Numerical fatigue life analysis of a high frequency mechanical impact treated industrial component based on damage mechanics models

After post weld treatment with high frequency mechanical impact (HFMI) treatment of welds, a significant increase of fatigue life (up to a factor of 10) can be achieved. During the last years numerous experimental tests of welded joints with simple geometry under constant amplitude loading have been performed to quantify the positive effect of high frequency mechanical impact treatment. Due to the lack of methods for the prediction of the high frequency mechanical impact benefits, a widespread use of this process is not the case yet. Furthermore, it is still not clear if the results of these fatigue tests can be transferred to complex geometries and complex loading conditions such as in industrial applications. Therefore, an approach to assess the fatigue life of complex welded structures under variable amplitude loading was developed. For this purpose, high frequency mechanical impact treatment and fatigue load of simple welded specimen made of S690QL steel were simulated with finite element analysis (FEA) firstly. Then, the needed damage parameters for the fatigue life correlation were evaluated from the finite element post‐processing. The calculated life time to crack initiation was in good agreement with the experimental fatigue test results. In the next step, this procedure was implemented on a welded arm of an evacuator of type EW180B of the company Volvo Construction Equipment made of S700MC. The variable amplitude load measured under real service condition was transferred to single constant amplitude load cycles using a rainflow‐counting algorithm. By simulation and damage mechanics evaluation of each load cycle the total damage sum could be calculated and compared with the experimental results from Volvo Construction Equipment.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Damage tolerance reliability analysis of automotive spot-welded joints

This paper develops a damage tolerance reliability analysis methodology for automotive spot-welded joints under multi-axial and variable amplitude loading history. The total fatigue life of a spot weld is divided into two parts, crack initiation and crack propagation. The multi-axial loading history is obtained from transient response finite element analysis of a vehicle model. A three-dimensional finite element model of a simplified joint with four spot welds is developed for static stress/strain analysis. A probabilistic Miner's rule is combined with a randomized strain-life curve family and the stress/strain analysis result to develop a strain-based probabilistic fatigue crack initiation life prediction for spot welds. Afterwards, the fatigue crack inside the base material sheet is modeled as a surface crack. Then a probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction for spot welds. Both methods are implemented with MSC/NASTRAN and MSC/FATIGUE software, and are useful for reliability assessment of automotive spot-welded joints against fatigue and fracture.     

Interior micro-defect induced cracking mechanism and life prediction of carburized Cr−Ni steel based on double nonlinear damage under variable amplitude loading

The constant/variable amplitude loading fatigue test with interior inclusion-fine granular area-fisheye induced failure under R=0 were carried out on carburized Cr−Ni steel. The results showed that the fatigue life under variable amplitude loading is longer than that under constant amplitude loading in very-high-cycle fatigue regime under same maximum stress level, and the surface morphology of fine granular area under variable amplitude loading is coarser than that under constant amplitude loading under same order of magnitude of fatigue life. Simultaneously, it can be determined that the formation micro-mechanism of fine granular area is caused by the continuous deboning due to stress concentration around interior micro-defects. Furthermore, the life prediction model based on double nonlinear fatigue damage, which considers the coupling effect of local equivalent stress (surface residual stress and local stress concentration effect), loading sequence, failure mechanism and nonlinear characteristics of fatigue damage under constant/variable amplitude loading is established, and predicted life has good accuracy within the factor-of-three lines.     

Variable amplitude fatigue of spot welds

A new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.     

An experimental approach to estimate damage and remaining life of metals under uniaxial fatigue loading

An experimental procedure to estimate damage evolution and remaining fatigue life of metals associated with fatigue loading is presented. Experimental phase involves uniaxial tension–compression fatigue tests performed with solid API 5L X52 and tubular carbon steel 1018 specimens subjected to both constant and variable amplitude loading. A correlation between the so-called damage parameter and the thermal response of a material at different damage levels is proposed. Results demonstrate that the correlation can estimate damage evolution with reasonable accuracy in both constant and variable amplitude fatigue processes. It is shown that under the conditions tested the evolution of damage parameter with respect to the normalized fatigue life is independent of the load amplitude, load ratio, loading sequence, material properties, and specimen geometry. The proposed correlation and the relationship between the damage parameter and the normalized fatigue life are employed to develop a non-destructive method to predict the remaining fatigue life of metallic specimens with prior fatigue damage. The method is applied to both constant and variable amplitude loading and the predicted results are found to be in good agreement with those obtained from the experiments.     

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

Low-cycle fatigue life prediction of spot welds based on hardness distribution and finite element analysis

Elasto-plastic finite element analysis was carried out for single spot tensile shear spot welds with software ANSYS. According to the relationship between micro-hardness and strength, cyclic material constants of different zones in the periphery of spot welds were determined in accordance with hardness distribution, as well as base material fatigue parameters. Using the local stress and strain obtained from finite element analysis, fatigue lives of spot welds were predicted with Morrow’s modified Manson–Coffin equation and Smith–Watson–Topper damage equation. Life prediction results showed that both equations gave good agreement with experimental data within low-cycle fatigue life regime.     

A study of factors affecting life prediction of composites under spectrum loading

The influence of damage accumulation metric, constant life diagram formulation and cycle counting method on life prediction schemes for composite materials under variable amplitude (VA) loading is investigated in this paper. Special focus is put on residual strength based methodologies; different degradation functions are implemented and compared with the Palmgren–Miner (PM) damage accumulation rule. The predictions are validated by comparison with experimental data from a unidirectional glass/epoxy laminate cycled with three different loading spectra. The effect of constant life diagram (CLD) and cycle counting method used in life prediction is investigated through implementation of alternative existing formulations. Results indicate that a net improvement is achieved when linear strength degradation is implemented as damage metric in life prediction schemes, over the state-of-the-art PM summation. Depending on the spectrum pattern itself, CLD and counting method might be of predominant role; Rainflow counting and the simplistic concept according to which a single S–N curve describes fatigue response of the material under any loading condition (R ratio) are shown to yield consistently best life predictions.     

Energy-based time derivative damage accumulation model under uniaxial and multiaxial random loadings

A new fatigue life prediction method using the energy-based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time-derivative damage accumulation unlike classical cycle-based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time-domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time-derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time-derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in-house testing under various constant and random spectrum loadings.     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

Numerical methods of multiaxial fatigue life prediction for elastomers under variable amplitude loadings

In this paper, numerical methods of fatigue life prediction for elastomers subjected to multidirectional, variable amplitude loadings are presented. Because experiments and numerical methods use different stress measures in large deformation, transformation between nominal stress and the second Piola–Kirchhoff stress is performed before fatigue life calculation. In order to incorporate the Mullins effect, the material properties of elastomers are calculated after an initial transition period. An efficient interpolation scheme using load stress/strain curves under unidirectional loading is proposed based on the fatigue characteristic of elastomers. A rainflow counting method with multi‐stress components is developed for variable amplitude loadings, and the critical plane method is applied to find the plane with the maximum damage parameter. Fatigue life predictions using the proposed numerical method are validated against experimental results. As a practical example, the fatigue life of a rubber engine mount is predicted using the proposed numerical method.     

基于机车车轮的动态疲劳可靠性研究

 随着火车速度的不断提高,对火车走行部件的疲劳可靠性要求也越来越高．根据疲劳寿命预测理论,建立了某机车车轮受力危险点在不同路况下的疲劳寿命曲线．以实测数据和有限元分析所得数据为基本参数,采用线性累积损伤法则和Monte-Carlo模拟,对车轮在等幅载荷和随机载荷谱共同作用下进行疲劳寿命预测,得到了车轮在不同路况下可靠度随路程变化的关系曲线．为火车的安全性维护提供了理论依据,对火车的安全运行有重大的实际应用价值．     

A non-linear damage accumulation fatigue model for predicting strain life at variable amplitude loadings based on constant amplitude fatigue data

A new phenomenological technique for using constant amplitude loading data to predict fatigue life from a variable amplitude strain history is presented. A critical feature of this reversal-by-reversal model is that the damage accumulation is inherently non-linear. The damage for a reversal in the variable amplitude loading history is predicted by approximating that the accumulated damage comes from a constant amplitude loading that has the strain range of the particular variable amplitude reversal. A key feature of this approach is that overloads at the beginning of the strain history have a more substantial impact on the total lifetime than overloads applied toward the end of the cycle life. This technique effectively incorporates the strain history in the damage prediction and has the advantage over other methods in that there are no fitting parameters that require substantial experimental data. The model presented here is validated using experimental variable amplitude fatigue data for three different metals.     

考虑应变均值影响的天然橡胶隔振元件疲劳寿命预测

对橡胶试柱进行单轴疲劳试验,分析了应变幅值一定时,应变均值对疲劳寿命的影响。以哑铃型天然橡胶试柱为研究对象,通过有限元计算分析,得到了加载位移与橡胶试柱危险位置处最大主应变的关系。构建了应变均值函数,以应变比R=0时的 曲线为基准疲劳寿命曲线,建立了不同应变均值和幅值下的天然橡胶隔振元件的疲劳寿命预测模型。使用该模型预测得到的哑铃型天然橡胶试柱疲劳寿命与试验疲劳寿命具有较好相关性。文中提出的天然橡胶元件的疲劳寿命预测模型,可用于建立天然橡胶材料的疲劳寿命数据库。     

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

基于模态频率的缺口梁疲劳裂纹扩展寿命预测

从试验出发,研究了含V型缺口悬臂梁在循环载荷作用下的疲劳裂纹扩展特性及其模态频率变化规律,分析了模态频率与裂纹扩展增量间的关联性。将裂纹扩展增量作为损伤参量,建立了基于模态频率下降率与损伤参量的关系。基于损伤力学,建立了裂纹损伤与循环加载次数的演化模型。结合模态频率下降率与裂纹损伤参量的关系,提出了一种基于模态频率下降率的缺口梁疲劳裂纹扩展寿命预测方法,实现了基于当前裂纹损伤和对应循环次数的疲劳裂纹扩展剩余寿命预测。结果表明,模态频率下降率对缺口梁的疲劳裂纹扩展寿命敏感,该方法预测的疲劳裂纹扩展寿命与实测的疲劳裂纹扩展寿命基本吻合。