Ideal strength and ductility in metals from second- and third-order elastic constants

$I\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0.333em}{0ex}}s\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}h$ is a fundamental property describing the upper bound on a material's strength in the absence of crystal defects. Similarly, the nature of the failure at the ideal strength can be related to the $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0.333em}{0ex}}d\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}y$ of metals and alloys. In this work, analytical expressions are derived for the ideal strength and intrinsic ductility with knowledge of only the second-order and third-order elastic constants. This analytical approach greatly improves the fundamental understanding of mechanical behavior in advanced materials.