Prediction of 42CrMo steel flow stress at high temperature and strain rate

The compressive deformation behavior of 42CrMo steel was investigated at temperatures ranging from 850 to 1150 °C and strain rates from 0.01 to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on the classical stress–dislocation relation and the kinematics of the dynamic recrystallization, the flow stress constitutive equations of the work hardening-dynamical recovery period and dynamical recrystallization period were established for 42CrMo steel, respectively. The stress–strain curves of 42CrMo steel predicted by the established models are in good agreement with experimental results when the strain rate is relatively low. So, the proposed deformation constitutive equations can be used to establish the hot formation processing parameters for 42CrMo steel.     

Instrumentation to control strain rate for materials undergoing plastic flow

An instrument is described which controls the head velocity and, therefore, the strain rate of specimens tested in electromechanical universal testing machines. Within the available speed limits of these machines, a predetermined strain rate is achieved by automatic adjustment of a variable resistance in the speed-control circuit. This adjustment is achieved by coupling a potentiometer to the crosshead movement with a cam. An exact mathematical solution is derived for general cam profiles which give either nondecreasing or nonincreasing strain rates. Numerical results are presented for cams which achieve constant true strain rate in tensile and compression testing. For these cases, instrument calibration curves and tensile stress-strain curves for iron at room temperature are presented.     

FCC金属塑性屈服的尺度效应和应变率响应

对纳米尺度单晶铜的剪切变形进行了分子动力学（MD）模拟．模拟结果表明,单晶铜的剪切屈服应力随模型几何尺度的增大而降低,而随着应变率的增大而升高．基于位错形核理论,建立了一个修正的指数法则来描述面心立方（FCC）金属的尺度效应,该法则与较大尺度范围内（从纳米到毫米以上）的数值模拟结果以及实验数据都符合得比较好．另外,MD模拟中发现单晶铜存在一个临界应变率,当施加的应变率小于该值,剪切屈服应力几乎不随应变率变化而变化;当大于该值,剪切屈服应力会随着应变率的增加迅速升高．最后根据模拟的结果建立了单晶铜和单晶镍塑性屈服强度的应变率响应模型．     

Continuity in the plastic strain rate and its influence on texture evolution

Classical plasticity models evolve state variables in a spatially independent manner through (local) ordinary differential equations, such as in the update of the rotation field in crystal plasticity. A continuity condition is derived for the lattice rotation field from a conservation law for Burgers vector content—a consequence of an averaged field theory of dislocation mechanics. This results in a nonlocal evolution equation for the lattice rotation field. The continuity condition provides a theoretical basis for assumptions of co-rotation models of crystal plasticity. The simulation of lattice rotations and texture evolution provides evidence for the importance of continuity in modeling of classical plasticity. The possibility of predicting continuous fields of lattice rotations with sharp gradients representing non-singular dislocation distributions within rigid viscoplasticity is discussed and computationally demonstrated.     

Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good agreement with the results of the proposed theoretical model.Finally, the stress-deformation curve, as predicted by the model, is plotted for the simple shear problem at room and elevated temperatures using the same material properties for AA5754-O aluminium alloy.     

Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.     

Formulation of stress-strain relation for plastic deformation of mild steel for strain trajectory consisting of two straight branches

A relation between the stress and incremental strain deviators, which are not coaxial, is derived by considering the characteristics in tensor space. On the bases of this relation and of precise experimental results for mild steel, a specific plastic stress-strain relation is formulated for a strain trajectory with a comer in a 3D-vector space corresponding to the strain deviator, as a typical example of plastic behaviour under complex loading. It may be confirmed that the effects of plastic anisotropy and of the third invariant of the strain deviator on the plastic behaviour of mild steel under complex loading are expressed precisely by means of the above formulation.     

On the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings

In this work a stability analysis on flow localization in the dynamic expansion of ductile rings is conducted. Within a 1-D theoretical framework, the boundary value problem of a radially expanding thin ring is posed. Based on a previous work, the equations governing the stretching process of the expanding ring are derived and solved using a linear perturbation method. Then, three different perfectly plastic material constitutive behaviours are analysed: the rate independent material, the rate dependent material showing constant logarithmic rate sensitivity and the rate dependent material showing non-constant and non-monotonic logarithmic rate sensitivity. The latter allows to investigate the interaction between inertia and strain rate sensitivity on necking formation. The main feature of this work is rationally demonstrate that under certain loading conditions and material behaviours: (1) decreasing rate sensitivity may not lead to more unstable material, (2) increasing loading rate may not lead to more stable material. This finding reveals that the relation between rate sensitivity and loading rate controls the unstable flow growth. Additionally a finite element model of the ring expansion problem is built in ABAQUS/Explicit. The stability analysis properly reflects the results obtained from the numerical simulations. Both procedures, perturbation analysis and numerical simulations, allow for emphasizing the interplay between rate sensitivity and inertia on strain localization.     

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.     

The influence of strain rate and strain ageing on the flow stress of commercially-pure aluminium

Tensile tests on annealed, commercially-pure, aluminium specimens were performed in a hard machine at different temperatures for a number of constant strain rates. The results show that a range of strain, strain rate, and temperature exists for which the flow stress decreases with strain rate. This material property, when coupled with suitable mechanical conditions, is believed to be the cause of discontinuous repeated yielding. Various experiments, especially relaxation and reloading tests, show that the decrease of flow stress with strain rate can be directly attributed to rapid strain ageing due to impurity diffusion. Other experiments indicate the same effect for different loading histories. An analytical representation of the strain rate and strain ageing of the material is developed which predicts results in very good agreement with the experiments.     

Assessment of flow stress and plastic strain by spectrum analysis

The relation between the angular distribution of the reflected-plus-scattered light intensity (scattered field) from a metallic surface and the flow stress, plastic strain the material has experienced is experimentally and theoretically investigated. A scattered field, which is obtained by illuminating a specimen surface using a laser beam, carries surface-feature-related information. Experimental evidence suggests that surface correlation length of a material decreases in proportion to the flow stress and plastic strain that the material experiences. A theoretical derivation based on Huygens-Fresnel principle, Fraunhofer approximation, and Wiener-Khintchine theorem shows that the correlation length may be obtained by performing a Fourier transform to the scattered field from the surface. This leads to the development of a noncontact, nondestructive, and remote technique for measuring flow stress and plastic strain.     

The void-size effect on plastic flow localization in the Gurson model

Recent studies have shown that the size of microvoids has a significant effect on the void growth rate. The purpose of this paper is to explore whether the void size effect can influence the plastic flow localization in ductile materials. We have used the extended Gurson‘s dilatational plasticity theory, which accounts for the void size effect, to study the plastic flow localization in porous solids with long cylindrical voids. The localization model of Rice is adopted, in which the material inside the band may display a different response from that outside the band at the incipient plastic flow localization. The present study shows that it has little effect on the shear band angle.     

Instability and localization of plastic flow in shear at high strain rates

Shear band formation in a thermal viscoplastic heat conducting material is described in a simple shear test at high strain rate with inertia effects. The classical perturbation method is discussed, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented. They respectively provide instability and localization criteria which are compared. Furthermore both are compared to available nonlinear exact results and to experimental data. The influence of material parameters, initial imperfections, and boundary conditions is described.     

Minimum theorems for displacement and plastic strain rate histories in structural elastoplasticity

Summary The finite element method approach is used to obtain formulations of analysis problems relative to elastic-plastic structures when subjected to prescribed programmes of loads, and under the restrictive hypotheses:a) the yielding surfaces are piecewise linearized, andb) the plastic flow-laws are supposed to be of holonomic type within a single “finite” time interval. For mulations are given as linear complementarity problems and quadratic programming problems: one pair of formulations in terms of velocity and plastic multiplier rate histories, and another pair in terms of plastic multiplier rate histories only. The solutions are shown to be characterized by two minimum principles for displacement and plastic strain rate histories. After some general remarks about computational procedures, the paper is concluded with some suggestions for future developments.

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Sommario Si usa il metodo degli elementi finiti per formulare problemi di analisi relativi a strutture elasto-plastiche soggette a prescritti programmi di carico, sotto le ipotesi restrittive:a) le superfici di plasticizzazione sono linearizzate a tratti, eb) la legge del flusso plastico è olonoma all'interno del singolo intervallo di tempo “finito”. Si danno formulazioni come problemi di complementarità lineare e come problemi di programmazione quadratica: due formulazioni sono in termini di storia delle velocità e dei coefficienti di attivazione plastica, altre due sono in termini di storia dei coefficienti di attivazione plastica soltanto. Si dimostra che le soluzioni sono caratterizzate da due principi di minimo per la storia delle velocità di deformazione. Dopo alcune osservazioni generali sui procedimenti di calcolo, il lavoro si conclude con dei suggerimenti per futuri sviluppi.

     

Precise measurement of plastic behaviour of mild steel tubular specimens subjected to combined torsion and axial force

In the present paper, as an investigation for obtaining detailed information about the plastic behaviour of real materials, precise measurement of plastic deformation of thin-walled tubular specimens of initially-isotropic mild steel was performed under combined loading of torsion and axial force having trajectories consisting of two straight lines at a constant rate of the effective strain.From the experimental results, it is found that the effect of the third invariant of the strain tensor appeared even for proportional deformation consisting of torsion and axial force. Moreover, it may be seen that the effective stress drops suddenly with increasing effective strain, and coaxiality between the stress deviator and the plastic strain increment tensor is seriously disturbed just after the corner of the strain trajectory. However, these local disturbances are recovered along the second branch of the trajectory.The effect of the third invariant of the strain tensor was eliminated from the experimental results by the introduction of the modified local stress space for isolating the influence of anisotropy due to the deformation history. This permits a systematic evaluation of the influence of anisotropy for various types of combined loading.     

珊瑚砂应变率效应研究

为研究应变率对珊瑚砂力学特性的影响,用直径37 mm的分离式Hopkinson压杆（SHPB）对两类珊瑚砂进行了冲击实验,得到了460~1300 s⁻¹应变率范围内不同密实度的一维应变压缩应力-应变关系;结合准静态（10⁻⁴ s⁻¹）压缩的实验结果,发现珊瑚砂存在明显的应变率效应;通过对比两类砂物理特性,认为应变率敏感性与内孔隙和粒间摩擦密切相关;提出了率型本构模型中动态增强系数的计算模型,可为珊瑚砂在冲击下的数值计算提供理论依据。

     

Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain

In the present paper, Hill's theory of bifurcation and stability in solids obeying normality is generalized to include a non-associated flow law. A one-parameter family of linear comparison solids has been found that admits a potential and has the property that if uniqueness is certain for the comparison solid then bifurcation and instability are precluded for the underlying elastic-plastic solid. The uniqueness criterion derived may be used as a device to determine lower bounds to the magnitudes of primary bifurcation and instability stresses which are ordinarily unknown. A second linear solid is introduced whose constitutive relations have the same form as the elastic-plastic solid “in loading”. The first eigenstate of this solid gives an upper bound to the primary bifurcation state of the underlying elastic-plastic solid. The search for the genuine primary bifurcation state is therefore replaced by a search for upper and lower bounds in the situation when normality fails to hold. The theory is applied to problems of homogeneous stress states.