Chapter 1:Introduction to Composite Materials/5 0a40a西6a40 Eo+E45*E0E 可 0g0 045 00 E,= 045 E 5 090 60 Fig.1.5 Element of composite ply material under stress 7 2 Positive angles are counterclockwise Ply coordinate system: 1-axis is parallel to the fiber direction. 2-axis is perpendicular to the fiber direction. 3-axis is normal to the plane of the ply. Fig.1.6 Ply angle definition
Chapter 1: Introduction to Composite Materials / 5 Fig. 1.5 Element of composite ply material under stress Fig. 1.6 Ply angle definition
6/Structural Composite Materials to the plane of the plate.The 1-2-3 coordinate Consider the unidirectional composite shown system is referred to as the principal material in the upper portion of Fig.1.7,where the unidi- coordinate system.If the plate is loaded parallel rectional fibers are oriented at an angle of 45 de- to the fibers (one-or zero-degree direction),the grees with respect to the x-axis.In the small, modulus of elasticity Eu approaches that of the isolated square element from the gage region,be- fibers.If the plate is loaded perpendicular to cause the element is initially square(in this ex- the fibers in the two-or 90-degree direction,the ample),the fibers are parallel to diagonal AD of modulus E22 is much lower,approaching that of the element.In contrast,fibers are perpendicular the relatively less stiff matrix.Since E>>E22 to diagonal BC.This implies that the element is and the modulus varies with direction within the stiffer along diagonal AD than along diagonal material,the material is anisotropic. BC.When a tensile stress is applied,the square Composites are a subclass of anisotropic mate- element deforms.Because the stiffness is higher rials that are classified as orthotropic.Ortho- along diagonal AD than along diagonal BC,the tropic materials have properties that are different length of diagonal AD is not increased as much in three mutually perpendicular directions.They as that of diagonal BC.Therefore,the initially have three mutually perpendicular axes of sym- square element deforms into the shape of a par- metry,and a load applied parallel to these axes allelogram.Because the element has been dis- produces only normal strains.However,loads torted into a parallelogram,a shear strain Yy is that are not applied parallel to these axes produce induced as a result of coupling between the axial both normal and shear strains.Therefore,ortho- strains Ex and Eyy tropic mechanical properties are a function of If the fibers are aligned parallel to the direc- orientation. tion of applied stress,as in the lower portion of Deformed Shape A Original Shape 45°Py 0°Py Fig.1.7 Shear coupling in a 45 ply.Source:Ref 1
6 / Structural Composite Materials to the plane of the plate. The 1-2-3 coordinate system is referred to as the principal material coordinate system. If the plate is loaded parallel to the fibers (one- or zero-degree direction), the modulus of elasticity E11 approaches that of the fibers. If the plate is loaded perpendicular to the fibers in the two- or 90-degree direction, the modulus E22 is much lower, approaching that of the relatively less stiff matrix. Since E11 >> E22 and the modulus varies with direction within the material, the material is anisotropic. Composites are a subclass of anisotropic materials that are classified as orthotropic. Orthotropic materials have properties that are different in three mutually perpendicular directions. They have three mutually perpendicular axes of symmetry, and a load applied parallel to these axes produces only normal strains. However, loads that are not applied parallel to these axes produce both normal and shear strains. Therefore, orthotropic mechanical properties are a function of orientation. Consider the unidirectional composite shown in the upper portion of Fig. 1.7, where the unidirectional fibers are oriented at an angle of 45 degrees with respect to the x-axis. In the small, isolated square element from the gage region, because the element is initially square (in this example), the fibers are parallel to diagonal AD of the element. In contrast, fibers are perpendicular to diagonal BC. This implies that the element is stiffer along diagonal AD than along diagonal BC. When a tensile stress is applied, the square element deforms. Because the stiffness is higher along diagonal AD than along diagonal BC, the length of diagonal AD is not increased as much as that of diagonal BC. Therefore, the initially square element deforms into the shape of a parallelogram. Because the element has been distorted into a parallelogram, a shear strain gxy is induced as a result of coupling between the axial strains exx and eyy. If the fibers are aligned parallel to the direction of applied stress, as in the lower portion of Fig. 1.7 Shear coupling in a 45° ply. Source: Ref 1
Chapter 1:Introduction to Composite Materials/7 Fig.1.7,the coupling between and g does ites are normally laminated materials (Fig.1.8) not occur.In this case,the application of a ten- in which the individual layers,plies,or laminae sile stress produces elongation in the x-direction are oriented in directions that will enhance the and contraction in the y-direction,and the dis- strength in the primary load direction.Unidirec- torted element remains rectangular.Therefore, tional(0)laminae are extremely strong and stiff the coupling effects exhibited by composites occur in the 0 direction.However,they are very weak only if stress and strain are referenced to a non- in the 90 direction because the load must be car- principal material coordinate system.Thus,when ried by the much weaker polymeric matrix. the fibers are aligned parallel(0)or perpendic- While a high-strength fiber can have a tensile ular(90)to the direction of applied stress,the strength of 500 ksi(3500 MPa)or more,a typical lamina is known as a specially orthotropic lam- polymeric matrix normally has a tensile strength ima(θ=0°or90°).A lamina that is not aligned of only 5 to 10 ksi(35 to 70 MPa)(Fig.1.9).The parallel or perpendicular to the direction of ap- longitudinal tension and compression loads are plied stress is called a general orthotropic lam- carried by the fibers,while the matrix distributes ima(6≠0°or90). the loads between the fibers in tension and stabi- lizes the fibers and prevents them from buckling in compression.The matrix is also the primary 1.2 Laminates load carrier for interlaminar shear(i.e.,shear be- tween the layers)and transverse (90)tension. When there is a single ply or a lay-up in which The relative roles of the fiber and the matrix in all of the layers or plies are stacked in the same detemining mechanical properties are summa- orientation,the lay-up is called a lamina.When rized in Table 1.1. the plies are stacked at various angles,the lay-up Because the fiber orientation directly impacts is called a laminate.Continuous-fiber compos- mechanical properties,it seems logical to orient 09 0 90 +45 45 +45 90 90 Unidirectional Lay-Up Quasi-lsotropic Lay-Up (Lamina) (Laminate) Fig.1.8 Lamina and laminate lay-ups
Chapter 1: Introduction to Composite Materials / 7 Fig. 1.7, the coupling between exx and eyy does not occur. In this case, the application of a tensile stress produces elongation in the x-direction and contraction in the y-direction, and the distorted element remains rectangular. Therefore, the coupling effects exhibited by composites occur only if stress and strain are referenced to a non– principal material coordinate system. Thus, when the fibers are aligned parallel (0°) or perpendicular (90°) to the direction of applied stress, the lamina is known as a specially orthotropic lamina (θ = 0° or 90°). A lamina that is not aligned parallel or perpendicular to the direction of applied stress is called a general orthotropic lamina (θ ≠ 0° or 90°). 1.2 Laminates When there is a single ply or a lay-up in which all of the layers or plies are stacked in the same orientation, the lay-up is called a lamina. When the plies are stacked at various angles, the lay-up is called a laminate. Continuous-fiber composites are normally laminated materials (Fig. 1.8) in which the individual layers, plies, or laminae are oriented in directions that will enhance the strength in the primary load direction. Unidirectional (0°) laminae are extremely strong and stiff in the 0° direction. However, they are very weak in the 90° direction because the load must be carried by the much weaker polymeric matrix. While a high-strength fiber can have a tensile strength of 500 ksi (3500 MPa) or more, a typical polymeric matrix normally has a tensile strength of only 5 to 10 ksi (35 to 70 MPa) (Fig. 1.9). The longitudinal tension and compression loads are carried by the fibers, while the matrix distributes the loads between the fibers in tension and stabilizes the fibers and prevents them from buckling in compression. The matrix is also the primary load carrier for interlaminar shear (i.e., shear between the layers) and transverse (90°) tension. The relative roles of the fiber and the matrix in detemining mechanical properties are summarized in Table 1.1. Because the fiber orientation directly impacts mechanical properties, it seems logical to orient Fig. 1.8 Lamina and laminate lay-ups
8/Structural Composite Materials 600 500 Fiber 400 Composite 300 200 100 Matrix 0 2 3 Strain (% Fig.1.9 Comparison of tensile properties of fiber,matrix,and composite Table 1.1 Effect of fiber and matrix on 1.3 Fundamental Property Relationships mechanical properties Dominating composite constituent When a unidirectional continuous-fiber lam- Mechanical property Fiber Matrix ina or laminate (Fig.1.11)is loaded in a di- Unidirectional rection parallel to its fibers(0 or 11-direction). Otension 0°compression the longitudinal modulus Eu can be estimated Shear from its constituent properties by using what is 90°tension known as the rule of mixtures: Laminate Tension Compression En=EVt+EmVm (Eq1.1) In-plane shear Interlaminar shear where E is the fiber modulus,Ve is the fiber vol- ume percentage,Em is the matrix modulus,and V is the matrix volume percentage. The longitudinal tensile strength ou also can as many of the layers as possible in the main be estimated by the rule of mixtures: load-carrying direction.While this approach may work for some structures,it is usually nec- Gu=GVt+GmV'm (Eq1.2) essary to balance the load-carrying capability in a number of different directions,such as the where of and om are the ultimate fiber and ma- 0°，+45°，-45°，and90°directions.Figure1.10 trix strengths,respectively.Because the proper- shows a photomicrograph of a cross-plied con- ties of the fiber dominate for all practical vol- tinuous carbon fiber/epoxy laminate.A balanced ume percentages,the values of the matrix can laminate having equal numbers of plies in the often be ignored;therefore: 0°，+45°，-45°，and90°degrees directions is called a quasi-isotropic laminate,because it car- En=EV (Eq1.3) ries equal loads in all four directions. o11=G' (Eq1.4)
8 / Structural Composite Materials as many of the layers as possible in the main load-carrying direction. While this approach may work for some structures, it is usually necessary to balance the load-carrying capability in a number of different directions, such as the 0°, +45°, -45°, and 90° directions. Figure 1.10 shows a photomicrograph of a cross-plied continuous carbon fiber/epoxy laminate. A balanced laminate having equal numbers of plies in the 0°, +45°, –45°, and 90° degrees directions is called a quasi-isotropic laminate, because it carries equal loads in all four directions. 1.3 Fundamental Property Relationships When a unidirectional continuous-fiber lamina or laminate (Fig. 1.11) is loaded in a di rection parallel to its fibers (0° or 11-direction), the longitudinal modulus E11 can be estimated from its constituent properties by using what is known as the rule of mixtures: E11 = Ef Vf + EmVm (Eq 1.1) where Ef is the fiber modulus, Vf is the fiber volume percentage, Em is the matrix modulus, and Vm is the matrix volume percentage. The longitudinal tensile strength s11 also can be estimated by the rule of mixtures: s11 = sVf + smVm (Eq 1.2) where sf and sm are the ultimate fiber and matrix strengths, respectively. Because the properties of the fiber dominate for all practical volume percentages, the values of the matrix can often be ignored; therefore: E11 ≈ Ef Vf (Eq 1.3) s11 ≈ sVf (Eq 1.4) Fig. 1.9 Comparison of tensile properties of fiber, matrix, and composite Table 1.1â•…Effect of fiber and matrix on mechanical properties Dominating composite constituent Mechanical property Fiber Matrix Unidirectional 0º tension √ … 0º compression √ √ Shear … √ 90º tension … √ Laminate Tension √ … Compression √ √ In-plane shear √ √ Interlaminar shear … √
Chapter 1:Introduction to Composite Materials/9 Fibers appear as ovals because they were cut at an angle to the0° direction. 0.0003in. 0.005 in.Thick Ply Diameter Carbon Fiber Fig.1.10 Cross section of a cross-plied carbon/epoxy laminate 90° 09 Fiber Direction Fig.1.11 Unidirectional continuous-fiber lamina or laminate
Chapter 1: Introduction to Composite Materials / 9 Fig. 1.10 Cross section of a cross-plied carbon/epoxy laminate Fig. 1.11 Unidirectional continuous-fiber lamina or laminate