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Home work 2.2 MEE661
3655 /20 /42
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1- (a)-A metallic rod (
, Y=50 Gpa at 800
) is
machined such that it perfectly fits inside an alumina tube. The assembly is then slowly heated ;at 800
the alumina tube cracks. Assume Poisson s '
ratio to 0.25 for both materials . Supposed
I=metallic road = inclusion '' where i
,Y =50 Gpa and i
=0.25''
M=alumina= matrix''where
,Y =460 m
and
m
=0.25''
( ) 1/2 ∂rad= ∂eq
( )() ∂rad= 341148325=170574162.7Pa=171MPa
(b)- Describe the state of stress that develops in the system as it is heated. Estimate the strength of the alumina tube . The state of stress is a axial and tangential or hoop stress where the nature of the thermal residual stresses that would be generated if a metallic road with
were fitted in a matrix (alumina road) with ; where the slowly heated ;at 800 the matrix and inclusion (metallic road ) the matrix expansion coefficient
will expanded both axially and radially were cusses' increased in size( internal diameter, external diameter and length ) but because the matrix will be rapidly expanded than inclusions the inclusion is restricted. Consequently, the stress required to fit the matrix to the metallic road will have to be axially tensile; when the matrix is welded to the metallic road and allowed to relax, this will place the metallic road in a state of axial residual compressive stress, which, in 2
turn, is balanced by an axial tensile stress in the matrix. Radially, the matrix will clamp down on the metallic road , resulting in radial compressive stresses in both the metallic road and the matrix, In addition the system will develop tensile tangential stresses, as shown in Fig( 1"a"). These stresses, if sufficiently high, can cause the matrix to crack radially.
Metallica road,
Figure "1" Radial and tangential stresses developed upon cooling of a metal in
a matrix for
<
.
2-(a)Is thermal shock more likely to occur as a result of rapid heating or rapid cooling ? explain. Solution:-
For a ceramic material, thermal shock is more likely for rapid cooling since the surface stresses are tensile in nature which will lead to stress concentrations at surface flaws that are present. No such stress amplification will result for compressive stresses which are established at the surface for rapid heating. The Crack formation and propagation from surface flaws are more probable when an imposed stress is tensile . For heating, the surface stresses will be
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compressive in nature since the interior expands to a lesser degree than the hotter surface. The capacity of a material to withstand this kind of failure is termed its thermal shock resistance . For a ceramic body that is rapidly cooled, the resistance to thermal shock depends not only on the magnitude of the temperature change, but also on the mechanical and thermal properties of the material. The thermal shock resistance is best for ceramics that have high fracture strengths and high thermal conductivities, as well as low module of elasticity and low coefficients of thermal expansion.
(b) a ceramic component with Young's modulus of 300 Gpa and a k Ic of 4 MPa 1/2
.m
is to survive a water quench from 500
material is on the order of 10
. if the largest flaw in that
, what is the maximum value of for this
ceramic for it to survive the equench?
,T =500, T = 25
Y=300 Gpa, a k Ic of 4 MPa .m1/2,c=10
∂eq√ From (1)
∂eq=
….
1
∂eq
2
=-Y
= √ √ ∂eq
= -714Mpa
( )() ) 5 4
3-(a) explain how a glaze with a different thermal expansion can influence the effective strength of a ceramic component . to increase the strength of a component , would you use a glaze with a higher or lower thermal expansion coefficient than the substrate ? explain . Solution:-
Glaze is brittle material . as such they are quite strong in compression. But very weak in tension. Ceramic bodies are also brittle material, but Their greater thickness than the glaze enable to carry a correspondingly greater tensile stress, Hence, if thermal expansion of the glaze is less than that of the body ,the glaze will be compressed, the substrate will be permanently stressed intension, and crazing will be avoided. On the other hand , when thermal expansion of glass is greater than the of the body, the glaze will compress the body ,and must there for carry a balancing tensile stress . glass is not able to withstand much of any tension force. The result is a fracture pattern called crazing .the opposite effect called peeling or shivering .wile a moderate compression of glaze, with corresponding tensile force in the body. can be tolerated. at a longer mismatch in thermal expansion compression is generated in the glaze that can exceed the strength of adhesion between glaze and substrate. This yields a stress relieving fracture at the interface. Glaze will carry at tensile stress resulting in crazing. this crazing may occur even when the thermal expansion of glaze is less than of the body. if the glaze expansion exceeds that of the engobe to which it is bonded, it does not matter whether or not it is less than that of the body, both sealing of the glaze to engobe and the body to the engobe result in tensile force on engobe. both coating in moderate compression and crazing is avoided. from that the glaze and substrates thermal expansion are compatible or near compatible as long as time.
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(b)- fully dense, 1cm-thick alumina plates are to be glazed with a porcelain glaze (Y=70 Gpa,
=0.25) of 1mm thickness with a thermal
.assuming the ''stress freezing'' temperature of the glaze to be 800 calculate the stress in the glaze at expansion coefficient of
room temperature . Solution:-
Y=70 Gpa ,=0.25, ∂ther = -
T1=800,T2=25
( )
- )()) ()
= -((
4-(a) if a glass fiber is carefully etched to remove all Griffith flaws from its surface, estimate the maximum temperature from which it can be quenched in a bath of ice water without failure . state all assumption . information you may find useful: Y= 70 Gpa,
=0.25,
, and
. (b) repeat (a) assuming 1
flaws are present on the surface .
(c)- rep part (b) for Pyrex, a borosilicate glass for which
.based on your results, explain why pyrex is routinely used in lab ware.
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Solution:-
(a)- Y=70 Gpa, =0.25,
, and .
∂ther=Y/10 ∂ther = -
( ) ( )
() ()
(b)-
√ = 204939.0135
KIc=
√ √ ) () ( 82.61
(c)-
()
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Result and Explain :-
of Pyrex is
higher consequently don’t thermal graduate occurs, and the
crakes is inhibited as result a the thermal expansion is lower that caused lower thermal shock Pyrex and used this fact for Pyrex lab ware.
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