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D. A. Hills et aliii, Frattura ed Integrità Strutturale, 25 (2013) 27-35; DOI: 10.3221/IGF-ESIS.25.05 29 strengths of the two competing terms vary with radial distance from the notch tip, which creates an intrinsic length scale in the solution; the mode I term is more strongly singular and dictates contact edge behaviour, whilst the mode II term less strongly singular (or for punch angles less than 77.4  the mode II term is bounded) and controls the stress field slightly further from the sharp corner. This length scale can be emphasised by replacing the two parameters I K and II K in Williams' solution with two new composite parameters 0 d and 0 G . The definition of these quantities involves raising the generalised stress intensity factors I K and II K , to fractional powers, and for this reason, we modify the definition depending on whether the remote loads excite positive or negative values of I K and , II K in order to avoid imaginary solutions. For simplicity, let us first consider the case when the remote loads excite positive values of the generalised stress intensity factors I K and II K . In this case, 0 d and 0 G are defined as 1 0 I II II I K d K           , 1 1 0 II I II I I II I II G K K            (11) where it is now clear that 0 d has the physical significance of representing the boundary, in some way, between mode I domination and mode II domination of the stress field, whilst 0 G represents the magnitude of loading. Eq. (1) can now be re-written as       1  1  0 0 0 , I II ij I II ij ij r r r f f G d d                       . (12) We now, as in Eq. (7) and (8), write out the direct   p x , and shearing   q x , tractions, but this time with the alternative formulation of the stress field, and we also, for compactness, use the shorthand   n n ij ij int f f   , as     1  1  0 0 0 0 , I II int I II r p x x x f f G G d d                          (13)     1  1  0 0 0 0 , I II r int I II r r r q x x x f f G G d d                         . (14) When the remote loads are such that the generalised stress intensity factors I K and II K , are of the same sign (either both positive or both negative), Williams' solution implies that the direct traction   p x , is of a different sign in the mode I and mode II dominated regions of the stress field. When I K and II K are both positive , there is implied separation at the edge of contact, but closure is implied further away from the contact edge. Conversely, when I K and II K are both negative , closure is implied at the edge of contact, but separation is implied to extend from the interior. It is particularly important in the latter case, to appreciate that a state of separation may not actually arise because, by the time the mode II solution dominates the mode I solution, the next term in the series, which has not been found, may be important . In any case, when the generalised stress intensity factors take on similar signs, the length along the interface at which Williams' solution implies that the boundary between separation and closure lies, based on violations of the condition   0 p x  , is denoted 0 x , and is given simply by setting   0 p x  , and solving for the value of 0 / x d at which this condition is met, which gives 1 0 0 I II II I x f d f             (15) Note that, perhaps surprisingly, when represented in this way, the strength of the remote loading 0 G , does not influence the position of the boundary between separation and closure 0 x , if normalised by 0 d . Also, note that, for remote loading that results in I K and II K taking on opposing signs, Williams' solution implies no change in sign of the direct traction