For targets struck by shaped charge warheads, besides the primary metal jet, the distribution of metal jet fragments from scattering and armor fragments from spallation also plays a crucial role in reflecting postpenetration damage. Figure 4 illustrates the distribution and combined velocity of postpenetration damage elemental scatterings after penetrating a steel target under intact liner conditions.
After the jet generated by the complete drug type hood penetrates the target board, the maximum combined velocity of the debris cloud behind the target is 2289m/s, and the maximum divergence angle is 44.14°.
In the overhead view, the debris cloud forms a uniform asterisk pattern, with the debris cloud being relatively concentrated and having a high density. The central jet is not disturbed and diverges uniformly. Based on the debris cloud behind the intact drug type hood target, an analysis of the effect of inclined grooves on the debris cloud behind the target is conducted.
The Impact of Depth on the Velocity and Divergence Angle of Fragmentation Clouds
Firstly, descriptive statistical methods will be employed to summarize the central tendencies and distribution of maximum combined velocity and maximum fragment divergence angle of fragmentation clouds at different levels of inclined groove depth. Key statistical measures will include mean, median, standard deviation, among others.

When the depth of the inclined grooves is 0.2mm, the mean of the maximum combined velocity of the debris cloud is 2916.67 m/s, with a median of 3192 m/s and a standard deviation of 482.10 m/s; the mean of the maximum fragment divergence angle is 57.95°, with a median of 60.18° and a standard deviation of 9.88°.

At a depth of 0.4mm for the inclined grooves, the mean of the maximum combined velocity of the debris cloud is 2479 m/s, with a median of 2419 m/s and a standard deviation of 173.94 m/s; the mean of the maximum fragment divergence angle is 58.05°, with a median of 55.78° and a standard deviation of 8.33°.

For a depth of 0.6mm of the inclined grooves, the mean of the maximum combined velocity of the debris cloud is 2674 m/s, with a median of 2735 m/s and a standard deviation of 408.93 m/s; the mean of the maximum fragment divergence angle is 58.34°, with a median of 56.05° and a standard deviation of 12.70°.
Next, box plots will be utilized to illustrate the distribution of cloud velocity and divergence angle at each depth level of the inclined grooves, along with any outliers, as depicted in Fig. 5, facilitating the observation of the data's range and central tendency.
Subsequently, scatter plots combined with trend lines will be used to explore the relationship between inclined groove depth and the velocity and divergence angle of fragmentation clouds. By observing the variation trends between groove depth and cloud attributes, as illustrated in Fig. 6, potential effects of depth variations on the fragmentation cloud can be inferred.
Figure 5 (a) illustrates the distribution of the maximum combined velocity of the debris cloud at different depths of the inclined grooves. We can observe a certain upward trend in the velocity as the depth increases, but there is also some fluctuation. Specifically, the velocity is highest at a depth of 0.2mm, and the data range is broader, indicating greater variability.
Figure 5 (b) presents the distribution of the maximum fragment divergence angle at different depths of the inclined grooves. The distribution of the divergence angle remains relatively stable at different depths, but at a depth of 0.6mm, there is a wider range of divergence angles, suggesting greater variability at this depth.
In Fig. 6 (a), it is shown that with the increase in depth of the inclined grooves, the maximum combined velocity of the debris cloud generally exhibits an upward trend, although there is some fluctuation in the data.
Figure 6 (b) demonstrates that there is no apparent linear relationship between the maximum fragment divergence angle and the depth of the inclined grooves, with the data distribution relatively dispersed.
The Influence of Segments on the Velocity and Divergence Angle of Fragmentation Clouds
To analyze the effect of the number of inclined groove segments on the maximum combined velocity and maximum fragment divergence angle of the fragmentation clouds, descriptive statistical analysis was employed. This involved calculating the mean, standard deviation, minimum, and maximum values of the maximum combined velocity and maximum fragment divergence angle to understand the distribution of the data.

Based on the analysis results, in terms of the maximum combined velocity of the debris cloud (m/s): Mean: 2649.8; Standard Deviation: 379.02; Minimum: 2238; Maximum: 3198.

Regarding the maximum fragment divergence angle (°): Mean: 56.72; Standard Deviation: 9.62; Minimum: 44.14; Maximum: 72.03.
Additionally, scatter plots with trend lines were created to visualize the relationship between the number of inclined groove segments and the maximum combined velocity of the fragmentation clouds, as well as the number of inclined groove segments and the maximum fragment divergence angle.
To provide a clearer observation of the maximum combined velocity and maximum fragment divergence angle of the fragmentation clouds under different numbers of inclined groove segments, grouped bar charts were plotted for comparison.
Figure 7 illustrates the relationship between the number of inclined groove segments and the maximum fragment divergence angle. The trend line depicts a slightly upward trend, but compared to the velocity variation, the increase in angle is not very pronounced.
In Fig. 8, the red bars represent the maximum combined velocity of the fragmentation clouds, while the blue bars represent the maximum fragment divergence angle. Adjacent to each bar corresponding to the number of inclined groove segments, the maximum combined velocity and maximum divergence angle of the fragmentation clouds are presented, allowing for a clear comparison of these metrics across different numbers of inclined groove segments.
From Figs. 7 and 8, it can be inferred that there is a positive correlation between the number of inclined groove segments and the maximum combined velocity of the fragmentation clouds, indicating that a greater number of groove segments result in higher maximum combined velocities of the fragmentation clouds. The number of inclined groove segments also has some impact on the maximum fragment divergence angle, although this effect is less pronounced compared to the maximum combined velocity of the fragmentation clouds.
Analysis of PostPenetration Damage to Aluminum Targets Due to Design of Inclined Grooves on the Interior Surface of Shaped Charge Liners
Under the effect of a shaped charge, Fig. 9 depict the penetration of an aluminum plate. The primary perforation area measures 1786.8mm², indicating a single penetration hole, with numerical simulation revealing only 3 small perforations, the largest of which measures 191.13mm².
Table 5 present the damage effects and specific damage values of other shaped charge liners with inclined grooves on the target plates. Aluminum targets numbered 1, 4, and 7 were subjected to postpenetration effects with grooves at a depth of 0.2mm, targets 2, 5, and 8 at a depth of 0.4mm, while targets 3, 6, and 9 underwent effects with grooves at a depth of 0.6mm. Each target plate exhibits primary perforations along with various sizes of secondary perforations.
Table 5. PostPenetration Perforation Effects of Inclined Groove Shaped Charge Liners on Aluminum Targets
 The primary perforation condition of the first aluminum plate.  The first aluminum plate small perforation condition. 

Aluminum Target No.1  1 hole / total area of 8007.5mm2  56 holes / maximum area of small enlarged hole is 524.88mm2 
Aluminum Target No.2  2 holes / total area of 3524.9mm2  82 holes / maximum area of small enlarged hole is 1053.1mm2 
Aluminum Target No.3  1 hole / total area of 6788.2mm2  30 holes / maximum area of small enlarged hole is 491.35mm2 
Aluminum Target No.4  1 hole / total area of 5034.4mm2  52 holes / maximum area of small enlarged hole is 715.15mm2 
Aluminum Target No.5  1 hole / total area of 3188.6mm2  25 holes / maximum area of small enlarged hole is 319.69mm2 
Aluminum Target No.6  5 hole / total area of 17040mm2  63 holes / maximum area of small enlarged hole is 307.94mm2 
Aluminum Target No.7  3 hole / total area of 4737.82mm2  55 holes / maximum area of small enlarged hole is 251.15mm2 
Aluminum Target No.8  1 hole / total area of 3527.0mm2  40 holes / maximum area of small enlarged hole is 546.04mm2 
Aluminum Target No.9  2 hole / total area of 1556.03mm2  27 holes / maximum area of small enlarged hole is 346.15mm2 
Analyzing the perforation areas of the three sets of aluminum targets (1, 4, 7; 2, 5, 8; 3, 6, 9), each set representing different groove depths (0.2mm, 0.4mm, 0.6mm).
Calculate the average perforation area for each set of aluminum targets, and compare the perforation areas between different sets, as well as comparing the average areas of single and multiple perforations for different groove depths.
Figure 11 displays the distribution of single perforation areas at different groove depths (0.2mm, 0.4mm, 0.6mm). In the box plot, the box represents the range of data from the first quartile to the third quartile, the horizontal line denotes the median, and the whiskers extend to the maximum and minimum values within a certain distance from the box, with individual points indicating potential outliers.

As shown in Fig. 10, the relationship between the average single orifice area and groove depth is not monotonic; the average single orifice area is larger at depths of 0.2mm and 0.6mm, while it is smaller at a depth of 0.4mm. The average maximum expansion area slightly increases with increasing groove depth, suggesting that groove depth may influence the area of maximum expansion.

In the box plot of single orifice area distribution in Fig. 11, it can be observed that the distribution of single orifice area on aluminum target plates at a depth of 0.2mm exhibits the greatest variance, followed by the 0.6mm depth, while the distribution on the 0.4mm depth target plate is relatively more concentrated.
Analyzing the perforation areas of three sets of aluminum target plates (1, 2, 3; 4, 5, 6; 7, 8, 9), where each set of aluminum target plates represents different numbers of grooves (4, 8, 12).
From Fig. 12, it can be observed that the group with 4 grooves exhibits higher median and trend range, indicating larger individual maximum perforation areas. Meanwhile, it is also noticeable that the group with 12 grooves shows a narrower range of maximum perforation areas and a lower median, suggesting relatively smaller maximum perforation areas for this group.

Analyzing the perforations under different numbers of groove segments yields the following conclusions: the average total single perforation area is highest in the 4groove segment group and lowest in the 12groove segment group.

When considering the maximum perforation area, the perforation area is larger in the 4groove segment group, while it is smaller in the 12groove segment group.

The standard deviation indicates that the distribution of single perforation areas in the 8groove segment group is relatively wider, suggesting a greater unevenness in the perforation areas within this group.
In summary, the design of shaped charge liners with inclined grooves not only surpasses the performance of liners without grooves in terms of primary and secondary perforations, but also exhibits specific trends in the number and area of primary perforations, as well as the coverage range of secondary perforations, which vary with groove depth and quantity. This provides controllable damage effects.