Research Journal of Engineering Sciences ___________________________________________ ISSN 2278 – 9472Vol. 2(5), 30-34, May (2013) Res. J. Engineering Sci. International Science Congress Association 30 Effect of Fiber Orientation on Mode I Crack Opening Stress Intensity of an Orthotropic Laminate Chaitanya G., Srinivas K. and Kumar J. Suresh Department of Mechanical Engineering, R.V.R and J.C College of Engineering, Guntur, AP, INDIA Department of Mechanical Engineering, JNTU College of Engineering, Hyderabad, AP, INDIAAvailable online at: www.isca.in Received 12th April 2013, revised 29th April 2013, accepted 13th May 2013 Abstract In this paper, the influence of fiber angle on Mode I transverse crack opening stress intensity in case of (AS4/3501-6) carbon/Epoxy laminate is studied. Ten independent fiber orientations are considered and both analytical and finite element solutions are presented using macro mechanics approach of analysis of orthotropic lamina and by using ANSYS10 finite element package. It is observed that the stress intensity at the crack tip increased gradually from zero degrees to seventy degrees and showed a decline after 70 degrees. It is observed that the variations in the load carrying capacity of matrix phase around the discontinuous fibers at the crack tip for different fiber orientations influenced the stress intensity variations. The results obtained from analytical and finite element approaches showed good congruence. Keywords: Fiber angle, stress intensity, transverse crack. Introduction Carbon/epoxy continuous fiber composite laminates are used as structural members due to their high strength and stiffness. Fracture of composite laminates is a serious phenomenon which needs meticulous attention. In Composite laminates, fracture crack propagation takes place through any of the three modes (Mode I, Mode II or Mode III) or through a combination of the three modes. Mode I represents the crack propagation under normal in plane loading where the crack is positioned perpendicular to the applied load. Mode II represents crack propagation due to shear type failure where the load applied is transverse to crack length. Mode III represents crack propagation due to tear type failure where the load applied is parallel to the crack length. Unlike metals, the laminate material properties in the loading direction depend on the fiber orientation and hence, the crack propagation is also influenced by fiber orientation. B.T. Astrom presented various manufacturing methods like Resin transfer molding, Autoclave molding...etc in detail for polymer matrix composites. P.K.Mallick gave a detailed and in depth information on materials, property characterization, testing and various methods of manufacture of fiber reinforced composites. Balaguru et al, presented a new material approach for aircrafts incorporating stealth technology using coir fiber composites made out of hand layup process. Sankaran Apoorva et al presented a very detailed and informative review on application of multi layered frp composites and their durability in construction and other civil applications. The semi empirical relation for transverse elastic modulus as a function of fiber volume fraction for unidirectional FRP composites was given by Halpin and Tsai. Halpin presented a semi empirical relation to determine the longitudinal elastic modulus of FRP composites as a function of fiber volume fraction, matrix modulus and fiber modulus. Z.Hashin developed a semi empirical relation for transverse elastic modulus of FRP laminates as a function of bulk modulus and transverse shear modulus of laminate based on solid mechanics approach. O.Ishai analyzed the transverse micro cracking of glass/epoxy laminate under unidirectional tensile loading. A theory based on stress tensors for predicting the failure behavior of composites under tension and compression was proposed by S.W.Tsai and E.M Wu. C.T Sun10 reviewed different failure theories and showed comparisons of theoretical predictions with experimental results for various composite material systems under different loading conditions. I.M.Daniel11 et al analyzed the effect of material and layer stacking sequence on the stress distribution around the holes of boron/epoxy laminates. H.J.Konish and J.M.Whitney12presented an approximate relation for stress distribution along the in plane transverse axis of the circular hole of an orthotropic plate subjected to loading in longitudinal direction. R.J.Nuismer and J.M.Whitney13 presented a relation to estimate the stress concentration factor for holed orthotropic plates subjected to uniaxial in plane loading based on laminate stffnesses. R.F.Karlak14 analyzed the effect of hole size on the stress distributions in various symmetrically stacked laminates. I.M.Daniel15 studied the failure of composite laminates due to stress concentration around the holes of various sizes and on through thickness cracks. J.Awerbuch and M.S.Madhukar16presented an elaborative review on various theoretical and experimental results on stress concentrations in notched composite laminates. M.Nikbakht and N.Choupani17investigated the crack initiation and propagation phenomenon in case of carbon/epoxy laminate using ARCAN test specimen and compared the results obtained using numerical analysis. A.B. de Moraisa18 et al estimated the critical strain energy release rates Research Journal of Engineering Sciences________________________________________________________ ISSN 2278 – 9472 Vol. 2(5), 30-34, May (2013) Res. J. Engineering Sci. International Science Congress Association 31 of carbon/epoxy composites under Mode-I fracture using double cantilever beam test and incorporating modified beam theory. In the present work, the Mode I crack opening stress intensity for AS4/3501-6 carbon/epoxy laminate is studied. The laminate properties along and transverse to the loading direction for the 10 different fiber angles are found by using the transformation relations. The stress intensity around the crack tip for different fiber orientations is estimated using the R.J.Nuismer and H.J.Konish approximate relations. Using the layered shell 99 elements, the finite element analysis for the different fiber angles is carried out to determine the stress intensity around the crack tip and the results are compared with the theoretical results. A good congruence is found between the theoretical and finite element results. Methodology Theoretical Approach:The properties related to AS4/3501-6 carbon/epoxy laminate are as shown in table 1. Table-1 Mechanical properties of Laminate Elastic Modulus (E 1 ) 177.325 (Gpa) Elastic Modulus (E 2 ) 10.413 (Gpa) Shear Modulus (G 12 ) 7.980 (Gpa) Major Poisson’s Ratio ( 12 ) 0.2375 Minor Poisson’s Ratio ( 21 ) 0.01394 The properties of the composite lamina parallel and perpendicular to the loading direction (parallel and perpendicular to the plate geometrical axes) for different fiber orientations are obtained using the following transformation relations. () () 222222122112 1oscossin ossinsinoscsinccEEEG qqqq qquqqu=-+-+ (1) () () 222222122112 1oscossin sinosossinsincccEEEG qqqq qquqqu=-+-+ (2) () () ( ) 2 22222212211212cossin14ossin4ossin11xyccGEEG qq qqqquu=++++ (3) () () 222222122112 cossincossin cossinsincosxyyxxyEEEEGuu qqqq quqquq==-+-+(4) The stress concentration around the crack tip of the laminate due to the applied far field unidirectional uniform stress along the longitudinal axis of the plate geometry for different fiber orientations is estimated using the H.J.Konish relation and Whitney-Nuismer equation as given below. ()2468max133157222ssrrrr---- - =++--    (5) max s is the max stress intensity around the crack tip vicinity. s is the far field uniform stress applied along the geometric longitudinal axis of plate. y a r = (Ratio of distance along the in plane transverse axis of crack tip to crack length) Where k is the stress concentration factor given by Whitney-Nuismer equation as shown xxyyxyxxyyxyyyssAAAkAAAAA    -   =+-+        (6) Where Axx, Ayy, Axy and Ass are the in plane extension stiffness components and are expressed as: ()() 1 xxxxkkAQZZ=- (7) ()() 1 yyyykkAQZZ=- (8) ()() 1 xyxykkAQZZ=- (9) ()() 1 sssskkAQZZ=- (10) Where Qxx, Qyy, Qxy and Qss are the in plane stffnesses with reference to the geometrical axes of the lamina under consideration. k=1 to n denotes the number of layers and Z , k-1 are the layer thicknesses measured from the mid plane of the laminate. For the present problem, since there is only a single layer, Zk-1=0, Z represents one half of the layer thickness and the number of layers n=1. The stffnesses along the plate geometrical axes are obtained by transforming the stffnesses along the material (fiber) directions using the following transformation equations. ( ) 442211221266 cossin22sincos xxQQQQQ qqqq =+++ (11) ( ) 442211221266 sincos22sincos yyQQQQQ qqqq =+++ (12) ( ) ( ) 2244112266124sincoscossinxyQQQQQ qqqq =+-++ (13) ( ) ( ) 2244112212666622sincoscossinssQQQQQQ qqqq =+--++ (14) The stffnesses along the material (fiber) direction are expressed in terms of lamina properties as shown: 11 1221 1EQ uu (15) Research Journal of Engineering Sciences________________________________________________________ ISSN 2278 – 9472 Vol. 2(5), 30-34, May (2013) Res. J. Engineering Sci. International Science Congress Association 32 221221uu (16) 122121221uu (17) 6612QG (18) The maximum stress intensity around the crack tip vicinity given by equation 5is estimated for different fiber orientations using equations 6 to 18. Finite Element approach: The plate geometry considered has the dimensions (Length=200mm, Width=100mm and thickness=15mm). It is modeled as a three layered composite laminate having transversely placed crack (Perpendicular to plate length) with a crack length of 20 mm. The Shell99 layered element available in the ANSYS10 element library are used to model the plate as well as the crack vicinity. The shell99 element coordinate system is initially reoriented in such a way that the shell99 element normals are parallel to the Z-axis of the global Cartesian coordinate system. The plate is modeled in such a way that the length of the plate is parallel to the reference y-axis of ANSYS coordinate system. The plate is modeled with a global element size of 3.5 mm for all the sides of the plate and with densely concentrated elements having skewed midside nodes around the crack tip. The plate is loaded by arresting all the degrees of freedom along the bottom edge of the plate and by applying a uniform pressure intensity of 10Mpa on the top edge. Figure 1 shows the finite element model of the plate with densely populated skewed elements around the crack tip vicinity. Results and Discussion The maximum stress intensity around the crack tip for different fiber orientations obtained from theory and finite element analysis are tabulated in table 2. The stress intensity distribution around the crack tip for zero degree fiber orientation is shown in figure 2 and variation of stress intensity around the crack vicinity with fiber angle is shown in figure 3. Figure-1 Meshed plate with dense skewed elements around the crack tip Table-2 Max stress intensity around the crack tip for different fiber angles Max Stress (Mpa) Angle in Degrees 0 10 20 30 40 50 60 70 80 90 Theory 14.851 15.122 16.985 17.452 18.394 19.027 19.687 20.021 18.988 17.012 Ansys 13.042 13.355 14.257 15.551 16.771 17.22 17.29 17.372 16.55 15.694 Research Journal of Engineering Sciences________________________________________________________ ISSN 2278 – 9472 Vol. 2(5), 30-34, May (2013) Res. J. Engineering Sci. International Science Congress Association 33 Figure-2 Stress intensity at the crack tip for zero degree fiber orientation Figure-3 Stress intensity variation with fiber orientation. Figure-3 shows the variation of stress intensity around the crack tip for different fiber orientations. It is observed that the stress intensity is maximum around 45 to 70 degrees and showed a decline later on. From zero degrees to 20degrees, the fibers are more or less approximately parallel to the crack front. The number of discontinuous fibers at the crack front are very less and the major portion of the load is taken up by the matrix phase. This results in low stress intensity distribution around the 101520250102030405060708090Fiber Angle in DegreesMax Stress Intensity in Mpa ANSYS THEORY Research Journal of Engineering Sciences________________________________________________________ ISSN 2278 – 9472 Vol. 2(5), 30-34, May (2013) Res. J. Engineering Sci. International Science Congress Association 34 crack tip. From 40 to 70 degrees, there is high probability of slippage of fibers due to induced shear stresses apart from the normal tensile stresses at fiber matrix interface. This results in high stress intensity around the crack tip. From 70 degrees to 90 degrees, the number of continuous fibers sharing the far field uniformly applied pressure intensity also increases resulting in reduction of stress intensity around the crack tip. Conclusion In the present work, the influence of fiber angle, on the stress intensity concentration around the crack tip of carbon / epoxy orthotropic laminate is analyzed using theoretical and finite element approaches. The results obtained from both the approaches showed that the combined influence of shear stresses at fiber matrix interface and the fiber discontinuity around the crack tip influenced the Mode I crack propagation stress intensity for fiber orientations around 40 to 70 degrees. References 1.Astrom B.T., Manufacturing of polymer composites, Chapman and Hall publications, London, (1992) 2.Mallick P.K., Fiber reinforced composites: materials, manufacture and design, Marcel-Dekker, edition , (1993) 3.Balaguru I., Senthil Kumar S., Sridhar K., Investigation of stealth strategies in coir fiber reinforced polymer matrix composites, Research Journal of Material Sciences,1(1), 6-10 (2013) 4.Sankaran Apurva, Bhuvaneswari B., Maheswaran S., Santhi A.S., Nagesh R., Iyer, Application of Multi layer composites in construction and their future challenges, Research Journal of Material Sciences,1(3), 12-18, (2013) 5.Halpin J.C. and Tsai S.W., Effects of environmental factors on composite materials, Airforce technical Report AFML-TR-67-423,Wright Aeronautical labs, Dayton, OH, (1967) 6.Halpin J.C., Stiffness and expansion estimates for oriented short fiber composites, Journal of Composite Materials,3,732-734 (1969) 7.Hashin Z., Analysis of composite materials-A Survey, ASME Journal of Applied Mechanics, 50, 481-505 (1983) 8.Ishai O., Failure of unidirectional composites in tension, J. Eng. Mech. Div, proceedings of ASCE, 97, 205-221,(1971) 9.Tsai S.W. and Wu E.M., A general theory of strength of anisotropic materials, Journal of Composite Materials,, 58-80 (1971) 10.Sun C.T., Strength analysis of unidirectional composites and laminates, in comprehensive composite materials, A. Kelly and C.Zweben edition, chapter 1.20, Elsevier science ltd, oxford, (2000)11.Daniel I.M., Rowlands R.E. and Whiteside J.B., Effects of material and stacking sequence on behaviour of composite plates with holes", Journal of Experimental Mechanics, 14, 1-9 (1974)12.Konish H.J. and Whitney J.M., Approximate stresses in an orthotropic plate containing a circular hole, Journal of composite materials,, 157-166 (1975)13.Nuismer R.J. and Whitney J.M., Uniaxial failure of composite laminates containing stress concentrations, in fracture mechanics of composites, ASTM STP 953, American Society for Testing Materials, 117-142 (1975)14.Karlak R.F., Hole effects in a related series of symmetrical laminates, proceedings in failure modes in composites, vol IV, The Metallurgical Society of AIME, Chicago, 105-112 (1977)15.Daniel I.M., Failure mechanisms and fracture of composite laminates with stress concentrations, proceedings of seventh international conference on experimental stress analysis, Israel, 1-20 (1982)16.Awerbuch J. and Madhukar M.S., Notched strength of composite laminates; predictions and experiments-A Review, Journal of Reinforced Plastics and Composites,, 3-159 (1985)17.Nikbakht M. and Choupani N., Numerical Investigation of delamination in carbon epoxy composite using Arcan specimen, International Journal of Aerospace and Mechanical Engineering,, 259-266 (2008)18.A.B. de Moraisa, M.F. de Mourab, A.T. Marquesb, P.T. de Castrob, Mode-I interlaminar fracture of carbon/epoxy cross-ply composites, Journal of Composites science and Technology (Elsevier),62, 679-686 (2002)