Finite element analysis of a modified progressive damage model for composite laminates under low-velocity impact

Abstract

In this paper, a 3D finite element model is established in ABAQUS/Explicit based on a modified progressive damage model to study the dynamic mechanical response and damage development in cross-ply composite laminates subjected to low-velocity impact. The 3D Hashin criterion and the damage evolution model with the through-thickness normal stress component σ 33 are applied to predict the intra-laminar damage initiation and evolution. The cohesive elements with the bilinear traction-separation relationship are inserted between layers to predict the inter-laminar delamination induced by impact loading. A user-material subroutine VUMAT involving the modified progressive damage model of intra-laminar and inter-laminar damage is coded and implemented in the finite element package ABAQUS/Explicit. The numerical results of three different impact energies (7.35, 11.03 and 14.70 J) are analyzed by the impact force-time, force-displacement and energy-time histories curves as well as different damage modes. The respectable relationship between numerical simulation and experimental result indicates that the proposed modified method is more suitable for low-velocity impact on composite laminates under different impact energies than the previous method without σ 33. Moreover, the effects of S mt and S mc on global mechanical response and local damage predictions for laminates are discussed in detail. It can be concluded that both of the coefficients should be adopted between 0.93 and 0.96 when using this damage model to simulate composite laminates under low-velocity impact.

Numerical investigation on the repeated low-velocity impact behavior of composite laminates

“…The local strain and stress can be calculated by ABAQUS according to the constitutive equation and material properties. Detailed equations for computing the equivalent displacement and equivalent stress were proposed and displayed in our previous work [14].…”

“…The enhanced Schapery theory (EST) [9] can be used as the intra-laminar constitutive model to capture the prepeak and post-peak behavior of a unidirectional lamina, which has been successfully applied to numerical simulation of lowvelocity impact on composites [10,11,12,13]. The progressive damage model (PDM), which considers damage initiation and subsequent stiffness degradation, has become the most popular numerical model to predict the different modes of damage for composites [14,15,16,17,18,19,20,21,22,23,24]. With regard to determination for damage initiation, the interactive criteria with individual equations to evaluate fiber and matrix damage under tensile and compressive loading have been implemented extensively, such as the Chang-Chang [25], Hou [26,27], Hashin [28,29] and Puck [30] criteria.…”

“…Once the failure criteria are met, a relevant damage evolution model is required to simulate the damage accumulation process around the damaged area. Compared to the constants predefined in a stiffness degradation matrix [31,32], the equivalent displacement method is preferred by most researchers to describe the loss of stiffness due to the involvement of mechanical parameters [14,15,18,19,20,33,34]. Among the typical damage modes for composites, delamination is regarded as the most significant mode because it may propagate undetectably and result in the unforeseen collapse of the structures [35].…”

“…The strength-based criterion and fracture energy criterion with the linear softening law are implemented to predict the damage initiation and evolution, respectively. Moreover, the bilinear traction-separation relationship is commonly adopted in the CZM-based interface elements to simulate the delamination of composites [14,33,44,45,46,47].…”

Mesh size sensitivity analysis for interlaminar fracture of the fiber-reinforced laminated composites

“…Some researchers kept the crack propagation length as 2 mm constant for VCCT but there is lack of the detailed analysis about optimum element length for both mode I and mode II fracture analyses. [19][20][21][22][23][24] Total number of the elements and the nodes are listed in Table 2 for each model. After the preparation of DCB and ENF numerical models, boundary conditions are applied and then the precracks are forced to propagate.…”