PSI - Issue 60

A.M. Sreenath et al. / Procedia Structural Integrity 60 (2024) 256–263

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4 A. M. Sreenath and R. V. Prakash / Structural Integrity Procedia 00 (2024) 000–000 2. Quasi-isotropic woven carbon fiber with orientation [(0/90), (+45/-45)]₂ₛ is considered as the material of the specimen. The material models will be discussed in the next session. The results show tensile damage at the bottom side of the specimen and compressive damage at the top side. Suppose the impact is approximated as a point load at the center: in that case, the simulation results agree with the expected stress distribution of a simply supported beam loaded by a point force at the center. The transient load-displacement curve during the impact is also shown in the figure 2.

Fig. 2: a) Impact setup used to simulate impact damage , b) Transient force variation during impact and c) Tensile and compressive damage occurred due to the impact 2.2 Material Models Woven composite material is a mechanically complex material and has several failure modes. The stiffness of the material degrades as the damage evolves in the material. A progressive damage model is used to simulate the behaviour. The stiffness of the material decreases as a function of the damage present in the material, as described in the matrix relating to stresses and strains shown below. � ε 11 ε 22 ε 12 el � = 1- d 1 1 � E 1 - ϑ 12 E 1 0 - ϑ 21 E 2 1 � 1- d 2 2 � E 2 0 (1) When the damage parameters equal unity, the material stiffness becomes zero, and the element may be considered deleted or wholly damaged. When the damage reaches 0.99, the elements are deleted to avoid the numerical instabilities associated with a zero stiffness member [Dassault (2008)]. The details of the material properties used for the simulation are given in Table 2. ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1 � 0 0 1 � 1- d 12 � 2G 12 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ � σ 11 σ 22 σ 12 �

Table 2. Material Properties of the carbon fiber reinforced composite [Hu et al.(2018)] Property Value Property Value Property Value Property

Value

E₁₊ E₁₋ E₂₊ E₂₋ G₁₂

50.43 GPa 49.03 GPa 50.43GPa 49.03 GPa 5.11 GPa

X₁₊ X₁₋ X₂₊ X₂₋

505.7 MPa 295.6 MPa 505.7 MPa 295.6 MPa 99.2 MPa

G 1f+ G 1f- G 2f+ G 2f-

44.9 kJ/m2 39.2 kJ/m2 44.9 kJ/m2 39.2 kJ/m2

σ yo

55 MPa

C

669.9 MPa

p

0.823

(d) max (ε el ) max (ε pl ) max

0.99 0.15 0.15

S

α₁₂

0.18634

ν₁₂

0.062

(d₁₂) max

0.99