Local Stress and Damage Response of Polycrystal Materials to Light Shock. . .
201
model for metallic materials and the representation of the abovementioned tantalum
on tantalum plate impact experiment. A single crystal model is then discussed for
representation of tantalum with non-Schmid effects. Numerical models of tantalum
are then presented, and load coupling with the macroscale model is described.
Numerical results of polycrystal calculations are then presented with an analysis
of the results in the context of relationship with shock loading conditions. Finally,
the results are discussed and concluding statements are offered.
2 Nomenclature
Standard direct notation is used throughout this paper. Second rank tensors are
denoted by boldface uppercase letters. Fourth rank tensors are denoted by underscored boldface uppercase letters. The following variables are used: I identity, F
deformation gradient, D stretch, T Cauchy stress, ρ density, and θ temperature. The
prime symbol A
indicates a deviatoric quantity. The inner product of two second
rank tensors A and B is defined by A·B = trace(A T B). The over-tilde ˜
A represents
the quantity A in the undamaged material.
3 Experimental Overview
The dynamic behavior of materials under shock loading conditions is commonly
studied with plate impact experiments. These are conceptually simple in that a
stationary circular disk (the target sample) is impacted by another circular disk
(the flyer) moving at high velocity. The flyer is accelerated through a gun barrel
by either compressed gas or in some cases gunpowder. The flyer is soft-mounted
on a sabot, which travels through the barrel. The primary diagnostic used in plate
impact experiments is the measurement of the velocity of the back of the target
sample subsequent to the impact of the two plates – free-surface velocity. Under
certain conditions, it is possible to recover the deformed sample for subsequent
metallographic analysis. Both of these sources of information are used in the present
work. Details of the plate impact experiment technique and focus on tantalum can
be found in Gray [19, 20], Gray and Vecchio [21], and Gray et al. [22, 23].
Here we focus on a single experiment where both the flyer plate material and
the sample plate material were fabricated from the same high-purity tantalum. The
details of the experiments and the conditions under which they were conducted can
be found in Gray et al. [24] and Bronkhorst et al. [10]. The flyer plate velocity was
249 m/s. The free-surface velocity trace for this experiment is given in Fig. 1. The
cross-sectional image of the recovered sample showing the porosity field is given in
Fig. 2. A higher magnification view of a region of the cross-sectioned sample which
displays early-stage coalescence behavior within the incipient spalled region of the
sample is given in Fig. 3. Although discussion of these details is outside the scope
201
model for metallic materials and the representation of the abovementioned tantalum
on tantalum plate impact experiment. A single crystal model is then discussed for
representation of tantalum with non-Schmid effects. Numerical models of tantalum
are then presented, and load coupling with the macroscale model is described.
Numerical results of polycrystal calculations are then presented with an analysis
of the results in the context of relationship with shock loading conditions. Finally,
the results are discussed and concluding statements are offered.
2 Nomenclature
Standard direct notation is used throughout this paper. Second rank tensors are
denoted by boldface uppercase letters. Fourth rank tensors are denoted by underscored boldface uppercase letters. The following variables are used: I identity, F
deformation gradient, D stretch, T Cauchy stress, ρ density, and θ temperature. The
prime symbol A
indicates a deviatoric quantity. The inner product of two second
rank tensors A and B is defined by A·B = trace(A T B). The over-tilde ˜
A represents
the quantity A in the undamaged material.
3 Experimental Overview
The dynamic behavior of materials under shock loading conditions is commonly
studied with plate impact experiments. These are conceptually simple in that a
stationary circular disk (the target sample) is impacted by another circular disk
(the flyer) moving at high velocity. The flyer is accelerated through a gun barrel
by either compressed gas or in some cases gunpowder. The flyer is soft-mounted
on a sabot, which travels through the barrel. The primary diagnostic used in plate
impact experiments is the measurement of the velocity of the back of the target
sample subsequent to the impact of the two plates – free-surface velocity. Under
certain conditions, it is possible to recover the deformed sample for subsequent
metallographic analysis. Both of these sources of information are used in the present
work. Details of the plate impact experiment technique and focus on tantalum can
be found in Gray [19, 20], Gray and Vecchio [21], and Gray et al. [22, 23].
Here we focus on a single experiment where both the flyer plate material and
the sample plate material were fabricated from the same high-purity tantalum. The
details of the experiments and the conditions under which they were conducted can
be found in Gray et al. [24] and Bronkhorst et al. [10]. The flyer plate velocity was
249 m/s. The free-surface velocity trace for this experiment is given in Fig. 1. The
cross-sectional image of the recovered sample showing the porosity field is given in
Fig. 2. A higher magnification view of a region of the cross-sectioned sample which
displays early-stage coalescence behavior within the incipient spalled region of the
sample is given in Fig. 3. Although discussion of these details is outside the scope