Equivalent Damage Research Articles

Characterization of microstructure and moisture distribution evolution of concrete using AC impedance spectroscopy

In this study, the AC impedance responses of concrete with different microstructures and water contents at elevated temperatures are examined. First, an equivalent circuit model of concrete is proposed. The simulation results of the equivalent circuit are in good agreement with the AC impedance spectrum. Then, semi-infinite, infinite, and barrier diffusion modes of water diffusion within concrete are proposed. The quantitative relationships between AC impedance parameters and moisture content of concrete are established. Finally, the equivalent porosity and thermal damage are characterized using AC impedance parameters. Both show linear relation with the total porosity obtained experimentally by porosity tests. Therefore, AC impedance spectroscopy can quantitatively characterize the internal microstructure and moisture content evolution, and further reveal the mechanism of the macro performance of concrete.

Predicting fatigue life of multi-defect materials using the fracture mechanics-based physics-informed neural network framework

To address the limitations of traditional methods (such as the S-N curves and Paris’s law) in evaluating the fatigue life of multi-defect materials, this study developed a fracture mechanics-based physics-informed neural network (PINN) to predict the lifetime of multi-defect materials using cyclic loading (Δσ) and the equivalent damage area (AD). Influences of multiple defects were unified characterized through the equivalent damage area, which was calculated based on the M−integral fatigue model. This model reflects the energy evolution of multi-defect fatigue damage. By embedding the prior knowledge of fracture mechanics derived from the M−integral fatigue model into the loss function of PINN, crucial physical information was captured during the training progress, enhancing the interpretability of the neural network. By integrating the advantage of the M−integral fatigue model in characterizing the fatigue performance of multi-defect materials and the nonlinear fitting ability of neural networks, the proposed approach effectively improves the generalization ability and predictive accuracy of limited fatigue data. The presented PINN models accurately forecast the fatigue life of multi-defect materials, with a squared correlation coefficient (R2) exceeding 0.9. The presented methodological framework addresses the existing gap in methods for evaluating the fatigue performance of multi-defect materials and reliance on fatigue testing.

A stochastic constitutive model and its application to HTPB propellant

AbstractTo address the issue of randomness in the mechanical properties of the hydroxyl‐terminated polybutadiene (HTPB) propellant, a stochastic constitutive model (SCM) with a lognormally distributed random parameter Λ was proposed to describe their mechanical behaviors, and the structural integrity of a HTPB propellant grain was analyzed based on it. The results indicate that the stress‐strain curves predicted by the SCM have a good agreement with the experimental curves, and the experimental curves fall within a 95 % probability interval predicted by the SCM. The mechanical response of HTPB propellant grain under ignition pressurization is associated with the random parameters Λ. The maximum equivalent stress and safety factor increase approximately linearly with the increase of random parameters Λ, while the maximum equivalent strain and maximum damage coefficient decrease approximately linearly with the increase of random parameters Λ. The error in the mechanical response of the grain obtained based on the SCM and the experimental constitutive model is basically not more than 2 %, the SCM can effectively characterize the randomness in the mechanical response of propellant grain caused by the dispersion of HTPB propellant mechanical properties.

Seismic behavior of CFDST frame with metallic dampers: Damage-controlled design and performance assessment

Current investigations on performance-based seismic design of structures generally employed story drift as performance objectives. However, the story drift could only partially reveal the global damage of a structure and not control the damage of important components. In order to control the damage of various components in a structure, this paper proposed a new damage-controlled seismic design method using the Park & Ang indexes of components. Firstly, the Park & Ang damage index was simplified as an equivalent ductility damage index for various components. The energy balance concept was used to observe the hysteretic energy demand which was subsequently distributed to all stories. Thus, the components of each story could be designed based on their damage indexes under design-based and maximum-considered earthquakes. Four concrete filled double skin tubular (CFDST) moment resisting frames equipped with metallic dampers with various layouts were designed based on the proposed design method. Time history analyses on these four structures were performed after validating the accuracy of nonlinear model by Opensees. Analysis results showed that the components in four structures exhibited expected damage states as illustrated by the design method. It also verified that proposed seismic design method was effective to control the damage of various components, which was beneficial for protecting the important components in a structure by setting low damage indexes for them. The seismic design method and analysis results also provided a reference for the design of moment resisting frame with energy devices.

Creep-fatigue interaction of soft adhesive under shear loading: Damage diagram and life prediction model

Soft adhesives used in cutting-edge technological fields are susceptible to shear fatigue failure under complex in-plane loadings. Although the interaction or coupling effect between creep and fatigue damage have been studied, the effect of the equivalent creep damage during typical fatigue loading on the fatigue life of soft adhesives, as well as the interaction between the equivalent creep damage and fatigue damage of soft adhesives have never been characterized. This study systematically investigates the creep-fatigue interaction of the soft adhesive under various loading conditions. It was found that significant equivalent creep damage occurs and accumulates under typical cyclic loading, which seriously accelerates the shear fatigue failure of soft adhesives. Furthermore, the contribution of the equivalent creep damage to the final shear fatigue failure is even more pronounced than the fatigue damage. The quantitative construction of creep-fatigue damage diagrams has led to the determination of strong creep-fatigue interaction, which could be understood by the interactive mechanism between the stretching, friction, pulling-out, and rupture of molecular chains. In light of the distinctive creep-fatigue interaction mechanism, a modified Chaboche damage model has been developed, which could accurately predict the shear fatigue life of soft adhesives under a wide range of loading conditions.

Research on size effects in the low‐velocity impact (LVI) and compression after impact (CAI) characteristics of composite laminates

AbstractThe load‐bearing capacity and failure characteristics of composite structures are closely related to their dimensions. In this study, low‐velocity impact, ultrasonic non‐destructive testing, and compression after impact tests were conducted on composite laminates of varying widths to investigate the influence of size effects. Distinct impact response profiles and compression failure modes were characterized. The results indicate that under impact loading, the delamination threshold load (6700 N ~ 7200 N) and the knee‐point energy (40 J) are not affected by width. However, variations in width lead to differences in indentation depth, impact duration, peak load, delamination characteristics, and energy absorption. Furthermore, increasing impact energy further magnifies these differences. Under compression loading, wider laminates exhibit lower residual strength, with the influence of impact energy on residual strength decreasing as width increases. Importantly, the observed compression failure deformation mode transitions from localized buckling to widespread sub‐layer delamination‐induced compression failure. This suggests that changes in width alter the governing mechanical mechanisms of CAI failure. Consequently, the use of a single‐size laminate to represent both LVI and CAI processes is not recommended. Based on experimental results, the reliability of the equivalent damage method in predicting the residual compression strength of laminates of different widths was confirmed, providing valuable insights for practical engineering applications.Highlights Assess the variations in the low‐velocity impact process of laminates with different widths. Evaluate the delamination damage of laminates after impacts by ultrasonic C‐scan techniques. Investigate the effect of variation in widths on the compression behavior of laminates after impact. Validate the feasibility of equivalent damage modeling for calculating residual strength.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

In-plane testing and hysteretic modeling of steel-spline cross-laminated timber diaphragm connection with self-tapping screws

ABSTRACT This study examines experimentally and numerically the in-plane behavior of a steel-spline Cross-Laminated Timber (CLT) connection with self-tapping screws. Although this connection is a strong, rapid, and cost-effective alternative suitable for CLT diaphragms of tall timber-concrete buildings, no previous cyclic/monotonic testing has been documented. Two specimens were tested under axial and in-plane shear loads, where a ductile failure mode was observed due to bending and withdrawal of screws, and deformation and buckling of the strap. Mechanic properties, such as strength capacity, stiffness, ductility, energy dissipation, equivalent viscous damping, stiffness/strength degradation, and damage index characterize the joint. Furthermore, the yield point and ductility were calculated with the EEEP, CEN, and Yasumura–Kawai methods, the last approach most accurate, with a mean ductility of 7.25 and 5.50 for the axial and in-plane shear tests, respectively. Overstrength factors of about 2.6 and 1.9 were also estimated for respective tests by comparing analytical expressions from timber codes and literature. Finally, three numerical models (SAWS, DowelType, and ASPID) were assessed to measure their epistemic uncertainty, showing an adequate force and dissipated energy history simulation, with a normalized root mean square less than 8.8% and 4.5%, and R 2 over 87% and 97%, respectively.

Experimental study of the importance of fiber breakage on the strength of thermoplastic matrix composites subjected to compression after impact

Post-impact strength and damage tolerance of composite structures stands as a paramount design consideration in the aeronautical industry. In the event of a low velocity impact, a set of damage manifestations within laminated structures are induced, including matrix cracking, delamination and fiber breakage. Despite the critical importance of discerning the influence of each damage type on post-impact compression strength, only a limited number of studies have endeavored to quantify these effects comprehensively. In response to this research gap, we have developed a novel methodology capable of mimicking damage extension and shape caused by a low-velocity impact, while preserving fiber integrity. This innovation is achieved through the application of induced electrical currents, thereby facilitating controlled damage simulation without compromising fiber structural integrity. Our investigation compares the residual stiffness and strength of AS4/PEEK laminates subjected to low velocity impacts and induction currents, under conditions of equivalent damage. Our findings reveal that fiber breakage significantly influences the loss of stiffness in the laminate, but not its strength. Moreover, our results confirm the role of delamination as the primary determinant of strength degradation in the damaged material.

Cyclic response and residual life prediction of Inconel 718 superalloy after overloading under hybrid stress-strain controlled creep-fatigue loading

Inconel 718 is a material for manufacturing turbine disks, which is subjected to complex loads of creep-fatigue during service. This paper examines the effect of constant stress overloading at various lifespan stages on subsequent cyclic deformation, fracture behavior, and residual lifetime in hybrid stress and strain-controlled creep-fatigue interaction (HCFI) experiments conducted at 650℃. Overloading of 800 MPa constant stress with 180 min dwell time is applied at the 10 %, 25 %, 50 %, 65 %, and 70 % lifespan of HCFI tests. Results show that overloading reduces the residual life of the material obviously and makes a significant impact on the subsequent creep-fatigue deformation behavior, and additional damage is induced when overloading is applied towards the end of the lifespan. Moreover, more severe grain boundary damage leading to the final intergranular fracture is identified through microstructural analysis following overloading. Finally, equivalent damage is proposed to quantify the creep-fatigue damage affected by overloading, resulting in accurate life prediction outcomes.

Blast mitigation effects of TPU polymers-based inflated membrane structures under external explosion

TPU polymers-based inflated membrane structures are a potential technology to protect pre-existing lightweight buildings, with the advantages of lightweight and simple building process. In this study, a series of field blast tests were performed for the structural response and blast load parameters to study the blast mitigation effect of the inflated membrane structures. The corresponding numerical models of the tests were then developed and validated to reproduce the fluid-structure interaction. Thin aluminum plates were used as the protected structure. Based on their maximum displacement, average plastic strain, depth of depression, and permanent deformation, damage factor was defined to evaluate their damage level. Both the experimental and numerical results show that inflated membrane structures can effectively mitigate blast loading and significantly reduce the permanent displacement of the aluminum plate by elastic compression deformation. The effects of the initial height and internal pressure of inflated membrane structures on the blast mitigation effectiveness were clarified by the parametric study. The overpressure-impulse equivalent damage curves were established by combining the damage factor and overpressure-impulse loads, which further confirmed the blast mitigation performance of inflated membrane structures. Our study has verified the blast mitigation effects of inflated membrane structures based on TPU polymers, which is potentially valuable in the field of protective engineering for lightweight construction.

Wind Turbine Blade Damage Evaluation under Multiple Operating Conditions and Based on 10-Min SCADA Data

The present paper aims to enable the assessment of the fatigue damage of wind turbine blades over a long duration (e.g., several months/years) in conjunction with different operating regimes and based on two information sources: the 10-min SCADA data and an interpolation using response surfaces identified using the FAST aeroelastic numerical tool. To assess blade damage, prior studies highlighted the need for a high-frequency (>1 Hz) sampling rate. Because of data availability and computation resource limitations, such methods limit the duration of the analysis period, making the direct use of such an approach based on a 1 Hz wind speed signal in current wind farms impractical. The present work investigates the possibility of overcoming these issues by estimating the equivalent damage using a 1 Hz wind speed for each 10-min sample stored in the SCADA data. In the literature, the influence of operating regimes is not considered in fatigue damage estimation, and for the first time, the present project takes a pioneering approach by considering these operating regimes.

Effect of drawing speed on the deformation characteristics, microstructure and properties of copper wire rod

Currently, copper-based wire has been extensively applied in the information industry and for signal transmission due to its excellent performance in practice. Drawing speed, as a key parameter of the drawing process, has a significant impact on the production and quality of the wire. In this study, both simulation and experiment are performed to explore the evolution of deformation and damage behavior of copper wire and its microstructural properties during the process of multi-pass continuous drawing, with the drawing speed set to the range from 60 to 300 m/min. This provides guidance on the production and process optimization of the wire. It is revealed in the study that the surface of the pure copper wire is deformed more significantly than the core region, and that there is a rise in the equivalent strain and damage occurring at different locations in the longitudinal section of the wire as the number of passes increases. With the drawing speed increasing, the strain and damage occurring in the core region are reduced, while the damage caused by severe deformation on the surface shows nonlinearity. When the drawing speed increases, there is a significant improvement in the strength of the dominant texture component <101> in the copper wire, and the grain size of the wire is significantly refined. In the meantime, there is an increase in the density of dislocation within the wire. The severity of distortion caused to the grain tends to decrease, and the grain boundary is gradually blurred. By increasing the drawing speed, the surface quality of the wire is improved. Apart from that, there is a slight increase in the tensile strength, DC resistance and electrical resistivity of the copper wire, despite a decline in the conductivity of the wire.

Material characterisation of anodising effects on small fatigue crack nucleation in AA7XXX alloys

The precursor cleaning steps in the anodising surface finish process for aluminium alloy aircraft parts are known to lead to etching of surface-breaking intermetallic particles and grain boundaries, which in turn leads to preferential sites for fatigue crack nucleation. Type 1C anodising per MIL-A-8625F, is a favoured aircraft aluminium part corrosion protection treatment meeting modern health and environmental requirements. Type 1C anodising uses electrolysis in a non-chromic acid bath (typically based on sulphuric, boric-sulphuric or phosphoric acid formulations) to develop a thick aluminium oxide surface layer. In previous studies the equivalent initial damage sizes of these nucleation sites was calculated from near surface fatigue crack growth measurements using quantitative fractography in both Type 1C anodised aluminium alloy 7050-T7451 and 7085-T7452. A notable difference was observed in the values for these two materials with AA7085-T7452 equivalent initial damage sizes being significantly smaller. Since these values are critical crack starting size assumptions in fatigue life analysis for aircraft fleets, the observed differences must be investigated and explained for notionally similar alloys under identical conditions.In this work, the material surrounding the population of crack nucleation sites in several Type 1C anodised fatigue tested specimens manufactured from AA7050-T7451 and AA7085-T7452 materials has been characterised using precise surface preparation methods and scanning electron microscopy techniques. It has been demonstrated that there is a statistically significant difference in the number, size, aspect ratio and distribution of surface breaking Al7Cu2Fe intermetallic particles beneath the anodising layer that, when etched out during the anodising process, are responsible for fatigue crack nucleation in 7050-T7451 over 7085-T7452 material. The increased size, angular shape and coverage of these intermetallics in AA7050 serves to increase their effectiveness as preferential locations for fatigue crack nucleation through two mechanisms, as a highly localised stress concentrating feature, as well as through their ability to sample more of the material's microstructural features ensuring a discontinuity is present in the most favourable orientation and location for fatigue crack nucleation.

A novel quantitative analysis approach for hole surface damage of ceramic matrix composites machined by abrasive waterjet

To realize low-damage hole-making machining of AWJ-machined CMC, it is necessary to achieve quantitative analysis of hole surface damage. Therefore, a novel approach to quantifying damage based on the principle of invariance of damage area is proposed in this study. The amount of total damage is attributed to the sum of the equivalent average damage lengths of the four common types of damage (peripheral compound damage, tearing damage, crack damage, and burrs damage), which are uniformly arranged inside and outside the hole in sequence according to the principle of constant area. The influence law and influence mechanism of common process parameters on the surface damage in Cf/SiC during hole making via AWJ are investigated based on the established quantitative damage analysis model. The total surface damage increases with the increase of the standoff distance, and decreases with the increase of waterjet pressure and abrasive flow rate. The most significant factor affecting the total surface damage is the standoff distance, followed by waterjet pressure and abrasive flow rate. However, the effect of traverse speed is not noteworthy. The approach of quantitative damage analysis will provide the necessary theoretical basis and technical guidance for achieving low damage hole-making surface utilizing AWJ.

Structural damage detection with two-stage modal information and sparse Bayesian learning

Sparse Bayesian learning (SBL) has been proved to be an effective damage detection strategy. In this research, a structural damage detection technique with two-stage modal information is incorporated into the SBL framework. As an approximate representative, the equivalent damage factor requires sufficient sparsity for damage locating in the first stage. To content this, the mode shape energy (MSE) with SBL is performed in the model updating. With limited sensors, more accurate elemental damage will be estimated using mode shapes in the second stage. For further simplified process of damage detection, model reduction method is conducted to decrease both the calculation of eigenvalue and the second derivative corresponding to damage factors. The performance of SBL in damage detection is significantly improved. The accuracy and efficiency of the proposed method is verified by a bridge numerical simulation and a simply supported beam test.

Comparative study of damage modeling techniques for beam-like structures and their application in vehicle-bridge-interaction-based structural health monitoring

Damage modeling techniques are essential tools for revealing the impact pattern of damage on structural responses. Currently, different damage level parameters are defined for different damage modeling techniques, but there is no established equivalence among them. This might plague researchers in their selection of damage modeling techniques for theoretical and numerical studies. To address this challenge, comparative studies of different damage modeling techniques for beam-like structures were conducted, and their impact on vehicle-bridge-interaction (VBI)-based structural health monitoring was analyzed. First, the theoretical basis of four damage modeling techniques, that is, element stiffness loss, element mass increase, cracked beam element, and crack spring element, were analyzed, and equivalent damage level relationships were established based on beam frequencies. Then, a finite element simulation of the VBI system consisting of a two-axle vehicle and a beam-like structure with damage was formulated and verified. Finally, the impacts of different damage modeling techniques with unified damage levels on the dynamic responses were studied, and the feasibilities of damage identification using vehicle and bridge responses under different damage modeling techniques were compared. The results indicated that the dynamic responses generated by different damage modeling techniques varied under the same damage level. The damage modeling technique using the crack spring element posed the most significant impact on the VBI responses, the cracked beam element and element stiffness loss techniques had the equivalent impact, but the element mass increase technique showed a negligible impact. Damage location and severity could be well detected by the cracked beam element and element stiffness loss techniques. However, the dynamic responses generated by the element mass increase technique could not be used to identify the damage. Vehicle responses were more useful than bridge responses for damage identification, demonstrating the advancement of indirect monitoring of bridge health conditions using an instrumented passing vehicle.

Damage of materials under proportional loading

The work is devoted to the study of material damage during elasto-plastic proportional loading, in particular, the influence of two loading mechanisms, detachment and shear, is taken into account. These mechanisms include viscous, brittle, and visco-brittle modes of failure. The accumulation of scattered damage is considered as a multi-scale and multi-stage phenomenon that occurs during proportional loading at the micro- and meso-levels of the destruction of the metal structural material. As part of the study, a quantitative assessment of the degradation of the physical and mechanical properties of materials was performed, in particular, changes in the modulus of elasticity E and G, and the definition of equivalent damage arising from an elastoplastic proportional load is proposed. Experimental data on the kinetics of damage accumulation on 12X18N10T steel samples, which were subjected to axial load (tension), shear (torsion) and proportional load with the stiffness parameter of the stress state K = 0.5 before failure, are considered. The work compares experimental results with theoretical data, damage accumulation. The obtained conclusions contribute to a deeper understanding of the mechanisms of destruction of materials under the action of a proportional load, and can also find practical application in the design and assessment of the load-bearing capacity of structural elements.

Degradation characteristics and equivalent analysis of InGaAsP space solar cells under proton and neutron irradiation

The effects of 2 MeV, 30 MeV proton and neutron irradiation on the performance of InGaAsP single junction solar cells were investigated. The degradation of electrical and optical properties was studied by experiment, such as I-V curve, external quantum efficiency, photoluminescence (PL) and scanning electron microscopy (SEM). Results show that the performance parameters of the solar cell degrade seriously with the increasing of the displacement damage dose. The PL results indicate that irradiation has a destructive effect on the photoelectric properties of materials. The carrier parameters were quantitatively calculated according to the PL normalized peak. The minority carrier lifetime attenuation model and equivalent displacement damage model were established to evaluate the on-orbit behavior of the InGaAsP solar cell.

A nonlinear cumulative fatigue damage life prediction model under combined cycle fatigue loading considering load interaction

In the present work, combined high and low cycle fatigue (CCF) tests were performed on GH4169 nickel-based alloy under stress-controlled conditions. The interaction between high cycle fatigue (HCF) and low cycle fatigue (LCF) results in a complex process of fatigue damage evolution under CCF loading. Based on the fatigue damage curve and the theory of equivalent damage, considering the interaction between HCF and LCF loading, a nonlinear cumulative damage model is proposed under CCF loading. The proposed model is deduced from the fatigue damage curve under CCF loading, which establishes a connection between the LCF and HCF damage curve. Three materials, including the other two materials, namely TC11 and Al 2024-T3, published in the relevant literature, are used to verify the proposed model. The experimental results demonstrate that the proposed model has better prediction results than those for Miner’s rule and the Trufyakov-Kovalchuk (T-K) model. The validation of the proposed model shows its superior performance.