高分子材料平面应变拉伸变形局部化

将基于应变软化玻璃状高分子材料微观特征建立的ＢＰＡ８－链分子网络模型引入ＵｐｄａｔｉｎｇＬａｇｒａｎｇｅ有限元方法，建立了适于变形局部化分析的大变形弹塑性有限元驱动应力法．在此基础上，数值模拟了初始各向同性高分子材料平面应变拉伸变形局部化的传播过程．探讨了ＢＰＡ模型对具有加工硬化特性的结晶性高分子材料变形分析的适应性；分析了局部化传播过程中颈缩截面的非均匀应力三轴效应；最后，讨论了网格尺寸以及初始几何不均匀性对颈缩扩散以及应力三轴效应的影响     

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.     

光滑圆柱拉伸试件的颈缩分析

对Gurson本构方程作了初步的研究，并对圆柱光滑拉伸试件在颈缩阶段用Gurson本构方程做了大应变弹塑性有限元分析。讨论了颈缩区空穴形核、扩张、静水应力以及材料软化的问题，初步揭示了空穴的演化过程和材料的破坏机理。有限元分析的结果表明，颈缩阶段空穴长大聚合机理非常显著，而形核作用相对较弱。     

预延伸非晶聚合物材料各向异性变形局部化

给出一种可描述预延伸各向异性特性的背应力张量三维表达式，引入大变形弹塑性有限元驱动应力法，结合ＢＰＡ８ 链细观分子网络模型，模拟了预延伸各向异性非晶聚合物材料平面应变拉伸变形局部化力学行为．详细讨论了预延伸比（ＩｎｉｔｉａｌＤｒａｗｉｎｇＲａｔｉｏ；ＩＤＲ）和预延伸方向（ＩｎｉｔｉａｌＤｒａｗｉｎｇＤｉｒｅｃｔｉｏｎ；ＩＤＤ）对变形抗力、颈缩规律、剪切带方向以及试件中心部位链延伸比的影响．     

Material aspects of dynamic neck retardation

Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.     

Inelastic deformation and localization in polycarbonate under tension

It is demonstrated that uniaxial tension deformation in polycarbonate and other polymers that exhibit large inelastic deformation is unstable beyond a certain stretch. The instability first appears as a shear banding phenomenon at a characteristic angle and is then followed by a stabilized neck generation and propagation. The intrinsic material law for polycarbonate is used in a numerical implementation to reproduce completely the deformation behavior observed in uniaxial tension. In particular, it is demonstrated through numerical simulations, that intrinsic material softening is not necessary for the formation of a shear band and continued growth of a stable neck and further that the interpretation of the tensile response in terms of the constitutive behavior of the material poses significant problems.     

Non-uniform deformation after prestrain

The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.     

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10^?3 and 10³ s^?1 for ?150, ?100, ?50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump. The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced. The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place. The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation. These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates

The effects of strain rate and temperature on the tension stress–strain responses of polycarbonate are experimentally investigated over a wide range of strain rates (0.001–1700 s⁻¹) and temperatures (0–120 °C). A modified split Hopkinson tension bar is used for high-rate uniaxial tension tests. Experimental results indicate that the stress–strain responses of polycarbonate at high strain rates exhibit the nonlinear characteristics including the obvious yielding and strain softening. The tension behavior is strongly dependent on the strain rate and temperature. The values of yield stress and strain at yield present a dramatic increase at higher strain rates and decrease with the increase in temperature. Moreover, there exists a significant rate-sensitivity transition in the polycarbonate tension yield behavior. Based on the experimental investigation, a physically based three-dimensional elastoplastic constitutive model for the finite deformation of glassy polymers is used to characterize the rate-temperature dependent yield and post-yield behavior of polycarbonate when subjected to tension loading. The model results are shown close to the experimental data within the investigated strain-rate and temperature ranges.     

高导无氧铜杆高应变率拉伸下的颈缩与断裂

采用Hopkinson拉伸实验装置和一种高速拉伸断裂实验新装置,对高导无氧铜(OFHC)杆件进行了一系列高应变率拉伸断裂试验.实验结果表明,局部化的断裂应变随拉伸速度增大并不明显增大,其断裂位置有随机性.存在一种临界拉伸速度,当冲击拉伸速度大于此值时,断裂即发生在冲击拉伸端附近,杆的其它部分几乎无应变.采用典型的Johnson-Cook本构关系,使用LS-DYNA程序进行一系列数值模拟,提出颈缩处直径收缩率达极值的颈缩失效判据,由此计算所得的局部化颈缩应变及断裂位置与试验回收结果有一定差别.     

Thermal softening induced plastic instability in rate-dependent materials

A linear perturbation analysis is performed for a class of rate-dependent materials, such as the Johnson-Cook model, in which the rate contribution to the stress can be separated from that of the plastic strain and temperature and in which the temperature rises adiabatically. The analysis is facilitated by perturbing both the rate of momentum equation and the momentum equation. An identical material stability/instability criterion is deduced from the characteristic spectral equations for one-dimensional deformation, one-dimensional shearing, and general three-dimensional field equations, and thus shows that the instability derived here is a material constitutive instability.The criteria indicate that the materials become unstable once the thermal softening overcomes the strain hardening, regardless of the strain rate. The strain rate enters the criteria through its effects on the accumulated temperature and the current stress. Based on the criterion, the three-dimensional instability surface is established in the space of plastic strain, plastic strain rate, and temperature. Instability surface is shown as a material property and independent of deformation histories or modes. Both necking and shear banding are simulated to validate the excellent predictive capability of the criterion.     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

Analysis of deformation localization based on proposed theory of ultrasonic wave velocity propagating in plastically deformed solids

The localization of plastic deformation is discussed as “stationary discontinuity” characterized by a vanishing velocity of an acceleration wave derived using the author’s proposed theory of ultrasonic wave velocities propagating in plastically deformed solids. To formulate the proposed theory, the elasto-plastic coupling effect was introduced to consider the elastic stiffness degradation due to the plastic deformation. The driving force of the deformation localization is caused by the yield vertex effect, which introduces a pronounced softening of the shear modulus, and geometrical softening due to double slip caused by lattice rotations. In the present paper, it is examined theoretically and experimentally that the diagonal terms of the introduced elasto-plastic coupling tensor represent a slight hardening followed by a pronounced softening of the elastic modulus induced by the point defect development caused by cross slides among dislocations at multiple slip stages similar to the yield vertex effects. The off-diagonal terms represent geometrical softening induced by lattice rotations such as texture evolution. Then, based on the coincidence of the onset strains between localization and acceleration waves of vanishing velocity, the diagrams of diffuse necking, localized necking and forming limit are analyzed by applying the proposed acoustic tensor, which is based on the generalized Christoffel tensor derived by the author, and solving cut off conditions of the quasi-longitudinal wave to determine the onset strains of deformation localization and localization modes. As a result, diagrams of diffuse necking, localized necking and forming limit were obtained. Moreover, the localization modes were determined and distinguished as the SH-mode, SV-mode, tearing mode and splitting mode.     

Plastic flow for axisymmetric-tension specimens with necking

Plastic deformation of a tension specimen bounded by a curved surface of revolution is considered. Such a configuration may occur, for example, as a result of necking. The specimen material satisfies the Tresca yield condition and the associated flow rule. Approximate solutions for the stress distribution in the neck were examined in [6]. The extension of notched bars was investigated by numerical and graphic methods in [2, 4]. Below, the problem is solved analytically for a sufficiently smooth neck; a small degree of nonuniformity of the plastic properties is taken into account.     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

Lüders bands propagation of 1045 steel under multiaxial stress state

Inhomogeneous plastic deformation of 1045 steel under monotonic loading was experimentally studied. Thin-walled tubular specimens were used in the experiments and custom-made small strain gages were bonded on the specimen surface to characterize the local deformation. Experiments were conducted under tension, torsion, and combined tension–torsion. During the propagation of Lüders bands, the local deformation experienced two-stage deformation: an abrupt plastic deformation stage followed by a slower deformation process. In some area of the gage section of the specimen, a small amount of initial plastic deformation occurred before the Lüders front reached. During the propagation of Lüders bands, multiple Lüders fronts can be formed. Under tension, torsion, and combined tension–torsion with a constant axial load, the Lüders front was approximately parallel to the material plane of maximum shear stress. When the combined axial-torsion followed a proportional fashion, the stress–extensometer strain responses were dependent on the axial/torsional loading ratio, and the Lüders fronts were oriented differently and propagated along the specimen axis at a different velocity. The local strain was inhomogeneous even at the work-hardening stage. The relationships between the equivalent stress and the equivalent plastic strain were found to be practically identical for all the loading cases studied.     

Stress–strain behaviour of aluminium alloys at a wide range of strain rates

The stress–strain behaviour of extruded AA6xxx and AA7xxx aluminium alloys in T6 temper was studied at a wide range of strain rates. Tensile tests at low to medium strain rates were performed in a standard tensile test machine, while a split-Hopkinson tension bar was used to carry out tests at high rates of strain. Extruded aluminium alloys have anisotropic mechanical properties, and tests were therefore done in three directions with respect to the extrusion direction. It is found that the AA6xxx alloys exhibit no significant rate sensitivity in the stress–strain behaviour, while moderate rate sensitivity was found for the AA7xxx alloys. There seems to be no significant difference between the rate sensitivity in the three tensile directions. The experimental data were used to identify the parameters of a thermo-viscoplastic constitutive relation for the extruded alloys, which includes the effects of strain hardening, strain-rate hardening, thermal softening and plastic anisotropy.     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Constitutive modeling of the dynamic fracture of smooth tensile bars

A recently developed viscoplastic-damage type of constitutive theory for high strain-rate flow processes and ductile fracture is used to model the deformation and fracture of dynamically loaded smooth cylindrical tensile bars. The analysis assumes polycrystalline materials which usually contain microvoids with an average density of the order of 10⁶ per cm³ that are dispersed homogeneously throughout. It is shown that for dynamically imposed loading that produce nominal strain rates ranging between 5 × 10² − 5 × 10³ sec ⁻¹, the inhomogeneous fields of stress and deformation caused by wave propagation and wave reflection induce necking at different locations along the gauge section, depending upon the strain-rate imposed. This occurs without imposition of any geometrical or material irregularity to preposition the location of the necking. The imposed rate of strain is also shown to affect the magnitude of the strain at which necking initiates, as well as the strain required for fracture.