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 quality control and increasing service life and performance when incorporated into practical structural design MAE08

I N T R O D U C T I O N Rationale 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 MAE08

I N T R O D U C T I O N Wedge disclination 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 MAE08

I N T R O D U C T I O N Wedge disclination 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 opening displacement, may emanate. On a larger scale, accumulation of such cracks within grains in polycrystalline aggregates may compromise the integrity of the overall structure, potentially resulting in structural failure and collapse MAE08

I N T R O D U C T I O N Objectives Investigate how Zener Compute energies of the 2 crack nucleation from the possible states within a grain single negative wedge of a polycrystalline aggregate, disclination defect depends with only a single negative on grain radius , wedge disclination defect disclination strength and and with nucleation of a surface energy of the pure Zener crack from the material making up the singular negative wedge grain disclination defect MAE08

.01 .02 Determining energy solutions Formulation of problem Calculations of required expressions to determine the crack Definition of terms involved in the problem and outline of nucleation criterion founded on the basis of energetic research direction favourability .03 .04 Determining energy solutions for Parametric study different metals Investigating the dependence of the crack nucleation criterion Calculations of required expressions with substitution of and Zener crack characteristics on various parameters: the various material constants of a series of common metals disclination power, the grain radius, as well as the surface energy of the material making up the grain MAE08

F O R M U L AT I O N O F P R O B L E M Diagram Diagram (Grain) (Element) A Zener crack of length 2 l and crack head opening b T nucleated from the singular negative wedge disclination defect of strength ω , in a circular grain of radius R MAE08 8

F O R M U L AT I O N O F P R O B L E M Defining energy terms if E c - E i < 0 Crack nucleation occurs due to energetic favourability (a lower energy state is preferred) if E c - E i > 0 Crack nucleation does not occur due to energetic favourability (a lower energy state is preferred)

Zener crack opening displacement F O R M U L AT I O N O F P R O B L E M Formulation of expressions Work done to nucleate Zener crack MAE08

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 Formulation of expressions MAE08

Expression for the total elastic energy of the cracked grain is differentiated with respect to b T and derivative is set equal to 0 to obtain F O R M U L AT I O N O F P R O B L E M Formulation of , which is substituted into the expression for the total elastic energy . expressions Obtaining the second partial derivative of Ec with respect to b T gives: > 0 , , indicating that the energy of the cracked grain is at a minimum and the crack head opening displacement is stable . The expression for the total elastic energy is 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 E c - E i , which if < 0 , indicates that crack nucleation occurs due to energetic favourability MAE08

Energy solutions for different metals 1 2 Surface energy Shear modulus 3 4 Poisson’s ratio Reference parameter values MAE08

Parametric Disclination Power ω is varied from 0.1° to 1° study A Grain Radius PARAMETERS B R is varied from 10-3 m to 10-6 m To better elucidate crack nucleation mechanisms, a parametric study is conducted, C Surface Energy in which three groups of parameters can be 𝛿 is varied from 0.10 J/m2 to 5.00 J/m2 identified, the material parameters , 𝛿 , μ , ν , D, the geometrical parameter R, and the Reference parameter values are those of beryllium , R=10-3 m, and loading parameter ω ω =-1° MAE08

R E S U L T S Energy solutions for different common metals 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, F I G . 1 energetically favourable and unfavourable, MAE08

R E S U L T S Disclination Power Fig. 2: Stable, favourable crack length against disclination power, ω , Fig. 3: Unstable, favourable crack length against disclination power, ω , where ω critical = 0.120°, determined to 3 decimal places, where ω critical = 0.120°, determined to 3 decimal places MAE08

R E S U L T S Disclination Power Fig. 4: Crack head opening displacement of stable cracks against Fig. 5: Crack head opening displacement of unstable cracks against disclination power, ω , where ω critical = 0.120°, determined to 3 disclination power, ω , where ω critical = 0.120°, determined to 3 decimal places decimal places MAE08

R E S U L T S Grain Radius Fig. 6: Stable, favourable crack length against lgR, where Fig. 7: Unstable, favourable crack length against lgR, where Rcritical = 10-4.9 m, determined to 1 decimal place Rcritical = 10-4.9 m, determined to 1 decimal place MAE08

R E S U L T S Grain Radius Fig. 8: Crack head opening displacements of stable cracks Fig. 9: Crack head opening displacements of unstable against lgR, where Rcritical = 10-4.9 m, determined to 1 cracks against lgR, where Rcritical = 10-4.9 m, determined decimal place to 1 decimal place MAE08

R E S U L T S Surface Energy Fig.10: Stable, favourable crack length against surface energy, 𝛿 Fig. 11: Unstable, favourable crack length against surface energy, 𝛿 MAE08

R E S U L T S Surface Energy Fig. 12: Stable crack head opening displacements against surface energy, 𝛿 Fig. 13: Unstable crack head opening displacements against surface energy, 𝛿 MAE08

C O N C L U S I O N Advantages 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 on generally, since a lower energy state is always preferred in natural systems Results have been consistent with findings derived from the mechanical approach MAE08

C O N C L U S I O N Limitations It is worth noting that in cases when crack However, effect of grain surface stresses and nucleation is not energetically favourable, traction on the possibility of composite Zener- structural integrity is not guaranteed , for Griffith crack nucleation from the disclination is nucleation of other defects such as dislocations not accounted for. Nevertheless, there is much might be favourable, and these are not potential in providing applicability to the real-life considered in the present study modelling of polycrystalline aggregates as a successful approach to predicting the potentiality of Zener crack nucleation from a single wedge disclination, and the equilibrium crack length and crack head opening displacement, is developed MAE08

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 Thank You Technological University for this opportunity to work on a research project under the Nanyang Research Programme. I am also grateful to my understanding parents and teachers for accomodating my busy schedule. Last but not least, I would like to thank Mr 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. _____________ 
 MAE08