Creep mechanism and creep constitutive model of aluminum silicate short-fiber-reinforced magnesium matrix composite

By the constant stress tensile creep test method, creep tests were performed on aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite with volume fraction of 30% and its matrix alloy AZ91D under different temperatures and stresses. The results indicate that the composite and the matrix have the same true stress exponent and true activation energy for creep, which are 3 and 144.63 kJ/mol, respectively. The creep of the composite is controlled by the creep of its matrix, which is mainly the controlling of viscous slip of dislocation, and the controlling of grain boundary slippage as a supplement. The creep constitutive model obtained from the experiment data can well describe the creep deformation pattern of the composite.

Constitutive modeling and springback simulation for 2524 aluminum alloy in creep age forming

The constitutive modeling and springback simulation for AA2524 sheet in creep age forming（CAF） process were presented.A series of creep aging tests were performed on AA2524 at the temperature of 180-200 °C and under the stress of 140-210 MPa for 16 h.Based on these experimental data,material constitutive equations which can well characterize creep aging behaviors of the tested alloy were developed.The effect of interior stress distributed along the sheet thickness on springback was simulated using FE software MSC.MARC by compiling the established constitutive models into the user subroutine.The simulation results showed that the amount of sheet springback was 61.12% when merely considering tensile stress existing along the sheet thickness;while sheet springback was up to 65.93% when taking both tensile and compressive stresses into account.In addition,an AA2524 rectangular sheet was subjected to CAF experiment in resistance furnace.The springback value of the formed rectangular sheet was 68.2%,which was much closer to 65.93%.This confirms that both tensile and compressive stresses across the sheet thickness should be considered in accurately predicting springback of the sheet after forming,which can be more consistent with experimental results.

An anisotropic constitutive model of geomaterials based on true triaxial testing and its application

Series of testing on coarse grained soils were carried out with a true triaxial testing apparatus. The loads were applied from the major principal and minor principal directions, respectively, to simulate the construction and water impounding process of a rock fill dam. The stress and strain relationships induced by the different loading methods were investigated. A remarkable stress-induced anisotropy under complex stress state was observed. Contrary to popular assumptions in traditional numerical analysis and constitutive models, it was found that different elastic modulus and Poisson ratio exist in different principal directions in rock fill dams. From the testing results, an anisotropic constitutive model based on Duncan-Chang nonlinear model is presented to overcome the limitations of axi-symmetric assumptions in conventional triaxial experiments and constitutive models. Both models were then applied in FEM analysis of an under-construction earth core high rock soil filled dam with the focus on hydraulic fracturing. The study reveals the major biases that exist when numerical analysis and constitutive models do not give serious consideration to the intermediate principal stress and anisotropy effects in soil rock built structures.

Consistent constitutive modeling of metallic target penetration using empirical, analytical, and numerical penetration models

Historically, there has been little correlation between the material properties used in(1) empirical formulae,(2) analytical formulations, and(3) numerical models. The various regressions and models may each provide excellent agreement for the depth of penetration into semi-infinite targets. But the input parameters for the empirically based procedures may have little in common with either the analytical model or the numerical model. This paper builds on previous work by Riegel and Anderson(2014) to show how the Effective Flow Stress(EFS) strength model, based on empirical data, can be used as the average flow stress in the analytical Walker–Anderson Penetration model(WAPEN)(Anderson and Walker,1991) and how the same value may be utilized as an effective von Mises yield strength in numerical hydrocode simulations to predict the depth of penetration for eroding projectiles at impact velocities in the mechanical response regime of the materials. The method has the benefit of allowing the three techniques(empirical, analytical, and numerical) to work in tandem. The empirical method can be used for many shot line calculations, but more advanced analytical or numerical models can be employed when necessary to address specific geometries such as edge effects or layering that are not treated by the simpler methods. Developing complete constitutive relationships for a material can be costly. If the only concern is depth of penetration, such a level of detail may not be required. The effective flow stress can be determined from a small set of depth of penetration experiments in many cases, especially for long penetrators such as the L/D = 10 ones considered here, making it a very practical approach. In the process of performing this effort, the authors considered numerical simulations by other researchers based on the same set of experimental data that the authors used for their empirical and analytical assessment. The goals were to establish a baseline with a full constitutive model and to determine if the EFS could be estimated from a standardized constitutive model. We were unable to accomplish this.Several papers detailing simulations using the Johnson–Cook(JC) constitutive model were located and used as a basis for comparison. The authors were somewhat surprised to find that the JC parameters employed in those studies were not actually developed for the target materials that were evaluated experimentally. More disconcerting was the fact that a number of different sets of JC parameters were published for presumably the same material. Although not intended to be a critique of the JC model, this research raises a serious concern regarding the manner in which the model has been applied to terminal ballistics problems. The details of the study are included in this paper because the authors believe it helps put the discussion of EFS into proper context.

Constitutive model depending upon temperature and strain rate of carbon constructional quality steels

The basic factors relating to the rheological stress in the constitutive equations were introduced.Carbon constructional quality steels were regarded as a kind of elastic-viscoplastic materials under high temperature and the elastic-viscoplastic constitutive models were summarized.A series of tension experiments under the same temperature and different strain rates,and the same strain rate and different temperatures were done on 20 steel,35 steel and 45 steel.52 groups of rheological stress-strain curves were obtained.The experimental results were analyzed theoretically.The rheological stress constitutive models of carbon steels were built combining the strong points of the Perzyna model and Johnson-Cook model.Comparing the calculation results conducted from the model with the experiment results,the results proves that the model can reflect the temperature effect and strain rate effect of carbon constructional quality steels better.

Constitutive model for thin sheet metal with one or several grains across thickness in micro-forming

Effects of four factors on thin sheet metal flow stress were considered, including grain size d, thickness t, grain number across thickness （t/d ratio） and surface property. Surface model was adopted to quantitatively describe the effect of t/d ratio on flow stress for pure copper. It is predicted that when t/d ratio is larger than a critical value, effect of t/d ratio on flow stress can be neglected. Existence of critical t/d ratio changes the Hall-Petch relationship and evolution of flow stress with thickness. A criterion was proposed to determine critical t/d ratio. Then a comprehensive constitutive model was developed to consider all the four factors, with parameters determined by fitting experimental data of high purity Ni. The predicted results show the same tendencies with experiment results. Particularly when t/d ratio decreases, Hall-Petch relationship and evolution of true stress show varied slopes with two transition points.

A STUDY OF B-P UNIFIED VISCOPLASTIC CONSTITUTIVE MODEL

By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this paper, and it's the first time that this materialmodel is used in a kind of engineering software-MARC. Thermal viscoplastic behavior of hightemperature alloy GH536 specimen with gap is analyzed by this program. The research results show itis feasible to analyze thermal viscoplastic behavior of specimen or structure by applying B-P model.

Dynamic constitutive model for soils considering asymmetry of skeleton curve

Based on the asymmetric characteristic of skeleton curve obtained from dynamic tests on soils,a function with double asymptotes is proposed for describing the dynamic constitutive relations of soils.The hysteresis loops observed during unloading and reloading show the same form as the skeleton curve and are constructed by taking the ultimate stress as the corresponding asymptote.The coeffcient of initial unloading modulus is used to ensure that the constructed hysteresis loop fts well with the experimental data.Then,a new dynamic constitutive model considering the asymmetry of skeleton curve is elaborated.The verifcation tests on saturated Nanjing fne sand are performed using a hollow cylinder apparatus to verify the applicability of the UD model.It is found that the predicted curves by the UD model agree well with the test data.

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

MECHANICAL BEHAVIORS OF SATURATED SAND UNDER COMPLICATED LOADING

The different physical states of saturated sand, including shear elasticity, positive dilatancy, and negative dilatancy (preliminary negative dilatancy, secondary negative dilatancy and reversal negative dilatancy) are revealed based on the pore water pressure response of saturated sand in undrained dynamic torsional tests of thin cylinder samples and also checked by the drained cyclic triaxial tests under a given mean effective normal stress. According to the effective stress path of different physical states under the undrained cyclic torsional tests the physical state transformation surface, stress history boundary and yield surface are determined, and the state boundary surface is also determined by the range of effective frictional stress state movement. Based on the moving yield surface without rotation, and the expanding stress history boundary surface relevant to the stress path variations under different physical states in 3D stress space, a physical state model is proposed to provide a new approach to calculating the transient pore water pressure under the undrained condition, and the volume strain of dilatation under drained condition in this paper.

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

Development of a constitutive model for rockfills and similar granular materials based on the disturbed state concept

Behavior of rockfills was investigated experimentally and theoretically.A series of standard triaxial compression tests were carried out on a quarried rockfill material at different stress levels.It was found that both the stress level and the shear stress ratio,like most of granular materials,controls the behavior of rockfill materials.At lower shear stress ratios the behavior is much more similar to a nonlinear elastic solid.When the shear stress goes further,the stressstrain curve shows an elasto-plastic behavior which suggests using the disturbed state concept to develop a constitutive model to predict the stress-strain behavior.The presented constitutive model complies reasonably with the experimental data.

非饱和黏性土的广义有效应力三剪弹塑性本构模型

将非饱和土广义有效应力原理与三剪强度准则相结合,提出了非饱和土广义有效应力三剪强度准则。将所提准则作为破坏准则,分别采用等量代换法和坐标平移法推导出新的破坏应力比,并将其与非饱和土修正剑桥模型相结合得到了新的屈服函数。相比于原来修正剑桥模型中的破坏应力比为定值,新的屈服函数可以更好地反应土体全应力状态、中间主应力效应和拉压不等效应。在弹塑性理论的框架下,建立了非饱和土的广义有效应力三剪弹塑性本构模型。以江西正常固结非饱和重塑红黏土作为试验研究对象,进行室内土工试验、土水特征曲线试验、压缩回弹试验、非饱和土常规三轴固结排水试验。将该本构模型计算结果与非饱和土三轴固结排水试验结果进行对比验证。结果表明:数值模拟结果与试验结果吻合较好,验证了该本构模型的正确性。在轴向应变较小时,等量代换法和坐标平移法模拟结果比较接近,随着轴向应变增大直至偏应力达到平稳状态的过程中,等量代换法计算结果要大于坐标平移法计算结果,且更接近于试验值。真三轴计算预测结果表明:在固结排水条件下,初始压实度、净围压、基质吸力相同,中间主应力影响系数越大,则剪应力和体应变越大。b值相同的情况下,轴向应变较小时,等量代换法计算结果和坐标平移法计算结果比较接近,随着轴向应变的增大,二者之间的差值也越来越大。

用BBM模型模拟非饱和重塑黄土的变形强度特性

对非饱和土BBM模型进行分析、研究、验证,并做进一步的修正,从而使模型更符合非饱和黄土的基质吸力的变化规律。对文献中等b等σ3且b=0应力路径下的BBM模型的迭代计算方法进行修正,进而给出等b等p且b=0时的BBM模型的迭代计算方法。基于非饱和黄土的控制吸力真三轴试验下的相关试验结果,求得BBM模型的相关模型参数,并利用相应的计算方法对等b等p且b=0路径下的非饱和黄土试验结果进行预测。考虑对于非饱和黄土,相关模型参数随基质吸力的非线性变化关系,采用一个双曲线函数关系式对BBM模型进行修正,并对修正后的模型进行验证,结果显示修正后模型整体预测结果理想,尤其是对于低吸力低净平均应力下的预测结果较原始模型更为理想。

混杂纤维高强轻骨料混凝土单轴受压试验研究

为了改善高强轻骨料混凝土(HSLC)的脆性破坏特征,采用钢纤维(SF)和聚丙烯纤维(PF)对HSLC进行增强,通过单轴受压试验研究两种纤维对HSLC单轴受压性能的影响。结果表明:SF和PF的体积掺量分别为2.0%和0.2%时具有最优的混杂效应,应力-应变曲线拐点处应力和收敛点处应变较单掺SF时分别提高了10.0%和56.5%,较单掺PF时分别提高了99.1%和150%;混杂纤维使HSLC的峰值应力、峰值应变和弹性模量最高分别提升了19.0%、1.20%和16.9%。最后,基于试验数据,提出了考虑两种纤维混杂效应的峰值应力、峰值应变和弹性模量的计算公式,建立了双参数混杂纤维增强HSLC的单轴受压本构模型,并且其与试验曲线吻合较好。该研究结果可为纤维增强HSLC的结构设计提供理论参考。

不同受力状态下木材本构模型研究进展

复杂的本构模型虽然可以精确地模拟不同受力状态下木材的力学性能,但模型的计算效率和收敛均存在较大的难度。阐述了现有木材本构模型研究中的屈服准则、强化准则、流动法则和损伤准则,对比了不同准则的优缺点。评估了不同本构模型在木材、木结构构件和节点数值模拟分析中的适用性。总结了不同受力状态下合理、高效的本构模型,为木材本构模型研究和木结构数值模拟分析提供参考。

饱和砂土动力特性及数值方法研究

典型的实验表明,颗粒状砂土的变形与破坏特征有赖于其自身构造特性(密度或孔隙率,各项异性程度)、多组分相特性(饱和或者准饱和)、作用荷载特性(载荷作用时间长短)、应力比和体积约束条件等。本文依据实验变形和破坏特征,采用平面应变弹塑性有效应力模型建立了适宜于饱和砂土的动力分析方法,编制了分析模块程序并与通用岩土分析软件FLAC接口,比较在爆炸荷载作用下饱和砂土中波传播特性的数值模拟结果与试验结果,证实了模型及程序的正确性与有效性。

隧道开挖围岩土压力拱效应分析

采用弹塑性理论应力反馈算法,研发材料本构模型子程序,将土的应力路径本构模型嵌入大型有限元软件ABAQUS,通过对三轴压缩和三轴拉伸试验条件的数值模拟,验证了子程序的精度。利用二次开发后的ABAQUS对隧道开挖过程进行了三维有限元分析,从不均匀变形、应力重分配、应力路径和地表沉降规律四个方面研究了由重力引起的大主应力改变产生的土压力拱效应。研究结果表明:隧道开挖过程中,围岩土体中的应力路径变化非常复杂,并受几何位置和开挖进程影响;隧道埋深较浅时,土压力拱作用至地表,尚未完全发挥支撑作用,表现为隧道上方土体的整体沉陷变形;隧道埋深较深时,土压力拱的作用未影响至地表,充分发挥了支撑作用,表现为隧道上方土体的塌落变形;土压力拱的作用范围受隧道埋深影响不大,约为隧道半径的3倍。

基于Finn本构模型的饱和砂土地震液化分析

天然地震作用下的饱和砂土液化问题是岩土地震工程研究的重要课题之一。目前,国内推荐使用的规范法是基于实际地震液化调查而建立的判别方法,方法本身缺乏理论基础。采用Finn液化本构关系建立了砂土液化数值分析模型,运用有限差分法的动力时程分析模块,分析了饱和砂土地基的地震液化问题。结果表明,将Finn本构模型应用于砂土液化分析,可以较好地给出地震作用过程中孔隙水压力和有效应力变化的规律。