Challenges in Understanding the Dynamic Behavior of Heterogeneous Materials
377
Lastly, the authors would be remiss if crystal plasticity and viscoplastic selfconsistent (VPSC) methods were omitted from this brief listing of ICMSE techniques to probe meso-scale heterogeneity. Specifically, Lebensohn and Tomé
developed the VPSC method [46] as an extension of the Eshelby formulation for
inclusions and inhomogeneities in a self-consistent continuum field. These codes
have been successful at modeling texture evolution under rolling conditions [47].
However, these techniques are currently limited to quasi-static boundary conditions,
although strides are being made to extend these techniques to model dynamic
behavior. The many works by Lebensohn should be referenced for further discussion
on these methods.
1.3 Outline of Chapter
The remainder of this chapter is devoted to outlining the challenges involved in the
investigation of dynamic behavior of heterogeneous materials, namely, understanding the shock compression response of these materials and the inherent difficulties in
experimentally assessing the equation of state of the aggregate material and defining
the local and global properties. A case study will be provided from the author’s
work investigating the intermetallic-forming Ti+B reactive powder mixture under
shock compression and high strain rate loading conditions. The importance of using
ICMSE methodologies to understand bulk dynamic behavior of reactive powder
mixtures will be presented. These methodologies provide insight into the physical
phenomena that can only be indirectly inferred from experimental measurements.
This chapter is divided into three subsequent sections. Section 2 provides a
brief background of shock compression science, focusing on the dynamic behavior
of powder mixtures, granular media, and energetic/reactive materials. Section 3
provides an introduction to reactive materials, which take the form of heterogeneous
powder mixtures. The case study on Ti+B reactive mixtures is presented and
demonstrates how ICMSE has been employed to investigate the shock compression
and dynamic behavior of this system. Section 4 provides a summary and concluding
remarks on how the ICMSE framework can provide useful information on the
response of heterogeneous materials to dynamic loading.
2 Background on Shock Compression Science
Dynamic behavior in heterogeneous materials has been studied in earnest since
the founding of shock compression as a science at the end of World War II.
Materials of interest included precipitation-hardened alloys, particulate mixtures,
plastic-bonded explosives (PBX), geological materials such as rock, and sand.
Powder and particulate mixtures in particular are of interest due to the spatial
arrangements of the microconstituents and the behavior this imparts. Reactive and
377
Lastly, the authors would be remiss if crystal plasticity and viscoplastic selfconsistent (VPSC) methods were omitted from this brief listing of ICMSE techniques to probe meso-scale heterogeneity. Specifically, Lebensohn and Tomé
developed the VPSC method [46] as an extension of the Eshelby formulation for
inclusions and inhomogeneities in a self-consistent continuum field. These codes
have been successful at modeling texture evolution under rolling conditions [47].
However, these techniques are currently limited to quasi-static boundary conditions,
although strides are being made to extend these techniques to model dynamic
behavior. The many works by Lebensohn should be referenced for further discussion
on these methods.
1.3 Outline of Chapter
The remainder of this chapter is devoted to outlining the challenges involved in the
investigation of dynamic behavior of heterogeneous materials, namely, understanding the shock compression response of these materials and the inherent difficulties in
experimentally assessing the equation of state of the aggregate material and defining
the local and global properties. A case study will be provided from the author’s
work investigating the intermetallic-forming Ti+B reactive powder mixture under
shock compression and high strain rate loading conditions. The importance of using
ICMSE methodologies to understand bulk dynamic behavior of reactive powder
mixtures will be presented. These methodologies provide insight into the physical
phenomena that can only be indirectly inferred from experimental measurements.
This chapter is divided into three subsequent sections. Section 2 provides a
brief background of shock compression science, focusing on the dynamic behavior
of powder mixtures, granular media, and energetic/reactive materials. Section 3
provides an introduction to reactive materials, which take the form of heterogeneous
powder mixtures. The case study on Ti+B reactive mixtures is presented and
demonstrates how ICMSE has been employed to investigate the shock compression
and dynamic behavior of this system. Section 4 provides a summary and concluding
remarks on how the ICMSE framework can provide useful information on the
response of heterogeneous materials to dynamic loading.
2 Background on Shock Compression Science
Dynamic behavior in heterogeneous materials has been studied in earnest since
the founding of shock compression as a science at the end of World War II.
Materials of interest included precipitation-hardened alloys, particulate mixtures,
plastic-bonded explosives (PBX), geological materials such as rock, and sand.
Powder and particulate mixtures in particular are of interest due to the spatial
arrangements of the microconstituents and the behavior this imparts. Reactive and