Meso-scale Damage Research Articles

A probabilistic mesoscale damage detection in polycrystals using a random matrix approach

This article is concerned with a probabilistic mesoscale damage detection in polycrystals. For this purpose, we make use of a stochastic model describing the linear elasticity matrix of material at the mesoscale. The model is constructed using a maximum entropy principle and random matrix theory and allows one to directly construct a probabilistic model for the system random matrices characterizing the constitutive behavior of the system. First, the theoretical framework and upscale scheme in the construction of the model are briefly reviewed. For each case of healthy and damaged materials, where the damage is introduced in the form of intergranular microcavities, the random matrix model is calibrated by performing simulations on an ensemble of statistical volume elements of microstructure. The calibrated models are then used in a simple coarse-scale simulation in order to explore the sensitivity of the model in detecting the location of mesoscale damages. The result shows that in most cases, one can identify the location of cracks by comparing the probabilistic description of a suitable response quantity of interest predicted for both healthy and damaged systems. Such a probabilistic description is suitable for detecting signature of fine-scale defects where the consequences are reflected at the coarse scale in the form of random fluctuations around the mean behavior. The model can be used as a predictive tool in the context of structural health monitoring and damage prognosis of metallic systems.

Multiscale modeling of matrix cracking coupled with interfacial debonding in random glass fiber composites based on volume elements

A multiscale numerical approach is established to model damage in random glass fiber composites. A representative volume element of a random glass fiber composite is employed to analyze microscale damage mechanisms, such as matrix cracking and fiber-matrix interfacial debonding, while the associated damage variables are defined and applied in a mesoscale stiffness reduction law. The macroscopic response of the homogenized mesoscale damage model is investigated using finite element analysis and validated through experiments. A case study of a random glass fiber composite plate containing a central hole subjected to tensile loading is performed to illustrate the applicability of the multiscale damage model.

OS0614 CFRP積層板のメゾスケール損傷発展シミュレーション

There has been much interest in Carbon Fiber Reinforced Plastics (CFRP) for its aerospace applications because of its high specific stiffness and strength. For adequate evaluation of its strength, that is indispensable for mechanical design, the authors have proposed meso-scale damage analysis, handling fiber bundle and matrix separately. In this paper, we demonstrate a damage simulation of quasi-static punch test of 12-layered CFRP laminates, which includes resin damage, delamination damage, and fiber bundle failure.

212 構成層厚の異なるCFRPアングルフライ積層板の力学的特性(0S12-2高分子系複合材料の成形と力学的特性II,0S12高分子系複合材料の成形と力学的特性)

We estimate effects of ply thickness in mechanical properties and damage evolution of CFRP angle-ply laminates under various tensile loading. It should be noted that the laminate thickness is almost the same, but the ply thickness are quite different. Monotonic tensile tests , cyclic loading-unloading tensile tests and stress relaxation tensile tests are performed on [(±)_12]_s(t-O.O5prepregx48plies), [(±)_4]_s(t-O.15prepregxl6plies) and [(+θ_4/(-θ)_4]_s (t-0.15prepregxl6plies) T700SC/2500 carbon/epoxy laminates with various fiber directions (θ=30, 40, 45, 50 and 67.5°) .Ply thickness is expressed as t-0 05, t-0 15 and t-0 6, respectively. Damage evolution can be determined by cyclic loading-unloading tests. We use mesoscale damage model to investigate damage evolution in CFRP laminates. We discuss effect of ply thickness on mechanical property of angle-ply laminates. Laminates have thin ply thickness showed high strength and fracture strain.

Analysis of meso-scale damage and crack for CuW alloys induced by thermal shock

Abstract Considering the mismatch of coefficient of thermal expansion (CTE) of Cu and W phase and temperature gradient, internal and external thermal load are applied on meso-scale 2D representative volume element (RVE) of CuW alloys under thermal shock, respectively. Void volume fraction (VVF) and VVF induced crack are determined by finite element method (FEM) utilizing Gurson–Tvergaard–Needleman (GTN) model, and the driving forces for damage nucleation and growth are analyzed with normal and shear stress as well. The simulation results show that damage and damage induced crack initiate from the vertex of W grain and grow along W/Cu interface, then propagate into Cu phase. After thermal shock experiment on CuW specimen by high voltage arc, micro cracks present along W/Cu interfaces and inside Cu phase, which is in good agreement with simulation results.

An Impact Protective Structure with Bistable Links

This article discusses a protective structure of a special morphology with an advanced impact resistance. We use a ‘bistable’ structure that is designed to have a non-unique stress–strain relation. When the strain reaches a threshold, some parts (sacrificial elements) yield and subsequently fail and the remaining parts (waiting elements) become active; the waiting elements carry the load and preserve structural integrity. Damage in bistable structures is more stable; the cracks do not develop due to yielding of structural elements and damage delocalization. The damage spreads in a larger region than in a conventional structure, and the load is redistributed. As a result of these effects, more impact energy is absorbed. We describe the response of bistable structures in macro- and microscales, numerically investigate a problem of projectile impacting a protective net, and introduce a mesoscale damage tensor that measures the degree of damage in a small region. We compare the structural responses of the bistable and conventional structure depending on mass and speed of the projectile. Typically, the bistable structure dissipates more energy by creating a partial damage in a large area.

Multi-scale analyses on seismic damage and progressive failure of steel structures

This paper is aimed to develop a numerical procedure for multi-scale analyses on seismic damage and progressive failure process in steel structures by considering meso-scale damage evolution based on CDM constitutive model at vulnerable locations. The mechanism of seismic damage or local progressive failure and their effect on nonlinear dynamic behavior of structures are then explored with the developed procedure. The multi-scale modeling of structural damage is developed to describe the phenomena that some joint parts at vulnerable locations with meso-defects in a structure show nonlinear damage evolution or local failure due to stress concentration while mostly parts of the structure remain elastic and show linear response. A ductile damage constitutive model is chosen as the description of meso-scale damage evolution in the numerical analysis on damage and progressive failure of steel structures under seismic loading, and the developed numerical procedure is implemented with the UMAT subroutine to introduce the damage constitutive equations and incorporate into multi-scale computations of seismic response performed with the software ABAQUS. Effects of meso-scale damage evolution on seismic response and progressive failure are analyzed, respectively, for a dog-bone joint component and a truss structure under ECCS cyclic loading with the developed numerical procedure. The results show that, the developed numerical procedure is available for analyses on seismic damage and progressive failure, and is useful for exploring mechanism of seismic damage and their effect on nonlinear dynamic behavior of structures under seismic excitations with micro-seismic scale intensities or several earthquake actions. The effect of evolving damage on the material degradation gives reasonable explanations for the phenomenon of large structural deformation and progressive failure under seismic loading. The global carrying capacity of the structure decreases with the increase in damaged area and progressive failure at the welded joint or other vulnerable areas, which at last leads to the occurrence of structure failure.

1504 FRP積層平板の強度評価に対するメゾスケール損傷解析の適用性(OS15. 複合材料における計算力学(1),オーガナイズドセッション講演)

1504 FRP積層平板の強度評価に対するメゾスケール損傷解析の適用性(OS15. 複合材料における計算力学(1),オーガナイズドセッション講演)

Moving finite element analyses for fast crack propagation in sheet metal

The conventional fracture mechanics parameters K IC and/or J IC are used as fracture toughness criteria necessary for the start of crack propagation under plane strain conditions. These criteria are defined only for small-scale yielding or infinitesimal deformation, though actual fractures involve large plastic deformation. Hence, measurement of fracture resistance during crack propagation is difficult with the conventional parameters. Estimating the mechanical conditions around the propagating crack tip is very useful for reducing damage during accidental fracture. Therefore, establishing a criterion for crack propagation with large-scale yielding is very important for not only science fields but also some industrial fields. For fractures with large-scale yielding, micro- or mesoscale damage processes in the crack tip vicinity have to be considered. In this study, Gurson's constitutive model for void occurrence and growth was introduced into the finite element method to discuss failure behavior in the crack tip vicinity. Fast crack propagation behavior under high-speed deformation was simulated using the moving finite element method based on the Delaunay automatic triangulation. The excellent far-field integral path independence of the T* integral was verified for pure mode I fast crack propagation and non-straight crack propagation under mixed mode conditions. The void growth conditions near the crack propagation path were evaluated.

Impact damage in layered glass

High-velocity impact onto a layered glass target produces a very extensive damage pattern exhibiting many distinct morphologies. Material around the penetration cavity is finely comminuted. Under the arrested projectile, the glass is largely intact with spoke-like fracture regions. Around the projectile cavity, needle fragments are formed; they are radial in outer layers and circumferential in inner layers. Extensive radial cracks occur in all layers, but the spacing and frequency of transverse fractures change in each layer. Damage from radial cracks also progresses from being hoop-stress-induced to flexural-induced through the depth of the target. Fan and dicing cracks occur near the periphery of the target. Mesoscale damage features include conventional mist and hackle markings indicating very fast cracks. The map of damage presented herein should be a valuable reference for attempts to model impact damage of glass.

An anisotropic mechanical fatigue damage evolution model for Pb-free solder materials

Evaluating state of damage in a ductile material as it experiences mechanical fatigue and cyclic loading poses much complexity, and has been the subject of many researches. This study revisits the anisotropic damage model developed by Lemaitre [Lemaitre, J. 1992. A course on damage mechanics. Springer-Verlag Publishing, Berlin] and proposes to use his model combined with two damage models, a micro-mechanics and mechanism-based damage evolution model (Energy Partitioning Damage Evolution (EPDE) [Ladani, L.J., Dasgupta, A., 2008b. A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials. Int. J. Fatigue 2. doi:10.1016/j.ijfatigue.2008.03.013]), and a Unified Creep Plasticity-based (UCP-based) model [ McDowell, D.L., Miller, M.P., Brooks, D.C., 1994. A unified creep plasticity theory for solder alloys. In: Schroeder, S.A., Mitchell, M.R. (Eds.), Fatigue of Electronic Materials, ASTM STP 1153. American Society of Testing and Materials, Philadelphia, pp. 42–59] to predict the state of damage. These two models are then examined for pure shear and are applied to Pb-free solder materials. New anisotropic damage model exponents are generated using experimental data for Pb-free solder for both EPDE and UPC-based models. The exponents generated using these anisotropic models are compared with exponents generated previously under the assumption of isotropic and homogenous damage evolution. These two models were verified using a 3-D Finite Element simulation of the test specimen. Load drops produced by EPDE and UCP-based models were compared with the experiments. The same test set up was used formerly (by Zhang [Zhang, Q. 2004. Isothermal Mechanical and Thermo-Mechanical Durability Characterization of Selected Pb-free solders. Ph.D. Dissertation Defense, Department of Mechanical Engineering, University of Maryland, College Park]) to generate the creep and plastic material properties, and E-P damage model constants for Pb-free solders. Therefore, EPDE exponents that were generated in this study show a much closer correlation with the experimental results.

Flood risk analyses—how detailed do we need to be?

Applied flood risk analyses, especially in urban areas, very often pose the question how detailed the analysis needs to be in order to give a realistic figure of the expected risk. The methods used in research and practical applications range from very basic approaches with numerous simplifying assumptions up to very sophisticated, data and calculation time demanding applications both on the hazard and on the vulnerability part of the risk. In order to shed some light on the question of required model complexity in flood risk analyses and outputs sufficiently fulfilling the task at hand, a number of combinations of models of different complexity both on the hazard and on the vulnerability side were tested in a case study. The different models can be organized in a model matrix of different complexity levels: On the hazard side, the approaches/models selected were (A) linear interpolation of gauge water levels and intersection with a digital elevation model (DEM), (B) a mixed 1D/2D hydraulic model with simplifying assumptions (LISFLOOD-FP) and (C) a Saint-Venant 2D zero-inertia hyperbolic hydraulic model considering the built environment and infrastructure. On the vulnerability side, the models used for the estimation of direct damage to residential buildings are in order of increasing complexity: (I) meso-scale stage-damage functions applied to CORINE land cover data, (II) the rule-based meso-scale model FLEMOps+ using census data on the municipal building stock and CORINE land cover data and (III) a rule-based micro-scale model applied to a detailed building inventory. Besides the inundation depths, the latter two models consider different building types and qualities as well as the level of private precaution and contamination of the floodwater. The models were applied in a municipality in east Germany, Eilenburg. It suffered extraordinary damage during the flood of August 2002, which was well documented as were the inundation extent and depths. These data provide an almost unique data set for the validation of flood risk analyses. The analysis shows that the combination of the 1D/2D model and the meso-scale damage model FLEMOps+ performed best and provide the best compromise between data requirements, simulation effort, and an acceptable accuracy of the results. The more detailed approaches suffered from complex model set-up, high data requirements, and long computation times.

A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials

This study presents an approach to predict the degree of material degradation and the resulting changes in elastic, plastic and creep constitutive properties of viscoplastic materials, during cyclic loading in micro-scale applications. The objective of the study is to address the initiation and growth of homogeneous meso-scale damage, in the form of distributions of micro-cracks and micro-voids, due to cyclic, plastic (rate-independent inelastic) and creep (rate-dependent inelastic) deformations in viscoplastic materials and to evaluate the resulting changes in the effective meso-scale elastic, plastic and creep constitutive properties. An energy partitioning damage evolution (EPDE) model is proposed to describe the viscoplastic damage evolution. Development of the EPDE model constants is then demonstrated for a Pb-free solder, based on cyclic fatigue test data. Application of the EPDE model is demonstrated for solder joint fatigue during thermal cycling of a ball grid array (BGA) electronic assembly. A 3D viscoplastic finite element analysis is conducted, and damage evolution is modeled using a successive initiation (SI) technique reported earlier by the authors. In this approach, the local (meso-scale) material properties are progressively degraded and highly damaged sections of the macro-scale structure are ultimately eliminated, using the EPDE model. Prediction of damage initiation and propagation is presented both with and without property updating, for comparison purposes. The analysis shows that the EPDE model can realistically capture the softening observed during cyclic loading.

Microstructure, deformation and failure of polymer bonded explosives

Polymer bonded explosives (PBXs) are highly particle filled composite materials comprised of explosive crystals and a polymeric binder (ca. 5–10% by weight). The microstructure and mechanical properties of two pressed PBXs with different binder systems were studied in this paper. The initial microstructure of the pressed PBXs and its evolution under different mechanical aggressions were studied, including quasi-static tension and compression, ultrasonic wave stressing and long-pulse low-velocity impact. Real-time microscopic observation of the PBXs under tension was conducted by using a scanning electron microscope equipped with a loading stage. The mechanical properties under tensile creep, quasi-static tension and compression were studied. The Brazilian test, or diametrical compression, was used to study the tensile properties. The influences of pressing pressures and temperatures, and strain rates on the mechanical properties of PBXs were analyzed. The mesoscale damage modes in initial pressed samples and the samples insulted by different mechanical aggressions, and the corresponding failure mechanisms of the PBXs under different loading conditions were analyzed.

Damage development in composites with large stress gradients

Implementation of a meso-scale damage model into the commercial finite element code ABAQUS via user-defined FORTRAN subroutines is described, and the results of investigations on damage development in structural configurations with large stress gradients are presented for carbon-fiber/polymer-matrix composites. The implemented model, which involves damage in both the meso-scale layer and an interface between the layers, is applied in a study of damage growth in finite-width angle-ply coupons and a composite panel with a terminated stiffener. The definition and evolution of state-dependent variables for layer damage is accomplished by means of a user-defined subroutine and the damageable interface is accomplished by using a user-defined element. It is demonstrated that as the fiber orientation progresses from 10 to 45°, the mode of damage changes from interlaminar damage, (i.e. delamination) to intralaminar damage, consistent with experimental observations. Analysis of damage development in the composite panel subjected to uniform compression shows that interlaminar shear stresses produce delamination at the skin-stiffener interface before failure of the panel due to tensile fiber rupture,— again consistent with experimental observations.

Damage evolution in [±45] s laminates with fiber rotation

The competing effects of increasing stiffness due to fiber rotation and decreasing stiffness due to damage evolution are incorporated into the Ladevèze mesoscale damage model to study the large strain response of [±45] s laminates of IM7-K3B, graphite-fiber/polyimide-matrix composite. It is shown that both of these competing effects are significant and the lack of their consideration can result in significant error when predicting large strain, non-linear response. Predictions of the model with and without fiber rotation are compared with experimental results for the tensile response of [±45] s laminates. It is also shown that variations in cross-sectional area of test specimens plays an important role in the large strain response of this high Poisson-ratio laminate. Improved correlation between theory and experiment is demonstrated when all competing effects are included in the analysis. The study includes predictions of stresses and damage variables in the individual layers of the laminate as a function of the modeling approach.

An elastoplastic constitutive relation of whisker-reinforced composite for meso damage: Part II – failure surfaces

An elastoplastic constitutive relation of whisker-reinforced composite was derived in Part I of this work [H.Q. Liu, N.G. Liang, An elastoplastic constitutive relation of whisker-reinforces composite for meso damage: Part I – formulation, J. Theoret. Appl. Fracture Mech. 33 (2000) 191–198]. Specific applications of this constitutive equation will be made to address mesoscale damage. Analyzed particularly is the relation between failure surface and dominant mechanism of brittle composites. The damage-induced anisotropy is exhibited using the damage distribution of whiskers in the orientation space. Qualitative agreement is obtained between the prediction and experimental results of carbon/epoxy laminates [S.R. Swanson, Introduction to Design and Analysis with Advanced Composite Materials, Prentice-Hall, Upper Saddle River, New Jersey, 1997].

Identification and forecast of delamination in composite laminates by an interlaminar interface model

For the forecasting of delamination initiation and propagation, a previously defined meso-scale damage model of composite laminates is used. At the meso scale, the laminate is described as an assembly of damageable layers and interlaminar interfaces. The aim of this work is to identify precisely the interlaminar interface model for ±θ interfaces, with θ = 0 °, 22.5 ° and 45 ° being the relative directions of the fibres of adjacent plies. This identification is based on initiation and propagation delamination tests. Our analysis of the conventional propagation tests makes use of the links existing between the critical-energy release rates and some of the model's parameters. In taking into account the part of the energy dissipated inside the layers, the interfaces can be classified into two categories: the 0 °/0 ° interfaces of brittle behaviour, and the interfaces at disorientated angles whose criticalenergy release rate is greater. Standard edge-delamination tension tests are also conducted and analysed in order to identify the other parameters of the interface damage model.

Studies For Hierarchical Ductile DamageSimulations

Three levels of damage interaction and complexity are investigated, using two dimensional simulation and experiments, to gain insight into ductile damage and fracture. Interactions between two holes are studied in detail to assess strain hardening influence and applied load. Pseudo-random sixteen hole arrays are used to examine nonuniform localization patterns. Massively parallel cellular automata are used to simulate complex mesoscale damage kinematics.