Numerical study on flanging and spring-back of stamped thick metal plate

A quasi-three-dimensional shell element model, which can be effectively used to simulate the flanging and spring-back deformation, is introduced into the independently developed CAE software, KMAS. In this model, a double surface contact algorithm, which allows the gap between punch and die to change, and a spring-back treatment scheme based on finite element meshing are described. And then the flanging and spring-back deformations of the retractor's kickstand of a railcar made of stamped thick metal plate are numerically simulated. The simulation results of flanging deformation are compared with those of international commercial software, PAM-STAMP, and experimental ones. Finally, a predicting scheme of spring-back quantily for this problem is given. Project supported by the National Natural Science Foundation of China (No. 19832020) and the Ministry of Education of China.     

Deformation localization and shear band fracture in strong anisotropy sheet tension

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-flow plastic constitutive theory^[1] and B-L planar anisotropy yield criterion^[2]. Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficientR and the shear band angle θ is found. The project supported by the National Natural Science Foundation of China and the Excellent Youth Teacher Foundation of the State Education Commission of China     

A finite element model for numerical simulation of thermo-mechanical frictional contact problems

Two kinds of variational principles for numerical simulation of heat transfer and contact analysis are respectively presented. A finite element model for numerical simulation of the thermal contact problems is developed with a pressure dependent heat transfer constitutive model across the contact surface. The numerical algorithm for the finite element analysis of the thermomechanical contact problems is thus developed. Numerical examples are computed and the results demonstrate the validity of the model and algorithm developed. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (50178016, 10225212) and the Foundation for University Key Teacher by the Ministry of Education of China     

Numerical simulation for the simple shear test in amorphous glassy polymers

In this paper, a driving stress finite element method of elastic-plastic large deformation based on implicit time integrating algorithm and an eight-chain molecular network model is used for the numerical simulation of the simple shear test of polycarbonate (PC) materials. The simulated results are compared with experimental ones. The strain localization propagation for the shear band deformation for simple shear deformation is investigated numerically. The effects of microstructure parameters in the model on strain softening and orientation hardening of the PC are discussed in detail. Supported by the National Natural Science Foundation of China.     

Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial Cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.The project supported by the National Natural Science Foundation of China (10272067, 10426024), the Doctoral Program Foundation of the Education Ministry of China (20030422046) and the Natural Science Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

Stokes＇ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

Stress-strain field near the notch tip of a rubber sheet

Analized in this paper is the elastostatic field near a notch tip in a rubber-like thin sheet. The asymptotic equations for the notch tip field are derived based on the constitutive relation given by Ref. [1]. Near field solutions are obtained in regions that decreases and increases in size as the notch tip is approached. Their singular character depends on the constitutive parameters as well as the angle of notch that is evaluated numerically. The project supported by the National Natural Science Foundation of China     

Effect of microstructure on the hardening and softening behaviors of polycrystalline shape memory alloys Part II: Numerical simulation under axisymmetrical loading

Based on the microstructure-based constitutive model established in Part I, a detailed numerical investigation on the role of each microstructure parameter in the kinematical and kinetic evolution of polycrystalline SMA under axisymmetrical tension loading is performed. Some macroscopic constitutive features of stress-induced martensite transformation are discussed. The subject supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangxi Province of China     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education     

Crack tip superblunting: experiment,theory and numerical simulation

Experimental revelation ofsuperblunting along plane strain predominant crack tip segment is reported here for modified polyproplene. As elucidated by a heuristic model of progressive circumferential cold-draw, the formation of superblunting crack tip depends critically on the ratio between the cold-draw propagation speed and the loading speed, and contributes significantly to the material toughening, especially for the improvement in impact toughness. Detailed numerical calculations are conducted based on a hyperelastic-viscoplastic and anisotropic damage constitutive model at finite deformation. The simulated results recapitulate the essential features of crack tip superblunting. The project supported by the National Natural Science Foundation of China     

A constitutive relation for pseudo-elastic behaviour in shape memory alloys

A constitutive relation to describe pseudo-elastic deformation in shape memory alloys is presented in this paper. It is capable of describing deformation behaviour of polycrystalline materials under triaxial stress state as well as of monocrystalline materials under one-dimensional condition. Total strain rate is supposed to be composed of elastic strain rate and transformation strain rate. Deformation behaviour of Cu−Zn−Sn alloy and Ti−ni alloy is simulated by use of the proposed constitutive relation. it is shown that simulated results are in a good agreement with experimental data. The project supported by National Natural Science Foundation of China.     

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

Man (Nondestr Test Eval 15:191–214, 1999) derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations. The project supported by the National Natural Science Foundation of China (10562004, 10662004), the Natural Science Foundation of Jiangxi of China (0512021), the Science Foundation of Jiangxi Educational Department of China([2006]3), and the Foundation of Training Academic and Technical Header for Main Majors of Jiangxi of China.     

Water and salt movements in simultaneous flood-irrigation and well-drainage operations

This paper describes a new technology for solonchak soil reclamation in which surface flood irrigation of fresh water and pumped wells drainage of salty groundwater are combined. The comprehensive investigation of water and salt movement has been conducted through field test, laboratory simulation and numerical calculation. The dependence of desalination on irrigation water quantity, drainage quantity, leaching time and other parameters is obtained based on the field tests. The entire desalination process under the flood-irrigation and well-drainage operations was experimentally simulated in a vertical soil column. The water and salt movement has been numerically analyzed for both the field and laboratory conditions. The present work indicates that this new technology can greatly improve the effects of desalination. The project supported by the National Natural Science Foundation of China     

Criterion for judging satisfaction of consistency conditions in rate-dependent constitutive relations

Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not. This research was funded by the National Natural Science Foundation of China (No. 59739180) and the Foundation of National Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (No. 9701).     

Constitutive relation of discontinuous reinforced metal-matrix composites

A micromechanical model is developed to simulate the mechanical behaviors of discontinuous reinforced composites. The analysis for a representative unit cell is based on the assumption of a periodic array of aligned reinforcements. The minimum energy principle is used to determine the unknown coefficients of the displacement field of the unit cell. The constitutive behavior of composites is studied to obtain the relationship between the main variables of matrix and reinforcements. It is concluded that the flow strength of composites is strongly influenced by volume fraction, aspect ratio of reinforcement, and the strain hardening exponent of matrix. An analytical constitutive relation of composites is obtained. The predicted results are in agreement with the existing experimental and numerical results. The project supported by the National Natural Science Foundation of China (19704100) and National Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

用HJC本构模型模拟混凝土SHPB实验

运用Holmquist-Johnson-Cook (HJC) 本构模型对混凝土的SHPB实验进行了数值模拟。解决了罚函数算法中罚因子合理数值的选取问题。利用模拟结果按SHPB两波法重构了试样的应力应变曲线。分析了混凝土材料的SHPB实验得到应力应变曲线的有效段范围和各段的力学规律。通过比较实际混凝土材料SHPB实验和数值模拟得到的应力应变曲线,发现两者体现的力学行为很相似,即HJC模型是描述该类材料的一种合理本构模型。模拟了试样不同平行度公差下的SHPB实验,发现在一定应变率范围内其影响程度远大于试样应力(应变)不均匀性。     

A constitutive equation of elastic-visco-plasticity for polymers

The rheological behavior and a constitutive relationship of elastic-visco-plasticity for polymers are investigated in this paper. Several sets of experiments have been carried out to determine the material constants and to test the validity of constitutive formulation. It is shown that the theoretical profiles are in good agreement with experimental results. The rheological characteristic and the strain-rate effect of model are analyzed by computer simulation.The project is supported by the National Natural Science Foundation of China     

A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (19872016, 50178016, 19832010) and the Foundation for University Key Teacher by the Ministry of Education of China     

Experimental and Numerical Analysis of Initial Plasticity in P91 Steel Small Punch Creep Samples

To date, the complex behaviour of small punch creep test (SPCT) specimens has not been completely understood, making the test hard to numerically model and the data difficult to interpret. This paper presents a novel numerical model able to generate results that match the experimental findings. For the first time, pre-strained uniaxial creep test data of a P91 steel at 600 ^°C have been implemented in a conveniently modified Liu and Murakami creep damage model in order to simulate the effects of the initial localised plasticity on the subsequent creep response of a small punch creep test specimen. Finite element (FE) results, in terms of creep displacement rate and time to failure, obtained by the modified Liu and Murakami model are in good agreement with experimental small punch creep test data. The rupture times obtained by the FE calculations which make use of the non-modified creep damage model are one order of magnitude shorter than those obtained by using the modified constitutive model. Although further investigation is needed, this novel approach has confirmed that the effects of initial localised plasticity, taking place in the early stages of small punch creep test, cannot be neglected. The new results, obtained by using the modified constitutive model, show a significant improvement with respect to those obtained by a ’state of the art’ creep damage constitutive model (the Liu and Murakami constitutive model) both in terms of minimum load-line displacement rate and time to rupture. The new modelling method will potentially lead to improved capability for SPCT data interpretation.     

A constitutive model and elastoplastic analysis of structures under cyclic loading

A constitutive model for cyclic plasticity is briefly outlined. Then the model is implemented in a finite element code to predict the response of cyclic loaded structural components such as a double-edge-notched plate, a grove bar and a nozzle in spherical shell. Comparision with results from other theories and experiments shows that the results obtained by using the present model are very satisfactory.The Project Supported by National Natural Science Foundation of China.