Higher-Order Beam Theories for Mode II Fracture of Unidirectional Composites

2003 ◽  
Vol 70 (6) ◽  
pp. 840-852 ◽  
Author(s):  
D. V. T. G. Pavan Kumar ◽  
B. K. Raghu Prasad
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Beam Theory ◽  
Strain Energy Release ◽  
Mode Ii ◽  
Third Order ◽  
Beam Theories

Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.

Efficient Computation of Strain Energy Release Rate in Crack Growth Simulation

1999 ◽  
Author(s):  
D. J. Chen
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Error Estimator ◽  
Efficient Computation

Abstract This paper utilizes an automated process to simplify the calculation of the strain energy release rate (SERR) during the crack propagation. The convergence of a finite element solution is achieved by adaptive re-meshing scheme with an error estimator of the linear strain triangular (LST) elements. As the desired mesh density is achieved, computation of the SERR using virtual crack closure technique (VCCT) can be obtained by using the static condensation scheme without re-analyzing the finite element models. Thus, the amount of computational and modeling time can be significantly reduced in the analysis of the crack propagation.

Strain Energy Release Rate Determination in the Case of Mode II Crack in Overhanging Bilayered Composite Beam

2013 ◽  
Vol 43 (3) ◽  
pp. 87-96
Author(s):  
Victor I. Rizov ◽  
Angel S. Mladensky
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Composite Beam ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Rectangular Cross Section ◽  
Strain Energy Release ◽  
Mode Ii ◽  
Mode Ii Crack

Abstract Mode II crack in overhanging bilayered composite beam is investigated. The beam has rectangular cross-section and is made by two unidirectional fiber reinforced composites. The formula for strain energy release rate, G, is obtained by linear elastic fracture mechanics compliance technique. The validity of the expression derived is established by comparison with solution for G in which the internal forces in front and behind the crack tip are used. The influence of the two layers moduli of elasticity ratio on the strain energy release rate is investigated. The dependence among the strain energy release rate and the ratio of the lengths of the overhang beam part and the beam span is also analyzed.

scholarly journals Analysis of Mixed Mode I/II/III Fracture in Foam Core Sandwich Structures Using Imposed Displacement Split Cantilever Beams

2015 ◽  
Vol 45 (3) ◽  
pp. 69-82
Author(s):  
V. Rizov
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Mixed Mode ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Mode I ◽  
Foam Core

Abstract Static fracture in foam core sandwich structures under mixed mode I/II/III loading conditions was studied theoretically. In order to generate such loading conditions, a thread guide was used to impose in- plane displacements of the lower crack arm of a sandwich Split Cantilever Beam (SCB). The upper crack arm was loaded by a transverse force. A three-dimensional finite element model of the imposed displacement sandwich SCB configuration was developed. The fracture was studied applying the concepts of linear-elastic fracture mechanics. The strain energy release rate mode components distribution along the crack front was analyzed using the virtual crack closure technique. The influence of the imposed displacement magnitude and the crack length on the fracture was evaluated. The effect of the sandwich core material on the mixed-mode I/II/III fracture was studied. For this purpose, finite element simulations were carried-out assuming that the core is made by different rigid cellular foams. It was found that the strain energy release rate decreases when the foam density increases.

scholarly journals Computation of mode I strain energy release rate of symmetrical and asymmetrical sandwich structures using mixed finite element

2021 ◽  
Vol 15 (56) ◽  
pp. 229-239
Author(s):  
Amina Mohamed Ben Ali ◽  
Salah Bouziane ◽  
Hamoudi Bouzerd
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Double Cantilever Beam ◽  
Mixed Finite Element ◽  
Strain Energy Release ◽  
Mode I

The use of composite materials is on the rise in different engineering fields, the main advantage of these materials for the aerospace industry is their low weight for excellent mechanical qualities. The analysis of failure modes, such as delamination, of these materials has received great attention from researchers. This paper proposes a method to evaluate the mode I Strain Energy Release Rate (SERR) of sandwich structures. This method associated a two-dimensional mixed finite element with virtual crack extension technique for the analysis of interfacial delamination of sandwich beams. A symmetrical Double Cantilever Beam (DCB) and asymmetrical Double Cantilever Beam (UDCB) have been analyzed in this study.  The comparison of the results obtained by this method and those found in the literature shows efficiency and good precision for the calculation of Strain Energy Release Rate (SERR).

scholarly journals Measurement of Delamination Fracture Energy Using Stepped Laminates

1992 ◽  
Vol 1 (4) ◽  
pp. 096369359200100 ◽  
Author(s):  
P Gopal ◽  
L R Dharani ◽  
S-C Yen
Keyword(s):  
Energy Release Rate ◽  
Fracture Energy ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Mode Ii ◽  
Delamination Fracture ◽  
Mode Of Failure ◽  
Good Agreement

Delamination is often the mode of failure in laminated composites. Therefore the quantification of delamination fracture energy is of vital importance. In this work, externally stepped graphite/epoxy (T300/934) laminates are tested in flexure, resulting in a series of delaminations at 0/90 interface. The delamination fracture energy is calculated based on the strain energy released and is found to be 535 J/m2. This value is in good agreement with the mode II strain energy release rate obtained by other workers.

Analysis of Mixed Mode II/III Crack in Bilayered Composite Beam

2012 ◽  
Vol 42 (4) ◽  
pp. 41-52 ◽  
Author(s):  
Angel S. Mladensky ◽  
Victor I. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Composite Beam ◽  
Mixed Mode ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Mode Ii ◽  
Applied Forces

Abstract Mixed mode II/III crack investigation in cantilever bilayered unidirectional fiber reinforced composite beam is reported. The crack is situated between the layers. The two crack arms have different widths. Formula for the strain energy release rate is obtained by the linear elastic fracture mechanics methods using the magnitude of the applied forces, geometrical characteristics of the cross-section, and the elastic moduli of the layers. An equivalent shear modulus of the un-cracked beam portion is used. Several diagrams illustrating the results of parametrical analysis of the strain energy release rate are presented. The paper is a part of a research in the field of fracture behaviour of composite beams.

Analysis of Mode II Crack in Bilayered Composite Beam

2012 ◽  
Vol 42 (2) ◽  
pp. 67-78 ◽  
Author(s):  
Victor Rizov ◽  
Angel Mladensky
Keyword(s):  
Fracture Mechanics ◽  
Energy Release Rate ◽  
Release Rate ◽  
Composite Beam ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Composite Beams ◽  
Mode Ii ◽  
Mode Ii Crack

Analysis of Mode II Crack in Bilayered Composite Beam Mode II crack problem in cantilever bilayered composite beams is considered. Two configurations are analyzed. In the first configuration the crack arms have equal heights while in the second one the arms have different heights. The modulus of elasticity and the shear modulus of the beam un-cracked part in the former case and the moment of inertia in the latter are derived as functions of the two layers characteristics. The expressions for the strain energy release rate, G are obtained on the basis of the simple beam theory according to the hypotheses of linear elastic fracture mechanics. The validity of these expressions is established by comparison with a known solution. Parametrical investigations for the influence of the moduli of elasticity ratio as well as the moments of inertia ratio on the strain energy release rate are also performed. The present article is a part of comprehensive investigation in Fracture mechanics of composite beams.

Energy method for the calculation of the energy release rate of delamination in composite beams

2018 ◽  
Vol 53 (4) ◽  
pp. 425-443 ◽  
Author(s):  
Weiling Zheng ◽  
Christos Kassapoglou
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Energy Method ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Crack Tip ◽  
Strain Energy Release ◽  
Small Cracks

An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model.

Sign in / Sign up

Export Citation Format

Share Document