PSI - Issue 52

Chenxu Jiang et al. / Procedia Structural Integrity 52 (2024) 63–71 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Slip direction α Slip system Strain energy density deviator Strain energy potential N The number of slip systems Volumetric strain energy 2. C onstitutive model

The crystal plasticity constitutive model together with the Arruda-Boyce model was used to describe the micromechanical behaviors of the crystalline lamellae and amorphous lamellae, respectively (Oktay & Gürses, 2015; Uchida & Tada, 2013; Uchida et al., 2010; Van Dommelen et al., 2003a). Semi-crystalline polymer crystal lamellae show viscoplastic behavior, which total deformation gradient can be decomposed into two elastic e and plastic p components = ∙ (1) Plastic deformation gradient p is caused by plastic shearing on crystallographic slip systems, which can be expressed as p =∑ +γ (α) ( (α) ⊗ (α) ) Nα=1 (2) where is the second-order unit tensor, γ (α) is the shear strain, α is the slip system, N is the number of slip systems, 0 (α) is the slip direction and 0 (α) is the normal vector to the slip plane. The rate of plastic deformation tensor p p = e ∙ ̇ P ∙ p−1 ∙ e−1 =∑ γ̇ (α) (α) ⊗ (α) Nα=1 (3) The rate-dependent crystalline phase viscoplastic deformation is caused by slip deformation on the αth slip system. The shear strain rate on a slip system by Power law as follows (Wei et al., 2019) γ̇ (α) =γ̇ 0 (α) sgn(τ (α) )| τ (α) τ c (α) | n (4) and sgn(x) = {−11, x, x≥<11 (5) where γ̇ 0 (α) is the reference value of the shear strain rate, n is the rate sensitive exponent, τ (α) is the resolved shear stress: τ (α) = : ( (α) ⊗ (α) ) (6) where is the Cauchy stress, τ c (α) is the flow stress, a variable used to describe the current strength of the slip system, also known as the critical resolved shear stress. The amorphous lamellae show hyperelastic behavior at room temperature. The Arruda-Boyce model in ABAQUS is used to simulate its mechanical behavior. The strain energy potential of isotropic and incompressible materials can be express as = (( ̅ 1 −3, ̅ 2 − 3) + ( −1)) (7) where (( ̅ 1 −3, ̅ 2 −3) is the strain energy density deviator, ( −1)) is the volumetric strain energy. By expanding in a Taylor series, the has the following form: = ∑ 2 −2 ( ̅ 1 −3 , ̅ 2 −3 )+ 1 ( 2 2 −1 − ) 5 =1 (8) where 0 =2/ is the initial bulk modulus, when D=0 the material is incompressibility. is elastic volume strain, ̅ 1 , ̅ 2 are elongation. While ̅ 2 is difficult to measure and the influence is much smaller than ̅ 1 , so it is neglected. The coefficient is a series expansion of the inverse Langevin function and arises in the statistical treatment of non-