Stiffness reduction of cracked general symmetric laminates using a. Hajikazemi, m, sadr, mh 2014a a variational model for stress analysis in cracked laminates with arbitrary symmetric layup under general inplane loading. Research areas angleply laminate, inplane shear, stiffness reduction, transverse cracking, variational analysis. The effect of matrix cracking on mechanical properties in. The method provides a lower bound for the stiffness matrix of a cracked angleply. In the present paper a new assumed stress finite element method, based on a complementary energy method, is. A unit cell based method is developed based on variational principles to derive the stress state and effective mechanical properties of angleply laminates of type. Since changes may be made before publication, this preprint is made available with. The cracks are assumed to be caused by the load actingin the axial x direction. Variational analysis of cracked laminates with imperfect interlaminar interface is developed on the basis of a generalized extemum principle of thermoelastic complementary energy. Application of dic to deformation measurement around damages in cfrp crossply laminates.
All models use the principle of minimum complementary energy for calculation of the stress state in a laminate element between two cracks, as was the case with the original model by hashin. Shortly speaking, approaches to the problem include finite element analysis, such as in, simple yet less accurate shearlag analysis based methods refs. Iraq abstract the paper presents mainly on the natural frequency of symmetric angle ply composite. Chandrashekhara and bangera investigated the free vibration of angle ply composite beams by a higherorder shear deformation theory using the shear flexible finite.
The proposed procedure is implemented in ansys as a usermaterial subroutine for transverse crack initiation and propagation in symmetric crossply and 0 r. Kuriakose s and talreja r 2004 variational solutions to stresses in cracked crossply. Models based on variational analysis are compared with respect to the elastic properties of crossply laminates with transverse cracks. International journal for numerical methods in engineering 120 5, 666705, 2019. Variational analysis of cracked angleply laminates using the principle of minimum complementary energy an optimal admissible stress field is derived that satisfies equilibrium, boundary and traction continuity conditions. Cfrp laminates is done by using the xray technique, while for gfrp laminates a dslr camera is used. Cracked laminates with imperfect interlaminar interface. Freeedge effects analysis of angle ply laminates under transverse loading using layerwise finiteelement method with semianalytical shear stress calculation. A variational approach for predicting initiation of matrix cracking and. Apr 01, 2010 variational analysis of cracked angleply laminates variational analysis of cracked angleply laminates vinogradov, v hashin, z. The cracks parallel to the fiber direction are extended over the full thickness of transverse plies and often cross the entire test specimen width.
Staff profile engineering, school of newcastle university. Kelly, a, zweben, c, talreja, r eds polymer matrix composites. Interlaminar stresses in composite laminates subjected to. Prediction of poissons ratio degradation in hygrothermal aged and cracked. Pdf stress redistribution in angleply laminates due to formation of intralaminar matrix cracks depends on the crack spatial distribution. Stress redistribution in angleply laminates due to formation of intralaminar matrix cracks depends on the crack spatial distribution. Talrejavariational solutions to stresses in cracked. Ii and the total g associated with angleply matrix cracking and local del. Hashin department of solid mechanics, materials and structures, tel aviv university, tel aviv, israel received 7 june 1985 crossply 0 90 laminates which contain distributions of intralaminar cracks within the 90ply are analyzed by variational methods for tensile and for shear. The obtained results show a good agreement comparing with experimental data 6 for different angleply laminate and without taking into.
The model is valid for multiple ply laminates that can be nonsymmetric. A stressbased variational model is developed to study stiffness reduction and stress distribution in angleply laminates. Manufacture, test and model angleply laminates in order to achieve ductility through fibre rotation and matched matrix response. Variational method article about variational method by. Multiscale creep analysis of angleply cfrp laminates based. Dye penetrantenhanced xradiography was used to document the onset of matrix cracking in the central. Variational analysis for angleply laminates with matrix cracks. Predictions of the nonlinear stressstrain responses of various angleply agree well with previous experimental results, which verifies that the present mesoscale model is available for the prediction of the pseudoductile behaviour of angleply laminates. During service loading of crossply laminates, transverse cracks occur in plies.
Rao department ofmechanical engineering indian institute of technology, kharagpur721 302. Asymptotic behavior of the laminate stiffness when the crack densities are low or high is derived and its importance is discussed. Comparison to published experimental data demonstrates very good agreement between the prediction and the experimental measurements for the youngs modulus of glassepoxy 0 45 s laminate. The admissible stress state of the cracked laminate was derived in each distribution pattern implementing ply refinement technique. Vinogradov, v, hashin, z 2010 variational analysis of cracked angleply laminates. Wisnom advanced composites centre for innovation and science, university of bristol, queens building, bristol, bs8 1tr. Delaminations were modeled in the 08 interface, bounded by a matrix crack and the stress free edge. Atlurit center for advancement of computational mechanics, georgia institute of technology, atlanta, ga. Laminae material is assumed to be linearly elastic, homogeneous and isotropicorthotropic.
If an angleply laminate has an even number of plies, then a16 a26 0. The measured stiffness reduction as a function of the crack density is compared to an analytical prediction for cracked angleply laminates based on a variational stress analysis. In this paper, transverse cracking of crossply 0290ns n 2,3,4 laminates under uniaxial tension load was studied by means of experimental and numerical methods. Free vibration analysis of symmetric angle ply composite laminated plate with temperature effect kawther khalid younus asst. A topdown analytic approach for the analysis of edge effects of angleply symmetric laminates. Using a variational approach with the principle of. Variational analysis of transverse cracking and local delamination in. The new analysis is applicable to any angleply laminate with parallel intralaminar cracks subjected to inplane membrane forces and moments.
Investigation of throughthickness stresses in composite. Interlaminar stresses in general laminates with straight. This method is also examined to study matrix crack evolution in tensile specimen with open hole, and the results found to be in good. Characterization and analysis of damage mechanisms in tensiontension fatigue of graphiteepoxy laminates effects of defects in composite materials philadelphia, pa astm 1984 21. In the current study, a variational model is developed for predicting stress transfer due to ply cracking in general crossply laminates subject to outofplane bending and biaxial inplane loading. It also yields approximate values for stress perturbations pro duced by the cracks. Most of the existing approaches for stress analysis of a cracked laminate are either limited to crossply laminates or to symmetrical arrays of cracks. Limits of the compliance elements and the stress distributions at the infinite crack density are compared to the results of the classical theory of laminates. Then, the present method is applied to the creep analysis of three kinds of angleply carbon fiberepoxy laminates, i. Stiffness reduction of angleply laminates of the type. Onset of matrix crackingin angleply ceramic matrix composites. A 2d shear lag method is used to determine stresses in a laminate representative segment containing one crack and two crack tip delaminations.
Pdf stress redistribution in angle ply laminates due to formation of intralaminar matrix cracks depends on the crack spatial distribution. Nairn and shoufeng hu department of materials science and engineering, university of utah, salt lake city, utah 84112, usa abstract the microcracking process in laminates which have outerply 90 plies e. Variational analysis of cracked angleply laminates. International journal for numerical methods in engineering 2019, 120 5, 666705. Assumed stress finite element analysis of throughcracks in. On transverse matrix cracking in crossply laminates loaded in simple bending on transverse matrix cracking in crossply laminates loaded in simple bending smith, p. The variational principle 9 provides a convenient framework for developing efficient plate bending elements for the analysis of thin and thick composite laminates. On transverse matrix cracking in crossply laminates.
In this paper, local delaminations growing uniformly from the tips of angle ply matrix cracks in composite laminates loaded in tension are modelled theoretically. International journal of solids and structures, vol. Pdf the effect of matrix cracking on mechanical properties in frp. The analyses of cracked laminates based on a variational principle and related approaches are appraised in this paper. For the open and closed cracks, the tensile force, the compressive force and the shear force are mainly studied by the stressbased variational approach with the pending partition loads at the statically indeterminate boundary, with considering not only three cases of the ideal transverse cracks, the smooth planesurface open crack, the smooth. Analysis of transverse cracking in composite crossply laminates. Micromechanics of cracked laminates under uniaxial load.
Constant amplitude tensiontension fatigue tests were conducted on as435016 graphite epoxy 0 2. Comparison of variational and generalized plane strain. Although most of the work has been done on cross ply laminates, the problems of stiffness degradation and damage accumulation in angle ply laminates have also been addressed. Prediction of poissons ratio degradation in hygrothermal. The variational analysis was utilized by vinogradov and hashin 2005 to estimate the stress fields in a cracked laminate subjected to an applied load and a temperature change. Analysis of local delaminations caused by angle ply matrix. Nevertheless, the stress analysis of cracked laminates needed in stiffness reduction and. Analysis of local delaminations in composite laminates with. Transverse cracking in laminated composites springerlink. Variational analysis of transverse cracking and local delamination in h m90 n s laminates. The firstorder shear deformation theory in conjunction with the variational energy method is employed in mathematical formulations. Variational analysis of angleply laminates with parallel. The eightnode lagrange finiteelement technique is used for.
A variational model for stress analysis in cracked. The orientation of the ith layer is specified by the angle i i. Free vibration analysis of laminated plates using a. The variational analysis developed permits the evaluation of stiffness reduction of any. Closed form results for effective youngs modulus, thermal expansion coefficient, shear modulus and internal stresses are developed for cracked crossply laminates. Parameter analysis of damaged region for laminates with. Read a variational model for stress analysis in cracked laminates with arbitrary symmetric layup under general inplane loading, international journal of solids and structures on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Assumed stress finite element analysis of throughcracks in angleply laminates 1125 t.
Analysis of the mode of initial damage due to applied axial load. Natural boundary conditions are derived from the variational principle to overcome the limitations of the existing variational methods on the analysis of cracked general crossply laminates. Abstract multiple transverse cracking is one of the most common faiure modes in composite laminates. Composite angle ply laminates and netting analysis 01pa3253 stress. Archive proceedings of the institution of mechanical engineers part c journal of mechanical engineering science 19891996 vols. Measurement of the mechanical properties of angle ply laminates doctor of phiiosophy 2000 jing wang department of chemical engineering and applied chemistry university of toronto abstract design of advanced fiber composite structures requires a knowledge of the strength and stiffness of laminates. The governing equations of the problem are derived on the basis of the generalized plane strain assumption and twodimensional equations of elasticity. Assumed stress finite element analysis of throughcracks. Thermal buckling behavior of hybridcomposite angleply.
Sadr aerospace engineering department and centre of excellence in computational aerospace engineering, amirkabir university of technology, tehran, iran. However, the resulting strain would cause the reinforcement to rotate to a new angle. Application of nonstraight or wavy fibres to provide deformation over a wider range of angles. Effect of angleply orientation on compression strength of. Effect of angleply orientation on compression strength of composite laminates christopher p. By employing the boundarydiscontinuous fourier expansion method, the governing.
A modified shearlag analysis was applied to describe the cyclenumberdependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. The orientation of the ith layer is specified by the angle. Materials free fulltext a simplified computational. The unit cell of a cracked h m90 n s laminate with delamination between two. Transverse cracking is probably the first and most dominant mode of damage in composite materials.
Variational analysis of freeedge stress and displacement fields in general unsymmetric and thinply laminates under inplane, bending and thermal loading. Free vibration analysis of laminated plates using a layerwise theory. A design methodology using biangle ply laminates made from. Fatigue tests were conducted at a frequency of 5 hz and an r ratio of 0. The formation and e ect of outerply microcracks in crossply laminates. A variational model for stress analysis in cracked laminates with arbitrary symmetric layup under general inplane loading m. Jan 28, 2009 a boundarydiscontinuous fourier expansion method to analyze the displacements and stresses in cross ply composite laminates with transverse cracks is presented. The experimental results for stiffness reduction agree well with the analytical results. Varnaanalytical modeling of stiffness reduction in symmetric and.
A refined higher order shear deformation theory for linear and geometrically nonlinear behavior of fiber. Varna, analysis of cracked general crossply laminates under general bending loads. Variational analysis of cracked general crossply laminates under bending and biaxial extension mohammad hajikazemi ugent, m homayoune sadr and ramesh talreja 2015 international journal of damage mechanics. A variational model for stress analysis in cracked laminates. Comparing laminates of glassepoxy and graphiteepoxy with the available finite element results shows that stress components are in very good accordance. Variational analysis of delamination growth for composite. Mechanics of materials 4 1985 1216 121 northholland analysis of cracked laminates. Sanial3, jp charles4 1 cea, dam, bruyeres le chatel 91297 arpajon, france. Micromacro approach for prediction of matrix cracking. Earlier finite element method analysis of laminates with cracked 90plies showed that the effective longitudinal modulus and poissons ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. The fatigue life of cross ply composite laminates was evaluated using a statistical model. The formation and e ect of outerply microcracks in cross.
In the numerical simulations, a simplified computational strategy only focusing on the damage of the resin was proposed and the. Thin prepreg angleply laminates university of bristol. Effect of angle ply orientation on tensile properties of bi. Stiffness degradation in hygrothermal aged crossply. In the field of matrix cracks analysis for symmetric laminates, the present. Thin prepreg angleply laminates project is part of the hiperduct programme grant key challenges. The interlaminar shear stresses between 90 and h 1plies and between h and h 2plies, respectively, are assumed to be in the form of general functions. Laminated composite materials have characteristics of high modulusweight 1 and strengthweight ratios, excellent fatigue properties, and noncorroding behaviour. Results for longitudinal stiffness of a cracked glassepoxy 0 45 s laminate are in very good agreement with experimental data. Variational analysis for angleply laminates with matrix cracks article in international journal of solids and structures 512122 october 2014 with 29 reads how we measure reads.
Hajikazemi, m, sadr, mh, talreja, r 2015 variational analysis of cracked general crossply laminates under bending and biaxial extension. Two different families of graphiteepoxy laminates with similar layups but different stacking sequences, 0e0s and 600s,were analyzed using threedimensional finite element analysis for 0 15 and 30 degrees. Composites science and technology 70 4, 638646, 2010. Assumed stress finite element analysis of throughcracks in angle ply laminates 1125 t. Local delamination in laminates with angle ply matrix cracks. Simulation of fatigue performance of crossply composite. Vibration and stability of angleply laminated composite plates subjected to inplane stresses. Their work showed that the probability density function for the specific surface energy requires modification when applying to different laminates. In this paper, transverse cracking of cross ply 0290ns n 2,3,4 laminates under uniaxial tension load was studied by means of experimental and numerical methods. It is widely recognized that the changes of laminate thermomechanical constants, caused by the transverse cracking of composite laminates, can be significant. Jul 31, 2015 1967 shelby gt500 barn find and appraisal that buyer uses to pay widow price revealed duration. Variational analysis of angleply laminates article pdf available in composites science and technology 704.
Variational analysis of cracked general crossply laminates under. A thermal buckling analysis of symmetric and antisymmetric angleply laminated hybrid composite plates with an inclined crack subjected to a uniform temperature rise is presented in this paper. In this analysis, a unit cell in the ply level of a composite laminate containing both. Comparison between the analysis results and experimental data reveals that the present method accurately predicts the creep behavior of unidirectional cfrp laminates.
A variational model for stress analysis in cracked laminates with arbitrary. A variational model for boundary layer effects in crossply laminates based on a c0continuous layerwise displacement formulation. Thermal buckling analysis of symmetric and antisymmetric crossply laminated hybrid composite plates with an inclined crack subjected to a uniform temperature rise are presented in this paper. Oct 15, 2014 read variational analysis for angle ply laminates with matrix cracks, international journal of solids and structures on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Pseudoductility of thin ply cfrp angleply laminates youtube. A unitcell based stress analysis was developed upon variational principles to permit the evaluation of stiffness reduction of any. The shearlag model and variational approach were used to predict the effect of transverse cracks on the stiffness degradation of transient hygrothermal aged angleply. The firstorder shear deformation theory in conjunction with variational energy method is. Simple bending theory is used in conjunction with a shearlag analysis, to.
Damage mechanisms and fatiguelife diagrams chapter 7. A variational model for stress analysis in cracked laminates with. Stress analysis of crossply composite laminates with. A variational method for analysis of laminates with parallel arrays of intralaminar cracks. Variational analysis of cracking in general composite laminates. Effective shear modulus of a damaged ply in laminate. In this study, an analytical method is developed to exactly obtain the interlaminar stresses near the free edges of laminated composite plates under the bending moment based on the reduced form of elasticity displacement field for a long laminate. Validating, using bem, a model for ply cracks in crossply laminates subject to combined inplane loading and.
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