Analysis of Fatigue Damage under Block Loading in a Low Carbon Steel

Abstract: The fatigue damage accumulation behaviour of the P355NL1 steel is characterised using block loading fatigue tests. First, the constant amplitude low‐cycle fatigue behaviour of the P355NL1 steel is evaluated through strain‐controlled fatigue tests of smooth specimens. Both fatigue and cyclic elastoplastic behaviours are analysed. Then, block loading is applied to identify the key features of the fatigue damage accumulation phenomena for the P355NL1 steel. The block loading is composed of two distinct low‐cycle constant amplitude strain‐controlled blocks. The first block is applied for a predefined number of loading cycles, being followed by a second block which is applied until failure. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles as a function of the strain amplitude. These observations suggest a nonlinear damage accumulation rule with load sequence effects. The linear Palmgren–Miner's rule used extensively in design is not verified for the P355NL1 steel. Finally, using the generated experimental data, the cyclic elastoplastic behaviour of the P355NL1 steel is modelled using a continuum plasticity model with nonlinear kinematic hardening, available in the commercial finite element code ansys ®.     

Assessment of fatigue response of thermally aged reduced activation ferritic-martensitic steel based on finite element analysis

Abstract

In the present investigation, effect of thermal ageing on low cycle fatigue (LCF) behaviour of Reduced Activation Ferritic Martensitic steel has been assessed by finite element analysis. The steel was thermally aged at 873 K for 3000 hour. Low cycle fatigue tests were carried out on both the as-received and thermally aged material at strain rate of 3×10^?3 s^?1 at 823 K, over strain amplitudes in the range of ± 0.25 to ± 0.8%. Continuous cyclic softening till final failure, except for initial few cycles especially at relatively lower strain amplitudes, was observed in both the material conditions. Thermal ageing resulted in marginally higher cyclic stress response accompanied by lower fatigue life. The differences in fatigue responses have been attributed to the coarsening of precipitates on thermal ageing. Finite element analysis has been carried out considering combined isotropic and kinematic hardening as material model to estimate the effect of thermal ageing on the response of material under LCF loading. Thermal ageing was found to decrease both the isotropic and kinematic hardening with appreciable effect on isotropic hardening. The predicted cyclic stress response and hysteresis loops were found to be in good agreement with the experimental data. The LCF life of the steel has been estimated based on the hysteresis energy approach.     

Taguchi sensitivity analysis of damage parameters for predicting the damage Mechanism of 9Cr steel under low‐cycle fatigue test

Numerical investigations of low‐cycle fatigue damage parameters of a 9Cr steel have been studied and compared with the previous results in order to understand the effect of the damage parameters on predicting the damage development of the material. Using the nonlinear kinematic softening criterion, the Chaboche constitutive equation is combined with the hysteresis total stress–strain energy concept to implement damage initiation and evolution; the remaining life of the specimen can be predicted. In this paper, the cyclic softening model in conjunction with the progressive damage evolution model successfully predicted the failure times of the experimental tests. By using a novel sensitivity analysis of the damage parameters c₁, c₂, c₃ and c₄ based on the Taguchi method, the highest parameter effect has been determined.     

Towards improved ODS steels: A comparative high‐temperature low‐cycle fatigue study

Within the frame of this work, the mechanical behaviour of a bimodal ferritic 12Cr‐ODS steel as well as of a ferritic‐martensitic 9Cr‐ODS steel under alternating load conditions was investigated. In general, strain‐controlled low‐cycle fatigue tests at 550°C and 650°C revealed similar cyclic stress response. At elevated temperatures, the two steels manifest transitional stages, ie, cyclic softening and/or hardening corresponding to the small fraction of the cyclic life, which is followed by a linear cyclic softening stage that occupies the major fraction of the cyclic life until failure. However, it is clearly seen that the presence of the nano‐sized oxide particles is certainly beneficial, as the degree of cyclic softening is significantly reduced compared with non‐ODS steels. Besides, it is found that both applied strain amplitude and testing temperature show a strong influence on the cyclic stress response. It is observed that the degree of linear cyclic softening in both steels increases with increasing strain amplitude and decreasing test temperature. The effect of temperature on inelastic strain and hence lifetime becomes more pronounced with decreasing applied strain amplitude. When analysing the lifetime behaviour of both ODS steels in terms of inelastic strain energy calculations, it is found that comparable inelastic strain energies lead to similar lifetimes at 550°C. At 650°C, however, the higher inelastic strain energies of 12Cr‐ODS steel result in significant lower lifetimes compared with those of the 9Cr‐ODS steel. The strong degradation of the cyclic properties of the 12Cr‐ODS steel is obviously linked to the fact that the initial hardening response appears significantly more pronounced at 650°C than at 550°C. Finally, the obtained results depict that the 9Cr‐ODS steel offers higher number of cycles to failure at 650°C, compared with other novel ODS steels described in literature.     

Uniaxial ratchetting in steels with different cyclic softening/hardening behaviours

The cyclic deformation of three structural steels, SS316L stainless steel, 40Cr3MoV bainitic steel and 25CDV4.11 steel, were studied experimentally by uniaxial cyclic straining or stressing tests at room temperature. The cyclic softening/hardening behaviours of the steels were discussed first by cyclic straining tests; and then the effects of cyclic softening/hardening behaviours on the uniaxial ratchetting of the materials were investigated by asymmetrical cyclic stressing tests. It is concluded from the experimental results that the ratchetting greatly depends on the cyclic softening/hardening behaviours of the materials, as well as the loading history. Different ratchetting and failure behaviours are observed for the prescribed steels. It is also stated that the proposed unified visco‐plastic constitutive model can provide a fairly reasonable simulation of the uniaxial ratchetting of SS316L stainless steel and 25CDV4.11 steel; but cannot simulate the ratchetting of 40Cr3MoV bainitic steel since the dependence of cyclic softening behaviours on the applied inelastic strain amplitude cannot be reasonably described in the discussed constitutive model. Some significant conclusions are obtained, which are useful to construct constitutive model to describe the ratchetting of the materials with different cyclic softening/hardening behaviours.     

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.     

基于不同强化模型的GTN损伤模型及其在板料回弹有限元分析中的应用

为了进一步提高板料成形中的回弹预测精度,分别建立了基于Ziegler 线性随动强化模型、Lemaitre-Chaboche 非线性随动强化以及非线性混合强化模型的Gurson-Tvergaard-Needleman(GTN)细观损伤本构模型,并给出有限元数值积分方法。通过用户自定义材料子程序VUMAT 将损伤模型嵌入到有限元软件ABAQUS 中,以NUMISHEET’93 板料U 型弯曲考题为例,应用显隐相结合的方法模拟分析了不同材料强化模型和损伤对板料回弹量的影响。结果表明:在相同GTN 损伤模型情况下,线性随动和非线性随动强化模型预测得到的板料回弹量较小,等向强化预测的板料回弹量偏大,非线性混合强化预测的板料回弹量介于它们之间。材料模型在考虑损伤因素后,预测的回弹严重程度比无损伤情况时略小,与实验值更相近。     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

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.     

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.     

钢管铅阻尼器构造优化及模拟分析

钢管铅阻尼器端部构造形式直接影响其破坏形式及力学性能。该文首先对钢管铅阻尼器钢管过渡段构造形式进行改进,提出一种新的构造形式;其次,建立钢管铅阻尼器的有限元模型,提出适合钢管铅阻尼器的金属材料随动强化混合模型参数的计算公式,开发了便于准确、快速建立钢管铅阻尼器有限元模型的参数化建模平台;再次,对比有限元分析与钢管铅阻尼器试验的结果,验证有限元模型的可靠性;最后,采用该有限元模型对改进的构造形式进行分析。研究结果表明：1）钢管铅阻尼器外钢管过渡段采用新的构造形式,能够增加过渡段强度,有效控制阻尼器塑性分布,使得阻尼器的变形和耗能集中在中部,防止阻尼器由于端部连接破坏而使阻尼器过早退出工作;2）采用该文提出的金属材料随动强化混合模型参数计算公式所建立的钢管铅阻尼器有限元模型,计算结果与试验结果吻合良好;3）钢管铅阻尼器参数化建模平台可以准确、快速建立不同构造参数的钢管铅阻尼器有限元模型,为大批量参数分析提供高效、可靠的工具。     

Cyclic stress-strain response during isothermal and thermomechanical fatigue

Isothermal high-temperature low-cycle fatigue and in-phase and out-of-phase thermomechanical fatigue tests were carried out on 316L austenitic stainless steel specimens controlled by computer. A non-linear kinematic hardening model with internal variables was used to simulate the cyclic stress-strain behaviour of isothermal fatigue. This model was modified by considering thermal cyclic effects in order to describe the cyclic stress-strain behaviour of thermomechanical fatigue (TMF) using only isothermal fatigue data and the material performance data. A very good approximation of the hysteresis loops was obtained by comparing with experiments of both in-phase and out-of-phase cases. The thermomechanical fatigue behaviour described by isothermal fatigue data gives the possibility of developing the TMF lifetime prediction technique.     

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.     

Bauschinger effect of alloys and plasticity-induced crack closure: a finite element analysis

The effect of overloads, underloads and stress ratio on plasticity-induced crack opening level is examined for different 'model' materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results.     

Torsional fatigue with axial constant stress of oligo‐crystalline 316L stainless steel thin wire

A series of symmetric torsional fatigue with axial constant stress tests, a kind of multiaxial fatigue test, was conducted on oligo‐crystalline 316L stainless steel thin wire, which was less than 3.5 grains across diameter of 200 μm. The material presents significant cyclic hardening under symmetric torsion cycling, and hardening is more obvious with the increasing shear strain amplitude. However, symmetric torsional cycle with constant axial stresses tests characterize rapid initial hardening and then gradually softening until fatigue failure. The axial stress has a great effect on torsional fatigue life. Fractography observation shows a mixed failure mode combined torsional fatigue with tensile strain because of axial tensile stress. A newly proposed model with axial stress damage parameter is used to predict the torsional fatigue life with constant axial stress of small scale thin wire.     

A nonlinear viscoelastic–viscoplastic model for adhesives

We consider the nonlinear viscoelastic–viscoplastic behavior of adhesives. We develop a one-dimensional nonlinear model by combining Schapery’s nonlinear single integral model and Perzyna’s viscoplastic model. The viscoplastic strain was solved iteratively using the von Mises yield criterion and nonlinear kinematic hardening. The combined viscoelastic–viscoplastic model was solved using Newton’s iteration and implemented into a finite element model. The model was calibrated using creep-recovery data from bulk adhesives and verified from the cyclic behavior of the bulk adhesives. The finite element model results agreed with experimental creep and cyclic responses, including recoverable and permanent strain after load removal. Although the contribution of the viscoplastic strain was small, both viscoplastic and viscoelastic components of strain response were required to describe the adhesive creep and cyclic response.

     

Simulation of low cycle fatigue stress‐strain response in 316LN stainless steel using non‐linear isotropic kinematic hardening model—A comparison of different approaches

Cyclic stress‐strain response of 316LN stainless steel subjected to low cycle fatigue at strain amplitude of ±0.4% and at 873 K is simulated using finite element analysis with non‐linear isotropic‐kinematic hardening Chaboche model. Four different approaches have been used in simulating cyclic stress response and hysteresis loops: 3 based on Chaboche model‐parameters and the fourth on direct experimental data (stabilized loop and cyclic stress‐strain curve [CSSC]). Among them, simulations performed with direct experimental data have not yielded expected initial cyclic response. The source of data used for evaluation of kinematic‐hardening (KH) parameters determined the extent of closeness between experimental results and Chaboche‐model predictions. KH parameters determined from first‐cycle loop and modified‐CSSC predicted the overall stress‐strain response (from initial to stabilized condition) with reasonable fit, compared with other approaches. All 4 approaches though predicted stabilized response, simulations based on “KH‐parameters from stabilized‐cycle” accurately described stabilized response with coefficient of determination (r²) 0.995.