2015 composites lab2
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compositeTRANSCRIPT
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Composite Materials
Lab 2
Alexandros IliopoulosArtemis Kalteremidou
December 9, 2015
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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
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1. Strength of Unidirectional Lamina
– Micromechanics (Chapter 5)
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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
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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
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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
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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
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Micromechanics
Problem 2 (5.4 in book)
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?
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Micromechanics
Problem 3 (5.6 in book)
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
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2. Strength of Composite Lamina
– Macromechanics (Chapter 6)
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Macromechanics
Single layer with material coordinate system
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Macromechanics
Flow chart of macromechanical failure
,x y
1,2
,x y
F
, ,t c s
F
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Macromechanics
Stress vector rotation
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Macromechanics
Macromechanics of failure
1) Maximum stress theory
2) Maximum strain theory
3) Tsai-Hill criterion
4) Tsai-Wu criterion
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Macromechanics
Maximum stress theory
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Macromechanics
Problem 4 (6.1 in book)
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?
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Macromechanics
Maximum strain theory
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Macromechanics
Maximum strain theory
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Macromechanics
Maximum strain theory
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Macromechanics
Problem 5 (6.6 in book)
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.
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Macromechanics
Problem 6 (6.8 in book)
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.
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Macromechanics
Problem 7 (6.10 in book)
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
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Macromechanics
Tsai-Hill Criterion
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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.
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Macromechanics
Problem 9 (6.23 in book)
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,
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Macromechanics
Tsai-Wu Criterion
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Macromechanics
Problem 10 (6.27 in book)
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 .