Fracture of Grooved Kinetic Energy Rods Subject to 

Oblique Impact 

by Robert L. Anderson 

ARL-TR-3923 September 2006 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-3923 September 2006 

Fracture of Grooved Kinetic Energy Rods Subject to 

Oblique Impact 

Robert L. Anderson 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
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4. TITLE AND SUBTITLE 

Fracture of Grooved Kinetic Energy Rods Subject to Oblique Impact 

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Robert L. Anderson 

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14. ABSTRACT 

Kinetic energy penetrators often possess buttress grooves that are used to aid in the launching process. The shock physics code 

CTH has been used to analyze the effect that these grooves have on tungsten heavy alloy rods during oblique impacts that create

asymmetric loading conditions. To examine this behavior, simulations were run in which grooved rods underwent 60° oblique 

impacts with finite thickness rolled homogeneous armor steel plates at 1300 m/s. Previous experimental work done by 

Raftenberg and Bjerke has shown that buttress grooves make the rods more susceptible to fracture, and it has been shown that 

CTH can predict the occurrence of fracture due to stress concentrations in bending loading when the simulation is run using 

reverse ballistics. The use of reverse ballistics has been shown to decrease the loss of groove definition. 

15. SUBJECT TERMS

oblique impact, kinetic energy rod, bending, fracture, buttress groove 

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Robert L. Anderson 

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iii

Contents 

List of Figures iv

Acknowledgments v

1. Introduction 1

2. Computational Method 2

3. Effects of Forward Ballistics vs. Reverse Ballistics 4

4. Effect of Grooves — Smooth Rod Shot 8

5. Plate Thickness Effects 9

6. Material Advection Sensitivity Study 12

7. Summary 13

8. References 14

Distribution List 15 
iv

List of Figures 

Figure 1. ARL6A-T penetrator geometry (1). ................................................................................2 

Figure 2. Sketch of impact conditions. ...........................................................................................3 

Figure 3. Forward ballistics simulation of ARL6A-T vs. 9.5-mm RHA plate (t = 220 μs): 

(a) post-impact rod geometry and (b) scalar damage contours..................................................4 

Figure 4. Reverse ballistics simulation of ARL6A-T vs. 9.5-mm RHA plate (t = 220 μs): 

(a) post-impact rod geometry and (b) scalar damage contours..................................................5 

Figure 5. Post-perforation radiograph of ARL6A-T (1). ................................................................6 

Figure 6. Rod minimum principle stress extrema (t = 145 μs).......................................................6 

Figure 7. Close-up image of minimum principle stress (t = 95 μs)................................................7 

Figure 8. Rod interaction with 16.1-mm RHA plate. .....................................................................7 

Figure 9. Reverse ballistics simulation of smooth rod vs. 9.5-mm RHA plate (t = 220 μs): 

(a) post-impact rod geometry and (b) scalar damage contours..................................................8 

Figure 10. Computational results of critical t/d ratio study: (a) t/d~0.4, (b) t/d~0.9, and 

(c) t/d~1.8.................................................................................................................................10 

Figure 11. Scalar damage contours for critical t/d ratio study: (a) t/d~0.4, (b) t/d~0.9, and 

(c) t/d~1.8.................................................................................................................................11 

Figure 12. Comparison of buttress groove resolution for (a) finite-element model, (b) CTH 

representation at t = 0, and (c) CTH representation after 43 cm of advection.........................12 
v

Acknowledgments 

The author would like to thank Todd Bjerke for his continued correspondence with regards to his 

experimental work. Thank you to Kent Kimsey for his technical review. Also, thank you to 

Steve Schraml and Kent Kimsey for their helpful suggestions with regards to the simulations. 

The simulations contained within this report were run using a U.S. Army Research Laboratory 

(ARL) Major Shared Research Center Linux cluster. Visualization of the scientific data was 

made possible through the use of tools developed by the ARL Scientific Visualization team.
vi

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

Kinetic-energy (KE) penetrators are often used in military anti-armor applications. These 

penetrators can have a tendency to fracture during oblique penetration, thereby reducing the 

rod’s ability to penetrate subsequent regions of the target. Under this premise, the military is 

interested in developing fracture resistant penetrator designs to better resist failure due to the 

lateral loading applied by oblique impact. 

In order to aid in the launching procedure, KE penetrators often have a series of buttress grooves 

covering some portion of the rod length. While exploring possibilities for fracture resistant 

penetrator design, a combined experimental and computational investigation by Raftenberg and 

Bjerke (1) focused on the effect that the buttress grooves have on rod breakup. The experiments 

involved firing ARL6A-T and ARL7-T rods composed of 93.1W-4.7Ni-2.2Co tungsten heavy 

alloy (WHA) at nominally 1300 m/s. The targets used were 9.5-mm rolled homogeneous armor 

(RHA) plates at 60° obliquity. Under these shot conditions, it was observed that rod breakup 

tended to occur. Also, a third set of firings involved ARL7-NT rods that contained no buttress 

grooves and were launched by means of a pusher plate method. The ARL7-NT rod experiments 

yielded varied results, leading to the conclusion that the grooves make the rods more susceptible 

to fracture. 

Observations from a similar study (2) showed that rod fracture tended not to occur for shots 

against relatively thinner targets. Experimentally, it was determined using the ARL7-T rod that 

the critical threshold for which fracture would occur is 

1 t

d

≅ . (1) 

In equation 1, t is the plate thickness, and d is the critical rod diameter. The critical rod diameter 

is defined as the minimum rod diameter at the groove root. 

The scope of this report is to examine the capability of CTH, an Eulerian shock physics code, to 

predict rod breakup under simulated experimental conditions. Computational studies were 

performed using the ARL6A-T rod and an ungrooved version analogous to the ARL7-NT rod to 

examine the code’s ability to predict fracture and to verify and characterize the fracture 

mechanisms that have been seen experimentally. Simulations were run using forward ballistics 

(rod in motion) and reverse ballistics (target in motion) simulations. The reverse ballistics 

simulations yield better results. Also, a computational study was done to examine the plate 

thickness effects of equation 1 using the ARL6A-T rod.
2

2. Computational Method 

Using a commercially available solid modeling software package, a model of the ARL6A-T rod 

was created from the drawing shown in figure 1. Target plates of various thicknesses were also 

modeled at their proper obliquity of 60°. The solid model of the projectile and target were then 

sectioned along a symmetry plane containing the rod axis and plate normal vector to reduce the 

computational cost of the three-dimensional (3-D) simulation. The next step involved using the 

Cubit finite-element meshing code to mesh the target and rod volumes with a hexahedron 

scheme (3). Once in this format, CTH possesses a material insertion capability that allows the 

hexahedral elements to be read directly into a 3-D Eulerian mesh as cell volume fractions. This 

method was used to create target and rod geometries that were as close as possible to the 

geometries that were tested experimentally. The impact velocity for all simulations was 1300 m/s. 

A detailed sketch of the initial impact conditions can be seen in figure 2. 

Figure 1. ARL6A-T penetrator geometry (1). 
3

Figure 2. Sketch of impact conditions. 

CTH is an Eulerian finite volume shock physics code that provides numerical solutions at finite 

intervals, or time steps, by using a two-part process involving a Lagrangian step followed by a 

re-map step. During the Lagrangian step, explicit finite volume equations are solved. For the 

second-order-accurate re-map step, an operator splitting technique is used to reduce multidimensional equations to sets of one-dimensional equations. CTH effectively handles problems 

involving explosive detonation, shock wave propagation, and elastic-plastic material behavior at 

high rates of deformation with multiple materials present (4). The simulations in this study were 

run using CTH version 7.0. 

The 3-D rectangular Eulerian mesh employed cubic computational cells in the region containing 

the rod and centered along its trajectory path (x-axis) with a uniform cell size of 0.025 cm per 

side. This size was selected to try to maintain maximum fidelity of the buttress groove geometry 

during material advection. The mesh was then coarsened in the directions normal to the shot line 

(y- and z-directions) with an expansion ratio of 5%. A reflecting boundary condition was 

prescribed to the mesh at the symmetry plane. 

The rod and target plate were both modeled using the Mie-Gruneisen analytical equation of state 

(EOS). The EOS properties used for the rod were CTH library values for tungsten, except that 

the density was set to 17.65 g/cm3

. The target plate properties were the standard library values 

for iron. The rod and target were both modeled using Johnson-Cook constitutive strength and 

Johnson-Cook cumulative damage models for their respective materials. The rod was modeled 

using standard CTH library values for tungsten, and the plates were modeled using standard 

2IN_RHA values with aj0 parameter scaling consistent with Meyer and Kleponis (5). The 

Johnson-Cook damage model specifies that for any material with a scalar damage value of unity, 

failure will occur. 
4

The CTH threshold fracture model was also used for the rod and target. The stress keyword was 

used to indicate that fracture should occur for any material in a cell with a minimum principal 

stress that is less than the dynamic tensile strength (convention exists that tensile strength values 

are negative) for that material. When the minimum principal stress exceeds the specified tensile 

strength for a material, void will be inserted in that cell to prevent stress states from reaching 

tensile values less than the dynamic tensile strength, thereby creating a fracture surface (6). 

Dynamic tensile strengths were set at –6.89E9 dynes/cm2

 and –2.5E10 dynes/cm2 for the 

tungsten rod and RHA target, respectively. 

3. Effects of Forward Ballistics vs. Reverse Ballistics 

The first simulation that was performed was a forward ballistics simulation of the ARL6A-T rod 

vs. 9.5-mm RHA plate, in which the target was initially stationary and the rod was in motion. 

Experimentally, it was found that the rod would fracture for these impact conditions, and in five 

out of five similar tests, a large nose fragment would separate from the larger portion of the rod 

(1). 

The simulation results for these conditions can be seen in figure 3a. The rod does not fracture, 

but a large zone of damage can be seen in figure 3b, which is a close-up view of the nose region. 

 (a) (b)

Damage Zone 

Figure 3. Forward ballistics simulation of ARL6A-T vs. 9.5-mm RHA plate (t = 220 μs): (a) post-impact rod 

geometry and (b) scalar damage contours. 
5

While the rod does not fracture, the fact that a localized damage zone appears is of interest. This 

indicates that the rod undergoes higher levels of stress in this zone. Using the results from the 

forward ballistics simulation, it was hypothesized that if the simulation were run with reverse 

ballistics (i.e., the rod being stationary and the plate in motion) that this would minimize material 

advection errors at the buttress grooves and capture stress concentrations in the groove roots. 

After running the simulation in reverse ballistics, it was observed that the rod could, in fact, be 

shown to fracture computationally. Figure 4a shows the result of the reverse ballistics 

simulation. Figure 4b is the reverse-ballistics analog of figure 3b, and it can be seen that along 

the fracture surface, the scalar damage magnitude is very close to zero, indicating that the rod 

does not fail by means of the Johnson-Cook damage model. 

 (a) (b) 

Damage Zone 

Figure 4. Reverse ballistics simulation of ARL6A-T vs. 9.5-mm RHA plate (t = 220 μs): (a) post-impact rod 

geometry and (b) scalar damage contours. 

The images in figure 5 show an experimental radiograph that corresponds to impact conditions 

that are consistent with the simulation. It can be seen through direct comparison of figures 4 and 

5 that the results are qualitatively consistent from the simulation to the experiment. 

As previously stated, the Johnson-Cook cumulative damage model is not the source of the 

material fracture. The only other failure model that was incorporated was the minimum principal 

stress criterion used in the CTH threshold fracture model. The plots in figures 6 and 7 represent 

the extreme minimum principal stress encountered by each cell up to the point in time at which 

the image was created. The reader should be aware that the stress values shown in figures 6 and 

7 do not necessarily correspond to the stress state at a given instant in time. Because the plot 

represents the extreme value of stress seen by a cell over an entire elapsed time interval, the 

stress values in the plot will remain constant even after stresses have relaxed back to zero. 

Figure 6 shows how the CTH shock physics code captures stress concentrations emanating from 

the groove roots.
6

Figure 5. Post-perforation radiograph of ARL6A-T (1). 

Figure 6. Rod minimum principle stress extrema (t = 145 μs). 

In figure 7, the initiation of the crack can be seen, and it is obvious from the stress values 

indicated that the fracture surface was spawned as a result of void insertion due to material 

failure as defined by the principle stress-based threshold fracture model.
7

Figure 7. Close-up image of minimum principle stress (t = 95 μs). 

One item of interest is the point in time that the lateral loading is applied that causes the fracture 

to occur. Figure 8 shows that as the rod exits the plate for the 16.1-mm plate, it reaches a state 

where the rod erosion rate slows and the rod begins to pass through the exit crater. 

Figure 8. Rod interaction with 16.1-mm RHA plate. 
8

The rounded shape of the exit crater applies a normal force with components that are both 

upward and rearward. This creates asymmetric loading on the nose. This loading provides the 

bending force required to break off the tip of the rod near the beginning of the grooved region. 

Raftenberg and Bjerke (1) showed that the buttress grooves cause the rod to be more prone to 

fracture under bending loads, and the simulation shows the asymmetric (i.e., bending) loading on 

the rod as it exits the plate. 

4. Effect of Grooves — Smooth Rod Shot 

In order to verify that the buttress grooves create stress concentrations in the rod, a simulation 

was performed in which a smooth rod was fired against a 9.5-mm RHA plate at 60° obliquity 

and a striking velocity of 1300 m/s. The diameter used to construct the smooth rod is the critical 

diameter of the grooved rod with respect to bending, which is the minimum diameter at the 

groove roots. To maintain consistency, this simulation was done using reverse ballistics. 

For the described conditions, it can be seen in figure 9 that the rod fractures numerically. 

Consistent with experiments by Raftenberg and Bjerke (1) involving the ARL7-NT rod, the 

fracture surface geometry is quite different from the fracture surface as seen when firing the 

grooved rod against the same target plate (see figure 4). Experimentally, the grooved rod fracture 

surface geometries consisted of a structured S-shape, whereas the fracture surface geometries of 

the smooth rods exhibited more randomness. Similarly, the numerical grooved rod fracture 

surface shown in figure 4 and the numerical smooth rod fracture surface shown in figure 9 follow 

the same trends as seen experimentally. 

 (a) (b) 

Figure 9. Reverse ballistics simulation of smooth rod vs. 9.5-mm RHA plate (t = 220 μs): (a) post-impact rod 

geometry and (b) scalar damage contours. 
9

The difference in numerical fracture surface geometry can be attributed to the stress 

concentration effects of the buttress grooves. The shape of the fracture surface in figure 9 is 

indicative of a stress pattern that is not as well defined as the sharp concentrations seen in figures 6 

and 7. It appears in figure 9 that the fracture initiates at the lower surface of the rod. The tip of 

the crack then acts as a stress raiser that provides the driving force necessary to propagate the 

fracture of the rod, and as it does so, it traverses a somewhat random path. In figure 9b, a small 

void can be seen at the tip of the crack. This void is due to the CTH threshold fracture model 

and has been inserted per criteria outlined in section 2. Conversely, the fracture of the grooved 

rod is due to the sudden onset of sharp stress gradients as seen in figures 6 and 7 that are 

developed due to the geometric discontinuities at the grooves. 

In experiments performed by Raftenberg and Bjerke (1), fracture occurred with less frequency 

and with great variation in the crack location for the cases in which fracture did occur. 

Raftenberg and Bjerke cited material flaws and machining imprecision as the cause of the 

randomness in the fracture surface geometry and its location on the rod. The numerical 

simulations support this case. If simulations were run using a stochastic constitutive model for 

the rod material, the fracture location in the numerical runs may be subject to the same random 

behavior. 

5. Plate Thickness Effects 

Experimental data by Raftenberg and Bjerke (2) regarding plate thickness effects have shown 

that for the ARL7-T rod fired at conditions consistent with figure 2, failure would occur for a 

target thickness to critical rod diameter ratio (see equation 1) of ~1. The experimental data show 

that for a t/d ratio of 0.4, fracture does not occur, but does occur for t/d = 0.9 and t/d = 1.8. 

Using experimental data as guidance, simulations were run using the ARL6A-T rod with target 

thicknesses of 3.6, 9.5, and 16.1 mm. This provided t/d ratios similar to the experiments. The 

results of these simulations are shown in figure 10. For the two images in which fracture occurs, 

the rod appears to separate in the same location—six grooves aft of the transition between the 

grooved and ungrooved sections of the penetrator. The fracture location is consistent with what 

is seen in figure 5. In figure 5, the crack responsible for the detachment of the second fragment 

initiates approximately five grooves from the nose of the penetrator. The fragment in figure 10c 

is smaller than that in figure 10b due to the additional erosion that occurred during the 

penetration of the thicker target. 

The images in figure 11 show the scalar damage plots of the rods in the plate thickness effect 

study. In the images that involve fracture, it is evident that for neither case did the fracture occur 

based on the scalar value of the Johnson-Cook damage model. Note that as the plate thickness 

increases, the scalar damage values indicate an increase in the severity of the loading on the rod.
10

(a) (t = 220 ms) 

(b) (t = 220 ms) 

(c) (t = 220 ms) 

Figure 10. Computational results of critical t/d ratio study: (a) t/d~0.4, 

(b) t/d~0.9, and (c) t/d~1.8.
11

(a) (t = 220 ms) 

(b) (t = 220 ms) 

(c) (t = 220 ms) 

Figure 11. Scalar damage contours for critical t/d ratio study: (a) t/d~0.4, 

(b) t/d~0.9, and (c) t/d~1.8.
12

6. Material Advection Sensitivity Study 

The reason the penetrator fails in reverse ballistics and not in forward ballistics can be attributed 

to loss of geometric sharpness as the penetrator material fluxes through the grid. The CTH 

interface tracking scheme that was used was the second-order-accurate Sandia Modified Youngs’ 

Reconstruction Algorithm (SMYRA), which is the recommended option when running 3-D 

problems (7). To examine the interface tracking ability of CTH SMYRA with the given 

resolution, a simulation was run for 330 μs without a target present, and buttress groove-profile 

images were generated at the initial and ending times. Figure 12 shows a comparison of the 

groove geometry for the (a) original finite-element model, (b) CTH model at time = 0 μs, and 

(c) CTH model at time = 330 μs. It is evident from comparison of (b) and (c) that as the 

penetrator material fluxes through the grid, the geometric sharpness of the grooves is lost, and 

thereby lessens the stress concentration factor. 

(a) (b)

(c) 

Figure 12. Comparison of buttress groove resolution for (a) finite-element model, (b) CTH representation at 

t = 0, and (c) CTH representation after 43 cm of advection. 
13

A comparison between figure 12b and figure 12c shows that, for the cell size used in the 

simulations run for this study, the grooves transform from their original, structured geometry to a 

rounded, sinusoidal shape. The more rounded shape would not lend itself to as great of a stress 

concentration factor as the original solid model configuration. Clearly, the sensitivity to material 

advection on stress concentrations is paramount in accurately predicting fracture at groove roots 

(see figure 3b and figure 4b). This effect could be lessened by increasing the Eulerian mesh 

resolution, which would increase the computational requirement. 

7. Summary 

Overall, it has been shown that the CTH shock physics code can be shown to predict fracture of 

buttress-grooved long-rod penetrators. The fracture surface initiates because the minimum 

principal stress in the rod is less than the dynamic tensile strength of the material (convention 

exists that tensile strength values are negative in CTH). The tensile strength value is exceeded 

due to stress concentrations at the traction grooves when the rod experiences a bending load as it 

passes through the oblique target. The effects of the grooves can be contrasted with the results of 

the smooth rod simulation, which has a much different fracture surface geometry. 

Two different versions of the grooved rod simulation were run. In the first simulation, the rod 

was fluxed through the Eulerian mesh, and the target was stationary. In the second simulation, 

the reverse was true. The fracture prediction abilities of the code seem to be enhanced when the 

item of greatest geometric detail—the rod—remains stationary and the target is fluxed through 

the grid instead. It is shown that this is due to loss of geometric fidelity caused by the advection 

scheme. 

It was shown in experimental data by Bjerke (2) that there exists a point when the t/d ratio 

exceeds some critical value, fracture of the rod will occur. Experimentally, the transition from 

no fracture in the penetrator to having a fractured penetrator will occur somewhere in the vicinity 

of ≅ 1.0

d

t . 

The ability of CTH to predict fracture as described in this report may prove to have more uses 

than just for predicting fracture of grooved rods during oblique impact with plates of finite 

thickness. The technique may prove to be transferable to other areas of technology in which 

ballistic impacts occur in the presence of geometric stress concentrations. 
14

8. References 

1. Raftenberg, M. N.; Bjerke, T. W. Bending of Threaded and Unthreaded Tungsten Rods 

Under Oblique Impact; ARL-TR-3578; U.S. Army Research Laboratory: Aberdeen Proving 

Ground, MD, August 2005. 

2. Bjerke, T. W. U.S. Army Research Laboratory, Aberdeen Proving Ground, MD. Private 

communication, September 2005.

3. Cubit 10.1 User Documentation. http://cubit.sandia.gov/help-version10.1 

/CUBIT_10.1_User_Documentation.pdf (accessed June 2006). 

4. McGlaun, J. M.; Thompson, S. L. CTH: A Three-Dimensional Shock Wave Physics Code. 

International Journal of Impact Engineering 1990, 10, 351–360.

5. Meyer, H. W.; Kleponis, D. S. An Analysis of Parameters for the Johnson-Cook Strength 

Model for 2-in-Thick Rolled Homogeneous Armor; ARL-TR-2528; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, June 2001. 

6. Crawford, D. A. Sandia National Laboratories, Albuquerque, NM. Private communication, 

20 October 2005. 

7. Bell, R. L.; Baer, M. R.; Brannon, R. M.; Crawford, D. A.; Elrick, M. G.; Hertel, E. S., Jr.; 

Schmitt, R. G.; Silling, S. A.; Taylor, P. A. CTH User’s Manual and Input Instructions, 

Version 7.0; Sandia National Laboratories: Albuquerque, NM, April 2005. 
NO. OF 

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 A COPLAND 

 D DIEHL 

 T FARRAND 

 E KENNEDY 

 M FERMAN-COKER 

 K KIMSEY 

 L MAGNESS 

 R MUDD 

 R PHILLABAUM 

 D SCHEFFLER 

 S SCHRAML 

 B SCHUSTER 

 B SORENSEN 

 R SUMMERS 

 W WALTERS 

 C WILLIAMS 

 AMSRD ARL WM TD 

 T BJERKE 

 M RAFTENBERG 

 E RAPACKI 

 S SEGLETES 
18

INTENTIONALLY LEFT BLANK.