Damage Growth Model Research Articles

Finite element modeling for cohesive/adhesive failure of adhesive structures with a thermosetting resin

In this study, we established a novel method based on the finite element method (FEM) for predicting the strength of adhesive structures. Viscoplasticity, void growth, and cohesive zone model were introduced into the FEM to create a nonlinear damage growth (NDG) model. This model was used to comprehensively analyze the process zones within the adhesive layer. Furthermore, the embedded process zone approach was used to develop an interface constitutive law that averages the mechanical response of the adhesive layer. This modified Ma–Kishimoto (MMK) model can accurately represent the adhesive layer as an interface element and is computationally efficient. Furthermore, the study obtained the necessary interface properties for the MMK model from the NDG model, creating a numerical material test that can approximate the effect of the process zone. To validate the proposed method, single-lap shear tests were performed, and the accuracy of the predicted strength and deformation field was evaluated. The damage evolution in the NDG model and the MMK model were compared, and the scope of application of the MMK model was discussed. The results of this study can be used as a reference for the failure mechanism of thermosetting adhesives and establishment of design indices for adhesive structural strength.

The effect of elevated temperature on LCF damage growth in 2024AA – Experiment and modeling

This paper presents the results of experimental low-cycle fatigue (LCF) tests conducted on EN-AW 2024 alloy in T3511 temper at 100 °C, 200 °C and 300 °C. The material's basic fatigue characteristics were determined, such as fatigue life curve and cyclic strain curve. Both the hysteresis loop and nature of fracture surfaces obtained in macro- and microscopic observations (scanning electron microscope, SEM) were accounted for. The results of tests at elevated temperature were compared with results obtained at room temperature in the authors’ previous papers. Based on the results of experimental tests, an analytical model of fatigue damage growth was proposed. In this model, it was assumed that damage accumulation mainly depends on the current normal stress and increment of plastic strain. Dependencies of the model's parameters with respect to temperature were determined, and the model was validated experimentally. Good concurrency of the numerical simulations with the experimental results was obtained.

Damage spreading in quasi-brittle disordered solids: II. What the statistics of precursors teach us about compressive failure

We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model of damage growth and localization developed by Berthier et al. (2017) that accounts for both microstructural disorder and non-local interactions. Its numerical implementation permits performing a complete scaling description of the failure precursors. In particular, we show that their size, duration and spatial extent are related to each other by robust scaling laws and that these three quantities diverge close to failure. By developing a theoretical model of damage growth in disordered elasto-damageable specimen, we demonstrate that these scaling relations emerge from the physics of elastic manifolds driven in disordered media, while the divergence of these quantities close to failure is reminiscent of the loss of stability of the specimen at the localization threshold. Our study sorts out a long-standing debate on the nature of the compressive failure and the origin of the universal statistics of the precursors preceding it. Our analysis rules out a critical-point scenario in which the divergence of the precursors size close to failure is signature of a second-order phase transition governed by the microstructural disorder. Instead, we show that while the jerky evolution of damage prior to failure results from the presence of material disorder, the latter does not significantly change the nature of the localization process, which is an instability well described by standard bifurcation theory of homogeneous systems. Finally, we harness our detailed understanding of the precursory statistics to design a methodology to estimate the residual lifetime of a structure from the statistical analysis of precursors. This method relevant for structural health monitoring is shown to perform rather accurately on our data.

Analysis of fatigue crack initiation in cyclic microplasticity regime

The present work provides description of fatigue crack initiation in metals subjected to cyclic loading within the nominal elastic or initial elastic-plastic regimes next passing to elastic response during cyclic deformation and shake down process. It is assumed that damage growth proceeds due to action of local stress, specified as the sum of mean stress and its fluctuations induced by material inhomogeneities such as grain boundaries, inclusions, cavities, boundary asperities, also due to design notches or holes introduced into the element. The damage growth model is proposed, based on the critical plane concept. The macrocrack initiation then corresponds to a critical value of accumulated damage. The modelling of damage growth is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using the coherent laser light. The damage growth effect is analysed by microindentation tests. The fatigue tests are performed for high strength steel specimens with central hole.

Combining the thick level set method with plasticity

The Thick Level Set (TLS) method has been proposed as a new approach to the modeling of damage growth in solids. The fronts of damaged zones are implicitly represented as a level set of an auxiliary field whose evolution is accomplished by the level set method. The TLS model contains a characteristic length to obtain a non-local description that prevents spurious localization in the strain field. The update of the damage is indirectly performed by integrating local values of energy release rate over this characteristic length. This model offers an automatic transition from damage to fracture, and deals with merging and branching cracks as well as crack initiation in an easy and robust manner. In this paper, the TLS is applied to simulate the formation of cusps in a polymer matrix loaded in shear. Realistic simulation of this process requires the damage model to be combined with plasticity in order to capture the behavior of the material prior to failure. To accommodate for plasticity, several changes to the TLS framework are introduced. A strength-based criterion for initiation of damage based on the ultimate yield surface of such plasticity model is proposed. A mapping operator for transferring history is included if the integration scheme in element changes. Furthermore, a new loading scheme is devised that does not rely on secant unloading. Numerical experiments demonstrate the accuracy and effectiveness of the proposed model to handle simulation of crack growth in a medium with hardening plasticity.

Prognosis of fatigue induced stiffness degradation in GFRPs using multi-modal NDE data

Prediction of expected life of a composite structure especially at the initial stages of degradation is challenging owing to inherent heterogeneity and lack of robust damage growth models. This paper focuses on prognostic study of matrix stiffness degradation in glass fiber reinforced polymers (GFRP) subjected to fatigue testing using data from multi-modal nondestructive evaluation (NDE) techniques, specifically the optical transmission and guided wave sensing. Combining information from multiple sensors exploits advantages of signal complementary and hence effectively improve damage growth modeling and prediction in composites. However, matrix stiffness inferred from two independent NDE techniques varies owing to differences in their sensitivity, measurement noise or model discrepancy, often leading to inconsistent and inaccurate reliability assessment. A joint likelihood updation technique is therefore proposed in existing particle filtering (PF) framework which enables dynamic optimization of Paris-Paris model parameters at every time step by discarding noisy or biased measurements. Comparison of stiffness prediction using multi-sensor data with prognosis results on single sensor or average measurement demonstrates the benefit of joint likelihood based prediction of residual stiffness. An additional advantage of the proposed approach towards reduction of particle count in existing particle filtering framework is discussed, thereby lowering prediction time and computation resources. Overall, multi-sensor NDE and prognosis methodology is discussed for reliable assessment of fatigue life in GFRP composites structures.

Numerical investigation of growth model for laser-induced damage in optics under high power laser irradiation

The laser-induced damage growth model in optics under high-power laser irradiation is described based on the Weibull distribution model. A parameter method for solving Weibull distribution model by using the least-square method is proposed. In addition, a Monte-Carlo analysis method is used to numerically simulate the growth law of laser-induced damage in optics based on the statistical theory. Furthermore, we have also predict the laser-induced damage growth trend for 20 shots in high-power laser systems.

Prediction of the ultimate strength of quasi-isotropic TP-based laminates structures from tensile and compressive fracture toughness at high temperature

This paper is intended to test the capacity of a simple model based on fracture mechanics concepts to predict the ultimate strength of notched hybrid carbon and glass fibers woven-ply reinforced PolyEther Ether Ketone (PEEK) thermoplastic (TP) quasi-isotropic (QI) laminates under different temperature conditions. In such materials, translaminar failure is the primary failure mode driven by the breakage of 0° and 45° oriented fibers in tension as well as the formation of kink-band in compression. Single-Edge-Notched Bending (SENB), Open-Hole-Tensile (OHT) and Open-Hole-Compression (OHC) specimens have been conducted at room temperature (RT) and at a temperature higher than the glass transition temperature (Tg). The Critical Damage Growth model derived from the Average Stress Criterion and Linear Elastic Fracture Mechanics (LEFM) have been applied to open-hole specimens to determine the critical damage zone from which the fracture toughness in tension (0° and 45° fibers breakage) KIctension and in compression (kink-band formation) KIccomp. are estimated. In Single Edge Notched Bending (SENB) specimens experience simultaneous tension/compression. From the estimation of KIctension and KIccomp., the ultimate strength of SENB specimens can be predicted. LEFM equations combined with the critical fracture toughness in tension give relatively accurate results, suggesting that failure is driven by fibers bundles breakage in tension.

Low cycle fatigue test and enhanced lifetime estimation of high-strength steel S550 under different strain ratios

This study investigates the low-cycle fatigue (LCF) behavior of the high-strength steel S550 (commonly used in ship and floating structures) under different strain amplitudes with different strain ratios at a room temperature. The test results characterize the cyclic stress-strain relationship, the mean stress relaxation behavior and the cyclic plasticity parameters of S550 steels. The scanning electron microscopy (SEM) examinations on the failure surface reveal the fatigue crack initiation and growth mechanism. Based on the experimental results, this study presents two enhanced approaches to estimate the low-cycle fatigue life of S550 steels. The energy-based approach modifies the original Smith-Watson-Topper model using the applied energy calculated in the first cycle to enhance the accuracy and facilitate engineering implementations. The damage mechanics-based approach calibrates the material parameters from the measured total fatigue life by combining the fatigue crack initiation model and the damage growth model. The computed fatigue life using the calibrated material parameters demonstrates a close agreement with the measured fatigue life in the experiment.

Influence of stiffener configuration on post-buckled response of composite panels with impact damages

In this paper, the effect of T, I and J stiffer configurations on post-buckling response of composite stiffened panels with impact damage is investigated through experiments and numerical simulations. Two identical panels in all three configurations were designed and manufactured. Each panel has four stringers of the same type. All panels were designed to have a skin buckling load of 92 kN ± 5 kN and weight of 1.45 kg ± 0.05 kg to separate the effect of impact damage irrespective of stiffener type. One panel from each configuration is impacted with 50 J energy above stiffener flange from skin side to create a Barely Visible Impact Damage (BVID) and followed by a compression test till collapse. A comparative study between pristine and impacted panels is presented. The effect of impact damage on buckling load, post-buckling response, collapse load and end-shortening were investigated. Moreover, finite element numerical models were developed for all panels which include intra-laminar and inter-laminar damage initiation and growth models. Impact damage area measured from ultrasonic C-scan was modelled in commercial finite element software Abaqus®. Failure modes in pristine and impacted panels such as disbond, tearing of stiffener web and locations from experiments are discussed and validated by numerical simulations.

Modeling Restrained Shrinkage Induced Cracking in Concrete Rings Using the Thick Level Set Approach

Modeling restrained shrinkage-induced damage and cracking in concrete is addressed herein. The novel Thick Level Set (TLS) damage growth and crack propagation model is used and adapted by introducing shrinkage contribution into the formulation. The TLS capacity to predict damage evolution, crack initiation and growth triggered by restrained shrinkage in absence of external loads is evaluated. A study dealing with shrinkage-induced cracking in elliptical concrete rings is presented herein. Key results such as the effect of rings oblateness on stress distribution and critical shrinkage strain needed to initiate damage are highlighted. In addition, crack positions are compared to those observed in experiments and are found satisfactory.

A Bayesian approach for a damage growth model using sporadically measured and heterogeneous on-site data from a steam turbine

Accurate prediction of the remaining useful life (RUL) of plant turbines is a major scientific challenge for effective operation and maintenance in the power plant industry. This paper proposes an RUL prediction methodology that incorporates a damage index into the damage growth model. A Bayesian inference technique is used to consider uncertainties while estimating the probability distribution of a damage index from on-site hardness measurements. A Bayesian approach is proposed for the damage growth model for use with aged steam turbines. The predictive distribution of the damage index is estimated using its mean and standard deviation. As a case study, real steam turbines from power plants are examined to demonstrate the effectiveness of the proposed Bayesian approach. The results from the proposed damage growth model can be used to predict the RULs of the steam turbines of power plants regardless of load types (peak-load or base-load) of the power plant.

Predictive airframe maintenance strategies using model-based prognostics

Aircraft panel maintenance is typically based on scheduled inspections during which the panel damage size is compared to a repair threshold value, set to ensure a desirable reliability for the entire fleet. This policy is very conservative since it does not consider that damage size evolution can be very different on different panels, due to material variability and other factors. With the progress of sensor technology, data acquisition and storage techniques, and data processing algorithms, structural health monitoring systems are increasingly being considered by the aviation industry. Aiming at reducing the conservativeness of the current maintenance approaches, and, thus, at reducing the maintenance cost, we employ a model-based prognostics method developed in a previous work to predict the future damage growth of each aircraft panel. This allows deciding whether a given panel should be repaired considering the prediction of the future evolution of its damage, rather than its current health state. Two predictive maintenance strategies based on the developed prognostic model are proposed in this work and applied to fatigue damage propagation in fuselage panels. The parameters of the damage growth model are assumed to be unknown and the information on damage evolution is provided by noisy structural health monitoring measurements. We propose a numerical case study where the maintenance process of an entire fleet of aircraft is simulated, considering the variability of damage model parameters among the panel population as well as the uncertainty of pressure differential during the damage propagation process. The proposed predictive maintenance strategies are compared to other maintenance strategies using a cost model. The results show that the proposed predictive maintenance strategies significantly reduce the unnecessary repair interventions, and, thus, they lead to major cost savings.

A failure mechanism based model for numerical modeling the compression-after-impact of foam-core sandwich panels

A failure mechanism-based progressive damage growth model is developed, applied and validated for modeling woven polymer-based foam-core sandwich panels under compression-after-impact. A Schapery theory based constitutive model, which takes account of intra-ply shear inelasticity and fiber kinking and resulting fracture is developed for the impacted plain weave fabric laminated face-sheets under compression loading. Each ply of the face-sheets is modeled as an orthotropic nonlinear elastic lamina degrading as characterized through laboratory experiments. The behavior of woven plies in the warp and fill directions is elastic until the attainment of local instability in compression. The phenomenon of fiber micro-buckling leading to kink banding, which was observed to be the mechanism controlling failure of the impacted face-sheets and hence the sandwich panels, is explicitly accounted for by allowing the fiber rotation at a material point. In the shear direction, plasticity is also considered to represent the elastic-plastic in-plane shear behavior of woven fabric plies. The constitutive model is numerically implemented using the commercially available finite element package ABAQUS through a user defined material subroutine (UMAT). The previous 3D damaged FE model which was proven to accurately capture the low–velocity impact damages is imported and subjected to a compression loading modeling. The numerical results in terms of deformation, failure mode and residual strength show a remarkable agreement with experimentally measured ones, allowing the model to be validated.

Bayesian inferences of damage index and damage growth model based on on-site measurement data of steam turbine

Accurate prediction of remaining useful life (RUL) of plant turbine is a major scientific challenge for effective operation and maintenance in the power plant industry. This paper proposes an RUL prediction methodology that incorporates a damage index into the damage growth model. Bayesian inference technique is used to estimate the probability distribution of a damage index from on-site hardness measurements with uncertainties. A Bayesian approach to the damage growth model is proposed for aged steam turbines and the predictive distribution of the damage index is estimated using its mean and standard deviation. As a case study, real steam turbines in power plants were used to demonstrate the effectiveness of the proposed Bayesian approach. The results from the proposed damage growth model can be used to predict the RULs of the steam turbines of power plants regardless of load types (peak-load or base-load) of the power plant.

Using physical based models for machinery RUL estimation

Machinery prognosis is the process of forecasting the remaining operational life (RUL), future condition, or probability of failure based on the acquired condition monitoring data. RUL forecast becomes crucial since it allows planning of efficient maintenance actions. In order to estimate the remaining usefull life it is needed, first, to estimate the damage severity or size, and then, to forecast the damage growth model. Damage size estimation is not yet developed and needs additional research. Classic theories assume that energy dissipation is proportional to fault size. For small faults, it is not correct. In general the energy-fault size relation depends on the transmission path from the defect to the snsor which differs for every case of defect location, machine and sensor. Therefore the estimation of the fault size is crucial. State of the art algorithm for bearings size estimation will be presented. The algorithm approach is based on insights from a general dynamic bearing model and an analytical model for RE-spall interaction. The outline of these models will be presented. Other machine components such as, gears and shafts will be discussed. In the second stage, understanding of the damage progression process is needed. This stage is essential for estimation the RUL. The required steps towards damage progression tools will be discussed. The models allow to examine the the algorithms sensitivity to different types of faults, geometric errors, misalignment, unbalance, system parameters etc.

Stress corrosion crack initiation of Zircaloy-4 cladding tubes in an iodine vapor environment during creep, relaxation, and constant strain rate tests

During accidental power transient conditions with Pellet Cladding Interaction (PCI), the synergistic effect of the stress and strain imposed on the cladding by thermal expansion of the fuel, and corrosion by iodine released as a fission product, may lead to cladding failure by Stress Corrosion Cracking (SCC). In this study, internal pressure tests were conducted on unirradiated cold-worked stress-relieved Zircaloy-4 cladding tubes in an iodine vapor environment. The goal was to investigate the influence of loading type (constant pressure tests, constant circumferential strain rate tests, or constant circumferential strain tests) and test temperature (320, 350, or 380 °C) on iodine-induced stress corrosion cracking (I-SCC). The experimental results obtained with different loading types were consistent with each other. The apparent threshold hoop stress for I-SCC was found to be independent of the test temperature. SEM micrographs of the tested samples showed many pits distributed over the inner surface, which tended to coalesce into large pits in which a microcrack could initiate. A model for the time-to-failure of a cladding tube was developed using finite element simulations of the viscoplastic mechanical behavior of the material and a modified Kachanov's damage growth model. The times-to-failure predicted by this model are consistent with the experimental data.

Simulation and Analysis of Ballistic Impact Using Continuum Damage Mechanics (CDM) Model

Ballistic Impact is the study of behaviour of ductile targets subjected to projectile impact. In this work, simulation and analysis is done by using the Continuum Damage Mechanics (CDM) model on ballistic impact of steel (IS2062: 2006 GR E410W A) target using a rigid projectile. The Continuum Damage Mechanics model is implemented in ABAQUS/Explicit through a user defined material model subroutine (VUMAT). The developed VUMAT is validated by comparing the simulated results in tensile test with experimental results. The effect of the temperature and the strain rate are included in the hardening model as well as in the damage growth model. A critical damage criteria is used to predict the fracture initiation and spread of fracture is simulated by tracing the path of failed elements.

Prediction of the notched strength of woven-ply PolyPhenylene Sulfide thermoplastic composites at a constant high temperature by a physically-based model

A simple physically-based model – the Critical Damage Growth model – derived from fracture mechanics criteria has been applied to quasi-isotropic carbon fibers woven-ply reinforced PolyPhenylene Sulfide (PPS) laminates to predict their notched strength under constant high temperature conditions. The tested notched specimens are characterized by an elastic-brittle response resulting from transverse matrix cracking and fiber breakage near the notch tip. This model requires only, as input parameters, the unnotched strength and fracture toughness of the laminate determined from the measurements of critical strain energy release rates. The translaminar fracture toughness has been calculated by means of the compliance method applied to quasi-isotropic Single-Edge Notch specimens with different initial crack lengths. For various hole diameters, the capabilities of the Critical Damage Growth model are very good to predict the notched strength of quasi-isotropic C/PPS laminates tested at a temperature higher than glass transition temperature when PPS matrix ductility and toughness are exacerbated.

Numerical predictions of carburisation and crack evolution using a combined diffusion rate and remaining multi-axial creep ductility damage model

A novel numerical damage model has been developed to combine Fick’s second law of diffusivity with microstructure modelling of environmentally assisted creep damage. The environmental acceleration of material degradation has been modelled and compared with experimental observations. The combined multi-site damage and crack growth model for creep and environmentally assisted time-dependent material oxidation/carburisation based on a gas/solid interface diffusion and non-linear time-dependent creep mechanism is proposed. Numerical predictions are presented to develop a methodology for component lifing. The model allows for the development of a hardened layer due to surface oxidation and predicts damage and cracking during subsequent creep under an applied load. The simulated grain mesh structure used can replicate surface healing or diffuse intergranular cracking and material depletion emanating from the gas/solid surface interface by quantifying the strength ratios between grain and grain boundaries. In this article, oxidation/carburisation is estimated both analytically and numerically using Fick’s diffusion laws and carbon/steel diffusion flux properties available in the literature. It is also shown that carbon diffusion distribution can be related to grain hardening due to carburisation as well as grain/grain boundary strength ratios which could vary as much as a factor of 0.5. The model is validated by comparing with actual oxidation/carburisation data for the long-term oxidised 9-12 Cr steels operating at high temperatures. Finally, it is shown that the mode and rate of surface oxidation and hardening, depending on whether the material is homogenous or contains micro-cracks substantially affects the life time of a component under high temperature creep loading.