Fracture Mechanics 1

Fracture Mechanics 1
FRACTURE MECHANICS
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Fracture Mechanics 2
Question 3 (Block 1 Learning Outcomes 2.3, 2.6, 4.2, 7.3)
This question carries 30% of the marks for this assignment
A composite is produced from titanium reinforced with aligned silicon carbide fibres. The
elastic modulus of titanium is 118 GPa and silicon carbide 380 GPa. The composite contains
approximately 60% titanium and 40% fibres.
 a.Calculate the overall modulus of the composite, explaining your calculations and the
assumptions you have made when it is loaded:
o i.Along the direction of fibre length.
EL- overall longitudinal modulus
ET - modulus of titanium
ES- modulus silicon carbide
VS- Volume of silicon carbide
VT- Volume of titanium
EL=ETVT+ESVS
EL =118(0.6) +380(0.4)
EL = 451.2 GPa
o ii.Perpendicular to the fibre length.
EP- overall perpendicular modulus
ET - modulus of titanium
ES- modulus silicon carbide
VS- Volume of silicon carbide
VT- Volume of titanium
EP= ETES /ETVT+ESVS
EP= 118*380 /118(0.6) +380(0.4)
EP=99.38 GPa

Fracture Mechanics 3
(8 marks)
 b.Explain briefly why a material might show different yield behaviour in tension and
compression when loaded cyclically.
Fatigue is a surface phenomenon in which the back and forth movement of dislocations
(upon cyclic loading) along slip planes/slip directions will lead to formation of
persistent slip bands-PSBs (a kind of slip traces that are permanent). These PSBs are
essentially an extra plane of atoms that upon reaching the specimen surface produces
small permanent projections, called extrusions (there are theories that say
complimentary intrusions....a sink-in of plane of atoms often forms). The extrusions
upon continuous cyclic loading will intensify and eventually create a surface
imperfection (notch effect) and a micro crack will finally initiate from the
intrusion/extrusion....that's is the theory of how a fatigue crack will initiate...
If your cycle is tension-tension or tension-compression, you are forcing the dislocations
to move outward, sufficient enough to create intrusions/extrusions after a reasonable
number of cycles. On the other hand if your cycle is compression-compression,
dislocation movement is largely inwards (barring a few dislocations that may go in the
other directions). The possibility of formation of intrusion/extrusion....the primary
phenomena that controls the fatigue life...is ceased or at least delayed substantially. That
is the reason why you would find longer fatigue life (higher fatigue strength as you put
it) in compression cycling Sun, (2016).
(4 marks)

Calculate the longitudinal and transverse stresses in the two phases from the measured
strains (assume that the longitudinal and transverse strains are the principal strain
components, and that the two transverse strain components are equal, i.e. .) Take the