Modeling of scattered damage accumulation kinetics under combined stress

An analysis of the reliability and range of application of a number of phenomenological damage models has been performed on the basis of experimental research carried out into the kinetics of damage accumulation in metallic structural materials under plane stress and active loading. Damage models are based on the main postulates of irreversible thermodynamics and continuum damage mechanics. The laws governing the effect of the type of stress state on scattered damage accumulation kinetics have been established.     

Enhancement of damage indicators in wavelet and curvature analysis

Damage in a structural element induces a small perturbation in its static or dynamic displacement profile which can be captured by wavelet analysis. The paper presents the wavelet analysis of damaged linear structural elements using DB4 or BIOR6.8 family of wavelets. An expression is developed for computing the natural frequencies of a damaged beam using first order perturbation theory. Starting with a localized reduction ofEI at the mid-span of a simply supported beam, damage modelling is done for a typical steel beam element. Wavelet analysis is performed for this damage model for displacement, rotation and curvature mode shapes as well as static displacement profiles. Damage indicators like displacement, slope and curvature are magnified under higher modes. Instantaneous step-wise linearity is assumed for all the nonlinear elements. A localization scheme with arbitrararily located curvature nodes within a pseudo span is developed for steady state dynamic loads, such that curvature response and damages are maximized and the scheme is numerically tested and proved. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

Seismic analysis of arch dams—a continuum damage mechanics approach

In this paper, the non‐linear seismic response of arch dams is presented using the concept of Continuum Damage Mechanics (CDM). The analysis is performed using the finite element technique and appropriate non‐linear material and damage models in conjunction with the α‐algorithm for time marching. Because of the non‐linear nature of the discretizied equations of motion, modified Newton–Raphson approach has been used at each time step. Damage evolution based on tensile principal strain using mesh‐dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation. As an application of the proposed formulation, a double curvature arch dam has been analysed and the results are compared with the solutions from linear analysis and it is shown that the structural response of arch dams varies significantly in terms of damage evolution. Copyright © 1999 John Wiley & Sons, Ltd.     

Damage propagation in composite structural elements-coupon experiments and analyses

An overview of experiments and analyses being performed at the coupon level within the GARTEUR (Group of Aeronautical Research in Europe) action group AG16: ‘Damage propagation in composite structural elements’ is given. Both basic delamination fracture experiments such as DCB, ENF, MMB, CLS and SEN and coupon tests with embedded artificial delaminations or impact damages are carried out. The experiments are analysed using different methods and energy release rate, stress-based failure criteria and damage models are evaluated.     

Damage tolerance assessment of composite sandwich panels with localised damage

The work described herein is part of a larger context in which the effect of damage in sandwich composite structures for marine applications has been investigated. The overall aim of this effort has been twofold: to develop and verify existing damage assessment models to be used to assess the effect of damage on marine sandwich structures, and to develop a damage assessment scheme to be used by shipyards, ship owners and navies.More specifically, this paper presents a sub-set of this overall effort looking at impact and indentation damage and its effect on the load carrying capacity of state-of-the-art carbon composite sandwich panels for marine applications. Damage types are modelled based on physical observations from tests. Testing is then performed on different scales in order to validate the models. The overall aim is to use such models to produce information that can be used for decision-making at two levels. The first is to evaluate the damage tolerance of ship structural components and thus to calculate the size and extent of damage that a component can have without risk of growth or failure at ultimate local or global loads on the entire ship. The second is to have information at hand to decide if, and when, a structural part needs to be repaired if damage has been detected. A scheme developed for this purpose is presented herein. Finally the paper will briefly describe a common framework for damage assessment in composite sandwich structures. Herein, models are used in conjunction with the design specifics and functional requirements to create a scheme for repair decisions.     

Defect tolerance assessment of ARIANE 5 structures on the basis of damage mechanics material modelling

Damage mechanics based material models have been applied to establish fracture control procedures for the failure prediction of ARIANE 5 main structural components as the booster cases including welds, the main stage, and the upper stage cryogenic tank. The main goals of the damage mechanics based investigations were the accurate failure prediction, the clarification of dependency of fracture toughness on geometry, the calibration of analytical methods and the interpretation and optimisation of small scale fracture tests for material characterization and quality assurance.The results of these investigations allowed a failure prediction accuracy with analytical tools which is close to 3D numerical simulations. This could be demonstrated both with ductile (Gurson) and brittle (RKR) damage mechanics models.     

A damage evolution study of E-glass/epoxy composite under low velocity impact

To predict the behavior of composites in case of low velocity impact, various material models are available in the literature. Damage evolves exponentially or linearly with strain in these models. These models are using either characteristic length ‘L_c’ or material exponent parameters, ’m’ to solve the problem of strain localization. A method to relate these parameter to each other is suggested here. The choice of material exponent, ‘m’ for a particular mesh size is also discussed. Low velocity impact simulations for E-glass/epoxy composite are performed using continuum damage mechanics based material model and compared with the experiments. The damage observed through the light projected area on the laminate, contact forces and displacement plots with respect to time were studied and compared with finite element analysis results to demonstrate the effectiveness of the model. Digital Image Correlation (DIC) technique is used for experimentation to obtain displacement on the surface of the plate.     

Comparison of static response of structures using convex models and interval analysis method

In this paper, by combining the finite element analysis and non‐probabilistic convex models, we present the numerical algorithm of non‐probabilistic convex models and interval analysis method for the static displacement of structures with uncertain‐but‐bounded parameters. Under the condition of the box or interval vector determined from the ellipsoid of the uncertain‐but‐bounded structural parameter vector, by comparing the numerical algorithm of non‐probabilistic convex models and the interval analysis method in the mathematical proof and the numerical example, we can see that the width of the maximum or upper and minimum or lower bounds on the static displacement yielded by the numerical algorithm of non‐probabilistic convex models is tighter than those produced by the interval analysis method. Copyright © 2003 John Wiley & Sons, Ltd.     

基于应变和比能双控的钢结构损伤模型

损伤模型是对经历地震后结构的剩余承载力进行定量评价的重要工具。本文提出了一个基于等效塑性应变和比能双控的损伤模型,从材料的角度出发,考虑了三轴应力对地震作用下结构性能的影响,可用于空间结构强震作用下的非线性分析。应用该模型对一个九层的benchmark结构进行了地震倒塌模拟分析,结果显示基于应变与比能双控的损伤模型能够很好地评估强震下钢结构竖向构件及层的损伤发展过程。     

Modeling errors due to Timoshenko approximation in damage identification

The use of accurate computational models for damage identification problems may lead to prohibitive costs. Damage identification problems are often characterized as inverse ill-posed problems. Thus, the use of approximate models such as simplified physical and/or reduced-order models typically yields misleading results. In this paper, we carry out a preliminary study on a particular simplified physical model, the Timoshenko beam model in the context of damage identification. The actual beam is a two-dimensional relatively high aspect ratio (thickness/length) beam with a distributed damage that is modeled as a spatially varying Young modulus. We state the problem in the Bayesian framework for inverse problems and carry out approximative marginalization over the related modeling errors. The numerical experiments suggest that the proposed approach yields more stable results than using the Timoshenko beam model as an accurate model. Due to the severity of the Timoshenko approximation, however, the posterior error estimates of the proposed approach are not always feasible in the probabilistic sense.     

Numerical simulation of damage progression and fracture in structures made of 3D woven ceramic matrix composites

This paper proposes numerical simulation to predict damage progression and critical strength in structural components made of 3D woven ceramic matrix composites (CMCs). This method implements three numerical approaches with the commercial finite element method. (i) Damage models are used to predict damage initiation and propagation of CMCs. (ii) The failure criterion based on the Weibull volumetric statistical strength model is implemented to take into account the size effects of fiber-bundle strength. (iii) The nonlocal damage theory is implemented to confirm the mesh independence of the results and the convergence of computation. To verify the accuracy of the two damage models, simulations of smooth SiC/SiC specimens were performed. Furthermore, several kinds of open-hole SiC/SiC tensile test were simulated to verify the accuracy of the proposed numerical simulation. Finally, the proposed numerical simulation was validated by detailed comparisons of experiment and simulation.     

An improved probit method for assessment of domino effect to chemical process equipment caused by overpressure

Overpressure is one important cause of domino effect in accidents of chemical process equipments. Damage probability and relative threshold value are two necessary parameters in QRA of this phenomenon. Some simple models had been proposed based on scarce data or oversimplified assumption. Hence, more data about damage to chemical process equipments were gathered and analyzed, a quantitative relationship between damage probability and damage degrees of equipment was built, and reliable probit models were developed associated to specific category of chemical process equipments. Finally, the improvements of present models were evidenced through comparison with other models in literatures, taking into account such parameters: consistency between models and data, depth of quantitativeness in QRA.     

Failure criterion for steel pipe elbows under cyclic loading

Steel elbow components are considered to be critical parts in industrial piping system due to their probability of collapse or failure. Therefore, the structural behavior of elbows is considered with respect to failure criteria through experiments and corresponding numerical models. Thirty-eight sets of experiments were conducted on three inch pipe elbow specimens. The numerical simulation results of the specimens are in good agreement with the test results. Damage indices available in the literature are used for failure estimation of the elbows. We suggest that the damage calculated using the Park and Ang damage index, and the Banon damage index, based on only one failed specimen under any constant amplitude cyclic loading, can be defined as the failure point and used to predict the failure of the component under other loading amplitudes. Therefore, the low cycle fatigue curve of an elbow can be derived using these simulation results. We also found that the calculated damage of an elbow component under constant, non-constant, and fully or partial amplitude reversals is quite similar.     

基于振动的结构损伤识别方法研究进展

对近几十年来基于振动的结构损伤识别方法进行了归纳和总结,重点阐述了无模型的损伤识别方法和损伤识别的模型修正法,对损伤识别的神经网络法、小波分析法和时域法等也作了一定程度的介绍。分析了各种方法的优点和不足之处,讨论了基于振动的损伤识别技术存在的主要问题,并对进一步的研究方向作了展望。     

A damage computational approach for composites: Basic aspects and micromechanical relations

The basic aspects of a damage mechanics approach for composites, capable of simulating complete fracture phenomena, are presented. First, for two material examples, ceramic composites and laminate composites, modelling difficulties and state-of-art modelling are outlined. Damage models with delay effects combined with a dynamic analysis are then introduced. Their possibilities are illustrated on one-dimensional bar problems. More complex examples, computed with a F. E. code specific to laminate damage analysis, are also highligted.Dedicated to J. C. Simo     

Multicontinuum Failure Analysis of Composite Structural Laminates

Damage in a composite typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. Accurate predictions of constituent damage at points in a laminate provide a genesis for progressively analyzing failure of a composite structure from start to finish. In this article we develop an efficient constituent-based failure analysis for composite structural laminates. Continuum-based (phase-averaged) constituent stress and strain fields are computed in a finite-element environment without a computational time penalty. Constituent stress-based failure criteria are developed and used to construct a progressive failure algorithm in which one constituent is allowed to fail while the other constituent remains intact, e.g., matrix cracking. The proposed failure algorithm was used to predict failure of a variety of laminates under uniaxial and biaxial loads. The results were shown to be superior to comparable single-continuum failure analyses and in good agreement with experimentally determined failure loads.     

Guided Wave Damage Characterization via Minimum Variance Imaging with a Distributed Array of Ultrasonic Sensors

Guided wave imaging with a distributed array of inexpensive transducers offers a fast and cost-efficient means for damage detection and localization in plate-like structures such as aircraft and spacecraft skins. As such, this technology is a natural choice for inclusion in condition-based maintenance and integrated structural health management programs. One of the implementation challenges results from the complex interaction of propagating ultrasonic waves with both the interrogation structure and potential defects or damage. For example, a guided ultrasonic wave interacts with a surface or sub-surface defect differently depending on the angle of incidence, defect size and orientation, excitation frequency, and guided wave mode. However, this complex interaction also provides a mechanism for guided wave imaging algorithms to perform damage characterization in addition to damage detection and localization. Damage characterization provides a mechanism to help discriminate actual damage (e.g. fatigue cracks) from benign changes, and can be used with crack propagation models to estimate remaining life. This work proposes the use of minimum variance imaging to perform damage detection, localization, and characterization. Scattering assumptions used to perform damage characterization are obtained through both analytical and finite element models. Experimental data from an in situ distributed array are used to demonstrate feasibility of this approach using a through-hole and two through-thickness notches of different orientations to simulate damage in an aluminum plate.     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.     

Bewertung von Schädigungserscheinungen in Thermoplasten mittels simultaner Messung der Spannungs-Dehnungs-Charakteristik und dielektrischer Kennfunktionen. Teil I: Schädigungsphänomene infolge mechanischer Belastung und Möglichkeiten der experimentellen Bewertung

Evaluation of damage effects in thermoplastics by means of simultaneous measurements of stress-strain characteristics and dielectric properties. Part I: Damage effects due to mechanical loading and possibilities of experimental evaluation The first part describes the mechanism of damage and failure of thermoplastics during mechanical loading. It will discussed the typical loading limits for characterization of structural changes due to quasistatic tests. In order to quantify the damage and failure effects in terms of critical stress or strain the experimental possibilities will described.