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5.

6.

7.

1.

2.

3.

4.

8.

9.

11.

12.

13.

10.

14.

 

(Major Poisson ratio)

(Shear Modulus)

(poisson effect value)

 

 

Theoretical Calculations of Material Properties

f: fiber, m: matris, c:kompozit, Vf : Fiber volumetric ratio, , Vm: Matrix volumetric ratio =1-Vf , ρ: density

(density of composite)

(modulus of elasticity in direction of fiber -1)

(E2: modulus of elasticity in the direction 2 ,

If p* is neglected)

(E2: modulus of elasticity in the direction 2 ,

If p* is not neglected)

(load rate coming to fiber in direction 1)

(composite strength in direction 1)

(Critical Fiber Volume fraction )

(minimum fiber Volume fraction)

(isotropic material property)

(normal stress in fiber direction)

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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at any instant

 

constrained in direction 1:

Temperature Differences for an orthotropic lamina

at strength limit

 

Free state:

CTE- coefficient of thermal expansion

(in direction 1)

(in direction 2)

THERMAL EQUATIONS

17

18

19

20

15

16

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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off -axis

Torsional Tube

45o

Iosipescu

(Rijitlik Modülü)

(Shear Strength)

Some Experimental Measurements

21

22

23

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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Transformation and Hooke’s Equations (For Stress and Strain Calculations)

 

32

 

33

 

34

 

35

θ: fiber orientation angle

θ: straingage angle

local

stresses

Global

stresses

Local

strains

Global

strains

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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36

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Maximum Stress Criterion

Maximum Strain Criterion

Tsai-Hill

Hoffman

Mises-Hencky

Hoffman Criterion

Tsai-Wu Criterion

Yield and Fracture Criteria in Composites (No Damage Inequalities)

37

Tsai-Hill Criterion

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40

Modified Tsai-Hill Criterion

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42

ult: Ultimate, C: Comporession , T: Tension

: Tensile strength in direction 1

: Tensile strength in direction 2

:Shear Strength

Semboller için Örnek Açıklama

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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Stifness Matrices [A], [B], [D] in CLT

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44

45

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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Homogenization in Laminated Composites

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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53

54

55

56

57

58

59

60

61

62

63

65

64

66

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68

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70

71

72

Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

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Strengt Limits in the Zor Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

73

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Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor

July 16, 2026