Thermo-mechanical coupling behavior of needle-punched carbon/carbon composites

1 Introduction

Needle-punched carbon/carbon (NP C/C) composites are produced with chemical vapor infiltration (CVI) or precursor infiltration pyrolysis technologies [1]. They are employed in thermal protection systems of re-entry engineering, propulsion systems, and rocket-engine components [2–4], thanks to excellent mechanical performance at high temperature.

Oxidation of C/C composites in oxygenated atmosphere occurs when the temperature reaches 400°C. Both heat transfer and oxygen diffusion in composites influence their oxidation behavior and should be considered in structural integrity assessment. Wang et al. [5] designed a comprehensive scheme combining a lattice Boltzmann method and a finite-volume method, to investigate the heat transfer process, and used it to study the effects of temperature and thermal conductivity of carbon fibers on the this process. Tian et al. [6] investigated the ablation-resist modified C/C composites with H_fC nanowires laminated with a carbon fiber cloth. It was found that their thermal conductivity in the Z-direction was enhanced in the range from 100 to 2,500°C thanks to the nanowires. Cao et al. [7] investigated the thermal conductivity of C_pf/SiC composites with heat transfer channels from room temperature to 500°C along the through-thickness and in-plane directions and established that they had excellent thermal conductivity in two directions. Guo et al. [8] proposed a multiscale model to predict the coefficients of thermal expansion and thermal conductivities of C/C composite, with the effects of needling parameters on thermophysical properties analyzed.

Some researchers focused on modifications to improve the oxidation resistance process. Levet et al. [9] studied the sublimation of carbonaceous material experimentally with heat fluxes of 8 to 10 MW/m², while the temperature inside the sample holder assembly and the flow field was reconstructed with computational fluid dynamics simulations. Tian et al. [10] investigated the effects of different surface structure units related to Z-pins-like V_0.9-Si_0.1 rods on the improvement of ablation resistance of C/C-ZrC-SiC and found different improvement mechanisms. Feng et al. [11] studied a novel multilayer coating containing ZrO₂-Y₂O₃, ZrC-ZrO₂, and ZrC-SiC layers (from surface inside), under exposure to an oxyacetylene torch above 2,000°C. Zhao et al. [12] tested wedge-shaped components made of ZrC-SiC-ZrB₂ and ZrC-SiC inhibited carbon/carbon composites with an oxyacetylene torch at the heat flux of 2.38 MW/m² for 120 s. Tong et al. [13] tested the ablation resistance of Zr-Ta-B-SiC multiphase-coated carbon/carbon composites at 2,300°C. It was found that the formed Zt-Ta-O phase presented a densified clustering ceramic layer on the surface, offering effective protection against erosion from high-speed and high-temperature flame. Shen et al. [14] investigated the ablation of C/C composites in a nitrogen plasma torch with a heat flux of ∼25 MW/m², with the reaction products calculated based on the principle of free-energy minimum.

It is well known that mechanical properties of C/C composites are influenced by oxidation because the solid-phase components transform into the gas phase. So, it is important to assess their mechanical behavior before and after oxidation. Xie et al. [15] analyzed the impact resistance of 3D needle-punched C/C composites at 1,200°C numerically and experimentally. Li et al. [16] studied tensile behavior of 3D needle-punched C_f/SiC-Al composites experimentally and analyzed their cross-section and fracture regions with scanning electron microscopy. Liu et al. [17] compared the mechanical properties and thermal conductivity of four C/C composites. Lim et al. [18] presented a material constitutive model for 3D needle-punched carbon/silicon carbide (C_f/SiC_m) composite with a complex mesoscale structure, with the Drucker–Prager plasticity theory employed to consider the effect of hydrostatic pressure. Xue et al. [19] measured the compressive strength of C_f/SiC-Al composites and showed that most of the pores in C_f/SiC were filled with Al alloy, enhancing the strength. Qi et al. [20] calculated local stiffness properties of four kinds of internal needle-punched features and established the relationship between the pinhole spacing and fiber breakage with Bayesian inference method. Xu et al. [21] proposed a modified double-notched specimen to investigate shear strength of 3D needled, 3D woven, and 4D woven carbon/carbon composites at 2,000, 2,400, and 2,800°C, and characterized their failure mechanisms. Han [22] proposed a solid-beam mixed mechanical model to investigate the tension properties and progressive damage of NP C/C composites, subsequently predicting [23] their residual mechanical properties after oxidation at 850°C. Still, most of researchers did not consider the effect due to coupling of dynamic oxidation and mechanical behavior.

Extended finite element method has the advantage to avoid a continuous mesh refinement at the tip of a propagating crack [24], thus reducing the computational cost and enabling an optimal convergence rate when capturing the stress concentrations near discontinuities or singularities. Strong formulation finite element method and isogeometric analysis are the potentials of two innovative techniques [25], for a correct determination of stress distributions and concentration factors near discontinuities, despite a limited number of degrees of freedom characterizing the problem. It is very valuable to simulate thermal–mechanical coupling problems with aforementioned computational tools, while there are a lot of difficulties in constructing high-order shape functions of elements under coupling action.

In this study, a thermo-mechanical coupling model was proposed, and the effects of high temperature on the strength and oxidation rate were considered. Then, the volume fraction of fiber bundle during oxidation process was assessed in order to predict the residual strength of the oxidized fiber bundles. A multiscale oxidation behavior of NP C/C composite was simulated, and the progressive damage and oxidation of structures with the coupling effects of the stress and oxidation were investigated.

2 Structure of NP C/C composite

The studied needle-punched composites were produced with needled preforms and a pyrocarbon matrix employing CVI or chemical vapor deposition at the temperature above 2,000°C. The preform was formed by stacking a unidirectional carbon cloth and short-cut fiber felts alternately (Figure 1). Subsequently, it was punched with a needle plate, and some short-cut fibers were carried into interlayers, improving the interlaminar properties.

Figure 1

Schematic diagram of NP C/C composite preform.

3 Homogenization procedure

To assess the effective properties of the manufactured composite, the Mori-Tanaka [26], mean-field homogenization scheme was employed. Under a remote uniform strain ε ¯ , the strain field inside the ellipsoidal inclusion is related to the remote strain by [27]

where the single-inclusion strain concentration tensor H is given as

where S is the Eshelby’s tensor and depends on the geometry of the inclusion and Poisson’s ration v 1 of the matrix.

The effective stiffness tensor 〈 C 〉 of the two-phase composites can be derived by substituting Equations (1) and (2) into Equation (3).

where I is the fourth-order symmetric identity tensor, and B is the strain concentration tensor [28].

4 Thermo-mechanical coupling model

Heat energy can be equivalent to a corresponding strain energy [29], so the strength of material at high temperature can be presented as a function of temperature:

where σ th 0 and E 0 are the initial strength and the elasticity modulus of the material at 30°C, respectively; C p is the specific heat capacity; and T ox is the oxidative induction temperature.

In the diffusion-controlled oxidation state, carbon-fiber bundles are oxidized from their surface inside, so the recession distance of the fiber bundle (Figure 2) x f is developed [30]:

where K f is the oxidation rate of fiber bundle, χ is the oxidant partial pressure, P is the total pressure (Pa), ρ c is the molar density of carbon fiber (mol/m³), R is the gas constant (J/mol K), T is the absolute temperature (K), and D k and D are the Knudsen and Fick diffusion coefficients, respectively.

Figure 2

Schematic diagrams of oxidation cross-section.

Oxidation of the pyrocarbon matrix is controlled by the reaction because oxygen is abundant on the surface, and the recession distance of the matrix x m is developed [28]:

where k 0 is a constant (m/s), Q is the activation energy (J/mol), and N is the molar density of pyrocarbon matrix (mol/m³).

The effective cross-sectional area A ( t ) of the fiber bundle is approximated as

where a and b are the length and the width of the cross-section, respectively.

The effective cross-sectional area of the matrix after oxidation is

where R f is the initial radius of the fiber bundle.

The volume fraction of the fiber bundle after oxidation can be written as follows:

The residual strength of the composite σ r was assessed with the rule of mixture:

5 Damage and failure

The NP C/C composite is a quasi-brittle material, with its failure behavior influenced by oxidation and stress. Oxidation causes the redistribution of stress. So, the damage due to temperature and stress loads should be analyzed. Hashin criteria [31] are employed to predict the failure of fiber bundles:

1. Longitudinal tension failure ( σ 1 > 0 ):

   (11) σ 1 X T 2 + σ 12 2 2 G 12 + 3 4 α σ 12 4 S 12 2 2 G 12 + 3 4 α S 12 4 + σ 13 2 2 G 13 + 3 4 α σ 13 4 S 13 2 2 G 13 + 3 4 α S 13 4 ≥ 1 .

2. Longitudinal compression failure ( σ 1 < 0 ):

   (12) σ 1 X C 2 ≥ 1 .

3. Transverse tension failure ( σ 2 > 0 ):

   (13) σ 2 Y T 2 + σ 12 2 2 G 12 + 3 4 α σ 12 4 S 12 2 2 G 12 + 3 4 α S 12 4 + σ 23 S 23 2 ≥ 1 .

4. Transverse compression failure ( σ 2 < 0 ):

   (14) σ 2 Y C 2 + σ 12 2 2 G 12 + 3 4 α σ 12 4 S 12 2 2 G 12 + 3 4 α S 12 4 + σ 23 S 23 2 ≥ 1 .

5. Out-of-plain tension failure ( σ 3 > 0 ):

   (15) σ 3 Z T 2 + σ 13 2 2 G 13 + 3 4 α σ 13 4 S 13 2 2 G 13 + 3 4 α S 13 4 + σ 23 S 23 2 ≥ 1 .

6. Out-of-plain compression failure ( σ 3 < 0 ):

   (16) σ 3 Z C 2 + σ 13 2 2 G 13 + 3 4 α σ 13 4 S 13 2 2 G 13 + 3 4 α S 13 4 + σ 23 S 23 2 ≥ 1 .

7. Shear failure ( σ 1 > 0 ):

where σ i ( i = 1 , 2 , 3 ) are the longitudinal, transverse, and normal stresses, respectively; σ i j ( i ≠ j ) are the shear stresses in three planes; X , Y _m and Z are the longitudinal, transverse, and normal strengths of fiber bundle, respectively; subscripts T and C denote the tension and compression, respectively; S i j and G i j are the transverse strengths and moduli, respectively; α is a nonlinear coefficient.

The failure of pyrocarbon matrix is predicted with the von Mises criterion:

where σ m is the matrix strength.

6 Simulation and discussions

6.1 Modeling strategy

A one-quarter finite-element model of a representative volume element (RVE) (Figure 3) was developed to improve computational efficiency; the flow chart of simulation is shown in Figure 4. The boundary conditions applied to this model were as follows:

1. The symmetric boundary conditions were applied on the symmetry planes (Figure 3b, blue flags).

2. The surface heat flows (750°C) were applied on other surfaces from outside to inside (Figure 3b, green arrows).

3. The tensile loads were applied on the free-side surface (Figure 3b, orange arrows).

Figure 3

Finite element model of RVE: (a) mesh and (b) boundary conditions.

Figure 4

Flow chart of simulation.

6.3 Progressive coupling damage behavior in oxidation and tension

The progressive damage in the RVE was analyzed with a UMAT subroutine using ABAQUS software package. Different damage modes and oxidation states of components were recorded with the corresponding state variables, in order to study the failure mechanism of NP C/C composites by coupling the effects of oxidation and mechanical loading.

Evolution of oxidation corrosion was investigated with its effect on tensile stress. Every oxidized and damaged element was recorded with state variables; the failed elements due to coupled dynamic oxidation and tension of fiber bundles are shown in Figure 5. Apparently when the axial strain reached 600 με (Figure 5a), failed elements appeared first near the needle-punched areas, due to the oxygen diffused from the cracks to the internal parts of bundles. More failed elements around the needle-punched areas of bundles appeared at 1,200 με (Figure 5b). With the load increased, the oxidized and damaged elements near adjacent punched areas connected gradually (Figure 5c), with more appearing in insular punching area. With the coupling effect of diffusion and mechanical stress, more oxidized and failed elements around punching areas appeared in different fiber bundles (Figure 4d–f). When the strain reached 4,200 με , most of the punched areas were damaged and oxidized (Figure 5g), with the initially oxidized fiber bundle loosing its load-bearing capacity. With the load increasing gradually and continuing oxygen diffusion, more fiber bundles were damaged and oxidized (Figure 5h). At last, the failed elements in each bundle formed a band, so that the composite could not carry any load (Figure 5i).

Figure 5

Evolution of failed elements under coupled effect of oxidation and mechanical loading in fiber bundles for various levels of ε 1 : (a) 600 με , (b) 1 , 200 με , (c) 1 , 800 με , (d) 2 , 400 με , (e) 3 , 000 με , (f) 3 , 600 με , (g) 4 , 200 με , (h) 4 , 800 με , and (i) 5 , 400 με .

7 Experimental verification

Uniaxial tension experiments on the studied NP C/C composite at RT and 750°C were performed, with their results listed in Table 3. The respective stress–strain curves are plotted in Figure 6. Apparently, oxidation caused the degradation of mechanical properties. After oxidation, the tested modulus decreased by 27.6%; the tested tensile strength decreased by 37.5%. The developed finite-element model reproduced the main features of mechanical behavior under combined action of oxidation and tension. The errors between the simulated results and test data were less than 11%; they agreed well with each other.

Figure 6

Stress–strain curves of NP C/C composite.

The ultimate strain of this composite was reduced by 5% due to oxidation. This can be explained by the fact that the un-oxidized pyrocarbon matrix and fiber bundles were exposed to high temperature and their brittleness increased.

8 Conclusion

During the re-entry of a space structure into atmospheric, oxidation and mechanical behaviors of the NP C/C composite interact with each other. The multiscale oxidation behaviors were assessed numerically; it was found that roughness of the oxidized surface was 2.5 mm. A thermo-mechanical coupled model was proposed to predict the residual strength of oxidized carbon-fiber bundles. The mechanical properties of the NP C/C composite were investigated before and after oxidation with simulation and experiment, considering the progressive damage with the coupling effects of tension and oxidation. The elastic modulus and strength of the composite were reduced by up to 40% due to oxidation at 750°C, while the ultimate strain was reduced by 5%. The proposed thermo-mechanical coupled model could be used to predict the failure and residual mechanical properties of C/C composites in the process of oxidation, relevant for their service.