An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models
TL;DR: In this paper, a methodology to determine the constitutive parameters for the simulation of progressive delamination is proposed, which accounts for the size of a cohesive finite element and the length of the cohesive zone to ensure the correct dissipation of energy.
About: This article is published in Engineering Fracture Mechanics.The article was published on 2007-07-01. It has received 1314 citations till now. The article focuses on the topics: Finite element method & Delamination.
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TL;DR: In this article, the authors highlight the limitations of existing formulae used to predict numerical cohesive zone length and demonstrate modifications necessary for improved accuracy, and provide a minimum number of interface elements within the cohesive zone.
446 citations
TL;DR: In this paper, the influence of the CZM shape (triangular, exponential or trapezoidal) used to model a thin adhesive layer in single-lap adhesive joints, for an estimation of its influence on the strength prediction under different material conditions.
436 citations
Cites background from "An engineering solution for mesh si..."
..., as a 0 0 elastic behaviour up to tn (tension) or ts (shear) and subsequent stiffness reduction, related to the progressive material degradation up to final failure [37,38]....
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TL;DR: In this paper, a methodology for predicting accurately the propagation of delamination under mixed-mode fracture with cohesive elements is proposed, where relations between the interlaminar strengths and the penalty stiffness are proposed which ensure a correct energy dissipation when delamination propagates.
402 citations
Cites methods from "An engineering solution for mesh si..."
...The most common approaches that have been proposed to simulate delamination are the Virtual Crack-Closure Technique (VCCT), either by post-processing finite element results [3] or by using special-purpose VCCT elements [4], and cohesive finite elements [5–11]....
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...Numerical representation of the CZM Cohesive finite elements capture the initiation and propagation of delamination [5–16] using the concept of CZM....
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TL;DR: In this article, a damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed, based on a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate.
Abstract: A damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed. The basis for the formulation is a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate dA/dN. The damage state is obtained as a function of the loading conditions as well as the experimentally-determined coefficients of the Paris law crack propagation rates for the material. It is shown that by using the constitutive fatigue damage model in a structural analysis, experimental results can be reproduced without the need of additional model-specific curve-fitting parameters.
339 citations
TL;DR: In this paper, a high-fidelity three-dimensional composite damage model was developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit, to predict both low-velocity impact damage and CAI strength of composite laminates.
Abstract: Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.
327 citations
Cites background or methods from "An engineering solution for mesh si..."
...4 10 / p k E t N mm α = = × was chosen according to [30], where α is a coefficient set at 50, 22 E is the transverse Young’s modulus of the composite and p t is the thickness of an adjacent double-ply (0....
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...[30] proposed the use of a lower interface strength with a coarser mesh size, which can still accurately capture the softening behaviour ahead of the crack tip....
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...To represent the distribution of tractions ahead of the crack tip accurately, at least three elements in the cohesive zone are required [30]....
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References
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TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
Abstract: Y ielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
6,830 citations
01 Jan 2008
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.
5,564 citations
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
5,505 citations
TL;DR: In this paper, the authors present a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discuss the results obtained thereby, and the object of the theory is the study of the equilibrium of solids in the presence of cracks.
Abstract: Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.
4,677 citations
Book•
29 Dec 1997
TL;DR: In this paper, the authors used the Weibull-type approach to measure the effect of size effect on structural strength of a crack and its size effect in terms of the number of cracks and the size of the cracks.
Abstract: Why Fracture Mechanics? Historical Perspective Reasons for Fracture Mechanics Approach Sources of Size Effect on Structural Strength Quantification of Fracture Mechanics Size Effect Experimental Evidence for Size Effect Essentials of LEFM Energy Release Rate and Fracture Energy LEFM and Stress Intensity Factor Size Effect in Plasticity and in LEFM Determination of LEFM Parameters Setting Up Solutions from Closed-Form Expressions Approximate Energy-Based Methods Numerical and Experimental Procedures to Obtain KI and G Experimental Determination of KIc and Gf Calculation of Displacements from KI-Expressions Advanced Aspects of LEFM Complex Variable Formulation of Plane Elasticity Problems Plane Crack Problems and Westergaard's Stress Function The General Near Tip Fields Path-Independent Contour Integrals Mixed Mode Fracture Criteria Equivalent Elastic Cracks and R-Curves Variability of Apparent Fracture Toughness for Concrete Types of Fracture Behavior and Nonlinear Zone The Equivalent Elastic Crack Concept Fracture Toughness Determination Based on Equivalent Crack Concepts Two Parameter Model of Jenq and Shah R-Curves Stability Analysis in the R-Curve Approach Determination of Fracture Properties from Size Effect Size Effect in Equivalent Elastic Crack Approximations Size Effect Law in Relation to Fracture Characteristics Size Effect Method: Detailed Experimental Procedures Determination of R-Curve from Size Effect Cohesive Crack Models Basic Concepts in Cohesive Crack Model Cohesive Crack Models Applied to Concrete Experimental Determination of Cohesive Crack Properties Pseudo-Boundary-Integral Methods for Mode I Crack Growth Boundary-Integral Methods for Mode I Crack Growth Crack Band Models and Smeared Cracking Strain Localization in the Series Coupling Model Localization of Strain in a Softening Bar Basic Concepts in Crack Band Models Uniaxial Softening Models Simple Triaxial Strain-Softening Models for Smeared Cracking Crack Band Models and Smeared Cracking Comparison of Crack Band and Cohesive Crack Approaches Advanced Size Effect Analysis Size Effect Law Refinements Size Effect in Notched Structures Based on Cohesive Crack Models Size Effect on the Modulus of Rupture of Concrete Compressing Splitting Tests of Tensile Strength Compression Failure Due to Propagation of Splitting Crack Band Scaling of Fracture of Sea Ice Brittleness and Size Effect in Structural Design General Aspects of Size Effect and Brittleness in Concrete Structures Diagonal Shear Failure of Beams Fracturing Truss Model for Shear Failure of Beams Reinforced Beams in Flexure and Minimum Reinforcement Other Structures Effect of Time, Environment, and Fatigue Phenomenology of Time-Dependent Fracture Activation Energy Theory and Rate Processes Some Applications of the Rate Process Theory to Concrete Fracture Linear Viscoelastic Fracture Mechanics Rate-Dependent R-Curve Model with Creep Time-Dependent Cohesive Crack and Crack Band Models Introduction to Fatigue Fracture and Its Size Dependence Statistical Theory of Size Effect and Fracture Process Review of Classical Weibull Theory Statistical Size Effect Due to Random Strength Basic Criticisms of Classical Weibull-Type Approach Handling of Stress Singularity in Weibull-Type Approach Approximate Equations for Statistical Size Effect Another View: Crack Growth in an Elastic Random Medium Fractal Approach to Fracture and Size Effect Nonlocal Continuum Modeling of Damage Localization Basic Concepts in Nonlocal Approaches Triaxial Nonlocal Models and Applications Nonlocal Model Based on Micromechanics of Crack Interactions Material Models for Damage and Failure Microplane Model Calibration by Test Data, Verification, and Properties of Microplane Model Nonlocal Adaptation of Microplane Model or Other Constitutive Models Particle and Lattice Models Tangential Stiffness Tensor via Solution of a Body with Many Growing Cracks References Index
2,255 citations