PSI - Issue 68

E. Ezgi Aytimur et al. / Procedia Structural Integrity 68 (2025) 540–546 E. Ezgi Aytimur / Structural Integrity Procedia 00 (2024) 000–000

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Fig. 4. Deceleration curves

Deceleration values on the target material following a single impact at a velocity of 16 m / s have been determined as 1.7x105, 1.5x105, and 1.2x105 g for Johnson-Cook, Cowper-Symonds, and Elastic models, respectively. Deceleration values are shown in Figure 4. Comparing these results reveals notable distinctions among the utilized models. The Johnson-Cook model exhibits the highest deceleration value, followed by Cowper-Symonds and Elastic models successively. This disparity suggests variations in the predictive capabilities of these models in capturing the deceleration phenomenon under the specified conditions. The higher deceleration value predicted by the Johnson-Cook model could imply its enhanced sensitivity to material behavior, particularly in dynamic scenarios. Conversely, the lower deceleration values projected by the Elastic models may indicate relatively conservative estimations or limitations in capturing intricate material responses to impact loading. Moreover, the selection of an appropriate model depends on the specific application requirements, such as accuracy, computational e ffi ciency, and complexity tolerance. While the Johnson-Cook model might o ff er superior predictive accuracy, it could demand higher computational resources compared to simpler models like the Elastic model. The restitution coe ffi cients on the target material are 0.41, 0.38 and 0.29 for the Johnson-Cook, Cowper-Symonds and Elastic models, respectively as shown in Table 3. The coe ffi cient of restitution represents the fraction of the kinetic energy of the material recovered after impact. As the value of the coe ffi cient of restitution approaches 1, it means that the material behaves more elastic against impact and recovers more energy. As the value of the restitution coe ffi cient approaches 0, it means that the material behaves more plastic to impact and recovers less energy (Yarar et al. (2021)). Comparison of these coe ffi cients reveals the distinctive features of each model in capturing the phenomena of energy dissipation and restitution. The Johnson-Cook model indicates a high level of energy recovery after impact with a coe ffi cient of 0.41. This can be attributed to its comprehensive formulation that takes into account material properties such as strain rate sensitivity and strain hardening. The slightly lower coe ffi cient obtained from the Cowper-Symonds model (0.38) indicates a marginally reduced ability to retain kinetic energy compared to the Johnson-Cook model. This may be due to di ff erences in the constitutive equations and parameters used in the formulation, leading to variations in prediction accuracy. Remarkably, the Elastic model exhibits the lowest coe ffi cient of 0.29, indicating relatively higher energy dissipation. As a result, it tends to overestimate energy dissipation and underestimate restitution in dynamic impact scenarios. The restitution coe ffi cient values obtained in this study show the impact of di ff erent modeling approaches on the restitution coe ffi cient estimates.

Table 3. Restitution coe ffi cient Material Model

Initial Velocity ( m / s )

Rebound Velocity ( m / s )

Restitution Coe ffi cient

Johnson Cook

16 16 16

6.7 6.1 4.7

0.41 0.38 0.29

Cowper Symonds

Elastic

The choice of the model used, and the interpretation of the results should be based on the material type, impact velocity and other factors to ensure the most accurate prediction. According to the study by Liu and Guedes Soares (2019) and the study by Zhang et al. (2023), the Cowper-Symonds material model gives accurate results for small