OTension-compression good Fibers support the tensile load,giving rise to high tensile strength. bad Here the resin is supporting the load, giving rise to low strength. Shear bad Here the resin is sheared,with low shear strength Figure 5.6 Effect of Ply Orientation bad -T 61 Figure 5.7 Bad Design 2003 by CRC Press LLC
Figure 5.6 Effect of Ply Orientation Figure 5.7 Bad Design TX846_Frame_C05 Page 74 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
mediocre 02 Figure 5.8 Mediocre Design good 62 459 Figure 5.9 Good Design +459 Figure 5.10 Common Orientations 5.2.3.2 Middle Plane By definition the middle plane is the one that separates two half-thicknesses of the laminate.In Figure 5.11,the middle plane is the planex-y.On this plane,z=0. 5.2.3.3 Description of Plies The description of plies is done by beginning with the lowest ply on the side z<0 and proceeding to the uppermost ply of the side z>0.In so doing, Each ply is noted by its orientation. The successive plies are separated by a slash "/" 2003 by CRC Press LLC
5.2.3.2 Middle Plane By definition the middle plane is the one that separates two half-thicknesses of the laminate. In Figure 5.11, the middle plane is the plane x–y. On this plane, z = 0. 5.2.3.3 Description of Plies The description of plies is done by beginning with the lowest ply on the side z < 0 and proceeding to the uppermost ply of the side z > 0. In so doing, Each ply is noted by its orientation. The successive plies are separated by a slash “/”. Figure 5.8 Mediocre Design Figure 5.9 Good Design Figure 5.10 Common Orientations TX846_Frame_C05 Page 75 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
upper plies lower plies Figure 5.11 Laminate and its Middle Plane x-y One must avoid the grouping of too many plies of the same orientation.2 However,when this occurs,an index number is used to indicate the number of these identical plies. 5.2.3.4 Midplane Symmetry One notes that a laminate has midplane symmetry or is symmetric when the stacking of the plies on both sides starting from the middle plane is identical. Example: PLY NUMBER ORIENTATIONCONVENTIONAL SYMBOL NOTATION 10 90 9 0 6 0° -459 6 mid +45 [90/0,/-45/45]s 12 5 plane +45 10→4(40%) 4 -45 0 2 0 1 90 Example: PLY NUMBER ORIENTATIONCONVENTIONAL SYMBOL NOTATION 7 08 6 +45° 5 -45° ~4、mid --90°- 2 plane [0/45/-45/901s +2(28% 3 -459 2 +45 1 0 This is to limit the interlaminar stresses (see Section 5.4.4 and Chapter 17).This precaution applies also to the fabrics (for example,no more than four consecutive fabric layers of carbon/ epoxy along one direction). 2003 by CRC Press LLC
One must avoid the grouping of too many plies of the same orientation.2 However, when this occurs, an index number is used to indicate the number of these identical plies. 5.2.3.4 Midplane Symmetry One notes that a laminate has midplane symmetry or is symmetric when the stacking of the plies on both sides starting from the middle plane is identical. Example: Example: Figure 5.11 Laminate and its Middle Plane x–y 2 This is to limit the interlaminar stresses (see Section 5.4.4 and Chapter 17). This precaution applies also to the fabrics (for example, no more than four consecutive fabric layers of carbon/ epoxy along one direction). TX846_Frame_C05 Page 76 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
heating (polymerization) ambient temperature aaoow2 0000.00000●●0● 3 3 no midplane symmetry with midplane symmetry Figure 5.12 Effect of Laminate Lay-up on Deformation 5.2.3.4.1 What Is the Need of Midplane Symmetry For the construction of laminated pieces,the successive impregnated plies are stacked at ambient temperature,then they are placed within an autoclave for curing. At high temperature,the extension of the whole laminate takes place without warping.However,during cooling,the plies have a tendency to contract differently depending on their orientations.From this,thermal residual stresses occur. When midplane symmetry is utilized,it imposes the symmetry on these stresses and prevents the deformations of the whole part,for example,warping as shown in Figure 5.12 5.2.3.5 Particular Cases of Balanced Fabrics Some laminates are made partially or totally of layers of balanced fabric.One then needs to describe on the drawing the composition of the laminate. Example: One layer One midplane One layer of fabric layer of fabric The previous laminate,made up of three layers of balanced fabric,has midplane symmetry.In effect,if one considers one woven fabric layer as equivalent to two series of unidirectional layers crossed at 90,it also has midplane symmetry.3 3 If this hypothesis is to be verified for a plain weave or a taffeta (see Section 3.4.1),and even for a ribbed twill,it becomes worse as long as the pitch of the weaving machine increases (pitch of the plain weave:2;ribbed twill:3;4-harness satin:4;5-harness satin:5;etc.).If one supposes that this pitch is increasing towards infinity,then the woven fabric becomes the superposition of two unidirectional layers crossed at 90.It then does not possess midplane symmetry any more.This property can be observed on a unique ply of 5-harness satin of carbon/epoxy as it is cured in an autoclave,which deforms(curved surface)on demolding (see Application 18.2.17). 2003 by CRC Press LLC
5.2.3.4.1 What Is the Need of Midplane Symmetry For the construction of laminated pieces, the successive impregnated plies are stacked at ambient temperature, then they are placed within an autoclave for curing. At high temperature, the extension of the whole laminate takes place without warping. However, during cooling, the plies have a tendency to contract differently depending on their orientations. From this, thermal residual stresses occur. When midplane symmetry is utilized, it imposes the symmetry on these stresses and prevents the deformations of the whole part, for example, warping as shown in Figure 5.12. 5.2.3.5 Particular Cases of Balanced Fabrics Some laminates are made partially or totally of layers of balanced fabric. One then needs to describe on the drawing the composition of the laminate. Example: The previous laminate, made up of three layers of balanced fabric, has midplane symmetry. In effect, if one considers one woven fabric layer as equivalent to two series of unidirectional layers crossed at 90∞, it also has midplane symmetry. 3 Figure 5.12 Effect of Laminate Lay-up on Deformation 3 If this hypothesis is to be verified for a plain weave or a taffeta (see Section 3.4.1), and even for a ribbed twill, it becomes worse as long as the pitch of the weaving machine increases (pitch of the plain weave: 2; ribbed twill: 3; 4-harness satin: 4; 5-harness satin: 5; etc.). If one supposes that this pitch is increasing towards infinity, then the woven fabric becomes the superposition of two unidirectional layers crossed at 90∞. It then does not possess midplane symmetry any more. This property can be observed on a unique ply of 5-harness satin of carbon/epoxy as it is cured in an autoclave, which deforms (curved surface) on demolding (see Application 18.2.17). TX846_Frame_C05 Page 77 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
50% 0% +台 x30°： 台 50% 0% 0% 50% ×台 0% 50% 33% 17% +×+台 十X+ ) ,33% 17% Figure 5.13 Laminate with Balanced Fabrics;Representation 1 As indicated in Section 3.4.2,one can consider the resulting laminate in two different ways': (a)Each layer of fabric is replaced by two identical plies crossed at 90 each with thickness equal to half the thickness e of the fabric layer and each with known elastic properties.This representation is convenient for the determination of the elastic properties of the laminate.One then has the equivalencies shown in Figure 5.13. (b)Each layer of fabric is replaced by one anisotropic ply with thickness e for which one knows the elastic properties and failure strengths.This representation is useful for the determination of the rupture stress of the laminate.One then has the equivalencies shown in Figure 5.14. 5.2.3.6 Technological Minimum Generally one uses a minimum amount of plies (from 5 to 10%)for each direction: 0°，90°，45°，-45°.The minimum thickness of a laminate3 should be of the order of one millimeter,for example,eight unidirectional layers,or three to four layers of balanced fabric of carbon/epoxy. 5.2.4 Arrangement of Plies The proportion and the number of plies to place along each of the directions-0 90°，45°，-45°-take into account the mechanical loading that is applied to the laminate at the location under consideration.A current case consists of loading 4 See Exercises 18.2.9 and 18.2.10. s Apart from space applications,where thicknesses are very small,the skins of sandwich plates are laminates which do not have separately midplane symmetry. 2003 by CRC Press LLC
As indicated in Section 3.4.2, one can consider the resulting laminate in two different ways 4 : (a) Each layer of fabric is replaced by two identical plies crossed at 90∞, each with thickness equal to half the thickness e of the fabric layer and each with known elastic properties. This representation is convenient for the determination of the elastic properties of the laminate. One then has the equivalencies shown in Figure 5.13. (b) Each layer of fabric is replaced by one anisotropic ply with thickness e for which one knows the elastic properties and failure strengths. This representation is useful for the determination of the rupture stress of the laminate. One then has the equivalencies shown in Figure 5.14. 5.2.3.6 Technological Minimum Generally one uses a minimum amount of plies (from 5 to 10%) for each direction: 0∞, 90∞, 45∞, -45∞. The minimum thickness of a laminate 5 should be of the order of one millimeter, for example, eight unidirectional layers, or three to four layers of balanced fabric of carbon/epoxy. 5.2.4 Arrangement of Plies The proportion and the number of plies to place along each of the directions—0∞, 90∞, 45∞, -45∞—take into account the mechanical loading that is applied to the laminate at the location under consideration. A current case consists of loading Figure 5.13 Laminate with Balanced Fabrics; Representation 1 4 See Exercises 18.2.9 and 18.2.10. 5 Apart from space applications, where thicknesses are very small, the skins of sandwich plates are laminates which do not have separately midplane symmetry. TX846_Frame_C05 Page 78 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC