Crack Nucleation from a Disclination Defect MAE08 Andre Lim Bu - - PowerPoint PPT Presentation
Crack Nucleation from a Disclination Defect MAE08 Andre Lim Bu Yun Assoc. Prof Wu Mao See I N T R O D U C T I O N Rationale Microstructural analyses have contributed to ongoing advancements in engineering materials Direct contributions to
MAE08 Andre Lim Bu Yun
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Microstructural analyses have contributed to ongoing advancements in engineering materials
I N T R O D U C T I O N
Direct contributions to quality control and increasing service life and performance when incorporated into practical structural design
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The structures of engineering materials often relate to arrangements of internal components Defects and imperfections are responsible for many resulting physical, chemical properties Characterisation is therefore, important in determining overall structural integrity
I N T R O D U C T I O N
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A wedge disclination coincides perpendicularly with the centre of a homogenous, isotropic circle, an approximation for the complex geometry of each grain. It is intuitively visualised as the insertion or removal of a wedge or sector of material into or from the circle, glued perfectly in place such that rejoined surfaces cannot be identified, giving rise to an internally-strained body with a negative or positive disclination respectively, when external forces are removed
I N T R O D U C T I O N
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A disclination defect possesses a singular stress field and under such large internal stresses within the grain, a pure Zener crack, wedged open at one end with a crack head
accumulation of such cracks within grains in polycrystalline aggregates may compromise the integrity of the overall structure, potentially resulting in structural failure and collapse
I N T R O D U C T I O N
Investigate how Zener crack nucleation from the single negative wedge disclination defect depends
disclination strength and surface energy of the material making up the grain Compute energies of the 2 possible states within a grain
with only a single negative wedge disclination defect and with nucleation of a pure Zener crack from the singular negative wedge disclination defect
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I N T R O D U C T I O N
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Definition of terms involved in the problem and outline of research direction
Formulation of problem
.01
Calculations of required expressions with substitution of various material constants of a series of common metals
Determining energy solutions for different metals
.03
Calculations of required expressions to determine the crack nucleation criterion founded on the basis of energetic favourability
Determining energy solutions
.02
Investigating the dependence of the crack nucleation criterion and Zener crack characteristics on various parameters: the disclination power, the grain radius, as well as the surface energy of the material making up the grain
Parametric study
.04
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A Zener crack of length 2l and crack head
wedge disclination defect of strength ω, in a circular grain of radius R
F O R M U L AT I O N O F P R O B L E M
F O R M U L AT I O N O F P R O B L E M
if Ec - Ei < 0
Crack nucleation occurs due to energetic favourability (a lower energy state is preferred)
if Ec - Ei > 0
Crack nucleation does not occur due to energetic favourability (a lower energy state is preferred)
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Zener crack opening displacement Work done to nucleate Zener crack
F O R M U L AT I O N O F P R O B L E M
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F O R M U L AT I O N O F P R O B L E M
Work done to nucleate Zener crack
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Expression for the total elastic energy of the cracked grain is differentiated with respect to bT and derivative is set equal to 0 to obtain , which is substituted into the expression for the total elastic energy. Obtaining the second partial derivative of Ec with respect to bT gives: > 0, , indicating that the energy of the cracked grain is at a minimum and the crack head
differentiated with respect to l and the derivative is plotted against l. The roots, which indicate stable and unstable lengths of possible cracks, are found and the values for l are substituted into Ec - Ei, which if < 0, indicates that crack nucleation occurs due to energetic favourability
F O R M U L AT I O N O F P R O B L E M
Poisson’s ratio Reference parameter values Surface energy Shear modulus
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To better elucidate crack nucleation mechanisms, a parametric study is conducted, in which three groups of parameters can be identified, the material parameters, 𝛿, μ, ν, D, the geometrical parameter R, and the loading parameter ω
ω is varied from 0.1° to 1°
Disclination Power
R is varied from 10-3 m to 10-6 m
Grain Radius
𝛿 is varied from 0.10 J/m2 to 5.00 J/m2
Surface Energy
A B C
PARAMETERS
Reference parameter values are those of beryllium, R=10-3 m, and ω=-1°
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R E S U L T S
An immediate impression upon plotting is that the graphs of the stable crack length solutions, energetically favourable and unfavourable, are the vertical reverse of the unstable crack length solutions, energetically favourable and unfavourable,
F I G . 1
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R E S U L T S
where ωcritical = 0.120°, determined to 3 decimal places
where ωcritical = 0.120°, determined to 3 decimal places,
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R E S U L T S
disclination power, ω, where ωcritical = 0.120°, determined to 3 decimal places
disclination power, ω, where ωcritical = 0.120°, determined to 3 decimal places
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R E S U L T S
Rcritical = 10-4.9 m, determined to 1 decimal place
Rcritical = 10-4.9 m, determined to 1 decimal place
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R E S U L T S
against lgR, where Rcritical = 10-4.9 m, determined to 1 decimal place
cracks against lgR, where Rcritical = 10-4.9 m, determined to 1 decimal place
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R E S U L T S
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Fig.10: Stable, favourable crack length against surface energy, 𝛿
R E S U L T S
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Compared to previous studies taking the viewpoint of classical mechanics, the energy analysis presents a much less computationally intensive method for predicting crack nucleation The energy analysis method can also be agreed
always preferred in natural systems Results have been consistent with findings derived from the mechanical approach
C O N C L U S I O N
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However, effect of grain surface stresses and traction on the possibility of composite Zener- Griffith crack nucleation from the disclination is not accounted for. Nevertheless, there is much potential in providing applicability to the real-life modelling of polycrystalline aggregates as a successful approach to predicting the potentiality
disclination, and the equilibrium crack length and crack head opening displacement, is developed
C O N C L U S I O N
It is worth noting that in cases when crack nucleation is not energetically favourable, structural integrity is not guaranteed, for nucleation of other defects such as dislocations might be favourable, and these are not considered in the present study
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Thank You
E N D
I would like to thank my mentor, Assoc Prof Wu Mao See at the School of Mechanical and Aerospace Engineering for his patience and guidance throughout this project. I would also like to thank Nanyang Technological University for this opportunity to work on a research project under the Nanyang Research
parents and teachers for accomodating my busy
Low Kay Siang, NRP coordinator for HCI, for assisting me in many administrative matters and also for his concern and advice throughout this research journey. _____________