200
C. A. Bronkhorst et al.
impact, explosively loaded material, and an expanding ring. Much later, this model
was also applied to the study of loading pulse duration in copper [33]. Addessio
and Johnson [1] adapted the work of Johnson [31, 32] by proposing a modified
Gurson [26]-type model, which also employed an overstress equation for the plastic
flow rule of the material. This equation introduces a length scale into the series of
equations and assists in regularizing the problem. This helps to alleviate issues of
numerical stability and severe mesh sensitivity. The authors also clearly recognized
the possibility that relying upon deformation rate sensitivity within the model would
not always solve the regularization issue, but that additional length scales (e.g.,
spatial gradients in physically based internal state variables) may be required in
general. A void nucleation model was not proposed, and the model was tested
against copper plate impact experiments. It was demonstrated that for the problems
examined, the use of the overstress model reduced the mesh sensitivity of the
simulated results. The model of Addessio and Johnson [1] was expanded upon
by Maudlin et al. [40] to include the effect of nonisotropic plastic flow. They
also included the ability to account for the anisotropic nature of the void as it
grows, but this capability is not exercised in the work presented here. Significant
advancements were made to the solution algorithm to improve the numerical
efficiency. This model was used on several dynamic loading boundary value
problems with success. The numerical algorithm initially developed in this work
was later published by Zuo and Rice [48]. Bronkhorst et al. [10] demonstrated the
limitations of such a model and general computational limitations for ductile damage against differing shock loading conditions. Recently, Versino and Bronkhorst
[46] proposed a computational framework to facilitate material variability for representation of porosity nucleation more accurately within a macroscale continuum
setting.
Material microstructure has long been known to play a key role in the process of
ductile damage where porosity is the dominant damage mechanism (e.g. [43, 47]).
Polycrystalline metallic materials at a local scale produce highly inhomogeneous
deformation fields upon mechanical loading (e.g. [8, 12]) and provide the conditions
for establishing a pore field. There remains tremendous potential to bring to bear
computational crystal plasticity tools to explore the physics of porosity-based
ductile damage in ways which are not approachable through experimental means
alone. This chapter has a focus on the ductile damage response of tantalum for
lightly loaded shock conditions. Tantalum is a body-centered cubic material whose
plastic deformation is dominated by the motion of screw dislocations. The natural
state of the screw dislocation within tantalum is not planar as in other cubic materials
but rather the core is split along additional planes [2, 3]. Recently a model for
representation of the deformation behavior of tantalum single crystals was proposed
[16] and will be employed to explore here the micromechanics of deformation
leading to the onset of porosity initiation in tantalum polycrystals.
The purpose of this chapter is to present the above discussion in the context of a
theoretical framework for models of porosity-based damage and failure. Numerical
results are presented in the context of experimental results presented by Gray et al.
[24]. This chapter begins by first presenting a simple macroscale ductile damage
C. A. Bronkhorst et al.
impact, explosively loaded material, and an expanding ring. Much later, this model
was also applied to the study of loading pulse duration in copper [33]. Addessio
and Johnson [1] adapted the work of Johnson [31, 32] by proposing a modified
Gurson [26]-type model, which also employed an overstress equation for the plastic
flow rule of the material. This equation introduces a length scale into the series of
equations and assists in regularizing the problem. This helps to alleviate issues of
numerical stability and severe mesh sensitivity. The authors also clearly recognized
the possibility that relying upon deformation rate sensitivity within the model would
not always solve the regularization issue, but that additional length scales (e.g.,
spatial gradients in physically based internal state variables) may be required in
general. A void nucleation model was not proposed, and the model was tested
against copper plate impact experiments. It was demonstrated that for the problems
examined, the use of the overstress model reduced the mesh sensitivity of the
simulated results. The model of Addessio and Johnson [1] was expanded upon
by Maudlin et al. [40] to include the effect of nonisotropic plastic flow. They
also included the ability to account for the anisotropic nature of the void as it
grows, but this capability is not exercised in the work presented here. Significant
advancements were made to the solution algorithm to improve the numerical
efficiency. This model was used on several dynamic loading boundary value
problems with success. The numerical algorithm initially developed in this work
was later published by Zuo and Rice [48]. Bronkhorst et al. [10] demonstrated the
limitations of such a model and general computational limitations for ductile damage against differing shock loading conditions. Recently, Versino and Bronkhorst
[46] proposed a computational framework to facilitate material variability for representation of porosity nucleation more accurately within a macroscale continuum
setting.
Material microstructure has long been known to play a key role in the process of
ductile damage where porosity is the dominant damage mechanism (e.g. [43, 47]).
Polycrystalline metallic materials at a local scale produce highly inhomogeneous
deformation fields upon mechanical loading (e.g. [8, 12]) and provide the conditions
for establishing a pore field. There remains tremendous potential to bring to bear
computational crystal plasticity tools to explore the physics of porosity-based
ductile damage in ways which are not approachable through experimental means
alone. This chapter has a focus on the ductile damage response of tantalum for
lightly loaded shock conditions. Tantalum is a body-centered cubic material whose
plastic deformation is dominated by the motion of screw dislocations. The natural
state of the screw dislocation within tantalum is not planar as in other cubic materials
but rather the core is split along additional planes [2, 3]. Recently a model for
representation of the deformation behavior of tantalum single crystals was proposed
[16] and will be employed to explore here the micromechanics of deformation
leading to the onset of porosity initiation in tantalum polycrystals.
The purpose of this chapter is to present the above discussion in the context of a
theoretical framework for models of porosity-based damage and failure. Numerical
results are presented in the context of experimental results presented by Gray et al.
[24]. This chapter begins by first presenting a simple macroscale ductile damage