Evolution of Crack Density in Cross-Ply Laminates - Application of a Coupled Stress and Energy Criterion

2016 ◽  
Vol 713 ◽  
pp. 262-265
Author(s):  
Maria Kashtalyan ◽  
I.G. García ◽  
Vladislav Mantič
Keyword(s):  
Composite Laminates ◽  
Crack Density ◽  
Great Influence ◽  
Energy Criterion ◽  
Matrix Cracking ◽  
Transverse Cracks ◽  
Transverse Cracking ◽  
Finite Fracture Mechanics ◽  
Equivalent Constraint Model ◽  
Constraint Model

The first damage mode to appear in continuous fibre-reinforced composite laminates subjected to in-plane loading is usually transverse cracking, i.e. matrix cracking in the off-axis plies of the laminate. Since the density of transverse cracks has a great influence on the subsequent failure steps like delaminations, it is important to be able to predict it accurately. In this paper, the evolution of crack density with increasing external load is predicted using a combination of the Coupled Criterion of Finite Fracture Mechanics and the Equivalent Constraint Model.

scholarly journals Application of the Equivalent Constraint Model to Investigate Stiffness Properties of Transversally Cracked and Split Frp Laminates

1999 ◽  
Vol 8 (5) ◽  
pp. 096369359900800 ◽  
Author(s):  
M. Kashtalyan ◽  
C. Soutis
Keyword(s):  
Matrix Cracking ◽  
Shear Lag ◽  
Transverse Cracks ◽  
New Approach ◽  
Shear Lag Model ◽  
Transverse Cracking ◽  
Stiffness Properties ◽  
Lag Model ◽  
Equivalent Constraint Model ◽  
Constraint Model

A new approach based on the Equivalent Constraint Model (ECM) [ 1 ] of the damaged lamina is applied to investigate the stiffness degradation in [0m/90n]s laminates due to matrix cracking both in the 90° (transverse cracking) and 0° (splitting) plies. The advantage of the approach is that it avoids cumbersome consideration of a repeated laminate element defined by the intersecting pairs of transverse cracks and splits, intrinsic to the earlier developed models [ 2 – 6 ]. Instead, two coupled problems for ECM laminates are solved. The stress field in the damaged lamina is determined by means of an improved 2-D shear lag analysis, and the reduced stiffness properties are described with the help of Insitu Damage Effective Functions, for which closed form expressions are obtained. Comparison of the new ECM/2-D shear lag model with the earlier developed models shows a reasonable agreement.

scholarly journals A Study of Matrix Crack Tip Delaminations and their Influence on Composite Laminate Stiffness

1999 ◽  
Vol 8 (4) ◽  
pp. 096369359900800 ◽  
Author(s):  
Maria Kashtalyan ◽  
Costas Soutis
Keyword(s):  
Transverse Crack ◽  
Crack Density ◽  
Crack Tip ◽  
Implicit Functions ◽  
Transverse Cracks ◽  
Transverse Cracking ◽  
Stiffness Properties ◽  
Equivalent Constraint Model ◽  
Constraint Model ◽  
Stiffness Loss

Reduction of the stiffness properties of cross-ply [0m/90n]s laminates due to delaminations, growing at the 0/90 interface from the tips of transverse cracks in the 90° plies and splits in the 0° plies, is analysed by means of a theoretical approach based on the Equivalent Constraint Model (ECM). Reduced stiffness properties of the damaged lamina are derived as explicit functions of the crack density and relative delamination area associated with that lamina and implicit functions of the two damage parameters associated with the neighbouring laminae. Transverse crack tip delaminations are found to cause significant reduction in the laminate shear modulus and Poisson's ratio. Contribution of each damage mode (transverse cracking, transverse crack tip delaminations, splitting and split tip delaminations) into stiffness loss is established.

Analysis of Fatigue Damage Mechanisms and Residual Properties of Polymer Matrix Composites

2000 ◽  
Author(s):  
Costas Soutis ◽  
Maria Kashtalyan
Keyword(s):  
Composite Laminates ◽  
Polymer Matrix Composites ◽  
Matrix Cracking ◽  
Matrix Composites ◽  
Residual Properties ◽  
Stiffness Properties ◽  
Observed Damage ◽  
Equivalent Constraint Model ◽  
Constraint Model ◽  
Longitudinal Cracks

Abstract Resin dominated damage modes such as matrix cracking in the off-axis plies and matrix crack-induced local and edge delaminations are common failure mechanisms in composite laminates under tensile or thermal fatigue. Accurate prediction of the laminate stiffness and strength must consider all the above-mentioned damage modes. In the present paper, an approach is developed for the analysis of cross-ply laminates damaged by transverse and longitudinal cracks and transverse and longitudinal delaminations that initiate and grow along these cracks. It is based on the Equivalent Constraint Model (ECM) of the damaged ply and employs an improved 2-D shear lag method to determine the stress field in the cracked and locally delaminated ply. The method is applied to predict residual stiffness properties of cross-ply graphite/epoxy laminates using experimentally observed damage patterns.

scholarly journals A variational approach for predicting initiation of matrix cracking and induced delamination in symmetric composite laminates under in-plane loading

2018 ◽  
Vol 25 (5) ◽  
pp. 855-868 ◽  
Author(s):  
Seyed Siamak Taghavi Larijani ◽  
Amin Farrokhabadi
Keyword(s):  
Composite Laminates ◽  
Variational Approach ◽  
Crack Density ◽  
Current Approach ◽  
Matrix Cracking ◽  
Stress Fields ◽  
Complementary Energy ◽  
Transverse Cracks ◽  
Critical Crack ◽  
Practical Applications

AbstractThis paper discusses the formation of matrix cracking and induced delaminations in a $[\phi _m^{(2)}/\psi _n^{(1)}]s$ laminate subject to arbitrary in-plane loading using a variational approach. To this end, the effects of delaminations coming from the tips of transverse cracks in the middle sublaminates are considered to specify the critical crack density points and finally understand which modes of damage are prospects for various lay-ups in the presence of transverse cracks as well as induced delamination. After deriving a very good approximation of the principle of minimum complementary energy by considering complex equations, the stress fields are provided. In this analysis, a unit cell in the ply level of a composite laminate containing both matrix cracking and delamination is considered. Then, the values of the admissible stresses and compliance of cracked laminate are employed to evaluate the energy release rate of each mentioned damage mode. Eventually, the graphs for different lay-ups in such symmetric laminate are drawn, which indicate important points for designers in practical applications. Afterwards, the effects of thickness on the dislocation of critical crack density points are checked. It can be emphasized that the current approach opens a new insight for perceiving the composites’ structural behavior in vulnerable positions.

A Damage Model Containing Delamination in Composite Laminates

2006 ◽  
Vol 324-325 ◽  
pp. 43-46
Author(s):  
Yu Pu Ma ◽  
Xin Zhi Lin ◽  
Qing Fen Li ◽  
Zhen Li
Keyword(s):  
Composite Laminates ◽  
Damage Model ◽  
Laminated Composite ◽  
Shear Lag ◽  
Analysis Model ◽  
Transverse Cracks ◽  
Transverse Cracking ◽  
Stiffness Reduction ◽  
Laminated Composite Materials ◽  
Modulus Reduction

When stress is high, delaminate damage can be induced by transverse cracks. A complete parabolic shear-lag damage model containing delamination induced by transverse cracks is therefore proposed and applied to predict the stiffness reduction by transverse cracking in cross-ply laminated composite materials. The predictions of the complete parabolic shear-lag analysis model, the incomplete parabolic shear-lag analysis model, and the complete parabolic shear-lag damage model containing delamination proposed in this paper have been compared. Results show that the young’s modulus reduction values obtained by our analysis model are better agreement with the experimental ones than other models.

Property Degradation of Anisotropic Composite Laminates with Matrix Cracking. Part 1: Development of Constitutive Relations for (θm/90n)s Cracked Laminates by Stiffness Partition

1996 ◽  
Vol 15 (11) ◽  
pp. 1149-1160 ◽  
Author(s):  
Hua Yu ◽  
Wang Xingguo ◽  
Li Zhengneng ◽  
He Qingzhi
Keyword(s):  
Composite Laminates ◽  
Constitutive Relations ◽  
Crack Density ◽  
Matrix Cracking ◽  
Normal Response ◽  
Shear Response ◽  
Plane Normal ◽  
Anisotropic Composite ◽  
Stiffness Partition

The study on property degradation of damaged composite laminates is extended to anisotropic laminates with matrix cracking. In Part 1 of the paper, an idea of “stiffness partition” is proposed to deal with the puzzle that the in-plane normal response is coupled with the shear response of the laminates. For (θ m/90 n), laminates containing transversely cracked layers under general in-plane loading, the constitutive relations are derived and the effective stiffnesses are expressed as the functions of crack density.

scholarly journals Continuum damage mechanics modeling of composite laminates including transverse cracks

2017 ◽  
Vol 27 (6) ◽  
pp. 877-895 ◽  
Author(s):  
Tomonaga Okabe ◽  
Sota Onodera ◽  
Yuta Kumagai ◽  
Yoshiko Nagumo
Keyword(s):  
Composite Laminates ◽  
Damage Mechanics ◽  
Elastic Moduli ◽  
Crack Density ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Transverse Cracks ◽  
Element Analysis ◽  
The Finite Element Analysis

In this study, the continuum damage mechanics model for predicting the stiffness reduction of composite laminates including transverse cracks is formulated as a function of crack density. To formulate the model, first the damage variable in the direction normal to the fiber of a ply including transverse cracks is derived. The damage variable is derived by the model assuming a plane strain field in the isotropic plane and using the Gudmundson–Zang model for comparison. The effective compliance based on the strain equivalent principle proposed by Murakami et al. and classical laminate theory are then used to formulate the elastic moduli of laminates of arbitrary lay-up configurations as a function of the damage variable. Finally, the results obtained from this model are compared to the finite-element analysis reported in previous studies. The model proposed in this paper can predict the stiffness of laminates containing damage due to transverse cracks (or surface crack) from just the mechanical properties of a ply and the lay-up configurations. Furthermore, this model can precisely predict the finite-element analysis results and experiment results for the elastic moduli of the laminate of arbitrary lay-up configuration, such as cross-ply, angle ply, and quasi-isotropic, including transverse cracks. This model only considers the damage of the transverse crack; it does not consider damage such as delamination. However, this model seems to be effective in the early stage of damage formation when transverse cracking mainly occurs. The model assuming plane strain field in the isotropic plane which is proposed in this paper can calculate the local stress distribution in a ply including transverse cracks as a function of crack density. The damage evolution of transverse cracks can thus be simulated by determining the fracture criterion.

scholarly journals Application of discrete damage mechanics for determination of the crack density in composite laminates

2020 ◽  
Vol 310 ◽  
pp. 00002
Author(s):  
Milan Žmindák ◽  
Eva Kormaníková ◽  
Pavol Novák ◽  
Josef Soukup ◽  
Kamila Kotrasová
Keyword(s):  
Fracture Toughness ◽  
Composite Laminates ◽  
Composite Structures ◽  
Damage Mechanics ◽  
Crack Density ◽  
Matrix Cracking ◽  
Mapping Algorithm ◽  
Damage Initiation ◽  
Return Mapping

The finite element method (FEM) is one of the most widely and most popular numerical methods for analyzing damage of composite structures, In this paper discrete damage mechanics (DDM) is used to predict inter-laminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the laminate. ANSYS commercial software is used for analysis of layered plate composite structure reinforced with long unidirectional fibers with Carbon/Epoxy material. Because ANSYS does not have a built-in capability for calculating crack density, we have to use plagin. A methodology for determination of the fracture toughness is based on fitting DDM model and these data are obtained from literature. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted. Evaluation of matrix cracking detected in lamina has been solved using return mapping algorithm.

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