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.
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.
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.
Experimental and numerical evaluation of plasticity model with ductile damage...IJERA Editor
This work aims to develop a methodology for numerical evaluation via finite elements applied to projects shields sheet metal. To validate the methodology physical test were conduct and were compare with the numerical simulation. In the simulation, a plasticity material modelit was used at high strain rates, besides the insertion of a damage model through forming limit diagram (FLD) to capture the initiation of damage and energy criteria for propagation of the fracture. The tested shielding design is for the II-A protection level using the type 9mm ammunition.
Experimental and numerical evaluation of plasticity model with ductile damage...IJERA Editor
This work aims to develop a methodology for numerical evaluation via finite elements applied to projects shields sheet metal. To validate the methodology physical test were conduct and were compare with the numerical simulation. In the simulation, a plasticity material modelit was used at high strain rates, besides the insertion of a damage model through forming limit diagram (FLD) to capture the initiation of damage and energy criteria for propagation of the fracture. The tested shielding design is for the II-A protection level using the type 9mm ammunition.
Modelling and Simulation of Composition and Mechanical Properties of High Ent...msejjournal
Magnesium alloys are high potential materials for application in the aerospace and automotive industries
due to their lightweight properties. They can help to lower dead weight and fuel consumption to contribute
to sustainability and efficiency. It is possible to achieve high specific strength and high stiffness of the
alloys by varying compositions of alloying elements. Applications of magnesium are limited due to its low
strength and relatively low stiffness. This research focuses on a recipe of multi component alloys of
magnesium with varied percentages of Mg, Al, Cu, Mn and Zn obtained from literature and optimizes the
percentage compositions to obtain for high specific strength and specific stiffness. Relationships among
percentage constituents of the alloy components are examined in Matlab R2022b using multiple linear
regression. Optimization is achieved using genetic algorithm to determine the specific strengths and
stiffness. The resulting optimal alloy component percentages by weight are used for microstructure
simulation of thermodynamic properties, diffusion and phase transformations of proposed alloy is done in
MatCalc software version 6.04. Results show potential for improved mechanical properties resulting from
disordered structure in the high entropy magnesium alloy. Future research should focus on production and
characterization of the proposed alloy.
Thermal and Metrological Studies on YTTRIA Stabilized Zirconia Thermal Barrie...msejjournal
Thermal Barrier Coatings (TBCs), routinely prepared from Ceramic based compositions (typically
8%Y2O3-ZrO2or 8YSZ) are being engineered to protect the metallic components from degradation in
applications like gas turbines, jet and automotive engines. With a goal of finding improved TBC materials
a wide variety of ceramics are being researched worldwide. Before physically preparing the TBCs of
uncommon compositions in the laboratory, their suitability to perform can be predicted. Limited
accessibility to detailed and realistic information on the influence of newer compositions (other than 8YSZ)
on TBCs warrants methods to obtain this information.
In this paper, 8YSZ TBCs coated onto aluminium substratesare studied for thermal fatigue, thermal barrier
and materials characteristics to determine the reliability of the coating configuration to withstand the
harshness of test conditions under the framework of experiments. Thereafter, the results have been used to
corroboratethe developed simulation model. Results obtained via thermal tests confirm the suitability of the
model and we can predict the thermal barrier effects of TBCs when prepared from materials other than
YSZ.
More Related Content
Similar to RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERMOPLASTIC COMPOSITES
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.
Experimental and numerical evaluation of plasticity model with ductile damage...IJERA Editor
This work aims to develop a methodology for numerical evaluation via finite elements applied to projects shields sheet metal. To validate the methodology physical test were conduct and were compare with the numerical simulation. In the simulation, a plasticity material modelit was used at high strain rates, besides the insertion of a damage model through forming limit diagram (FLD) to capture the initiation of damage and energy criteria for propagation of the fracture. The tested shielding design is for the II-A protection level using the type 9mm ammunition.
Experimental and numerical evaluation of plasticity model with ductile damage...IJERA Editor
This work aims to develop a methodology for numerical evaluation via finite elements applied to projects shields sheet metal. To validate the methodology physical test were conduct and were compare with the numerical simulation. In the simulation, a plasticity material modelit was used at high strain rates, besides the insertion of a damage model through forming limit diagram (FLD) to capture the initiation of damage and energy criteria for propagation of the fracture. The tested shielding design is for the II-A protection level using the type 9mm ammunition.
Modelling and Simulation of Composition and Mechanical Properties of High Ent...msejjournal
Magnesium alloys are high potential materials for application in the aerospace and automotive industries
due to their lightweight properties. They can help to lower dead weight and fuel consumption to contribute
to sustainability and efficiency. It is possible to achieve high specific strength and high stiffness of the
alloys by varying compositions of alloying elements. Applications of magnesium are limited due to its low
strength and relatively low stiffness. This research focuses on a recipe of multi component alloys of
magnesium with varied percentages of Mg, Al, Cu, Mn and Zn obtained from literature and optimizes the
percentage compositions to obtain for high specific strength and specific stiffness. Relationships among
percentage constituents of the alloy components are examined in Matlab R2022b using multiple linear
regression. Optimization is achieved using genetic algorithm to determine the specific strengths and
stiffness. The resulting optimal alloy component percentages by weight are used for microstructure
simulation of thermodynamic properties, diffusion and phase transformations of proposed alloy is done in
MatCalc software version 6.04. Results show potential for improved mechanical properties resulting from
disordered structure in the high entropy magnesium alloy. Future research should focus on production and
characterization of the proposed alloy.
Thermal and Metrological Studies on YTTRIA Stabilized Zirconia Thermal Barrie...msejjournal
Thermal Barrier Coatings (TBCs), routinely prepared from Ceramic based compositions (typically
8%Y2O3-ZrO2or 8YSZ) are being engineered to protect the metallic components from degradation in
applications like gas turbines, jet and automotive engines. With a goal of finding improved TBC materials
a wide variety of ceramics are being researched worldwide. Before physically preparing the TBCs of
uncommon compositions in the laboratory, their suitability to perform can be predicted. Limited
accessibility to detailed and realistic information on the influence of newer compositions (other than 8YSZ)
on TBCs warrants methods to obtain this information.
In this paper, 8YSZ TBCs coated onto aluminium substratesare studied for thermal fatigue, thermal barrier
and materials characteristics to determine the reliability of the coating configuration to withstand the
harshness of test conditions under the framework of experiments. Thereafter, the results have been used to
corroboratethe developed simulation model. Results obtained via thermal tests confirm the suitability of the
model and we can predict the thermal barrier effects of TBCs when prepared from materials other than
YSZ.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
New Experiment System for the Interaction Between Soft Rock and Water : A Cas...msejjournal
The strength of rock strongly depends on the water content especially when the rocks contain clay
materials. The interaction between soft rock and water always threaten the soft rock engineering projects.
For this problem, new sets of laboratory experiment systems are developed to simulate the interaction
between soft rock and water or vapor. In this paper, the principles of experiment systems are introduced
with particular reference to the application on soft rock in Mogao Grottoes, one of the world famous
ancient sites in China. Two kinds of rock samples, the sandstone and muddy sandstone, are obtained by insitu sampling system. Then the laboratory experiments are performed under different environment
conditions. By the specific boundary conditions design, the physical-chemical effect and mechanic effect on
water absorption of rock samples are separated for further mechanism study by the experiment system, and
the different hydrological actions of water and vapor under variable experiment environment are obtained.
The interaction mechanism is discussed with assistant methods, such as SEM (Scanning Electron
Microscope), mercury injection test, X-ray diffraction analysis and etc. With the relation between water
content and soft rock strength, the study may provide guidance and basis for the soft rock engineering in
the future.
International Conference on Embedded Systems and VLSI (EMVL 2023)msejjournal
International Conference on Embedded Systems and VLSI (EMVL 2023) will provide an excellent International forum for sharing knowledge and results in theory, methodology and applications of Embedded Systems.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
Modeling, Analyzing and Safety Aspects of Torsion and Noise Effects on Round ...msejjournal
Each material has its own effect and behavior on external impacts like heat, force, tension, compression,
torsion etc. It is important to study and analyze these behaviors before selecting a material for an
engineering application in the design aspects itself. If predicted values analyzed by both mathematical and
software are available it is easy to get the reliable details in the pre design itself. By this one can ensure the
safety of the component and the system also. In this investigation, the effects of torsional loads on mild steel
round shafts with various diameters and lengths have been analyzed. The additional effects like angle of
rotation, rpm and duration also considered to find the optimum predicted value. The data observed by
various experiments are analyzed by design of experiments especially by response surface methodology.
Minitab software is used for canalization. The data are tabulated and kept for future reference. Noise effect
due to the gradual torsional load performed in the gear box and other rotating components is also studied
for healthy working environment. The nature and characteristics of material also be explained by this noise
analysis.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
On Decreasing of Dimensions of Field-Effect Transistors with Several Sourcesmsejjournal
We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several
sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture
heterostructure with specific configuration. After that it is necessary to dope required areas of the heterostructure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlinearity of mass and heat transport and variation in space and time (at one time) physical parameters of these
processes
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Using Advanced Inspection Method (Three-Dimensional Ultrasonic) in Recognitio...msejjournal
In this study, using Harfang Code 32 device, the slag catcher pipelines in one of the South Pars phases
were tested. In radiography method of these lines, no clear defect was observed in radiographic films due
to the high thickness of 40 mm. However, marvelous results were obtained using advanced ultrasonic.
Review and analysis of the results will result in high potential of three-dimensional ultrasonic method in
identifying defects in pipelines with high thicknesses and preventing financial and life-threatening risks
during the use of these refineries in the future.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Flammability Characteristics of Chemical Treated Woven Hemp Fabricmsejjournal
Woven hemp fabric was treated with sodium hydroxide, commercial flame retardant chemical, and
combination of both to increase its fire-retardant properties. Treatments of fire-retardant changed the
properties of woven hemp fabric such as increased its fabric shrinkage and density of fibres which ranges
from 0.67 to 5% and 1.43 to 1.53 g/cm3
respectively. After the treatment, the fire retardancy of the fabric
increased tremendously which was observed by the burning, thermogravimetry and limiting oxygen index
tests. Some of the samples were not burnt when exposed to flame source and the burning rate needed to be
measured under exaggeration of flame at longer time. The limiting oxygen index value increased from 18.6
to 51 after the treatments which explained the scenario happened in the burning tests. Nevertheless, its
mechanical properties decreased slightly that ranges from 18 to 32% and 23 to 39% for warp and weft
respectively compared to untreated fibre.
Advances in Materials Science and Engineering: An International Journal (MSEJ) msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ) msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal ...msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
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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
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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
σ
x
(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
σ
x
(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
σ
y
(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
σ
y
(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
σ
y
(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
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0 1 2 3 4 5
-30
-15
0
15
30
45
60
75
90
σ
y
(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
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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).