Cyclic stress-strain behaviour of alloy AA6060 T4, part II: Biaxial experiments and modelling

Laboratory tests have been conducted to investigate the inelastic behaviour of aluminium alloy AA6060 T4 subjected to non-proportional cyclic loading. The results of four tests with variable strain path shapes and strain amplitudes are reported in this paper. The tests were carried out by applying combined axial force and torque to thin-walled tubular specimens, using effective strain amplitudes in the range 0.4–0.8%. Major emphasis has been put on the two important material properties: plastic anisotropy and influence of strain range and strain path shapes on cyclic hardening. A constitutive model for cyclic plasticity is used to predict the stress response of the alloy for the non-proportional strain paths applied in the experiments. The model adopts a quadratic yield function and multi-component non-linear isotropic and kinematic hardening rules to describe plastic anisotropy, the shape of the hysteresis loops and the evolution of cyclic hardening. Good agreement is obtained between the physical and correlated stress response of the alloy.     

An experimental study of cyclic deformation of extruded AZ61A magnesium alloy

Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension-compression, torsion, and combined axial-torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension-compression at strain amplitudes higher than 0.5%, the stress-strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress-strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial-torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress-shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy.     

Model for plasticity effects in metals under nonproportional cyclic loading

A possible physical mechanism for additional hardening is proposed on the basis of an analysis of experiments on nonproportional cyclic loading of metals. A model for an elastoplastic polycrystal with a hardening law taking into account the interaction of slip systems is developed. The effect of additional hardening for elliptic strain paths and the shapes of stress paths and hysteresis loops typical of elliptic strain paths are described qualitatively. A violation of the assumption of the local determinacy and orientations of stress paths is considered for the square strain paths taking place in tests of chromium-nickel austenite stainless steels. Perm' State Technical University, Perm', 614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 144–151, November–December, 1999.     

304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

Cyclic behaviour of short glass fibre reinforced polyamide: Experimental study and constitutive equations

Polymer matrix composites are widely used in the automotive industry and undergo fatigue loadings. The investigation of the nonlinear cyclic behaviour of such materials is a required preliminary work for a confident fatigue design, but has not involved many publications in the literature. This paper presents an extensive experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibres (PA66 GF35), at room temperature. The material was tested in two conditions: dry-as-moulded (DAM) and at the equilibrium with air containing 50% of relative humidity (RH50).An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recordings. Such an extended database allowed us to highlight several complex physical phenomena: viscoelastic effects at different time scales, irrecoverable mechanisms, non-linear kinematic hardening, non-linear viscous flow rule, cyclic softening.Taking into account this advanced analysis, a constitutive model describing the cyclic behaviour is proposed. As the experimental database only includes uniaxial tensile tests, the general 3D anisotropic frame is reduced to an uniaxial model valid for a specific orientation distribution. The robust identification process is based on tests which enable the uncoupling between the underlined mechanical features. This strategy leads to a model which accurately predicts the cyclic behaviour of conditioned as well as dry materials under complex tensile loadings.     

Artificial aging and shear deformation behaviour of 6022 aluminium alloy

In this study, the artificial aging behaviour of 6022-T4 alloy is investigated over a wide temperature range. Hardness readings, TEM and XRD analyses were performed. It was shown that 6022-T4 alloy can be substantially hardened through a short aging treatment at temperatures in excess of 200 °C. The strain hardening curves of the 6022 alloy in different aging conditions were measured using the simple shear test and analysed in terms of their respective microstructures. The under-aged and pre-peak-aged exhibited a good combination of strength and strain hardening while the peak-aged alloy was characterised by maximum strength, albeit with a drastic reduction in strain hardening ability. Strain reversal experiments in simple shear were carried out in order to characterize the Bauschinger effect for the different heat treatment conditions. It was shown that the T4 and under-aged conditions lead to permanent softening of the flow stress.     

96.5Sn-3.5Ag钎料合金的时相关单轴应变循环变形行为及其本构关系研究

在室温下对96.5Sn-3.5Ag钎料合金进行了不同加载波形下的单轴应变循环实验。研究了在具有不同保持时间、不同应变率、不同应变幅值及其历史对材料的循环变形行为的影响。基于材料时相关变形行为,提出了统一粘塑性本构模型,并对该材料的变形行为进行本构模拟。实验结果表明:该钎料合金单轴变形行为具有应变率、保持时间以及应变幅值依赖性。本构关系的预言结果与实验结果吻合得一致性说明该种模型能够很好地描述材料的单轴应变循环变形行为。     

Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304

A recent study by Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] demonstrated that some of the nonproportional ratcheting responses under stress-controlled loading histories cannot be simulated reasonably by two recent cyclic plasticity models. Two major drawbacks of the models identified were: (i) the stainless steel 304 demonstrated cyclic hardening under strain-controlled loading whereas cyclic softening under stress-controlled loading, which depends on the strain-range and which the existing models cannot describe; (ii) the change in biaxial ratcheting responses due to the change in the degree of nonproportionality were not simulated well by the models. Motivated by these findings, two modified cyclic plasticity models are evaluated in predicting a broad set of cyclic and ratcheting response of stainless steel 304. The experimental responses used in evaluating the modified models included both proportional (uniaxial) and nonproportional (biaxial) loading responses from Hassan and Kyriakides [Hassan, T., Kyriakides, S., 1994a. Ratcheting of cyclically hardening and softening materials. Part I: uniaxial behavior. Int. J. Plasticity, 10, 149–184; Hassan, T., Kyriakides, S., 1994b. Ratcheting of cyclically hardening and softening materials. Part II: multiaxial behavior. Int. J. Plasticity, 10, 185–212.] and Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] The first model studied is a macro-scale, phenomenological, constitutive model originally proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Fifth International Conference on SMiRT, Div. L, Berlin, Germany, L11/3.]. This model was systematically modified for incorporating strain-range dependent cyclic hardening–softening, and proportional and nonproportional loading memory parameters. The second model evaluated is a polycrystalline model originally proposed by Cailletaud [Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity, 8, 55–73.] based on crystalline slip mechanisms. These two models are scrutinized against simulating hysteresis loop shape, cyclic hardening–softening, cross-effect, cyclic relaxation, subsequent cyclic softening and finally a broad set of ratcheting responses under uniaxial and biaxial loading histories. The modeling features which improved simulations for these responses are elaborated in the paper. In addition, a novel technique for simulating both the monotonic and cyclic responses with one set of model parameters is developed and validated.     

Inversion of Ramberg–Osgood equation and description of hysteresis loops

The Ramberg–Osgood equation has been approximately inverted. Four orders of approximations providing progressively more accurate inversions are considered. The second order inversion is used to develop closed-form relations for stress in terms of strain and for cyclic stress in terms of cyclic strain. Explicit relations between the cyclic-strength coefficient and the cyclic strain-hardening exponent and between the cyclic strain-hardening exponent and the elastic modulus are developed. Application to nine different engineering metals shows that the proposed approximate inversion provides a powerful tool for describing stress–strain relations. Examples of hysteresis loops for a number of strain time-histories are presented. Also, it is shown that augmenting the strain time-history with fictitious strain segments to close all the hysteresis loops yields the same stress–strain relation as that obtained through the rain-flow counting method.     

New flow rules in elasto-viscoplastic constitutive models for spheroidal graphite cast-iron

A specific flow rules and the corresponding constitutive elasto-viscoplastic model combined with new experimental strategy are introduced in order to represent a spheroidal graphite cast-iron behaviour on a wide range of strain, strain rate and temperature. A “full model” is first proposed to correctly reproduce the alloy behaviour even for very small strain levels. A “light model” with a bit poorer experimental agreement but a simpler formulation is also proposed. These macroscopic models, whose equations are based on physical phenomena observed at the dislocation scale, are able to cope with the various load conditions tested – progressive straining and cyclic hardening tests – and to correctly describe anisothermal evolution. The accuracy of these two models and the experimental databases to which they are linked is estimated on different types of experimental tests and compared with the accuracy of more standard Chaboche-type constitutive models. Each test leads to the superiority of the “full model”, particularly for slow strain rates regimes. After developing a material user subroutine, FEM simulations are performed on Abaqus for a car engine exhaust manifold and confirm the good results obtained from the experimental basis. We obtain more accurate results than those given by more traditional laws. A very good correlation is observed between the simulations and the engine bench tests.     

一个非比例循环粘塑性本构模型

本文提出地一个考虑材料非比例循环附加强效应，非比例循环加载历史产应和应变幅值历史效应的粘塑性体构模型。在该模型中，引入了对加载过程非常弹性应变幅值的记忆变量ｑ；定义了新的非比例度；引入了考虑材料非比例度的循环饱和各向同性变形阻力参量Ｑｓ；对各向同性变开引入了具有先前加载历史记忆的演化方程，将本文模型用于１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢高温循环变形行为描述，其预言结果与实验结果吻合得很好，表明该模型能很好     

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.     

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.     

1Cr18Ni9Ti不锈钢的非比例循环强化性能

对1Cr18Ni9Ti不锈钢进行了各种比例和非比例循环本构实验,其中包括圆路径、正方形、正菱形、蝶形、三角形和两种十字形应变路径。表明其具有明显的非比例循环附加强化。在相同的等效应变幅值上,材料的附加强化与路径密切相关。对于圆路径,其附加强化度最大可达60％。通过对不同应变历史的实验研究表明,先前小的非比例度的加载历史对后继大的非比例度路径的强化没有影响;而先前大非比例度的加载路径对后继小非比例度路径的循环强化有较大影响。     

Hysteresis cycles and fatigue criteria using anelastic models based on fractional derivatives

The constitutive equation and the fatigue of anelastic media are described by using fractional order derivatives. The stress–strain relation, based on a generalization of the Kelvin–Voigt model, describes typical hysteresis cycles with the stress increasing as the number of cycles increases, a phenomenon known as cyclic hardening and observed in many materials such as, for instance, steel. Criteria are established to find the number of cycles which may cause fatigue for a strain with a given amplitude and frequency. They are based on the yield and fatigue stresses, on the melting temperature through the dissipated energy, and on the strain energy. In all the cases, it is seen that the number of cycles to failure is inversely proportional to the amplitude and to the frequency of the applied strain. Comparison to experimental data indicates that the model satisfies, at least qualitatively, the behavior of real materials under cyclic loading.     

Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures

Two recently proposed Helmholtz free energy potentials including the full dislocation density tensor as an argument within the framework of strain gradient plasticity are used to predict the cyclic elastoplastic response of periodic laminate microstructures. First, a rank-one defect energy is considered, allowing for a size-effect on the overall yield strength of micro-heterogeneous materials. As a second candidate, a logarithmic defect energy is investigated, which is motivated by the work of Groma et al. (2003). The properties of the back-stress arising from both energies are investigated in the case of a laminate microstructure for which analytical as well as numerical solutions are derived. In this context, a new regularization technique for the numerical treatment of the rank-one potential is presented based on an incremental potential involving Lagrange multipliers. The results illustrate the effect of the two energies on the macroscopic size-dependent stress–strain response in monotonic and cyclic shear loading, as well as the arising pile-up distributions. Under cyclic loading, stress–strain hysteresis loops with inflections are predicted by both models. The logarithmic potential is shown to provide a continuum formulation of Asaro's type III kinematic hardening model. Experimental evidence in the literature of such loops with inflections in two-phased FFC alloys is provided, showing that the proposed strain gradient models reflect the occurrence of reversible plasticity phenomena under reverse loading.