A new visco–elasto-plastic model via time–space fractional derivative

To characterize the visco–elasto-plastic behavior of metals and alloys we propose a new constitutive equation based on a time–space fractional derivative. The rheological representative of the model can be analogous to that of the Bingham–Maxwell model, while the dashpot element and sliding friction element are replaced by the corresponding fractional elements. The model is applied to describe the constant strain rate, stress relaxation and creep tests of different metals and alloys. The results suggest that the proposed simple model can describe the main characteristics of the experimental observations. More importantly, the model can also provide more accurate predictions than the classic Bingham–Maxwell model and the Bingham–Norton model.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

正交玻璃布/环氧复合材料蠕变损伤实验研究

本文在实验基础上,研究了正交玻璃布/环氧复合材料的蠕变损伤行为。考虑到材料剪切屈服效应,对Kachanov-Rabotnov理论引入了附加项,得到了材料的损伤演化方程和蠕变表达式。实验结果表明:沿纤维方向材料的蠕变量很小,可略而不计。沿其它方向加载时,由于基体参予承载,蠕变十分明显。当剪切应力在其强度极限的45%～60%范围内时,实验数据较为稳定,和本文理论曲线吻合。     

Nonlinear creep damage constitutive model for soft rocks

In some existing nonlinear creep damage models, it may be less rigorous to directly introduce a damage variable into the creep equation when the damage variable of the viscous component is a function of time or strain. In this paper, we adopt the Kachanov creep damage rate and introduce a damage variable into a rheological differential constitutive equation to derive an analytical integral solution for the creep damage equation of the Bingham model. We also propose a new nonlinear viscous component which reflects nonlinear properties related to the axial stress of soft rock in the steady-state creep stage. Furthermore, we build an improved Nishihara model by using this new component in series with the correctional Nishihara damage model that describes the accelerating creep, and deduce the rheological constitutive relation of the improved model. Based on superposition principle, we obtain the damage creep equation for conditions of both uniaxial and triaxial compression stress, and study the method for determining the model parameters. Finally, this paper presents the laboratory test results performed on mica-quartz schist in parallel with, or vertical to the schistosity direction, and applies the improved Nishihara model to the parameter identification of mica-quartz schist. Using a comparative analysis with test data, results show that the improved model has a superior ability to reflect the creep properties of soft rock in the decelerating creep stage, the steady-state creep stage, and particularly within the accelerating creep stage, in comparison with the traditional Nishihara model.     

A micromechanics model of creep deformation in dispersion-strengthened metals

A micromechanics model, in which work-hardening caused by second-phase particles and a recovery process by diffusion of atoms were taken into account, has been proposed for explaining the creep deformation of dispersion-strengthened metals in high-temperature creep. A constitutive equation of the projection was employed to describe the whole creep curves from the onset of loading to rupture. The results of the calculations based on the present model have been compared with those of experiments on the carbon steels containing spherical cementite particles. There was a correlation between the experimental creep curves and the calculated ones. The changes in the calculated creep strain and creep rate with time have also been compared with the experimental results on carbon steels. The micromechanics model was found to be applicable to any kind of two-phase material, if the constitutive equation was appropriately chosen.     

Creep and creep recovery of cast aluminum alloys

Constant load uniaxial creep tests were performed on four aluminum alloys (designated M4032-2, 332, 332RR, and 333) at stresses of 31.5 MPa, 56.5 MPa, and 73 MPa and temperatures of 220°C and 260°C. Of the four materials, M4032-2 had the greatest resistance to creep, while 332RR alloy had the least. In addition to creep, the creep recovery phase was observed as well. It was found that, even for short loading periods, much of the time-dependent strain was not recoverable for all of the materials studied. Hardening was observed to occur in each of the alloys, resulting in a reduced creep rate on subsequent loadings. A constitutive equation for creep and recovery incorporating both stress and temperature dependence was developed for each of the alloys tested based on a viscous-viscoelastic model.     

A cyclic viscoplastic and creep damage model for lead free solder alloys

The reliability of microelectronic components under cyclic thermomechanical loading is an important problem especially for new leadfree solder alloys. To investigate the low cycle fatigue strength of solder joints, material models are required, that can describe the constitutive inelastic deformation and damage behavior of solder materials. Such models form the basis for advanced numerical analyses by the finite element method. In the present contribution an appropriate material model that combines the viscoplastic constitutive model of Chaboche-type with the damage law of A.C.F. Cocks for porous creep will be introduced. The algorithm is reported for an implementation as a user defined material subroutine into the FEM-code ABAQUS®. The necessary parameters of the material model are identified using results of miniaturized double lap-shear experiments and tensile tests for a Sn96Ag3Cu1 solder alloy at various temperatures. The comparison of experimental and numerical results shows a good agreement with respect to strain rate sensitivity, relaxation and damage behavior of the investigated solder material. Finally, some numerical applications to surface mounted microelectronic devices are presented.     

A coupled creep damage evolution model and creep life evaluation

Due to the damage accumulation during creep deformation, creep failure after a certain service time is the most important failure mode for metal structures working at high temperatures. Considering the coupled damage evolution of geometric and material’s damage, a creep life evaluation method based on continuum damage mechanics has been proposed and examined. It is found that the geometric damage evolution model can be deduced theoretically from the creep constitutive equation, while the material’s damage evolution can be assumed in the same way as that for static fatigue problems. Through solving the coupled damage evolution models, creep lives under various stress levels and temperatures can be evaluated in a unified way, just by several material constants which can be determined by some creep tests only.     

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。      

A mean-field micromechanical formulation of a nonlinear constitutive equation of a two-phase composite

In this paper, a mean-field micromechanical approach has been employed to formulate a nonlinear constitutive equation and yield conditions of a two-phase composite considering plastic and creep deformation of constituent phases. The derived constitutive equation is expressed in a piecewise linear-rate form, so it can be easily combined with common structural analyses such as a finite element analysis as well as lamination theories for typical continuous fiber-reinforced composite structures. The model has taken into account the threshold creep of constituent phases and diffusional mass transfer at the inclusion/matrix interface, which play a significant role in high-temperature deformation of short-fiber-reinforced metal matrix composites. A numerical study on anisotropy in Bauschinger effect and thermal-cycling creep of SiC whisker/Al matrix composites has been made based on the developed model.     

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.     

Multi-axial thermo-mechanical analysis of power plant components from 9–12% Cr steels at high temperature

The aim of this paper is to analyze local changes of stress and strain states in a power plant component under a transient thermal environment. A robust constitutive model is developed to describe inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature and in a multi-axial stress state. The model includes the constitutive equation for the inelastic strain rate tensor, the evolution equation for a tensor-valued state variable to reflect hardening/recovery processes and two evolution equations for two scalar-valued variables that characterize softening and damage states. The model is calibrated against experimental creep curves and verified for inelastic responses under different isothermal and non-isothermal loading paths. Steam temperature and loading profiles that correspond to an idealized start-up, holding and shut-down sequence of a power plant component are assumed. To estimate the thermal fields, transient heat transfer analysis is performed. The results are applied in the subsequent structural analysis using the developed inelastic constitutive model. The outcome is a multi-axial thermo-mechanical fatigue loop which can be used for damage assessment.     

An approach to modeling time-dependent creep and residual stress relaxation around cold worked holes in aluminium alloys at room temperature

Creep behaviour of aluminium alloys is also observed at room temperature. As a result, a relaxation occurs of deliberately introduced beneficial residual stresses around fastener holes, before the relevant structural component is subjected to exploitation. Therefore, to adequately asses the life-time of the component with cold worked holes, it is necessary to quantify this relaxation. In this paper a combined iterative approach for building a time-dependent creep constitutive model of aluminium alloys at room temperature has been developed in order to be used in finite element (FE) simulations of the cold hole working process. The approach is based on an experimental study of the change in diameters of cold worked holes through mandrel cold working method and a subsequent series of FE simulations of the cold working process and of the following creep behaviour to determine the necessary equivalent stresses in the constitutive model. The obtained creep constitutive model has been founded on the power-law model. The model parameters A, n and m have been determined on the basis of a developed by the authors algorithm. The approach has been illustrated on D16T aluminium alloy widely used in the airspace industry. The material behaviour in the plastic field has been described by the nonlinear kinematic hardening model, obtained through a uniaxial tensile test. Both constitutive models have been used in FE simulations of the cold working processes and of subsequent residual stress relaxation around the cold worked open holes due to creep at room temperature. On the base of the FE results, mathematical models describing the residual stress relaxation have been obtained. Thus, the residual stresses are adequately evaluated immediately before introducing the structural component in operation.     

Comparative study on stress–strain hysteresis response of SAC solder joints under thermal cycles

The present study attempts to evaluate the stress-strain hysteresis responses of SAC solder joints in Resistor and FleXBGA144 packages subjected to thermal cyclic loading using several constitutive models. The total deformation of the solder material consists of elastic, rate-independent plastic and rate-dependent creep components. The constitutive models discussed in this study each weighted elastic, plastic and creep deformations differently. At low stresses SAC solder alloys were found to be creep resistant, where at higher stresses, the influence of different microstructures disappears as matrix-creep dominates in this region. Thus, the proper constitutive model requires all the three ingredients of the elastic, the creep, and the time-independent plastic data for different stress levels to effectively predict the hysteresis behavior of the SAC solder alloys. The hysteresis loops predicted by constitutive models were also found in close agreement with the loops generated by FEM for the SAC solder joint subjected to thermal cycling.     

The effective stress function algorithm for pressure-dependent plasticity applied to hot isostatic pressing

An algorithm for unconditionally stable and accurate integration of elasto-viscoplastic pressure-dependent constitutive model is presented. Rate form constitutive equations of thermal-elastoviscoplastic type with compressibility take into account the changes in relative density. The algorithm computes the deviatoric and volumetric creep strains by finding the value of the effective stress which satisfies the functional relationship, the effective stress function. Thus, one non-linear scalar equation is solved to find the unknown volumetric and deviatoric components of creep strain tensor. The tangent modulus is evaluated consistent with the integration algorithm. The application of the method to the simulation of hot isostatic pressing of metal powder is shown. The paper presents the solution of the verification problem and comparison with the experimental result. © 1998 John Wiley & Sons, Ltd.     

Grain boundary precipitation strengthening in high temperature creep of Fe15Cr25Ni alloys

Grain boundary carbide precipitation gives rise to a dramatic decrease in creep rates compared with those of a single phase alloy. The high stress exponent (n=7) and creep activation energy (Q_C > Q_sd) have been found due to these intergranular carbides, indicating that they both increase creep resistance and change creep characteristics of alloys. The model present here rationalizes the observed behavior in single phase and two phase alloys with grain boundary carbides by a unified power law equation involving boundary obstacle stress. The predictions of this model are in close agreement with experimental results.     

Large strain constitutive modelling and computation for isotropic,creep elastoplastic damage solids

A three-dimensional fully coupled creep elastoplastic damage model at finite strain for isotropic non-linear material is developed. The model is based on the thermodynamics of an irreversible process and the internal state variable theory. A hyperelastic form of stress–strain constitutive relation in conjunction with the multiplicative decomposition of the deformation gradient into elastic and inelastic parts is employed. The pressure-dependent plasticity with strain hardening and the damage model with two damage internal variables are particularly considered. The rounding of stress–strain curves appearing in cycling loading is reproduced by introduction of the creep mechanism into the model. A numerical integration procedure for the coupled constitutive equations with three hierarchical phases is proposed. A consistent tangent matrix with consideration of the fully coupled effects at finite strain is derived. Numerical examples are tested to demonstrate the capability and performance of the present model at large strain.     

混凝土结构非线性徐变计算方法研究

为准确分析既有病害条件下的混凝土结构长期变形及受力行为, 该文进行了混凝土材料非线性徐变计算方法研究。以非线性弹性徐变本构理论为基础, 利用Hongnestad模型推导出材料软化系数, 提出一种新的非线性徐变本构模型, 采用初应变法进行显式迭代, 实现混凝土材料非线性徐变分析。以混凝土徐变及开裂的线性耦合假定为基础, 模拟长期持载过程中裂缝的扩展。采用ADINA用户子程序二次开发实现了相关算法, 并通过混凝土非线性徐变经典试验的对比分析, 验证了计算方法的可靠性。