Nonlinear Damage Accumulation Model Research Articles

A novel two-scale nonlinear damage accumulation model for vibration fatigue life prediction

Vibration is the main factor causing high cycle fatigue. The macro-response stress and strain of the structure under the excitation of vibration load are generally in the elastic stage. However, fatigue failure still occurs due to long-term cyclic load, which is unexplainable by the macro-plastic accumulation method. Therefore, a two-scale nonlinear damage accumulation model is proposed for vibration fatigue based on the physical characteristics of multi-scale fatigue damage evolution. In this model, two-scale elastic-plastic constitutive equations based on the equivalent inclusion theory are built, and a two-stage damage accumulation strategy with two critical damages is designed. A resonance fatigue life prediction algorithm is established based on the proposed model, and a validation test is carried out using the cantilever beam made of GH4169 alloy. The results show that the deviation between the vibration fatigue life prediction and test results is within a scatter band of factor 2, indicating that the two-scale nonlinear damage accumulation model is effective in the vibration fatigue region.

High Temperature Strength Property and Creep-Fatigue Life Prediction of a Temper Bead Welded CrMo Casting Steel

Cr-Mo casting steels are widely used as casings and valves in thermal power plants. Creep fatigue damage gradually proceeds in these high-temperature components during operation resulting in creep voids and micro crack initiation in which repair welding is considered to be applied for life extension. In this study, a temper bead welded joint of Cr-Mo casting steel as well as fine and coarse grain simulated materials were prepared. Creep and fatigue, creep-fatigue tests were performed using specimens taken from base and weld metals of the welded joint, the simulated materials and cross welded specimens. Material constants of creep deformation and cyclic stress-strain properties for constituted materials of the welded joint were obtained from the creep and fatigue tests. Minimum creep strain rate of the base metal at the same stress was the highest than that of other materials. Plastic deformation resistance is higher in the order of the base metal, fine grain, coarse and weld metal. Creep-fatigue life of the welded joint, which failed at the base metal 2mm away from the boundary between the base metal and fine grain, was shorter than that of the uniform base metal specimen indicating that the temper bead welding may reduce the creep-fatigue life. Finite element analysis of the cross welded specimen showed that elastic-plastic and creep strains accumulated at the base metal near the boundary are higher than those at other regions causing life reduction and failure at the base metal. The creep-fatigue life prediction by using the analysis results indicated that the nonlinear damage accumulation model gave more accurate life prediction results than the time fraction and ductility exhaustion rules.

Influence of Increasing Mean Stress on Fatigue Properties of Shale during Pulsating Hydraulic Fracturing

During pulsating hydraulic fracturing (PHF), reservoir rock can be subjected to constant amplitude, constant mean stress (CACMS) cyclic loading or constant amplitude, increasing mean stress (CAIMS) cyclic loading. The influence of increasing mean stress on rock fatigue strength, fatigue lifetime, fatigue damage, and energy evolution of shale is rarely investigated, and which type of cyclic loading is more efficient for PHF has not been determined and demonstrated. In this Article, a series of uniaxial compression tests under these two types of cyclic loading are first conducted. A fatigue lifetime model for CAIMS is established. The shale strength and fatigue lifetime for CACMS and CAIMS are then compared. Their differences are explained by their dissipated energy density evolution and damage evolution. Finally, a nonlinear damage accumulation model to predict damage evolution for CAIMS cyclic loading is proposed. It is suggested that CAIMS is a better cyclic loading type when its amplitude is higher than 30% UCS (uniaxial compressive strength) of rock. This provides a meaningful amplitude threshold for CAIMS parameter optimization in the PHF construction. In this case, compared with CACMS cyclic loading, CAIMS cyclic loading significantly decreases the shale strength by up to 20% UCS and the fatigue lifetime from over 500 to 9. Different from an inverted-S-shaped damage evolution for CACMS cyclic loading, damage evolution for CAIMS cyclic loading exhibits a monotonic increasing trend. The damage variable growth rates of CACMS and CAIMS both show a three-stage trend: (1) their growth rates both decrease; (2) the growth rate for CACMS remains stable, while for CAIMS its growth rate slowly increases; and (3) their growth rates both increase sharply. Correspondingly, the dissipated energy density evolutions for CACMS and CAIMS show a similar three-stage trend. It can be concluded that during the second stage, for CAIMS microfractures and plastic deformation inside specimens are developed and accumulated more and faster than those for CACMS cyclic loading. This explains the phenomenon that the fatigue lifetime and strength of CAIMS cyclic loading are less than those of CACMS. The nonlinear damage accumulation model proposed in this Article can well fit experimental results. This model can be used for accurately describing reservoir rock mechanical property degradation during hydraulic fracture simulation induced by PHF.

An event-oriented reliability assessment for DC link capacitors in grid connected inverter with low voltage ride through operation

Low voltage ride-through (LVRT) capability has been standard into the operating specifications of grid-connected inverters in many countries. Due to the mismatch of the time scale and lack of stress description model under the LVRT operation, the traditional mission profile reliability analysis tools are difficult to be applied for capacitors under LVRT operation. To overcome the above issue, this paper analysis the electrical and thermal stress of the DC link capacitors under LVRT operation, and established a lifetime model for the LVRT operation by the accelerated aging test. An extended mission profile and a nonlinear damage accumulation model have been proposed to evaluate the impact of the LVRT event on the reliability of DC link capacitors. A reliability assessment has been conducted for a 7.5 kW inverter which experienced one LVRT incident as an analytical example.

Method for statistical evaluation of cumulative damage models applied to block loading

AbstractThere is an abundance of nonlinear fatigue damage accumulation models but a lack of verification and comparison to experimental datasets. First, an extensive two‐level block loading experimental fatigue dataset is reprocessed according to current standard practice. Next, four nonlinear damage accumulation models and the Palmgren–Miner linear damage rule are critically compared using a range of statistical metrics. For the considered dataset, the Palmgren–Miner rule consistently performs worst and the damage curve approach is found to perform significantly better than the other nonlinear models. This study shows that the current practice of performance verification of new fatigue damage accumulation models in literature is too limited which enables cherry‐picking of verification datasets to improve perceived performance. Future fatigue damage accumulation models should be verified much more rigorously to both readily available and new experimental datasets.

A nonlinear uniaxial fatigue damage accumulation model based on the theory of material configurational forces

AbstractTo ensure the integrity and reliability of structures, it is of great importance to understand the fatigue damage mechanism of materials under different amplitude loading conditions. For this purpose, a nonlinear fatigue damage accumulation model based on material configurational forces is developed in this paper. Specially, since the material configurational force is defined on the material space point and directly associated with the evolution of material configuration, it is introduced as an internal variable to describe fatigue damage accumulation. Additionally, the corresponding relation between configurational force and stress state is presented. Meanwhile, the damage increasing among every loading cycle, that is, the damage rate, is dependent on the stress state and damage state variable. Therefore, the formulation of damage rate is proposed by a function of material configurational force and damage state variable. Further, numerical implementation of this proposed nonlinear fatigue damage accumulation model has been carried out through two notched structures to describe the fatigue damage evolution and predict the fatigue life of materials. The results indicate that the numerical results are consistent with previous experimental data.

An investigation of the nonlinear creep damage accumulation of different materials: Application of a novel damage model

AbstractVariable creep load is one of the most important failure modes for the hot components in aero‐engines. To accurately predict creep damage and remaining life, a novel nonlinear creep damage accumulation model was proposed based on the Wilshire equation and isodamage line, which takes the influence of load history into account and uses ultimate tensile strength to compensate the temperature effect. Two‐step loading experimental results of GH4169, X8CrNiMoNb‐16‐16, Al‐99.98, and Sn‐3.5Ag‐0.5Cu were utilized to verify the accuracy of the proposed model and to compare it with the existing models (i.e., Pavlou, Batsoulas, Hu, and time fraction models). It was determined that the novel model was better at predicting damage accumulation than all others model. Furthermore, two cases of damage evolution process exist for different materials under the same variable loading conditions.

Quantitative thermography for fatigue damage assessment and life prediction of welded components

The objective of this paper is to use quantitative thermography for fatigue damage assessment and life prediction of welded components. The energy dissipation during fatigue process is taken as an effective index of fatigue damage to develop a nonlinear damage accumulation model, and the model is extended to evaluate the fatigue damage and residual life of the specimen subjected to variable loading. Experiments are performed to validate its applicability, and the relationships between the fatigue damage variable to the cycle number and the accumulated energy dissipation are presented and discussed. The results show that the energy dissipation has the same trend as the temperature increment evolution, and a power law relationship between the stress range and the energy dissipation is experimentally determined. The linear relationship between the accumulated energy dissipation and the cycle number is confirmed at different constant stress levels, and the total energy dissipation to failure is shown to be a constant value. The developed nonlinear damage accumulation model is used to predict the residual fatigue life, and a good agreement is achieved. It is concluded that the developed approach is applicable for fatigue damage accumulation and residual life evaluation of materials.

In situ and experimental analysis of longitudinal load on carbody fatigue life using nonlinear damage accumulation

In this paper, a multi-disciplinary analysis method is proposed for evaluating the fatigue life of railway vehicle car body structure under random dynamic loads. Firstly, the hybrid fatigue analysis method was used with Multi-Body System simulation and finite element method for evaluating the carbody structure dynamic stress histories. The dynamics stress is calculated from the longitudinal load using longitudinal train dynamics. Secondly, the nonlinear damage accumulation model was used in fatigue analysis, and carbody structure fatigue life and fatigue damage were predicted. The mathematical model simulations are compared with results produced experimentally, showing good agreement. Finally, the mode is determined after the finite element model is established. To achieve the dynamic stress at each node, the modal response is used as excitation. The carbody damage was obtained by combining dynamics stress with the NMCCMF damage accumulation model. As a result, the effect of longitudinal load on carbody fatigue damage is investigated. The longitudinal load contributes significantly to the fatigue damage of the carbody.

An Improved Nonlinear Cumulative Damage Model Considering the Influence of Load Sequence and Its Experimental Verification

According to the change characteristics in the toughness of the metal material during the fatigue damage process, the fatigue tests were carried out with the standard 18CrNiMo7-6 material. Scanning the fracture with an electron microscope explains the lack of linear cumulative damage in the mechanism. According to the obtained results, a nonlinear damage accumulation model which considered the loading sequence state under the toughness dissipation model was established. The recursive formula was devised under two-level. The fatigue test data verification of three metal materials showed that using this model to predict fatigue life is satisfactory and suitable for engineering applications.

Threshold damage-based fatigue life prediction of turbine blades under combined high and low cycle fatigue

Life prediction based on the damage mechanics of aero-engine turbine blades is crucial for performing their strength design and ensuring the operational reliability under combined high and low cycle fatigue (CCF) loadings. In view of this, a simple and efficient life prediction method is developed to consider the interaction of high cycle fatigue (HCF) and low cycle fatigue (LCF) without any additional material constants, and as a basis of that a new nonlinear damage accumulation model is proposed by introducing threshold damage of the component related to material type and current HCF damage. In order to validate the presented methodology, model predictions were compared with the experimental data sets of turbine blades and its alloy materials. The predicted results indicate that the simple life prediction model is capable of estimating the fatigue life quickly with an acceptable accuracy in contrast to other four existing ones. Moreover, the threshold damage-based method provides the higher prediction accuracy than others due to improved HCF damage determined by the damage threshold.

Fatigue life prediction based on a novel improved version of the Corten-Dolan model considering load interaction effect

Corten-Dolan nonlinear damage accumulation model can well describe the fatigue behavior of engineering materials and structures under variable amplitude loads, while the determination of parameter d is difficult and still open. In this paper, a new improved version of Corten-Dolan model is proposed in which the parameter d is modified by introducing the power form of the stress ratio between two consecutive load levels to reflect the nonlinear effect of load interaction. Furthermore, a generalized expression of the new model is developed, which gives a unified theoretical formulation for the presented and some typical existing versions. The proposed model is validated by comparison with existing versions based on the experimental data of typical engineering materials under two-level and multilevel loads. An effective validation scheme is introduced to comprehensively investigate the validity and applicability of the developed model. In this scheme, parts of data those are not used in modeling are regarded as the check data to examine the prediction accuracy. The results show that the developed model can well reflect load interaction effect and give more satisfactory prediction of fatigue life.

Models of Nonlinear Fatigue Damage Accumulation Under Cyclic Block Loadings of Layered Composites

Considered are two types of multistage cyclic block loading rather common in the practice of fatigue tests and fatigue life predictions for layered polymer composite materials: block loading by four-stage cyclic regular zero-tension loads and block loading by multistage (8-10 levels) asymmetric cyclic loads. In order to improve the prediction accuracy for the fatigue life of carbon-fiber-reinforced plastics under such loadings, special nonlinear fatigue damage accumulation models are proposed. Elaborated are methods for predicting the fatigue life of carbon-fiber-reinforced plastics by the models proposed. The prediction methods are verified by the example of T800/5245 and AS4/3501-6 carbon-fiber-reinforced laminates. A relatively high accuracy of fatigue life predictions for the laminates was obtained as compared with that given by prediction methods using the Palmgren–Miner rule.

Modeling nonlinear fatigue damage accumulation in a welded runway girder

Due to its inherent linear nature, Miner’s damage accumulation rule is widely known to produce unsatisfactory results for lifetime prediction under variable amplitude loading. This can be attributed to its incapability of accounting for load sequence and load interaction effects. In this study, one piece-wise linear and three non-linear damage accumulation models have been implemented in a numerical framework for fatigue lifetime assessment of welded details of industrial assets. Lifetime predictions obtained by these models are first compared to lifetime predictions using Miner’s rule and to experimental data of two-level loading sequences. The results reveal that the studied damage models perform better than Miner’s rule for two-level load sequences within the scope of the studied dataset. Finally the different models are used to estimate the fatigue life of a weld detail that is part of a crane runway girder. A much larger (relative) discrepancy is observed between the lifetime predictions of the different models for a realistic load case than for simple two-level block loads.

A Numerical framework for fatigue lifetime prediction of complex welded structures

Ageing infrastructure has been a significant concern for different industrial sectors across Europe. Fatigue cracking is one of the most important damage mechanisms that affect structural health of welded steel structures. Fatigue assessment of welded details in large, complex structures is a difficult and time consuming task. In this paper a numerical framework for fatigue assessment of welded details is presented. In view of industrial applications, automated hot spot stress algorithms for plate and tubular joints were developed and integrated in the framework. The framework provides practicing engineers with an effective tool for fatigue assessment of different components in conformity with leading design codes. Furthermore, apart from Miner’s rule the framework allows easy implementation of different non-linear damage accumulation models in order to account for load interaction and load sequence effects.

Fatigue Life Estimation for Layered Composites Under a Plane Stress State with the Use of a Nonlinear Fatigue Damage Accumulation Model

A new fatigue failure criterion to predict the fatigue life of layered composites under a plane stress state is presented. The criterion is based on a nonlinear phenomenological fatigue damage accumulation model. It was verified by predicting the fatigue life of [3016] off-axis specimens under a uniaxial cyclic loading, and an acceptable accuracy of the prediction was found to exist.

Nonlinear fatigue damage accumulation and life prediction of metals: A comparative study

AbstractFatigue damage modelling and life prediction of engineering components under variable amplitude loadings are critical for ensuring their operational reliability and structural integrity. In this paper, five typical nonlinear fatigue damage accumulation models are evaluated and compared by considering the influence of load sequence and interaction on fatigue life of P355NL1 steels. Moreover, a new nonlinear fatigue damage accumulation model is proposed to account for these two effects. Experimental datasets of pressure vessel steel P355NL1 and four other materials under two‐block loadings are used for model comparative study. Results indicate that the proposed model yields more accurate fatigue life predictions for the five materials than the other models.

Study on the fatigue life and damage accumulation of a compressor blade based on a modified nonlinear damage model

AbstractComparing with the fatigue test results of Ti‐6Al‐4V, the widely used Chaboche damage model shows considerable differences in fatigue life prediction under asymmetric load, which is potentially caused by the local plastic deformation. In this paper, a modified nonlinear damage accumulation model is developed to improve the prediction accuracy for asymmetric loading condition. To account for the elastic and plastic strains, an elastoplastic fatigue factor is developed with 2 weighting factors based on the Ramberg‐Osgood equation and introduced into the stress term of the damage model. The validation of the proposed damage model is verified against the experimental data of Ti‐6Al‐4V titanium alloy and 2024‐T3 aluminium alloy with various stress ratios. Comparing with the original Chaboche model, the predicted life of the proposed model shows much better agreement with the experimental results. Then, the proposed model is used to estimate the fatigue life of a compressor blade of aero‐engine. Considering the variable amplitude loads and the loading sequence, the damage accumulation and the fatigue life of the blade are calculated, and the results indicate a longer fatigue life with slower damage accumulation rate in the early life stage.

A nonlinear continuous damage model based on short‐crack concept under variable amplitude loading

AbstractIn this paper, a modified nonlinear damage accumulation model is proposed by using intrinsic crack size as the damage variable in the stress‐control condition. The model's development is based on the Chaboche nonlinear damage law and the short‐crack theory. The validations are confirmed by using the experimental data of Ti–6Al–4V and 2024‐T3 collected from tests and literature. The model capabilities of predicting damage accumulation and crack growth rate in the multi‐level loading condition as well as the variable amplitude loading condition with single and multiple over‐load are investigated and discussed in detail. Comparison results show that the proposed model is able to consider the loading ratio, the loading sequence and the over‐load effect on damage accumulation correctly. Meanwhile, the damage accumulation in the last stage of fatigue life can be described more clearly by the proposed model attributed to the use of crack size as the damage variable.

A nonlinear fatigue damage accumulation model considering strength degradation and its applications to fatigue reliability analysis

Fatigue is a damage accumulation process in which the material property deteriorates and degenerates continuously under cyclic loading. The analysis of damage accumulation plays a key role in preventing the occurrence of fatigue failures, and the damage evolution mechanism is one of the important focuses of fatigue behavior. In this paper, a residual strength degradation model according to the stress–strength interference (SSI) model is introduced firstly; then a modified nonlinear fatigue damage accumulation model based on the Manson–Halford theory is proposed. Combining the proposed nonlinear damage accumulation model with the residual strength degradation model, a new method is developed for fatigue life prediction under constant and variable amplitude loading, which considers not only the effects of load interactions, but also the phenomenon of strength degradation of materials induced by loading history, and it can be used to predict the reliability and fatigue life of mechanical components. Moreover, the material parameter for the residual strength degradation can be obtained directly from S–N curve without running extra experiments. Finally, experimental data are used to compare with the predicted value in order to demonstrate the proposed residual strength degradation model. In addition, two sets of experimental data are also used to verify the proposed nonlinear fatigue damage accumulation model which is applied to predict fatigue life under two-stress level loading and reliability prediction under multi-stress level loading. The results show that the proposed method has a good agreement between the experimental data and predicted values.