Comparison of prior exposure tensile damage and fracture of two-dimensional C/SiC and SiC/SiC fiber-reinforced ceramic-matrix composites

Abstract

In this paper, a micromechanical constitutive model for prior exposure tensile damage and fracture of fiber-reinforced ceramic-matrix composites is developed considering the multiple damage mechanisms of matrix multicracking, interface debonding and oxidation, and fiber fracture. The relationships between prior exposure temperature, duration time, interface debonding fraction, broken fiber fraction, tensile strength, and fracture strain of C/SiC and SiC/SiC composites are established. The experimental prior exposure tensile damage evolution and final fracture of two-dimensional (2D) C/SiC and SiC/SiC composites are predicted for different temperatures and duration times. The comparison analysis of prior exposure composite tensile strength, fracture strain, interface debonding fraction, and broken fiber fraction between 2D C/SiC and SiC/SiC composites is investigated. The effects of constituent properties and temperature on prior exposure tensile damage and fracture of 2D C/SiC and SiC/SiC composites are discussed. For 2D C/SiC and SiC/SiC composites under prior exposure at 1300℃, the fracture strain decreased with fiber volume, interface shear stress, and prior exposure temperature, and increased with fiber characteristic strength; the tensile strength increased with fiber volume and fiber characteristic strength, and decreased with prior exposure temperature; the interface debonding fraction decreased with fiber volume, and increased with prior exposure temperature; and the fiber broken fraction decreased with fiber volume and fiber characteristic strength, and increased with prior exposure temperature.

Keywords

ceramic-matrix composites prior exposure tensile damage and fracture matrix cracking interface debonding fiber failure

Advancements in aerospace and air vehicle technology rely heavily on the development of structural materials that maintain mechanical performance at elevated temperatures. The engine-related components (i.e., engine ducts, engine vanes, and exhaust flaps) are exposed to extreme temperature environments. Metals and metallic super-alloys have been developed to increase temperature capability, but their melting temperatures are being met and exceeded by current and future operating conditions. The temperature capability of high-performance monolithic ceramic materials far exceeds that of metals, which makes ceramics an obvious candidate for high-temperature applications. However, under mechanical or thermal loading, the high-performance monolithic ceramics are prone to catastrophic failure. Ceramic-matrix composites (CMCs) with the incorporation of reinforcements improve the fracture toughness over that of monolithic ceramics and have already been applied in the hot section components of aero engines (i.e., tail nozzle, combustion chamber, turbine vanes, and blades).^1,2

Under tensile loading, the damage evolution of fiber-reinforced CMCs usually includes three fundamental domains,^3–7 that is: (1) at the applied stress level lower than the proportional limit stress, matrix cracking originates from the defect in the matrix, and following the interface debonding between the fiber and the matrix⁸; (2) at the applied stress level between the proportional limit stress and saturation matrix cracking stress, multiple matrix cracking evolves⁹; and (3) at the applied stress level higher than the saturation matrix cracking stress, fiber failure occurs leading to final fracture of the composite.¹⁰ Naslain et al.¹¹ established the relationship between statistical parameters of both the fiber and the matrix, the fiber/matrix interfacial parameters, environment, and the tensile curves of Nicalon™ SiC/SiC. Nozawa et al.¹² found that the axial fiber volume played an important role in achieving good tensile properties. The tensile strength, elastic modulus, and proportional limit stress increased with fiber volume. Guo and Kagawa¹³ investigated the tensile mechanical properties of Nicalon™ and Hi-Nicalon™ SiC/BN/SiC composites at temperatures between 298 and 1400 K in an air atmosphere. The tensile strength dropped from σ_UTS = 140 MPa at T = 800 K to σ_UTS = 41 MPa at T = 1200 K. Zhu et al.¹⁴ investigated the tensile behavior of a three-dimensional (3D) Si-Ti-C-O (Tyranno™) fiber-reinforced [Si-Ti-C-O] matrix composite at room temperature, 1200℃, 1300℃, 1400℃, and 1450℃ in an air atmosphere. The tensile strength and fracture strain decreased with temperature. Ruggles-Wrenn et al.¹⁵ investigated the effect of the loading rate (i.e., 0.0025 and 25 MPa/s) on the monotonic tensile behavior and tensile strength of a Nextel™ 720/Alumina composite at 1200℃ in an air atmosphere. At the loading rate of 0.0025 MPa/s, strain increased nonlinearly with stress, and the change rate of strain reversed its sign at the loading rate of 25 MPa/s. Wallentine¹⁶ investigated the effect of prior exposure at elevated temperature on tensile properties and the stress–strain behavior of different fiber-reinforced CMCs, that is, SiC/[Si-N-C], C/SiC, C/[SiC-B₄C], and SiC/[SiC-B₄C]. The CMCs were heat treated in laboratory air for duration times of 10, 20, 40, and 100 h at over-temperature (1300℃ or 1400℃) and for 100 h at operating temperature (1200℃ or 1300℃), and then tensile loaded to failure at room temperature. The prior exposure at elevated temperature caused a reduction of tensile strength and changed the tensile stress–strain behavior due to oxidation of the interphase and fibers. Li et al.¹⁷ developed an approach to predict the tensile damage evolution of a unidirectional C/SiC composite at room temperature. Wang et al.¹⁸ analyzed the monotonic and cyclic loading/unloading tensile behavior of a two-dimensional (2D) C/SiC composite at room temperature, obtained the interfacial sliding stress and thermal residual stress through hysteresis analysis, and predicted first the matrix cracking stress and stress–strain behavior. Dassios et al.¹⁹ investigated the effects of thermal residual stress, cyclic loading, and the presence of notches on the tensile performance of a SiC/barium-magnesium aluminosilicate (BMAS) composite at room temperature. Li et al.,⁴ Li,⁶ and Liang and Jiao²⁰ predicted the tensile behavior of cross-ply, 2D, and 2.5D CMCs at room temperature considering different damage mechanisms. Li²¹ investigated matrix multiple cracking and interface debonding of minicomposite, unidirectional, and 2D SiC/SiC composites with different fiber volumes and interphases. However, in the researches mentioned above, the constitutive relationship and damage models for prior exposure tensile damage evolution and fracture were not developed, and comparisons of prior exposure tensile damage evolution and fracture between C/SiC and SiC/SiC composites were not conducted.

The objective of this paper is to develop micromechanical prior exposure tensile damage and fracture models and perform comparison analysis of prior exposure tensile damage and fracture between 2D C/SiC and SiC/SiC composites. Multiple damage mechanisms of matrix cracking, interface debonding and oxidation, and fiber fracture are considered in the prior exposure temperature and duration time-dependent tensile damage and fracture. The effects of material properties and temperature on the prior exposure tensile damage and fracture of 2D C/SiC and SiC/SiC composites are discussed. The experimental prior exposure tensile damage and fracture of 2D C/SiC and SiC/SiC composites are predicted for different temperatures and duration times.

Materials and experimental procedures

Two-dimensional C/SiC composite

The Hex Tow® IM7 carbon fiber-reinforced SiC matrix composite was processed by polymer infiltration and pyrolysis (PIP). The Hex Tow® fibers were woven into a 5HSW fabric and coated with BN + Si₃N₄ using chemical vapor infiltration (CVI). The experimental results were obtained by Wallentine.¹⁶ The fiber volume of the C/SiC composite was about 45.7%, and the composite density was about 2.1 g/cm³. The dimensions of the dog bone-shaped specimen were 100 mm total length, 8 mm width, and 2.8 mm thickness in the gage section.

The 2D C/SiC composite was subjected to thermal exposure at 1200℃ and 1300℃ for different duration times. A Barnstead International, ThermoLyne model 46200 high-performance 1700℃ furnace was utilized for thermal exposures. The furnace was controlled externally by computer and programmed to heat at 10℃/minute until reaching the prescribed temperature. Following the prescribed exposure time at temperature, the furnace was cooled at 10℃/minute or slower until it reached approximately 60℃. All heat treatments were accomplished in air. After thermal exposure, the monotonic tensile tests were performed using an MTS Systems Corporation model 810 Material Test System servo hydraulic load frame equipped with an MTS model 632.13E-20 axial extensometer. To elucidate the deformation mechanisms, displacement controlled tensile tests were performed with a displacement rate of 0.05 mm/s. Six specimens were tested for each condition after thermal exposure at 1200℃ for 100 h and 1300℃ for 40 and 100 h. The representative tensile stress–strain curve was chosen for the present analysis.

Two-dimensional SiC/SiC composite

The Hi-Nicalon™ SiC fiber-reinforced layered silicon carbide and boron carbide matrix composite was processed by CVI. The Hi-Nicalon™ fibers were woven into a 5HSW fabric and were coated with pyrolytic carbon and boron carbide via CVI. The experimental results were obtained by Wallentine.¹⁶ The fiber volume of the SiC/SiC composite was about 34.1%. The dimensions of the dog bone-shaped specimen were 100 mm total length, 8 mm width, and 2.8 mm thickness in the gage section.

The 2D SiC/SiC composite was subjected to thermal exposure at 1300℃ and 1400℃ for different duration times. A Barnstead International, ThermoLyne model 46200 high-performance 1700℃ furnace was utilized for thermal exposures. The furnace was controlled externally by computer and programmed to heat at 10℃/minute until reaching the prescribed temperature. Following the prescribed exposure time at temperature, the furnace was cooled at 10℃/minute or slower until it reached approximately 60℃. All heat treatments were accomplished in air. After thermal exposure, the monotonic tensile tests were performed at room temperature. To elucidate the deformation mechanisms, displacement controlled tensile tests were performed with a displacement rate of 0.05 mm/s. Six specimens were tested for each condition after thermal exposure at 1300℃ for 100 h and 1400℃ for 10 h. The representative stress–strain curve was chosen for the present analysis.

Theoretical analysis

Under prior exposure at elevated temperature, oxygen enters into the composite through processing-induced microcracks, leading to oxidation of the interphase and fibers.^22–27 When matrix cracking and interface debonding occur, the oxidation region affects the micro stress field of the damaged composite. In this section, a micromechanical constitutive model for prior exposure tensile damage and fracture of fiber-reinforced CMCs is developed considering multiple damage mechanisms of matrix cracking, interface debonding, and fiber fracture. The damage parameters of matrix crack spacing, interface debonding length, and fiber broken fraction are used to describe tensile damage evolution.

Stress analysis considering prior exposure damage

A unit cell is extracted from the damaged composite to analyze the micro stress field, as shown in Figure 1. The unit cell is divided into the interface oxidation region (x ∈ [0, ζ(t)]), the interface slip region (x ∈ [ζ(t), l_d(t)]), and the interface bonding region (x ∈ [l_d(t), l_c(t)/2]). In the interface oxidation and slip regions, stress carried by the fiber depends on the interface frictional sliding stress²⁸

\frac{d σ_{f} (x)}{dx} = - \frac{2 τ_{i} (x)}{r_{f}}

(1)

where τ _i (x) is the interface shear stress along the x axial and r_f is the fiber radius.

Figure 1.

Unit cell of the shear-lag model.

In the interface oxidation region (x ∈ [0, ζ(t)]) and interface slip region (x ∈ [ζ(t), l_d(t)]), the interface shear stress is given by

τ_{i} (x) = {\begin{matrix} τ_{f}, x \in [0, ζ (t)] \\ τ_{i}, x \in [ζ (t), l_{d} (t)] \end{matrix}

(2)

where ζ(t) is the time-dependent interface oxidation length and l_d(t) is the time-dependent interface debonding length.

In the interface bonding region (x ∈ [l_d(t), l_c(t)/2]), the interface shear stress is given by

τ_{i} (x) = \frac{G_{m} (w_{m} - w_{f})}{r_{f} \ln (\bar{R} / r_{f})}, x \in [l_{d} (t), \frac{l_{c} (t)}{2}]

(3)

where w_f = w(r_f, x) and w_m = w(

\bar{R}

, x) are the axial displacements of the fiber and the matrix, respectively, and l_c(t) is the time-dependent matrix crack spacing.

Considering fiber failure, the fiber axial stresses in the interface oxidation region (x∈[0, ζ(t)]), interface slip region (x∈[ζ(t), l_d(t)]), and interface bonding region (x∈[l_d(t), l_c(t)/2]) are given by

σ_{f} (x) = {\begin{matrix} Φ (t) - \frac{2 τ_{f}}{r_{f}} x, x \in [0, ζ (t)] \\ Φ (t) - \frac{2 τ_{f}}{r_{f}} ζ (t) - \frac{2 τ_{i}}{r_{f}} [x - ζ (t)], x \in [ζ (t), l_{d} (t)] \\ σ_{fo} + {Φ (t) - \frac{2 τ_{f}}{r_{f}} ζ (t) - \frac{2 τ_{i}}{r_{f}} [l_{d} (t) - ζ (t)] - σ_{fo}} \\ exp (- ρ \frac{x - l_{d} (t)}{r_{f}}), x \in [l_{d} (t), \frac{l_{c} (t)}{2}] \end{matrix}

(4)

where ρ is the shear-lag model parameter, σ_fo is the fiber axial stress in the interface bonding region, and Φ(t) is the intact fiber stress.

Matrix cracking considering prior exposure damage

The stochastic matrix cracking model is used to describe multiple matrix cracking evolution inside fiber-reinforced CMCs

l_{c} (σ, t) = Λ δ_{R} (t) {1 - exp [- (\frac{σ - (σ_{mc} - σ_{th})}{(σ_{R} - σ_{th}) - (σ_{mc} - σ_{th})})^{m}]}^{- 1}

(5)

where Λ is the final nominal crack space, m is the matrix Weibull modulus, σ_mc is the first matrix cracking stress, σ_th is the thermal residual stress, σ_R is the matrix cracking characteristic strength, and

δ_{R} = (1 - \frac{τ_{f}}{τ_{i}}) ζ (t) + \frac{r_{f}}{2 τ_{i}} \frac{V_{m} E_{m}}{V_{f} E_{c}} σ_{R}

(6)

where V_f and V_m are the fiber and matrix volume, respectively, and E_m and E_c are the elastic modulus of the matrix and composite, respectively.

Interface debonding considering prior exposure damage

The fracture mechanic criterion is used to determine time-dependent interface debonding length²⁹

ξ_{d} = \frac{r_{f} σ}{4 V_{f}} \frac{\partial w_{f} (x = 0, t)}{\partial l_{d}} - \frac{1}{2} \int_{0}^{l_{d}} τ_{i} \frac{\partial v (x, t)}{\partial l_{d}} d x

(7)

where ξ_d is the interface debonding energy, w_f(x = 0) is the fiber axial displacement at the matrix cracking plane, and v(x) is the relative displacement between the fiber and the matrix.

Substituting w_f(x = 0, t) and v(x, t) into Equation (7), the time-dependent interface debonding length is obtained as

\begin{matrix} l_{d} (t) = (1 - \frac{τ_{f}}{τ_{i}}) ζ (t) + \frac{r_{f}}{2} (\frac{V_{m} E_{m} σ}{V_{f} E_{c} τ_{i}} - \frac{1}{ρ}) \\ - \sqrt{(\frac{r_{f}}{2 ρ})^{2} + \frac{r_{f} V_{m} E_{m} E_{f}}{E_{c} τ_{i}^{2}} ξ_{d}} \end{matrix}

(8)

Fiber failure considering prior exposure damage

The Global Load Sharing criterion is used to determine the stress distribution between the intact and fracture fibers⁰

\frac{σ}{V_{f}} = Φ (1 - P (Φ)) + \frac{2 τ_{f}}{r_{f}} á L ñ P (Φ)

(9)

where

á L ñ

denotes the average fiber pullout length and P(Φ) is the fiber broken fraction

P (Φ) = 1 - exp [- (\frac{Φ}{σ_{c}})^{m_{f} + 1}]

(10)

where m_f is the fiber Weibull modulus and σ_c is the fiber characteristic strength of a fiber length δ_c.

Tensile stress–strain relationship considering prior exposure damage

When no damage occurs, the composite strain is determined as

ɛ_{c} = σ / E_{c}

(11)

When damages of matrix cracking, interface debonding, and fiber fracture occur, the composite strain is

ɛ_{c} = \frac{2}{E_{f} l_{c}} \int_{l_{c} / 2} σ_{f} (x) d x - (α_{c} - α_{f}) Δ T

(12)

where α_f and α_c are the fiber and composite thermal expansion coefficient, respectively, and ΔT is the temperature difference between the test temperature and the fabricated temperature.

When matrix cracking, interface debonding, and fiber failure occur, substituting Equation (4) into Equation (12), the composite strain is

\begin{matrix} ɛ_{c} (t) = \frac{Φ}{E_{f}} η (t) + \frac{τ_{f}}{E_{f}} \frac{l_{d}}{r_{f}} η (t) ϕ^{2} (t) - \frac{2 τ_{f}}{r_{f} E_{f}} \frac{l_{d}}{r_{f}} η (t) ϕ (t) \\ - \frac{τ_{i}}{E_{f}} \frac{l_{d}}{r_{f}} η (t) (1 - ϕ (t))^{2} + \frac{σ_{fo}}{E_{f}} (1 - η (t)) \\ + \frac{2}{ρ E_{f}} {Φ \frac{r_{f}}{l_{c}} - τ_{f} η (t) ϕ (t) - τ_{i} η (t) (1 - ϕ (t)) - σ_{fo}} \\ \times [1 - exp (- \frac{ρ}{2} \frac{l_{c}}{r_{f}} (1 - η (t)))] - (α_{c} - α_{f}) Δ T \end{matrix}

(13)

where the intact fiber stress is given by Equation (9), the time-dependent interface debonding length is given by Equation (8), and the time-dependent matrix crack spacing is given by Equation (5), η(t) is the interface debonding fraction, and ϕ(t) is the interface oxidation fraction

η (t) = \frac{2 l_{d} (t)}{l_{c}}, ϕ (t) = \frac{ζ (t)}{l_{d} (t)}

(14)

Results and discussion

The effects of constituent properties and prior exposure temperature on prior exposure tensile damage and fracture of C/SiC and SiC/SiC composites are analyzed. The material properties of the C/SiC and SiC/SiC composites are listed in Table 1.

Table 1.

Material properties of two-dimensional C/SiC and SiC/SiC composites

Items	C/SiC	SiC/SiC
V _f	0.3	0.3
E_f/GPa	230	220
r_f/µm	3.5	7
α_f/(10^–6/K)	0	3.5
α_m/(10^–6/K)	4.6	4.6
τ_i/MPa	40	20
τ_f/MPa	30	1
ζ_d/(J/m²)	0.1	0.1

Effects of fiber volume, interface shear stress, fiber strength, and temperature on prior exposure tensile damage and fracture of C/SiC

The effects of fiber volume, interface shear stress, fiber characteristic strength, and prior exposure temperature on prior exposure tensile damage and fracture of the C/SiC composite are shown in Figures 2–5.

Figure 2.

Effect of fiber volume (V_f = 0.2, 0.3, and 0.4) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the C/SiC composite under prior exposure at T = 1300℃ and duration time t = 40 h.

Figure 5.

Effect of prior exposure temperature (T = 800℃, 1000℃, and 1200℃) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the C/SiC composite.

Under prior exposure temperature T = 1300℃ and duration time t = 40 h, the nonlinear tensile strain decreases and the fracture strength increases with fiber volume; the interface debonding fraction and broken fiber fraction decrease with fiber volume, as shown in Figure 2. When the fiber volume increases from V_f = 0.2 to 0.4, tensile fracture strain decreases from ɛ_c = 0.469% to 0.432%, and the fracture strength increases from σ_UTS = 222 to 445 MPa. When V_f = 0.2, the interface debonding fraction increases to η = 0.69 at σ_UTS = 222 MPa, and the broken fiber fraction increases to P = 0.12 at σ_UTS = 222 MPa; and when V_f = 0.4, the interface debonding fraction increases to η = 0.69 at σ_UTS = 445 MPa, and the broken fiber fraction increases to P = 0.13 at σ_UTS = 445 MPa. When the fiber volume increases, the stress carried by the fiber increases, leading to the decrease of the interface debonding length, as shown in Equation (8). The interface debonding is the main reason for the nonlinear strain of CMCs. The decrease of the interface debonding fraction leads to the decrease of nonlinear strain during matrix cracking and interface debonding.

Under prior exposure temperature T = 1300℃ and duration time t = 40 h, the nonlinear tensile strain decreases with interface shear stress, as shown in Figure 3. When the interface shear stress increases from τ_f = 10 to 30 MPa, the tensile failure strain decreases from ɛ_c = 0.57% to ɛ_c = 0.44%. When the interface shear stress increases, the stress transfer between the fiber and the matrix increases, leading to the decrease of the interface debonding length, as shown in Equation (8). For high interface shear stress, the fiber pullout length is much shorter than that of low interface shear stress, which leads to low fracture strain at tensile strength.

Figure 3.

Effect of interface shear stress (τ_f = 10, 20, and 30 MPa) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the C/SiC composite under prior exposure at T = 1300℃ and duration time t = 40 h.

Under prior exposure temperature T = 1300℃ and duration time t = 40 h, the nonlinear tensile strain and the fracture strength increase with fiber characteristic strength, and the broken fiber fraction decreases with fiber characteristic strength, as shown in Figure 4. When fiber characteristic strength increases from σ_c = 1 to 2 GPa, the tensile failure strain increases from ɛ_c = 0.255% to 0.573%, and the fracture strength increases from σ_UTS = 208 to 417 MPa. When the fiber characteristic strength increases, fiber fracture occurs at the high stress level, and the stress carrying capacity of the fiber increases, leading to high composite tensile strength and fracture strain.

Figure 4.

Effect of fiber characteristic strength (σ_c = 1, 1.5, and 2 GPa) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the C/SiC composite under prior exposure at T = 1300℃ and duration time t = 40 h.

Under prior exposure temperature T = 800℃, 1000℃, and 1200℃ and duration time t = 40 h, the nonlinear tensile strain and fracture strength decrease with the prior exposure temperature, the interface debonding fraction increases with prior exposure temperature, and the broken fiber fraction increases with prior exposure temperature, as shown in Figure 5. When prior exposure temperature increases from T = 800℃ to 1200℃, the tensile failure strain decreases from ɛ_c = 0.267% to ɛ_c = 0.183%, and the fracture strength decreases from σ_UTS = 229 MPa to σ_UTS = 132 MPa. When the prior exposure temperature is T = 800℃, the interface debonding fraction increases to η = 0.1 at σ_UTS = 229 MPa, and the broken fiber fraction increases to P = 0.12 at σ_UTS = 229 MPa; and when T = 1200℃, the interface debonding fraction increases to η = 0.68 at σ_UTS = 132 MPa, and the broken fiber fraction increases to P = 0.124 at σ_UTS = 132 MPa. When the prior exposure temperature increases, the damages of interface oxidation and degradation of fiber strength increase, leading to the increase of fiber broken fraction, and the decrease of fracture strength and strain.

Effects of fiber volume, interface shear stress, fiber strength, and temperature on prior exposure tensile damage and fracture of SiC/SiC

The effects of fiber volume, interface shear stress, fiber characteristic strength, and prior exposure temperature on prior exposure tensile damage and fracture of the SiC/SiC composite are show in Figures 6–9.

Figure 6.

Effect of fiber volume (V_f = 0.2, 0.3, and 0.4) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the SiC/SiC composite under prior exposure at T = 1300℃ and duration time t = 100 h.

Under prior exposure temperature T = 1300℃ and duration time t = 100 h, the nonlinear tensile strain decreases, and the fracture strength increases with fiber volume; the interface debonding fraction and broken fiber fraction decrease with fiber volume, as shown in Figure 6. When fiber volume increases from V_f = 0.2 to 0.4, the tensile fracture strain decreases from ɛ_c = 0.93% to 0.92%, and the fracture strength increases from σ_UTS = 354 to 709 MPa. When V_f = 0.2, the interface debonding fraction increases to η = 1 at σ = 192 MPa, and the broken fiber fraction increases to P = 0.12 at σ_UTS = 354 MPa; and when V_f = 0.4, the interface debonding fraction increases to η = 1 at σ_UTS = 459 MPa, and the broken fiber fraction increases to P = 0.13 at σ_UTS = 709 MPa.

Under prior exposure temperature T = 1300℃ and duration time t = 100 h, the nonlinear tensile strain decreases with interface shear stress, as shown in Figure 7. When the interface shear stress increases from τ_f = 5 to 15 MPa, the tensile failure strain decreases from ɛ_c = 0.89% to 0.76%.

Figure 7.

Effect of interface shear stress (τ_f = 5, 10, and 15 MPa) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the SiC/SiC composite under prior exposure at T = 1300℃ and duration time t = 100 h.

Under prior exposure temperature T = 1300℃ and duration time t = 100 h, the nonlinear tensile strain and the fracture strength increase with fiber characteristic strength, and the broken fiber fraction decreases with fiber characteristic strength, as shown in Figure 8. When fiber characteristic strength increases from σ_c = 1 to 2 GPa, the tensile failure strain increases from ɛ_c = 0.35% to 0.73%, and the fracture strength increases from σ_UTS = 208 to 417 MPa.

Figure 8.

Effect of fiber characteristic strength (σ_c = 1, 1.5, and 2 GPa) on (a) the prior exposure tensile stress–strain curves, (b) the interface debonding fraction versus applied stress curves, and (c) the broken fiber fraction versus applied stress curves of the SiC/SiC composite under prior exposure at T = 1300℃ and duration time t = 100 h.

Figure 9.

Under prior exposure temperature T = 800℃, 1000℃, and 1200℃ and duration time t = 100 h, the nonlinear tensile strain and fracture strength decrease with prior exposure temperature, the interface debonding fraction increases with prior exposure temperature, and the broken fiber fraction increases with prior exposure temperature, as shown in Figure 9. When the prior exposure temperature increases from T = 800℃ to 1200℃, the tensile failure strain decreases from ɛ_c = 0.213% to 0.087%, and the fracture strength decreases from σ_UTS = 149 to 86 MPa. When the prior exposure temperature is T = 800℃, the interface debonding fraction increases to η = 0.54 at σ_UTS = 149 MPa, and the broken fiber fraction increases to P = 0.12 at σ_UTS = 149 MPa; and when T = 1200℃, the interface debonding ratio increases to η = 0.22 at σ_UTS = 86 MPa, and the broken fiber fraction increases to P = 0.13 at σ_UTS = 86 MPa.

Experimental comparisons

The experimental prior exposure tensile damage and fracture of 2D C/SiC and SiC/SiC composites under prior exposure at T = 1200℃, 1300℃, and 1400℃ are predicted using the developed damage models.

Tensile damage and fracture of 2D C/SiC under prior exposure at T = 1200℃ and 1300℃

The tensile damage and fracture of the 2D C/SiC composite at room temperature and after prior exposure at T = 1200℃ and 1300℃ are shown in Figure 10. The tensile stress–strain relationship can be determined by Equation (11) when the composite is without damage and Equation (13) when the composite is damaged. After prior exposure at elevated temperature, the damages of interface oxidation and degradation of fiber strength occur inside of the C/SiC composite, leading to the increase of interface debonding fraction during the stage of matrix cracking and interface debonding, and the decrease of tensile strength.

Figure 10.

(a) Experimental and predicted tensile stress–strain curves. (b) The interface debonding fraction versus applied stress curve. (c) The broken fiber fraction versus applied stress curve of the two-dimensional C/SiC composite at room temperature and after prior exposure at elevated temperature. RT: room temperature.

At room temperature, the tensile stress–strain curve of the 2D C/SiC composite exhibits obvious nonlinear with fracture strain ɛ_c = 0.45% and tensile strength σ_UTS = 286 MPa. The interface debonding fraction increases to η = 0.38 and the broken fiber fraction increases to P = 0.134. Under prior exposure temperature T = 1300℃ and duration time t = 40 h, the composite fracture strain is ɛ_c = 0.475% and the fracture strength is σ_UTS = 256 MPa. The interface debonding fraction increases to η = 0.7, and the broken fiber fraction increases to P = 0.127. Under prior exposure temperature T = 1300℃ and duration time t = 100 h, the composite fracture strain is ɛ_c = 0.526% and the fracture strength is σ_UTS = 227 MPa. The interface debonding fraction increases to η = 0.7, and the broken fiber fraction increases to P = 0.118. Under prior exposure temperature T = 1200℃ and duration time t = 100 h, the composite fracture strain is ɛ_c = 0.536% and the fracture strength is σ_UTS = 262 MPa. The interface debonding fraction increases to η = 0.7, and the broken fiber fraction increases to P = 0.12.

Tensile damage and fracture of 2D SiC/SiC under prior exposure at T = 1300℃ and 1400℃

The tensile damage and fracture curves of the 2D SiC/SiC composite at room temperature and after prior exposure at T = 1300℃ and 1400℃ are shown in Figure 11. After prior exposure at elevated temperature, the composite tensile strength of the SiC/SiC composite decreased due to the strength degradation of the fiber. However, the interface debonding length approached the matrix crack spacing before the final fraction at room temperature, and after prior exposure, the interface debonding fraction increased at the low stress level, and approached complete interface debonding before final fracture.

Figure 11.

(a) Experimental and predicted tensile stress–strain curves. (b) The interface debonding fraction versus applied stress curve. (c) The broken fiber fraction versus applied stress curve of the two-dimensional SiC/SiC composite at room temperature and after prior exposure at elevated temperature. RT: room temperature.

At room temperature, the tensile stress–strain curve of the 2D SiC/SiC composite exhibits obvious nonlinear with fracture strain ɛ_c = 0.84% and tensile strength of σ_UTS = 392 MPa. The interface debonding fraction increases to η = 1 and the broken fiber fraction increases to P = 0.128. Under prior exposure temperature T = 1300℃ and duration time t = 100 h, the composite fracture strain is ɛ_c = 0.983% and the fracture strength is σ_UTS = 303 MPa. The interface debonding fraction increases to η = 1.0, and the broken fiber fraction increases to P = 0.125. Under prior exposure temperature T = 1400℃ and duration time t = 10 h, the composite failure strain is ɛ_c = 0.958% and the fracture strength is σ_UTS = 267 MPa. The interface debonding fraction increases to η = 1.0, and the broken fiber fraction increases to P = 0.118.

Comparison analysis of C/SiC and SiC/SiC composites

Due to interface oxidation and fiber strength degradation after prior exposure at elevated temperature, the composite tensile strength decreased, and the interface debonding fraction increased. Under prior exposure temperature T = 1300℃ and duration time t = 100 h, for the C/SiC composite, the tensile fracture strength decreased 20.6%, and the interface debonding fraction increased 84.2% compared with tensile strength at room temperature; however, for the SiC/SiC composite, the tensile fracture strength decreases 22.7%, and the interface debonding fraction remains unchanged compared with tensile strength at room temperature, due to the complete interface debonding before final fracture.

Conclusions

In this paper, a micromechanical constitutive model for predicting prior exposure tensile damage and fracture of fiber-reinforced CMCs is developed considering the damage mechanisms of matrix cracking, interface debonding, and fiber fracture. The damage evolution process of C/SiC and SiC/SiC composites after prior exposure at elevated temperature for different duration times is obtained using the damage parameters of interface debonding fraction and broken fiber fraction. The effects of fiber volume, interface shear stress, fiber characteristic strength, and temperature on tensile damage and fracture of 2D C/SiC and SiC/SiC composites are discussed.

When the fiber volume increased, the interface debonding fraction decreased, leading to the decrease of the nonlinear tensile strain caused by matrix cracking and interface debonding; and the loading carrying capacity of fiber increased, leading to the increase of fracture strength and the decrease of the broken fiber fraction.

When interface shear stress increased, the loading transfer between the fiber and the matrix increased, and the interface debonding length decreased, leading to the decrease of nonlinear tensile strain during matrix cracking and interface debonding.

When fiber characteristic strength increased, the broken fiber fraction decreased, leading to higher tensile fracture strength.

When the prior exposure temperature increased from T = 800℃ to 1200℃, the interface oxidation length increased, and the fiber strength decreased, leading to the increase of the interface debonding length and broken fiber fraction, and the decrease of tensile fracture strength.

The effects of prior exposure in different environments of steam and combustion on the tensile damage and fracture of C/SiC and SiC/SiC composites will be investigated, and the dispersity of the mechanical behavior will also be considered in a further study.

Footnotes

Acknowledgements

The author would also thank the anonymous reviewers and the editor for their valuable comments on an earlier version of the paper.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. NS2019038).

ORCID iD

Longbiao Li

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