Cyclic viscoelastoplasticity of polypropylene/nanoclay composites

Observations are reported on isotactic polypropylene/organically modified nanoclay hybrids with concentrations of filler ranging from 0 to 5 wt.% in cyclic tensile tests with a stress?Ccontrolled program (oscillations between various maximum stresses and the zero minimum stress). A pronounced effect of nanofiller is demonstrated: reinforcement with 2?wt.% of clay results in strong reduction of maximum and minimum strains per cycle and growth of number of cycles to failure compared with neat polypropylene. To rationalize these findings, a constitutive model is developed in cyclic viscoelasticity and viscoplasticity of polymer nanocomposites. Adjustable parameters in the stress?Cstrain relations are found by fitting experimental data. The model correctly describes the growth of the ratcheting strain and shows that fatigue failure is driven by a pronounced increase in plastic strain in the crystalline phase. To assess the influence of loading conditions on the changes in the material parameters, experimental data on polypropylene are studied in cyclic tests with a strain?Ccontrolled program (oscillations between fixed maximum and minimum strains) and a mixed program (oscillations between various maximum strains and the zero minimum stress). Numerical simulation confirms the ability of the model to predict the evolution of stress?Cstrain diagrams with the number of cycles.     

Multi-cycle viscoplastic deformation of polypropylene

Experimental data are reported on isotactic polypropylene in tensile cyclic tests with a strain-controlled program (150 cycles) and various maximum strains. A model is developed in cyclic viscoplasticity of semicrystalline polymers. The constitutive equations describe the mechanical response along each individual cycle of loading–unloading. Material constants in the stress–strain relations are found by fitting observations during several first cycles. For cyclic deformation with a large number of cycles, phenomenological equations are introduced to account for the effect of plastic flow and damage accumulation on adjustable parameters. It is demonstrated that the model qualitatively predicts changes in maximum stress and minimum strain per cycle with number of cycles. The stress–strain relations are applied to assess growth of residual strain under cyclic loading with large (tens of thousand) number of cycles.     

Ratcheting progress at notch root of 1045 steel samples over asymmetric loading cycles: Experiments and analyses

The present study examines ratcheting response of steel samples with various notch diameters through conducting several cyclic tests. Ratcheting strain values were measured through strain gauges mounted at different distances from the notch root. Local ratcheting at the notch region was highly influenced by notch diameter, notch shape, distance from the notch root, and magnitude of the nominal mean/amplitude of loading cycles. Nominal force‐controlled cycles were kept below the yield point and the Neuber's rule accommodated for the maximum/minimum local stress components along those local strains measured through the strain gauges at the notch region. Plastic strains at the vicinity of notch root over loading cycles were further accumulated by means of the Chaboche hardening model. The local ratcheting strain while progressed at the notch root plastic zone over loading cycles resulted in mean stress relaxation controlled by the model.     

Ratcheting response of nylon fiber reinforced natural rubber/styrene butadiene rubber composites under uniaxial stress cycles: Experimental studies

The present study intends to study the ratcheting response of nylon fiber reinforced natural rubber (NR)‐styrene butadiene rubber (SBR) composite samples under asymmetric stress cycles. Uniaxial tests conducted on composite samples have shown how influential the weight fraction of short nylon fibers on the stress‐strain curves/loops under monotonic and cyclic loads is. NR/SBR composite samples with various fiber contents of 0, 10, 20, 30, and 40 per hundred rubber (phr) were tested under asymmetric stress cycles. In these tests, stress‐strain hysteresis loops were progressively shifted over stress cycles resulting in progressive plastic strain accumulation. Over stress cycles, ratcheting strain progressed within the first few cycles with a relatively high rate, and as the number of cycles increased, this rate decayed resulting in a plateau in strain accumulation (shakedown). The ratcheting strain rate and magnitude resulting in shakedown were highly affected by the nylon fiber content. The experimental observations showed that this plateau (shakedown) occurred after a number of cycles in NR/SBR composite samples where the widths of hysteresis loops stayed unchanged. Samples with no fiber and that with 10 phr fiber content possessed high ratcheting rates leading samples to failure after a few stress cycles. Fracture surfaces in these samples were further analyzed through SEM investigation.     

Key issues in cyclic plastic deformation: Experimentation

Cyclic plastic deformation phenomena include the Bauschinger effect, cyclic hardening/softening, strain range effect, loading history memory, ratcheting, mean stress dependent hardening, mean stress relaxation and non-proportional hardening. In this work, different cyclic plastic deformation responses of piping materials (SA333 C-Mn steel and 304LN stainless steel) are experimentally explored. Cyclic hardening/softening is depends upon loading types (i.e. stress/strain controlled), previous loading history and strain/stress range. Pre-straining followed by LCF and mean stress relaxation shows similar kind of material response. Substantial amount of non proportional hardening is observed in SA333 C-Mn steel during 90° out of phase tension-torsion loading. During ratcheting, large amount of permanent strain is accumulated with progression of cycles. Permanent strain accumulation in a particular direction causes cross-sectional area reduction and which results uncontrollable alteration of true stress in engineering stress controlled ratcheting test. In this work, true stress control ratcheting on piping materials has been carried out in laboratory environment. Effects of stress amplitude and mean stress on the ratcheting behaviors are analyzed. A comparison has also been drawn in between the true and engineering stress controlled tests, and massive difference in ratcheting life and strain accumulation is found.     

McDowell模型改进及1070钢棘轮效应的预测

利用McDowell 模型对1070 钢比例和非比例循环加载条件下的棘轮效应进行了预测,通过对McDowell模型的修正,为McDowell 模型中的单轴参数Ai引入了与塑性应变累积相关的演化方程,改进后的McDowell 模型能精确的预测具有拉压平均应力的单轴棘轮效应,具有平均应力的拉扭比例加载,常轴向应力的扭转循环,非比例循环载荷以及多重步骤加载条件下单轴平均应力变化的棘轮效应,改进的模型对较大循环数的棘轮效应也能给予较好的描述。     

The effect of low cycle fatigue,ratcheting and mean stress relaxation on stress–strain response and microstructural development in a dual phase steel

This study examines the cyclic plastic deformation behavior and microstructural development of a dual phase steel in both symmetric and asymmetric cycling in strain and stress control modes. The low-cycle fatigue (LCF) and mean stress relaxation (MSR) tests show very similar fatigue lifetimes. However, fatigue lifetimes reduce and prominent accumulation of directional strain was observed in ratcheting. A microstructural analysis has revealed that the type of cyclic test carried out has a noticeable impact on the substructural development, and this has been correlated with differences in accumulated tensile strain. Electron backscatter diffraction investigation has shown larger in-grain misorientation for ratcheting specimen in comparison with LCF and MSR specimens. The orientation of ferrite grains was found to have very little effect on their substructural development, and strain localization commonly occurred in the ferrite at the ferrite/martensite interface.     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1 wt.% of nanoclay induces an increase in time to failure by an order of magnitude.     

Ratcheting assessment of steel alloys under uniaxial loading: a parametric model versus hardening rule of Bower

This study intends to compare ratcheting response of 42CrMo, 1020, SA333 and SS304 steel alloys over uniaxial stress cycles evaluated by a parametric ratcheting model and Bower's hardening rule. The parametric ratcheting equation was formulated to describe triphasic stages of ratcheting deformation over stress cycles. Mechanistic parameters of mean stress, stress amplitude, material properties and cyclic softening/hardening response of materials were employed to calibrate parametric equation. Based on the framework of cyclic plasticity theory, the modified Armstrong–Frederick nonlinear hardening rule of Bower was employed to assess ratcheting response of steel alloys under uniaxial stress cycles. Bower's model was chosen mainly due to simplicity of the model and its lower number of constants required to predict ratcheting strain over stress cycles as compared with other hardening rules. Ratcheting strain values predicted by Bower's model showed good agreements over stage I of stress cycles as compared with experimental values of ratcheting strain. Beyond of stage I stress cycles, Bower ratcheting strain rate stayed constant resulting in an arrest in ratcheting process. The predicted ratcheting strains based on the parametric equation were found in good agreements over three stages of ratcheting as compared with those of experimentally obtained.     

Effects of extrusion ratio on the ratcheting behavior of extruded AZ31B magnesium alloy under asymmetrical uniaxial cyclic loading

Magnesium alloys are increasingly used in the automotive and aerospace industries for weight reduction and fuel savings. The ratcheting behavior of these alloys is therefore an important consideration. The objective of this investigation was to study the effects of extrusion ratio on the ratcheting behavior of extruded AZ31B magnesium alloy. The experiments have shown that the extruded AZ31B Mg alloy presented the following characteristic behavior with increasing number of loading cycles: first an apparent cyclic softening was observed, then a cyclic hardening occurred, and finally a stable state was reached. This generic behavior can be explained by the fact that the variation trend of the maximum strain with the number of cycles differs from that of the minimum strain. The extrusion ratio did not influence the cyclic softening/hardening behavior or the final ratcheting strain variation trend of the extruded AZ31B Mg alloy with the mean stress and the peak stress. However, the extrusion ratio influenced the final ratcheting strain variation trend of the extruded AZ31B Mg alloy with the stress amplitude. Increasing the extrusion ratio also reduced the ratcheting strain and the effects of the load history on the ratcheting behavior of the extruded AZ31B Mg alloy.     

Effects of pre-strain on uniaxial ratcheting and fatigue failure of Z2CN18.10 austenitic stainless steel

Effects of both tensile and compressive pre-strain on cyclic deformation of Z2CN18.10 austenitic stainless steel under stress cycling with mean stress are studied. As compared to as-received material, ratcheting strain of subsequent stress cycling decreases with increasing tensile pre-strain (TP) level. Lower level of compressive pre-strain (CP) is found to accelerate ratcheting strain accumulation while higher level of CP retards the accumulation. Tensile pre-straining is beneficial to ratcheting–fatigue life while compressive pre-straining is detrimental. A modified fatigue model to address the effect of pre-straining is proposed to predict the fatigue lives of the stress cycling tests with mean stress.     

Experimental Study on the Uniaxial Cyclic Deformation of 25CDV4.11 Steel

The strain cyclic characteristics and ratcheting behavior of 25CDV4.11 steel were studied by the experiments under uniaxial cyclic loading with relatively high cyclic number and at room temperature. The cyclic hardening/softening feature of the material was first observed under the uniaxial strain cycling with various strain amplitudes. Then, the ratcheting behavior of the material was researched in detail, and the effects of stress amplitude and mean stress on the ratcheting were discussed under uniaxial asymmetrical stress cycling. Comparing with the experimental results of SS316L stainless steel, it is concluded that the material exhibits remarkable cyclic softening feature, and then a special ratcheting behavior is caused. Some conclusions useful to establish corresponding constitutive model are obtained.     

Effect of prestrain on tensile properties and ratcheting behaviour of Ti-stabilised interstitial free steel

Effect of prestrain ranging between 2.5 and 15 percent on tensile properties, and ratcheting behaviour of an interstitial free steel has been studied at two different stress combinations. It is found that while yield strength increases in two distinctly different stages, the increase of tensile strength follows perfect linear relationship with increase in the amount of prestrain. The ratcheting strain accumulation direction during initial stage of asymmetric cyclic loading at constant tensile mean stress depends upon imposed maximum stress and the amount of prestrain. Number of cycles for accumulation of 16.30 pct true ratcheting strain increases with the amount of prestrain following perfect exponential relationships for both the stress combinations; but it increases in a perfectly bilinear manner with tensile yield strength of prestrained specimens. With 16.30 pct accumulated ratcheting strain the amount of back stress is found as 110 MPa irrespective of the amount of prestrain. Marginal variation in post-ratcheting tensile properties as a function of tensile prestrain has been observed.     

Effect of stress parameters on ratcheting deformation stages of polycrystalline OFHC copper

Engineering stress‐controlled ratcheting tests under different sets of stress amplitudes and mean stresses show that ratcheting deformation in polycrystalline OFHC copper occurs in three different stages. A plateau region with almost no accumulation of inelastic strain follows general ratcheting deformation during initial loading cycles. With breakdown of the plateau region inelastic ratcheting deformation occurs at an increasingly rapid rate. The effect of the stress amplitude on the ratcheting process is found to be more than mean stress effect. Reconstruction of the ratcheting curves clearly separates the conditions for stress‐controlled low cycle fatigue with zero mean stress and ratcheting with tensile mean stress.     

聚碳酸酯的单轴棘轮行为研究

在常温常湿下,对聚碳酸酯(PC)材料进行了一系列单轴应变循环和非对称应力循环实验。讨论了PC材料在不同加载水平、加载历史、应力率和峰值保持时间下的循环变形特征。结果表明:PC材料在应变循环过程中体现出了一定程度的循环软化特性,其响应应力幅值在应变循环中随着循环周次的增加而下降,但不是很明显;PC材料在非对称应力循环加载过程中产生明显的棘轮行为,棘轮应变随着平均应力和应力幅值的增加而增加,并且平均应力的影响大于应力幅值的影响;加载历史对于棘轮变形行为的影响较为明显,但对应变循环特性影响不大;PC材料的棘轮变形随着应力率的减小和峰值保持时间的增加而增加,体现明显的时相关性。     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.