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.     

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.     

96.5Sn-3.5Ag 钎料合金的含非比例度的多轴时相关本构模型研究

基于96.5Sn-3.5Ag钎料合金的多轴时相关变形行为,提出了一个考虑其多轴变形特性的本构模型.在该模型背应力演化方程中,引入了非比例度对背应力演化率的影响,并提出了模型参数的确定方法.在室温下对96.5Sn-3.5Ag钎料合金进行了十字形、双三角形及椭圆形等拉扭组合非比例循环应变路径下的变形行为的本构模拟,并将预言结果与实验结果进行了比较.预言结果表明,该模型对于96.5Sn-3.5Ag钎料合金的多轴应变循环变形行为具有很好的预言能力.     

A two-surface model describing ratchetting behaviors and transient hardening under nonproportional loading

A new superposed rule of Mroz's kinematic hardening rule and Ziegler's kinematic hardening rule based on two-surface model is proposed in the paper. Some experimental results on ratchetting of 2014-T6 aluminum alloy are predicted very well under multiaxial loading. In addition the conformability of the model is discussed for transient cyclic hardening under two kinds of nonproportional cyclic loading paths, i.e. square and rhombic path. The project supported by the National Natural Science Foundation of China     

一种考虑拉伸保持效应的多轴疲劳寿命模型

通过定义考虑拉伸保载效应的CFI因子(creep-fatigue interaction factor)，将拉伸蠕变损伤和疲劳损伤进行非线性耦合. 根据断裂实验的观察，针对拉伸主 导的裂纹萌生、扩展及破坏的多轴疲劳问题，给出了一个基于临界面方法的能量型高温多轴 疲劳寿命预测模型. 所给出的模型可对不同温度、不同载荷特点、不同保载时间的多轴疲劳 寿命进行预测，模型的材料参数不依赖于温度和载荷. 并且此方法可以很方便地推广到其它 因素主导破坏的高温多轴疲劳寿命预测. 通过拟合高温合金Udimet720Li单轴带保持时间的 低循环疲劳(low cycle fatigue, LCF)寿命试验数据，得到了材料常数. 结合黏 塑性有限元分析方法，对高温双轴带保载循环载荷下Cruciform试件的寿命进行了 预测，预测结果基本落在2倍分散带内，达到工程的要求，证明了该模型的有效性.     

拉扭复合加载下循环应力应变关系的研究

以拉扭簿壁管试件为研究对象,根据多轴临界面上的应力应变特性及多轴疲劳临界面法的结果,结合单轴循环应力应变关系,研究了多轴比例与非比例加载下的循环应力应变关系,推导出多应力应变关系模型,经拉扭复合比例与非比例物载试验难证,其预测结果与实测值相符合。     

A more comprehensive method for yield locus construction for metallic alloys and composites

Conventional methods for constructing yield loci rely on the assumption that nonlinear strains are permanent strains, which is not always the case. A nickel-base alloy, SiC fiber-reinforced titanium, an aluminum alloy, and particlereinforced aluminum have been observed to violate this assumption. We present a method for constructing yield loci using a proof strain criterion for the permanent strain that relies on cyclic, proportional, probes of the yield surface. Two criteria are implemented: one for stress reversal and one for yielding. The method is demonstrated by the construction of initial and subsequent yield loci in the axial-shear stress plane using thin-walled tubular specimens. Results are presented for 6061-T6 aluminum as well as for 6092/SiC/17.5p-T6, which is 6092 aluminum reinforced with 17.5 volume percent silicon carbide particulate. The centers of the initial yield loci for the composite are eccentric to the origin of the stress plane most likely because of the residual stresses induced during processing. Material hardening due to multiaxial stress states can be described by tracking evolution of the subsequent yield surfaces and here hardening of the particulate composite was primarily kinematic     

Viscoplastic constitutive modeling with one scalar state variable

State variables have been used to represent the material resistance to plastic deformation in the recent development of the viscoplastic constitutive equations. In a previous paper, an experimental method was suggested to identify the relative roles to be played by the scalar state variable (drag stress) and the tensorial state variable (back stress) in the state-variable based constitutive equations. The results on 2618-T61 aluminum alloy tested at 200°C suggested that the scalar state variable alone should be enough to model the experimental results of 2618-T61 aluminum alloy.

In the current work, an early version of the viscoplastic constitutive equation proposed by Bodner and Partom, which was formulated with one scalar state variable, was adopted to model the experimental results of 2618-T61 aluminum. Experiments included creep tests under stepwise loadings, controlled-strain-rate tests, and creep tests under nonproportional loadings. A constitutive equation based on strain hardening approach, which was developed in an earlier work, was also studied.

In order to improve the results of the Bodner and Partom's model, a recovery term which was an explicit function of the time exposed to the test temperature was suggested for the scalar state variable. Aging was discussed as one possible softening mechanism for the current material.     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

State Equations of Unsteady Creep under Complex Loading

A mathematical model describing the unsteady creep of metals under complex loading is proposed. The results of numerical simulation of creep of St.304 steel in complex regimes of block multiaxial cyclic deformation are given. The numerical calculation results obtained are compared with the data of full-scale experiments. Creep is simulated in complex deformation processes accompanied by the rotation of main regions of stress, strain, and creep strain tensors.     

A unified constitutive law for cyclic viscoplasticity

A phenomenological constitutive model for cyclic viscoplasticity is presented within the framework of unified state variable theory. The model utilizes three distinct parameters to account for the cyclic (isotropic) hardening: drag stress, isotropic stress and rate sensitivity parameter causing the back stress to be rate-dependent. With the help of a rate-dependent format of the back stress, the constitutive model can reproduce positive, zero and negative strain rate sensitivity of the flow stress in a concise manner. The purpose of the paper is to investigate the influence of the three parameters on stress relaxation behavior and rate-dependent cyclic hardening concerned with the variation in strain rate sensitivity. The applicability of the model to monotonic and cyclic loading is validated by comparing the predictions with experiments of two stainless steels and an aluminum alloy reported in literature.     

Development of viscoplastic constitutive equation through biaxial material testing

Internal-state variables have been used to represent the deformation historyin the recently proposed viscoplastic constitutive equations. In the current study, creep tests under nonproportional loadings were used to study the relative roles played by the internal-state varaibles in the constitutive equation by tracing the strain trajectory in strain space for a given stress trajectory in stress space. An experimental approach to studying the evolution rule for the tensorial state variable is also proposed. The experimental results on 2618-T61 aluminum alloy suggest that the scalarstate variable should play a much more dominant role than the tensorial state varaible in the constitutive modeling of 2618-T61 aluminum alloy.     

Experimental study of the cyclic visco-elasto-plastic behaviour of a polyamide fibre strap

Experimental tensile tests were performed on polyamide-based (PA66) woven strap samples. A strain measuring device was used to measure the strain in the middle and effective part of the woven tensile sample. The tests were performed, on the one hand under monotonous tension at different strain rates and on the other hand under sophisticated cyclic loading histories, including relaxation and creep sequences. The analysis of experimental results was made through a visco-elasto-hysteresis model, based on the superimposition of three stress components. The proposed method allows for characterizing the steady state viscous stress as a function of strain and strain rate, the time-independent irreversible behaviour and the instantaneous modulus increasing with the strain. Based on the visco-elasto-hysteresis model, an analysis enabled us to understand and predict the change in relaxation and creep orientations during complex loading histories.     

高速列车用6008铝合金动态变形本构与损伤模型参数研究

高速列车在实际服役过程中会经受复杂的应力状态和环境条件,铝合金型材以其优良的力学和加工性能被广泛应用于新型高速列车的吸能结构,其防撞性能对高速列车的安全运行至关重要。本文针对一种新型轨道车辆用材料6008-T4铝合金型材进行了多种力学性能测试,包括动静态拉压实验、准静态高低温实验、不同应力路径的断裂实验等,提出了一种计算局部断裂应变的新方法,进而标定和获取了Johnson-Cook本构和损伤模型参数。最后利用平板侵彻实验来对所获取的参数进行检验,发现模拟和实验结果吻合良好,说明本文所获取的参数和参数标定方法都是有效的。     

Investigations into cyclic creep of materials (review)

Conclusions In this review, we analyzed the studies known to the author on cyclic creep of structural materials published since 1936. Some of the studies could not be examined but references to these studies and a brief analysis of the results can be found in [3, 54–56, 115]. The classification of these studies and interpretation of the results presented by the author and also the terminology used do not pretend to be unambiguous and universal. Slghtly different approaches to solving this problem were proposed in, for example, [7, 55, 66].It is important to continue investigations in the cyclic creep area in the following directions:generalization of the unidimensional models of cyclic creep for the multiaxial stress states;experimental examination and construction of the theory of cyclic creep for nonstationary loading conditions;examination of the development of cyclic creep in heterogeneous and anisotropic materials;development of the method of calculating the stress-strain state and endurance of structural members in the creep conditions in cyclic loading.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev, Translated from Prikladnaya Mekhanika, Vol. 23, No. 12, pp. 3–19, December, 1987.     

Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths

Some novel discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate cyclic deformation behavior of materials with low and high sensitivity to non-proportional loadings. Tubular specimens made of 1050 QT steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were used. 1050 QT steel was found to exhibit very similar behavior under various multiaxial loading paths, whereas significant effects of loading sequence were observed for 304L stainless steel. In-phase cycles with a random sequence of axial-torsion cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsion on an equivalent strain circle results in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening is lower than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Armstrong–Fredrick incremental plasticity model, and Kanazawa et al.’s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsion strain paths. Consistent results between experimental observations and predictions were obtained by employing the Tanaka’s non-proportionality parameter. In contrast, the empirical model resulted in significant over-prediction of stresses for 304L stainless steel.     

Micromechanical model of the high temperature cyclic behavior of 9–12%Cr martensitic steels

9–12%Cr quenched and tempered martensitic steels are known to soften under cyclic loadings at high temperature. The present article proposes a model based on physical mechanisms described at the scale of slip systems. This model describes explicitly the microstructural recovery (corresponding to a decrease of the dislocation density and subgrain coarsening) observed experimentally. The scale transition is carried out in the framework of self-consistent homogenization schemes. The model assumptions and its physical basis are explicitly discussed. The parameters are identified on a very limited amount of experimental data. The model turns out to give very good predictions and extrapolations for the cyclic softening effect observed in uniaxial tension–compression loadings for strain ranges larger than 0.3%. Stress–relaxation and creep behavior can also be simulated for high stresses. In addition the cyclic softening effect is reproduced for multiaxial tension–torsion loadings.     

Multiaxial constitutive model accounting for the strength-differential in Inconel 718

The nickel-base alloy Inconel 718 exhibits a strength-differential, that is, a different plastic flow behavior in uniaxial tension and uniaxial compression. A phenomenological viscoplastic model founded on thermodynamics has been extended for material behavior that deviates from classical metal plasticity by including all three stress invariants in the threshold function. The model can predict plastic flow in isotropic materials with or without a flow stress asymmetry as well as with or without pressure dependence. Viscoplastic material parameters have been fit to pure shear, uniaxial tension, and uniaxial compression experimental results at 650°°C. Threshold function material parameters have been fit to the strength-differential. Four classes of threshold functions have been considered and nonproportional loading of hollow tubes, such as shear strain followed by axial strain, has been used to select the most applicable class of threshold function for the multiaxial model as applied to Inconel 718 at 650 °C. These nonproportional load paths containing corners provide a rigorous test of a plasticity model, whether it is time-dependent or not. A J₂J₃ class model, where J₂ and J₃ are the second and third effective deviatoric stress invariants, was found to agree the best with the experimental results.     

一种考虑非比例附加损伤的多轴低周疲劳模型

在实际工作环境中,机械结构往往承受着多轴非比例循环载荷.相比多轴比例循环加载,多轴非比例循环加载由于产生了附加强化现象,造成机械结构疲劳寿命下降.通过分析薄壁圆筒管件在非比例加载工况下应力应变变化规律和发生破坏位置,本文基于临界面法提出一种考虑多轴非比例附加损伤的疲劳模型.该模型将最大剪切应变幅平面作为临界面,提出一个新的附加强化因子,结合临界面上切应变幅和正应变幅组成新的多轴疲劳损伤参量.此参量不仅考虑了非比例加载下临界面上正应变幅和切应变幅对材料造成的疲劳损伤,还考虑到应变路径的变化和材料非比例加载敏感特性对材料疲劳寿命的影响.考虑到实际情况下模型所需材料附加强化系数有时难以获得的情况,给出了材料附加强化系数的有关近似计算公式.只需要材料基本力学参数便可得到材料附加强化系数,方便工程实际应用.采用8种材料的多轴疲劳寿命数据对提出的新模型进行检验,结果表明所提出的新模型与传统多轴疲劳模型相比预测寿命精度更高.