1. Pendahuluan Material Komposit
BAB 3 Micromechanical Analysis of a Lamina
Modulus Elastis
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw

2. Strength of Materials Approach

3. Strength of Materials Approach

4. Strength of Materials Approach
Gambar 3.3
Representative volume element of a unidirectional lamina.

5. Strength of Materials Approach
Gambar 3.4
A longitudinal stress applied to the representative volume element to calculate the longitudinal Young’s modulus for a unidirectional lamina.

6. Longitudinal Young’s Modulus

7. Longitudinal Young’s Modulus

8. Longitudinal Young’s Modulus

9. Longitudinal Young’s Modulus
Gambar 3.5
Fraction of load of composite carried by fibers as a function of fiber volume fraction for constant fiber to matrix moduli ratio.

10. Example
Example 3.3
Find the longitudinal elastic modulus of a unidirectional Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively. Also, find the ratio of the load taken by the fibers to that of the composite.

11. Example
Example 3.3
Ef = 85 Gpa
Em = 3.4 GPa

12. Example Example 3.3 Gambar 3.6
Longitudinal Young’s modulus as function of fiber volume fraction and comparison with experimental data points for a typical glass/polyester lamina.

13. Example
Example 3.3

14. Transverse Young’s Modulus
Gambar 3.7
A transverse stress applied to a representative volume element used to calculate transverse Young’s modulus of a unidirectional lamina.

15. Transverse Young’s Modulus

16. Transverse Young’s Modulus

17. Example
Example 3.4
Find the transverse Young's modulus of a Glass/Epoxy lamina with a fiber volume fraction of 70%. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

18. Example
Example 3.4
= 85 GPa
Em = 3.4 GPa

19. Transverse Young’s Modulus
Gambar 3.8
Transverse Young’s modulus as a function of fiber volume fraction for constant fiber to matrix moduli ratio.

20. Transverse Young’s Modulus

21. Transverse Young’s Modulus
Gambar 3.9
Fiber to fiber spacing in (a) square packing geometry and (b) hexagonal packing geometry.

22. Transverse Young’s Modulus
Gambar 3.10 Theoretical values of transverse Young’s modulus as a function
of fiber volume fraction for a boron/epoxy unidirectional lamina (Ef = 414 GPa, vf = 0.2, Em = 4.14 GPa, vm = 0.35) and comparison with experimental values. Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

23. Transverse Young’s Modulus
Gambar 3.11
A longitudinal stress applied to a representative volume element to calculate Poisson’s ratio of unidirectional lamina.

24. Major Poisson’s Ratio

25. Major Poisson’s Ratio

26. Major Poisson’s Ratio

27. Example
Example 3.5
Find the Major and Minor Poisson's ratio of a Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

28. Example
Example 3.5

29. Example
Example 3.5
E1 = Gpa
E2 = GPa

30. Example
Example 3.5

31. In-Plane Shear Modulus
Gambar 3.12
An in-plane shear stress applied to a representative volume element for finding in-plane shear modulus of a unidirectional lamina.

32. In-Plane Shear Modulus

33. In-Plane Shear Modulus

34. In-Plane Shear Modulus

35. Example
Example 3.6
Find the in-plane shear modulus of a Glass/Epoxy lamina with a 70% fiber volume fraction. Use properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

36. Example
Example 3.6

37. Example
Example 3.6

38. Example
Example 3.6

39. In-Plane Shear Modulus
Gambar 3.13 Theoretical values of in-plane shear modulus as a function of fiber volume fraction and comparison with experimental values for a unidirectional glass/epoxy lamina (Gf = GPa, Gm = 1.83 GPa). Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

40. Longitudinal Young’s Modulus

41. Example
Example 3.7
Find the transverse Young's modulus for a Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties for glass and epoxy from Tables 3.1 and 3.2, respectively. Use Halphin-Tsai equations for a circular fiber in a square array packing geometry.

42. Example Example 3.7 Gambar 3.14
Concept of direction of loading for calculation of transverse Young’s modulus by Halphin–Tsai equations.

43. Example
Example 3.7
Ef = 85 GPa
Em = 3.4 GPa

44. Example
Example 3.7

45. Transverse Young’s Modulus
Gambar 3.15 Theoretical values of transverse Young’s modulus as a function of fiber volume fraction and comparison with experimental values for boron/epoxy unidirectional lamina (Ef = 414 GPa, νf = 0.2, Em = 4.14 GPa, νm = 0.35). Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

46. Transverse Young’s Modulus
Ef/Em = 1 implies = 0, (homogeneous medium)
Ef/Em implies = 1, (rigid inclusions)
Ef/Em implies (voids)

47. Transverse Young’s Modulus
Gambar 3.16
Concept of direction of loading to calculate in-plane shear modulus by Halphin–Tsai equations.

48. Transverse Young’s Modulus

49. Example
Example 3.8
Using Halphin-Tsai equations, find the shear modulus of a Glass/Epoxy composite with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively. Assume the fibers are circular and are packed in a square array. Also get the value of the shear modulus by using Hewitt and Malherbe’s8 formula for the reinforcing factor.

50. Example
Example 3.8

51. Example
Example 3.8

52. Example
Example 3.8

53. Example
Example 3.8

54. Example
Example 3.8

55. END

56. Pendahuluan Material Komposit
BAB 3 Micromechanical Analysis of a Lamina
Coefficients of Thermal Expansion
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw

57. Coefficients of Thermal Expansion

58. Longitudinal Thermal Expansion Coefficient

59. Longitudinal Thermal Expansion Coefficient

60. Longitudinal Thermal Expansion Coefficient

61. Transverse Thermal Expansion Coefficient

62. Transverse Thermal Expansion Coefficient

63. Transverse Thermal Expansion Coefficient

64. Example
Example 3.18
Find the coefficients of thermal expansion for a Glass/Epoxy lamina with 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

65. Example
Example 3.18

66. Example
Example 3.18

67. Example Example 3.18 Gambar 3.38
Longitudinal and transverse coefficients of thermal expansion as a function of fiber volume fraction for a glass/epoxy unidirectional lamina.

68. Example Example 3.18 Gambar 3.39
Unidirectional graphite/epoxy specimen with strain gages and temperature sensors for finding
coefficients of thermal expansion.

69. Example
Example 3.18

70. Example Example 3.18 Gambar 3.40
Induced strain as a function of temperature to find the coefficients of thermal expansion of a unidirectional graphite/epoxy laminate.

71. END

72. Pendahuluan Material Komposit
BAB 3 Micromechanical Analysis of a Lamina
Coefficients of Moisture Expansion
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw

73. Coefficients of Moisture Expansion

74. Coefficients of Moisture Expansion

75. Coefficients of Moisture Expansion

76. Coefficients of Moisture Expansion

77. Example
Example 3.19
Find the two coefficients of moisture expansion for a Glass/Epoxy lamina with 70% fiber volume fraction. Use properties for glass and epoxy from Tables 3.1 and 3.2, respectively. Assume glass does not absorb moisture.

78. Example = 2500 kg/m3 = 0.3 = 1200 kg/m3 = 2110 kg/m3 = 0.33 m/m/kg/kg
= GPa
= 3.4 GPa
= 0.230

79. Example
Example 3.19

80. Example
Example 3.19

81. Pendahuluan Material Komposit
BAB 4 Macromechanical Analysis of a Laminate
Objectives and Laminate Code
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw

82. Laminate Stacking Sequence
Gambar 4.1
Schematic of a lamina

83. BAB Objectives Understand the code for laminate stacking sequence
Develop relationships of mechanical and hygrothermal loads applied to a laminate to strains and stresses in each lamina
Find the elastic stiffnesses of laminate based on the Modulus Elastis of individual laminas and the stacking sequence
Find the coefficients of thermal and moisture expansion of a laminate based on Modulus Elastis, coefficients of thermal and moisture expansion of individual laminas, and stacking sequence

84. Laminate Code
-45 90 60 30

85. Laminate Code
-45 90 60

86. Laminate Code
-45 60

87. Laminate Code
-45 60

88. Laminate Code
Graphite/Epoxy
Boron/Epoxy 45
-45

89. Special Types of Laminates
Symmetric Laminate: For every ply above the laminate midplane, there is an identical ply (material and orientation) an equal distance below the midplane.
Balanced Laminate: For every ply at a +θ orientation, there is another ply at the – θ orientation somewhere in the laminate.

90. Special Types of Laminates
Cross-ply Laminate: Composted of plies of either 0° or 90° (no other ply orientation).
Quasi-isotropic Laminate: Produced using at least three different ply orientations, all with equal angles between them. Exhibits isotropic extensional stiffness properties.

91. Laminate Behavior The Stacking Position Thickness
Modulus Elastis
The Stacking Position
Thickness
Angles of Orientation
Coefficients of Thermal Expansion
Coefficients of Moisture Expansion

92. Strains in a beam (4.1) Gambar 4.2
A beam under (a) axial load, (b) bending moment, and (c) combined axial and bending moment.

93. Types of loads allowed in CLT analysis
Nx = normal force resultant in the x direction (per unit length)
Ny = normal force resultant in the y direction (per unit length)
Nxy = shear force resultant (per unit length)
Gambar 4.3
Resultant forces and moments on a laminate.

94. Types of loads allowed in CLT analysis
Mx = bending moment resultant in the yz plane (per unit length)
My = bending moment resultant in the xz plane (per unit length)
Mxy = twisting moment resultant (per unit length)

95. END