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Trapped cracks at indentations

Part II Fracture mechanics model

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Abstract

A fracture-mechanics model for indentation cracking in phase-transforming materials is developed, based on the competing interaction of the tensile residual-mismatch field and the compressive contact-induced transformation field. In addition to the usual subthreshold and well-developed cracking ranges, the model predicts the trapping of cracks at indentations, within the transformation zone. As an example, the model is used to describe the dependence of radial crack length on indentation load in a range of yttria-tetragonal zirconia polycrystals (Y-TZP), explicitly addressing the trapping behaviour observed in Part I. The crucial parameters of the model obtained from the experimental fits, the size of the transformation zone relative to the contact impression,b/a, and the magnitude of the transformation stress relative to the hardness, σT/H, agree with independent measurements. Although applied to phase-transforming materials here, the principles of the model are generally applicable to systems with short-range, compensating stress fields competing with longer-ranged, dominant fields, leading to two discrete crack populations.

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Abbreviations

a:

Contact-impression semi-diagonal

b:

Contact-induced transformation-zone dimension

c:

Total crack length, c=l+s

cn :

Contact impression crack nucleus dimension, cn<s

f:

Stress-intensity factor weighting term, K=(Ha1/2)f

H:

Hardness

Kr :

Residual stress-intensity factor

Kt :

Transformation stress-intensity factor

l:

Radial crack length

P:

Indentation load

s:

Contact-impression tensile-zone dimension

T1 :

Toughness in the transformation zone

T2 :

Toughness outside the transformation zone

α:

Stress coefficient, σ=αH

σr :

Residual-stress-field amplitude

σt :

Transformation-stress-field amplitude

Ψ1 :

Crack-geometry parameter in the transformation zone

Ψ2 :

Crack-geometry parameter outside the transformation zone

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Authors and Affiliations

  1. IBM Research Division, T. J. Watson Research Center, 10598, Yorktown Heights, New York, USA

    R. F. Cook

  2. Ceramics Division, National Institute of Standards and Technology, 20899, Gaithersburg, MD, USA

    L. M. Braun

Authors
  1. R. F. Cook
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  2. L. M. Braun
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Cook, R.F., Braun, L.M. Trapped cracks at indentations. J Mater Sci 29, 2192–2204 (1994). https://doi.org/10.1007/BF01154700

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