Homogenization of diffuse delamination in composite laminates

Diffuse delamination induced by transverse cracking is usually the secondary damage mode when a composite laminate experiences tensile loading. The fist damage mechanism in such a laminate is transverse cracking which has been widely investigated with both analytical methods and " mechanism-based" constitutive laws. Delamination induced by matrix cracking is already studied extensively by analytical approaches, however, a proper homogenization way has not been proposed yet. In this paper, a modification to an available cohesive constitutive law is proposed which is capable of considering the effect of diffuse delamination without the necessity of consideration of an actual discontinuity between the layers. The proposed constitutive law is then compared against its equivalent models containing interlaminar discontinuity and it is shown that the obtained results from both models are in good. Then the proposed modification is used in Double Cantilever Beam (DCB) specimen and the obtained results are found coincident with the equivalent model with diffuse discontinuities at the interface. Finally, a damaged cross-ply laminate is modeled under the boundary conditions of tensile loading and also 3-point bending with and without the proposed cohesive modification. In tensile loading, the results of both cases are similar; however, it is shown that in bending, the unmodified cohesive law predicts the lateral stiffness larger than the proposed modification. The lateral stiffness of the equivalent model with discontinuities as crack indicates that the proposed modification is able to properly consider the lateral stiffness decrease

Shear-Mode Viscoelastic Damage Formulation Interface Element

In this paper, a viscoelastic-damage cohesive zone model is formulated and discussed. The interface element constitutive law has two elastic and damage regimes. Viscoelastic behaviour has been assumed for the shear stress in the elastic regime. Three element Voigt model has been used for the formulation of relaxation modulus of the material. Shear Stress has been evaluated in the elastic regime of the interface with integration over the history of the applied strain at the interface. Damage evolution proceeds according to the bilinear cohesive constitutive law up to the complete decohesion. Numerical examples for one element model has been presented to see the effect of parameters on cohesive constitutive law

Numerical modeling of diffuse transverse cracks and induced delamination using cohesive elements

This article is devoted to the modeling of spread kind of damages such as matrix cracking and induced delamination in symmetric and asymmetric cross-ply laminates of composite materials using cohesive elements. For matrix crack modeling, parallel rows of cohesive elements are used between every row of 2D elements in 90° layers. Delamination is also modeled by cohesive elements at the 90°/0° interface. Since matrix cracking is a diffuse kind of damage mechanism, application of cohesive elements is not straightforward, and special techniques are necessary to resolve the modeling difficulties. For this purpose, two techniques of "bisecting" and "random distribution of strength of cohesive elements" are proposed here. Both techniques are applied to various symmetric laminates of [0/903]s and [90n/0]s (n=1 to 3). The predicted stiffness and damage progresses from both techniques are in good agreement with the experimental results. Then, asymmetric cross-ply laminates of [90n/0] (n=1 to 3) are analyzed to show the capability of this method in progressive damage analyses. The proposed method is less restricted in comparison with available micromechanical methods and is able to predict damage initiation, propagation and damage-mode transition for any symmetric and asymmetric cross-ply sequence. Therefore, this method can be used for development of "in-plane damage" of constitutive laws especially when specimens are subjected to complex loading and boundary conditions

Micro/macro Approach for Prediction of Matrix Cracking Evolution in Laminated Composites

A computational constitutive model is presented to predict matrix cracking evolution in laminates under in-plane loading. Transverse cracks are treated as separate discontinuities in the micro-model that provides damage parameters for the macro-model. Both micro- and macro-models are implemented using finite element analysis, specifically, ANSYS, to avoid limitation of analytical micro-modeling. The computational cost of the micro-model is limited to constructing a database of micro-model predictions a priori. The macro-model is simply a finite element analysis discretization of the structure using plane stress or shell elements in ANSYS. The macro-model queries the database, which effectively becomes a constitutive model. The damage surfaces in the database are obtained from the results of large number of finite element micro-scale (unit-cell) analyses. The proposed procedure is implemented in ANSYS as a usermaterial subroutine for transverse crack initiation and propagation in symmetric cross-ply and [0r/(θ/-θ)s/0n]s laminates under in-plane loads. This method is also examined to study matrix crack evolution in tensile specimen with open hole, and the results found to be in good agreement with available experimental data

Experimental and numerical study of oblique transverse cracking in cross-ply laminates under tension

The first damage mode in cross-ply laminates under tension is broadly accepted as transverse cracks normal to the loading direction in the 90° layers, but there is not the same agreement about the second damage mode. While most of the analytical and experimental results are based on delamination induced by transverse cracking, another type of damage, oblique cracks within the 90° layers, has also been observed as the second damage mode in [0/904]s laminates. To understand the cause of this phenomenon, FE analyses considering damage development at the interfaces were performed. The obtained results indicate that the main reason for the oblique cracking damage mode is the higher toughness of the material in mode-II compared with mode-I: when the value of shear toughness is close to the opening toughness, the second damage mode in cross-ply laminates under tensile loading is delamination induced by transverse cracks, however, if the difference between the two values is large, oblique cracks in the 90°layers are likely to appear. In the specific tested and analysed laminate, if the mode II toughness is double the mode I toughness, oblique cracking occurs but if the values of mode I and mode II toughness are close, delamination is the second damage mode

Interlaminar Fracture Toughness Evaluation in Glass/Epoxy Composites Using Acoustic Emission and Finite Element Methods

© 2014, ASM International. Delamination is one of the most common modes of failure in laminated composites and it leads to the loss of structural strength and stiffness. In this paper, mode I, mode II, and mixed of these pure modes were investigated using mechanical data, Finite Element Method (FEM) and Acoustic Emission (AE) signals. Experimental data were obtained from insitu monitoring of glass/epoxy laminated composites with different lay-ups when subjected to different modes of failure. The main objective was to investigate the behavior of delamination propagation and to evaluate the critical value of the strain energy which is required for onset of the delamination (GC). For the identification of interlaminar fracture toughness of the specimens, four methods were used: (a) ASTM standard methods, (b) FEM analysis, (c) AE method, and (d) sentry function method which is a function of mechanical and AE behaviors of the specimens. The results showed that the GC values obtained by the sentry function method and FEM analysis were in a close agreement with the results of nonlinearity methods which is recommended in the ASTM standards. It was also found that the specimens under different loading conditions and various lay-up have different GC values. These differences are related to different stress components distribution in the specimens which induce various damage mechanisms. Accordingly, stress components distribution obtained from FEM analyses were in agreement with SEM observations of the damaged surfaces of the specimens

Numerical Aspects of Delamination Modeling Using Interface Elements

In spite of a vast background on cohesive constitutive law and its use for various analyses such as delamination in composite laminates, some numerical aspects of that have been less explored and reported in the literature. The aim of this paper is to study the phenomenon of spurious stress oscillation and also dominant process zone (where damage has its most significant evolution) in delamination modeling. For this purpose, distribution of normal stress and damage parameter of different DCB specimen are analyzed. Distribution of stress around the process zone indicates spurious oscillation just ahead of the delamination tip where damage parameter is zero and no effect of this phenomenon is seen on results of applied load versus opening displacement. Additionally, it is shown that larger values of penalty stiffness lead in smaller length of dominant process zone and very large values of penalty stiffness pushes the distribution of damage parameter to become step-like function. Authors believe that this effect is in fact the main reason of un-converged solution of models with too large penalty values

Comprehensive progressive damage analyses of mixed-mode repaired panels - How composite patch sizes and layups affects restarting fatigue crack growth

In this paper, comprehensive progressive damage analyses are performed to evaluate the effects of patch sizes and layups on restarting crack growth of single-side repaired aluminum panels with central inclined cracks under high cycle fatigue loading. Complicated nonlinear damage behavior of adhesive bonding, composite patch, mixed-mode cracks, and fatigue loadings require precise numerical tools to consider and analyze the coupling effects of various damages on fatigue life of such complex component. In progressive damage analysis, high cycle fatigue cohesive zone modeling is used for debonding of patch, and high cycle fatigue continuum damage model used for composite patches. Practical composite patch layups and sizes are selected in huge number of models, and the restarting crack growth life is predicted. The obtained results show the possibility of increasing the restarting crack growth life using an appropriate composite patch layup and geometry dimensions.</p