Bounding-surface plasticity for non-linear analysis of space structures

This paper presents a method for the non-linear analysis of space structures subjected to static and cyclic loading. A bounding-surface kinematic hardening plasticity model is used to simulate the hardening and hysteritic material behaviour. The model is used in conjunction with the lumped plasticity assumption coupled with the concept of a yield surface in force space. A hardening coefficient matrix which is a function of the plastic strain and the elastic stiffness matrix is introduced while the vectorial nature of the material memory parameters is maintained. This provides a smooth transition from the elastic to the plastic regime which simulates the hysteresis loops quite accurately. An updated Lagrangian formulation is used together with a predictor/corrector solution method. Several examples are presented to demonstrate the accuracy and efficiency of the method.     

Technology and equipment for plasma surface hardening of heavy-duty parts

Local heat treatment is justifiable in many cases in terms of technology and cost effectiveness, where only the most loaded working surface is subjected to hardening, while the bulk of a material remains untreated. Plasma surface hardening allows wear to be decreased and service life of heavy-loaded machine parts to be extended 2-5 times. The novel method of plasma hardening is technically and economically preferable for heat treatment of a large number of parts. One example of its application is high-speed surface hardening of all types of passenger, freight, and locomotive train wheelsets. Tests show that in all cases the amount of wear of the wheelset ridges after plasma hardening is much lower (2.5-3.0 times) than that of the ridges after standard heat treatment.     

Tensile and bending behaviour of a strain hardening cement-based composite: Experimental and numerical analysis

IFSTTAR has developed a Multi-Scale Cement Based Composite (MSCC). This composite material is strain hardening in tension and exhibits ultra-high strengths as well in both compression and tension. The main research objectives for the present paper are the determination of the strain hardening properties of the material: using a newly developed tensile test in conjunction with a finite-element-based inverse analysis, the input parameters of an (adapted) numerical model can be identified. Therefore, numerical simulations can be performed to describe the bending behaviour of a thin slab having a thickness representative of the corresponding industrial application.The main conclusions of this study are:

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The studied material clearly exhibits strain hardening in tension with a uniaxial tensile strength of about 20 MPa and a modulus of rupture of about 50 MPa.

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Elasto-plastic behaviour with strain hardening is a relevant mechanical model (for the studied material) for designing (by the finite element method) structural elements behaving principally in bending.

     

基材属性对铝蜂窝共面力学性能的影响

目的研究不同属性的基体材料对铝蜂窝共面压缩力学性能的影响。方法在保持正六边形蜂窝结构参数不变的情况下,改变基材属性,基体材料模型分别选择不同应变强化参数的双线性各向同性强化模型和理想弹塑性模型,建立相关可靠的有限元模型并进行大量的模拟计算。获得相应的变形模式和应力-应变曲线,对曲线进一步处理得到蜂窝共面静动态峰应力,并将结果以图表形式展示并分析。结果随着冲击速度的增加,样品依次出现了"X","V","一"字型3种变形模式,基体材料的应变强化效应使变形趋于均匀化;基体材料的应变强化效应显著增加了蜂窝的静态峰应力,对动态峰应力增量的影响可以忽略,对计算数据处理后得到了应变强化参数与动态峰应力的计算公式。结论基材具有强化特性的蜂窝,其共面静态力学性能优于基材为弹性理想塑性材料模型的蜂窝;在利用数值模拟的方法来研究蜂窝结构共面静态力学行为时,需要考虑基体材料的强化效应。     

金属薄板循环塑性强化模型及实验研究进展

金属薄板塑性成形及回弹预测精度在很大程度上取决于所采用的强化模型能否对材料变形行为准确描述。梳理了各向同性强化模型、随动强化模型、旋转强化模型、畸变强化模型以及各类微观强化模型,对不同模型的特点及局限性进行了分析。同时,总结并讨论了标定强化模型中材料参数的各类循环加载实验方法。针对强化模型参数识别的问题,总结了常用的参数标定方法,分析了影响识别精度的因素。最后,介绍了不同强化模型在回弹预测方面的应用并分析了影响预测精度的因素。     

Determination of Stress-Strain State and Strength of Structural Elements on the Basis of Strain-Hardening Analysis

We outline the fundamentals of the method whereby the stress-strain state and strength of structural elements loaded along linear paths and small-curvature paths are determined by allowing for strain hardening of material of the structure or plastic indicators attached to it. The method is based on a model of hardening which assumes that during the deformation beyond an elastic range the loading surface separating elastic and elastoplastic deformation ranges changes its shape and shifts in the direction of the vector which connects its center and an image point on the loading path. It is assumed that the material in its initial state is isotropic and the hypotheses for the unified stress-strain curve and for the proportionality of stress and strain deviators are met.__________Translated from Problemy Prochnosti, No. 2, pp. 28 – 48, March – April, 2005.     

Cyclic hardening behavior of roller hemming in the case of aluminum alloy sheets

A method to investigate the cyclic hardening behavior of roller hemming in the case of aluminum alloy sheets is described in this approach. Roller hemming hardening behaviors are studied with numerical simulation. The minimum sets of uniaxial experiments are established for the determination of accurate constitutive parameters. A special specimen holder, together with modified uniaxial specimens with two side fins is used in uniaxial tension and compression tests to determine combined hardening parameters. The material parameters are verified by pre-hemming roll-in/out data. It is also demonstrated that the combined hardening parameters derived from the minimum set of uniaxial tests with the aid of special specimen holder and modified specimens are accurate and believable.     

Plane strain crack closure and cyclic hardening

This study is focused on the understanding of the mechanical effects of cyclic hardening on crack tip plasticity and on plasticity-induced crack closure. Various finite element analyses were conducted using abaqus. Cyclic hardening is found to affect both crack closure and the shape of the plastic zone at the crack tip. Crack growth modelling in plane strain conditions in a cyclically hardening material is discussed. An empirical formula is provided which allows the calculation of the crack tip plastic zone size under plane strain conditions in a cyclically hardening material. The effects of overloads are also examined.     

Strain hardening and fracture of VT6 alloy synthesized by the method of powder metallurgy

We study the deformation behavior of VT6 alloy produced by the method of powder metallurgy and according to the traditional technology (casting and high-temperature deformation). It is shown that, in both types of materials, the evolution of the dislocation structure and strain hardening in tension obey the same physical laws. The deformation and hardening of both the powder material and VT6 alloy with lamellar structure obtained by using the traditional technology are controlled by the β-phase with bcc lattice according to the mechanism of composition hardening. Independently of the temperature of sintering, powder alloys fail according to the mechanism of ductile shear and tension. The residual pores in the powder material do not play the role of sites of crack initiation. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 3, pp. 107–111, May–June, 2008.     

材料硬化模式对弯曲回弹模拟精度的影响

回弹的模拟精度低，是几乎所有软件在计算大型复杂件的回弹时都存在的缺点，因此提高回弹模拟精度成为回弹仿真研究的重点和难点，利用自主开发的二维弹塑性有限元程序，分别采用线性硬化模型和弹塑性幂次硬化模型对V型自由弯曲的回弹进行模拟，探讨材料硬化模式对回弹模拟精度的影响，特别对于硬化模型中代表弹性变形阶段的重要参数一弹性模量，考虑了其随塑性变形进行而发生的变化，结果表明：材料的硬化模式直接影响回弹模拟精度，而采用的硬化模式越能真实地反映材料变形规律，回弹模拟的精度就越高，尤其是采用随塑性变形而发生变化的弹性模量，使模拟精度进一步提高。     

On the identification of kinematic hardening material parameters for accurate springback predictions

An experimental method that frequently has been used for the determination of material hardening parameters is the three-point bending test. The advantage of this test is that it is simple to perform, and standard test equipments can be used. The disadvantage is that the material parameters have to be determined by some kind of inverse approach. The test has then been simulated by means of the Finite Element Method, and the material parameters have been determined by finding a best fit to the experimental results by means of a Response Surface Methodology. An alternative method is the tensile/compression test of a sheet strip. In practice such a test is very difficult to perform, due to the tendency of the strip to buckle in compression. In spite of these difficulties some successful attempts to perform cyclic tension/compression tests have been reported in the literature. However, a few writers have reported that there are substantial differences between hardening parameters determined from bending tests and those determined from tensile/compression tests. The purpose of the present study is to try to understand the background of these differences, to find out the influence on predicted springback, and to determine which of the two methodologies for hardening parameter identification is the most suitable one.     

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” ε _aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa ε _aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ _y, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.     

Usage of the small-punch-test for the characterisation of reactor vessel steels in the brittle–ductile transition region

This paper presents a method for the identification of hardening parameters and Weibull-parameters in the brittle and brittle–ductile transition region. A small-punch-test device is developed for hot cells, where a miniaturised disk-like specimen is manufactured and deformed by a spherical punch until failure. Its load–displacement-curve is analysed regarding its information about the material behaviour. Using neural networks, an identification routine is developed, which avoids time-consuming calculations with FEM during an optimisation algorithm. Identified material properties are compared with data from tensile tests. Using the identified hardening parameters, Weibull-parameters are calculated for temperatures at which cleavage fracture occurs.     

Influence of prior cyclic hardening on high temperature deformation and crack growth in type 316L (N) stainless steel

For power generating equipment subjected to cyclic loading at high temperature, crack growth could arise from the combinations of fatigue and creep processes. There is potential for the material to undergo hardening (or more generally changes of material state) as a consequence of cyclic loading. Results of an experimental study to examine the influence of prior cyclic hardening on subsequent creep deformation are presented for type 316L(N) stainless steel at 600°C. Experiments were also carried out to explore creep crack growth at constant load, and crack growth for intermittent cyclic loading. For the as-received material there is substantial primary creep (hardening) at constant load, while for the cyclically hardened material at constant load the creep curves show recovery, and increasing creep rate with increasing time. Specimens subjected to prior cyclic hardening were also used for a series of creep and creep-fatigue crack growth tests. These tests demonstrated that there was accelerated crack growth compared to crack growth in as-received material.     

Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Effeet of Hardening on Elastic-plastic Curved Crack Tip Displacement Under Dynamic Load

In this article,elastic-plastic curved crack tip opening displacement maximum in hardened material under dynamic load has been studied,and curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method and theorem of surname KA,where the effects of dynamic applied stresses and dynamic normal and shear stresses on the boundaries of plastic area are synthetically taken into considerations. Diagrams have been constructed to analyz the transformation relationships between the curved crack tip opening displacement and the work hardening exponents. Curved crack tip opening displacement will decrease with the increasing of hardening exponents in hardened material. The decrease extent of curved crack tip dynamic opening displacement will be more and more severe when hardening exponents increase evenly. Maximum dynamic opening displacement of curved crack tip will decrease when external load decrease with the same hardening exponents.     

Application of extended crystal plasticity to the modeling of glide and kink bands and of crack opening in single crystals

In this work, the influence of the development of geometrically necessary dislocations (GNDs) at a crack tip in single crystals on the hardening and crack propagation behaviour is investigated. In particular, we are interested in examining the effect of such additional hardening on the development of glide and kink bands at the crack tip as well as on the process of crack opening. To this end, following Nye and many others, local deformation incompatibility in the material is adopted as a measure of the density of GNDs. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening. A thermodynamic formulation of the model in the context of the dissipation principle facilitates the derivation of the corresponding hardening relation. Results suggest that this additional hardening retards kink-band development, but has little or no influence on glide-band development. It also influences the crack tip opening displacement (CTOD). It turns out that the simulated CTOD correlates well with experimentally determined crack-propagation rates for different crack growth direction in the crystal.     

A Method for the Evaluation of Fatigue Life under Nonproportional Low-Cycle Loading

We consider a method for the evaluation of fatigue life under multiaxial nonproportional low-cycle loading based on the concept of equivalent strains. The expression for the equivalent strain range is a function only of the strain path and contains a constant depending on the additional hardening of the material under nonproportional loading. We propose a new parameter of the material based on the work of plastic strains in a cycle. This parameter is universal when applied to materials with both low and high degrees of additional hardening. It is in good agreement with the results of testing of 08Kh18N10T stainless steel and VT9 titanium alloy under nonproportional low-cycle loading.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.