The formation of crenulation cleavage j. W. COSGROVE SUMMARY Investigation of a theory of buckling of an mineral fabrics or finely laminated multi- anisotropic material has enabled the micro- layers. Crenulation cleavage planes are gener- folding of mineral fabrics to be more clearly ally formed as a consequence of mineral understood. It is shown that "crenulations" migration which occurs in response to stress (microfolds) are associated with a variety of gradients intimately associated with the devel- buckling instabilities which develop in stressed oping microfolds. 2~LTHOUOH a large variety of cleavages has been described in the literature it is possible to consider just four "end members" of a cleavage tetrahedron (Fig. x) with all other varieties of cleavage as intermediate forms. Each of the four end members, slaty cleavage, fracture cleavage, pressure solution cleavage and crenulation cleavage can be readily recognised in the field. Slaty cleavage is a penetrative cleavage and is the result of the development of a pervasive mineral fabric. Fracture cleavage and pressure solution cleavage are non-pervasive cleavages. In pressure solution cleavage the discrete planes of weakness that constitute the cleavage are the result of localised pressure solution and migration away from thesite of solution of various mineral species, particularly quartz and calcite. Crenulation cleavage is another non-pervasive cleavage which deveIops in finely laminated rocks and mineral fabrics as a result of micro- buckling together with some pressure solution and redistribution of minerals. Gradations between these four basic types of cleavage are commonly found in nature. Often a fracture cleavage is found superposed on a slaty cleavage. A certain type of crenulation cleavage when fully developed becomes almost indistinguishable from a slaty cleavage. Another type of crenulation cleavage found in association with normal kink bands (P1. I f) may become indistinguishable from pressure solution cleavage. The aim of this paper is to investigate the development of the crenulation cleavage "end member"; only a brief discussion of some of the more closely associated intermediate forms of cleavage is given. Crenulation cleavage has been given various names in the literature, e.g. close-joints cleavage (Sorby i857), ausweichungs-Clivage (Hiem x878), strain- slip cleavage (Bonney I886), cataclastic cleavage (Knopf I93t), transposition cleavage (Weiss I949) , slip cleavage, secondary cleavage and false cleavage (Dale x892 , t894, I897, I899)Runzelcfivage (Born I929)Gleitshieferung (Schmidt I932), Umfaltungsclivage (Sander I934) Schubkluftung (Sholtz i93o), zweite Schieferung (Hoeppener i956 ) herringbone cleavage, shear schistosity, shear cleavage (Mead 194o, Wilson 1946), fracture cleavage (Agron 195o), crenulation cleavage (KnUl i96o , Rickard i96i ) and crenulation foliation (Whitten x966 ). This large number of names for crenulation cleavage reflects the wide variety of microstructures encompassed by the term. This paper demonstrates that all varieties of crenulation cleavage are formed by essentially the same process, and Jlgeol. Sot. Lond. vol. x32, I976, pp. t55-t78. I8 Figs, 2 Plates. PHnted in N. Ireland. Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/132/2/155/4892673/gsjgs.132.2.0155.pdf by guest on 25 September 2021 15 6 J. IV. Cosgrove it is unnecessary to postulate several profoundly different mechanisms to account for the many natural types of crenulation cleavage. The formation of crenulation cleavage can for convenience be divided into two stages. The first stage is the development of buckling instabilities in an anisotropic medium which may be either a mineral fabric (P1. z a, f) or a multilayer (P1. x c-d). The second stage is the development of discrete crenulation cleavage planes which are found closely associated with the microbuckles. This generally involves the processes of pressure solution and mineral redistribution. Until recently the buckling behaviour of mineral fabrics was not under- stood. Conventional buckling theories were unsuitable as they considered either single or multilayer models with various competence contrasts between the layer and matrix or between adjacent layers. None of these models approxi- mated well enough to a mineral fabric to allow them to be used to predict the buckling behaviour successfully. However in the last decade a theory of buckling has been developed which considers the buckling behaviour of an anisotropic material, i.e. a material in which the resistance to shear differs from the resis- trance to compression in the same direction. (Biot i964, Cobbold et al. i971 and Cosgrove i972 ) . Many mineral fabrics approximate well to this theoretical anisotropic material and the buckling theory can be successfully used to account for their buckling behaviour. This theory is summarised below, emphasising those aspects that have particular relevance to the understanding of crenulation cleavage. Although the buckling theory of an anisotropic material can be used to explain the initiation of buckling instabilities that occur in many mineral fabrics and multilayers, it cannot account for the formation of the discrete planes of weakness that are often associated with the crenulations and which constitute the actual crenulation cleavage planes. These planes of weakness are generally the result of pressure solution and mineral redistributions. The intimate association of micro- folding and mineral redistribution (metamorphic differentiation) can be explained in terms of mineral migration in response to stress gradients that are established during microfolding. The nature of these stress gradients and the effect of the detailed features of a mineral fabric or multilayer on the final form of the crenu- lation and crenulation cleavage planes, are discussed in the second part of this paper. The buckling behaviour of anisotropic materials Several examples of microstructures which fall under the general heading of crenulation cleavage are shown in P1. xa-f. It is not difficult to see why at least n Cleavage rTessure Solution Cleavage Fio. I. The cleavage tetrahedron. Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/132/2/155/4892673/gsjgs.132.2.0155.pdf by guest on 25 September 2021 Formation of crenulation cleavage x 57 two schools of thought arose on the origin of crenulation cleavage. One con- siders that crenulation cleavage is the result of "microfaulting" (P1. If) and the other that it is the result of "microfolding" (P1. ta). In addition to these two types another type has been frequently described: crenulation cleavage occurring in conjugate sets. The first account of conjugate crenulation cleavage was given by Muff (in Peach et al t 9o9). Muff's original diagram and a slight modification of this by Wilson (I96I) are shown in Fig. 2. It can be seen that both writers con- sidered the cleavage to be a consequence of microfaulting. It will now be dem- onstrated that these three varieties of crenulation cleavage are simply different expressions of buckling instabilities developed in anisotropic materials. For the convenience of the following analysis the coordinate directions x and y are chosen to coincide with the symmetry axes of the material. It is assumed that (a) the material is linearly elastic or Newtonian viscous, (b) the material is anisotropic and homogeneous, (c) the material deforms by plane swain, (d) there is no volume change during the deformation and (e) that the maximum principal compressive stress is applied parallel to the coordinate directions (i.e. mineral fabric). From the assumption (e) one may infer that the combined symmetry of the material properties and the stress field is orthotropic, i.e. that the principal stress axes coincide with or are symmetrically oriented with respect to the symmetry axes of the material properties. It is also assumed that the material is in a state of initial stress and that this initial stress gives rise to an initial uniform state of homogeneous flattening within the material. The aim of the analysis is to in- vestigate the types of instability which disrupt this initial uniform state. These instabilities result in ordered, non-uniform displacement patterns which are described by displacement vectors U and V in the x and y directions respectively. By stating the conditions (a) to (e) mathematically and by combining the resulting equations, it is possible to develop a single equation, solutions to which automatically satisfy these five conditions. The buckling equation that results from the analysis is ( Q- ( Q+ (I) \ b :.. Fxo. 2. (a) Formation of conjugate crenulation cleavage (after Muff in Peach et al. t9o9) (b) A modification of Fig. 2a by Wilson (t96x). Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/132/2/155/4892673/gsjgs.132.2.0155.pdf by guest on 25 September 2021 I58 J. W. Cosgrove where 4 is a displacement function related to the displacements U and V u = & (2) V - ~4~ (3) P is the differential stress (al -- a3) Q is a measure of resistance to shear and N is a measure of the resistance to com- pression in the direction of the maximum principal compressive stress al. The resistance to shear and compression are stress dependent and it is convenient to express the shear and compressive moduli M and L for any stress condition in terms of Q and N and the stress value. These moduli can be written P M : N +- (4) 4 P r~ = Q +- (5) 2 The ratio M]L is a measure of the anisotropy of a material. Materials