Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure

This paper evaluates seven cyclic plasticity models for structural ratcheting response simulations. The models evaluated are bilinear (Prager), multilinear (Besseling), Chaboche, Ohno–Wang, Abdel Karim–Ohno, modified Chaboche (Bari and Hassan) and modified Ohno–Wang (Chen and Jiao). The first three models are already available in the ANSYS finite element package, whereas the last four were implemented into ANSYS for this study. Experimental responses of straight steel pipes under cyclic bending with symmetric end rotation history and steady internal pressure were recorded for the model evaluation study. It is demonstrated that when the model parameters are determined from the material response data, none of the models evaluated perform satisfactorily in simulating the straight pipe diameter change and circumferential strain ratcheting responses. A detailed parameter sensitivity study with the modified Chaboche model was conducted to identify the parameters that influence the ratcheting simulations and to determine the ranges of the parameter values over which a genetic algorithm can search for refinement of these values. The refined parameter values improved the simulations of straight pipe ratcheting responses, but the simulations still are not acceptable. Further, improvement in cyclic plasticity modeling and incorporation of structural features, like residual stresses and anisotropy of materials in the analysis will be essential for advancement of low-cycle fatigue response simulations of structures.     

单轴循环冲击下弱风化花岗岩的损伤演化

为研究爆破应力波作用下弱风化花岗岩的力学特性和损伤演化机理,利用直径50 mm的改进分离式Hopkinson压杆装置,开展以不同速度对花岗岩进行单次和等速循环冲击下的实验研究。研究结果表明：单次冲击中,用能量法确定的损伤阈值,可用于循环冲击实验中;不同应变率下弱风化岩石裂纹扩展阶段存在应力松弛平台,且随应变率升高而愈发明显,峰值应力与应变率呈正相关。等速循环冲击中,最大应力、应变与冲击速度呈正相关,与岩样累积冲击总次数呈负相关;损伤演化具有3个阶段呈倒S形,由其构建的双参数损伤演化模型拟合效果理想,且具有物理意义;利用模型中的参数α和β可计算中值点处的损伤度和相对循环次数,且与冲击速度正相关;不同损伤变量计算的损伤演化模型不同,合理定义损伤变量是必要的。

     

An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression

Strength and deformability characteristics of rock with pre-existing fissures are governed by cracking behavior. To further research the effects of pre-existing fissures on the mechanical properties and crack coalescence process, a series of uniaxial compression tests were carried out for rock-like material with two unparallel fissures.In the present study, cement, quartz sand, and water were used to fabricate a kind of brittle rock-like material cylindrical model specimen. The mechanical properties of rock-like material specimen used in this research were all in good agreement with the brittle rock materials. Two unparallel fissures(a horizontal fissure and an inclined fissure) were created by inserting steel during molding the model specimen.Then all the pre-fissured rock-like specimens were tested under uniaxial compression by a rock mechanics servocontrolled testing system. The peak strength and Young's modulus of pre-fissured specimen all first decreased and then increased when the fissure angle increased from 0?to 75?.In order to investigate the crack initiation, propagation and coalescence process, photographic monitoring was adopted to capture images during the entire deformation process.Moreover, acoustic emission(AE) monitoring technique was also used to obtain the AE evolution characteristic of prefissured specimen. The relationship between axial stress, AE events, and the crack coalescence process was set up: when a new crack was initiated or a crack coalescence occurred, thecorresponding axial stress dropped in the axial stress–time curve and a big AE event could be observed simultaneously.Finally, the mechanism of crack propagation under microscopic observation was discussed. These experimental results are expected to increase the understanding of the strength failure behavior and the cracking mechanism of rock containing unparallel fissures.     

Multiscale experimental investigations about the cyclic behavior of the 304L SS

This work follows a series of experiments carried out earlier at INSA of Rouen (Hassan, T., Taleb, L., Krishna, S., 2008. Influence of non-proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889). It investigates the elastoplastic cyclic behavior of a 304L stainless steel at room temperature. In a first step the cross path effect on ratcheting is confirmed, as well as the crucial role of the loading path non-proportionality. Strain controlled tests are also conducted for different strain amplitudes and loading paths. Cross-hardening effect appears more important when the shearing sequence is followed by the axial one. Moreover for alternating axial and shearing cycles, this phenomenon occurs after each crossing sequence leading to a very significant strain hardening, at least of the same order as the one obtained after a circular strain path. Yet, the magnitude of the observed over hardening does not necessarily seem a function of the cumulated plastic strain.     

Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models

Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

An experimental study of inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading

An experimental study was conducted on the inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading. Thin-walled tubular specimens were used and small strain gages were bonded on the specimen surface to characterize the local deformation. The controlled loading paths included cyclic tension–compression, cyclic torsion, proportional axial-torsion, 90°-out-of-phase axial-torsion, and fully reversed torsion with a constant axial stress. The maximum stress in each experiment was lower than the lower yield stress of the material. It was found that the cyclic plastic deformation within the gage section of the specimen under multiaxial stress state followed the three-stage process that was observed from uniaxial loading, namely, incubation, propagation, and saturation. The plastic deformation was significantly inhomogeneous during the propagation stage, and the inhomogeneity continued through the saturation stage. The duration of each stage and the saturated strains were dependent on the cyclic stress amplitude and the loading path. Multiaxial stress state reduced the incubation stage. With identical equivalent stress magnitude, the nonproportional loading path resulted in the shortest incubation and propagation stages, and the saturated equivalent plastic strain magnitude was the smallest. Although the deformation over the gage section was inhomogeneous, the plastic deformation in a given local area was found to be practically isotropic.     

A study of directionality of latent hardening behavior in aluminium single crystals

By defining the yield stress in a latent hardening test as the first deviation from the elastic straight line, the yielding and hardening behavior on a latent system in the positive and negative slip direction was studied in aluminium single crystals. It is shown that the yield stresses on both the positive and negative latent systems are about equal to or a little lower than the maximum resolved shear stress in the primary test, but much higher than that of the active system. The influence of relative orientation and prestrain on latent hardening and initial work-hardening in the secondary test was also investigated, and it was found that there is a considerable effect on initial work-hardening, but none on latent hardening. With reasonable approximation, a hardening rule for single crystal could be proposed from the experimental results, that is, except for the yield stress on the system negative to the active system that is very low, hardening on the other systems is nearly the same as self-hardening.     

热冲击下 A3 钢力学性能的研究

对一定拉伸预载下的Ａ３钢试样进行了快速加热实验,研究了温升率对Ａ３钢力学性能的影响。结果表明：温升率对自由热膨胀影响不大;温升率越大,产生相同塑性变形需要的温度越高;温升率明显影响Ａ３钢内部变化机制;温升率将决定试样热冲击后的晶粒大小。     

平面碰撞与强激光加载下金属铝的层裂行为

在轻气炮和神光Ⅱ强激光装置上开展了金属铝的层裂实验。针对激光打靶层裂实验中样品自由面速度剖面后期振荡容易丢失问题,改进靶设计,获得很好效果。利用轻气炮加载和强激光加载层裂实验应变率的显著差异,并通过数值模拟,讨论了在建立具有预测能力的理论建模中需要关注的损伤成核、演化与汇合问题中的材料特性与应变率相关特性因素。结果表明,对于我们以前建立的动态损伤与断裂模型,微孔洞成核的平均半径、阈值压力、成核速率相关参数以及微孔洞长大的阈值压力等具有材料特性属性,但微孔洞的表面能以及决定材料发生完全层裂的临界损伤度等具有明显的应变率效应。另外,分析还发现,虽然层裂强度具有明显的应变率效应,但是在样品层裂当地,样品由持续拉伸向收缩转变的临界行为,取决于一个很小的临界损伤,这个临界值很可能是材料常数,与应变率无关。     

An experimental study on the flow behavior of micellar solutions

At higher concentration levels, the inner structure of micellar solutions cannot be detected directly by optical means. Nevertheless, the flow behavior of the micellar solutions reflects their micellar structures. Hence, in this study the material behavior of micellar surfactant solutions was investigated by rheometrical means in steady and oscillatory shear flows. The flow behavior of the solutions was found to be strongly dependent on the concentration of the surfactants. At very low concentrations, the surfactant solution shows Newtonian behavior. With increasing concentration, a transition to shear thinning behavior and increasing viscoelasticity was found. The complex material structure is modeled according to the flow behavior by discrete and continuous relaxation time spectra, depending on the concentration. Received: 3 May 2000/Accepted: 18 September 2000     

An experimental study of uniaxial creep,cyclic creep and relaxation of aisi type 304 stainless steel at room temperature

Following previous work (Krempl, 1979), a servocontrolled testing machine and strain measurement at the gage length were used to study the uniaxial rate(time)-dependent behavior of AISI Type 304 stainless steel at room temperature. The test results show that the creep strain accumulated in a given period of time depends strongly on the stress-rate preceding the creep test. In constant stress-rate zero-to-tension loading the creep strain accumulated in a fixed time-period at a given stress level is always higher during loading than during unloading. Continued cycling causes an exhaustion of creep ratchetting which depends on the stress-rate. Periods of creep and relaxation introduced during completely reversed plastic cycling show that the curved portions of the hysteresis loop exhibit most of the inelasticity. In the straight portions, creep and relaxation are small and there exists a region commencing after unloading where the behavior is similar to that at the origin for virgin materials. This region does not extend to zero stress.The results are at variance with creep theory and with viscoplasticity theories which assume that the yield surface expands with the stress. They support the theory of viscoplasticity based on total strain and overstress.     

Visco-plastic constitutive modeling on Ohno-Wang kinematic hardening rule for uniaxial ratcheting behavior of Z2CND18.12N steel

Experimental results of monotonic uniaxial tensile tests at different strain rates and the reversed strain cycling test showed the characteristics of rate-dependence and cyclic hardening of Z2CND18.12N austenitic stainless steel at room temperature, respectively. Based on the Ohno-Wang kinematic hardening rule, a visco-plastic constitutive model incorporated with isotropic hardening was developed to describe the uniaxial ratcheting behavior of Z2CND18.12N steel under various stress-controlled loading conditions. Predicted results of the developed model agreed better with experimental results when the ratcheting strain level became higher, but the developed model overestimated the ratcheting deformation in other cases. A modified model was proposed to improve the prediction accuracy. In the modified model, the parameter m_i of the Ohno-Wang kinematic hardening rule was developed to evolve with the accumulated plastic strain. Simulation results of the modified model proved much better agreement with experiments.     

不同循环加载应力下花岗岩Kaiser效应特征的试验研究

为了更准确地获取花岗岩的Kaiser效应点对应的应力值σAE,利用RMT-100B岩石力学伺服试验机和Micro-Ⅱ Express型声发射监测系统,研究不同循环加载应力σci下岩石Kaiser效应特征.结果表明:相比单次加载,在循环加载作用下,试样的应力-应变曲线在加载初期下凸减弱,压密阶段变短;由于试样的加卸载曲线...     

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.     

An experimental study of the elasto-plastic behavior of certain grid frameworks

An experimental investigation of the elastoplastic behavior of certain torsionless grid frameworks is presented. The purpose of the test program was to determine the significance of the stiffness criterion in the evaluation of collapse loads of interconnected beam systems. The load-deflection relationships in the various members, the sequence of hinges and moment redistribution are studied. The test values are used to verify the theoretical values obtained by the application of the simple plastic theory.     

循环爆破开挖下隧道围岩振动效应与损伤演化的模型实验

针对推进式循环爆破开挖下隧道围岩振动效应与损伤演化问题,按照相似比理论进行模型实验研究,实验模型采用1:15比例浇筑制成。通过模拟隧道推进式循环爆破开挖方式,以同一测点处爆破前后岩体声速变化评价隧道围岩损伤程度,探寻爆破参量变化对振动效应的影响,探索围岩损伤演化与爆破次数之间的关系。研究结果表明:在最大段药量大致相同情况下,起爆段数对萨道夫斯基公式的介质系数K影响很小,而对萨道夫斯基公式的衰减系数α影响较大;隧道在推进式循环爆破开挖下,同一深度距离爆区相同的测点,其声速降低率存在较大差异,围岩的爆破损伤范围在深度和广度方面均具有典型的各向异性特征;当爆炸参量基本相同时,不同循环爆破开挖下测点的累积声速降低率呈非线性增长趋势;在推进式循环爆破加载下,围岩爆破累积损伤量D与爆破次数n之间存在非线性演化特性,不同的测点具有各自的爆破累积损伤扩展模型,距离爆源越近爆破损伤扩展越快,围岩爆破累积损伤效应具有典型的非线性演化特性和各向异性特征。     

An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension

In the experiments on stress-induced phase transitions in SMA strips, several interesting instability phenomena have been observed, including a necking-type instability (associated with the stress drop), a shear-type instability (associated with the inclination of the transformation front) and an orientation instability (associated with the switch of the inclination angle). In order to shed more lights on these phenomena, in this paper we conduct an analytical study. We consider the problem in a three-dimensional setting, which implies that one needs to study the difficult problem of solution bifurcations of high-dimensional nonlinear partial differential equations. By using the smallness of the maximum strain, the thickness and width of the strip, we use a methodology, which combines series expansions and asymptotic expansions, to derive the asymptotic normal form equations, which can yield the leading-order behavior of the original three-dimensional field equations. An important feature of the second normal form equation is that it contains a turning point for the localization (necking) solution of the first equation. It is the presence of such a turning point which causes the inclination of the phase transformation front. The WKB method is used to construct the asymptotic solutions, which can capture the shear instability and the orientation instability successfully. Our analytical results reveal that the inclination of the transformation front is a phenomenon of localization-induced buckling (or phase-transition-induced buckling as the localization is caused by the phase transition). Due to the similarities between the development of the Luders band in a mild steel and the stress-induced transformations in a SMA, the present results give a strong analytical evidence that the former is also caused by macroscopic effects instead of microscopic effects. Our analytical results also reveal more explicitly the important roles played by the geometrical parameters.