A nonlinear CDM model for ductile failure analysis of steel bridge columns under cyclic loading

A nonlinear cyclic plasticity damage model for ductile metals, which is able to take large deformation effects into consideration, has been developed using a new damage dissipation potential formulation in order to predict the cyclic inelastic behavior of steel bridge piers. The cyclic constitutive equations that employ the combined isotropic–kinematic hardening rule for plastic deformation is incorporated into the damage mechanics in conjunction with the large strain formulation. The damage growth law is based on the experimental observations that the evolution of microvoids results in nonlinear damage accumulation with plastic deformation. The damage model parameters and the procedure for their identification are presented. The proposed model has been validated and successfully applied to thin-walled steel bridge tubular columns subjected to alternating lateral displacements to evaluate the seismic performance.     

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

In this paper a modified multiplicative decomposition of the right stretch tensor is proposed and used for finite deformation elastoplastic analysis of hardening materials. The total symmetric right stretch tensor is decomposed into a symmetric elastic stretch tensor and a non-symmetric plastic deformation tensor. The plastic deformation tensor is further decomposed into an orthogonal transformation and a symmetric plastic stretch tensor. This plastic stretch tensor and its corresponding Hencky’s plastic strain measure are then used for the evolution of the plastic internal variables. Furthermore, a new evolution equation for the back stress tensor is introduced based on the Hencky plastic strain. The proposed constitutive model is integrated on the Lagrangian axis of the plastic stretch tensor and does not make reference to any objective rate of stress. The classic problem of simple shear is solved using the proposed model. Results obtained for the problem of simple shear are identical to those of the self-consistent Eulerian rate model based on the logarithmic rate of stress. Furthermore, extension of the proposed model to the mixed nonlinear isotropic/kinematic hardening behaviour is presented. The model is used to predict the nonlinear hardening behaviour of SUS 304 stainless steel under fixed end finite torsional loading. Results obtained are in good agreement with the available experimental results reported for this material under fixed end finite torsional loading.     

RPC200塑性与各向异性损伤耦合本构建模研究

针对活性粉末混凝土 (RPC200:Reactive Powder Concrete 200MPa)的非线性行为,将连续损伤力学和塑性力学结合起来,建立了RPC200的弹塑性各向异性损伤耦合本构。在有效应力空间内,采用非关联流动法则和非均匀等向强化法则建立了RPC200的塑性本构。基于损伤能释放率建立了损伤准则,并由正交法则给出损伤演化法则,同时采用两个不同的损伤硬化法则来描述拉、压性能不同的损伤硬化。证明了该文所建模型与热动力学基本原理的相容性。最后,给出了RPC弹塑性各向异性损伤耦合本构模型数值计算流程,并以简单例证证明了所建模型的预测能力。     

Fatigue and ratcheting assessment of AISI H11 at 500°C using constitutive theory coupled with damage rule

Hot extrusion is one of the most commonly used manufacturing methods for metal plastic deformation, and the consumption of extrusion tooling is considerably high due to its fatigue damage under cyclic serving condition. Hot‐work tool steel AISI H11 is one of these typical materials employed in extrusion tooling. This work is dedicated to calculating the stress/strain state of AISI H11 and predicting its lifetime at high temperature 500°C by building a unified constitutive model coupled with Lemaitre's damage law. Tensile tests and strain/stress reversed cycling tests have been conducted at 500°C to investigate mechanical properties and damage evolution. A unified constitutive model with Armstrong‐Fredrick/Ohno‐Wang kinematic hardening rule and a new proposed isotropic hardening rule is built; Lemaitre's damage law is employed as well. Parameters are determined based on tests and are temperature dependent. Finite element simulation of the deformation behaviour and fatigue lifetime is implemented into commercial software ABAQUS Standard v6.14‐2 with user material subroutine to validate the proposed method. The comparison shows good agreement with experimental results, and this part of work is essential and crucial to subsequent structure analysis.     

Dynamic shear response and evolution mechanisms of adiabatic shear band in an ultrafine-grained austenite–ferrite duplex steel

The dynamic properties of an intercritically annealed 0.2C5Mn steel with ultrafine-grained austenite–ferrite duplex structure were studied under dynamic shear loading. The formation and evolution mechanisms of adiabatic shear band in this steel were then investigated using interrupted experiments at five different shear displacements and the subsequent microstructure observations. The dynamic shear plastic deformation of the 0.2C5Mn steel was observed to have three stages: the strong linear hardening stage followed by the plateau stage, and then the strain softening stage associated with the evolution of adiabatic shear band. High impact shear toughness was found in this 0.2C5Mn steel, which is due to the following two aspects: the strong linear strain hardening by martensite transformation at the first stage, and the suppressing for the formation of shear band by the continuous deformation in different phases through the proper stress and strain partitioning at the plateau stage. The evolution of adiabatic shear band was found to be a two-stage process, namely an initiation stage followed by a thickening stage. The shear band consists of two regions at the thickening stage: a core region and two transition layers. When the adjoining matrix is localized into the transition layers, the grains are refined along with increasing fraction of austenite phase by inverse transformation. However, when the transition layers are transformed into the core region, the fraction of austenite phase is decreased and almost disappeared due to martensite transformation again. These interesting observations in the core region and the transition layers should be attributed to the competitions of the microstructure evolutions associated with the non-uniformly distributed shear deformation and the inhomogeneous adiabatic temperature rise in the different region of shear band. The 0.2C5Mn TRIP steel reported here can be considered as an excellent candidate for energy absorbers in the automotive industry.     

Simulation of meso–macro dynamic behavior using steel as an example

Presented in this paper is a model, where strain hardening and strain rate sensitivity are taken into account. The cellular automata rules are included into a continuum mechanics formulation to describe shear band propagation at the mesoscale. We apply the model in simulating deformation of the 20MnMoNi55 steel as an example. The macro stress–strain behavior and plastic strain patterns at the mesolevel are analyzed in the course of a computational tension test.     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

地震作用下钢结构损伤过程数值模拟

采用弹塑性损伤本构模型,该模型结合了非线性各向同性和随动强化准则以及基于塑性位移的损伤演化规律,利用ABAQUS对一个9层钢结构在EL-Centro地震波作用下塑性变形和损伤区域的发展过程进行了数值模拟.结果表明,上部楼层的梁端产生较明显的塑性变形并形成损伤部位.这与在Northridge地震中观测到的高层钢结构的地震...     

Effect of the grain boundary on the evolution of deformation in a bicrystal

The role of grain boundary constraint in strain localization and concomitant constitutive response was examined by performing a series of uniaxial compression tests on a tantalum bicrystal. Tantalum single crystals were diffusion bonded to form a (011) 90^∘ twist boundary that was compressed along the common [011] direction. The plastic deformation resulted in the creation of deformation bands away from the highly constraining grain boundary, resembling those bands known from single crystal plastic deformation. Near the grain boundary, such deformation band formation could not be detected. Instead a distinctive pattern of crystal lattice rotation was observed that filled a rather large volume (several millimeters in size) around the bicrystal grain boundary. The internal deformation band structure as well as the crystal lattice rotation pattern near the bicrystal grain boundary were characterized and found to give greater rates of work hardening in the neighborhood of the grain boundary.     

Multiscale constitutive modeling for plastic deformation of nanocrystalline materials

Macroscopic and microscopic constitutive modeling that can display large plastic deformation with shear band were presented for nanocrystalline materials subjected to uniaxial load over a wide strain rate range. The macroscopic model implemented with parameters microscopic meaning was established based on the theory of plastic dissipation energy. The microscopic model based on deformation mechanisms was composed of two parts: hardening and softening stages. In the hardening stage, the phase mixture model was used and a shear band deformation mechanism was proposed in the softening stage. Numerical simulations shown that the predications were in good agreement with experimental data. Finally, a parameter of normalized softening rate was proposed and its characteristics were evaluated quantitatively. It can be concluded that the failure strain could be prolonged when the normalized softening rate decrease through changing the softening path.     

Localized shear in metals under impact loading

The results of studies on localized shear strain in high-strength steel, a titanium alloy, and mild sheet steel under impact loading are given. The analysis of experimental results, microstructural changes, and numerical simulation demonstrates that adiabatic shear bands formed at high-rate deformation are influenced by strain hardening and heating in plastic flow and phase transformations in a material. The distribution of temperatures in the regions of strain localization is responsible for the development of microstructural changes. Nonuniform deformation without intense strain localization develops at lower shear rates and small strain increments per loading cycle, eliminating considerable heating of a material. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 27–42, March–April, 2000.     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

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.     

Cyclic deformation behavior of austenitic Cr–Ni-steels in the VHCF regime: Part II – Microstructure-sensitive simulation

In Part I – Experimental study, the cyclic deformation behavior of two austenitic stainless steel grades (AISI 304, AISI 316 L) were experimentally investigated at low stress amplitudes in the very high cycle fatigue (VHCF) regime. The observations indicate that during VHCF the metastable austenitic stainless steel (304 grade) performs a pronounced localization of plastic deformation in shear bands followed by a deformation-induced martensitic phase transformation. The 316 grade undergoes only a very limited local plastic deformation in shear bands with almost no phase transformation. Consequently, both materials exhibit distinctly different cyclic softening and hardening characteristics during VHCF. In order to provide a more detailed knowledge about the individual deformation mechanisms and their effect on the cyclic softening and hardening behavior the experimental study is extended by microstructure-sensitive modeling and simulation. Two-dimensional (2-D) microstructures consisting of several grains are represented using the boundary element method and plastic deformation within the microstructure is considered by a mechanism-based approach. Specific mechanisms of cyclic plastic deformation in shear bands and deformation-induced martensitic phase transformation – as documented by experimental results and based on well-known model approaches – are defined and implemented into the simulation. The fatigue behavior at low stress amplitudes observed in experiments can be well represented in simulations so that the underlying model helps to understand the cyclic deformation behavior of austenitic stainless steels at low stress amplitudes in the regime of VHCF strength. In a comparative study based on the resonant behavior the effect of certain deformation mechanisms on the global cyclic softening and hardening characteristics is pointed out for both materials.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity

The paper discusses the application of a newly developed material model for finite anisotropic plasticity to the simulation of earing formation in cylindrical cup drawing. The model incorporates Hill-type plastic anisotropy, nonlinear kinematic and nonlinear isotropic hardening. The constitutive framework is derived in the context of continuum thermodynamics and represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime. Plastic anisotropy is described by means of second-order structure tensors which are used as additional tensor-valued arguments in the representation of the yield criterion and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that fullfils plastic incompressibility and preserves the symmetry of the internal variables. The numerical examples investigate the influence of the hardening behaviour on an initially anisotropic yield criterion. In particular, the influence of using the kinematic hardening component of the model in addition to isotropic hardening in the earing simulations is examined. Comparisons with test data for aluminium and steel sheets display a good agreement between the finite element results and the experimental data.     

A Numerical Study of Strain Localization in Elasto-Thermo-Viscoplastic Materials using Radial Basis Function Networks

This paper presents a numerical simulation of the formation and evolution of strain localization in elasto-thermo-viscoplastic materials (adiabatic shear band) by the indirect/integral radial basis function network (IRBFN) method. The effects of strain and strain rate hardening, plastic heating, and thermal softening are considered. The IRBFN method is enhanced by a new coordinate mapping which helps capture the stiff spatial structure of the resultant band. The discrete IRBFN system is integrated in time by the implicit fifth-order Runge-Kutta method. The obtained results are compared with those of the Modified Smooth Particle Hydrodynamics (MSPH) method and Chebychev Pseudo-spectral (CPS) method.     

Higher order asymptotic solutions of V-notch tip fields for damaged nonlinear materials under antiplane shear loading

The higher order solutions of stress and deformation fields near the tip of a sharp V-notch in a power-law hardening material with continuous damage formation are analytically investigated under antiplane shear loading condition. The interaction between a macroscopic sharp notch and distributed microscopic damage is considered by describing the effect of damage in terms of a damage variable in the framework of damage mechanics. A deformation plasticity theory coupled with damage and a damage evolution law are formulated. A hodograph transformation is employed to determine the solution of damaged nonlinear notch problem in the stress plane. Then, inversion of the stress plane solution to the physical plane is performed. Consequently, higher order terms in the asymptotic solutions of the notch tip fields are obtained. Analytical expressions of the dominant and second order singularity exponents and associated angular distribution functions of notch tip stress and strain are presented. Effects of damage and strain hardening exponents and notch angle on the singular behavior of the notch tip quantities are discussed detailly. It is found that damage can lead to a weaker singularity of the dominant term of stress on one hand, but to stronger singularities of the second order term of stress and the dominant and second order terms of strain compared to that for undamaged case on the other. Also, both hardening exponent and notch angle have important effects on the notch tip quantities. Moreover, reduction of the notch tip solutions to a damaged nonlinear crack problem is carried out, and higher order solutions of the crack tip fields are obtained. Effects of damage and hardening exponents on the dominant and second order terms in the crack tip solutions are detailly discussed. Discussions on some other special cases are also presented, which shows that if damage exponent equals to zero, then the present solutions can be easily reduced to the solutions for undamaged cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strain localization and superplastic-like flow in copper at high temperature

The localization of plastic deformation at high temperature and its influence on the mechanical performance of polycrystalline copper were studied. The results showed that the instability of the load during high-temperature deformation is caused by the localization of plastic flow within shear bands. This in turn leads to heterogeneity of the dislocation structure and becomes a motive for selective static recrystallization along shear bands. Under appropriate conditions the balance between the formation of new shear bands and recrystallization (or recovery) within already inactive shear bands leads on a global scale to superplastic-like behaviour of the metal.