used. The proposed time dependent fracture parameter is obtained for different creep constants of WM and BM. A transition time and fracture parameter for the homogeneous and welded specimens are defined such that the results can be normalized and presented in a general form for assessing the crack growth life.     

基于多因素的焊接结构疲劳裂纹扩展速率分析

以Donahue等提出的疲劳裂纹扩展速率计算模型为基础,通过引入形状系数、张开比和残余应力等参数,建立了适用于焊接结构的疲劳裂纹扩展速率计算模型,分析了多种因素对焊接结构疲劳裂纹扩展速率的影响规律。结果表明,焊板厚度和焊缝余高的变化均会对焊接结构疲劳裂纹的扩展速率产生影响,在对焊接结构表面形状进行设计时应保有一定的焊缝余高;有效应力比的增大会降低焊接结构疲劳裂纹的扩展速率,且裂纹深度的变化不会改变有效应力比对焊接结构疲劳裂纹扩展速率的影响;残余应力的增大会提高焊接结构疲劳裂纹的扩展速率,且残余应力对疲劳裂纹扩展速率的促进作用随着裂纹深度的增加而增大,在对焊接结构的疲劳性能进行设计时须考虑残余应力对结构性能的影响。     

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.     

焊接接头低周疲劳裂纹扩展的统计分析与可靠性最弱环模型

在相同的试验条件下,对１６ＭｎＲ压力容器用钢焊接接头焊缝区、热影响区和母材区,分别做了１５ 根试样的低周疲劳试验,获得了三个区的低周疲劳寿命分布与裂纹扩展规律。试验表明,Ｐａｒｉｓ公式中的两个参数ｍ 和ｃ 分别服从正态分布和对数正态分布,ｍ 和ｌｏｇ ｃ 呈现统计线性关系。根据文中的统计结果,采用蒙特卡洛法对给定的两个裂纹长度间的扩展寿命进行了预测,预测结果与试验结果符合良好。文中还对焊接接头三个区的低周疲劳寿命进行了统计分析,获得了相应的概率密度函数,初步提出了整个焊接接头的可靠性最弱环模型。     

Creep damage and life analysis of anisotropic materials

Summary  This paper provides a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries in such a way so that damage accumulation occurs. The paper is divided into three parts. Firstly, the damage state in a uniaxial tension specimen is discussed and the time to rupture calculated. The second part is concerned with the creep behaviour of materials in multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure's orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material, which is in a state of multiaxial stress, can only be described in a tensorial form. Thus, tensorial constitutive and evolution equations have been developed. Some examples for practical use are discussed. Finally, some own experiments are mentioned which have been carried out in order to validate the mathematical modelling. Received 16 July 1999; accepted for publication 8 March 2000     

Characterization of mechanical properties by indentation tests and FE analysis – validation by application to a weld zone of DP590 steel

In this work, the mechanical properties of the metal active gas (MAG) weld zone and heat affected zone (HAZ) were characterized utilizing the continuous indentation method together with its finite element (FEM) analysis. To verify the measured properties, uni-axial tension and three point bending tests were performed for DP590 welded specimens. For numerical simulations, the isotropic hardening law was assumed along with the non-quadratic anisotropic yield function, Yld2000-2d. As for the failure criterion of the base material and weld zones particularly for the failure evaluation in the uni-axial tension test, Hill’s bifurcation theory and the M–K theory were applied to calculate the forming limit diagrams considering all measured properties including strain-rate sensitivity.     

The investigation of the metal damage at the creep by the method of electrical resistance measuring

In this paper the method of damage measurement of metal structure at the creep is proposed. In contrast to other methods, it allows the measurement of this damage to be carried out in the process of creep test without unloading and cooling of specimens. Experimental damage curves during creep are obtained as a result of test data processing by the suggested method. The analysis of these curves leads to a conclusion that the material damage at repture is monotonically decreasing function of the applied stress. This conclusion is an experimental verification of the theoretical result, obtained earlier. Visiting scholar (1988–1989) at South China University of Technology     

Theory of creep deformation with kinematic hardening for materials with different properties in tension and compression

A constitutive model for creep deformation that describes the loading-history-dependent behavior of initially isotropic materials with different properties in tension and compression under stress vector rotations limited by 50–60° is presented within a thermodynamic framework. In the proposed constitutive model a kinematic hardening rule is adopted. This model also introduces an effective equivalent stress in the creep potential that is based on the first and second invariants of the effective stress tensor, and on the joint invariant of the effective stress tensor and eigenvector associated with the maximum principal Cauchy stress. The formulation of the kinematic hardening rule is presented and discussed. All the material parameters in the model have been obtained from a series of proposed basic experiments with constant stresses. These model parameters are then used to predict the creep deformation of the aluminum alloy under multiaxial loading with constant stresses, and under non-proportional uniaxial and non-proportional multiaxial loadings for both isothermal and nonisothermal processes.     

焊接接头局部塑性行为的循环压痕实验研究

基于纳米压痕技术,对转子钢焊接接头不同区域（母材、焊缝和热影响区）开展了压入位移控制的单向压痕实验和压入载荷控制的循环压痕实验研究．首先,通过压入位移控制的单向压痕实验,采用多次测试取平均值的方式获得了焊接接头各个区域的弹性模量和硬度分布特征,同时对各区域弹性模量中值点的载荷-压入深度曲线进行了分析;其次,对各个区域进行压入载荷控制的循环压痕实验,比较其压入深度随循环周次的演化特征．结果表明,焊接接头不同区域力学性能差异较大,热影响区的弹性模量、硬度、抗拉强度和抗循环变形能力最高,焊缝次之,母材最弱;三个区域在循环压痕载荷下的接触载荷-压入深度滞回环曲线均表现出类似棘轮变形的演化特征,且母材演化速度高于焊缝,高于热影响区．研究结果对汽轮机焊接转子的焊接工艺的优化、寿命预测和可靠性设计具有重要的借鉴意义．     

Orthotropic elastic–plastic material model for paper materials

Paper and paperboard generally exhibit anisotropic and non-linear mechanical material behaviour. In this work, the development of an orthotropic elastic–plastic constitutive model, suitable for modelling of the material behaviour of paper is presented. The anisotropic material behaviour is introduced into the model by orthotropic elasticity and an isotropic plasticity equivalent transformation tensor. A parabolic stress–strain relation is adopted to describe the hardening of the material. The experimental and numerical procedures for evaluation of the required material parameters for the model are described. Uniaxial tensile testing in three different inplane material directions provides the calibration of the material parameters under plane stress conditions. The numerical implementation of the material model is presented and the model is shown to perform well in agreement with experimentally observed mechanical behaviour of paper.