Simulation and analysis of delamination damage propagation in CFRP structures

For aerospace vehicles, composite materials are used in large-scale integral panels due to their excellent material properties. In the structure of vehicles, this kind of composite material panel is connected to the internal structure through fasteners. During the composite material molding process and the process of drilling connection holes, some local delamination sometimes occurs, this delamination is hardly detected in time, it can cause great damage to the compressive strength of the structure. In this paper, the ABAQUS/Explicit solver is introduced to analyze the progressive damage of interlaminar separation with cohesive elements, the accuracy difference between different damage modes with typical solvers is verified. Then based on the self-compiled three-dimensional Hashin failure criterion subroutine, the numerical simulation is carried out on the compressive strength of the composite laminate under different pre-delamination damage ranges, and the compressive strength of the single-fastener connection structure with pre-delamination, indicates the fiber damage, matrix damage and delamination damage, in order to explore its failure mode and residual strength law.


Introduction
For aerospace vehicles, composite materials are used in large-scale integral panels due to their excellent material properties.In the structure of vehicles, this kind of composite material panel is connected to the internal structure through fasteners.During the composite material molding process and the process of drilling connection holes, some local delamination sometimes occurs, this delamination is hardly detected in time, it can cause great damage to the compressive strength of the structure.In order to evaluate the effect of this layered destruction, some scholars have done a lot of work through numerical methods and experiments.Fu et al. [1] studied the delamination damage mechanism and prediction method of composite laminates, established a macro-micro finite element model of orthogonal laminates that focused on the resin enrichment area between layers.Based on the three-dimensional Hashin failure criterion, the quadratic nominal stress criterion and the BK failure criterion in the bilinear Cohesive damage model, Zhang [2]used the VUMAT subroutine in the ABAQUS/Explicit module to simulate delamination damage during drilling of carbon fiber composite unidirectional laminates.Based on the research on the delamination failure mechanism of composite materials based on the cohesion theory, Gu [3] proposed a cohesive force/friction contact coupling model to explore the influence of friction coefficient, cohesive force strength, ply angle, etc. on friction delamination and load response.Xiao [4] and Jia [5] explored the residual strength of damaged composite laminates.Wu [6] and Zhang [7] conducted numerical simulation research on the propagation behavior of delamination defects.Zhao et al. [8] simulated the mode I and mode I/II delamination expansion of multidirectional laminates based on the cohesion model.Maruschak et al. [9] analyzed the initiation process of metal cracks from the quasi-brittle stage to fatigue cracks from a microscopic level.Composite material structures will face internal interlayer damage caused by low-speed impacts during use.During the drilling process of connection holes, the stress-sensitive areas around the holes will also face the same problem.Evaluation of delamination effects for different initial delamination ranges and analysis of damage progression help to evaluate the remaining mechanical properties of the structure.Although the above results partially introduce explicit solvers, they do not discuss the scope of application of the explicit solver in different modes of damage, and the error analysis with the implicit solver.For the orthogonal unidirectional tape-laminated carbon fiber reinforced composite materials and composite material connecting joints used in a specific project, the damage effects under different damage effects also need to be discussed.In this paper, the ABAQUS/Explict solver is introduced to analyze the progressive damage of interlaminar separation with cohesive elements, the accuracy difference between different damage modes with typical solvers is verified in section 2. Then combined with the self-compiled three-dimensional Hashin failure criterion subroutine, and introduce defining an independent reduction factor for each damage mode, the reduction factor is directly multiplied by the material stiffness coefficient to establish a progressive damage model suitable for low-velocity impact of carbon fiber reinforced composite laminates.the numerical simulation is carried out on the compressive strength of the composite plate under different pre-delamination damage ranges, and the compressive strength of the single-fastener connection structure with pre-delamination, indicates the fiber damage, matrix damage and delamination damage, in order to explore its failure mode and residual strength law.In the last section, based on the Hashin failure criterion, the compressive strength of singlenail connected composite laminated panels with preset delamination is simulated and analyzed, and the failure modes around the connection holes are observed.

Comparison of explicit and implicit calculation results of three model of cracks
The ABAQUS/Explict solver was originally used to simulate transient problems such as impact and collisions.Compared with the ABAQUS/Standard solver, it is more conducive to solving complex contact problems, avoiding non-convergence problems in implicit solutions, require less computing power [10].When using the ABAQUS/Explict solver to analyze quasi-static problems, a longer analysis step time and a smooth amplitude curve are used to slow the loading process, so that the dynamic effects in the model are not obvious, and the results close to the static analysis are obtained as much as possible.Generally, it can be considered that the calculation accuracy of the ratio of kinetic energy to internal energy of the system is less than 5%, which is acceptable for engineering.

Mode Ⅰ Mode Ⅱ Mode Ⅲ
Figure 1.Simulation model and different modes of damage.In order to verify the similarities and differences between the explicit solution and the implicit solution of ABAQUS in typical mode of cracks growths, the finite element calculation and analysis of three different fracture modes are specially selected for delamination evolution examples.As shown in the figure, two thick metal plates which have sufficient rigidity stacked up and down.The head end of the two plates is a free end, which is a square preset layer inside.The boundary condition of the plate is four-sided hinged support on the bottom surface (U1=U2=U3=0), the free end surface is coupled a reference point, and the displacement in the corresponding direction is applied according to different damage types.
Cohesive elements damage is divided into two stages: damage initiation and damage evolution.In this example, the BK failure criterion is used to predict the damage evolution, and the quadratic nominal stress criterion is used to define the damage initiation stage.the expression is as follows [11]: In the formula,   is the normal stress in the thickness direction, 〈  〉 is the Macaulay Bracket formula of   ,   , and   are the shear stress parallel to and perpendicular to the thickness direction,   0 ,   0 and   0 are the maximum nominal stresses of the cohesion model under pure tension or pure shear deformation.
In the formula, G Ⅰ , G Ⅱ and G T are the energy release rate of type Ⅰ, type Ⅱ and the total energy release rate respectively.G ⅠC , G ⅡC and G TC are type Ⅰ, type II critical energy release rate and composite critical energy release rate, η is a material parameter, which is taken as 1.45 here.The properties of the cohesive layer elements are shown in the table below: Table 1.Property parameters of cohesive element material.[2] ρ/ton• mm -9  Enn/GPa Ess/GPa σ n 0 /MPa σ s 0 =σt/MPa GⅠC/kJ• m -2 GⅡC=GⅢC/kJ• m -2 1.65×10 -9  7.63 4.36 26 54 0.28 0.81 The plate adopts reduced integration, hourglass-controlled eight-node linear hexahedron element (C3D8R), and the cohesive layer bonding element adopts viscous element (COH3D8).For the damage propagation under each damage mode, the implicit solution, the explicit solution without mass scaling, and the explicit solution with the incremental step increasement of 2×10 -6 as the mass scaling target are used for analysis.And compare the evolution of the support reaction with the loading displacement at the reference point of the applied load.According to the comparison of the results of the explicit solution and the implicit solution under the three different modes of damage, it can be seen that the ABAQUS/Explicit solver can better fit the calculation of the ABAQUS/Standard solver for the two types of damage expansion of damage mode I and mode III, for the extension of damage mode II, the solution effect of the explicit algorithm is not ideal.In order to improve the calculation efficiency, mass scaling can be set during the explicit solution process.In the explicit calculation of damage expansion of mode I and mode III, the explicit calculation with mass scaling is more effective than the explicit calculation without mass scaling.The error of the explicit calculation with mass scaling is within 1% compared with the explicit calculation without mass scaling.Therefore, for this two modes of damage, the explicit calculation with mass scaling can be adopted.

Analysis of compressive strength of composite laminates under different preset delamination damage ranges
As mentioned above, in this example, the ABAQUS/Explicit solver is used to simulate the delamination expansion of a composite laminate with internal preset delamination damage, the compression performance of the composite laminate under different levels of preset delamination is explored.According to the ASTM-D7136 test standard [12], the length and width of the composite laminate used in this example is 150mm×100mm, with a total of 11 layers of T800 carbon fiber reinforced epoxy resinbased unidirectional tape prepreg layup, the length direction of the plate is 0° direction, the layup is set to [0°/90°/0°/90°/0°/90 ̅̅̅ °]S, each layer of unidirectional prepreg is 0.2mm, insert cohesive elements between the third and the forth layers.The mechanical parameters of ply in the laminate are as table 2 The Hashin criterion is used to write a subroutine to analyze the damage of the fiber and the matrix during the impact and buckling of composite laminates.The criterions of different types of failure are as follows: Table 3. Simplified Hashin failure criterion.[11] Failure Type Failure Criterion Fiber Tensile  The composite laminates is fixed at one end along the length (U1=U2=U3=UR1=UR2=UR3=0), and the other end is subjected to a compressive displacement at the reference point and acts on the end face.1% of the displacement of the first-order buckling mode is introduced as the initial damage, after setting the variable output, submit the job and post-process.
In order to make the nodes in a steady state before and after the incremental step as much as possible, the incremental time step should be small enough, the relevant physical quantities in each incremental step are approximately constant.The stable incremental time step is as follow: In the formula, e L is the characteristic length of the element, generally adopts the shortest element size, d C is the wave velocity of the material.For a linear elastic material with Poisson's ratio zero: In the formula, E is the elastic modulus of the material, ρ is the density of the material.During the calculation process, the stability time increment of the analysis step is about 6×10 -7 .The compression force of composite laminates under different pre-delaminated areas varies with loading conditions is shown in the figure.It can be seen from the table that for a laminate without predelaminated and with a pre-delaminated circle area of 10 mm, there is no significant difference in the compressive strength, about 70kN, but for the laminate with the pre-delaminated circle area of 20mm and 30mm, the compressive strength is significantly reduced, about 60kN, the larger the damage area, the faster the structural damage.Therefore, in actual engineering, it can be considered that a circle with a delamination area below 10mm is acceptable.

Simulation analysis of compressive strength of single-fastener connected composite laminates with pre-delaminated
In this example, the standard single-fastener connected test piece in ASTM D5961M-08 [13] is used as the simulation object, two composite plates with ply scheme [0°/90°/0°/90°0°/90°/0°/ 90 ̅̅̅ °]S are connected by countersunk fasteners, and thickened reinforcement areas are arranged at both ends.Clamps are used to clamp and apply loads in the test.In this example, delamination is arranged on the inside of each composite plate at 1/4 thickness from the outer surface, the pre-delamination area is a circle with a radius of 12mm, which is concentric with the connection hole.In this example, the buckling mode of the connected composite structure is first calculated, 1% of the first-order mode displacement is extracted as the initial damage.One end of the plate connector is fixed, the other end is fixed, both the sides limit the out-of-plane displacement.The self-written subroutine based on the three-dimensional Hashin failure criterion is used to analyze the fiber damage, matrix damage and delamination expansion during the compression process.Through finite element simulation analysis, it can be obtained that when the analysis step time reaches 0.2, the composite material in the area around the connecting hole begins to be damaged due to compression; when it reaches 0.34, the damage trend begins to become obvious; when it reaches 0.8, the damage of fibers and matrix has already becomes serious, at which point the preset delamination begins to expand.It can be seen from the numerical simulation that for this kind of connection structure, due to the effect of the connecting fasteners, the delamination damage area expansion in the local area near the connecting area does not play a dominant role in the failure mode, the interlaminar failure of the material at this time is caused by the intralaminar failure of the material.Therefore, for this kind of small-scale preset delamination damage, the failure caused by structural strength damage can be more considered when designing the structure.
Table 4. Destruction of connected regions at different analysis steps.
Step Time Fiber destruction Matrix damage Interlayer damage T=0.25 T=0.5 T=0.9 The The ABAQUS/Explicit solver can be used to solve the delamination expansion simulation of the damage mode Ⅰ and damage mode Ⅲ.On the premise of meeting engineering accuracy, the use of explicit solvers in these two types of damage modes can effectively solve the problem of difficulty in convergence of implicit solvers in interlayer damage expansion analysis, and significantly improve the calculation speed.2. For this kind of T800 carbon fiber reinforced epoxy resin-based unidirectional composite laminate with prepreg layup, the delamination damage below 10mm will not cause significant damage to the static compressive strength.For the delamination damage in tiny areas that cannot be detected by the existing ultrasonic C-scan detection level during the molding and use of composite materials, it can be considered that it will not cause destructive effects on the structural strength.3.For this type of single-fastened composite laminates with pre-delamination, since the delamination area is very small, the pretightening force of the fastener connection is more significant at this time, which limits the deflection of the material in the local area under pressure deformation, the local delamination damage around the fastener does not dominate the damage failure around the connection structure.

Figure 2 .
Figure 2. Variation of compressive force with loading under different modes of damage.(c) Mode Ⅲ

Figure 3 .
Figure 3.Variation of compressive force with loading under different preset damages.

Figure 4 .
Figure 4. Standard test piece for bearing response of polymer matrix composite laminates.