Comparative study on biaxial low-cycle fatigue behaviour of three structural steels

In this study the uniaxial/biaxial low‐cycle fatigue behaviour of three structural steels (Ck45 normalized steel, 42CrMo4 quenched and tempered steel and AISI 303 stainless steel) are studied, evaluated and compared. Two parameters are considered for estimating non‐proportional fatigue lives: the coefficient of additional hardening and the factor of non‐proportionality. A series of tests of uniaxial/biaxial low‐cycle fatigue composed of tension/compression with cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Several loading paths were carried out, including proportional and non‐proportional ones, in order to verify the additional hardening caused by different loading paths. The experiments showed that the three materials studied have very different additional hardening behaviour. Generally, the transient process from the initial loading cycle to stabilized loading cycle occurs in a few cycles. The stabilized cyclic stress/strain parameters are controlling parameters for fatigue damage. A factor of non‐proportionality of the loading paths is evaluated based on the Minimum Circumscribed Ellipse approach. It is shown that the microstructure has a great influence on the additional hardening and the hardening effect is dependent on the loading path and also the intensity of the loading.     

Effects of changes in strain path on the anisotropy of yield stresses of low-carbon steel and 70-30 brass sheets

Uniaxial tensile tests in various directions following uniaxial extension, equibiaxial stretching or plane strain rolling have been performed to study the effects of changes in strain path on the anisotropy of yield stresses of aluminium-killed low-carbon steel and 70-30 brass sheets. The anisotropy could be predicted from the specimen textures, if dislocation structure were equiaxed, as in the case of equibiaxial stretching. However, elongated dislocation cell structures, developed in the steel specimens prestrained in uniaxial tension or plane strain rolling, gave rise to the second-stage yield stresses higher than predicted from textures in the directions different from the maximum prestrain direction. Planar dislocation structures in the brass specimens prestrained in uniaxial tension or plane strain rolling gave the second-stage yield stresses lower than predicted from the textures in the directions different from the maximum prestrain direction. The phenomena are discussed based on textures and dislocation structures.     

加载路径对5A06铝合金力学性能和微观组织的影响

目的 通过力学性能测试和微观组织表征等手段研究预加载方向和双向加载对5A06铝合金组织性能的影响。方法 分别沿轧制方向(RD)和垂直于轧制方向(TD)施加预变形,然后沿RD进行拉伸试验,对比研究预加载方向对合金力学性能的影响。通过双向拉伸试验研究合金在双向加载时力学性能的变化情况;采用透射电镜观察预加载和双向加载条件下典型试样内的位错组态,分析加载路径对位错组态的影响。结果 预加载使5A06铝合金的屈服强度提高,伸长率下降。与RD预加载相比,TD预加载对屈服强度和伸长率的影响更小,TD预加载试样的抗拉强度更高。不同预加载方向下试样的位错组态不同:预加载与二次加载方向一致会使位错沿单一方向塞积;预加载与二次加载方向垂直时会出现平行位错列交错缠结现象。双向加载时,不同加载比例下合金的应力–应变关系不同,加载比例越接近等比例双向拉伸情况,加工硬化系数越大,在等比例双轴拉伸时达到最大。在应力状态从单拉状态变化到等双拉状态的过程中,不同阶段屈服点间隔不同,在等比例双轴拉伸时达到最大,在单向拉伸时最小。对于不同加载比例的试样,其位错密度随中心区应变量的增大而增大。结论 预加载方向会显著影响5A06铝合金的力学性能和位错组态。不同比例的双向加载会影响5A06铝合金的应力–应变关系。     

A plasticity model for multiaxial cyclic loading and ratchetting

Summary The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.     

Behavior of high performance fiber reinforced cement composites under multi-axial compressive loading

Experiments were conducted to better understand the behavior of strain hardening, high performance fiber reinforced cement composites (HPFRCC) when subjected to uniaxial, biaxial, and triaxial compression. The experimental parameters were: type of fiber, fiber volume fraction, and loading path. Two types of commercially available fibers, namely high-strength hooked steel fiber and ultra high molecular weight polyethylene fiber, with volume fractions ranging from 1.0% to 2.0%, were used in a 55-MPa mortar matrix. The selected loading paths consisted of uniaxial compression and tension, equal biaxial compression, and triaxial compression with two levels of lateral compression. The test results revealed that the inclusion of short fibers can significantly increase both strength and ductility under uniaxial and biaxial loading paths, but that the role of volume fraction is rather small for the range of fiber volume contents considered. The results also showed that the confining effect introduced by the fibers becomes minor in triaxial compression tests, where there is relatively high external confining pressure. The experimental information documented herein can serve as input for the development of multiaxial constitutive models for HPFRCCs.     

Stabilized cyclic stress-strain calculation for metals under multiaxial loading

A simple plasticity model for modeling the stabilized cyclic stress-strain responses is developed to consider the effect of non-proportional additional hardening. In the proposed model, the plastic modulus for uniaxial loading is extended to multiaxial loading by introducing the non-proportionality factor and the additional hardening coefficient. The two introduced factors take into account the effects of non-proportional additional hardening, not only on the shape of the loading path, but also on the material and its microstructure. And then, the basic Armstrong-Frederick nonlinear hardening rule is modified to model the evolution of the back stress. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. The proposed model requires only six material constants for estimating the stabilized responses. Comparisons between the test results (30CrNiMo8HH steel, SA 333 Gr.6 steel, and 1 %CrMoV steel) and model predictions show that the proposed model predicts relatively accurate stress responses under both proportional and non-proportional loading paths.     

高强轨道钢双轴压-扭棘轮行为的实验和模拟

在室温下对高强轨道钢进行了单轴和非比例双轴压-扭循环变形行为的实验,讨论了不同加载路径对轨道钢棘轮变形行为的影响。结果显示:该轨道钢呈现出明显的循环软化效应和压缩方向的棘轮行为,且棘轮行为的演化表现出强烈的加载路径相关性;在椭圆路径下,棘轮应变较其他四种路径更小。进而建立了基于Abdel Karim-Ohno非线性随动硬化律的非比例多轴循环棘轮本构模型,并通过在随动硬化和各向同性软化律中引入非比例因子来考虑非比例路径对双轴压-扭棘轮行为的影响。实验结果和模拟结果的对比表明:该本构模型能够较好地模拟高强度轨道钢的非比例双轴压-扭棘轮行为。     

Strain Hardening of Initially Isotropic Metals under Loading along Slightly Curved Trajectories

By the example of martensitic steel we study regularities of strain hardening under loading along two-link broken paths corresponding to slightly curved strain paths. It is shown that the loading surface separating the domains of elastic and elastoplastic strains (yield surface) is displaced in the direction of a vector connecting the surface center with the loading path image point, while the shape of its frontal part remains unchanged. The yield surface center displacement versus the intensity of accumulated plastic strains is described by a curve invariant to the loading path.     

Induced anisotropy by the Mullins effect in filled silicone rubber

This study is concerned with the experimental characterization of anisotropy induced by the Mullins effect in a particle-reinforced silicone rubber. Experimental data concerning the influence of type and direction of initial loading on the subsequent stress softening are quite scarce. In this scope, a set of experimental tests were carried out on a filled silicone rubber. Uniaxial tensile tests and bulge tests were used to precondition the samples, i.e., to induce some primary stress softening. In both cases, subsequent uniaxial tensile tests were conducted on preconditioned specimens. The first set of experiments consists of a uniaxial tension path followed by uniaxial tension along different directions. It appears that the stress softening varies from a maximum in the same direction load to a minimum in the orthogonal direction, with respect to the first tensile load direction. Next, the bulge test is proposed as an original way to yield very different biaxial tensile strain-histories for first loading path. The fact that the biaxiality ratio varies from the pole (uniaxial tension) until the bulge border (planar tension), permits to analyze second tensile load curves in a material that experienced a more complex first load path. These experimental data allow to discuss the most appropriate criteria to describe the strain-induced anisotropy phenomenon.     

Effect of prestrain paths on mechanical behavior of dual phase sheet steel

The tensile and fatigue performance of dual phase (DP600) sheet steel was investigated with specimens, as-received, and with two different prestrain path conditions, uniaxial and plane strain. First, tensile tests of the as-received condition of DP600 were performed to obtain mechanical properties, specifically the uniform elongation, for determining the prestrain levels of the specimens. Then three prestrain levels from each strain path were applied onto the sheet steel. Tensile and fatigue specimens were prepared from the prestrained coupons. Mechanical properties were obtained from the uniaxial tests of the as-received and prestrained specimens for comparison. Fatigue testing was also conducted with strain controlled to acquire fatigue properties. The fatigue life curves were plotted as a function of strain range and Neuber factor. The uniaxially prestrained specimens exhibited higher fatigue strength than that of the as-received ones for the long life region, but the opposite effect was observed for the short life region of less than 10⁴ reversals.     

Deformation mechanisms and the yield surface of low-density,closed-cell polymer foams

The geometry of low-density, closed-cell, polyethylene and polystyrene foams was modelled with a Kelvin foam having uniform-thickness cell faces; finite element analysis (FEA) considered interactions between cell pressures and face deformation. Periodic boundary conditions were applied to a small representative volume element. In uniaxial, biaxial and triaxial tensile stress states, the dominant high-strain deformation mechanism was predicted to be tensile yield across nearly flat faces. In uniaxial and biaxial compression stress states, pairs of parallel plastic hinges were predicted to form across some faces, allowing them to concertina. In hydrostatic compression, face bowing was predicted. The rate of post-yield hardening changed if new deformation mechanisms became active as the foam strain increased. The effects of foam density and polymer type on the foam yield surface were investigated. Improvements were suggested for foam material models in the FEA package ABAQUS.     

Numerical simulation of low-velocity impact loading of a ductile polymer material

Mechanical impact loading of injection-moulded components was simulated. The material was a talc-filled and elastomer-modified polypropylene used in automotive exterior parts. The material model was the linear-elastic–viscoplastic SAMP-1 model, which features pressure-dependent yield stress, plastic dilatation and a simple damage model. The model was calibrated with data from tests in uniaxial tension, shear and uniaxial compression, utilising 3D digital image correlation for full-field displacement measurements. With the calibrated model, two load cases were simulated; centrally loaded clamped plates and three-point bending of bars. The predictions of force vs. deflection were good to fair. The results are discussed in terms of deficiencies of the calibration data, heterogeneity and anisotropy of injection-moulded components, and shortcomings of the model. In particular, the hardening curves at high strain rates are uncertain, and tests in biaxial tension would be useful.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Large-strain Bauschinger effect in austenitic stainless steel sheet

Large-strain Bauschinger effect in cold-rolled austenitic stainless steel sheet is investigated after large amounts of prestrain. The material is prestrained in uniaxial tension, and the tensile properties of the prestrained material are measured in different angles with respect to the prestraining direction. By comparing the differences in the yield stresses in different orientations, the effect of prestraining on material anisotropy is studied. The method is applied to AISI 304-type stainless steel sheet. The test results are analyzed using a combined isotropic–kinematic hardening model. The results indicate that this kind of material shows a considerable Bauschinger effect. Transient and permanent softening is observed in the experiments. The experimental Young's modulus also seems to decrease with prestrain.     

Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction

This study deals with simulation for cyclic stress/strain evolutions and redistributions, and evaluation of fatigue parameters suitable for estimating fatigue lives under multiaxial loadings. The local cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures of ABAQUS finite element code for both smooth and notched specimens made of three materials: a medium carbon steel in the normalized condition, an alloy steel quenched and tempered and a stainless steel, respectively. Emphasis is on the studying of ‘intelligent’ material behaviors to resist fracture, such as stress redistribution and relaxation through plastic deformations, etc. For experimental verifications, a series of tests of biaxial low cycle fatigue composed of tension/compression with static and cyclic torsion were carried out on a biaxial servo-hydraulic testing machine (Instron 8800). Different multiaxial loading paths were used to verify their effects on the additional cyclic hardening. The comparisons between numerical simulations and experimental observations show that the FEM simulations allow better understanding on the evolutions of the local cyclic stress–strain and it is shown that strong interactions exist between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the local cyclic elastic–plastic stress–strain responses, the energy-based multiaxial fatigue damage parameters are applied to correlating the experimentally obtained lives. Improved correlations between the predicted and the experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses.     

Characterization of stress–strain behavior of a cast TRIP steel under different biaxial planar load ratios

This paper investigates the stress–strain curves of different load paths and the initial yield surface of a metastable austenitic stainless cast steel under biaxial planar loading using cruciform specimens. These tests were carried out on a 250 kN biaxial servohydraulic tension-compression testing machine. The laborious stress determination was undertaken with a new testing method by using global elastic unloading to measure the local stiffness. Isotropic yielding and mainly isotropic strain hardening were found. To evaluate the microstructure, the martensite formation was detected by use of a ferrite sensor and scanning electron microscopy and electron backscatter diffraction were applied.     

Effects of particle plasticity characteristics on local interface stress in particle reinforced composite during uniaxial tension

For elastoplastic particle reinforced metal matrix composites, failure may originate from interface debonding between the particles and the matrix, both elastoplastic and matrix fracture near the interface. To calculate the stress and strain distribution in these regions, a single reinforcing particle axisymmetric unit cell model is used in this article. The nodes at the interface of the particle and the matrix are tied. The development of interfacial decohesion is not modelled. Finite element modelling is used, to reveal the effects of particle strain hardening rate, yield stress and elastic modulus on the interfacial traction vector (or stress vector), interface deformation and the stress distribution within the unit cell, when the composite is under uniaxial tension. The results show that the stress distribution and the interface deformation are sensitive to the strain hardening rate and the yield stress of the particle. With increasing particle strain hardening rate and yield stress, the interfacial traction vector and internal stress distribution vary in larger ranges, the maximum interfacial traction vector and the maximum internal stress both increase, while the interface deformation decreases. In contrast, the particle elastic modulus has little effect on the interfacial traction vector, internal stress and interface deformation.     

Molecular dynamics evaluation of strain rate and size effects on mechanical properties of FCC nickel nanowires

Based on molecular dynamics method, an atomistic simulation scheme for damage evolution and failure process of nickel nanowires is presented, in which the inter-atomic interactions are represented by employing the modified embedded atom potential. Extremely high strain rate effect on the mechanical properties of nickel nanowires with different cross-sectional sizes is investigated. The stress–strain curves of nickel nanowires at different strain rates subjected to uniaxial tension are simulated. The elastic modulus, yield strength and fracture strength of nanowires at different loading cases are obtained, and the effect of strain rate on these mechanical properties is analyzed. The numerical results show that the stress–strain curve of metallic nanowires under tensile loading has the trend identical to that of routine polycrystalline metals, and the yield strain of nanowires is independent of the strain rate and cross-sectional size. Based on the simulation results, a set of quantitative prediction formulas are obtained to describe the strain rate sensitivity of nickel nanowires on the mechanical properties, and the resulting formulas of the Young’s modulus, yield strength and fracture strength of nickel nanowires exhibit a linear relation with respect to the logarithm of strain rate. Furthermore, some comprehensive correlation equations revealing both the strain rate and size effects on mechanical properties of nickel nanowire are proposed through the numerical fitting and regression analysis, and the mechanical behaviors observed in this study are consistent with those from the experimental and available numerical results.     

EBSD study of micromechanisms involved in high deformation ability of DP steels

Notched and un-notched tensile specimens of fine grained commercial DP780 steel were deformed in uniaxial tension until fracture. Micro-texture analysis was performed by using an FE-SEM equipped with an EBSD detector and the data were analyzed to quantify orientation gradients within the microstructure of the deformed specimens in terms of Image Quality, Inverse Pole Figure and Taylor Factor map. High deformation ability of DP steels was found to be mostly due to such mechanisms as grain rotation, void creation and evolution, substructure formation within the ferrite grains and the highly plastic stretching of martensite during the deformation process. The true strain of martensite was measured up to 64% and 74% for the un-notched and notched specimens, respectively.