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Heat transfer and fluid flow analysis of self-healing in metallic materials

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Abstract

This paper explores imparting self-healing characteristics to metal matrices similar to what are observed in biological systems and are being developed for polymeric materials. To impart self-healing properties to metal matrices, a liquid healing method was investigated; the met hod consists of a container filled with low melting alloy acting as a healing agent, embedded into a high melting metal matrix. When the matrix is cracked; self-healing is achieved by melting the healing agent allowing the liquid metal to flow into the crack. Upon cooling, solidification of the healing agent occurs and seals the crack. The objective of this research is to investigate the fluid flow and heat transfer to impart self-healing property to metal matrices. In this study, a dimensionless healing factor, which may help predict the possibility of healing is proposed. The healing factor is defined as the ratio of the viscous forces and the contact area of liquid metal and solid which prevent flow, and volume expansion, density, and velocity of the liquid metal, gravity, crack size and orientation which promote flow. The factor incorporates the parameters that control self-healing mechanism. It was observed that for lower values of the healing factor, the liquid flows, and for higher values of healing factor, the liquid remains in the container and healing does not occur. To validate and identify the critical range of the healing factor, experiments and simulations were performed for selected combinations of healing agents and metal matrices. The simulations were performed for three-dimensional models and a commercial software 3D Ansys-Fluent was used. Three experimental methods of synthesis of self-healing composites were used. The first method consisted of creating a hole in the matrices, and liquid healing agent was poured into the hole. The second method consisted of micro tubes containing the healing agent, and the third method consisted of incorporating micro balloons containing the healing agent in the matrix. The observed critical range of the healing factor is between 407 and 495; only for healing factor values below 407 healing was observed in the matrices.

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Abbreviations

Amush :

Mushy zone

Cp :

Specific heat (kJ/kg K)

CTE:

Coefficient of thermal expansion

d:

Crack characteristic length (m)

D:

Diffusion

Fα :

External force (N)

g:

Gravity (m/s2)

H:

Heat transfer coefficient (w/m2 K)

h :

Enthalpy (kJ/kg)

hpf :

Self-healing predicting factor

Hf :

Healing factor

jm :

Momentum flux

L :

Latent heat (kJ/kg)

k:

Thermal conductivity (w/m K)

P:

Pressure (Pa)

q:

Heat flux (kJ/m2)

r:

Radius of the curvature (m)

R:

Gas constant (kJ/kg K)

RTot :

Total thermal resistance

s:

Saturation

t:

Time (s)

T:

Temperature (K)

TH :

Healing temperature (K)

\(\overrightarrow {{v_{p} }}\) :

Pull velocity (m/s)

V:

Bulk velocity (m/s)

Vf :

Volume of fraction

Wik :

Amount of work (j)

x, y, z:

Coordinate system

α:

Thermal diffusivity (m2/s)

β:

Liquid fraction

\(\gamma\) :

Interfacial tension (N/m)

\(\Delta H_{f}\) :

Latent heat of fusion (KJ)

θ:

Contact angle

λ:

Free mean path

µ:

Dynamic viscosity (kg/m s)

ρ:

Density (kg/m3)

σik :

Interface tension

σ:

Electrical conductivity (S/m)

υ:

Kinematic viscosity (m2/s)

ϕ0 :

Liquid healing agent

i, j:

Term index

References

  1. Burgess SC (2002) Reliability and safety strategies in living organisms: potential for biomimicking. Proc Inst Mech Eng Part E J Process Mech Eng 216(1):1–13

    Article  MathSciNet  Google Scholar 

  2. Van der Zwaag S (ed) (2007) Self healing materials—an alternative approach to 20 centuries of materials science. Springer, Dordrecht

    Google Scholar 

  3. Van der Zwaag S (2009) Self-healing behaviour in man-made engineering materials: bioinspired but taking into account their intrinsic character. Philos Trans R Soc A 367:1689–1704

    Article  Google Scholar 

  4. Ghosh SK (ed) (2009) Self-healing materials: fundamentals, design strategies, and applications. Wiley, Weinheim

    Google Scholar 

  5. Wang ZX, Dutta I, Majumdar BS (2005) Thermo-mechanical response of a lead-free solder reinforced with a shape memory alloy. Scr Mater 54(4):627–632

    Article  Google Scholar 

  6. Manuel M (2007) Design of a biomimetic self-healing alloy composite. PhD Thesis, under supervision of Prof. Gregory Olson, Northwestern University

  7. Manuel MV, Olson GB (2007) Biomimetic self-healing metals. In: Proceedings of the 1st international conference on self-healing materials, Noordwijk aan Zee, The Netherlands, 18–20 Apr 2007

  8. Olson GB, Hartman H (1982) Martensite and life—displacive transformations as biological processes. J Phys 43(NC-4):855–865

    Google Scholar 

  9. Olson GB (1997) Computational design of hierarchically structured materials. Science 277(5330):1237–1242

    Article  Google Scholar 

  10. Perkins J (1981) Ti–Ni and Ti–Ni–X shape memory alloys. Metals Forum 4(3):153–163

    Google Scholar 

  11. Perkins J (1981) Shape memory behavior and thermoelastic martensitic transformations. Mater Sci Eng 51:181–192

    Article  Google Scholar 

  12. Brinson LC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct 4:229–242

    Article  Google Scholar 

  13. Burton DS, Gao X, Brinson LC (2006) Finite element simulation of a self-healing shape memory alloy composite. Mech Mater 38(5–6):525–537

    Article  Google Scholar 

  14. Hautakangas H, Schut S, van der Zwaag PE, Rivera Diaz del Castillo J, van Dijk NH (2007) Positron annihilation spectroscopy as a tool to develop self healing in aluminium alloys. Phys Stat Sol (c) 4(10):3469–3472. doi:10.1002/pssc.200675747

    Article  Google Scholar 

  15. Hautakangas H, Schut S, van der Zwaag PE, Rivera Diaz del Castillo J, van Dijk NH (2007) The role of the aging temperature on the self healing kinetics in an under aged AA2024 aluminium alloy. In: Proceedings of the first international conference on self-healing materials, Noordwijk aan Zee, The Netherlands, 18–20 Apr 2007

  16. Lumley RN, Morton AJ, Polmear LJ (2002) Enhanced creep performance in an Al–Cu–Mg–Ag alloy through underageing. Acta Mater 50:3597–3608

    Article  Google Scholar 

  17. Zhu AW, Chen J, Starke EA (2000) Precipitation strengthening in stress-aged Al–xCu alloys. Acta Mater 48:2239–2246

    Article  Google Scholar 

  18. Bear J (2013) Dynamics of fluids in porous media. Dover Books on Physics & Chemistry. Dover Publications, Inc, New York

  19. van der Zwaag S (2007) Self healing materials: an alternative approach to 20th centuries of materials science. Springer, London

    Book  Google Scholar 

  20. Ghosh SK (2009) Self-healing materials, fundamentals, design, strategies, and applications. Wiley-VCH, Weinheim. doi: 10.1002/9783527625376

  21. Muskat M (1937) The flow of homogeneous fluids through porous media. McGraw-Hill, New York

    MATH  Google Scholar 

  22. Chakraborty S. Simulation of micro-scale flows. Mechanical Engineering Department Indian Institute of Technology, Kharagpur

  23. Chen Q, Amano RS, **n M (2005) Experimental and computational study of R134A condensation heat transfer inside the micro-fin tubes. Int J Heat Mass Transf 41:785–791

    Article  Google Scholar 

  24. Chakraborty S (2006) Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients. Int J Heat Mass Transf 49:810–813

    Article  MATH  Google Scholar 

  25. Stefanescu DM. Science and engineering of casting solidification, 2nd edn, pringer, US. doi: 10.1007/b135947

  26. Fluent software tutorial

  27. Voller R, Swaminathan CR (1991) Generalized source-based method for solidification phase change. Numer Heat Transf B 19(2):175–189

    Article  Google Scholar 

  28. Voller VR, Prakash C (1987) A fixed-grid numerical modeling methodology for convection–diffusion mushy region phase-change problems. Int J Heat Mass Transf 30:1709–1720

    Article  Google Scholar 

  29. Liu Z, Bando Y, Mitome M, Zhan J (2004) Unusual freezing and melting of gallium encapsulated in carbon nanotubes. Phys Rev Lett 93(9):93–102

    Article  Google Scholar 

  30. Martinez Lucci J, Amano RS, Rohatgi PK, Schultz B (2008) Experiment and computational analysis of self-healing in an aluminum alloy. In: Proceedings of the mechanical congress and exhibition, IMECE2008-68304

  31. Martinez Lucci J, Amano RS, Rohatgi PK, Schultz B, Nosonovsky M (2009) Physical chemistry of self-organization and self-helaing in metals. J Phys Chem Chem Phys 11(41):9530–9536

    Article  Google Scholar 

  32. Martinez Lucci J, Amano RS, Rohatgi PK, Schultz B (2008) Self-healing in an aluminum alloy reinforced with microtubes. In: EnergyNano08 ASME turbo expo ENIC2008-53011

  33. Lee E, Amano R, Rohatgi PK (2007) Metal matrix composite solidification in the presence of cooled fibers: numerical simulation and experimental observation. Heat Mass Transf 43:741–748

    Article  Google Scholar 

  34. Martinez Lucci J, Amano RS, Rohatgi PK, Schultz B (2008) Computational analysis of self-healing in a polymer matrix with microvascular networks. In: Proceedings of the ASME design engineering technical conferences, DETC2008-50148

  35. Martinez Lucci J, Amano RS, Rohatgi PK, Schultz B (2009) Self-healing in an aluminum alloy reinforced with carbon fiber microtubes. In: Conference of AIAA, Orlando USA, 3–6 Jan 2009

  36. Tzeng PY, Soong CY, Liu MH, Yen TH (2008) –02) A Novel Wall-Fluid Collision Rule for Adiabatic Condition of Solid-Wall in Atomistic Simulation of Micro Thermal Fluids. Int. J Heat Mass Transf 51(3–4):445–456

    Article  MATH  Google Scholar 

  37. Mohamed Gad-el-Hak (1999) The fluid mechanics of microdevices—the Freeman scholar lecture. J Fluids Eng 121:5–33

    Article  Google Scholar 

  38. Stone HA, Strook AD, Ajdari A (2004) Engineering flows in small devices microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:65–102

    Article  MATH  Google Scholar 

  39. Tang GY, Yang C, Chai JC, Gong HQ (2004) Joule heating effect on transport in a microcapillary. Electroosmotic Flow Mass Species Int J Heat Mass Transf 47:215–227

    Article  MATH  Google Scholar 

  40. Stone HA, Kim S (2001) Microfluidics: basic issues, applications and challenges. AIChE J 47:1250–1254

    Article  Google Scholar 

  41. Ruzek AC (2009) Synthesis and characterization of metallic systems with potential for self-healing. Master Thesis, University of Wisconsin Milwaukee

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Authors and Affiliations

  1. University of Wisconsin-Milwaukee, Madrid, Spain

    R. S. Amano & P. K. Rohatgi

  2. Universidad Europea de Madrid, Madrid, Spain

    J. Martínez Lucci

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  1. J. Martínez Lucci
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  3. P. K. Rohatgi
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Correspondence to R. S. Amano.

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Martínez Lucci, J., Amano, R.S. & Rohatgi, P.K. Heat transfer and fluid flow analysis of self-healing in metallic materials. Heat Mass Transfer 53, 825–848 (2017). https://doi.org/10.1007/s00231-016-1837-y

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