Werkstoffmechanische Beanspruchungsanalyse gekerbter Strukturen bei synchronen Belastungskombinationen

Elastic‐Plastic analysis of notched structures under synchronous cyclic loading This paper focuses on analysing the elastic‐plastic stress‐strain behaviour at the failure‐critical location of notched components and structures under multiaxial synchronous cyclic loading. For this, various load configurations are investigated numerically consisting of constant and cyclic load components with constant and variable amplitudes. The von Mises yield criterion and the kinematic hardening rule of Prager and Ziegler describe the elastic‐plastic material property. The finite element software of ABAQUS is used to solve the boundary element problem. A parametrical study is carried out and numerical results are presented to show the effects of load amplitude, mean load and spectrum shape on the local stress‐strain paths.     

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.     

Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis

Life prediction for GH4169 superalloy thin tubular and notched specimens were investigated under proportional and nonproportional loading with elastic–plastic finite element analysis (FEA). A strain-controlled tension–torsion loading was carried out by applying the axial and circular displacements on one end of the specimen in the cylindrical coordinate system. Uniaxial cyclic stress–strain data at high temperature were used to describe the multi-linear kinematic hardening of the material. The comparison between FEA and experimental results for thin tubular specimen showed that the built model of FE is reliable. A fatigue damage parameter was proposed to predict the fatigue crack initiation life for notched specimen. The results showed that a good agreement was achieved with experimental data.     

Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

Elasto-plastic finite element analysis

An elasto-plastic finite element small displacement procedure to predict the behaviour of structures under cyclic loads is presented. The solution combines incremental procedure with correction for equilibrium and iterative scheme. Applications are made for a rectangular strip and a notched bar under cyclic axial loads. Flow theory of plasticity with either isotropic hardening or kinematic linear hardening is used.     

TA17合金薄片材料毫小试样疲劳性能研究

关键工程结构、小尺寸零部件和焊接区的疲劳寿命评估中往往无法采用传统大试样进行疲劳试验,因此本文提出了一种采用毫米级别薄片试样获取材料循环本构关系和低周疲劳寿命的新方法。在Care原位试验机上完成毫米级别薄片漏斗试样的加载工装和低周疲劳试验的基础上,通过变幅对称循环试验和等辐循环试验分别实现了材料循环本构关系和低周疲劳性能的获取。该文提出了一种对不同幂律材料和不同几何尺寸构型均具有良好普适性的材料循环本构关系预测模型,并通过有限元实现了模型准确性的正反向预测验证。将循环本构关系用于有限元计算中,给出了薄片漏斗试样漏斗两侧名义应力、名义应变和漏斗根部真实应力、真实应变的转换方程,进而预测材料的低周疲劳寿命。该文完成了TA17合金等直圆棒试样和1.2 mm厚度薄片漏斗试样的对称变幅循环试验和多级等辐循环试验。由模型预测获得的TA17合金循环本构关系与等直圆棒试样的试验结果比较表明:两种曲线的弹性段和0.009 mm/mm~0.011 mm/mm应变段吻合良好,在弹塑性过渡段（0.004 mm/mm~0.009 mm/mm）模型预测结果最大相对误差小于9%。根据两组应力和应变转换方程获得的漏斗试样材料代表性体积单元疲劳寿命和Manson-Coffin寿命预测模型与等直圆棒试样试验结果均吻合良好。     

Crack Initiation under Cyclic Compression

The crack initiation behaviour under cycliccompression foy the notched specimen wasinvestigated. It has been found that the cyclesfor crack initiation increase with the increaseof compressive mean stress, and the decreaseof stress amplitude. The stress amplitude playsa more important role than the mean stress does.Photoelastic coating and finite element methodswere employed to measure and calculate the stressfield in the notched part. The resul ts showthat the crack initiation under compressionis attributed to the tensile stress which mayexist during unloadtng. If the true stress statein the notch is compressive, no crack initiates.     

A notch strain calculation of a notched specimen under axial-torsion loadings

In this paper, a notch analysis model is presented for the numerical prediction of multiaxial strains of a notched 1070 steel specimen under combined axial and torsion loadings. The proposed model is based on the notion of a structural yield surface and uses a small-strain cyclic plasticity model to describe stress–strain relations. A notch load–strain curve is calculated with Neuber’s rule and incremental nonlinear finite element analysis. The presented model is applied to simulate the notch root deformations of a circumferentially notched specimen under cyclic tension–compression–torsion loading histories. The model predictions are evaluated with strain measurements at the notch root of the specimen in a comprehensive set of cyclic tests. The computed strain loops were in accord with experimental data and matched qualitatively with measured shear–axial strain histories irrespective of loading path of the test. In proportional balanced torsion-axial loading, the nonlinear shear strain–axial strain loops were calculated properly. The modeling errors were determined to be a function of the loading path shape, and compared to shear strains, axial strain predictions were more accurate.     

Q690D高强钢基于连续损伤模型的断裂破坏预测分析

高强钢材在实际钢结构中已经开始逐步得到应用,该文针对Q690D高强度结构钢材,进行了钢材圆棒试样在单调加载和超低周循环加载下的断裂破坏试验,研究了试样裂纹的起始位置,分析了加载制度对试样承载能力和变形能力的影响,并采用扫描电镜观察了试样断口的微观形貌,断口呈现韧窝形式的延性断裂特征。基于Q690D钢材缺口圆棒试样的单调拉伸试验结果,结合有限元分析,标定了钢材的连续损伤模型参数。最后,应用钢材的连续损伤模型,对圆棒试样和带初始间隙试样在不同加载制度下的断裂破坏进行预测分析,得到试样的裂纹起始位置、荷载-位移曲线、断裂位移和疲劳寿命均与试验结果吻合良好。     

Fatigue properties of transformation-induced plasticity and dual-phase steels for auto-body lightweight: Experiment,modeling and application

The substitution of conventional high strength steels (HSS) with advanced high strength steels (AHSS), e.g., low-alloy multiphase transformation-induced plasticity steel (TRIP steel) or dual-phase steel (DP steel), for body lightweight brings about increased stress of notched components. Thus the fatigue properties of TRIP and DP steels and the fatigue life of notched lightweight design are important considerations for reasonable material selection during the design stage of auto-body. For the mentioned issue, cyclic strain-controlled fatigue properties of TRIP and DP steels with equivalent grade and lightweight result were investigated experimentally. Different cyclic behaviors of TRIP and DP steels were observed due to different interior microstructures. The cyclic stress behavior of TRIP steel is characterized by cyclic hardening followed by stable at lower strain amplitudes, and softening at higher strain amplitudes; however cyclic softening followed by stable occurs consistently for DP steel throughout entire strain amplitude range of test. TRIP steel possesses enhanced fatigue life and cyclic stress at the same strain amplitude than DP steel. Furthermore, local strain-life models of two steels were developed by linear regression of experimental data, to predict and compare the fatigue life of notched body structures made of them by finite element method. The simulation result illustrates that TRIP steel can provide more beneficial potential than DP steel for the lightweight design of notched body structures from the viewpoint of fatigue resistance.     

Fatigue life estimation of notched specimens of modified 9Cr-1Mo steel under uniaxial cyclic loading

Accuracy in the estimation of low cycle fatigue life of modified 9Cr-1Mo steel notched specimen by different analytical methods such as linear rule, Neuber’s rule, strain energy density method and numerical method such as finite element analysis have been studied in this investigation. The fatigue tests on notched specimens having notch radius of 1.25 mm, 2.5 mm and 5.0 mm were carried out at 823 K with net stress amplitudes of 250 MPa, 300 MPa and 350 MPa. The fatigue tests on smooth specimens were carried out with strain amplitudes ranging from ±0.3% to ±0.8% with a strain rate of 3 × 10^?3 s^?1 at 823 K to evaluate the fatigue life of notched specimen through strain-life approach. In order to predict the cyclic stress response of the material, Chaboche non-linear hardening model was employed considering two back stress components. Predicted hysteresis loops for smooth specimen were well in agreement with experimental results. Estimated fatigue lives of notched specimens by analytical methods and finite element analysis were within a factor ±16 and ±2.5 of the experimental lives respectively.     

ELASTIC-PLASTIC BEHAVIOUR AND UNIAXIAL LOW CYCLE FATIGUE LIFE OF NOTCHED SPECIMENS

Experimental and numerical analyses were carried out to examine the elastic-plastic behaviour and low cycle fatigue (LCF) life of EN15R steel notched specimens. Notch root strains were measured and compared with estimates obtained from three methods: Neuber, Glinka and hite element (FE) analyses. All methods provided fairly accurate estimates of cyclic strain up to net section yield, from which point the Neuber and Glinka predictions were greater than measured. The finite element results compared well with measured results. The estimated notch root strains were used to predict the life of the notched specimens based on LCF results from unnotched specimens. Uniaxial Coffom-Manson and multiaxial Lohr-Ellison approaches were used. Improved fatigue life predictions were obtained when the FE predictions of the multiaxial strains were combined with a multiaxial strain parameter. The possible influence of strain gradient is inferred by comparing LCF lives for hollow thin-walled and solid bar specimens.     

A coupled FE–EFG approach for modelling crack growth in ductile materials

In this work, a coupled finite element–element free Galerkin approach has been used to model crack growth in ductile materials under monotonic and cyclic loads. In this approach, a small discontinuous domain near crack is modelled by EFG method, whereas the rest of the domain is modelled by FEM to exploit the advantages of both the methods. A ramp function has been used in the transition region to maintain the continuity between FE and EFG domains. Two plasticity models (GTN and von‐Mises) and three hardening rules (isotropic, kinematic and mixed) have been used to model the nonlinear material behaviour. Four different problems, i.e. single edge notched tension specimen, double edge notched tension specimen, compact tension specimen and three‐point bend specimen, are solved under plane strain condition using J–R curve approach. Finally, a CT specimen problem is also solved by coupled approach using three hardening rules and two plasticity models under cyclic loading.     

建筑结构钢超低周疲劳断裂破坏的损伤预测模型

针对地震作用下建筑结构钢的超低周疲劳断裂问题,在单调加载损伤模型的基础上,提出了一种适用于超低周循环加载情况下的损伤预测模型,并借助ABAQUS软件的用户自定义材料子程序模块,将建立的损伤预测模型引入到有限元分析程序中。然后分别依据建筑钢结构母材、热影响区和焊缝金属缺口试样的单调加载和超低周循环加载试验,标定了材料的损伤模型参数,并对比分析了缺口圆棒试样在不同加载方式下的损伤演化规律,损伤分析结果表明缺口圆棒试样的裂纹都产生于试样截面中心处,这与试验结果一致。最后,以钢框架梁柱焊接节点为研究对象,应用损伤模型分析了节点危险部位的损伤演化规律,数值模拟了节点的超低周疲劳断裂破坏过程,最终得到节点的疲劳寿命与试验结果吻合良好。     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Modelling the HRR-singularity with akin and conventional singular elements

A single edge notched plate of elastic-plastic material has been analysed using different finite element meshes and different singular crack tip element. Especially the Akin element was of interest since it gives a possibility to model the HRR-singularity.     

Finite element analysis of a cyclically loaded notched bar using constitutive models based on the cyclic nonhardening region

It is shown that simple and elaborate constitutive models based on the cyclic nonhardening region are implemented without difficulty in existing finite element methods. The cyclic nonhardening region, which is defined in plastic strain space, enables us to describe an important feature of cyclic plasticity, i. e., dependence of cyclic hardening of materials on the cyclic strain and stress ranges. This dependence is essential to structural analysis of cyclic plasticity, because structures have, in general, nonuniform distributions of the cyclic strain and stress ranges, resulting in nonuniform development of cyclic hardening. An axisymmetric notched bar subjected to axial cyclic loading is analyzed as an example, and the results by the simple and elaborate models are compared.This paper was presented at International Conference on Computational Mechanics, May 25–29, 1986, Tokyo     

Elastic-plastic fem calculations of the stress distribution of notches with different geometry

A two-dimensional elasto-plastic finite element analysis of double notched rectangular tensile specimens with different notch geometries has been performed. The maximum value of stress concentration below the notch is given as function of the applied stress for varying notch radius and notch angles. The results of the finite element method are compared with the predictions of the slip line theory.     

Finite element analysis and experimental research on notched strengthening effect of P92 steel

Abstract

The notched strengthening effect during creep of P92 steel has been studied by finite element analysis and experimental research. It was found that there was a transforming tendency from ductile to brittle at the root of the notch and the extent of the transforming intensified with the increment of the nominal stress. It was the transforming tendency that increased the value of creep life enhancement factor. With the help of finite element software, Kachanov–Rabotnov creep damage constitutive model was embedded into the interface program and the notched specimens creep was simulated. The result has shown the Kachanov–Rabotnov model can be used to simulate the notched strengthening effect of P92 steel accurately when the material constant α?=?0·73.