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Ramesh Talreja - One of the best experts on this subject based on the ideXlab platform.
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a synergistic Damage Mechanics approach to mechanical response of composite laminates with ply cracks
Journal of Composite Materials, 2013Co-Authors: Chandra Veer Singh, Ramesh TalrejaAbstract:We treat selected test cases in the third world wide failure exercise by the approach described as synergistic Damage Mechanics. This approach utilizes microMechanics and continuum Damage Mechanics to predict the overall mechanical response of composite laminates with ply cracking in multiple orientations. The material constants needed in the continuum Damage mechanic formulation are calculated from stiffness property changes incurred in a reference laminate. For other laminate configurations, the stiffness changes are derived using a relative constraint parameter which is calculated from the constraint on the opening displacement of ply cracks within the given cracked laminate evaluated numerically by a finite element analysis of appropriately constructed representative unit cell. The number density of ply cracks (cracks per unit length normal to the crack planes) under quasi-static loading is calculated by an energy-based approach. Finally, the stress–strain response of a laminate is determined by combi...
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a synergistic Damage Mechanics approach for composite laminates with matrix cracks in multiple orientations
Mechanics of Materials, 2009Co-Authors: Chandra Veer Singh, Ramesh TalrejaAbstract:Abstract This paper treats the problem of elastic response of composite laminates containing matrix cracks in plies of multiple orientations. The approach taken has been described as synergistic Damage Mechanics (SDM) and has been previously illustrated for [ 0 m / ± θ n / 0 m / 2 ] s laminates with cracks of equal density in + θ and - θ plies [Singh, C.V., Talreja, R., 2008. Int. J. Solids Struct. 45(16), 4574–4589]. The current work extends the approach to [ 0 m / ± θ n / 90 r ] s and [ 0 m / 90 r / ± θ n ] s laminates with cracks additionally in the 90°-plies. The interaction between the ± θ -cracks and the 90°-cracks is analyzed in terms of the crack surface displacements using a three-dimensional finite element (FE) model and found to be significant only for crack orientations close to 90°. The stiffness degradation of the laminate with all cracking modes simultaneously present is formulated by continuum Damage Mechanics using a second order tensor characterization of Damage. The elastic moduli changes predicted by the SDM procedure are validated by independent three-dimensional FE calculations. For a particular case of quasi-isotropic [ 0 / 90 / ∓ 45 ] s laminate, the elastic moduli predictions are evaluated against experimental data. Finally, a parametric study is performed to examine the effects of ply thickness changes on stiffness properties.
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a synergistic Damage Mechanics approach to viscoelastic response of cracked cross ply laminates
International Journal of Damage Mechanics, 2004Co-Authors: Janis Varna, Andrejs Krasnikovs, Rajesh Kumar, Ramesh TalrejaAbstract:A synergistic Damage Mechanics approach, i.e., a combined continuum Damage Mechanics (CDM) and microMechanics approach, is developed to characterize the viscoelastic response of cross-ply laminates with transverse cracks. The approach relies upon a second-order tensor-based description of Damage wherein the crack opening displacement appears as an explicit function. The time variation of this function is calculated by microMechanics and is inserted into the continuum Damage formulation. The relaxation moduli calculated for fixed states of Damage (transverse crack density) by this approach agree well with independently calculated values by a CDM approach and finite element model.
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a synergistic Damage Mechanics analysis of transverse cracking in θ 904 s laminates
Composites Science and Technology, 2001Co-Authors: Janis Varna, Roberts Joffe, Ramesh TalrejaAbstract:Abstract The deformational response of [± θ /90 4 ] s laminates under longitudinal tensile loading is treated by a synergistic approach that combines continuum Damage Mechanics (CDM) and microMechanics. The constraint of θ ° plies on transverse cracks in 90° plies is represented by a crack-opening displacement (COD) parameter in the CDM model and is expressed in terms of the ply properties and ply thickness ratios on the basis of a finite-element calculation. A methodology is proposed for predicting the laminate stiffness variations with crack density and applied strain (or stress) for various values of ply orientation θ and is found to give good results.
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Damage Mechanics and fatigue life assessment of composite materials
International Journal of Damage Mechanics, 1999Co-Authors: Ramesh TalrejaAbstract:The present state of fatigue life assessment of composite materials is largely empirical. This paper discusses how the discipline of Damage Mechanics can elevate this status to a mechanisms-based methodology. Specific topics addressed are mechanisms of fatigue Damage, characterization of Damage and its evolution, criticality of Damage and prediction of fatigue life. Data and analysis results for cross ply laminates are used to illustrate and discuss the topics.
George Z Voyiadjis - One of the best experts on this subject based on the ideXlab platform.
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On the decomposition of the Damage variable in continuum Damage Mechanics
Acta Mechanica, 2017Co-Authors: George Z Voyiadjis, Peter I. KattanAbstract:Refinements and generalizations of the decomposition of the Damage variable are presented within the framework of continuum Damage Mechanics. It is assumed that Damage in a solid is due mainly to cracks and voids. The classical decomposition of the Damage variable into a Damage part due to cracks and another Damage part due to voids is examined and extended consistently and mathematically. This is further elaborated upon by considering a solid with three types of defects: cracks, voids, and a third defect that is unspecified. Initially, the decomposition issues are carried out in one dimension using scalars. But this is generalized subsequently for the general case of three-dimensional deformation and Damage using tensors. Finally, the special case of plane stress is illustrated as an example. It is shown that in the case of plane stress, two explicit decomposition equations are obtained along with a third implicit coupling equation that relates the various “crack” and “void” Damage tensor components.
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fatigue and fretting fatigue life prediction of double lap bolted joints using continuum Damage Mechanics based approach
International Journal of Damage Mechanics, 2017Co-Authors: Ying Sun, George Z Voyiadjis, Fei Shen, Qingchun MengAbstract:Fatigue and fretting fatigue are the main failure mode in bolted joints when subjected to cyclic load. Based on continuum Damage Mechanics, an elastic–plastic fatigue Damage model and a fretting fa...
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new tensors for anisotropic Damage in continuum Damage Mechanics
Journal of Engineering Materials and Technology-transactions of The Asme, 2012Co-Authors: George Z Voyiadjis, Mohammed A. Yousef, Peter I. KattanAbstract:In this work, new proposed Damage tensors are studied in order to investigate the Damage effect variables in the mechanical behavior of materials. All cases studied in this work are defined in terms of the elasticity of the material and based on the hypotheses of both elastic strain equivalence and elastic energy equivalence. Moreover, the new proposed Damage tensors are anisotropically expressed in terms of the well-known Damage effect tensor M. The principal-valued Damage effect tensor is used to obtain the first scalar invariant of that tensor and its inverse, which are employed in expressing and verifying the new proposed Damage tensors. The study demonstrates that most of the new proposed Damage tensors are verified within the framework of continuum Damage Mechanics. In addition, new hybrid Damage tensors are proposed which are defined in terms of the Damage effect tensor and the new proposed Damage tensors. The new hybrid Damage tensors are eventually expressed in terms of the Damage effect tensor.
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micromechanical approach to Damage Mechanics of composite materials with fabric tensors
Composites Part B-engineering, 2007Co-Authors: George Z Voyiadjis, Ziad N Taqieddi, Pete I KattaAbstract:Abstract The purpose of this study is to apply continuum Damage Mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of Damage Mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of Damage of composite materials will allow for an enhanced and better understood physical meaning of Damage. The micromechanical approach will be used here to relate the Damage effect through fabric tensors to the behavior of composite materials. In this approach, Damage Mechanics is introduced separately to the constituents of the composite material through different constituents’ Damage effect tensors. The Damaged properties of the composite system as a whole can then be obtained by proper homogenization of the Damaged properties of the constituents. The derivation of a generalized formulation of Damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, Damage evolution for the one-dimensional tension case is also illustrated.
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continuum approach to Damage Mechanics of composite materials with fabric tensors
International Journal of Damage Mechanics, 2007Co-Authors: George Z Voyiadjis, Pete I Katta, Ziad N TaqieddiAbstract:The major objective of this work is to apply continuum Damage Mechanics introduced through the concept of fabric tensors to composite materials within the framework of elasticity theory. A model of directional data Damage Mechanics for composite materials is formulated using fabric tensors. The physical meaning of Damage is enhanced and understood better through the introduction of fabric tensors into the analysis of Damage of composite materials. The 'continuum approach' is used here to link the fabric tensors' Damage effect to the behavior of composite materials. In this approach, Damage with fabric tensors is introduced to the composite medium, where the latter is treated as a homogenized material. Also, the overall properties of the composite system as a whole are used without using the constituent properties. A generalized formulation of Damage evolution is derived in a mathematically consistent manner that is based on sound thermodynamic principles. A numerical example is presented to show the applicability. In addition, Damage evolution for the one-dimensional tension case is also illustrated.
Pete I Katta - One of the best experts on this subject based on the ideXlab platform.
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micromechanical approach to Damage Mechanics of composite materials with fabric tensors
Composites Part B-engineering, 2007Co-Authors: George Z Voyiadjis, Ziad N Taqieddi, Pete I KattaAbstract:Abstract The purpose of this study is to apply continuum Damage Mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of Damage Mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of Damage of composite materials will allow for an enhanced and better understood physical meaning of Damage. The micromechanical approach will be used here to relate the Damage effect through fabric tensors to the behavior of composite materials. In this approach, Damage Mechanics is introduced separately to the constituents of the composite material through different constituents’ Damage effect tensors. The Damaged properties of the composite system as a whole can then be obtained by proper homogenization of the Damaged properties of the constituents. The derivation of a generalized formulation of Damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, Damage evolution for the one-dimensional tension case is also illustrated.
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continuum approach to Damage Mechanics of composite materials with fabric tensors
International Journal of Damage Mechanics, 2007Co-Authors: George Z Voyiadjis, Pete I Katta, Ziad N TaqieddiAbstract:The major objective of this work is to apply continuum Damage Mechanics introduced through the concept of fabric tensors to composite materials within the framework of elasticity theory. A model of directional data Damage Mechanics for composite materials is formulated using fabric tensors. The physical meaning of Damage is enhanced and understood better through the introduction of fabric tensors into the analysis of Damage of composite materials. The 'continuum approach' is used here to link the fabric tensors' Damage effect to the behavior of composite materials. In this approach, Damage with fabric tensors is introduced to the composite medium, where the latter is treated as a homogenized material. Also, the overall properties of the composite system as a whole are used without using the constituent properties. A generalized formulation of Damage evolution is derived in a mathematically consistent manner that is based on sound thermodynamic principles. A numerical example is presented to show the applicability. In addition, Damage evolution for the one-dimensional tension case is also illustrated.
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advances in Damage Mechanics metals and metal matrix composites with an introduction to fabric tensors
2006Co-Authors: George Z Voyiadjis, Pete I KattaAbstract:Chapter 1. Introduction Part I: Isotropic Damage Mechanics - Scalar Formulation Chapter 2. Uniaxial Tension in Metals Chapter 3. Uniaxial Tension in Elastic Metal Matric Composites Chapter 4. Uniaxial Tension in Elasto-Plastic Metal Matric Composites: Vector Formulation of the Overall Approach Part II: Anisotropic Damage Mechanics - Tensor Formulation Chapter 5. Damage and Elasticity in Metals Chapter 6. Damage and Plasticity in Metals Chapter 7. Metal Matrix Composites - Overall Approach Chapter 8. Metal Matrix Composites - Local Approach Chapter 9. Equivalence of the Overall and Local Approaches Chapter 10. Metal Matrix Composites - Local and Interfacial Damage Chapter 11. Symmetrization of the Effective Stress Tensor Chapter 12. Experimental Damage Investigation Chapter 13. High Cyclic Fatigue Damage for Uni-Directional Metal Matrix Composites Chapter 14. Anisotropic Cyclic Damage-Plasticity Models for Metal Matrix Composites Part III: Advanced Topics in Damage Mechanics Chapter 15. Damage in Metal Matrix Composites Using the Generalized Model Cells Chapter 16. The Kinematics of Damage for Finite-Strain Elasto-Plastic Solids Chapter 17. A Coupled Anisotropic Damage Model for the Inelastic Response of Composite Materials Part IV: Damage Mechanics and Fabric Tensors Chapter 18. Damage Mechanics and Fabric Tensors Chapter 19. Continuum Approach to Damage Mechanics of Composite Materials with Fabric Tensors Chapter 20. Micromechanical Approach to Damage Mechanics of Composite Materials with Fabric Tensors Chapter 21. Experimental Study and Fabric Tensor Quantification of Micro-Crack Distributions in Composite Materials
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Damage Mechanics with fabric tensors
Mechanics of Advanced Materials and Structures, 2006Co-Authors: George Z Voyiadjis, Pete I KattaAbstract:A new formulation is presented to link continuum Damage Mechanics with the concept of fabric tensors within the framework of classical elasticity theory. A fourth-rank Damage tensor is used and its exact relationship to the fabric tensors is illustrated. A model of Damage Mechanics for directional data is formulated using fabric tensors. The applications of the new formulation to micro-crack distributions are well illustrated in two solved examples. In the first example, a micro-crack distribution is considered with its data represented by a circular histogram. The values of the fabric tensors and Damage tensor are calculated in this case. In the second example, two sets of parallel micro-crack distributions with two different orientations are investigated. In addition, a general hypothesis for Damage Mechanics is postulated. It is seen that the two available hypotheses of elastic strain equivalence and elastic energy equivalence may be obtained as special cases of the postulated general hypothesis. This ...
Bruce R Ellingwood - One of the best experts on this subject based on the ideXlab platform.
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continuum Damage Mechanics analysis of fatigue crack initiation
International Journal of Fatigue, 1998Co-Authors: Baidurya Bhattacharya, Bruce R EllingwoodAbstract:The crack initiation period in an originally defect-free component can be a significant portion of its total fatigue life. The initiation phase is generally believed to constitute the nucleation and growth of short cracks, but the threshold crack length at which initiation occurs lacks a uniform definition. Moreover, available methods for predicting fatigue Damage growth usually require an existing flaw (e.g. Paris law) and may be difficult to apply to the initiation phase. This paper presents a continuum Damage Mechanics-based approach that estimates cumulative fatigue Damage, and predicts crack initiation from fundamental principles of thermodynamics and Mechanics. Assuming that fatigue Damage prior to localization occurs close to a state of thermodynamic equilibrium, a differential equation of isotropic Damage growth under uniaxial loading is derived that is amenable to closed-form solution. Damage, as a function of the number of cycles, is computed in a recursive manner using readily available material parameters. Even though most fatigue data are obtained under constant amplitude loading conditions, most engineering systems are subjected to variable amplitude loading, which can be accommodated easily by the recursive nature of the proposed method. The predictions are compared with available experimental results.
Magd Abdel Wahab - One of the best experts on this subject based on the ideXlab platform.
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fretting fatigue crack initiation lifetime predictor tool using Damage Mechanics approach
Tribology International, 2013Co-Authors: Reza Hojjatitalemi, Magd Abdel WahabAbstract:Abstract Fretting fatigue is a combination of two complex mechanical phenomena. Fretting appears between components that are subjected to small relative oscillatory motions. Once these connected components undergo cyclic fatigue load, fretting fatigue occurs. In general, fretting fatigue failure process can be divided into two main portions, namely crack initiation and crack propagation. Fretting fatigue crack initiation characteristics are very difficult to detect because Damages such as micro-cracks are always hidden between two contact surfaces. In this paper Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Analyses (FEA) is used to find a predictor tool for fretting fatigue crack initiation lifetime. For this purpose an uncoupled Damage evolution law is developed to model fretting fatigue crack initiation lifetime at various fretting condition such as contact geometry, axial stress, normal load and tangential load. The predicted results are validated with published experimental data from literature.
