Finite Element Modeling for Stress and Failure Analysis of Different
types of Laminated Composite Structures with Cut-Out
Umesh C K
1H.V.Lakshminarayana
2 1Assistent Professor
2Professor
1,2Department of Mechanical Engineering
1MVJ College of Engineering, Bangalore, India
2Dayananda Sagar College of Engineering, Bangalore,
India
Abstract— The structural elements of composite materials are normally fabricated by lamination process, in whicha number of laminae are oriented in a predetermined manner in order to form a laminate. This paper presents the results of an investigation into stress analysis and progressive failure analysis of a laminated composite rectangular panel with circular cut-out subjected to axial tension, a laminated composite square plate with a central circular cut-out subjected to lateral pressure and a cylindrical shell with circular cut-out under axial tension. The powerful analysis and post processing capability in ANSYS software is exploited. Significant results are graphically presented and discussed in this paper.
Key words: FEA, ANSYS, NDT
I. INTRODUCTION
Finite element Modeling is defined here as the analyst’s choice of material models (constitutive equations), finite elements, meshes, constraint equations, analysis procedures, governing matrix equations and their solution methods specific pre-and post processing options available in a chosen commercial FEA software(ANSYS) for accurate stress analysis and progressive failure analysis (first ply failure to last ply failure) of specific problems identified for this study.
In the present analysis a unidirectional lamina is modeled as a homogeneous, orthotropic, elastic continuum characterized by the experimentally measured effective module namely longitudinal modulus of elasticity along the fiber direction E1, transverse modulus of elasticity E2, in-plane shear modulus G12 and major Poisson’s ratio υ12. Lamination theories are then used to derive constitutive relations for a multilayered multidirectional laminate resulting in stretching, bending, stretching-bending coupling stiffness matrices. Finite element formulations available in commercial FEA programs are widely used for the analysis of laminated composite structures.
Lakshminarayana and Viswanath[1]have presented a correlation study to evaluate the effectiveness of finite-element modeling for the stress analysis ofComposite material laminates. A rectangular panel with a circular cut out subjected to uniform uni-axial tension is revisited in this paper. Sundareshan and Lakshminarayana [3] have
Studied stress concentration around circular cut-outs in laminated composite cylindrical shells. Experimental investigation was carried out to measure the strain distribution around circular holes in cross ply and angle ply laminated E-glass epoxy composite cylindrical shells subjected to axial tension. This problem is revisited in this study. Kim and Hong[4] have presented a progressive failure model for the analysis of laminated composites based on
Finite Element Approach. Fu-Kuo Chang and Kuo-Yen Chang [5] have presented a progressive damage model for laminated composites containing stress concentrations to predict ultimate tensile strength. Chapelle and Bathe[6]presented fundamental considerations for the finite element analysis of shell structures where bending dominated and membrane dominated cases are highlighted. In this study the problem of a laminated composite plate bending behaviour is included.
This paper presents significant results ofstress and progressive failure analysis of
(1) Laminated composite Panel with circular cutout under axial tension,
(2) Laminated composite Square plate with circular cutout under lateral pressure and
(3) Laminated composite Cylindrical shell with circular cutout under axial tension.
Accurate stress analysis to predict ply by ply stresses in the material co-ordinates(σ1 σ2 τ12) is a prerequisite for progressive failure analysis. A verified lamina failure criteria along with measured strength properties of material systems involved is also essential.
II. FINITE ELEMENT MODELING
A. Rectangular panel with a circular cut-out under axial tension:
The test specimen shown in fig1.Is alaminated graphite-epoxy composite panel with [0/45/-45/0/90]Sply orientations. The parameters used inthe computations areL =
330.2mm, W = 127mm, t = 1.1684mm a =
12.7mm.Graphite-Epoxy composite material stiffness and strength properties used in the analysis are E1 = 206.844GPa, E2 = 5.1711GPa, G12 = 3.10266GPa, υ12 = 0.25, ( )ult = 1500MPa, ( )ult = 1500MPa, ( )ult = 40MPa,
)ult = 246MPa,(τ ult, = 68MPa.
Fig. 1: Rectangular panel with a circular opening under axial tension
Fig. 2: Finite element model of laminated composite panelwith a circular cut-out. (quarter symmetry)
B. Clamped Square plate with a circular cut-out under lateral pressure.:
[image:2.595.310.546.68.518.2]The problem is illustrated in fig 3,the parameters used in the analysis are W = 80mm, a=40mm, t= 2mm, lateral pressure p (variable). The pressure loading of a plate with an circular cut-out deserved an explicit attention because the hole must be considered covered and the pressure load on the cover should be transferred to the hole boundary in a consistent way to ensure accurate stress analysis. This was accomplished, guided by recent research as an edge bonded low modulus inclusion to model the cover.The test specimen shown in fig 3 is a graphite-epoxy composite cross-ply laminate with [0/90/0/90]2Sply orientations. The finite element model developed using SHELL281 element in ANSYS is shown in fig 4.The mesh involves 1400 elements and 4281 nodes. The properties of graphite epoxy composite material used in the analysis are same as above.The properties of the inclusion are E=5.1711GPa and υ=0.3
Fig. 3: Graphite-epoxy plate with a circular opening under lateral pressure.
Fig. 4: Finite element model of laminated composite plate
C. Cylindrical shell with a circular cut-out under axial tension:
The test specimen shown in fig 5 is a cross ply laminated E-glass-epoxy composite cylindrical shell with [0/90/0/90/0/90/0]ply orientations. The parameters defining the problem are R=76.2mm,t=1.92mm, L=457.2mm, a=19.05mm.The finite element model developed using SHELL281 element in ANSYS is shown in fig 6. The mesh consists of 2800 elements and 8599 nodes. The stiffness and strength properties of E-glass epoxy composite lamina used
in the analysis are
E1=37.3GPa,E2=10.68GPa,υ12=0.28,G12=4.205828GPa,( )ult=
1062MPa, ( )ult=610MPa, ( )ult=31MPa,
)ult=118MPa,(τ ult,=72MPa.
Fig. 5: Glass-epoxy cylindrical shell with a circular opening under axial tension
Fig. 6: Finite element model of laminated composite cylindrical shell with circular cut-out.
III. RESULTS PRESENTATION AND DISCUSSION
A. A rectangular panel with a circular cut-out under axial tension.
The calculated strain concentration factor in this study is 3.3 Target solutions reported in reference [1]are 3.49 (numerical), 3.45 (analytical) and 3.34 (experimental). The proposed FE Model using ANSYS is not only validated but also verified.
[image:2.595.91.247.614.740.2]At the last ply failure load contour plots of Tsai-Wu failure index are created for each layer in the panel. These results quantify the onset and growth, nature and extent and shape and size of the damage in each layer.
An ensemble of these results is desirable to quantify the shape and size of damage zone in the panel because this is the only information available using state of the art NDT (computerised ultrasonic C scan facility).Unfortunately this capability is not available in ANSYS software.
Sequence of ply failure
Failed layer numbers
Failure loads(N/m)
1st 5,6 348706
2nd 1,4,7,10 358061
3rd 2,9 463453
[image:3.595.297.558.67.708.2]4th 3,8 485195
Table 1: PLY BY PLY FAILURE RESULT
B. Clamped Square plate with acircular cut-out under lateral pressure.:
The predicted pressure levels from first ply failure to last ply failure are presented in table II. Typical results of stress analysis are graphically presented as contour plots of (σ1 σ2 τ12) in fig (7,8,9)for layer number 1 at p=1N/m2. The clarity and resolution in these figures should be appreciated. The authors are not aware of any experimental technique to verify such results of FEA.
Tsai-Wu failure index contourplots for all 16 layers in the plate subjected to last ply failure pressure p=1124729N/m2are displayed in figures (10 to 25). They display the onset and growth of failure in constituent plies. However the mode of failure cannot be identified. An ensemble of all these figures is required to display the shape and size of damage in the plate. It is unfortunate that ANSYS does not offer this capability.
The present analysis has predicted the onset of failure in the last ply however this is not the ultimate strength of the component. Relabel prediction of this demands non-linear analysis where the geometry is updated in each load step and failed plies are discounted (both stiffness and strength) to reflect material failure. This is identified as topic for future research.
[image:3.595.45.292.173.276.2]State of the art NDT namely computerized ultrasonic C-scancan be used to measure the shape and size of damage zone. This information is essential to verify the numerical results of present study.
Fig. 7: Stress plot along the longitudinal direction in layer 1
Fig. 8: Stress plot along the transverse direction in layer 1
Fig. 9: Stress plot along 1-2 plane in layer 1
Ply failure sequence
Failed layer number
Pressure at which failure occurred
(N/m²)
1st 1 339100
2nd 2 343549
3rd 16 359370
4th 3 454694
5th 4 481363
6th 14 482378
7th 5 646478
8th 12 702888
9th 6 757600
10th 15 804098
11th 9 915379
12th 8 917938
13th 10 931155
14th 11 954502
15th 7 975926
16th 13 1124729
[image:3.595.86.238.612.734.2]Fig. 10: Tsai-wu failure indexcontour plot for layer number 13 at p=1124729N/m2
Fig. 11: Tsai-wu failure indexcontour plot for layer number 1 at p=1124729N/m2
Fig. 12: Tsai-wu failure indexcontour plot for layer number 2 at p=1124729N/m2
[image:4.595.45.547.52.545.2]Fig. 13: Tsai-wu failure indexcontour plot for layer number 3 at p=1124729N/m2.
Fig. 14: Tsai-wu failure indexcontour plot for layer number 4 at p=1124729N/m2.
Fig. 15: Tsai-wu failure indexcontour plot for layer number 5 at p=1124729N/m2.
Fig. 16: Tsai-wu failure indexcontour plot for layer number 6 at p=1124729N/m2.
Fig. 18: Tsai-wu failure indexcontour plot for layer number 8 at p=1124729N/m2.
Fig. 19: Tsai-wu failure indexcontour plot for layer number 9 at p=1124729N/m2.
Fig. 20: Tsai-wu failure indexcontour plot for layer number 10 at p=1124729N/m2.
[image:5.595.50.536.50.727.2]Fig. 21: Tsai-wu failure indexcontour plot for layer number 11 at p=1124729N/m2.
Fig. 22: Tsai-wu failure indexcontour plot for layer number 12 at p=1124729N/m2
Fig. 23: Tsai-wu failure indexcontour plot for layer number 14 at p=1124729N/m2
Fig. 24: Tsai-wu failure indexcontour plot for layer number 15 at p=1124729N/m2
C. Cylindrical shell with a circular cut-out under axial tension:
The results of progressive failure analysis are displayed in table III.
A wealth of experimentally measured results are available in reference [3] .This is used to verify the prediction from the present study and reported elsewhere
Order of ply failure
Failed layer numbers
Ply failure load(N)
1st 1 12734.2
2nd 3 14803.7
3rd 5 17675.8
4th 7 21930.6
5th 6 40601.8
6th 4 45878.1
[image:6.595.38.296.138.283.2]7th 2 52201.2
Table 3: PLY BY PLY FAILURE RESULT
IV. CONCLUSIONS
Accurate prediction of ply by ply stresses in the material coordinates in a laminate is an indispensible prerequisite for progressive failure analysis of the problems identified for this study.This in fact was the motivation to use the finite element method in general and ANSYS software in particular. The analyst can recover ply by ply stress (σ1 σ2 τ12) at bottom, mid, top surface of each layer with in every element in the finite element model created using ANSYS software.
Ultimate strength prediction of a laminated composite structure is an order of magnitude more complicated then stress analysis. In this study the Tsai-Wu failure criteria along with experimentally measured lamina stiffness and strength properties and the concept of strength ratio are used to predict the first ply failure load and upto the load last ply failure load.
The powerful post possessing capability in ANSYS software is exploited to graphically present contour plots of ply by ply stress and Tsai-Wu failure index.
Based on the present study it can be concluded that the FEM in general and commercial FEA software ANSYS in particular is a unified approach for stress analysis and progressive failure analysis of laminated composite structures.
In this study correlation of numerical results of FEA was restricted to limited experimental results reported for the problems on hand. However there is a real need for sophisticated experimental investigations to verify all the results presented here. This is identified as future work.
V. REFERENCES
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[2] Lakshminarayana H.V.; Stress distribution around a semicircular edge notch in a finite size laminated composite plate under axial tension, Journal of composite materials, 1983, pp 356-367.
[3] Lakshminarayana H.V. and M.J.Sundareshan : stress concentration around circular cut outs in laminated cylindrical shells, experimental investigation and finite element analysis,Journal of Aeronautical society of India,vol.35,1983,pp 13-22.
[4] Y.W. Kim and C.S. Hong;Progressive Failure Model for the Analysis of Laminated Composites based on Finite Element Approach;Journal of Reinforced Plastics and Composites 1992,pp 11 to 1078.
[5] Fu-Kuo Chang And Kuo-Yen Chang,A Progressive
Damage Model For Laminated Composites
Containing Stress Concentrations,Journal Of Composite Materials, Vol21,Sept 1987,pp24-834.
[6] D.Chapelle and K.J.Bathe; Fundamental
considerations for the finite element analysis of shell structures; computers and structures vol.66, No. 1 pp,1998, 19-36.
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