Use of the tapered double-cantilever beam geometry for fracture toughness measurements and its application to the quantification of self-healing

Abstract

The successful invention of self-healing polymer composites a decade ago necessitated a methodology to quantify the ability of the material to heal and recover structural properties following damage. Healing efficiency was defined as the ratio of healed to virgin fracture toughness, η = K_{IC_healed}/K_{IC_virgin}. Early work took advantage of the crack length independence offered by a tapered double-cantilever beam (TDCB) fracture geometry to simplify calculation of healing efficiency to the ratio of healed to virgin critical loads, η = P_{C_healed}/P_{C_virgin}. The current work investigates the application of the TDCB geometry and three common geometries utilized in the broader fracture literature (the compact tension (CT), single-edge notch bend (SENB), and single-edge notch tension (SENT) geometries) to the measurement of healing efficiency. While the TDCB geometry simplifies the calculation of healing efficiency because the crack lengths do not need to be accounted for, it is shown that if the virgin and healed crack lengths are not accurately accounted when using the CT, SENB, and SENT geometries, errors in calculated healing efficiency can be several hundred per cent. The TDCB geometry is reviewed at length, including the underlying theory and experimental calibration and validation of TDCB geometry.

Keywords

fracture toughness tapered double-cantilever beam TDCB self-healing auto-nomic healing

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References

White

S. R.

Sottos

N. R.

Geubelle

P. H.

Moore

J. S.

Kessler

M. R.

Sriram

S. R.

Brown

E. N.

Viswanathan

Autonomic healing of polymer composites. Nature, 2001, 409, 794–797.

Brown

E. N.

Sottos

N. R.

Performance of embedded microspheres for self-healing polymer composites. In Proceedings of the SEM IX International Congress on Experimental Mechanics, 2000, pp. 563–566.

Brown

E. N.

Sottos

N. R.

White

S. R.

Fracture testing of a self-healing polymer composite. Expl Mechanics, 2002, 42, 372–379.

Caruso

M. M.

Davis

D. A.

Shen

Odom

S. A.

Sottos

N. R.

White

S. R.

Moore

J. S.

Mechanically-induced chemical changes in polymeric materials. Chem. Rev., 2009, 109, 5755–5798.

D. Y.

Meure

Solomon

Self-healing polymeric materials: A review of recent developments. Prog. Polym. Sci., 2008, 33, 479–522.

Bergman

S. D.

Wudl

Mendable polymers. J. Mater. Chemistry, 2008, 18, 41–62.

Wool

R. P.

Self-healing materials: a review. Soft Matter, 2008, 4, 400–418.

Kessler

M. R.

Self-healing: a new paradigm in materials design. Proc. IMechE, Part G: J. Aerospace Engineering, 2007, 221(G4), 479–495. DOI: 10.1243/09544100JAERO172.

Trask

R. S.

Williams

G. J.

Bond

I. P.

Self-healing polymer composites: mimicking nature to enhance performance. Bioinspiration and Biomimetics, 2007, 2, P1–P9.

10.

Blaiszik

B. J.

Kramer

S. L. B.

Olugebefola

S. C.

Moore

J. S.

Sottos

N. R.

White

S. R.

Self-healing polymers and composites. Ann. Rev. Mater. Res., 2010, 40, 179–211.

11.

Gibson

R. F.

A review of recent research on mechanics of multifunctional composite materials and structures. Composite Structs, 2010, 92, 2793–2810.

12.

Murphy

E. B.

Wudl

The world of smart healable materials. Prog. Polym. Sci., 2010, 35, 223–251.

13.

Grande-Allen

K. J.

The evolution of the field of biomechanics through the lens of experimental mechanics. Expl Mechanics, 2010, 50, 667–682.

14.

Brown

E. N.

Moore

J. S.

White

S. R.

Sottos

N. R.

Fracture and fatigue behavior of a self-healing polymer composite. Mater. Res. Soc. Symp. Proc., 2003, 735, 101–106.

15.

Brown

E. N.

White

S. R.

Sottos

N. R.

Microcapsule induced toughening in a self-healing polymer composite. J. Mater. Sci., 2004, 39, 1703–1710.

16.

Jones

A. S.

Rule

J. D.

Moore

J. S.

White

S. R.

Sottos

N. R.

Catalyst morphology and dissolution kinetics of self-healing polymers. Chemistry Mater., 2006, 18, 1312–1317.

17.

Cho

S. H.

Andersson

H. M.

White

S. R.

Sottos

N. R.

Braun

P. V.

Polydimethylsiloxane-based self-healing materials. Advd Mater., 2006, 18, 997–1000.

18.

Caruso

M. M.

Delafuente

D. A.

Sottos

N. R.

Moore

J. S.

Whites

S. R.

Solvent-promoted self-healing epoxy materials. Macromolecules, 2007, 40, 8830–8832.

19.

Yuan

Liang

G. Z.

Xie

J. Q.

S. B.

Synthesis and characterization of microencapsu-lated dicyclopentadiene with melamine-formalde-hyde resins. Colloid and Polym. Sci., 2007, 285, 781–791.

20.

Yuan

Y. C.

Rong

M. Z.

Zhang

M. Q.

Chen

Yang

G. C.

X. M.

Self-healing polymeric materials using epoxy/mercaptan as the healant. Macromolecules, 2008, 41, 5197–5202.

21.

Wilson

G. O.

Moore

J. S.

White

S. R.

Sottos

N. R.

Andersson

H. M.

Autonomic healing of epoxy vinyl esters via ring opening metathesis polymerization. Advd Functional Mater., 2008, 18, 44–52.

22.

Wilson

G. O.

Henderson

J. W.

Caruso

M. M.

Blaiszik

B. J.

McIntire

P. J.

Sottos

N. R.

White

S. R.

Moore

J. S.

Evaluation of peroxide initiators for radical polymerization-based self-healing applications. J. Polym. Sci., Part A, 2010, 48, 2698–2708.

23.

Meure

D. Y.

Furman

Polyethylene-co-methacrylic acid healing agents for mendable epoxy resins. Acta Materialia, 2009, 57, 4312–4320.

24.

Brown

E. N.

White

S. R.

Sottos

N. R.

Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite - Part 1: Manual infiltration. Composites Sci. Technol., 2005, 65, 2466–2473.

25.

Brown

E. N.

White

S. R.

Sottos

N. R.

Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite - Part II: In situ self-healing. Composites Sci. Technol., 2005, 65, 2474–2480.

26.

Brown

E. N.

White

S. R.

Sottos

N. R.

Fatigue crack propagation in microcapsule-tough-ened epoxy. J. Mater. Sci., 2006, 41, 6266–6273.

27.

Brown

E. N.

Kessler

M. R.

Sottos

N. R.

White

S. R.

In situ poly(urea-formaldehyde) microencapsulation of dicyclopentadiene. J. Microencapsulation, 2003, 20, 719–730.

28.

Rule

J. D.

Brown

E. N.

Sottos

N. R.

White

S. R.

Moore

J. S.

Wax-protected catalyst micro-spheres for efficient self-healing materials. Advd Mater., 2005, 17, 205–208.

29.

Mauldin

T. C.

Rule

J. D.

Sottos

N. R.

White

S. R.

Moore

J. S.

Self-healing kinetics and the stereoisomers of dicyclopentadiene. J. R. Soc. Interface, 2007, 4, 389–393.

30.

Kirkby

E. L.

Rule

J. D.

Michaud

V. J.

Sottos

N. R.

White

S. R.

Manson

J. A. E.

Active repair of self-healing polymers with shape memory alloy wires. Proc. Soc. Photo-Opt. Instrumn Engrs, 2007, 6526, E5261–E5261.

31.

Kirkby

E. L.

Rule

J. D.

Michaud

V. L.

Sottos

N. R.

White

S. R.

Manson

J. A. E.

Embedded shape-memory alloy wires for improved performance of self-healing polymers. Advd Functional Mater., 2008, 18, 2253–2260.

32.

Kirkby

E. L.

Michaud

V. L.

Manson

J. A. E.

Sottos

N. R.

White

S. R.

Performance of self-healing epoxy with microencapsulated healing agent and shape memory alloy wires. Polymer, 2009, 50, 5533–5538.

33.

Zhao

Schadler

L. S.

Hillborg

Auletta

Improvements and mechanisms of fracture and fatigue properties of well-dispersed alumina/epoxy nanocomposites. Composites Sci. Technol., 2008, 68, 2976–2982.

34.

Caruso

M. M.

Blaiszik

B. J.

White

S. R.

Sottos

N. R.

Moore

J. S.

Full recovery of fracture toughness using a nontoxic solvent-based self-healing system. Advd Functional Mater., 2008, 18, 1898–1904.

35.

Jones

A. S.

Rule

J. D.

Moore

J. S.

Sottos

N. R.

White

S. R.

Life extension of self-healing polymers with rapidly growing fatigue cracks. J. R. Soc. Interface, 2007, 4, 395–403.

36.

Rule

J. D.

Sottos

N. R.

White

S. R.

Effect of microcapsule size on the performance of self-healing polymers. Polymer, 2007, 48, 3520–3529.

37.

Blaiszik

B. J.

Sottos

N. R.

White

S. R.

Nanocapsules for self-healing materials. Composites Sci. Technol., 2008, 68, 978–986.

38.

Wilson

G. O.

Caruso

M. M.

Reimer

N. T.

White

S. R.

Sottos

N. R.

Moore

J. S.

Evaluation of ruthenium catalysts for ring-opening metathesis polymerization-based self-healing applications. Chem. Mater., 2008, 20, 3288–3297.

39.

Kamphaus

J. M.

Rule

J. D.

Moore

J. S.

Sottos

N. R.

White

S. R.

A new self-healing epoxy with tungsten (VI) chloride catalyst. J. R. Soc. Interface, 2008, 5, 95–103.

40.

Mangun

C. L.

Mader

A. C.

Sottos

N. R.

White

S. R.

Self-healing of a high temperature cured epoxy using poly(dimethylsiloxane) chemistry. Polymer, 2010, 51, 4063–4068.

41.

Wool

R. P.

O’Conner

K. M.

A theory of crack healing in polymers. J. Appl. Physics, 1981, 52, 5953–5963.

42.

Gross

Srawley

Brown

W. F.

Stress-intensity factors for a single-edge-notch tension specimen by boundary collocation of a stress function. NASA Technical Note D-2395, NASA, USA, August 1964.

43.

Plaisted

T. A.

Nemat-Nasser

Quantitative evaluation of fracture, healing and re-healing of a reversibly cross-linked polymer. Acta Materialia, 2007, 55, 5684–5696.

44.

Kessler

M. R.

Sottos

N. R.

White

S. R.

Self-healing structural composite materials. Composites Part A, 2003, 34, 743–753.

45.

Plaisted

T. A.

Amirkhizi

A. V.

Nemat-Nasser

Compression-induced axial crack propagation in DCDC polymer samples: experiments and modeling. Int. J. Fracture, 2006, 141, 447–457.

46.

Keller

M. W.

Sottos

N. R.

White

S. R.

“A self-healing poly(dimethyl siloxane) elastomer. Advd Functional Mater., 2007, 17, 2399–2404.

47.

Toohey

K. S.

Sottos

N. R.

White

S. R.

Characterization of a microvascular-based self-healing coating. Expl Mechanics, 2009, 49, 707–717.

48.

Pang

J. W. C.

Bond

I. P.

A hollow fibre reinforced polymer composite encompassing self-healing and enhanced damage visibility. Composites Sci. Technol., 2005, 65, 1791–1799.

49.

Trask

R. S.

Williams

G. J.

Bond

I. P.

Bioinspired self-healing of advanced composite structures using hollow glass fibres. J. R. Soc. Interface, 2007, 4, 363–371.

50.

Williams

G. J.

Bond

I. P.

Trask

R. S.

Compression after impact assessment of self-healing CFRP. Composites Part A, 2009, 40, 1399–1406.

51.

Mostovoy

Crosiey

P. B.

Ripiing

E. J.

Use of crack-line loaded specimens for measuring plane-strain fracture toughness. J. Mater., 1967, 2, 661–681.

52.

Giedhiii

R. A.

Kinioch

A. J.

Shaw

S. J.

Self-toughening mechanism in epoxide-resins. J. Mater. Sci., 1979, 14, 1769–1772.

53.

Beres

Koui

A. K.

Thambraj

A tapered double-cantilever-beam specimen designed for constant-Ktesting at elevated temperatures. J. Test. Evaluation, 1997, 25, 536–542.

54.

Jung

Hegeman

Sottos

N. R.

Geubeiie

P. H.

Whites

S. R.

Self-healing composites using embedded microspheres. Am. Soc. Mech. Engrs, Mater. Div., MD, 1997, 80, 265–275.

55.

Meiiier

Roche

A. A.

Sautereau

Tapered double-cantilever-beam test used as a practical adhesion test for metal/adhesive/metal systems. J. Adhesion Sci., 1999, 13, 773–788.

56.

Biackman

B. R. K.

Hadavinia

Kinioch

A. J.

Paraschi

Wiiiiams

J. G.

The calculation of adhesive fracture energies in mode I: revisiting the tapered double cantilever beam (TDCB) test. Engng Fracture Mechanics, 2003, 70, 233–248.

57.

Qiao

P. Z.

Wang

J. L.

Davaios

J. F.

Tapered beam on elastic foundation model for compliance rate change of TDCB specimen. Engng Fracture Mechanics, 2003, 70, 339–353.

58.

Irwin

G. R.

Kies

J. A.

Critical energy rate analysis of fracture strength. Am. Weld. Soc. J., 1954, 33, 193-s–198-s.

59.

Theocaris

P. S.

Hadjijoseph

Transient lateral contraction ratio of polymers in creep and relaxation. Kolloid-Zeitschrift und Zeitschrift fUr Polymere, 1965, 202, 133–193.

60.

Verdu

Tcharkhtchi

Elastic properties of thermosets in glassy state. Die Angewandte Makro-molekulare Chemie, 1996, 240, 31–38.

61.

Timoshenko

S. P.

Theory ofelasticity, 3rd edition, 1970, pp. 41–47 and 355–367 (McGraw-Hill, New York).

62.

Saint-Venant

A. J. C. B.

Memoire sur la flexion des prismes. J. Mathematiques de Liouville, 1856, 2, 89–189.

63.

Saxena

Hudak

S. J.

Review and extension of compliance information for common crack growth specimens. Int. J. Fracture, 1978, 14, 453–467.

64.

Marcus

H. L.

Sih

G. C.

A crackline-loaded edge-crack stress corrosion specimen. Engng Fracture Mechanics, 1971, 3, 453–461.

65.

Gaiiagher

J. P.

Experimentally determined stress intensity factors for several contoured double cantilever beam specimens. Engng Fracture Mechanics, 1971, 3, 27–43.

66.

Jakubowski

Geometry factors in corrosion fatigue crack propagation. Fatigue and Fracture Engng Mater. Structs, 1993, 16, 495–507.

67.

Meiiier

Roche

A. A.

Sautereau

Tapered double-cantilever-beam test used as a practical adhesion test for metal/adhesive/metal systems. J. Adhesion Sci., 1999, 13, 773–788.

68.

Brown

E. N.

Datteibaum

D. M.

The role of crystalline phase on fracture and microstructure evolution of polytetrafluoroethylene (PTFE). Polymer, 2005, 46, 3056–3068.

69.

Brown

E. N.

Rae

P. J.

Orier

E. B.

Gray

G. T.

Datteibaum

D. M.

The effect of crystallinity on the fracture of polytetrafluoroethylene (PTFE). Mater. Sci. Engng C, 2006, 26, 1338–1343.

70.

Brown

E. N.

Rae

P. J.

Orier

E. B.

The influence of temperature and strain rate on the constitutive and damage responses of polychloro-trifluoroethylene (PCTFE, Kel-F 81). Polymer, 2006, 47, 7506–7518.

71.

Rae

P. J.

Brown

E. N.

Orier

E. B.

The mechanical properties of poly(ether-ether-ketone) (PEEK) with emphasis on the large compressive strain response. Polymer, 2007, 48, 598–615.

72.

Freed

C. N.

Kraft

J. M.

Effect of side grooving on measurements of plane-strain fracture toughness. J. Mater., 1966, 1, 770–790.

73.

Srawiey

J. E.

Gross

Stress intensity factors for crackline-loaded edge-crack specimens. Mater. Res. Standards, 1967, 7, 155–162.