5 CONCEPTION AND DESIGN A different paradigm:As every mechanical part,a composite part has to withstand loadings.In addition,the conception process has to extend over a range much larger than for a component made of "pre-established"material.In fact, For isotropic materials,the classical process of conception consists of selection of an existing material and then design of the piece. For a component made of composites,the designer "creates"the material based on the functional requirements.The designer chooses the reinforce- ment,the matrix,and the process for curing. Following that the designer must define the component architecture,i.e.,the arrangement and dimensions of plies,the representation of these on the designs, etc.These subjects are covered in this chapter. 5.1 DESIGN OF A COMPOSITE PIECE The following characteristic properties always have to be kept in mind by the designer: Fiber orientation enables the optimization of the mechanical behavior along a specific direction. The material is elastic up to rupture.It cannot yield by local plastic deformation as can classical metallic materials. Fatigue resistance is excellent. A Very Good Fatigue Resistance The specific fatigue resistance is expressed by the ratio (o/p),with p being the specific mass.For composite materials,this specific resistance is three times higher than for aluminum alloys and two times higher than that of high strength steel and titanium alloys because the fatigue resistance is equal to 90%of the static fracture strength for a composite,instead of 35%for aluminum alloys and 50% for steels and titanium alloys (see Figure 5.1).' TSee Section 5.4.4. 2003 by CRC Press LLC
5 CONCEPTION AND DESIGN A different paradigm: As every mechanical part, a composite part has to withstand loadings. In addition, the conception process has to extend over a range much larger than for a component made of “pre-established” material. In fact, For isotropic materials, the classical process of conception consists of selection of an existing material and then design of the piece. For a component made of composites, the designer “creates” the material based on the functional requirements. The designer chooses the reinforcement, the matrix, and the process for curing. Following that the designer must define the component architecture, i.e., the arrangement and dimensions of plies, the representation of these on the designs, etc. These subjects are covered in this chapter. 5.1 DESIGN OF A COMPOSITE PIECE The following characteristic properties always have to be kept in mind by the designer: Fiber orientation enables the optimization of the mechanical behavior along a specific direction. The material is elastic up to rupture. It cannot yield by local plastic deformation as can classical metallic materials. Fatigue resistance is excellent. A Very Good Fatigue Resistance The specific fatigue resistance is expressed by the ratio (s/r), with r being the specific mass. For composite materials, this specific resistance is three times higher than for aluminum alloys and two times higher than that of high strength steel and titanium alloys because the fatigue resistance is equal to 90% of the static fracture strength for a composite, instead of 35% for aluminum alloys and 50% for steels and titanium alloys (see Figure 5.1).1 1 See Section 5.4.4. TX846_Frame_C05 Page 69 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
rupture aluminum alloy unidirectional composite number of cycles number of cycles Figure 5.1 Comparison of Fatigue Behavior Between Composite and Aluminum The percent elongation is not the same as that for metals (attention should be paid to the metal/composite joints). Complex forms can be easily molded. It is possible to reduce the number of parts and to limit the amount of processing work. One must adapt the classical techniques of attachments and take into account their induced problems:fragility,delustering,fatigue,thermal stresses. 5.1.1 Guidelines for Values for Predesign Figure 5.2 shows a comparison between different materials,which can help in the choice of composite in the predesign phase. Figure 5.3 allows the comparison of principal specific properties of fibers which make up the plies.The specific modulus and specific strength are presented in the spirit of lightweight structural materials. The safety factors are defined to take care of uncertainties on The magnitude of mechanical characteristics of reinforcement and matrix The stress concentrations The imperfection of the hypotheses for calculation The fabrication process The aging of materials The orders of magnitude of safety factors are as follows: High volume composites: Static loading short duration: 2 long duration: 4 Intermittent loading over long term: 4 Cyclic loading: 5 Impact loading: 10 High performance composites: 13to1.8 2003 by CRC Press LLC
The percent elongation is not the same as that for metals (attention should be paid to the metal/composite joints). Complex forms can be easily molded. It is possible to reduce the number of parts and to limit the amount of processing work. One must adapt the classical techniques of attachments and take into account their induced problems: fragility, delustering, fatigue, thermal stresses. 5.1.1 Guidelines for Values for Predesign Figure 5.2 shows a comparison between different materials, which can help in the choice of composite in the predesign phase. Figure 5.3 allows the comparison of principal specific properties of fibers which make up the plies. The specific modulus and specific strength are presented in the spirit of lightweight structural materials. The safety factors are defined to take care of uncertainties on The magnitude of mechanical characteristics of reinforcement and matrix The stress concentrations The imperfection of the hypotheses for calculation The fabrication process The aging of materials The orders of magnitude of safety factors are as follows: Figure 5.1 Comparison of Fatigue Behavior Between Composite and Aluminum High volume composites: Static loading short duration: 2 long duration: 4 Intermittent loading over long term: 4 Cyclic loading: 5 Impact loading: 10 High performance composites: 1.3 to 1.8 TX846_Frame_C05 Page 70 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
density 1000 10.000 (kg/m3) wood 100 aluminum composites steel and thermoplastics concrete titanium tensile fracture strength (MPa) 100 1000 10,000 10 Wood light alloys 2 concrete steels composites thermoplastics modulus of elasticity 10,000 100.000 1.000.000 (MPa)1000l 1 sees thermoplastics wood concrete aluminum titanium steel composites price per unit mass 1994 2 20 200 600 ($kg) 1 ▣steels and aluminum alloys titanium 7 thermoplastics Kevlar-carbon glass composites boron Figure 5.2 Comparison of Characteristics of Different Materials aluminum alloys Eglass Kevlar 49 High strength carbon High modulus carbon boron 风 specific modulus of elasticity tensile strength specific tensile modulus density density strength Figure 5.3 Specific Characteristics of Different Fibers 2003 by CRC Press LLC
Figure 5.2 Comparison of Characteristics of Different Materials Figure 5.3 Specific Characteristics of Different Fibers TX846_Frame_C05 Page 71 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
impregnated mesh separators Figure 5.4 Unidirectional Layer 5.2 THE LAMINATE Recall that laminates result in the superposition of many layers,or plies,or sheets, made of unidirectional layers,fabrics or mats,with proper orientations in each ply.This is the operation of hand-lay-up. 5.2.1 Unidirectional Layers and Fabrics Unidirectional layers are as shown in Figure 5.4.The advantages of unidirec- tional layers are: They have high rigidity (maximum number of fibers in one direction). The ply can be used to wrap over long distance.Then the load transmission of the fibers is continuous over large distance. ■They have less waste. The disadvantages of unidirectional layers are The time for wrapping is long. One cannot cover complex shapes using wrapping Example:Carbon/epoxy unidirectionals:Width 300 or 1000 mm,preimpreg- nated with resin;usable over a few years when stored at cold temperature (-18C). Fabrics can be found in rolls in dry form or impregnated with resin (Figure 5.5). The advantages of fabrics are Reduced wrapping time Possibility to shape complex form using the deformation of the fabric Possibility to combine different types of fibers in the same fabric The disadvantages of fabrics are Lower modulus and strength than the case of unidirectionals Larger amount of waste material after cutting Requirement of joints when wrapping large parts 2003 by CRC Press LLC
5.2 THE LAMINATE Recall that laminates result in the superposition of many layers, or plies, or sheets, made of unidirectional layers, fabrics or mats, with proper orientations in each ply. This is the operation of hand-lay-up. 5.2.1 Unidirectional Layers and Fabrics Unidirectional layers are as shown in Figure 5.4. The advantages of unidirectional layers are: They have high rigidity (maximum number of fibers in one direction). The ply can be used to wrap over long distance. Then the load transmission of the fibers is continuous over large distance. They have less waste. The disadvantages of unidirectional layers are The time for wrapping is long. One cannot cover complex shapes using wrapping. Example: Carbon/epoxy unidirectionals: Width 300 or 1000 mm, preimpregnated with resin; usable over a few years when stored at cold temperature (–18∞C). Fabrics can be found in rolls in dry form or impregnated with resin (Figure 5.5). The advantages of fabrics are Reduced wrapping time Possibility to shape complex form using the deformation of the fabric Possibility to combine different types of fibers in the same fabric The disadvantages of fabrics are Lower modulus and strength than the case of unidirectionals Larger amount of waste material after cutting Requirement of joints when wrapping large parts Figure 5.4 Unidirectional Layer TX846_Frame_C05 Page 72 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
satin tabnc Figure 5.5 A Fabric Layer 5.2.2 Importance of Ply Orientation One of the fundamental advantages of laminates is their ability to adapt and control the orientation of fibers so that the material can best resist loadings.It is therefore important to know how the plies contribute to the laminate resistance,taking into account their relative orientation with respect to the loading direction.Figures 5.6 through 5.9 show the favorable situations and those that should be avoided. Recall the Mohr circle: normal stresses shear stresses cf.for example the stress state below and the associated Mohr circle Gy In Figure 5.7,the Mohr circle for stresses shows that the 45fibers support the compression,o=-t(t is the arithmetic value of shear stress),while the resin supports the tension,o2=t,with low fracture limit.The fibers in Figure 5.8 support the tension,o=t,whereas the resin supports the compression,o2=-t.In Figure 5.9,one has deposited the fibers at 45and-45.Taking into account the previous remarks,one observes that the 45fibers can support the tension o=t, whereas the -45 fibers can support the compression,02=-t.The resin is less loaded than previously. 5.2.3 Code to Represent a Laminate 5.2.3.1 Normalized Orientation Considering the working mode of the plies as discussed in the previous section, the most frequently used orientations are represented as in Figure 5.10.The direction called "0"corresponds to either the main loading direction,a preferred direction of the piece under consideration,or the axis of the chosen coordinates. Note:One also finds in real applications plies with orientations +30 and +60. 2003 by CRC Press LLC
5.2.2 Importance of Ply Orientation One of the fundamental advantages of laminates is their ability to adapt and control the orientation of fibers so that the material can best resist loadings. It is therefore important to know how the plies contribute to the laminate resistance, taking into account their relative orientation with respect to the loading direction. Figures 5.6 through 5.9 show the favorable situations and those that should be avoided. Recall the Mohr circle: cf. for example the stress state below and the associated Mohr circle In Figure 5.7, the Mohr circle for stresses shows that the 45∞fibers support the compression, s1 = -t (t is the arithmetic value of shear stress), while the resin supports the tension, s2 = t, with low fracture limit. The fibers in Figure 5.8 support the tension, s1 = t, whereas the resin supports the compression, s2 = -t. In Figure 5.9, one has deposited the fibers at 45∞and –45∞. Taking into account the previous remarks, one observes that the 45∞fibers can support the tension s1 = t, whereas the -45∞ fibers can support the compression, s2 = -t. The resin is less loaded than previously. 5.2.3 Code to Represent a Laminate 5.2.3.1 Normalized Orientation Considering the working mode of the plies as discussed in the previous section, the most frequently used orientations are represented as in Figure 5.10. The direction called “0∞” corresponds to either the main loading direction, a preferred direction of the piece under consideration, or the axis of the chosen coordinates. Note: One also finds in real applications plies with orientations ±30∞ and ±60∞. Figure 5.5 A Fabric Layer TX846_Frame_C05 Page 73 Monday, November 18, 2002 12:09 PM © 2003 by CRC Press LLC
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 z0.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. 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