Equivalent Damage Research Articles

Equivalent initial damage sizes (EIDS) for type 1C anodised aluminium alloy 7085-T7452 under variable amplitude loading

Aluminium alloy (AA) 7085-T7452 is a high strength, low weight alloy used in large forgings in primary airframe applications. For corrosion protection, airframe components are anodised and this study looks at the influence of type 1C anodising on the fatigue crack growth behaviour in AA 7085-T7452 specimens that were fatigue tested with fighter wing spectrum loading. Surface etch pits formed during essential anodising preparatory processes were the primary cause of fatigue crack nucleation. The severity of the early crack growth caused by those etch pits that nucleated the worst crack in each specimen was evaluated using quantitative fractography-based fatigue crack growth measurements and the equivalent initial damage size (EIDS) of those etch pits was determined. Characterising the EIDS distribution of aircraft alloys with representative surface treatments is a fundamental input into Linear Elastic Fracture Mechanics (LEFM) based fleet failure analysis of aircraft structures. In this study, a notable increase in the average EIDS value for the worst crack present was observed whenever material or loading condition changes led to a significantly increased number of crack nucleation sites. In particular, an increase in the cyclic stress spectrum’s severity increased the number of nucleation sites in a specimen and significantly increased the average EIDS. It appears that due to variable nucleating discontinuity properties (e.g. size, shape and orientation) and material property variations, an increased number of nucleation sites increases the probability that the worst crack present will nucleate at a location that is conducive for relatively fast early crack growth. This will potentially cause shorter overall airframe component fatigue lives and so both the mechanisms and conditions of etch pit fatigue nucleation in this material and material finish shall be discussed for the benefit of failure analysts evaluating unexpected fleet fatigue cracking.

New Fatigue Life Prediction Model for Composite Materials Considering Load Interaction Effects

Damage to composite structures can accumulate over time and lead to fatigue failure in their actual use environment. Therefore, it is critical to establish a suitable fatigue life prediction model. This work developed an improved fatigue life prediction model based on the effects of equivalent damage and load interactions. Validation and comparison of the improved fatigue life prediction model were carried out using test data of composites subjected to secondary and tertiary loading. The analysis indicates that the accuracy of fatigue life prediction for composites under variable amplitude load is improved by the damage equivalence prediction model, which accounts for the influence of load application sequence and load interaction. Furthermore, a comparison with existing fatigue life prediction models reveals that the proposed model predicts fatigue life more accurately under different amplitude loads.

Pseudo-anisotropic damage model of randomly oriented strands (ROS) for reproducing flexural damage behavior

We developed a pseudo-anisotropic damage model of randomly oriented strands (ROS) reinforced thermoplastic composites for reproducing flexural deformation and damage behavior by finite element analysis (FEA). The damage model applied stress triaxiality to capture the differences in the damage initiations among the tensile, compressive, and shear stress states. The damage model also included equivalent damage propagation function depending on the interlaminar shear property of ROS. The developed FE model was focused on the characteristics that ROS composites show macroscopic in-plane isotropic and out-of-plane anisotropic mechanical properties because of the laminated structure of ROS. Furthermore, all of the material parameters in the FE model were identified by performing simple deformation tests. As a result, the flexural numerical simulation could reproduce the experimental flexural deformation and damage behaviors of ROS plates with different thickness despite a complex stress state including in-plane and out-of-plane stresses. The developed FE model has potential to evaluate the safety of ROS-manufactured structural components. The evaluation of safety by FEA constructed in this study can improve the applicability of ROS composites.

Damage identification of arch dams based on post-earthquake residual displacement gradients

Current research on the identification of damage to arch dams under strong earthquakes is few, and the limited damage identification methods are primarily based on seismic acceleration records. For statically indeterminate arch dams, these methods can only represent the overall equivalent damage, but the identification accuracy of dam damage, particularly local damage, is not very good. Using the displacement monitoring system installed at the dam, the post-earthquake residual displacement (RD) of the arch dam may be obtained; however, the correlation between the RD at the dam crest and the dam damage is poor and does not permit a quantitative assessment of the dam damage. Therefore, a damage identification method based on post-earthquake RD gradients is proposed in this paper. First, the RD distribution and damage distribution features of Baihetan arch dam (289 m) under strong earthquakes are examined. Then, the relationship between the RD and the position and magnitude of the damage in the mid-upper region along the arch crown cantilever (ACC) of the arch dam was determined. Finally, parametric analysis was used to investigate the effects of the measuring point layout scheme on the reconstructed RD information along the ACC. The results indicate that the dam damage identification method based on RD gradients is accurate, and the proposed simplified measuring point layout scheme can capture RD gradient information along the ACC with high precision.

Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions

The phenomenon of surrounding rock damage and rupture caused by high temperatures is widespread, and has become a potential threat to the safety of nuclear waste disposal repositories. In order to reveal the energy distribution pattern of fractured granite during the failure process under different confining pressures, triaxial compression tests were carried out on rocks with different initial thermal damage. Firstly, the rock was treated at a high temperature to analyze the change rule of the porosity of the rock after high-temperature treatment, define the equivalent damage coefficient, and analyze the influence of confining pressure and equivalent damage coefficient on the peak stress and peak strain of the rock. The results show that, after high-temperature treatment, the porosity increases with the increase in temperature. The peak stress and corresponding strain of rock samples with similar equivalent damage factors increase with the increase in confining pressure. By comparing the rock samples with the same confining pressure and different initial thermal damage, the larger the confining pressure, the smaller the difference of peak stress of different initial thermal damage specimens. Then, the energy density of rock in a triaxial compression test is quantitatively analyzed by energy theory. The results show that, as long as the confining pressure is the same, the proportion of the dissipated energy of the specimen has a similar evolution trend with the strain. When the confining pressure is the same, the proportion of dissipated energy decreases rapidly with the change of strain due to the increase in equivalent damage factor, but the rate of decline will gradually slow down; however, when the confining pressure increases, the difference caused by the equivalent damage factor will gradually decrease, because the fracture is bound by the confining pressure. Finally, we analyze the maximum dissipated energy during rock deformation and failure. According to the inflection point of maximum dissipated energy, the optimum time for critical support of the key rock mass is determined.

Fatigue Damage Study of Steel–Aluminum Friction Stir Welding Joints Based on Equivalent Damage Model

Abstract An equivalent damage model was established to study the fatigue damage behavior of steel–aluminum friction stir welding (FSW) joints. Internal defects of friction stir welding joint under various cyclic loading stages were observed by X-ray microcomputed tomography (X-CT). For the characteristics of defects of the steel–aluminum FSW joints, a simplified method of defects considering key parameters is proposed, and then, the defect model is established. The FSW joint model was established based on the steel–aluminum boundary contour identified by using image processing techniques. Based on the defect model and the FSW joint model, the equivalent damage model was developed. The equivalent damage model was subjected to finite element analysis and compared with the test using strain amplitude as the damage variable. The equivalent damage model can be used to assess fatigue damage in steel–aluminum FSW joints, which provides some theoretical basis for fatigue life prediction.

Damage identification method on shield tunnel based on PLSR and equivalent damage analysis

Damage identification plays a critical role in the maintenance of the shield tunnel structure. This study proposes a damage identification method for shield tunnel lining based on back analysis, which lays emphasis on the mechanical responses of the structure. The connection between mechanical parameters and the structural response is extracted by the finite element model. With the employment of Partial Least Squares Regression (PLSR), the load on shield tunnel lining can be determined by the monitoring data, the variation of which before and after structural damage, regarded as damage index, is used to identify the damage position. The equivalent damage load is defined to establish the equations of the load, deformation and damage, which solves the problems induced by the randomness of damage position. To clarify the validation, the method is verified by previous experimental results. Involving the structural damage of various positions and intensities, this method is applied with the numerical models based on circular shield tunnel. The parametric study shows the accuracy of the method under different damage conditions. The effects of monitoring data of radial displacement and circumferential strain were also compared. As a result, the primary input from the circumferential strain has better sensitivity than that of the radial displacement.

Investigation of mechanical properties and elastoplastic numerical calculation model of frozen soil containing ice lenses

As the natural foundation of engineering structures in cold regions, the frozen soil has a vital impact on the deformation of structures during construction and operation stage. The particularity of frozen soil is mainly reflected in its sensitivity to temperature and cryostructure. In this research, a series of uniaxial compressive tests were conducted on four structural types of frozen soil under different temperatures. The test results showed that the axial stress-strain curves of frozen soil containing compaction stage, elastic deformation stage, strain hardening at pre-peak, and failure at post-peak. The unconfined compression strength (UCS) increases as the temperature decreases, the failure strain increases with decreasing temperature when temperature is higher than −3 °C and decreases with decreasing temperature when temperature is lower than −3 °C. Compared with homogeneous frozen soil, the failure surface of heterogeneous frozen soil is formed along the ice-frozen soil interface and the cracks at the tip of ice lenses. Subsequently, the damage variable considering the influence of ice lens and initial defects was deduced based on equivalent strain principle and continuous damage mechanics. An elastoplastic model of heterogeneous frozen soil containing ice lensed is established by using associated flow criterion and Mises strength criterion, and the model was redeveloped in COMSOL Multiphysics. The rationality of the proposed model was verified, and exhibits that the proposed model can capture the mechanical properties of heterogeneous frozen soil.

Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation

Modern lightweight materials are often decomposed into several distinct materials, e.g. a matrix material and some reinforcements. A manufacturing process for these materials often induces eigenstrains, both reversible and non reversible. This could lead to an initial damage of a composite material, and eventually result into fracture of the structure. This contribution deals with non-local integral-type damage of composites subjected to eigenstrains. It is well known that local damage models lead to mesh sensitive simulation results. To avoid this effect, non-local integral-type regularization of equivalent strains and damage variables are exploited. Effective macroscopic properties are obtained using mean-field homogenization methods. A regularization in each material phase within the framework of an iterative Newton–Raphson procedure leads to the update of a non-local tangent stiffness matrix at each equilibrium iteration. To reduce the computational time parallel non-local assembly and averaging procedures are introduced. In this regard, the performance of different representations of dynamic sparse matrices and the scalability of the parallel implementation are investigated. Various microstructural morphologies are distinguished in representative examples to show the capability of the proposed work. Furthermore, the transition from damage to fracture is performed by aid of an element deletion method. To achieve the best compromise between memory consumption and speed over a range of non-zero entries, an array of flatmaps should be used. It is shown that the introduced parallel algorithms enable a drastic reduction of computational time. Moreover, it is illustrated that for various volume fractions of an inclusion a mesh sensitivity is clearly reduced.

Improving the lifetime of mechanical systems during transit established on quantum/transport life-stress prototype and sample size

Parametric accelerated life testing (ALT) with the reliability quantitative (RQ) statements is offered as a reliability methodology to identify and rectify design flaws. The methodology includes: (1) BX lifetime with ALT scheme, (2) fatigue design, (3) ALTs with alterations, and (4) discernment whether the design(s) obtains targeted BX life. A quantum/transport-based life-stress prototype and sample size for generating RQ specifications were suggested. The equivalent elevated damage potential in parametric ALT was applied, represented by a field power spectral density (PSD). A case study was used to evaluate refrigerator fatigue failures that occurred during rail transport. In the 1st ALT, for RQ specifications, the refrigerator tubes made of ethylene propylene diene monomer (EPDM) rubber fractured because of the compressor mount design. The failure in the 1st ALT was similar to those found from failed refrigerators in the field. After the compressor mounts and tubes were redesigned, there were no difficulties during the 2nd ALT. The refrigerator was then assured to fulfil a B1 lifetime for required travel distance.

Rapid prediction of compression after impact properties of composite structures: An equivalent strategy for impact damage

Combined with the results of finite element simulation and experimental ultrasonic C-scan, a phenomenological-based equivalent impact damage finite element model was proposed and established to rapidly predict the damage evolution and buckling deformation of composite structures in compression after impact. An image recognition technology was adopted to divide the impact damage of composite laminates and stiffened panels into different regions, and a damage equivalent was conducted based on the measured impact damage size and morphology. Additionally, the material stiffness and strength parameters in different damage equivalent regions were reduced appropriately by different degrees. The impact pit deformation was equivalent to the element node offset in the corresponding area of the model, and the interface delamination and debonding were equivalent to the voids without elements. The equivalent impact damage model was applied to evaluate the buckling behavior and compressive strength after impact for laminates and stiffened panels using ABAQUS software. Moreover, a three-dimensional damage model considering the interaction of interlaminar delamination damage and interlaminar matrix and fiber damage was introduced to characterize the damage initiation, evolution, and extension behaviors of different damage modes. The comparative analysis indicated that the buckling and failure modes and compression after the impact strength simulated using the equivalent model were identical to the experimental results and had high correlation. This confirmed the accuracy, effectiveness, and applicability of the established equivalent impact damage model in predicting the compression buckling as well as residual strength and fracture modes for composite laminate and stiffened panel with simultaneous multi-zone impact damage.

Self-Organized Neural Network Method to Identify Crash Hotspots

Crash hotspot identification (HSID) is an essential component of traffic management authorities’ efforts to improve safety and allocate limited resources. This paper presents a method for identifying hotspots using self-organizing maps (SOM). The SOM method was used to identify high-risk areas based on five commonly used HSID methods: crash frequency, equivalent property damage only, crash rate, empirical Bayes, and the societal risk-based method. Crashes on a major road in Iran were examined using the proposed method. Based on these criteria, high-risk locations were grouped into six clusters, which provided appropriate criteria for each location depending on the importance of the cluster. The findings show that the identification of crash hotspots tends to focus on areas with more crashes and deaths, demonstrating that the research methodology was appropriate.

Influence of Loading Sequence Effect on Cyclic Hysteresis Characteristics of an Al–Mg–Si Alloy

The alloy materials of automotive chassis are subjected to sequential time-varying loads due to road unevenness. The continuous change of the loading mode and the stress ratio leads to cyclic plasticity of the material, which induces cyclic hardening. The estimation of hardening effects seriously affects the structural's fatigue properties. Therefore, herein, a hardening model and the corresponding fatigue life prediction model are proposed. Then, the loading sequence effect's influence on an Al–Mg–Si alloy's cyclic hysteretic characteristics is analyzed. The steering knuckle is taken as the verification object. The acquired load spectrum is transformed into three sequential forms according to the equivalent damage principle for the verification test. The test results verify the conjecture of the loading sequence effect and confirm the accuracy of the proposed prediction model.

Fatigue load model of orthotropic steel deck for port highway in China

Vehicle load is an important factor for the fatigue damage of the orthotropic steel decks. The traffic vehicles for port highway in China are mainly multi-axle container trucks, which show different characteristics from conventional highways. Based on the multi-period traffic flow data collected by weight-in-motion system of a bridge over the sea in Zhejiang, China, this study has investigated the traffic load characteristics of the port highway bridge. Eight typical vehicles of fatigue load spectrum are classified according to the number of axles and wheelbase. The distribution characteristics of the gross vehicle weight (GVW) and axle weights of typical vehicles are analyzed by lane. Depended on the equivalent fatigue damage principle, the vehicle load spectrum for fatigue evaluation of the port highway bridges is established. The results show that the average proportion of the trucks (weighing greater than 3 tons) in the total traffic flow is 73.2%, and trucks with more than four-axle accounted for 89.0%. Heavy vehicles are mainly concentrated on the outer lanes, and the probability of vehicles driving in the heavy lane increases with the increase of gross vehicle weight. The maximum equivalent gross vehicle weight is 62.5 tons, which appeared in V7 in the exiting island direction. The simplified fatigue vehicle model in the heavy lane for Chinese port highway bridges is proposed, based on the six-axle vehicle which contributed the most fatigue damage. The proposed fatigue load model can better represent the actual traffic load level of port highway bridges in China.

Generation of vibration load spectrum for fatigue analysis of equipment mounted on bogie frame of railway vehicle based on fatigue damage spectrum

The equipment mounted on the bogie frame of railway vehicles is subjected to non-stationary vibrations from the bogie frame. Currently, the vibration load spectrum for fatigue analysis of equipment is expressed with the power spectral density, which is generally obtained with the power values of measured vibrations or stationary Gaussian vibrations collected at the specific operating conditions. However, this does not have the equivalent damage potential as the non-stationary vibrations. Thus, a generation method of the vibration load spectrum is proposed based on the fatigue damage spectrum (FDS) to obtain the equivalent damage potential as the one from the non-stationary vibrations in this paper. That is, the FDS of non-stationary vibration is calculated with the time domain method, and the vibration load spectrum is generated in the frequency domain with this FDS. Then the method is verified by the measured vibration and dynamic strain of equipment. Finally, the vibration load spectrum of equipment mounted on the bogie frame is generated with the measured vibrations in a maintenance cycle and the fatigue analysis is performed. The results show that the generated vibration load spectrum can validly contain the high power in non-stationary vibrations and express the distribution of power over frequency, which gives much better estimates of the fatigue damage of equipment than other load spectra. The generated vibration load spectrum is suitable for quantifying the actual non-stationary vibrations and can be used for the anti-fatigue design of equipment.

Plastic damage analysis of concrete around misaligned dowel bar in jointed concrete pavement

ABSTRACT Dowel bar misalignment causes stress concentration in jointed concrete pavements, and misaligned dowel bars may lose their ability to transfer loads. To examine this problem, a concrete damage plasticity (CDP) model and a method were implemented using ABAQUS to evaluate its parameters. The CDP model simulated the stress–strain relationship for tension and compression in concrete specimens, and was validated through experimental testing. A three-dimensional finite element model of a misaligned dowel in a jointed concrete pavement was developed, and the equivalent stress, plastic strain, and plastic damage under loads for various misalignment conditions were determined. The simulation results of uniaxial tension and compression in a concrete sample were compatible with the experimental results, demonstrating the high accuracy of the CDP model. Under the action of a wheel load, the concrete below a misaligned dowel undergoes plastic damage. The damage extended from the bottom of the dowel to the sides as the misaligned dowel deviated vertically from the alignment with the pavement’s longitudinal axis, especially in the case of twin bars misaligned in opposite directions. The plastic damage ratio is close to unity, which indicates complete failure of the concrete below the misaligned dowel. The equivalent stress below the dowel tends to be zero and shifts to the sides of the dowel. Consequently, the concrete below the misaligned dowel failed to support the load, reducing the load-carrying capacity of the dowel. When a fully elastic model was used, the stresses below the dowel exceeded the ultimate strength of the concrete, which contradicts the actual occurence. Therefore, the CDP model is recommended for analyzing the stress in the concrete around a misaligned dowel.

Accelerated durability evaluation of automotive components under multi-channel random loading

Accelerated durability evaluation aims to quantify the fatigue damage of automotive components in a shorter time. The quality of accelerated editing directly affects the evaluation’s efficiency and accuracy. In this paper, an index-controlled accelerated spectrum editing method is proposed, and the equivalent fatigue damage model of the component is derived. Taking an automotive steering knuckle as the verification object, the proposed accelerated editing method is evaluated from multiple perspectives. The evaluation results show that the proposed method has apparent advantages in compression efficiency, damage consistency, and retaining the frequency domain impact on the component.

Dynamic synthetic inertial control method of wind turbines considering fatigue load

This paper proposes a dynamic synthetic inertia control method, considering the fatigue loads of the wind turbine. The control objectives include reducing the rate of change of frequency and frequency nadir of the power system and the fatigue load of the shaft and tower of the wind turbine. A frequency regulation model of the power system containing the primary operating dynamics of the wind turbine is established. The dynamic synthetic inertia control method is proposed according to the relationship between fatigue load, wind velocity, and frequency. Case studies are conducted with a wind turbine fatigue load under a synthetic inertia control with different weights for different wind velocities and system loads. Therefore, the dynamic weights are obtained. Comparing the rate of change of frequency and frequency nadir and equivalent damage load, the efficacy of the proposed method is verified.

Post-earthquake reconstruction of residential buildings in historical centers: damage indices of structural aggregates

The post-earthquake reconstruction process of historical centers discloses several issues due to the complexity of the built heritage, typically consisting of Building Aggregates (BA). These are characterized by structures deriving from progressive volume increases that, due to partially effective connections, can interact under seismic actions. Therefore, the repair and reconstruction work after seismic event, the conservation of the architectural values and the improvement of seismic and energy performances must rely on a deeper knowledge of the BA seismic behavior and on an unitary design approach. This paper presents an analysis of the damage caused by the 2009 earthquake to the buildings of the historical centers in the Abruzzo Region, with particular interest to the BA considered as a single structural block. A new perspective of the damage on structural and non-structural components, detected by means of the AeDES form, a first level survey form for post-earthquake damage and usability assessment, is proposed. The data related to the building damage are converted into an equivalent global building damage associated to the BA using conversion metrics found in the literature. Finally, some considerations are provided to evaluate the global building damage, necessary to the development of a comprehensive damage state.

Fatigue performance and fatigue equation of crumb rubber concrete under freeze–thaw cycles

To prepare crumb rubber concrete (CRC) by grinding rubber particles is one of the most efficient ways to recycle waste tires. In cold regions, the concrete is simultaneously subjected to fatigue loading and freeze–thaw cycles. In order to reveal the effect of freeze–thaw cycles on fatigue strain and fatigue life of CRC, CRC was made by substituting sand with equivalent volumes of rubber granules of 30 mesh, and after freeze–thaw cycles, the experimental study and theoretical analysis of the uniaxial compression and constant amplitude fatigue properties of the specimens were carried out. The results show that the fatigue strain of CRC presents a three-stage variation and is basically unaffected by freeze–thaw cycles. The fatigue life of CRC after freeze–thaw cycles accords with the Weibull distribution, The fatigue life of CRC mainly depends on the actual stress level. The test results of the fatigue life of CRC were analyzed for reliability by probabilistic statistical methods to obtain fatigue equations for different survival rates. Based on the principle of equivalent damage, the fatigue equation considering freeze–thaw cycles was established which can be used to predict fatigue life of CRC in engineering structures in the seasonal frozen regions.