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A quantitative study of deformation mechanisms and finite strain in quartzites

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Abstract

The Weverton quartzites in the Maryland Blue Ridge are deformed by one major period of greenschist-grade deformation. The components of finite strain due to different independent mechanisms have been measured for these rocks. The total strain is split up into two major components:

$$\varepsilon ^t = \varepsilon ^p + \varepsilon ^d .$$

The finite natural strain caused by dislocation creep (ɛd) is measured by a new technique using folded and stretched rutile needles which are good strain markers within the quartz crystals. Pressure solution strain (ɛp) is measured from the ratio of the area of new crystals and fibers to the whole rock area in principal sections. Grain boundary sliding is a dependent process which accompanies both mechanisms. Pressure solution obeys a linear Newtonian flow law, \(\left| {\dot \gamma _0^p } \right| = A_p \left| {\tau _0 } \right|\), while dislocation creep obeys a power law of the form \(\left| {\dot \gamma _0^d } \right| = A_d \left| {\tau _0 } \right|^n \) where \(\dot \gamma _0^p ,\dot \gamma _0^d \) are octahedral shear strain rates, τ0 is the octahedral shear stress and A p , A p and n are constants. A direct correlation between finite strain measurements and the operating flow laws can be made. Application of these methods and principles to a few field examples indicates that the rocks obey a flow law partly governed by each mechanism. Any set of physical conditions defines a unique flow law and there is a transition in creep behavior from dominantly Newtonian to a power law with increasing strain rate.

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Abbreviations

T :

Stretch (= l′/l 0)

ɛt :

Total natural strain (= In T)

ɛp, ɛd :

Natural strain due to pressure solution and dislocation creep

\(\dot \varepsilon ,\overline {\dot \varepsilon } \) :

Natural strain rate and average strain rate

T:

Axial ratio of strain ellipsoid

a > b >c:

Principal semi-axes of strain ellipsoid

γ0, \(\dot \gamma _0 \) :

Natural octahedral shear strain and strain rate

ν:

Lode's number

θ:

Angle between principal axes of p.s. and d.c. strain ellipsoids

\(\hat \gamma _0 \) :

Octahedral strain activity

σ d :

Deviatoric stress.

τ0 :

Octahedral shear component of deviatoric stress

Γp, Γd :

Fractions of total strain contributed by pressure solution and dislocation creep

Ac/At, Bc/Bt:

Area ratios of fibers to whole rock for a — c and b — c principal sections

D gb , D l :

Grain boundary and lattice diffusion coefficients

X :

Grain size

r :

Axial ratio of grain

Ω:

Atomic volume of diffusing species

h :

Width of grain boundary

k :

Boltzman's constant

T c :

Critical temperature for hydrolytic weakening

T m :

Temperature of melting

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This research was supported by NSF Grant. No. DES 74-17467 of the Earth Sciences section to D. Elliott.

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Mitra, S. A quantitative study of deformation mechanisms and finite strain in quartzites. Contr. Mineral. and Petrol. 59, 203–226 (1976). https://doi.org/10.1007/BF00371309

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