一种超细晶材料的混合硬化模型及其数值模拟

针对超细晶材料强度高、塑性能力不佳以及饱和应力跟晶粒尺寸和应变率等因素有关的特点,在Johnson-Cook模型的基础上引入Hall-Petch关系式,再与Armstrong-Frederick非线性随动硬化规律进行叠加,提出一种同时包含各向同性硬化和非线性随动硬化的混合硬化模型。该数学模型不仅考虑了超细晶材料的尺寸效应,还计及了加工硬化和包辛格效应的组合效应。在推导出该混合硬化模型的积分算法的基础上进行有限元数值分析和试验数据的对比分析。对比结果表明,不同晶粒大小与不同应变率下的超细晶材料的数值仿真结果与试验数据均吻合较好,进而证明该数学模型的合理性。因此,该混合硬化模型不仅丰富了塑性力学的内容,也可为超细晶材料的结构件设计提供一定的理论依据。     

粉煤灰漂珠/聚氨酯复合泡沫铝材料压缩性能与本构关系研究

采用压力渗透法制备出了铝基复合泡沫材料,填充材料是以粉煤灰漂珠为主要组分、硬质聚氨酯泡沫为粘结剂的复合泡沫材料.通过准静态实验和分离式霍普金森压杆(Split Hopkinson pressure bar,SHPB)动态压缩的方法研究了复合泡沫铝的压缩力学响应,然后建立了动态本构关系.研究表明,复合泡沫铝的压缩应力-应变曲线与其它泡沫材料的应力-应变曲线类似,文中的两种铝基复合泡沫具有应变率效应,复合泡沫铝较密度相近未填充前的泡沫铝基具有更高的压缩强度与能量吸收能力.但由于漂珠尺寸的不同,导致两种复合泡沫铝的动态压缩结果不尽相同,且小颗粒复合泡沫铝在动态冲击下吸能效果最好.在本研究实验的应变率和密度范围内,本文建立的本构模型曲线与实验曲线吻合较好.     

粉煤灰漂珠/聚氨酯复合泡沫铝材料压缩性能与本构关系研究

采用压力渗透法制备出了铝基复合泡沫材料,填充材料是以粉煤灰漂珠为主要组分、硬质聚氨酯泡沫为粘结剂的复合泡沫材料.通过准静态实验和分离式霍普金森压杆(Split Hopkinson pressure bar,SHPB)动态压缩的方法研究了复合泡沫铝的压缩力学响应,然后建立了动态本构关系.研究表明,复合泡沫铝的压缩应力-应变曲线与其它泡沫材料的应力-应变曲线类似,文中的两种铝基复合泡沫具有应变率效应,复合泡沫铝较密度相近未填充前的泡沫铝基具有更高的压缩强度与能量吸收能力.但由于漂珠尺寸的不同,导致两种复合泡沫铝的动态压缩结果不尽相同,且小颗粒复合泡沫铝在动态冲击下吸能效果最好.在本研究实验的应变率和密度范围内,本文建立的本构模型曲线与实验曲线吻合较好.     

A general constitutive relation for linear elastic foams

A three-dimensional linear elastic constitutive relation is formulated based on a representative unit cell of foam using elasticity theory and micromechanics homogenization scheme. The displacement and strain fields of the unit cell are obtained from elasticity theory and used to derive the macroscopic strain field defined on the outer surface of unit cell through homogenization scheme. By assuming a uniform macroscopic stress on the unit cell surface and the existence of strain energy potential, the constitutive relation of linear elastic foams is obtained. The newly derived constitutive relation is a function of mechanical property of solid constituent, the geometry of cell struts, and the porosity of foams and is able to characterize the anisotropic behavior of foams due to non-uniform strut geometry. The linear elastic response of open-celled foams with both low- and medium-relative densities can be studied using the derived constitutive relation. The effective elastic modulus for uniform strut geometry is reduced from the constitutive relation and agrees well with Gibson and Ashby's semi-empirical equation, Warren and Kraynik's, and Zhu's analytical models within relative density ranging from 0 to 0.35. For non-uniform strut geometry, the calculated effective elastic moduli in three axial directions are different and the material displays anisotropic behavior. The bulk modulus shows less dependence on the variation of the strut geometry. Poisson's ratios are also reduced from the compliance matrix.     

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

The molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior are used to derive a constitutive equation for rubber. The new eight-chain-like model contains eight standard models consisting of Langevin springs and dashpot to account for the interaction of chains with their surroundings. Monotonic and cyclic deformation behavior of rubber with relaxation under different strain rates have been examined. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes. The validity of the results is checked through comparison with experimental results. The deformation behaviors of a plane strain rubber unit cell containing carbon-black (CB) under monotonic and cyclic straining are investigated by computational simulation using the proposed constitutive equation and homogenization method. The results reveal the substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation of rubber. The role of strain rate sensitivity on such characteristic deformation behaviors as increases in the resistance to deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior is clarified. The increases in the volume fraction and in the aggregation of the distribution of CB substantially raise the resistance to deformation and hysteresis loss.     

Experimental studies and constitutive modelling of the hardening of aluminium alloy 7055 under creep age forming conditions

A test programme has been designed to characterise the creep-ageing behaviour of Aluminium Alloy 7055, commonly termed AA7055, under creep age forming (CAF) conditions. Creep ageing tests have been carried out for a range of stress levels at 120 °C for 20 h, which is the typical period for a CAF process. Interrupted creep tests have also been carried out to rationalise the effect of stress levels on age hardening. Based on experimental observations, a set of mechanism-based unified creep ageing constitutive equations has been formulated, which models creep induced evolution of precipitates, dislocation hardening, solid solution hardening and age-precipitation hardening. A multiple-step reverse process has been introduced to determine, from creep ageing test data, the values of constants arising in the constitutive equations. Close agreement between experimental data and computed results are obtained for creep and age hardening data for the stress range tested. The determined equation set has been integrated with the commercial FE code MSC.MARC via the user defined subroutine, CRPLAW, for CAF process modelling. In addition to springback, the evolution of precipitate size and creep induced precipitation hardening can be predicted.     

考虑加载历史影响的蠕变律

考虑到蠕变过程中,材料内部微观结构的变化,会使材料的变形行为发生改变,本文引入硬化状态变量表征加载历史对材料变形行为的影响,提出的蠕变律可以正确反映蠕变三个阶段的变形规律,由此导出的蠕变损伤演变方程与加载历史有关。其结果可以为分析多级蠕变加载时损伤演变过程和剩余寿命估算提供新的思路。     

Validation of constitutive models applicable to aluminium foams

An extensive experimental database has been established for the structural behaviour of aluminium foam and aluminium foam-based components (foam-filled extrusions). The database is divided into three levels, these are: (1) foam material calibration tests, (2) foam material validation tests and finally (3) structural interaction tests where the foam interacts with aluminium extrusions. This division makes it possible to validate constitutive models applicable to aluminium foam for a wide spectrum of loading configurations. Several existing material models for aluminium foam from the literature are discussed and compared. To illustrate the use of the database, four existing material models for foams in the explicit, non-linear finite element code LS-DYNA have been calibrated and evaluated against configurations in the database.     

A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

The determination of residual stresses induced by welding or heat treatment operations requires the use of complex models taking into account thermal, metallurgical and mechanical phenomena. In this paper, we propose a mechanical model in which each phase can follow its own constitutive law. This model also takes into account phase transformation plasticity, which is treated independently of the behavior of each phase. This model has been implemented into the French FEM code Castem 2000. The interest of the proposed method is that it allows one to mix any type of nonlinear behavior using Taylor homogenization hypothesis. There is no need to develop a theory to get the equations of the homogenized material law. Two numerical examples demonstrate the efficiency and the flexibility of this approach. The results obtained are compared to experimental values for a typical welding situation and a high-temperature response. This comparison seems to indicate that viscous effects in the materials have a significative influence on the residual stresses produced by welding.     

Determination of combined hardening material parameters under strain controlled cyclic loading by using the genetic algorithm method

In this paper, experimental and numerical investigations on mechanical behaviors of SS304 stainless steel under fully reversed strain-controlled, relaxation, ratcheting and multiple step strain-controlled cyclic loading have been performed. The kinematic and isotropic hardening theories based on the Chaboche model are used to predict the plastic behavior. An iterative method is utilized to analyze the mechanical behavior under cyclic loading conditions based on the Chaboche hardening model. A set of kinematic and isotropic parameters was obtained by using the genetic algorithm optimization approach. In order to analyze the effectiveness of this optimization procedure, numerical and experimental results for an SS304 stainless steel are compared. Finally, the results of this research show that by using the material parameters optimized based on the strain-controlled and relaxation data, good agreement with the experimental data for ratcheting is achieved.     

基于连续介质损伤力学的7075铝合金高温成形极限理论预测与数值仿真

开展7075铝合金高温单向拉伸试验和成形极限试验,获得了不同温度和应变率的应力-应变曲线和成形极限曲线。结果表明,在较高的温度和应变率时7075铝合金的强度减小、成形性提高。为描述7075铝合金高温损伤演化过程,提出一种改进的连续介质损伤模型,并建立了耦合损伤的多轴统一黏塑性本构模型。基于试验结果,运用NSGAII遗传算法标定了模型中的参数,标定后的本构模型可以很好地预测7075铝合金的高温热力行为和极限应变。通过有限元软件Abaqus的用户材料子程序VUMAT,该本构模型被编入到Abaqus软件中进行数值仿真计算。结果表明,仿真获得的成形极限曲线和应变场分布与试验和理论结果吻合度好,进一步证明了所建立的耦合损伤的多轴本构模型的正确性及其在高温成形极限有限元仿真中的适用性。     

Modelling the plane strain compression test to obtain constitutive equations of aluminium alloys

Hot plane strain compression tests on 1050, 1198, 3003 and 3004 aluminium alloys have been conducted. Based on these experiments and on a set of internal type constitutive equations for hot working, the values of the parameters in the constitutive functions are determined. The constitutive equations proposed here, with the constitutive functions and material parameters associated, accurately reproduce the basic tests. The procedure used to fit the material parameters is improved, in comparison with classical slip line analysis, by using a finite element modelling of the plane strain compression test. It is demonstrated that accurate plane strain or three-dimensional large strain finite element analysis can be used to correct the friction and lateral spread effects. Furthermore, it is demonstrated from comparison with the experimental observations that microstructural parameters can be accurately determined from numerical modelling. The constitutive equations and finite element procedure proposed here can be useful for obtaining an improved analysis of hot rolling of aluminium alloys.     

Hardening laws, surface roughness and biaxial tensile limit strains of sheet aluminium alloys

The roles of hardening laws and surface roughness have been assessed in the prediction of biaxial tensile limit strains of two A1 alloy sheet materials with different strain hardening characteristics namely AA6111-T4 and AA5754-O, utilizing the surface roughness model proposed by Parmar, Mellor and Chakrabarty [6]. In the work of Parmar et al., the predictions of limit strains were based on the Marciniak—Kuczynski inhomogeneity analysis and utilized the commonly used power hardening law (Hollomon equation) to describe the stress—strain behavior of the material. In the present work, (i) the suitability of a Voce hardening law, (ii) the effect of surface roughness parameters and (iii) the effect of grain size parameters on the prediction of biaxial limit strains has been studied. The biaxial limit strains based on Voce equation were obtained by modifying the set of equations of Parmar et al. and utilizing the experimentally measured surface roughness in 3-D, grain size parameters and stress—strain curves from uniaxial tensile and hydraulic bulge tests for the two A1 sheet materials. The predictions from Voce and Hollomon equations have been compared with the experimental forming limits determined by hemispherical punch stretching of gridded blanks. The discrepancy between predictions from Holloman equation and experiments is small for the low strain hardening AA6111-T4 material but is quite significant for the high strain hardening AA5754-O material. Further, the predictions are also strongly dependent upon the measure of surface roughness and the grain size utilized in the calculations. The results indicate good predictions of limit strains for the two alloys when (i) stress—strain data from tensile or hydraulic bulge tests are fitted to a Voce equation and (ii) half of the maximum peaks-to-valley height and grain thickness are utilized as a measure of surface roughness and grain size respectively. The results are discussed in the context of the characteristics of the hardening laws, assumptions of surface roughness model and surface and grain characteristics of the alloys studied.     

Dynamic indentation and penetration of aluminium foams

Failure of metal foams caused by dynamic indentation and penetration is very common in practice, such as light-weight structural sandwich panels, packing materials and energy absorbing devices. Rational application of these materials requires a sound understanding of deformation and energy absorption mechanisms of the aluminium foams as well as the effect of impact velocity. In this study, following experimental investigations into compression, tension, sharing and indentation of CYMAT aluminium foams of various densities, a finite element (FE) analysis using ABAQUS is conducted for dynamic indentation process of aluminium foams under a rigid, flat-headed indenter. Two methods of applying impact velocities are considered: the indenter is pushed into the foam at a constant velocity through the whole process or with an initial velocity which then decreases with indentation. Two energy dissipation mechanisms are considered: compression of the foam ahead of the indenter and fracture along the indenter edge. Effect of impact velocity is noted on the size of a localized deformation and the total energy absorbed. A plastic structural shock theory developed by previous researchers is applied to calculate the resistance force with indentation depth during indentation process and fair agreement is obtained between the analytical and numerical results.     

Creep simulation of adhesively bonded joints using modified generalized time hardening model

Creep behavior of double lap adhesively bonded joints was investigated using experimental tests and numerical analysis. Firstly, uniaxial creep tests were carried out to obtain the creep characteristics and constitutive parameters of the adhesive at different stress and temperature levels. Generalized time hardening model was used to predict the creep behavior of the adhesive. This model was modified to simulate the creep behavior at different stress and temperature levels. Secondly, the developed model was used to simulate the creep behavior of bonded joints using finite element based numerical analysis. Creep deformations of the joints were measured experimentally and good agreement was observed in comparison with the results obtained using numerical simulation. Afterward, stress redistribution due to the creep along the adhesively bonded joint was obtained numerically. It was observed that temperature level had a significant effect on the stress redistribution along the adhesive thickness.     

Prediction of deformation behavior and microstructure evolution in heavy forging by FEM

A numerical simulation of multi-stage heavy forging process using the finite element method (FEM) is presented in this study. The process of heavy forging is highly non-linear, where both microstructure and boundary conditions are altered by plastic deformation during forming. Therefore, it is necessary to understand the problem of plastic deformation in heavy forging. In order to investigate deformation behavior and microstructure evolution in heavy forging, a constitutive equation considering the effects of strain hardening and dynamic softening of the IN718 alloy is built. The constitutive equation and microstructure models are implemented into the finite element code to simulate deformation behavior and microstructure evolution in the rotary forging of heavy container head. As a result, variations of flow stress, effective strain, temperature, damage, and grain size in every stage are predicted.     

A single cone-cap plasticity with an isotropic hardening rule for powder materials

In this paper, a new single cone-cap plasticity with an isotropic hardening rule is presented for powder materials. A general form is developed for the cap plasticity, which can be compared with some common double-surface plasticity models proposed for powders in literature. The constitutive elasto-plastic matrix and its components are derived based on the definition of yield surface, hardening parameter and nonlinear elastic behavior, as a function of relative density of powder. Different aspects of the model are illustrated and the procedure for determination of powder parameters is described. Finally, the applicability of the proposed model is demonstrated in numerical simulation of triaxial and confining pressure tests.     

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response.     

过共晶Al-Si合金半固态触变成形本构方程

通过对过共晶Al-20Si-3Fe-1Mn-4Cu-1Mg合金进行半固态单向压缩热模拟试验,研究变形温度为833 K、853 K 、873 K,应变速率为0.1 s–1、0.01 s–1、0.001 s–1的半固态触变成形行为。试验结果表明,变形抗力随变形温度的升高而降低,随应变速率的增加而增大。对试验得到的真实应力应变曲线进行分析,提出将不同真应变范围的半固态触变成形过程划分为类弹性变形、应变硬化和流变-黏塑性变形阶段的新方法,并分阶段建立半固态触变本构方程,采用多元回归得到各阶段的本构方程表达式。所建半固态触变本构方程与试验曲线的比较结果表明,大多数相关系数均在0.95以上,相伴概率均小于0.001,说明根据所建本构方程计算得到的真应力-真应变曲线与试验曲线吻合良好,所建本构方程有意义且具有较高的精度,能够体现出该合金半固态触变过程变形行为,可以将其应用于过共晶Al-20Si-3Fe-1Mn-4Cu-1Mg合金半固态触变成形过程的数值模拟。