On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.     

Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

Modelling of the plastic flow of trip-aided multiphase steel based on an incremental mean-field approach

An incremental mean-field model is developed for the prediction of transformation induced plasticity (TRIP) in multiphase steel. The partitioning of strain between softer and harder constituents is computed based on an elastic-plastic Mori–Tanaka approach that accounts for the progressive transformation of austenite into martensite. The latter transformation is predicted using an energy-balance criterion that is formulated at the level of individual austenite grains. The model has been tested against experimental data. Macroscopic stress-strain curves and rate of martensite formation have been measured on sheet samples subjected to various loading modes: uniaxial tension, simple shear, and (in-plane) uniaxial compression. These experiments were performed at 20 °C and the uniaxial tensile test was repeated at ?30 °C. The mean-field model produces fair predictions of the macroscopic hardening resulting from TRIP on the condition that a sufficient proportion of the load is carried by the very hard martensite inclusions. Such prediction implies that one accounts for the stress heterogeneity across the ferrite-based matrix. At the same time, the model reproduces the elastic lattice strains and the plastic elongation which are measured within the phases by neutron diffraction and by image correlation in a scanning electron microscope, respectively. The model can be used in finite element simulations of forming processes which is illustrated in a study of necking of a cylindrical bar under uniaxial tension.     

Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling

A newly developed multi-axial testing technique for sheet materials is employed to investigate the inelastic response of a temper-rolled stainless steel 301LN under isothermal quasi-static loading conditions at room temperature. The experimental technique consists of a flat sheet specimen, which is subject to combinations of shear and normal loading using a custom-made dual-actuator system. The large deformation behavior under monotonic loading is determined along more than 20 distinct radial paths in the stress space. The experimental results indicate that Hill's quadratic yield function along with an associated flow rule provides a good approximation of the initial yield behavior of this anisotropic two-phase FCC/BCC sheet material. Based on the experimental data for radial monotonic loading, it is concluded that conventional isotropic-kinematic hardening models cannot successfully describe the strain hardening of this austenitic steel. Instead, a non-associated anisotropic hardening model is proposed that relates the increase in yield strength to an isothermal martensitic transformation kinetics law. The comparison of the model predictions with the experimental results shows very good agreement for all biaxial and uniaxial experiments.     

Modeling lattice strain evolution at finite strains and experimental verification for copper and stainless steel using in situ neutron diffraction

An elasto-plastic self-consistent (EPSC) polycrystal model is extended to account, in an approximate fashion, for the kinematics of large strains, rigid body rotations, texture evolution and grain shape evolution. In situ neutron diffraction measurements of the flow stress, internal strain, texture and diffraction peak intensity evolutions were performed on polycrystalline copper and stainless steel, up to true tensile strains of ε = 0.3. Suitably adjusted slip system hardening model parameters enable the model to quantitatively describe the flow stress of the polycrystalline aggregate. Quantitative predictions of the texture evolution and the internal strain evolution along the stress axis are good, while predictions of transverse internal strains (perpendicular to the tensile loading direction) are less satisfactory. The latter exhibit a large dispersion from grain to grain around a macroscopic average, and the implications of this finding for the interpretation of in situ neutron diffraction method are explored. Finally, as a demonstration of the applicability of the model to problems involving finite rotation, as well as deformation, simulations of simple shear were conducted which predict a texture evolution in agreement with published experimental data, and other modeling approaches as well.     

Microscale prediction of deformation in an austenitic stainless steel under uniaxial loading

In this study, the deformation behaviour of polycrystalline austenitic 316H stainless steel under uniaxial loading is investigated by means of in-situ neutron diffraction (ND) measurement and crystal plasticity-based finite element (FE) modelling. Data have been obtained for the macroscopic stress–strain response and the lattice strain evolution in the longitudinal and transverse direction relative to the uniaxial loading axis. Comparison between the model predictions and the ND measurements suggests that in most cases the FE model can predict the lattice strain evolution at the microscale and capture the general trends observed in the experiments. Both ND measurements and FE modelling simulations identify little effect of micromorphology effect on the longitudinal lattice strain evolution, while the transverse lattice strain response appears to be sensitive to the microstructure, in particular the initial crystallographic orientation of the material.     

单轴拉伸过程中双相不锈钢局部微观变形行为的细观力学有限元分析

针对双相不锈钢中奥氏体相和铁素体相分别展开了纳米压痕实验,并通过有限元反演得到两相各自的拉伸应力-应变关系,利用Voronoi Tessellation法生成代表性的微结构体积单元,对双相不锈钢的单轴拉伸行为进行了有限元仿真和模拟,研究了双相不锈钢在拉伸过程中的局部应力、应变分布和演化规律．结果表明,利用Voronoi Tessellation法建立单元模型,结合本文通过纳米压痕实验获取的两相力学性能参数,可以很好地模拟双相不锈钢的整体单拉行为,奥氏体比铁素体软,拉伸载荷下双相不锈钢的应变集中在奥氏体中,应力集中在铁素体中;局部应力应变的分布特征与两相分布特征和晶粒形状有关,最大应变值主要集中在奥氏体晶粒狭长且尖锐的区域,而最大应力则主要发生在铁素体晶粒狭长和尖锐的区域;对于奥氏体和铁素体晶粒占比相当的双相不锈钢,其虽然可以具有较为综合的宏观力学性能,但是其微观应力集中的区域和应力最大值相对较大．研究成果为进一步揭示双相不锈钢局部失效机理奠定了基础．     

DP钢板应变路径多步演变下的弹塑性力学行为

针对DP高强双相钢板在复杂载荷作用下的弹塑性力学特征,提出利用三步拉伸力学实验,对比分析单轴循环加载和非等轴加载下材料的各向异性硬化、永久软化和弹性模量衰减特性等力学行为,揭示应变路径多步演变下的弹塑性力学特性.研究结果表明:材料再加载初期的瞬态行为与应变路径有关,在初期瞬态阶段显示出明显的各向异性,且再加载角度、预应...     

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.     

Measurement of the Residual Stress Tensor in a Compact Tension Weld Specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens.     

The Evolution of Effective Elastic Properties of a Cold Formed Stainless Steel Sheet

In accordance with the great importance given to the subject of stiffness degradation, in particular with regard to metal forming, this work experimentally investigates the anisotropic elastic properties of plastically prestrained cold-rolled sheet metal (stainless steel EN 1.4301, also AISI 304). From the experiments performed, two main conclusions regarding stiffness degradation can be extracted. First, since under specific stretching the intensity of the normalized Young’s moduli degradation in both directions remains approximately similar, it may be concluded that the potential initial elastic anisotropy tends to be preserved during loading. Second, as the evidenced stiffness degradation has proved to be strongly correlated with the stretching direction of the sheet metal, it can be concluded that the stiffness evolution in the cold rolled sheet steel is path dependent. These interesting discoveries also provide some answers for modelling the kinetic damage evolution laws in damage mechanics.     

Effect of mechanical stresses on the magnetic characteristics of pipe steel

The effect of elastic deformation in tension (compression) torsion, internal pressure loading, and their combination on the magnetic characteristics of 09G2S pipe steel is studied. It is found that in the cases of compression, torsion, and internal pressure loading, the coercive force, residual induction, and maximum magnetic permeability are uniquely dependent on the stress. It is shown that the strength of the applied magnetic field in which the magnetostriction becomes negative decreases under the action of tensile stresses. It is found that in the case of combined tension (compression) and torsion, shear stresses weaken the effect of normal stresses on the magnetic properties. In the case of a combination of all three types of loading, increasing internal pressure leads to an increase in the coercive force and a decrease in the residual induction and maximum magnetic permeability. Measurement results were used to plot the dependence of the stress intensity on the coercive force for different values of the Lode parameter, which determines the type of stress state of the object.     

Residual-stress measurement using surface displacements around an indentation

An experimental method is described which can measure the direction and magnitude of residual and applied stress in metals. The method uses optical interference to measure the permanent surface deformation around a shallow spherical indentation in a polished area on the metal specimen. The deviation from circularly symmetrical surface deformations is measured at known values of applied stress in calibration specimens. This deviation from symmetry can then be used to determine the direction and magnitude of tensile residual stress in specimens of the same material. Determination of compressive residual stress is more limited. A model of the indentation process is offered which qualitatively describes experimental results in 4340 steel for both tensile and compressive stress. The model assumes that the deformation around an indentation os controlled by stresses analogous to those around a hole in an elastic plate. Various conditions are discussed which affect the indentation process and its use to measure stress, including (a) the rigidity of support of the indentor and specimen, (b) the size and depth of the indentation, (c) the uniaxial stress-strain behavior of the specimen material.     

A magnetic method for the determination of residual stress

A magnetic method for the measurement of residual longitudinal stress in the outer portions of cylindrical bars is developed and applied to nickel and steel. It involves measurement of the reversible effective permeability over a range of frequency of the applied alternating field. Special composites specimens, in which any desired level of residual stress can be produced, serve as idealized test specimens. Magnetic stress measurements made on cold-drawn, machined and quenched rods are compared with measurements by X-ray diffraction and mechanical relaxation (slitting). A combination of magnetic and X-ray measurements yields qualitative information about the stress gradient in the outer portion of a bar. A rapid magnetic-test method, suitable for practical application, is described.     

Deformation behavior and microstructure/texture evolution of an annealed 304 AISI stainless steel sheet. Experimental and micromechanical modeling

Different tensile tests are performed at −60 °C, on a 304 AISI stainless steel, to produce strain induced α′ martensite. Using EBSD analysis and X-ray diffraction methods, the corresponding texture and microstructure evolutions is studied, as well as the γ → α′ transformation mechanism. It is shown that α′ martensite is associated with {1 1 1}_γ faulted bands, partially ε bands, as often reported in the literature for low SFE stainless steels. As a consequence, these deformation bands play a key role in the nucleation and growth of α′ martensite. A micromechanical model is applied to simulate the deformation behavior of the stainless steel as well as the corresponding transformation kinetic and γ texture evolution. Different simulations are proposed, using various assumptions for the γ → α′ transformation mechanism. The simulation data are in better agreement with the experimental ones, when the γ → α′ transformation strain is derived from the Bowles–MacKenzie theory using the (1 1 1)_γ[−1 2 −1]_γ stacking fault shear system as lattice invariant shear.     

类岩石材料力学特性的试验及数值模拟研究

在进行多组不同配比类岩石材料单轴压缩试验和巴西试验的基础上,详细分析了石膏水泥比和石英砂含量对类岩石材料的单轴抗压强度、抗拉强度及弹性模量等力学参数的影响规律,力图找到适合模拟现场砂质泥岩的类岩石材料及配合比。利用颗粒流程序(PFC)模拟,进一步研究了高径比和围压对类岩石材料力学特性的影响。结果表明:随着石膏水泥比的增大,抗压强度和弹性模量均逐渐减小,而抗拉强度逐渐增大;随着石英粉含量的增大,抗压强度和弹性模量均先增大后减小,而抗拉强度则为先减小后增大。结合单轴压缩过程的声发射特征,揭示了裂纹扩展与声发射有密切的关系。PFC2D模拟获得的力学参数与室内试验相近,破裂模式也与实际情况相似。通过尺寸效应的研究可知试样的高径比在2.0~2.5较合理。随着围压的增大,试样的峰值强度、残余强度、峰值应变及弹性模量等力学参数均增大,且围压会改变试样的破裂模式。     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

Inverse Eigenstrain Analysis of the Effect of Non-uniform Sample Shape on the Residual Stress Due to Shot Peening

This paper deals with the analysis of elastic strain and eigenstrain in non-uniformly shaped shot-peened 17-4PH stainless steel samples. Based on residual strain measurements by synchrotron X-ray diffraction, the finite element (FE) models are established for the inverse problem of eigenstrain analysis in slice conical sample. The eigenstrains obtained in the slice are then implemented into the FE model of the solid conical sample. It is found that the dependence of elastic strain distributions on the peening intensity and sample shape/thickness could be elucidated via the understanding of underlying permanent strain, or eigenstrain. The effect of the peening process is therefore best described in terms of the induced eigenstrain. The proposed framework is useful for the predictive modelling of residual stresses in non-uniformly shaped shot-peened materials, in that it allows efficient reconstruction of complete residual stress states. In addition, it provides an excellent basis for developing predictive tools for in service performance and design optimisation.     

On the identifiability of the Hill-1948 model with one uniaxial tensile test

A uniaxial experiment is performed on an ultra-thin specimen made of 17-7 precipitation hardened stainless steel. An anti-wrinkling setup allows for the characterization of the mechanical behavior with Integrated Digital Image Correlation (IDIC). The result shows that a single uniaxial experiment investigated via IDIC possesses enough data (and even more) to characterize a complete anisotropic elastoplastic model.     

Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation

The aim of this work is to show first, how the springback of a steel sheet drawn part is affected by the stiffness degradation, as it results from the damage evolved during forming process, and second, to build a respective modeling approach to take this degradation into account. For the consideration of the orthotropic elastic properties degradation we develop an approach, based on the Mori-Tanaka theory, where damage is considered by inclusion of ellipsoidal cavities. The respective void shape evolution is proposed to be identified with the measurements of elastic modulus in two perpendicular directions during the uniaxial tensile test of a flat specimen at different loading stages. The proposed approach is coupled with the Gurson-Tvergaard-Needleman (GTN) plastic potential, though it could be substituted by almost any other continuum damage model. At the end the presented approach is experimentally validated by a simple springback test, developed by authors. A very good agreement between by calculation predicted and measured springback amount is observed.