Semi-brittle Deformation of Carrara Marble: A Complex Interplay of Strength, Hardening and Deformation Mechanisms
Authors: Rybacki Erik , Niu Lu , Evans Brian 
Published: March 2022

&lt;p&gt;Semi-brittle flow occurs when crystal plasticity and cataclastic mechanisms operate concurrently and may be common in the middle Earth&amp;#8217;s crust. To better constrain the characteristics of semi-brittle deformation, we performed triaxial tests up to 12% strain on dry samples of Carrara marble, spanning a wide range of temperature (&lt;em&gt;T&lt;/em&gt; = 20 - 800&amp;#176;C), confining pressures (&lt;em&gt;P&lt;/em&gt;&lt;sub&gt;C &lt;/sub&gt;= 30 &amp;#8211; 300 MPa), and strain rates (&lt;em&gt;&amp;#949;&lt;/em&gt;'= 10&lt;sup&gt;-3&lt;/sup&gt; - 10&lt;sup&gt;&amp;#173;-6&lt;/sup&gt; s&lt;sup&gt;-1&lt;/sup&gt;). The (differential) stress (&amp;#916;&lt;em&gt;&amp;#963;&lt;/em&gt; = &lt;em&gt;&amp;#963;&lt;/em&gt;&lt;sub&gt;1&lt;/sub&gt; - &lt;em&gt;P&lt;/em&gt;&lt;sub&gt;C&lt;/sub&gt;) and the hardening coefficient (&lt;em&gt;h = &lt;/em&gt;&amp;#8706;&amp;#916;&lt;em&gt;&amp;#963;&lt;/em&gt;/&amp;#8706;&lt;em&gt;&amp;#949;&lt;/em&gt; &lt;em&gt;) &lt;/em&gt;depend on the applied conditions. At most conditions, &amp;#916;&lt;em&gt;&amp;#963;&lt;/em&gt; increases with strain, whereas &lt;em&gt;h &lt;/em&gt;decreases with increasing strain. At 5% strain, stress and the hardening coefficient increase as &lt;em&gt;T&lt;/em&gt; decreases and &lt;em&gt;P&lt;/em&gt;&lt;sub&gt;C&lt;/sub&gt; increases: Remarkably, both are relatively insensitive to temperature and to rate in the range of &amp;#8776; 200 &lt;&lt;em&gt; T&lt;/em&gt; &lt; 400&amp;#176;C. At &lt;em&gt;T&lt;/em&gt; &amp;#8818; 400&amp;#176;C, the mechanical behavior of the marble is very similar to that exhibited by high-strength, high-ductility, hexagonal metals that deform by processes called twinning induced plasticity (TWIP). Qualitative microstructural observations show that twinning, dislocation motion, and inter- and intra-crystalline micro-fractures are abundant in the deformed samples over the entire range of conditions. The interplay of these deformation mechanisms leads to complex relationships of &amp;#916;&lt;em&gt;&amp;#963;&lt;/em&gt; and &lt;em&gt;h&lt;/em&gt; with the applied &lt;em&gt;&amp;#949;'&amp;#160; - T &amp;#8209; P&lt;/em&gt;&lt;sub&gt;C&lt;em&gt; &lt;/em&gt;&lt;/sub&gt;&lt;em&gt;&amp;#8209; &lt;/em&gt;&amp;#160;conditions. Models for TWIP behavior suggest that hardening increases with decreasing twin spacing and increasing dislocation density. The low sensitivity of &amp;#916;&lt;em&gt;&amp;#963;&lt;/em&gt; and &lt;em&gt;h&lt;/em&gt; to &lt;em&gt;T&lt;/em&gt; at 200 to 400&amp;#176;C may be explained by the relatively low temperature sensitivity of the critical resolved shear stress for twinning and dislocation slip in calcite in this range. None of the existing models for the brittle-ductile transition or the brittle-plastic transition are able to fully predict our experimental results, and micro mechanism-based constitutive laws for semi-brittle deformation are missing so far. Nevertheless, our observations suggest that peak strengths for calcite rocks deforming by semi-brittle processes will occur at &lt;em&gt;P&lt;/em&gt;&lt;sub&gt;C&lt;em&gt; &lt;/em&gt;&lt;/sub&gt;&lt;em&gt;&amp;#8209; T&lt;/em&gt; conditions of the middle crust, but that the strengths are probably more strongly influenced by total strain rather than by strain rate.&lt;/p&gt;