2015 Composites Lab2

Composite Materials

Lab 2

Alexandros IliopoulosArtemis Kalteremidou

December 9, 2015

Outline

These labs are following the book:

I. M. Daniel, O. Ishai, Engineering mechanics of composite materials,

second edition, 2006

1. Strength of unidirectional lamina – Micromechanics (Chapter 5)

Micromechanics of failure

2. Strength of composite lamina – Macromechanics (Chapter 6)

Macromechanical failure theories

1. Strength of Unidirectional Lamina

– Micromechanics (Chapter 5)

Micromechanics

Micromechanics of failure

1) Longitudinal Tension

2) Longitudinal Compression

3) Transverse Tension

4) Transverse Compression

5) In-Plane Shear

6) Out-of-Plane Loading

Micromechanics

Failure Mechanisms and Strength of Longitudinal Tension

u u

ft mt

1m

t ft f m

f

EF F V V

E

1

f

t mt f m

m

EF F V V

E

Y N

Micromechanics

Problem 1 (5.2 in book)

Determine the longitudinal modulus E1 and the longitudinal

tensile strength F1t of a unidirectional carbon/epoxy composite

with the properties

Vf=0.65

E1f=235 Gpa

Em=4.14 Gpa

Fft=3450 Mpa

Fmt=104 Mpa

Micromechanics


Determine the longitudinal modulus E1 and the longitudinal

tensile strength F1t of a unidirectional silicon carbide/ceramic

composite with the properties

Vf=0.40

E1f=172 Gpa

Em=97 Gpa

Fft=1930 Mpa

Fmt=138 Mpa

Assume linear elastic behavior for both fiber and matrix.

Everything else being equal, how does the strength F1t vary

with fiber modulus E1f?

Micromechanics


A glass matrix is reinforced with unidirectional silicon carbide

fibers and loaded in longitudinal tension until matrix failure.

Determine the minimum fiber volume ratio, so that the composite

does not fail catastrophically (i.e. the unbroken fibers can support

the load) immediately after matrix failure, for the constituent properties

E1f=400 Gpa

Em=69 Gpa

Fft=3175 Mpa

Fmt=125 Mpa

2. Strength of Composite Lamina

– Macromechanics (Chapter 6)

Macromechanics

Single layer with material coordinate system

Macromechanics

Flow chart of macromechanical failure

,x y

1,2

,x y

F

, ,t c s

F

Macromechanics

Stress vector rotation

Macromechanics

Macromechanics of failure

1) Maximum stress theory

2) Maximum strain theory

3) Tsai-Hill criterion

4) Tsai-Wu criterion

Macromechanics

Maximum stress theory

Macromechanics


A unidirectional lamina is under biaxial normal loading σx=-2σy=2σ0

at 45° to the fiber direction as shown in the figure below. The basic

strength properties of the material are F1t=F1c=3F2c=5F6=12F2t=600

Mpa. Determine the stress level σ0u at failure of the lamina according

to the maximum stress theory. What is the failure mode?

Macromechanics

Maximum strain theory

Macromechanics


A unidirectional lamina is under biaxial tensile normal loading as

shown in the figure below. For the material properties of AS4/3501-6

carbon/epoxy, determine the maximum value that σ2 can reach at failure,

Based on the maximum strain theory.

E1=147 Gpa,

E2=10.3 Gpa,

v12=0.27,

v21=0.02,

F1t=2280 Mpa,

F2t=57 Mpa,

F1c=1725 Mpa,

F2c=228 Mpa,

ε1tu=0.015,

ε2tu=0.006.

Macromechanics


A unidirectional S-glass/epoxy lamina is loaded in tension at an angle

to the fiber direction as shown in the figure below. Using the maximum

strain criterion, determine the off-axis strength, Fxt, and the fiber orientation

at which the predictions of the in-plane shear and transverse tensile failure

coincide.

F1t=1280 Mpa,

F2t=50 Mpa,

F6=70 Mpa,

v12=0.27,

v21=0.06.

Macromechanics


For the off-axis lamina under positive and negative shear stress as shown

in the figure below, and using the maximum strain theory, express the

positive and negative shear strengths, and , in terms of the basic

lamina strengths (F1t, F1c,…) and material Poisson’s ratios. Assume:

F1t >F1c >>F2c >F2t ,

F6= F2t,

F2c=3F2t

sF

sF

Macromechanics

Tsai-Hill Criterion

Macromechanics

Problem 8

Compare the maximum strain theory and the Tsai-Hill failure theory

to determine maximum shear strength of lamina τs (τs >0) in the

shear test shown in the figure below with the following properties:

v12=0.27,

v21=0.06.

Macromechanics


A 45°off-axis lamina is loaded under the biaxial stresses σx=-σy=2τs.

Using the Tsai-Hill failure criterion, determine the strength σxu=-σy

u=

2τsu=F0 for an E-glass/epoxy material with properties listed below.

F1t=1140 Mpa,

F1c=620 Mpa,

F6=89 Mpa,

F2t=39 Mpa,

F2c=128 Mpa,

Macromechanics

Tsai-Wu Criterion

Macromechanics


Using the Tsai-Wu failure criterion for pure shear loading of a lamina

at 45° to the fiber direction, express the shear stress at failure τsu=Fs

u

in terms of the Tsai-Wu coefficients (Figure below). Then, obtain an

approximate expression when F1t >F1c >>F2c >F2t .

Any questions:

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2015 Composites Lab2

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