An anisotropic creep damage model for multiaxial cyclic loading histories

The purpose of this study is the development of an anisotropic creep damage theory within the continuum damage mechanics, applicable to creep-dominated cyclic loading histories. A damage distribution is expressd in rate form as a symmetric tensor of rank necessary to match physically measured damage. A theoretical model which expresses general anisotropic creep damage phenomena with power law cavity growth is proposed. The coupling of damage with a bounding surface cyclic viscoplasticity theory is also accomplished. Comparison with experimental results are made for weakly anisotropically damaging materials, type 304 stainless steel at 593°C. Good correlation of rupture time, secondary creep, and tertiary creep has been obtained for proportional and nonproportional, isothermal, constant isochronous nominal stress loading histories. A modification of the isochronous stress (the set of stress state which have a same rupture time) for compressive hydrostatic stress state has been offered.     

Second-order continuity tensor and stiffness degradation of aluminum alloy 2024T3 under large strain at room temperature

A symmetric second-order continuity tensor is proposed to characterize anisotropic damage of anisotropic materials based on the hypothesis of equivalent elastic strain energy. On the basis of the equivalent elastic strain energy hypothesis, the relation between the effective elastic properties and the continuity tensor has been formulated. The current formulation does not require the assumption that the principal coordinate system of damage must coincide with that of the material. In a two-dimensional damage analysis, the state of damage can be represented by a Mohr’s circle of continuity. The proposed damage characterization technique has been successfully applied to an example case, where aluminum alloy 2024T3 specimens were strain-damaged by uni-axial tension. The experimental results show that the effects of strain damage can cause degradation of the material stiffness. On the other hand, the overall elastic orthotropy of the material does not increase with the degree of damage. The proposed continuity tensor has been found to be capable of describing this phenomenon. The principal values and the principal directions of the continuity tensor have been determined. The mean value of the principal values can represent the magnitude of the damage, while the principal direction of the continuity tensor may provide information about the damage mechanism.     

On constructing an explicit algebraic stress model without wall-damping function

In the present study, an explicit algebraic stress model is shown to be the exact tensor representation of algebraic stress model by directly solving a set of algebraic equations without resort to tensor representation theory. This repeals the constraints on the Reynolds stress, which are based on the principle of material frame indifference and positive semi-definiteness. An a priori test of the explicit algebraic stress model is carried out by using the DNS database for a fully developed channel flow at Re_δ=135. It is confirmed that two-point correlation function between the velocity fluctuation and the Laplacians of the pressure-gradient i s anisotropic and asymmetric in the wall-normal direction. Thus, a novel composite algebraic Reynolds stress model is proposed and applied to the channel flow calculation, which incorporates non-local effect in the algebraic framework to predict near-wall behavior correctly.     

Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The material's strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.     

Finite element study for determination of material’s creep parameters from small punch test

Compared with the conventional tensile creep test, it is much more difficult to obtain the creep properties of a material by the small punch creep test due to the complex deformation response and stress distribution in the miniature specimen of the material. Although creep behavior has been investigated by the small punch test, most studies have been limited to a specimen geometry and therefore, cannot be extended to other conditions conveniently. In this study, a new developed analysis routine is presented to derive the creep parameters of a material using data obtained from the small punch creep test. With the aid of the finite element method, the displacement and the displacement rate of the small punch are obtained for different load levels. The relationship between the stress and creep strain of the specimen and the applied load and the punch displacement is obtained by a dimensional analysis and the membrane stretching model. The creep properties obtained from small punch tests and the conventional creep tests are also compared. The values of the creep properties between the two types of tests agree well with each other within an acceptable accuracy range. This indicates that it is possible to obtain the creep parameters of a material from the small punch creep test instead of the conventional creep test by the analysis routines proposed in this study. Some suggestions for data reduction of the small punch creep tests are also presented to obtain more accurate material creep parameters.     

An alternative definition of the reference temperature to estimate the creep deformation of a thermally loaded tube

The reference concept is applied to the creep deformation of an axially loaded tube subjected to a two-dimensional temperature distribution. First the analytical method given in the literature for the determination of the reference stress is extended, resulting directly in expressions for both the reference stress and the reference temperature. Since these expressions can be solved only with a considerable amount of computation, an alternative definition of the reference values is suggested, which is rather simple in application. A further advantage of the new method is that the creep rate resulting from a uniaxial, isothermal creep test at its reference values can be transfered directly to the structure. The prediction of creep rate is in a good agreement with the steady state solution which is shown for various types of temperature fields. The absolute magnitude of error may be somewhat larger for the new method compared to the old one. But even if an unfavourable combination of material constants is used, this disadvantage is not serious since the errors do not surpass the scatter of experimental data usually obtained in creep tests. Regarding the tendency to overestimate or underestimate the creep rate, it cannot be decided in general whether the new or the old definition provides the better prediction, since the error is a complex function of the temperature field applied.     

A novel evolutionary algorithm for determining unified creep damage constitutive equations

The determination of material constants within unified creep damage constitutive equations from experimental data can be formulated as a problem of finding the global minimum of a well defined objective function. However, such an objective function is usually complex, non-convex and non-differentiable. It is difficult to be optimised by classical gradient-based methods. In this paper, the difficulties in the optimisation are firstly identified. Two different objective functions are proposed, analysed and compared. Then three evolutionary programming algorithms are introduced to solve the global optimisation problem. The evolutionary algorithms are particularly good at dealing with problems which are complex, multi-modal and non-differentiable. The results of the study shows that the evolutionary algorithms are ideally suited to the problem. Computational results of using the algorithms to determine the material constants in a set of physically based creep damage constitutive equations from experimental data for an aluminium alloy are presented in the paper to show the effectiveness and efficiency of the three evolutionary algorithms.     

基于损伤力学的Cr25Ni35Nb炉管材料蠕变损伤有限元分析

基于修正的Kachanov—Rabotnov本构方程,编制了用于计算管单元的用户子程序,并且与ABAQUS有限元分析软件耦合。通过拟合不同温度和不同应力下的Cr25Ni35Nb钢炉管材料蠕变试验数据,得到了蠕变损伤力学本构方程中的材料参数,对炉管运行10万h后的蠕变损伤进行数值模拟,得到了整体损伤分布与最大损伤部位。     

Transient creep analysis of ball indentation

The effect of transient creep on the indentation behaviour of a creeping solid has been investigated for a strain hardening primary creep law. Numerical analyses have been performed to obtain the full field solution for a frictionless ball indenter. The functional form of the relationship between the uniaxial response of the solid and the indentation behaviour of the material is explored. The implications of the results are discussed with regard to displacement- and load- controlled indentation creep tests, and the time hardening creep law. Experiments on primary creep indentation of lead support the indentation theory.     

Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells

Based on the three-dimensional fundamental equations of anisotropic elasticity, a state equation with variable coefficients is derived in a unified matrix form. The free vibration of simply supported, fluid-filled cylindrically orthotropic functionally graded cylindrical shells with arbitrary thickness is then investigated. A laminate approximate model is employed which is suitable for an arbitrary variation of material constants along the radial direction. Numerical examples are presented and compared with existing results. The effects of related parameters on natural frequencies are discussed finally.     

Representation of uniaxial creep curves using continuum damage mechanics

A methodology has been developed for the numerical determination of the material constants in the uniaxial creep constitutive equations based on continuum damage mechanics. The method developed overcomes former problems with convergence, and is based on a normalization technique. Temperature variation is included in the model.An algorithm for the digitization of continuous creep curves has been developed that enables a true representation of uniaxial creep behaviour using only 20 data points. Consequently large amounts of data covering many tests may therefore be stored in data bases, and, the method leads to short CPU times for fitting the material model.The algorithm for digitization and the constant determination methods have been applied to data for alloy 800H at 850°C; and, to at 550°C. For both materials good comparisons have been obtained between experimental and predicted uniaxial creep behaviour. The material model has been shown to be suitable for large strain behaviour.Uniaxial creep tests have been carried out on grade 1 cast copper nominal composition 99.99% Cu, 0.005% O₂, B.S. 1035–1037 at 150, 250 and 500°C, and an anisothermal continuum damage mechanics creep model developed for the temperature range 150–500°C. Model predictions are in good agreement with test results.     

Formability evaluation of friction stir welded 6111-T4 sheet with respect to joining material direction

In order to evaluate the formability of friction stir welded (FSW) automotive TWB (tailor-welded blank) sheets with respect to base material direction, the aluminum alloy 6111-T4 sheet was joined with three different types of combination: RD||RD, TD||RD, TD||TD (Here, RD and TD mean the rolling direction and transverse direction, respectively). Formability performance was experimentally and numerically studied in three applications including the simple tension tests, hemisphere dome stretching and cylindrical cup drawing tests. For numerical simulations, the non-quadratic orthogonal anisotropic yield function, Yld2004-18p and the isotropic hardening law were implemented into the material constitutive model. As for the failure criterion, the forming limit diagram (FLD) was utilized to determine the failure strain.     

The effect of ‘material ratchetting’ on the incremental growth of beams subjected to steady axial loads and cyclic bending

An elastic-plastic material behaviour model capable of predicting material ratchetting, cyclic relaxation and cyclic hardening has been incorporated into finite element programs. The resulting programs have been used to predict the behaviour of beams subjected to the steady axial loads and cyclic bending. The results are compared with experimental data obtained from three tests performed on beams made from a model material. Overall, the predictions were found to be good; discrepancies in the results for the most highly loaded beam were attributed to creep effects in the experiment.The results indicate that an elastic-perfectly plastic material behaviour model, with an equivalent yield stress, does not allow acceptable prediction of the beam behaviour to be obtained.     

拉深筋对板材变形特征和力学性能的影响研究

采用实验方法将金属板材拉过不同尺寸的拉深筋镶块,分析了拉深筋高度、圆角半径以及过筋次数对板材变形特征的影响规律,研究了过筋产生的预应变对板材后续力学性能的影响规律。结果表明：板材流过拉深筋后,流动方向上发生均匀的拉伸变形;过筋产生的预应变随着拉深筋高度增大而增大,随着圆角半径增大而减小,随着过筋次数增加而近似线性增大;预应变越大,材料后续屈服强度和抗拉强度越高,但后续延伸率越小,总延伸率随着预应变增大表现出先减小后增大的趋势。     

助基于磁梯度张量的金属磁记忆检测方法

金属磁记忆是对铁磁材料早期微观损伤及应力集中进行无损检测的有效方法。为提高磁记忆检测的可靠性,充分利用磁记忆信号的矢量信息,将磁梯度张量测量及分析方法引入磁记忆检测中。根据张量缩并分析理论得到了磁记忆信号的磁梯度张量模量,通过求解梯度局部相位的一阶导数得到信号的梯度局部波数,然后分析信号的磁梯度张量模量和梯度局部波数分布特征,得到磁梯度模量和梯度局部波数极值点分别与应力集中边界和中心位置的对应关系。实验结果表明：磁梯度张量方法能够克服检测方向与缺陷夹角变化对测量信号的影响,准确地对应力集中进行判断。     

Multi-axial creep rupture of a model structure using a two parameter material model

A simplified, two parameter creep curve model is developed, which represents primary-secondary-tertiary creep behaviour. The two parameters are related via the secondary strain respectively to: the sum of secondary and primary strains; and, the sum of secondary and tertiary strains. Techniques are described for fitting the model to laboratory data; and, for the determination of the parameters which characterize primary-secondary and secondary-tertiary creep. The single state variable theory used to describe tertiary creep is compared with mechanisms based models and shown to closely predict the effect of stress-state on rupture strain. A two bar plane strain model component subjected to steady load is studied and used to determine the effect on the component lifetime of primary creep; and, of the multi-axial creep rupture criterion. The representative rupture stress is found to be weakly dependent on primary creep and strongly dependent on the multi-axial rupture criterion of the material.     

Using the model of a mixture of a uniform distribution and a von Mises distribution for segmentation of anisotropic images

An algorithm is proposed for segmenting anisotropic image based on estimates of the local orientation of textures obtained using a gradient structural tensor. A mixture of a uniform distribution and a von Mises distribution is used as the estimate model. An estimation algorithm for the unknown parameters of the mixture based on trigonometric moments is obtained. Examples are given demonstrating the effectiveness of the segmentation algorithm in identifying textures with one dominant direction.     

Effects of hydrostatic pressure and material anisotropy on the transient creep of thick-walled tubes

Effects of hydrostatic pressure and material anisotropy on the transient creep of pressurized thick-walled tubes are discussed. Constitutive equations which include these factors are formulated first of all so that the creep of a thick-walled tube of 0.19% carbon steel at 450°C is analysed by means of them. Strain-hardening and time-hardening hypotheses are employed. The results of the analyses are compared with those of the von Mises and Tresca-type theories together with corresponding experimental results hitherto reported. Material anisotropy of 10 per cent as between creep rates in the axial and circumferential direction is found insufficient to account for the deviations of the analytical results due to the von Mises or Tresca-type theory from the experimental ones. The effect of hydrostatic pressure is also found not to have a significant influence on the present problem. The validity of the assumption of vanishing axial strain which has been employed in preceding papers is also examined.