## Abstract

Ultra-high-temperature materials have been widely used as key components in high-end equipment. However, the existing studies are mainly conducted at room and moderate temperatures. Besides, they are mainly carried out by experiments. Theories on the temperature dependence of fracture strength are rarely reported. In this work, experimental methods for the ultra-high-temperature tensile properties of advanced materials and the elastic–plastic properties of coatings are developed, respectively, based on induction heating and radiation furnace heating technologies. A temperature-dependent fracture strength model for ceramics is proposed in the view of energy. The experimental methods and theoretical model are verified on the 2D plain-weave carbon fiber reinforced silicon carbide thermal structure composite, yttria-stabilized zirconia thermal barrier coating, and Si3N4 ceramics. The study shows that the mechanical properties of materials decrease significantly at ultra-high temperatures. The results are useful for the applications of ultra-high-temperature materials in thermal structure engineering.

## 1 Introduction

Ultra-high-temperature materials have been widely used as key components in high-end equipment [1]. For example, the materials for thermal protection purposes of hypersonic vehicles can serve above 1800 °C even to 2400 °C temporarily [2]. The hot structures of the high thrust-weight ratio aero-engines can work long term above 1600 °C [3]. Ceramics not only have good temperature capability but also excellent resistance to environment erosion-corrosion, which make them the potential candidates for the ultra-high-temperature applications, such as, the blades, nozzles, and combustor liners of the ceramic gas turbine [4]. However, due to the inherent brittleness, the thermal shock resistance of ceramics is poor [5,6]. To overcome this main drawback, ceramic matrix composites have been developed and are referred to as the most promising materials for ultra-high-temperature structural applications in thermal shock environments, such as the space vehicle's thermal protection systems and the exit cones of non-cooled liquid rocket engines [1,2]. Besides, coatings are often used to improve the resistance to temperature or protect the hot components in harsh environments and extend the component lifetimes [1,2].

Recently, a lot of efforts have been made to study the mechanical properties of advanced materials and coatings at elevated temperatures. Zhang et al. [7] Wang et al. [8] and Cheng et al. [9] investigated the monotonic tensile and tension–tension fatigue characteristics of a 2D plain-weave carbon fiber reinforced silicon carbide (C/SiC) composite at room temperature (RT) and 1300 °C. In their experiments, the middle of the specimen was heated by an induction coil, and the two ends of the specimen were clamped and connected to an Instron 8801 hydraulic servo fatigue testing system. Yang et al. [10] studied the tensile behavior of a 2D C/SiC material from RT to 1200 °C by using a mechanical testing machine (CSS-DNS-100, Changchun, China) to load and a furnace to heat the middle part of the specimen. Yoon et al. [11] investigated the tensile and compressive properties of a C/SiC composite at RT, 500 °C, and 900 °C on an MTS 810 universal testing machine equipped with a furnace. In addition, Watanabe et al. [12] designed a probe for measuring the plastic deformation of porous thermal barrier coatings (TBCs) and studied the mechanical properties of yttria-stabilized zirconia containing 7 wt % yttria (7YSZ) at temperatures up to 1137 °C. Jan et al. [13] investigated the indentation creep behavior of a free-standing 7YSZ TBC on an impression test system with a flat-ended cylindrical indenter from 1100 °C to 1300 °C. Kim and Heuer [14] studied the elastic and plastic deformation behaviors of an electron beam physical-vapor-deposited YSZ TBC from RT to 900 °C using an instrumented high-temperature vacuum displacement-sensitive indenter. Overall, these studies have deepened the understanding of the mechanical properties and fracture mechanisms of ultra-high-temperature materials. However, they are mainly carried out at room and moderate temperatures. Besides, the mechanical properties of materials at elevated temperatures are mainly studied by experiments. Theories on the temperature-dependent fracture strength of solids are rarely reported.

In the present work, ultra-high-temperature mechanical testing methods for both advanced materials and coatings are presented. Besides, a temperature-dependent fracture strength model for ceramics is proposed. The tensile properties of a 2D plain-weave chemical vapor infiltrated (CVI) C/SiC composite, the elastic–plastic properties of an 8YSZ coating, and the fracture strength of Si3N4 ceramics at elevated temperatures are studied to verify the developed methods. The results contribute to a broader understanding of the mechanical properties of ultra-high-temperature materials. At the same time, the study is useful for the design, application, and evaluation of the reliability of ultra-high-temperature materials in thermal structure engineering.

## 2 Experimental and Theoretical Methods

### 2.1 Ultra-High-Temperature Tensile Testing for Advanced Materials.

An ultra-high-temperature testing machine for the mechanical properties of advanced materials is developed based on the induction heating technology. It allows for mechanical testing (tension, compression, bending, and shear) of materials in controlled environments (air, inter atmosphere, and oxygen partial pressure from 4 Pa to 0.91 atm) and can achieve testing temperatures as high as 1950 °C in oxygen atmosphere with a heating rate of >250 °C min–1 and 2600 °C in inert atmosphere with a heating rate of > 600 °C min–1. As illustrated in Fig. 1, the specimen is heated by heat radiation from the susceptor heated by induction heating and is clamped by high-temperature alloy grips outside the insulations. The deformation of the specimen is measured by a high-temperature axial extensometer. The temperature of the specimen is measured by a two-color optical pyrometer. The force is measured by a weighing sensor calibrated before the tests.

The C/SiC specimens used in this study were fabricated by the CVI process in the Science and Technology on Thermostructural Composite Materials Laboratory, Northwestern Polytechnical University, Xi'an, China [15]. The tensile tests were performed according to ASTM C1359—13. The pressure in the high-temperature furnace was vacuumed to <5 Pa, followed by introducing high-purity argon (>99.999%) to prevent the specimen from oxidation during testing. The heating rate was ∼50 °C min–1. The specimen was held at each testing temperature for 10 min to reach thermal equilibrium. The temperature fluctuation was ±1 °C at each holding temperature. The beam speed of the test machine was 0.5 mm min–1. At each temperature, 3–5 specimens were tested based on the dispersion of the results. The microstructures of the specimens after testing were checked by scanning electron microscopy (SEM; S-3400, Hitachi, Ltd., Tokyo, Japan).

### 2.2 Ultra-High-Temperature Indentation Testing for Coatings.

8YSZ coating, kindly provided by Beijing Golden Wheel Special Machine Co., Ltd., Beijing, China, was chosen and evaluated in this study. The coating was deposited on the flat polycrystalline alumina by the air plasma spraying process [16]. To study the elastic–plastic behavior, a Vickers tip was adopted to conduct the indentation tests on the surface of the top ceramic coating under a maximum load of 15 N at RT. A spherical tip was used at high temperatures under a maximum load of 1 N. To minimize the thermal drift, the indenter was first moved to contact with the specimen with an extremely light load for a few minutes at high temperatures. When the thermal drift rate remained almost the same, the indenter was penetrated into the coating to conduct indentation tests.

### 2.3 Temperature-Dependent Fracture Strength Model for Ceramics.

The increases both in stress and temperature contribute to the fracture of materials. Assume that the total energy associated with the onset of fracture of ceramics is temperature-independent. This energy storage capacity can be expressed by the strain energy and heat energy as [17]
$WTOTAL=Wσth(T)+k(WT(T)+ΔH)$
(1)
where WTOTAL is the energy storage capacity per unit volume, $Wσth(T)$ and WT(T) are, respectively, the strain energy and the heat energy at temperature T, k is the transfer coefficient between the strain energy and heat energy, and ΔH is the heat energy consumption during the melting process.
$Wσth(T)$ can be expressed as [18]
$Wσth(T)=πs(T)σf2(T)E(T)$
(2)
where σf (T), s(T), and E(T) are the fracture strength, critical flaw size, and Young's modulus of materials at temperature T, respectively.
WT(T) can be expressed as
$WT(T)=∫T0TCp(T)dT$
(3)
where Cp(T) is the specific heat of materials at temperature T.
Due to $Wσth(Tm+)=0$ and WT(T0) = 0, k can be obtained as
$k=1∫T0TmCp(T)dT+ΔHπs(T0)σf2(T0)E(T0)$
(4)
where ΔH = ΔHM is the latent heat of materials.
Combing Eqs. (1)(4), the temperature-dependent fracture strength model for the ceramics can be obtained as
$σf(T)=σf(T0)[s(T0)s(T)E(T)E(T0)(1−∫T0TCp(T)dT∫T0TmCp(T)dT+ΔHM)]1/2$
(5)

## 3 Results and Discussion

### 3.1 Ultra-High-Temperature Tensile Behavior and Fracture Mechanism of the C/SiC Composite.

The typical tensile stress–strain curves of the C/SiC composite measured at RT and 2600 °C in inert atmosphere are shown in Fig. 3. One can see that the C/SiC composite shows linear deformation behavior firstly and then nonlinear characteristics at both RT and 2600 °C. The nonlinear behavior is attributed to the initial defects and cracks which propagate under low tensile load at RT. That at 2600 °C is due to the plastic deformation at ultra-high temperatures. In all cases, the specimens fracture at the maximum load points immediately. (To make the figure clear, the vertical lines falling down from the peak points are not shown in Fig. 3.) The tensile strengths at RT and 2600 °C are 225 ± 39 MPa and 65 ± 15 MPa, respectively. Young's moduli at RT and 2600 °C are, respectively, 85 ± 8.3 GPa and 15 ± 2.5 GPa. The reductions of strength and modulus are, respectively, 71% and 82% of that at RT. This indicates that both the tensile strength and Young's modulus of the C/SiC composite decrease significantly at ultra-high temperatures.

The morphologies of the fractured surfaces of C/SiC specimens tested at RT and 2600 °C in inert atmosphere are checked by SEM and shown in Fig. 4. The stratification phenomenon can be observed, and the fractured surfaces are rather jagged with long fiber bundles for specimens tested at RT (see Fig. 4(a)). The fiber pullout phenomenon is hard to see (Fig. 4(b)). However, fiber bundle debonding and matrix cracking phenomena occur at 2600 °C (Figs. 4(c) and 4(d)). These demonstrate that the mechanical properties of carbon fibers and the SiC matrix degenerate significantly at ultra-high temperatures and explain the reductions in tensile strength and Young's modulus.

### 3.2 Ultra-High-Temperature Elastic–Plastic Properties of YSZ Coating.

The typical load–displacement curves of 8YSZ coating tested at RT, 1400 °C, and 1500 °C in air are shown in Fig. 5. The elastic modulus and hardness can be determined from the load–displacement curves. The values of elastic modulus for 8YSZ coating are 54.34 ± 7.26 GPa, 29.05 ± 6.31 GPa, and 15.20 ± 5.21 GPa at RT, 1400 °C, and 1500 °C, respectively. The corresponding values for hardness are 1.54 ± 0.30 GPa, 0.84 ± 0.13 GPa, and 0.48 ± 0.14 GPa. It is found that the elastic modulus and hardness of 8YSZ coating are sensitive to temperature. Both the elastic modulus and hardness decrease with increasing temperature. The decreases observed in the elastic modulus and hardness may correspond to the enhancement of plasticity. Especially, the dwell displacement at the maximum load become obvious and gets larger at 1400 °C and 1500 °C. This indicates that 8YSZ coating exhibits severe creep behavior during testing. Besides, the authors also measured the fracture toughness of 8YSZ coating at elevated temperatures; see Ref. [16] for details.

### 3.3 Fracture Strength of Si3N4 Ceramics at Elevated Temperatures.

Equation (5) establishes a quantitative relationship between the temperature dependence of the fracture strength and that of Young's modulus, specific heat, and critical flaw size of the materials. As an example, the fracture strength of Si3N4 ceramics at elevated temperatures is calculated. The temperature-dependent Young's modulus used in the calculations is fitted based on the data in Ref. [19]:
$E(T)=310−0.02(T+273.15)exp(−440T+273.15)$
(6)
The specific heat is from Ref. [20]:
$Cp(T)=18.231+26.048×10−3(T+273.15)−1.559×105(T+273.15)−2−6.467×10−6(T+273.15)2$
(7)

In Eqs. (6) and (7), E is in GPa, Cp is in cal mol−1, and T is in °C. Reference temperature T0 = RT and reference strength σf (T0) = 1062 MPa [21]. The latent heat is not considered in this calculation. The flaw size is considered to be temperature-independent. As shown in Fig. 6, the fracture strength of Si3N4 ceramic decreases as the temperature increases. The theoretical values agree well with the experimental results [21]. This indicates that the temperature dependence of the fracture strength of Si3N4 ceramics is mainly determined by the temperature dependences of Young's modulus and specific heat.

## 4 Conclusions

Experimental methods for the ultra-high-temperature tensile properties of advanced materials and the elastic–plastic properties of coatings were presented and verified by testing the mechanical properties of the C/SiC composite and 8YSZ coating. The C/SiC composite shows linear deformation behavior firstly and then nonlinear characteristics at both RT and 2600 °C. The tensile strength and Young's modulus of the C/SiC composite decrease significantly at ultra-high temperatures because of the mechanical properties degradations of carbon fibers and the SiC matrix. The elastic modulus and hardness of 8YSZ coating decrease with increasing temperature due to the enhancement of plasticity. Severe creep behavior of 8YSZ coating was observed at high temperatures. In addition, a temperature-dependent fracture strength model for ceramics was proposed and tested by predicting the tensile strength of Si3N4 ceramics. The results indicate that the temperature dependence of the fracture strength of Si3N4 ceramics is mainly determined by the temperature dependences of Young's modulus and specific heat.

## Funding Data

• National Natural Science Foundation of China (Grant Nos. 11802019, 11802021, and 11727802; Funder ID: 10.13039/501100001809).

• Natural Science Foundation of Chongqing, China (Grant No. cstc2019jcyj-msxmX0038; Funder ID: 10.13039/501100005230).

• Preferential Funds for the Postdoctors Residing in and Coming to Chongqing to Work (Grant No. 2018LY48).

• National Science and Technology Major Project (Grant No. 2017-VI-0020-0093).

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