The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
Improving the Properties of Self-compacted Concrete with Using Combined Silic...Pouyan Fakharian
The viscosity is the main property of self- compacted concrete (SCC) and using of pozzolan material such as metakaolin (MK) and Silica fume (SF) can help to achieve that goal. The effect of simultaneous substitution of MK and SF instead of cement on the rheological and mechanical properties of self-compacted concrete was experimentally investigated in this paper. Seventeen mix designs were cast with a substitution weight percentage (5, 10, 15, 20 %) in water to adhesive material ratio equal 0.32. All mixes were examined by compressive, tensile strengths and water absorption tests with an appropriate fluidity, without having signs of segregation or instability. The test results were indicated that the SCC mixes containing MK and SF had higher compressive and tensile strengths in comparison with no-pozzolan concrete. The comparison of linear multiple regression techniques (LMRT) and nonlinear multiple regression technique outputs with experimental results showed an appropriate similarity.
Shear Strength Prediction of Reinforced Concrete Shear Wall Using ANN, GMDH-N...Pouyan Fakharian
To provide lateral resistance in structures as well as buildings, there are some types of structural systems such as shear walls. The utilization of lateral loads occurs on a plate on the wall's vertical dimension. Conventionally, these sorts of loads are transferred to the wall collectors. There is a significant resistance between concrete shear walls and lateral seismic loading. To guarantee the building's seismic security, the shear strength of the walls has to be prognosticated by using models. This paper aims to predict shear strength by using Artificial Neural Network (ANN), Neural Network-Based Group Method of Data Handling (GMDH-NN), and Gene Expression Programming (GEP). The concrete's compressive strength, the yield strength of transverse reinforcement, the yield strength of vertical reinforcement, the axial load, the aspect ratio of the dimensions, the wall length, the thickness of the reinforced concrete shear wall, the transverse reinforcement ratio, and the vertical reinforcement ratio are the input parameters for the neural network model. And the shear strength of the reinforced concrete shear wall is considered as the target parameter of the ANN model. The results validate the capability of the models predicted by ANN, GMDH-NN, and GEP, which are suitable for use as a tool for predicting the shear strength of concrete shear walls with high accuracy.
Optimization of Varying Orientation of Continuous Fiber Direction and Its App...CrimsonPublishersRDMS
Optimization of Varying Orientation of Continuous Fiber Direction and Its Applications to New Methods of Additive Manufacturing by Luca De Vivo Nicoloso* in Crimson Publishers: Peer Reviewed Material Science Journals
Comparative study of experimental and analytical results of frp strengthened ...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks.
Improving the Properties of Self-compacted Concrete with Using Combined Silic...Pouyan Fakharian
The viscosity is the main property of self- compacted concrete (SCC) and using of pozzolan material such as metakaolin (MK) and Silica fume (SF) can help to achieve that goal. The effect of simultaneous substitution of MK and SF instead of cement on the rheological and mechanical properties of self-compacted concrete was experimentally investigated in this paper. Seventeen mix designs were cast with a substitution weight percentage (5, 10, 15, 20 %) in water to adhesive material ratio equal 0.32. All mixes were examined by compressive, tensile strengths and water absorption tests with an appropriate fluidity, without having signs of segregation or instability. The test results were indicated that the SCC mixes containing MK and SF had higher compressive and tensile strengths in comparison with no-pozzolan concrete. The comparison of linear multiple regression techniques (LMRT) and nonlinear multiple regression technique outputs with experimental results showed an appropriate similarity.
Shear Strength Prediction of Reinforced Concrete Shear Wall Using ANN, GMDH-N...Pouyan Fakharian
To provide lateral resistance in structures as well as buildings, there are some types of structural systems such as shear walls. The utilization of lateral loads occurs on a plate on the wall's vertical dimension. Conventionally, these sorts of loads are transferred to the wall collectors. There is a significant resistance between concrete shear walls and lateral seismic loading. To guarantee the building's seismic security, the shear strength of the walls has to be prognosticated by using models. This paper aims to predict shear strength by using Artificial Neural Network (ANN), Neural Network-Based Group Method of Data Handling (GMDH-NN), and Gene Expression Programming (GEP). The concrete's compressive strength, the yield strength of transverse reinforcement, the yield strength of vertical reinforcement, the axial load, the aspect ratio of the dimensions, the wall length, the thickness of the reinforced concrete shear wall, the transverse reinforcement ratio, and the vertical reinforcement ratio are the input parameters for the neural network model. And the shear strength of the reinforced concrete shear wall is considered as the target parameter of the ANN model. The results validate the capability of the models predicted by ANN, GMDH-NN, and GEP, which are suitable for use as a tool for predicting the shear strength of concrete shear walls with high accuracy.
Optimization of Varying Orientation of Continuous Fiber Direction and Its App...CrimsonPublishersRDMS
Optimization of Varying Orientation of Continuous Fiber Direction and Its Applications to New Methods of Additive Manufacturing by Luca De Vivo Nicoloso* in Crimson Publishers: Peer Reviewed Material Science Journals
Comparative study of experimental and analytical results of frp strengthened ...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A new proposed approach for moment capacity estimation of ferrocement members...Pouyan Fakharian
Ferrocement composites are widely used as a novel method for many different structural purposes recently. The uniform distribution and the high surface area-to-volume ratio of the reinforcement of such composites would improve the crack-arresting mechanism. Given these properties, ferrocement is an ideal option as a replacement for some traditional structures methods. In members with axially loaded reinforced concrete ferrocement composite, it would be the best alternative to use ferrocement members. Lack of sufficient research in this approach is the cause of not well defining this field for RC structures. This study has aimed to evaluate the moment capacity of ferrocement members using the GMDH method. Mechanical and geometrical parameters including the width of specimens, total depth specimens, compressive strength of ferrocement, ultimate strength of wire mesh and volume fraction of wire mesh are considered as inputs to predict the moment capacity of ferrocement members. For evaluating this model, mean absolute error (MAE), root mean absolute error (RMAE), normalized root mean square error (NRMSE) and mean absolute percentage error (MAPE) were carried out. The results conducted that the GMDH model is significantly better than some previous models and comparable to some other methods. Moreover, a new formulation for moment capacity of ferrocement members based on GMDH approach is presented. Finally, Sensitivity analysis is operated to understand the influence of each input parameters on moment capacity of ferrocement members.
Analysis of Functionally Graded Material Plate under Transverse Load for Vari...IOSR Journals
Functionally gradient materials (FGM) are one of the most widely used materials in various
applications because of their adaptability to different situations by changing the material constituents as per the
requirement. Most structural components used in the field of engineering can be classified as beams, plates, or
shells for analysis purposes. In the present study the power law, sigmoid and exponential distribution is
considered for the volume fraction distributions of the functionally graded plates. The work includes parametric
studies performed by varying volume fraction distributions and boundary conditions. Also static analysis of
functionally gradient material plate is carried out by sigmoid law and verified with the published results. The
convergence study of the results is optimized by changing the mesh size and layer size. Power law and
exponential law are applied for the same material and set of conditions.
A composite material can be defined as a combination of two or more materials that
gives better properties than those of the individual components used alone. In contrast to
metallic alloys, each material retains its separate chemical, physical, and mechanical
properties. The two constituents are reinforcement and a matrix. The main advantages of
composite materials are their high strength and stiffness combined with low density when
compared to classical materials. Micromechanical approach is found to be more suitable for
the analysis of composite materials because it studies the volume proportions of the
constituents for the desired lamina stiffness and strength.
Predicting Resilient Modulus of Clayey Subgrade Soils by Means of Cone Penetr...Pouyan Fakharian
Resilient modulus (Mr) of subgrade soils is considered as one of the most important factors for designing flexible pavements using empirical methods as well as mechanistic-empirical methods. The resilient modulus is commonly measured by a dynamic triaxial loading test, which is complex and expensive. In this research, back-propagation artificial neural network method has been employed to model the resilient modulus of clayey subgrade soils based on the results of the cone penetration test. The prediction of the resilient modulus of clayey subgrade soil can be possible through the developed neural network based on the parameters of the cone tip resistance (qc), sleeve friction (fs), moisture content (w), and dry density (γd). The results of the present study show that the coefficients of determination (R2) for training and testing sets are 0.9837 and 0.9757, respectively. According to the sensitivity analysis results, the moisture content is the least important parameter to predict the resilient modulus of clayey subgrade soils, while the importance of other parameters is almost the same. In this study, the effect of different parameters on the resilient modulus of clayey subgrade soil was evaluated using parametric analysis and it was found that with increasing the cone tip resistance (qc), the sleeve friction (fs) and the dry density (γd) and also with decreasing the moisture content (w) of soils, the resilient modulus of clayey subgrade soils increases.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Numerical Analysis of Engineered Steel Fibers as Shear Reinforcement in RC BeamsP singh
Using suitable fibers and additives in concrete to enhance its performance is an important consideration in the concrete industry with regard to the structural aspects of concrete. The purpose of this project is to investigate numerically the effectiveness of the engineered steel fiber as shear reinforcement in RC beams. Here steel fibers completely replaces the shear reinforcement (stirrups & links). The dimension of beam taken was 1000*150*150 mm with aspect ratio 80. The beams were reinforced with 10 mm steel bars as secondary reinforcement and 12 mm bars as main reinforcement on the tension side. Numerical analysis using ANSYS R16.1 software package was carried out. The load-deflection curves for the beams with different dosage of fibers were drawn superimposing their numerical values. Initially, in all three cases the curve was linear elastic and about 80% of ultimate load they tend to be non-linear. It was observed that there was fair agreement between the results which indicates some favourable aspects concerning the use of steel fibres as shear reinforcement in concrete beams. It was investigated that the inclusion of steel fibres (Hook End Type) improves the shear strength of RC beams without stirrups by improving the matrix between concrete and steel fibers. Thus this project focuses in the design and analysis using the software ANSYS R16.1 for an alternative steel reinforcement with better or equivalent performance.
Nano Scale Surface Characterization of Poly Ethyleneterephthalate Silicon Rub...ijtsrd
Atomic force microscopy has been used to investigated the surface properties of different materials, in this paper it is used to measure the surface roughness and surface adhesive force of three different membrane samples Poly ethyleneterephthalate PET , Silicon Rubber SR and PET SRcopolymers. This analytical method allows images representing the topography and adhesive force Phase image of the surface to be captured simultaneously at a molecular nanometer resolution. The distribution of hydrophilic polar groups and the surface roughness on the investigated surfaces ofthese membrane samples influences the subsequent processing of polymeric membrane manufacture as well as their performance. From the results a clear distinction was observed between the three samples in both images the topography surface roughness images and adhesive force images. Promising result were obtained for the PET SRcopolymer samples to be a good candidate in membrane separation applications. This study may also help to explain the differences in membrane performances and efficiency during applications in the separation process. Dr. Abduelmaged Abduallah | Dr. Kamal M. Sassi | Dr. Mustafa T. Yagub "Nano-Scale Surface Characterization of Poly (Ethyleneterephthalate) - Silicon Rubber Copolymers using Atomic Force Microscopy" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd43688.pdf Paper URL: https://www.ijtsrd.comengineering/chemical-engineering/43688/nanoscale-surface-characterization-of-poly--ethyleneterephthalate--silicon-rubber-copolymers-using-atomic-force-microscopy/dr-abduelmaged-abduallah
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Three dimensional finite element modeling of pervious concrete pavementeSAT Journals
Abstract Pervious concrete has the unique characteristic of allowing water to pass through its porous matrix. . Pervious concrete pavement systems usually have three main layers, pervious concrete on the top, a subbase layer of aggregate for water storage in the middle and the subgrade (soil) layer below. Finite element modeling of this novel material is challenging due to its complex porous characteristics. In this paper, a method has been proposed to model pervious concrete pavement using finite element methods, which includes a modified approach to capture the unique vertical porosity distribution in the pervious concrete layer by averaging the distribution in three distinct vertical sections. The mechanical properties of the pervious concrete layer are assumed to vary along its depth since the porosity of the pervious concrete also varies with depth. ABAQUS, a general-purpose finite element software package was used to develop the model and perform the analysis. The model was validated through a convergence study, and in comparison with the analytical theory of tensile stress and deflection for traditional concrete pavement. In addition, the significance of the porosity distribution model was validated by comparing the results from EverFE – a specific software for pavement structure analysis. It was found that there is significant difference in tensile stress if modeled using the modified vertical porosity distribution in the previous concrete layer to more fully capture its vertical porosity distribution, as compared to an averaged porosity model in the previous concrete layer. It was also noted that compressive stress demand may have increased importance for pervious concrete, but only for highly porous applications which are not commonly used. Keywords: pervious concrete, vertical porosity, finite element, critical loading, stress, deflection
Effect of lamination angle on maximum deflection of simply supported composit...RAVI KUMAR
In this project a composite laminated beam is studied with glass-epoxy and graphite-epoxy combination. The beam is composed of four layers of different combination of composite material (glass epoxy and graphite epoxy composite). The beam is simply supported at both the ends and is subjected to uniformly distributed load along the length. Transverse deflection is computed for different lamination angle (0^0-〖90〗^0) by using Euler- Bernoulli’s theory (or CLPT). Maximum transverse deflection analysis is carried out using derived analytical expressions. The research carried out in this project will enable to determine the beam strength due to bending loads. The importance of fibre reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. MATLAB codes are generated to implement analytical expiations of the composite beam.
The main objective of the paper is to find out the lamination angle at which minimum deflection is obtained & to find out the effect of lamination angle on maximum transverse deflection of the beam.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A new proposed approach for moment capacity estimation of ferrocement members...Pouyan Fakharian
Ferrocement composites are widely used as a novel method for many different structural purposes recently. The uniform distribution and the high surface area-to-volume ratio of the reinforcement of such composites would improve the crack-arresting mechanism. Given these properties, ferrocement is an ideal option as a replacement for some traditional structures methods. In members with axially loaded reinforced concrete ferrocement composite, it would be the best alternative to use ferrocement members. Lack of sufficient research in this approach is the cause of not well defining this field for RC structures. This study has aimed to evaluate the moment capacity of ferrocement members using the GMDH method. Mechanical and geometrical parameters including the width of specimens, total depth specimens, compressive strength of ferrocement, ultimate strength of wire mesh and volume fraction of wire mesh are considered as inputs to predict the moment capacity of ferrocement members. For evaluating this model, mean absolute error (MAE), root mean absolute error (RMAE), normalized root mean square error (NRMSE) and mean absolute percentage error (MAPE) were carried out. The results conducted that the GMDH model is significantly better than some previous models and comparable to some other methods. Moreover, a new formulation for moment capacity of ferrocement members based on GMDH approach is presented. Finally, Sensitivity analysis is operated to understand the influence of each input parameters on moment capacity of ferrocement members.
Analysis of Functionally Graded Material Plate under Transverse Load for Vari...IOSR Journals
Functionally gradient materials (FGM) are one of the most widely used materials in various
applications because of their adaptability to different situations by changing the material constituents as per the
requirement. Most structural components used in the field of engineering can be classified as beams, plates, or
shells for analysis purposes. In the present study the power law, sigmoid and exponential distribution is
considered for the volume fraction distributions of the functionally graded plates. The work includes parametric
studies performed by varying volume fraction distributions and boundary conditions. Also static analysis of
functionally gradient material plate is carried out by sigmoid law and verified with the published results. The
convergence study of the results is optimized by changing the mesh size and layer size. Power law and
exponential law are applied for the same material and set of conditions.
A composite material can be defined as a combination of two or more materials that
gives better properties than those of the individual components used alone. In contrast to
metallic alloys, each material retains its separate chemical, physical, and mechanical
properties. The two constituents are reinforcement and a matrix. The main advantages of
composite materials are their high strength and stiffness combined with low density when
compared to classical materials. Micromechanical approach is found to be more suitable for
the analysis of composite materials because it studies the volume proportions of the
constituents for the desired lamina stiffness and strength.
Predicting Resilient Modulus of Clayey Subgrade Soils by Means of Cone Penetr...Pouyan Fakharian
Resilient modulus (Mr) of subgrade soils is considered as one of the most important factors for designing flexible pavements using empirical methods as well as mechanistic-empirical methods. The resilient modulus is commonly measured by a dynamic triaxial loading test, which is complex and expensive. In this research, back-propagation artificial neural network method has been employed to model the resilient modulus of clayey subgrade soils based on the results of the cone penetration test. The prediction of the resilient modulus of clayey subgrade soil can be possible through the developed neural network based on the parameters of the cone tip resistance (qc), sleeve friction (fs), moisture content (w), and dry density (γd). The results of the present study show that the coefficients of determination (R2) for training and testing sets are 0.9837 and 0.9757, respectively. According to the sensitivity analysis results, the moisture content is the least important parameter to predict the resilient modulus of clayey subgrade soils, while the importance of other parameters is almost the same. In this study, the effect of different parameters on the resilient modulus of clayey subgrade soil was evaluated using parametric analysis and it was found that with increasing the cone tip resistance (qc), the sleeve friction (fs) and the dry density (γd) and also with decreasing the moisture content (w) of soils, the resilient modulus of clayey subgrade soils increases.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Numerical Analysis of Engineered Steel Fibers as Shear Reinforcement in RC BeamsP singh
Using suitable fibers and additives in concrete to enhance its performance is an important consideration in the concrete industry with regard to the structural aspects of concrete. The purpose of this project is to investigate numerically the effectiveness of the engineered steel fiber as shear reinforcement in RC beams. Here steel fibers completely replaces the shear reinforcement (stirrups & links). The dimension of beam taken was 1000*150*150 mm with aspect ratio 80. The beams were reinforced with 10 mm steel bars as secondary reinforcement and 12 mm bars as main reinforcement on the tension side. Numerical analysis using ANSYS R16.1 software package was carried out. The load-deflection curves for the beams with different dosage of fibers were drawn superimposing their numerical values. Initially, in all three cases the curve was linear elastic and about 80% of ultimate load they tend to be non-linear. It was observed that there was fair agreement between the results which indicates some favourable aspects concerning the use of steel fibres as shear reinforcement in concrete beams. It was investigated that the inclusion of steel fibres (Hook End Type) improves the shear strength of RC beams without stirrups by improving the matrix between concrete and steel fibers. Thus this project focuses in the design and analysis using the software ANSYS R16.1 for an alternative steel reinforcement with better or equivalent performance.
Nano Scale Surface Characterization of Poly Ethyleneterephthalate Silicon Rub...ijtsrd
Atomic force microscopy has been used to investigated the surface properties of different materials, in this paper it is used to measure the surface roughness and surface adhesive force of three different membrane samples Poly ethyleneterephthalate PET , Silicon Rubber SR and PET SRcopolymers. This analytical method allows images representing the topography and adhesive force Phase image of the surface to be captured simultaneously at a molecular nanometer resolution. The distribution of hydrophilic polar groups and the surface roughness on the investigated surfaces ofthese membrane samples influences the subsequent processing of polymeric membrane manufacture as well as their performance. From the results a clear distinction was observed between the three samples in both images the topography surface roughness images and adhesive force images. Promising result were obtained for the PET SRcopolymer samples to be a good candidate in membrane separation applications. This study may also help to explain the differences in membrane performances and efficiency during applications in the separation process. Dr. Abduelmaged Abduallah | Dr. Kamal M. Sassi | Dr. Mustafa T. Yagub "Nano-Scale Surface Characterization of Poly (Ethyleneterephthalate) - Silicon Rubber Copolymers using Atomic Force Microscopy" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd43688.pdf Paper URL: https://www.ijtsrd.comengineering/chemical-engineering/43688/nanoscale-surface-characterization-of-poly--ethyleneterephthalate--silicon-rubber-copolymers-using-atomic-force-microscopy/dr-abduelmaged-abduallah
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Three dimensional finite element modeling of pervious concrete pavementeSAT Journals
Abstract Pervious concrete has the unique characteristic of allowing water to pass through its porous matrix. . Pervious concrete pavement systems usually have three main layers, pervious concrete on the top, a subbase layer of aggregate for water storage in the middle and the subgrade (soil) layer below. Finite element modeling of this novel material is challenging due to its complex porous characteristics. In this paper, a method has been proposed to model pervious concrete pavement using finite element methods, which includes a modified approach to capture the unique vertical porosity distribution in the pervious concrete layer by averaging the distribution in three distinct vertical sections. The mechanical properties of the pervious concrete layer are assumed to vary along its depth since the porosity of the pervious concrete also varies with depth. ABAQUS, a general-purpose finite element software package was used to develop the model and perform the analysis. The model was validated through a convergence study, and in comparison with the analytical theory of tensile stress and deflection for traditional concrete pavement. In addition, the significance of the porosity distribution model was validated by comparing the results from EverFE – a specific software for pavement structure analysis. It was found that there is significant difference in tensile stress if modeled using the modified vertical porosity distribution in the previous concrete layer to more fully capture its vertical porosity distribution, as compared to an averaged porosity model in the previous concrete layer. It was also noted that compressive stress demand may have increased importance for pervious concrete, but only for highly porous applications which are not commonly used. Keywords: pervious concrete, vertical porosity, finite element, critical loading, stress, deflection
Effect of lamination angle on maximum deflection of simply supported composit...RAVI KUMAR
In this project a composite laminated beam is studied with glass-epoxy and graphite-epoxy combination. The beam is composed of four layers of different combination of composite material (glass epoxy and graphite epoxy composite). The beam is simply supported at both the ends and is subjected to uniformly distributed load along the length. Transverse deflection is computed for different lamination angle (0^0-〖90〗^0) by using Euler- Bernoulli’s theory (or CLPT). Maximum transverse deflection analysis is carried out using derived analytical expressions. The research carried out in this project will enable to determine the beam strength due to bending loads. The importance of fibre reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. MATLAB codes are generated to implement analytical expiations of the composite beam.
The main objective of the paper is to find out the lamination angle at which minimum deflection is obtained & to find out the effect of lamination angle on maximum transverse deflection of the beam.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Abstract The present research work is to determine buckling load per unit length in rectangular plate with circular cut-outs under bi-axial compression using 2D finite element analysis. The commercial finite element analysis software ANSYS has been successfully executed. The buckling factors are evaluated by changing the position of the holes, length to thickness ratio. The effect of changing the position of holes, a/b ratio, b/t ratio and buckling load per unit length is discussed. The results shows that buckling load per unit length is in clamped-clamped boundary conditions and buckling load is more at top positioned hole, decreases with increase in aspect ratio, decrease with increase breadth to thickness ratio. Keywords: Buckling analysis, Finite element method, Buckling load per unit length , carbon/epoxy composite plate, aspect ratio, b/t ratio, and Biaxial load.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
We conducted molecular dynamics simulations to investigate the atomistic edge crack vacancy interactions in graphene. We demonstrate that the crack tip stress field of an existing crack in graphene can be effectively tailored (reduced by over 50% or increased by over 70%) by the strategic placement of atomic vacancies of varied shapes, locations, and orientations near its tip. The crack vacancy interactions result in a remarkable improvement (over 65%) in the fracture strength of graphene. Moreover, at reduced stiffness of graphene, due to a distribution of atomic vacancies, a drastic difference (~60%) was observed between the fracture strengths of two principal crack configurations (i.e. armchair and zigzag). Our numerical simulations provide a remarkable insight into the applicability of the well-established continuum models of crack microdefect interactions for the corresponding atomic scale problems. Furthermore, we demonstrate that the presence of atomic vacancies in close proximity to the crack tip leads to a multiple stage crack growth and, more interestingly, the propagating cracks can be completely healed even under a significantly high applied tensile stress level (~5 GPa). Our numerical experiments offer a substantial contribution to the existing literature on the fracture behavior of two dimensional nanomaterials.
Prediction of Deflection and Stresses of Laminated Composite Plate with Arti...IJMER
A true understanding of their structural behaviour is required, such as the deflections, buckling loads
and modal characteristics, the through thickness distributions of stresses and strains, the large deflection
behaviour and, of extreme importance for obtaining strong, reliable multi-layered structures, the failure
characteristics. In the past, the structural behaviour of plates and shells using the finite element method has been
studied by a variety of approaches. Choudhary and Tungikaranalyzed the geometrically nonlinear behavior of
laminated composite plates using the finite element analysis.
In this paper we have analyzed the stress distribution over a rectangular specimen
with hybrid composite material at its central hole. Using Vacuum bag technique the
material has been fabricated and it consists of carbon and glass fiber with epoxy. The
cross ply lamina arrangement with alternate carbon and glass has increased the
strength of the structure. This is because carbon properties are high compared to
glass. The cutouts made in typical aircraft and automobile components reduce the
weight and bulking load carrying capacity of the aircraft according to the weight
reduction law. Three specimens were used to carry out experimental investigations as
per ASTM D5766 in the universal testing machine. We have analyzed and compared
the results of the stress concentration in the rectangular specimen with a hole using
FEA
Experimental Study, Simulation and Model Predictions of Recycled PET Strip-Re...IJERA Editor
This study presents results from a theoretical-experimental program of beams partially pre-stressed made with continuous recycled PET strip-reinforced concrete (plain concrete strength of 20 MPa). These studies mainly attempted to determine the stripinfluence in altering the flexural strength at first and final crack. Also the load-deflection, ductility, energy absorption capacity of the beams are observed and the studies can be used in predicting the flexural behavior of longitudinally reinforced concrete. The model theory assumes that concrete has a tensile load capacity different from zero, characterized by a uniaxial tensile stress-strain diagram. The need for non-linear geometric and the material models imply the use of numerical methods such as the finite element method; so that, a finite element analysis of reinforced concrete beam with strips-reinforced plastic is performed. The obtained results were compared with computer analysis and experimental data to corroborate the validity of the suggested method, showing that the theory also predicts correctly the post-cracking creep deformation.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERMOPLASTIC COMPOSITES
1. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
DOI:10.5121/msej.2017.4301 1
RESULTS OF FINITE ELEMENT ANALYSIS FOR
INTERLAMINAR FRACTURE REINFORCED
THERMOPLASTIC COMPOSITES
P.J. Charitidis
Center of Orthopaedic Research (C.O.RE) at Center for Interdisciplinary Research and
Innovation-Aristotle University of Thessaloniki ( CIRI-AUTH), Greece
ABSTRACT
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
KEYWORDS:
double cantilever beam, FEA, fabric reinforced composites, thermoplastic matrix, X-FEM
1. INTRODUCTION
A unidirectional continuous fiber reinforcement in high performance composite materials leads to
high specific strength and stiffness in fiber direction but very low properties transverse to it.
Usually laminates made of plies with different fiber orientation or of plies with woven fabric fiber
reinforcement are used in structures to overcome this problem in three dimensions. A critical
failure mode of these laminates is the interlaminar fracture or the delamination [1-4]. Delamination
can occur during the manufacturing process due to contaminated reinforcing fibers, insufficient
wetting of fibers, machining and mechanical loading such as impact loading. Delamination can
also occur due to the lack of reinforcement in the thickness direction and, also, since interlaminar
stresses exist in the boundary layer of laminates under transverse loading [5,6,7]. Components
made of epoxy-based materials have provided out- standing mechanical, thermal, and electrical
properties [8]. The laminated fiber-reinforced composite materials such as carbon fiber epoxy
composites are widely applied in packaging, coating, electronics, automotive, and aerospace
industries [9,10]. They have high strength-to-weight and stiffness-to-weight ratios. These
composites have unique advantages over monolithic materials, such as high strength, high
stiffness, long fatigue life, low density, corrosion resistance, wear resistance, and environmental
stability [11]. Mechanical properties of epoxy polymeric composites can be enhanced through the
improvement of the interlaminar properties by toughening resin matrix [12,13], and fiber
reinforcement [14, 15]. In unidirectional carbon and glass fibre with epoxy matrices, typical values
of interlaminar fracture toughness GIc are in the range 200-400 J/m2
. Modification of the epoxy
matrix with rubber particles leads to improvement in GIc up to approximately 800-1000 J/m2
. For
composites reinforce by woven glass fibres typical values of the fracture toughness are ≈1000 J/m2
2. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
2
[16]. A lot of investigations have been published so far dealing with the measurement of the
critical energy to cause delamination and to characterize the materials by means of this property.
However, most of these studies were carried out using unidirectional reinforced laminate
specimens and were focused on the test procedure, geometry and data reduction methods. In order
to predict delamination onset or growth for two-dimensional problems, these calculated G
components are compared to interlaminar fracture toughness properties measured over a range
from pure mode I loading to pure mode II loading [17, 18]. Simulating the propagation of cracks
by using finite element method is quite challenging because the topology of the domain changes
continuously. For this reason, the extended finite element method (XFEM) is being used to model
cracks because the mesh can be created independent from the crack geometry. Actually, XFEM
lies in applying the appropriate enrichment function locally in the domain of interest using the
partition of unity. This method was first proposed by Belytschko et al. [19], where they applied the
partition of unity methods to the problem of using finite elements with discontinuous basis
functions. Further on, Moes, et. al. [20], used XFEM to create a technique for simulating crack
propagation in two dimensions without remeshing the domain, while the extension to three
dimensions was begun by Sukumar et al. [21], where they used the two dimensional enrichment
functions for planar cracks, and then extended in [22-26]. XFEM has demonstrated more accurate
and stable solutions while the conventional finite element results were rough or highly oscillatory
[27, 28]. In this study we trying to analyzing stress distribution for the local region ahead the crack
tip for a very thin resin layer by using extended finite element method (Abaqus). This thickness
which is almost 0.0004mm, was "received" by the experimental procedure [29, 30], which
indicates a very thin resin-rich layer between neighboring plies.
2. ANALYTICAL THEORIES
2.1 SIMPLE BEAM THEORY
The simple beam theory expression for the compliance of a perfectly built-in DCB specimen
results in the following equation for GIc:
where P and δ are the load and displacement values, respectively calculated from the P-δ curve
at the point of deviation from linearity, determined by drawing a straight line from the origin
but ignoring any initial deviations due to take-up of play in the loading system [31].
Furthermore, B is the specimen width and α the initial crack length.
2.2 CORRECTED BEAM THEORY
The above expression will underestimate the compliance as the beam is not perfectly built-in
[32]. Thus, a correcting factor ∆ is introduced assuming that the real crack is slightly longer
(α+∆) than the one measured experimentally. ∆ may be found experimentally as the deviation
from the origin by plotting the cube root of the compliance as a function of crack length.
3. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
3
while the compliance C is given by,
where E is the Young's modulus. A constant value for ∆ is assumed during the whole crack
propagation procedure.
2.3 EXPERIMENTAL COMPLIANCE METHOD
This is the most accurate method, and could be characterized as an alternative method which is
to plot compliance versus crack length. It is the most popular theory one in literature [33, 34],
where the compliance values are obtained directly from the measured load and displacement
values (C=δ/P versus an
). Actually, is a two parameter approach according to,
where n is the slope of the plot.
2.4 THE AREA METHOD
In this method, the crack extension is related directly to the area enclosed between loading and
unloading curves. To be more specific, the energy release rate is calculated from the energy
consumed by the crack extension divided by the area of the new crack surface [35, 36]. Thus,
where ∆Α is the area enclosed by the loading-unloading path.
2.5 MODIFIED MODEL PROPOSED BY BISHOPP AND DRUCKER
Thin composite specimens, very often used for DCB tests, result in large deflections and
rotations due to their low flexural rigidity. The correction to linear beam theory for these
factors, introduced by Bishopp and Drucker [37], has recently been developed further by Devitt
et al. [38] and applied to a series of glass/epoxy composites of three different thicknesses. Good
agreement between predicted and experimental values for the three different thicknesses was
observed when a constant average value of EI was used for each laminate.
2.6 MODIFIED MODEL PROPOSED BY FREEMAN
A finite displacement analysis for the DCB test method was first introduced by Freeman [39].
Williams [40] has developed this model further, to include the effects of end blocks. This
formulation is valid for any type of anisotropic elastic behaviour of the beam, since it is based
on slender beam analysis and ignores transverse stresses. According to Freeman, the final
expression for GIc, ignoring the end block effects, is:
4. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
4
where P is the applied load, B the width of the DCB specimen and φο, the end slope of the
cantilever. The analysis was successfully applied to experimental results.
2.7 THE PROPOSED APPROACH
All the above theories are based on certain assumptions, such as: (1) homogeneity and isotropy;
(2) certain geometric conditions are respected; (3) St. Venant's principle applies; and (4) plane
sections remain plane after loading. However, these assumptions are hardly ever fullfilled in
practice. In that case, it is proposed the following approach [41]. According to the geometry
(figure 1),
Figure 1. Double Cantilever Beam (Dcb) Geometry.
And
where δ is the displacement, P the load, α the crack length, E the bending modulus, B the
specimen's width, h the thickness and C the compliance. From equation (2), we calculate the
crack length,
while from the definition of GIc it follows that:
5. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
5
By introducing expression (3) into (4) we finally find:
where A=Bh is the cross-sectional area of the bending beam. Thus, according to equation (5)
the parameters for evaluation of GIc are P, A, C, E, and B which are all completely defined by
the experimental procedure applied and the specimen's geometry.
3. MATERIAL AND METHOD
3.1 JOINT CONFIGURATION AND MATERIAL
The DCB specimen is often used to determine the mode I interlaminar fracture toughness, GIc,
and it is widely used on unidirectional reinforced laminates. In this finite element study the
specimen is composed of two uniform thickness sub laminates with 0 degree composite material
plies (CF/Ep). In figure 1 a schematic overviews of a DCB specimen is shown, while the
analyzed materials are shown in table 1 [42, 43, 44].
Table 1. Double Cantilever Beam (DCB) geometry.
3.2 EFFECT OF THE FIBER REINFORCEMENT AND MATRIX
The strengthening ingredient material in a composite is the fiber, which mainly carries the load
through the composite laminate. The fiber maintains the rigidity of the composite while impeding
crack or damage propagation and can be arranged in many different types of reinforcement.
Depending on the type of reinforcement, the fibres can be oriented randomly, all in one direction
(unidirectional or UD), or in a number of different directions [45]. Carbon fibres are one of the
most advanced and promising engineering materials, and are most commonly used as
reinforcements in advanced polymer-matrix composites [46] due to its many unique properties. In
6. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
6
figure 2, it can be seen the effect of different fiber reinforcements in a brittle epoxy and a tough
polyetherimide matrix. The CF(UD) reinforcements results in comparison to a fabric CF
reinforcement in much lower values for GIc, due to inhomogeneity and waviness of the fabric
reinforcement which causes a more complex failure and rougher fracture surface profile [47].
Thus the surface per unit crack length becomes larger in fabric reinforced composites. The
fiber/matrix bonding can be responsible for different interlaminar fracture toughnesses measured.
On the other hand, the tougher the matrix material is, the higher are the values of the interlaminar
fracture toughness (figure 3). For the neat polymers, the fracture energy values roughly vary
between GIc =0.1kJ/m2
for EP and 2.5 kJ/m2
for PEI [48]. This means, that the ratio of interlaminar
composite toughness to neat resin toughness is high in the case of an EP-matrix, but very low in
cases of PEI matrices [47].
Figure 2. Fiber reinforcement, GIc.
Figure 3. Matrix reinforcement, GIc
7. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
7
4. MATERIAL AND METHODS
Finite element analysis were carried out by using Abaqus. The analysis were based on two
dimensional finite element models, by using extended finite element method (XFEM), which
simplify the solution of problems such as, (a) the propagation of cracks, the evolution of
dislocations, (c) the modeling of grain boundaries and the (d) evolution of phase boundaries.
Figure 1 shows the DCB specimen configuration and loading analyzed in this study. The specimen
dimensions and materials were selected to represent those typical of currently used test specimens.
The CPS4, a 4-node bilinear plane stress quadrilateral was used for two dimensional modeling of
the specimen. The size of elements in the specimen was 0.042 mm using maximum principal
stress of 58 MPa (Maxps Damage) and displacement at failure at 5mm (Damage evolution). It
should be noted that the response after peak load in not as sensitive to mesh refinement.
Parametric analysis was performed with a loading displacement (δ=3 and 5 mm) which was
applied at the upper and lower corner of the specimen (Figure 1). In order to ensure a smooth
propagation, a very small increment values were considered. As, for boundary conditions the left
edges of the specimen were restricted as shown in figure 1 (point C), while the initial crack (point
AB=30mm) as well as the thickness of the resin in all cases was kept constant (0.0004mm).
5. FINITE ELEMENT AND ANALYTICAL RESULTS
5.1 FINITE ELEMENT RESULTS
The stress distributions ahead of the crack tip are analyzed for DCB specimen using carbon/epoxy
(CF/EP UD), carbon epoxy fabric (CF/EP) and carbon / polyethermide (CF/PEI). We started by
investigating the P-δ curves, obtained from the numerical model (figure 4 and 5). Once the
maximum force is attained, a stable crack propagation accompanied by a decrease in the force,
which is in a very good agreement with the experimental results (figure 6a). Moreover, the load
decreased at slow rate after a maximum, sometimes with localized stick-slip instabilities [49]
occurs. In that case, the critical strain energy release rate could be determined by using parameters
such as force, displacement and initial crack length. During the analysis, it was found that the
force-displacement curve is dependent on the choice of maximum principal stress. For instance,
changing the maximum principal stress (Maxps) values of 50MPa to 10MPa in the case of CF/PEI,
the maximum reaction force would be decreased by 11.47%. That means, the crack length for a
given displacement will be decreased.
However, for the same loading displacement, the maximum reaction force was found in the case of
the CF/Epoxy (UD). The crack was increased by 2.95mm and 4.95mm for loading displacement 3
and 5mm, respectively (figure 7). On the other hand, the minimum crack growth was found in the
case of CF/PEI (1.07 and 1.70mm). This is true, because PEI increase the viscosity of the resin
mixture, which reduces the rate of phase separation [50, 51]. Furthermore, has more resistance
towards deformation by an applied force, thus posses high stiffness [52]. Now, if the crack reaches
the tougher region, it slows down until the rate of release of elastic stored energy is sufficient to
propagate the crack through the tougher region. The release rate of stored energy is then more
than that required for stable growth. The crack then accelerates and unstable fracture occurs.
Generally, Mode I interlaminar fracture toughness for the satin woven fabric composites greatly
depended on both the interfacial properties and weave structure (figure 6b). At last, but not least,
for the case of the CF/PEI, the load instantly dropped at several points during the delamination
propagation in the load displacement curves, followed by a further increase of the load (figure 6b,
detail squared region). This behaviour was referred to as “stick-slip” crack propagation [53],
8. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
8
accompanying a series of unstable crack propagation and arrest. Again, the finite element results
are in good agreement with the experimental results [54].
Figure 4. Reaction force displacement relationship (δ=3mm).
Figure 5. Reaction force displacement relationship (δ=5mm).
9. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
9
Figure 6. (a) Useful comparisons between FEA vs Experimental results for (a) CF/Epoxy (UD) and (b)
CF/Epoxy (Fabric) for δ=5mm.
A closer look at the crack length results indicates that CF/PEI exhibits lower values (for all cases),
even when in this material is applied the maximum loading displacement compared to the
minimum loading displacement (figure 7).
Figure 7. Maximum crack length.
10. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
10
Further on, figures 8-9 and 10-11 shown the σx and σy distributions along the interface, where the
maximum values are found at the crack tip. The most dominant stress for the opening mode is σy.
It can be seen from figures 8 and 9, that σy remains tensile from the crack tip and no compressive.
The CF/PEI (UD) curve shows an elevation at the crack tip. It is clear that the differences in the σy
distributions related to the differences in the elastic properties as well as in the thickness of the
specimens. The higher value of young modulus (E2), produced higher stresses. The two fabric
materials, have an E2 that is about almost seven and six times more than the CF/EP (UD). In that
case, the σy distributions appears to be influenced by the adherends stiffness in the thickness
direction and does not seem to be influenced by the adherend stiffness in the longitudinal direction
[55]. Furthermore, the ductile matrices to deform plastically is restricted due to the preferential
occurance of unstable crack propagation in the woven fabric laminates (figures 12 and 13). As for
the critical strain energy release, depends from matrix toughness and the crack initiation region
which is usually associated with a slow stable crack growth [56].
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
σx
(Pa)
True Distance (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Crack tip
Figure 8. Stress distribution (σx) at the interface of substrate and resin (δ=3mm).
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
1400
1600
1800
σx
(Pa)
True Distance (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Crack tip
Figure 9. Stress distribution (σx) at the interface of substrate and resin (δ=5mm).
11. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
11
0 5 10 15 20 25 30
-5
0
5
10
15
20
25
30
35
40
45
σy
(Pa)
True Distance (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Crack tip
Figure 10. Stress distribution (σy) at the interface of substrate and resin (δ=3mm).
0 5 10 15 20 25 30
-5
0
5
10
15
20
25
30
35
40
45
50
55
σy
(Pa)
True Distance (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Crack tip
Figure 11. Stress distribution (σy) at the interface of substrate and resin (δ=5mm).
0.0 0.5 1.0 1.5 2.0 2.5 3.0
35
40
45
50
55
60
65
70
75
σy
(Pa)
Crack length (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Figure 12. Stress distribution (σy) at the interface after the 30mm (δ=3mm).
12. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
12
0 1 2 3 4 5
-30
-15
0
15
30
45
60
75
90
σy
(Pa)
Crack length (mm)
CF/Epoxy (UD)
CF/Epoxy (Fabric)
CF/PEI (Fabric)
Figure 13. Stress distribution (σy) at the interface after the 30mm (δ=5mm).
Other parameters such as the specimen width and the effect of adherend transverse thickness
appears to had a small effect on the DCB critical strain energy release rate GIc.
5.2 ANALYTICAL RESULTS
It is well known that in mode I tests, three basic regions appeared in the load-displacement curves,
these corresponding to linear elastic, non-linear elastic and non-linear inelastic behaviour. By
using the finite element method, it was observed that non-linear elastic behaviour was found after
the 30mm length (fig. 12 and 13), and this could be as a result of low flexural rigidity, as well as
fibre bridging mechanism. During crack propagation some of the fibers were pulled out, these
caused the extensive fiber bridging between the crack faces. This feature increased the resistance
to delamination, and consequently, a higher load value was required for the crack advance.
Therefore, further work is required to clarify these results. it should be mentioned that compliance
callibration method is the only data reduction technique, which considers the effect of fiber-
bridging, but it is sensitive to the accuracy of the displacement measurement.
Another parameter which is important to examine is the crosshead speed. Papanicolaou et al. [41],
shows that independently of the displacement rate applied, the linear elastic region is followed by
a large non-linear elastic region and this in turn by an inelastic response. The low flexural rigidity
of the specimens is mainly due to their low thickness (2h = 3.3-4.6mm). Thus large displacements
and rotations occur, leading to a non-linear elastic response.
Furthermore, results that comes from the above theories (analytical), are summarized in tables 2
and 3. In all cases, the modified model proposed by Freeman gives the highest values, while the
end slope of the cantilever (φo) ranges between 5.20-8.96o
. In all cases, crack initiation took
place well within the non-linear part (fig. 12 and 13).
13. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
13
Table 2. Analytical results (J/m2
) for different theories (δ=3mm).
Table 3. Analytical results (J/m2
) for different theories (δ=5mm).
It seems that both beam and corrected beam theory underestimates GIc values. Generally, GIc
increases as δ increases, but most of the energy supplied to the specimen is therefore consumed
in the development of secondary cracks in front of the crack tip, this further splitting resulting
in higher GIc values (fig. 14). As already mentioned, in the above theories-methods the fracture
toughness values depend on the specific data-reduction method applied. But in our case, the
corrected beam theory and the area method is impossible.
Figure 14: Primary and Secondary Cracks
6. CONCLUSIONS
A finite element formulation for double cantilever beam is presented and analyzed the distribution
of the stresses ahead of the crack tip using the extended finite element code (XFEM) in ABAQUS.
XFEM is a partition of unity based method which is able to incorporate functions, typically non-
polynomials into the standard finite element approximating space. The method relies on an
enhancement of the approximating space with enrichment functions. Based on the results, it can
be concluded that the correct crack path is imperative for determining the true failure strength of
the material. The strength will be affected by three parameters such as the length of the initial
crack, the mesh refinement and the domain for interaction integral. As it can be seen from the
above figures, the maximum stresses are found to increase as the crack grows more than 30mm.
It is also expected, that (a) the tougher the composite laminate is, the greater becomes the effect
14. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 4, No. 1/2/3, September2017
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of different kinds of precracks on the crack initiation, and the greater is the difference in crack
initiation and propagation values for GIc, and (b) fabric reinforced composite laminates result in
higher interlaminar fracture toughnesses than unidirectional reinforced materials, because of a
more complex fracture behavior. As already mentioned, the load instantly dropped at several
points during the delamination propagation in the load displacement curves, followed by a further
increase of the load (CF/Ep. and CF/PEI fabrics).
Furthermore, it is important to combine analytical-experimental approach in order to investigate
the fiber bridging effect in unidirectional mode I double cantilever beam specimens with
midplane delaminations. The bridging law was composed by the product of two terms: the fiber
force and the number of bridging fibers per unit area of crack face. The functions of these two
parameters were determined based on experiments. The bridging fibers enhance the resistance to
delamination and usually the energy release rate increases with the crack length (Resistance-curve
effect).
STATEMENT
This research received no specific grant from any funding agency in the public, commercial, or
not for-profit sectors.
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AUTHOR
Panagiotis Charitidis is researcher at the Center of Orthopaedic Research(C.O.RE) at
Center for Interdisciplinary Research and Innovation-Aristotle University of Thessaloniki (
CIRI-AUTH)). He holds Ph.D in applied mechanics from the University of Patras. During
this period, he is professor at Democritus University of Xanthi (Greece).