• Advances in aircraft and spacecraft science
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• v.1 no.2
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• pp.177-196
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• 2014

A theoretical exploration for determining the characteristic length of the cohesive zone for a double cantilever beam (DCB) specimen under mode I loading was conducted. Two traction-separation laws were studied: (i) a law with only a linear elastic stage from zero to full traction strength; and (ii) a bilinear traction law illustrating a progressive softening stage. Two analytical solutions were derived for the first law, which fit well into two existing solution groups. A transcendental equation was derived for the bilinear traction law, and a graphical method was presented to identify the resultant cohesive zone length. The study using the bilinear traction law enabled the theoretical investigation of the individual effects of cohesive law parameters (i.e., strength, stiffness, and fracture energy) on the cohesive zone length. Correlations between the theoretical and finite element (FE) results were assessed. Effects of traction law parameters on the cohesive zone length were discussed.

• Computers and Concrete
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• v.1 no.1
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• pp.47-60
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• 2004

The influence of the fracture process zone (FPZ) on the fracture properties is one of the hottest topics in the field of fracture mechanics for cementitious materials. Within the FPZ in front of a traction free crack, cohesive forces are distributed in accordance with the softening stress-separation constitutive relation of the material. Therefore, further crack propagation necessitates energy dissipation, which is the work done by the cohesive forces. In this paper $g_f$, the local fracture energy characterizing the energy consumption due to the cohesive forces, is discussed. The computational expression of $g_f$ in the FPZ can be obtained for any stage during the material fracture process regarding the variation of FPZ, whether in terms of its length or width. $G_{fa}$, the average energy consumption along the crack extension region, has also been computed and discussed in this paper. The experimental results obtained from the wedge splitting tests on specimens with different initial notch ratios are employed to investigate the property of the local fracture energy $g_f$ and the average value $G_{fa}$ over the crack extension length. These results can be used to indicate the influence of the FPZ. Additionally, changes in the length of the FPZ during the fracture process are also studied.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.11
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• pp.1265-1272
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• 2014

This study performed the progressive failure analysis of adhesive joints of a composite pressure vessel with a separated dome by using a cohesive zone model. In order to determine the input parameters of a cohesive element for numerical analysis, the interlaminar fracture toughness values in modes I and II and in the mixed mode for the adhesive joints of the composite pressure vessel were obtained by a material test. All specimens were manufactured by the filament winding method. A mechanical test was performed on adhesively bonded double-lap joints to determine the shear strength of the adhesive joints and verify the reliability of the cohesive zone model for progressive failure analysis. The test results showed that the shear strength of the adhesive joints was 32MPa; the experiment and analysis results had an error of about 4.4%, indicating their relatively good agreement. The progressive failure analysis of a composite pressure vessel with an adhesively bonded dome performed using the cohesive zone model showed that only 5.8% of the total adhesive length was debonded and this debonded length did not affect the structural integrity of the vessel.

• Computers and Concrete
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• v.9 no.1
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• pp.1-19
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• 2012

The size-effect study of various fracture parameters obtained from two parameter fracture model, effective crack model, double-K fracture model and double-G fracture model is presented in the paper. Fictitious crack model (FCM) for three-point bend test geometry for cracked concrete beam of laboratory size range 100-400 mm is developed and the different fracture parameters from size effect model, effective crack model, double-K fracture model and double-G fracture model are evaluated using the input data obtained from FCM. In addition, the fracture parameters of two parameter fracture model are obtained using the mathematical coefficients available in literature. From the study it is concluded that the fracture parameters obtained from various nonlinear fracture models including the double-K and double-G fracture models are influenced by the specimen size. These fracture parameters maintain some definite interrelationship depending upon the specimen size and relative size of initial notch length.

• Computers and Concrete
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• v.29 no.6
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• pp.393-405
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• 2022

Lightweight concrete is a superior material due to its light weight and high strength. There however remain significant lacunae in engineering knowledge with regards to shear failure of lightweight fiber reinforced concrete beams. The main aim of the present study is to investigate the optimum usage of steel fibers in lightweight fiber reinforced concrete (LWFRC). Multi-scale finite element model calibrated with experimental results is developed to study the effect of steel fibers on the mechanical properties of LWFRC beams. To decrease the amount of steel fibers, it is preferred to reinforce only the middle section of the LWFRC beams, where the flexural stresses are higher. For numerical simulation, a multi-scale finite element model was developed. The cement matrix was modeled as homogeneous and uniform material and both steel fibers and lightweight coarse aggregates were randomly distributed within the matrix. Considering more realistic assumptions, the bonding between fibers and cement matrix was considered with the Cohesive Zone Model (CZM) and its parameters were determined using the model update method. Furthermore, conformity of Load-Crack Mouth Opening Displacement (CMOD) curves obtained from numerical modeling and experimental test results of notched beams under center-point loading tests were investigated. Validating the finite element model results with experimental tests, the effects of fibers' volume fraction, and the length of the reinforced middle section, on flexural and residual strengths of LWFRC, were studied. Results indicate that using steel fibers in a specified length of the concrete beam with high flexural stresses, and considerable savings can be achieved in using steel fibers. Reducing the length of the reinforced middle section from 50 to 30 cm in specimens containing 10 kg/m3 of steel fibers, resulting in a considerable decrease of the used steel fibers by four times, whereas only a 7% reduction in bearing capacity was observed. Therefore, determining an appropriate length of the reinforced middle section is an essential parameter in reducing fibers, usage leading to more affordable construction costs.

• Composites Research
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• v.15 no.4
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• pp.23-31
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• 2002

The two dimensional size effect of specimen gauge section ($length{\;}{\times}{\;}width$) was investigated on the compressive behavior of a T300/924 $\textrm{[}45/-45/0/90\textrm{]}_{3s}$, carbon fiber-epoxy laminate. A modified ICSTM compression test fixture was used together with an anti-buckling device to test 3mm thick specimens with a $30mm{\;}{\times}{\;}30mm,{\;}50mm{\;}{\times}{\;}50mm,{\;}70mm{\;}{\times}{\;}70mm{\;}and{\;}90mm{\;}{\times}{\;}90mm$ gauge length by width section. In all cases failure was sudden and occurred mainly within the gauge length. Post failure examination suggests that $0^{\circ}$ fiber microbuckling is the critical damage mechanism that causes final failure. This is the matrix dominated failure mode and its triggering depends very much on initial fiber waviness. It is suggested that manufacturing process and quality may play a significant role in determining the compressive strength. When the anti-buckling device was used on specimens, it was showed that the compressive strength with the device was slightly greater than that without the device due to surface friction between the specimen and the device by pretoque in bolts of the device. In the analysis result on influence of the anti-buckling device using the finite element method, it was found that the compressive strength with the anti-buckling device by loaded bolts was about 7% higher than actual compressive strength. Additionally, compressive tests on specimen with an open hole were performed. The local stress concentration arising from the hole dominates the strength of the laminate rather than the stresses in the bulk of the material. It is observed that the remote failure stress decreases with increasing hole size and specimen width but is generally well above the value one might predict from the elastic stress concentration factor. This suggests that the material is not ideally brittle and some stress relief occurs around the hole. X-ray radiography reveals that damage in the form of fiber microbuckling and delamination initiates at the edge of the hole at approximately 80% of the failure load and extends stably under increasing load before becoming unstable at a critical length of 2-3mm (depends on specimen geometry). This damage growth and failure are analysed by a linear cohesive zone model. Using the independently measured laminate parameters of unnotched compressive strength and in-plane fracture toughness the model predicts successfully the notched strength as a function of hole size and width.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.88-91
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• 2002

The two dimensional size effect of specimen gauge section (length x width) was investigated on the compressive behavior of a T300/924 [45/-45/0/90]3s, carbon fiber-epoxy laminate. A modified ICSTM compression test fixture was used together with an anti-buckling device to test 3mm thick specimens with a 30$\times$30, 50$\times$50, 70$\times$70, and 90mm$\times$90mm gauge length by width section. In all cases failure was sudden and occurred mainly within the gauge length. Post failure examination suggests that $0^{\circ}$ fiber microbuckling is the critical damage mechanism that causes final failure. This is the matrix dominated failure mode and its triggering depends very much on initial fiber waviness. It is suggested that manufacturing process and quality may play a significant role in determining the compressive strength. When the anti-buckling device was used on specimens, it was showed that the compressive strength with the device was slightly greater than that without the device due to surface friction between the specimen and the device by pretoque in bolts of the device. In the analysis result on influence of the anti-buckling device using the finite element method, it was found that the compressive strength with the anti-buckling device by loaded bolts was about 7% higher than actual compressive strength. Additionally, compressive tests on specimen with an open hole were performed. The local stress concentration arising from the hole dominates the strength of the laminate rather than the stresses in the bulk of the material. It is observed that the remote failure stress decreases with increasing hole size and specimen width but is generally well above the value one might predict from the elastic stress concentration factor. This suggests that the material is not ideally brittle and some stress relief occurs around the hole. X-ray radiography reveals that damage in the form of fiber microbuckling and delamination initiates at the edge of the hole at approximately 80% of the failure load and extends stably under increasing load before becoming unstable at a critical length of 2-3mm (depends on specimen geometry). This damage growth and failure are analysed by a linear cohesive zone model. Using the independently measured laminate parameters of unnotched compressive strength and in-plane fracture toughness the model predicts successfully the notched strength as a function of hole size and width.

• Composites Research
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• v.34 no.5
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• pp.323-329
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• 2021

In this paper, the characteristics of fracture in mode I loading were analyzed for adhesively bonded joints with non-uniform adhesion. The Double Cantilever Beam test was performed and mode I fracture toughness was obtained. In the case of non-uniform adhesively bonded joints, the stable crack growth sections and unstable crack growth section were shown. The fracture characteristics of each section were observed through the load-displacement curve of the DCB test and the fracture surface of the specimen. Finite Element Analysis was performed at the section based on segmented section by crack length measured through the test and using the mode I fracture toughness of each section. Through DCB test results and finite element analysis results, it was confirmed that the fracture behavior of specimens with non-uniform adhesion can be simulated.