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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3

the LS-DYNA material cards based on LS-DYNA Keyword User’s Manual Volume II (2014): The Johnson-Cook material model is described with MAT 98 Simplified Johnson Cook and Cowper-Symonds is described with MAT 24 Piecewise Linear Plasticity. Also, MAT 01 Elastic material card is used to define non-strain rate parameters of mild steel. The preparation of the simulation is described step by step. The first step is to prepare a deformable plate and an impactor as shown in Figure 1. The deformable plate is a rectangular prism with dimensions of 30x40 mm and a thickness of 15 mm and the impactor is a sphere with a diameter of 10 mm. The plate is defined as flexible while the impactor is defined as rigid to account for the deformation of the plate. The second step is to define the materials. The material of the deformable plate is changed for each impact simulation while the impactor material is fixed as structural steel. Firstly, the Johnson-Cook material model is applied to a deformable plate. MAT 98 Simplified Johnson Cook material model is defined with material model parameters such as density, Young’s modulus, Poisson’s ratio, initial yield stress, strain rate parameters of B, n and c. The calculation of flow stress is shown in Eqn. (1) without temperature term (Sˇ krlec and Klemenc (2016), Altair Radioss Manual (2021), LS-DYNA Keyword User’s Manual Volume II (2014)). In the equation, ε p indicates the plastic strain and ˙ ε represents the strain rate while B is hardening modulus, n is hardening exponent and c is strain rate coe ffi cient. σ =  A + B ε n p   1 + c ln ˙ ε ˙ ε 0  (1) where ˙ ε 0 is the reference strain-rate which is defined as 1 s − 1 and A is initial yield stress. Then, the Cowper-Symonds material model is assigned with MAT 24 Piecewise Linear Plasticity material card. Material model parameters are density, Young’s modulus, Poisson’s ratio, tangent modulus ( E t ), strain rate parameters of C and p. The flow stress is given in Eqn. (2) (Sˇkrlec and Klemenc (2016), Altair Radioss Manual (2021), LS-DYNA Keyword User’s Manual Volume II (2014)). In the equation, ε p represents the plastic strain with hardening exponent n and ˙ ε denotes the strain rate while C is strain rate coe ffi cient and 1 / p is strain rate exponent. σ =  A + b ε n p    1 +  ˙ ε C  1 p    (2) where b is the tangent modulus and A is the yield stress At last, MAT 01 Elastic material card is used without apply strain rate parameters. Material parameters of the three material cards are given in Table 1.

Table 1. Material Parameters

Density  kg / m 3  Young’s Modulus ( GPa ) Poisson’s Ratio Yield Stress ( MPa ) Strain-rate Parameters

B( GPa ) n

c

Johnson Cook

7850

210

0.3

185

1.925

0.8183 0.0972

E t ( GPa ) C ms − 1

p

Cowper Symonds 7850

210

0.3

185

0.955

41.0133 6.2

Elastic

7850

210

0.3

185

-

-

-

In the third step, the impact duration, which is the end time, is defined as 0.1 milliseconds. Following that, the initial condition which is a velocity of 16 m / sec (35 mph) is defined to the impactor based on the regulation. This is set as the initial condition because the simulation starts just before the impact. Then, boundary conditions are applied to prevent undesired movement, as shown in Figure 1. The deformable plate is fixed at its bottom surface to restrict the movement in all directions. However, the impactor movement is constrained in all directions except the x-direction as it strikes the plate in the x-direction. It is redefined for the LS-DYNA as a rigid body constraint. The frictional contact is defined as the contact between the deformable plate and the impactor with a friction coe ffi cient of 0.1 (Reid and Hiser (2004)). It directly refers to the LS-DYNA contact type ’ A¨utomatic Surface to Surface¨ ’, which is recommended for crash simulations as outlined in LS-DYNA Support Contact Types (2001). Lastly, the mesh is defined as 1.2 mm global element sizing. The mesh size is then refined