Evolution of mechanical properties for a dual-phase steel subjected to different loading paths

The evolution of the mechanical properties of a dual-phase (DP590) steel sheet after being prestrained by uniaxial tension, plane strain and equal biaxial stretching was investigated. Specimens were first loaded using the three prestraining modes. Then, from the prestrained specimens, a few sub-sized samples were machined along the rolling direction and the transverse direction for further uniaxial tension testing. Six loading paths were provided. Equal biaxial stretching was performed using a cruciform specimen. The evolution of work hardening performance, elastic modulus, yield stress and tensile stress under the six loading paths were discussed in detail. The results indicate that loading paths can affect the latent work hardening performances, strain hardenability, yield stress and tensile stress evolution as well as the elastic modulus decrease during plastic deformation. The uniaxial tension–uniaxial tension path results in a cross-softening phenomenon, the largest yield stress enhancement and a mild maximum tensile stress increase. The equal biaxial stretching-uniaxial tension path leads to a cross-hardening phenomenon, the least yield stress enhancement and the largest tensile strength increase maximum tensile strength. The elastic modulus of DP590 steel not only changes with the accumulated plastic strain but also varies with the loading paths. The largest decrease of the elastic modulus equal biaxial stretching–uniaxial tension can reach 12.7% beyond 8% equivalent strain, which is 5.2% greater than that in the monotonic uniaxial tension path.     

Design optimisation of biaxial tensile test specimen using finite element analysis

One of the most restricting aspects of the biaxial tensile test for sheet metal is the design of the cruciform specimen. Although specimens of the cruciform type have been investigated quite extensively previously, no standard geometry for the cruciform specimen exists. Using a specifically designed pantograph apparatus for operation in a standard tensile testing machine, various cruciform specimens machined from low-carbon cold rolled steel sheet were analysed experimentally. Finite element modelling of the specimens was conducted in parallel to the experimental test programme to establish optimum specimen geometry. Through a process of optimisation, a standard cruciform specimen was designed which can be used to accurately predict the mechanical behaviour of the mild steel when formed in multiple directions simultaneously. This paper describes the optimisation process and the results obtained from both the experimental testing and numerical modelling.     

双轴载荷下复合材料十字型试样几何形状对中心测试区系数的影响

基于双轴拉伸载荷下复合材料十字型试样的设计特点,对比分析了不同几何形状的十字型试样在不同厚度比和载荷比条件下中心测试区应力集中系数和承力系数的变化规律,并开展了不同载荷比的双轴拉伸实验进行验证。研究表明:十字型试样中心测试区系数与载荷大小无关,与试样几何形状、厚度比及载荷比有关;等宽加载臂宽度越小、厚度比越大,应力集中系数越小,载荷比不同,应力集中系数也不同;一般而言,中心测试区承力系数随厚度比增加而增大,x向承力系数βx随载荷比增加呈非线性增大,y向承力系数βy随载荷比增加呈线性减小;在双轴拉伸载荷条件下,形状D十字型试样在载荷比f=4/1时中心测试区y向应力分量为负值,表现为压应力状态。     

The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification

An equivalent plastic strain-dependent anisotropic material model was developed for 5754O aluminum alloy sheet. In the developed model, the anisotropy coefficients for Barlat’s Yld2000-2d anisotropic yield function were established as a function of the equivalent plastic strain. The developed anisotropic material model was implemented into the commercial FEM code ABAQUS as a user material subroutine (UMAT) for simulations. In order to evaluate the accuracy of the developed material model, biaxial tensile tests were carried out using cruciform specimens and a biaxial loading testing machine. The results show that the developed material model predicts the experimental results better than the other three material models (Yld2000-2d, Mises and Hill48 yield functions). It is also found that the developed material model describes the uniaxial tensile test curves better than Yld2000-2d yield function. The deep drawing test for 5754O aluminum alloy sheet was carried out and was simulated with different material models. The comparison between the experimental and simulation results indicates that the developed material model predicts the earing profile better than other material models. It is concluded that the equivalent plastic strain-dependence of the material coefficients should be considered for the accurate prediction of the anisotropic deformation behavior of materials.     

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.     

Enhanced fracture assessment under biaxial external loads using small scale cruciform bending specimens

The present study is concerned with an enhanced fracture mechanics characterization of engineering materials using small scale cruciform bending specimens. Based on the regular SE(B) specimen geometry with a shallow crack, two additional loading legs allow the application of an additional stress component acting longitudinally to the crack front. Compared to standard specimen types, the biaxial loading conditions for the cruciform specimens are in general closer to the situation in pressurized vessels and pipes, especially under thermal shock loading conditions. In a combined experimental and numerical approach, detailed assessments of the local stress and strain fields in comparison to the crack front stress and strain states of standard specimens with deep and shallow cracks are provided. The cruciform bending specimen geometry is demonstrated to be suitable even in small scale dimensions. It permits the application of different combined external loading situations and thus a fracture assessment under conditions close to various situations in engineering application. Due to its small size, the specimen geometry can be employed even if only a limited amount of material is available.     

A survey of test methods for multiaxial and out-of-plane strength of composite laminates

This review paper gives an overview of test methods for multiaxial and out-of-plane strength of composite laminates, with special consideration of non-crimp fabrics (NCF) and other textile systems. Tubular and cruciform specimens can provide arbitrary in-plane loading, while off-axis and angle-ply specimens provide specific biaxial loadings. Tensile and compressive out-of-plane strength may be determined by axial loading of specimens with a waisted gauge section, while bending of curved specimens allow determination of the out-of-plane tensile strength. Tests suited for out-of-plane shear strength include the short beam shear test, the inclined double notch test and the inclined waisted specimen. Testing of arbitrary tri-axial stress states using tubular or cruciform specimens with superimposed through-the-thickness loading is highly complex and significant problems have been reported in achieving the intended stress states and failure modes. Specific tri-axial stress states can be obtained by uniaxial loading of specimens with constrained expansion, as in the die channel test.     

Practical strain extensometry for biaxial cruciform specimens—Part 1

Of a number of methods for testing materials under biaxial stress conditions, the cruciform specimen with tension/compression loading of the arms allows exploration of the whole in-plane failure envelope. This paper highlights the problems arising in the measuring, monitoring and control of strains in cruciform specimens subject to static and cyclic biaxial loading. Three extensometers are described which have been used respectively for testing high strain fatigue in steels, fatigue crack propagation in steels and fatigue and fracture of a glass reinforced polyester composite. Each extensometer uses a full bridge resistance strain gauge circuit; two are based on bending of a beam and the third on deformation of a thin ring. Examples are shown of stress/strain loops for equibiaxial and shear conditions from fatigue tests on a steel and g.r.p.     

Design of a cruciform specimen for biaxial testing of fibre reinforced composite laminates

To study the behaviour of fibre reinforced composite laminates under static and cyclic in-plane complex stress states, a biaxial loading frame has been developed. A cruciform type specimen is biaxially loaded in its plane using four independent servo-hydraulic actuators. An appropriate control unit keeps the centre of the specimen at the same position during the test. For obtaining reliable biaxial failure data the design of the cruciform specimen is of paramount importance. Finite element simulations of the cruciform specimen to study the influence of various geometrical parameters and experiments on nine selected cruciform specimen types using both strain gages and an optical-numerical full field method for strain determination over the entire biaxially loaded test zone have been carried out. In the present paper, the four most important geometries will be discussed. Since stresses in the biaxially loaded zone cannot be calculated from the experimentally applied loads due to the ill definition of the load bearing area, strain values – the only measurable quantity – are used for the comparison of the different geometry types. For the glass fibre reinforced composite material with a [(±45/0)₄/±45]_T lay-up this led to the proposal of an optimized geometry: a plane cruciform type specimen with a circular central region of reduced thickness and an adapted corner fillet at the intersection of the arms. Using this geometry failure will occur in the biaxially loaded test zone, rather than in the uniaxially loaded arms, at failure strains in the centre of the specimen comparable for the uniaxial load ratios to strains obtained on standard beam specimens. Tests at different load ratios were performed to obtain data as input for failure criteria. This paper focuses on the design of the specimen. In the near future, the biaxial test results will be compared with existing failure criteria.     

双轴受压状态下的高延性纤维增强水泥基复合材料本构模型

基于Darwin和Pecknold考虑混凝土双轴力学行为的方法,建立一个同时考虑双轴受压状态下非线性力学行为和抗压强度变化的高延性纤维增强水泥基复合材料(ECC)二维正交各向异性本构模型。在因双轴加载而产生的正交各向异性的2个方向上引入等效单轴应变,建立非线性应力-等效单轴应变关系以考虑ECC的双轴非线性行为,并采用一条双轴强度包络线确定2个方向上的抗压强度。推导模型的显式数值算法,编写包含该算法的用户自定义材料子程序UMAT,并嵌于有限元计算程序ABAQUS v6.14中。通过对两组不同配合比的ECC试件在不同应力比下的双轴受压加载试验进行数值分析验证本模型的有效性。数值计算得到的主压应力方向上的应力-应变曲线及预测的抗压强度与试验结果吻合较好,表明该文提出的本构模型能够有效地预测ECC在双轴受压状态下的非线性力学行为和破坏强度。     

Nonlinear Analysis of Woven Fabric-Reinforced Graphite/PMR-15 Composites under Shear-Dominated Biaxial Loads

An elastic-plastic, time-independent, macroscopic, homogenous model of an 8HS woven graphite/PMR-15 composite material has been developed that predicts the nonlinear response of the material subjected to shear-dominated biaxial loads. The model has been used to determine the response of woven composite off-axis and Iosipescu test specimens in nonlinear finite element analyses using a multilinear averaging technique. The numerically calculated response of the specimen was then compared to experimentally obtained data. It has been shown that the numerically calculated stress - strain diagrams of the off-axis specimens are very close to the experimentally obtained curves. It has also been shown that the numerically determined shear stress - strain and load-displacement curves of the woven Iosipescu specimens are close to the experimentally obtained curves up to the point of significant interlaminar damage initiation and propagation. The results obtained in this study clearly demonstrate that the nonlinear material behavior of the graphite/polyimide woven composites subjected to shear-dominated biaxial loading conditions cannot be ignored and should be considered in any stress analysis. The linear-elastic approach grossly overestimates the loads and stresses at failure of these materials in the off-axis and Iosipescu tests. It can be assumed that the same discrepancies will arise in the numerical analysis of the woven composites tested under other biaxial shear-dominated loading conditions using other biaxial test methods.     

Effect of continuous strain path changes on forming limit strains of DP600

The strain path may change in actual sheet metal‐forming processes, so the determination of formability of sheet metal should consider the nonlinear strain path. For identifying the forming limit (FL) strains under nonlinear strain path, a conventional two‐step procedure with unloading is classically used to produce the strain path change, which results in no continuous measure of strain. The in‐plane biaxial tensile test with a cruciform specimen is an interesting alternative to overcome the drawbacks of conventional method. The strain path change can be made without unloading during a single test. In this work, the experimental FL strains of DP600 sheets under two types of nonlinear strain path are investigated and then compared with those under linear strain paths. The Oyane ductile fracture criterion is used in the finite element simulation to predict the experimental results.     

2-D biaxial testing and failure predictions of IM7/977-2 carbon/epoxy quasi-isotropic laminates

In previous research, a series of a thickness-tapered cruciform specimen configurations have been used to determine the biaxial (two-dimensional, in-plane) and triaxial (three-dimensional) strength of several carbon/epoxy and glass/vinyl-ester laminate configurations. Refinements to the cruciform geometry have been shown capable of producing acceptable results for cross-ply laminate configurations. However, the presence of a biaxial strengthening effect in quasi-isotropic, [(0_N/90_N/ ± 45_N)_M]_S, laminates have brought into question whether the cruciform geometry could be used to successfully generate two-dimensional strength envelopes. In the present study, a two-dimensional failure envelope for a IM7/977-2 carbon/epoxy laminate was developed at the Air Force Research Laboratory, Space Vehicles Directorate, using a triaxial test facility. The electromechanical test frame is capable of generating any combination of tensile or compressive stresses in σ₁:σ₂:σ₃ stress space and can evaluate the uniaxial (one-dimensional, in-plane), biaxial or triaxial response of composite materials. Results are promising as they indicated that failure in the majority of the IM7/977-2 specimens occurred in the gage section. This leads the authors to believe that maximum biaxial stress states were correctly generated within the test specimen. In addition to the experimental data presented, multi-continuum theory (MCT) was used to predict and analyze the onset of damage and ultimate failure of a biaxially loaded IM7/977-2 laminate. Multi-continuum theory is a micromechanics based theory and associated numerical algorithm for extracting, virtually without a time penalty, the stress and strain fields for a composites’ constituents during a routine structural finite element analysis. Damage in a composite material typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. An accurate prediction of constituent failure at sampling points throughout the laminate provides a genesis for progressively analyzing damage propagation in a composite specimen allowing identification of intermediate damage modes. A constituent-based, quadratic, stress-interactive, failure criterion was used to take advantage of the micro-scale information provided by MCT. There was reasonable correlation between analytically and experimentally developed IM7/977-2 2D failure envelope which leads us to believe that the thickness-tapered cruciform specimen can be used to determine the biaxial strength of quasi-isotropic laminates.     

Fracturing behaviour of sandstone specimens with a cavity formed by intersecting excavations under compression: Experimental study and numerical modelling

To investigate the mechanical properties, damage characteristics, and fracturing behaviour of specimens with a cavity formed by intersecting excavations, a series of uniaxial compression tests were conducted incorporating digital image correlation (DIC) and acoustic emission (AE) techniques. PFC^2D modelling was conducted to further study the failure modes and crack evolution under biaxial loading. The results showed that the mechanical properties are significantly weakened by the cavity and influenced by its shape. The failure of the specimens containing a cavity under uniaxial compression can be considered as a progressive process of crack initiation, propagation, and coalescence of different cracks with each other, leading to forming macrofractures, which can be visually displayed by the DIC technique. A new method for determining the crack closure stress is proposed, and the crack initiation stress and the crack damage stress of specimens are also obtained by the AE measurements. The failure mode of the intact specimen changed from the tensile–shear failure mode under the uniaxial compression to the shear‐dominated failure mode under the biaxial compression. Failure of the specimens with a cavity is dominated by shear cracks rather than tensile cracks. Under high confining stresses, almost no macrotensile cracks appeared on the roof or floor of the cavity; instead, several spalling fractures were visible on the two sides of the cavity. The fracturing mechanism is well explained by the evolution of the internal stresses in the specimens.     

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.     

Three-Dimensional Static and Dynamic Analysis of a Composite Cruciform Structure Subjected to Biaxial Loading: A Discontinuum Approach

A three-dimensional structural integrity analysis using the eXtended Finite Element Method (XFEM) is considered for simulating the crack behaviour of a chopped fibre-glass-reinforced polyester (CGRP) cruciform specimen subjected to a quasi-static tensile biaxial loading. This is the first time this problem is accomplished for computing the stress intensity factors (SIFs) produced in the biaxially loaded area of the cruciform specimen. A static crack analysis for the calculation of the mixed-mode SIFs is carried out. SIFs are calculated for infinite plates under biaxial loading as well as for the CGRP cruciform specimens in order to review the possible edge effects. A ratio relating the side of the central zone of the cruciform and the crack length is proposed. Additionally, the initiation and evolution of a three-dimensional crack are successfully simulated. Specific challenges such as the 3D crack initiation, based on a principal stress criterion, and its front propagation, in perpendicular to the principal stress direction, are conveniently addressed. No initial crack location is pre-defined and an unique crack is developed. Finally, computational outputs are compared with theoretical and experimental results validating the analysis.     

A FRACTURE MECHANICS APPROACH TO HIGH-CYCLE FATIGUE CRACK GROWTH UNDER IN-PLANE BIAXIAL LOADS

Abstract Fatigue crack growth under biaxial tensile load conditions is reported for a structural sheet steel. The new test facility can operate at high frequency (0–40 Hz) thereby permitting real-time testing required for threshold investigations; specimens are of the cruciform type.
It is found that crack growth rate is affected by a cyclic tensile load applied in the direction of growth which decreases as the said load increases. The rate however increases if the biaxial loads are increasingly out of phase.
Within the test conditions reported LEFM can be applied to crack growth under biaxial load conditions. The threshold stress intensity range is shown to be a function of load biaxiality, phase difference and stress ratio.     

Stress–strain curves of metallic materials and post‐necking strain hardening characterization: A review

For metallic materials, standard uniaxial tensile tests with round bar specimens or flat specimens only provide accurate equivalent stress–strain curve before diffuse necking. However, for numerical modelling of problems where very large strains occur, such as plastic forming and ductile damage and fracture, understanding the post‐necking strain hardening behaviour is necessary. Also, welding is a highly complex metallurgical process, and therefore, weldments are susceptible to material discontinuities, flaws, and residual stresses. It becomes even more important to characterize the equivalent stress–strain curve in large strains of each material zone in weldments properly for structural integrity assessment. The aim of this paper is to provide a state‐of‐the‐art review on quasi‐static standard tensile test for stress–strain curves measurement of metallic materials. Meanwhile, methods available in literature for characterization of the equivalent stress–strain curve in the post‐necking regime are introduced. Novel methods with axisymmetric notched round bar specimens for accurately capturing the equivalent stress–strain curve of each material zone in weldment are presented as well. Advantages and limitations of these methods are briefly discussed.     

Experimental characterization of orthotropic technical textiles under uniaxial and biaxial loading

The paper deals with the development of an experimental protocol for the mechanical characterization of plain weave technical textiles. The textiles are modelled as orthotropic materials with known directions of material symmetry, and a “linear-by-step” approximation is introduced to account for the nonlinearity exhibited by the stress–strain behaviour. Material coefficients are determined by fitting uniaxial stress–strain curves along the warp, weft and 45° directions. The full-field evaluation of the strain distribution on the specimen surface, carried out by an optical approach, allows to assess the absence of edge effects and to quantify the shear strains introduced by off-axis loading.The protocol is applied to the characterization of a monofilament polyester textile and the model identified upon uniaxial data is validated by comparing analytical simulations with experimental data obtained under biaxial stress conditions. Finally the reliability of failure criteria based upon both uniaxial and biaxial data is investigated.