Damage Accumulation Model Research Articles

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.

A deterministic algorithm for nonlinear, fatigue‐based structural health monitoring

AbstractThe irregularity of peak and valley stress values of loading histories is the main impediment for accurate fatigue‐based structural health monitoring. Since the available fatigue material data (e.g., S‐N curves) have been derived by cyclic loading tests, and the existing damage accumulation models can be implemented on structures under cyclic loading, cycle‐counting algorithms for the transformation of a spectrum loading into an equivalent cyclic one are necessary for deterministic fatigue damage estimation and life prediction. The existing four cycle‐counting algorithms have an inherent disadvantage; the sequence of the derived cycles is unknown, and the loading sequence effect on the fatigue damage estimation and life prediction cannot be accounted for (linear damage summation). The present work proposes a new damage estimation algorithm containing two modules: a new cycle‐counting algorithm and a new damage summation algorithm. Unlike the existing methods, the proposed algorithm takes into account the loading sequence effect and has a solid physical base because it simulates the nonlinear damage accumulation with a multi‐linear damage summation procedure. With the aid of a new concept of inserting fictitious loading cycles in the irregular spectrum, the proposed cycle counting module counts loading cycles that correspond to loading loops with an algorithm that is easily applicable in engineering practice. According to the author's knowledge, nonlinear damage accumulation estimation in structures under an irregular loading spectrum is carried out for the first time. The effect of the loading sequence to high‐low two‐stage random loading, low‐high two‐stage random loading, decreasing amplitude multi‐stage random loading, increasing amplitude multi‐stage random loading, and alternating amplitude random loading is examined and discussed.

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

AbstractA 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.

Reliability analysis of k-out-of-n system with load-sharing and failure propagation effect

In complex systems, functional dependency and physical dependency may have a coupling effect. In this paper, the reliability of a k-out-of-n system is analyzed considering load-sharing effect and failure mechanism (FM) propagation. Three types of FMs are considered and an accumulative damage model is proposed to illustrate the system behavior of the k-out-of-n system and the coupling effect between load-sharing effect and FM propagation effect. A combinational algorithm based on Binary decision diagram (BDD) and Monte-Carlo simulation is presented to evaluate the complex system behavior and reliability of the k-out-of-n system. A current stabilizing system that consists of a 3-out-of-6 subsystem with FM propagation effect is presented as a case to illustrate the complex behavior and to verify the applicability of the proposed method. Due to the coupling effect change, the main mechanism and failure mode will be changed, and the system lifetime is shortened. Reasons are analyzed and results show that different sensitivity factors of three different FMs lead to the change of the development rate, thus changing the failure scenario. Neglecting the coupling effect may lead to an incomplete and ineffective measuring and monitoring plan. Design strategies must be adopted to make the FM propagation insensitive to load-sharing effect.

Mathematical modeling of the VHCF resonance loadings with a progressive damage accumulation

One of the most critical in-situ loading modes is resonant. Such loading conditions may lead to premature fatigue damage accumulation and failure. The progressive fatigue damage changes the natural frequency of a structure and causes a permanent modification of loading conditions. This paper considers the model of fatigue damage accumulation regarding its evolution and resonant loading parameters. To describe the evolution of material degradation due to fatigue a complex kinetic model of damage development and numerical algorithm are introduced. The model contains the evolution equation for the damage function depending on stress state. The algorithm is based on a special post proceeding of a numerical solution for an elastic solid mechanics problem that can be also applied for elastic-plastic case. Different loading conditions can be considered by choosing the method of solution for solid mechanics problem. This paper is focused on the comparison between quasi-static and resonant loading conditions used for damage function calculation. It was shown that use of resonant loading solution leads an earlier crack initiation and shorter fatigue life results compared to quasi-static solution. A spatial development of the fatigue damage zone is also different for these two cases. The normal crack opening mechanism is discussing in this paper.

In-Service Reliability Assessment of Turbine Blade Thermal Barrier Coatings Based on a Novel Cumulative Damage Index Model

Abstract Thermal barrier coating (TBC) has been used widely on turbine blades to provide temperature and oxidation protection. With the turbine inlet temperature continuously increasing, TBCs have become more likely to oxide spallation, leading to premature failure of blade metal substrates. Thus, It is necessary to accurately evaluate the in-service reliability of TBCs for blade life assessment and engine operation safety. Nowadays, it is common to dynamically record aero-engine operating and performance data, called dynamic covariate data, which provides periodic snapshots for obtaining reliability information of engine components. Nevertheless, existing TBC life prediction models that pay adequate attention to dynamic covariate information are rare. This paper focuses on using limited failure samples with associated dynamic covariate data to make in-service reliability assessments of TBCs through a proposed cumulative damage index model. For the demonstration of the proposed approach, an integrated TBC life simulation approach has been introduced, which comprises engine performance, blade thermal, TBC damage, and damage accumulation models. The case study shows that the proposed cumulative damage index model-based method provides more stable and accurate results than the traditional statistical method based on failure-time data.

An approach for predicting fatigue life of CFRP retrofitted metallic structural details

This paper presents a new approach to estimate the fatigue life of metallic details retrofitted with bonded CFRP patch. Existing phenomenological and analytical methods to predict the fatigue life of metallic structural details retrofitted with bonded CFRP patch do not consider the cyclic degradation of the composite patch. As for all materials the composite patch (CFRP and adhesive) will experience degradation during fatigue cyclic loading. In this regard, a new approach that takes into account the fatigue cyclic degradation of the composite patch is proposed in this paper by introducing in the fatigue damage accumulation model of the metallic element, a cycle-dependent stiffness degradation parameter of the composite patch. The stiffness degradation parameter is obtained using a fatigue stiffness degradation model calibrated from experimental fatigue data of CFRP adhesively bonded double strap joints. Experimental data available in the literature of central hole aluminium plates bonded with CFRP are utilized for validation of the approach.

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.

Reliability Updating of Offshore Wind Substructures by Use of Digital Twin Information

This paper presents a probabilistic framework for updating the structural reliability of offshore wind turbine substructures based on digital twin information. In particular, the information obtained from digital twins is used to quantify and update the uncertainties associated with the structural dynamics and load modeling parameters in fatigue damage accumulation. The updated uncertainties are included in a probabilistic model for fatigue damage accumulation used to update the structural reliability. The updated reliability can be used as input to optimize decision models for operation and maintenance of existing structures and design of new structures. The framework is exemplified based on two numerical case studies with a representative offshore wind turbine and information acquired from previously established digital twins. In this context, the effect of updating soil stiffness and wave loading, which constitute two highly uncertain and sensitive parameters, is investigated. It is found that updating the soil stiffness significantly affects the reliability of the joints close to the mudline, while updating the wave loading significantly affects the reliability of the joints localized in the splash zone. The increased uncertainty related to virtual sensing, which is employed to update wave loading, reduces structural reliability.

An elasto-plastic damage accumulation model for fatigue life predication of ductile metals at the yield stress

From the analysis of massive fatigue test data, we find a mismatch between the fatigue life predictions done by stress-life method (SN) and those by strain-life method (εN) around the yield stress of ductile metals. Since the SN and εN methods are widely used in engineering applications, this work aims to explain such mismatch and thereby to address the fatigue life prediction at material’s yield stress, at which the material’s elastic damage and plastic damage are comparable. Based on a normalized damage concept, we propose an elasto-plastic damage accumulation model, a data-driven approach, to evaluate the fatigue damage at the yield stress. By differentiating the damage caused by the elastic from the plastic, the damage of each loading cycle is formulated as a function of both stress and strain amplitudes to accurately capture the material’s response state. With introducing the strain-energy-density based weighting factor, the proposed model can accord well with the classical methods from low-cycle fatigue to high-cycle fatigue. When it comes to the yield stress, the fatigue life estimated by the proposed model compares favorably with the fatigue test data. Therefore, beyond clarifying the mismatch between the classical approaches, the proposed model is expected to improve the accuracy in fatigue damage evaluation of ductile metals at the yield stress.

A modified damage accumulation model for life prediction of aero‐engine materials under combined high and low cycle fatigue loading

AbstractAero‐engine hot section components experience combined high and low cycle fatigue (CCF) loading under actual working conditions. This paper proposes a modified fatigue damage accumulation model to precisely predict lifetimes of aero‐engine materials according to the newly presented interaction factor, which is able to quantitatively map damage interactions introduced by high cycle fatigue (HCF) and low cycle fatigue (LCF) loads. With the model, the lifetimes of four typical engine materials are predicted and compared to their factual data from experiments. The validation of the model is illustrated by a comprehensive comparison of the results concluded by the proposed model and that of other classical methodologies, which indicates that the new model holds the best performance in lifetime predictions. Moreover, an actual engineering case, which is the lifetime prediction of third stage turbine blades of an aero‐engine, is completed to validate the feasibility of the proposed method.

Crack growth path of 30CrMnSiA steel under variable amplitude multiaxial loading

Two-level step multiaxial fatigue tests were conducted to investigate the crack growth behavior and damage accumulation of 30CrMnSiA steel. When the first load step (50% of the fatigue failure life) is completed, main cracks of specimens have entered the stage Ⅱ propagation. The cracks gradually turn direction to propagate along the maximum normal stress planes of load step 2 under the second load step. The damage accumulation is mainly affected by the angle between the maximum normal stress planes of the two-level step loadings and the crack propagation length along the depth direction, it will also lead to large error of fatigue life prediction by the commonly used damage accumulation models.

A new fatigue damage model for pavement concrete beams bearing multi-level bending loads.

MTS-810 material testing machine and acoustic emission signal analyzer were adopted to explore the mechanical behavior of concrete beams broken by the static load and the nonlinear cumulative damage law of concrete beams broken by fatigue bending from single-stage loading. Then, by introducing the Ramesh Talreja’s Damage Criterion, the damage rule of single-stage loading was extended to the damage accumulation rule under multi-stage loading, and the results were verified by the results of two-stage and three-stage fatigue loading tests. Two main conclusions are achieved: first, affected by four-point bending load, the fatigue life of the concrete specimen is in line with the law of the two-parameter Weibull distribution, namely the higher the stress level is, the shorter the fatigue life is. Second, an obvious nonlinear relationship was discovered in the damage of concrete. The model deduced in this paper and the Palmgren-Miner linear damage accumulation model were adopted to compare the test results of flexural fatigue under single, two and three stage loads. The calculation results of this model were more reliable.

Modeling Fatigue Damage Accumulation in Power Engine Structures

sThe article describes the development of a new design technology for power engine structures (PES) hulls of increased reliability, based on the methods of system analysis using computer modeling of damage accumulation in structural elements, as well as the development of technical solutions for creating the PES hull design using new heat-resistant composite carbon-carbon and carbon-ceramic materials. To calculate the accumulation of damage, the chemical criteria of durable strength is used, for numerical calculation of the stress-strain state of structures taking into account creep, an iterative method for solving a three-dimensional problem of thermomechanics using the finite element method is applied. An example of the calculation of a high-pressure structural element, performed in the work, showed the possibility of practical implementation of the proposed technique and its effectiveness, in terms of reducing or replacing experimental studies to substantiate the reliability of structures.

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.

Apatite (U-Th)/He thermochronometric constraints on the northern extent of the Deccan large igneous province

The volcanic emplacement and subsequent weathering of the Deccan Traps of India is believed to have had a significant influence in driving global climatic shifts from the Late Cretaceous and through the Cenozoic. The magnitude of the Deccan Traps' impact on Earth's surface environment is largely dependent on the speculated original footprint of the large igneous province. To test established estimates for the pre-erosive northern extent of the Deccan Traps, we applied low-temperature apatite (U-Th)/He thermochronology (AHe) on rocks from the Bundelkhand craton and overlying Proterozoic Vindhyan successions of central India ∼150–200 km northeast of the northernmost preservation of Deccan basalts. New AHe data reveal young ∼5–85 Ma AHe dates with low effective uranium concentrations (eU) between 5–22 ppm, with a steep positive date-eU correlation that plateaus at ∼350 Ma in grains with eU values >50 ppm. Inverse thermal history modeling—utilizing AHe diffusion parameters of the Radiation Damage Accumulation and Annealing Model (RDAAM)—indicate that observed AHe date-eU correlations are most consistent with thermal histories that require the craton and Vindhyan strata to be at or near surface temperatures by ∼66 Ma, followed by a discrete reheating event associated with Deccan volcanism. These results establish new minimal areal constraints for the northern extent of Deccan volcanism which thermally perturbed much of the Vindhyan succession. Thermal alteration of organic rich Vindhyan sediment may have provided an additional source of volatile emissions that facilitated late Maastrichtian warming at the onset of Deccan volcanism. New minimal northern constraints on Deccan volcanism additionally confirm that large volumes of Deccan basalts have been stripped away since the time of their emplacement, which poses considerable implications for unraveling their role in Cenozoic cooling.

On the prediction of fatigue life subjected to variable loading sequence

AbstractMiner's rule is one of the most widely used cumulative damage equations for evaluating useful fatigue life. However, it often yields unsatisfactory predictions due to its linearity of the damage accumulation. In this paper, a new nonlinear fatigue damage accumulation model is developed that treats loading sequence effect and, also, enables one to predict the rate of damage by introducing a loading sequence parameter. This parameter is defined using the loading sequence ratio, which depends on material properties. Applicability of the proposed model is validated using the results of nine sets of independent experimental measurements of fatigue life under multiple loading sequences. It is shown that the predictions are in agreement with measured results and that the model provides a reliable estimation of fatigue life.

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.

A framework for fatigue life prediction of materials under the multi-level cyclic loading

Fatigue life prediction of materials under the cyclic loading is still a particularly challenging task remains to be resolved. This study aims to develop a generic framework for fatigue life prediction under the multi-level cyclic (MLC) loading with consideration of the loading sequence effects. Firstly, a conditional probability density function (PDF) model is presented to quantify the fatigue life distributions of materials under any constant amplitude cyclic (CAC) loading. Subsequently, a fatigue damage accumulation model is proposed from the perspective of cumulative failure probability, which is capable of accounting for the nonlinear characteristics of damage accumulation and the loading sequence effects. Finally, a generic framework for fatigue life prediction of materials under the MLC loading is developed based on the proposed models. The fatigue life data of fiber reinforced composites under the two-level and three-level cyclic loading are utilized to verify the proposed framework. The results show that the predicted fatigue lives agree well with the fatigue test data of fiber reinforced composites. Moreover, the proposed framework can be easily extended to calculate fatigue life of materials under any MLC loading.

Cyclic behavior and hysteresis model of beam-column joint under salt spray corrosion environment

This paper aims to investigate a method predicting the cyclic behaviors of welded beam-column joints exposed to the salt spray corrosion environment based on the analysis of the quasi-static tests and numerical simulation results. Experimental results indicated that the reduction of the section caused by corrosion damage was the main factor affecting the degradation degree of bearing capacity and stiffness of the beam-column joints. The rough surface profile and significant corrosion loss of different flanges and webs could be observed for beam-column joints with long-term exposure to the salt spray environment, which had a noticeable influence on the local buckling and fracture of welded zones connecting beam and column, accelerating the failure process. As a result, the number of cycles and the area of the hysteresis hoop gradually decreased as the corrosion degree increased, so that the cyclic deformation capacity and the energy dissipation capacity deteriorated rapidly. When the exposure time was 18 months (the corrosion depth and the maximum pitting depth were 2.13 mm and 1.48 mm), the yield moment and ultimate moment of the beam-column joint decreased by 28.2% and 32.1%, the total rotation and total energy dissipation decreased by 49.4% and 70.8%. A finite element modeling method depended on the shell element was selected to carry out a series of numerical analyses to investigate the impacts of different corrosion factors on the seismic performances of beam-column joints, which pointed out the corrosion damage in the beam and panel zone causing the nonlinear degradation of seismic performance indices, then the linear skeleton curve model of the corroded beam-column joints was proposed. Furthermore, this paper discussed the effects of the plastic post-buckling strength degradation caused by the corrosion damage on the strength and stiffness of hysteresis curves, thereby the cyclic damage accumulation model and hysteresis model which included the characteristic parameters of corrosion was established to predict the hysteresis behaviors of corroded beam-column joints.