# Effect of Interface Properties on Tensile and Fatigue Behavior of 2D Woven SiC/SiC Fiber-Reinforced Ceramic-Matrix Composites

Authors: Longbiao Li
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

In this paper, the effect of the fiber/matrix interface properties on the tensile and fatigue behavior of 2D woven SiC/SiC ceramic-matrix composites (CMCs) is investigated. The relationships between the interface parameters of the fiber/matrix interface debonding energy and interface frictional shear stress in the interface debonding region and the composite tensile and fatigue damage parameters of first matrix cracking stress, matrix cracking density, and fatigue hysteresis-based damage parameters are established. The effects of the fiber/matrix interface properties on the first matrix cracking stress, matrix cracking evolution, first and complete interface debonding stress, fatigue hysteresis dissipated energy, hysteresis modulus, and hysteresis width are analyzed. The experimental first matrix cracking stress, matrix cracking evolution, and fatigue hysteresis loops of SiC/SiC composites are predicted using different interface properties.


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## Body

## 1. Introduction

Ceramic matrix composites (CMCs) are widely used in the high-temperature field as a light and high-performance structural composite material. High-quality and high-temperature properties make it possible to replace superalloy materials as one of the candidate materials for aero-engines, especially for aero-engine core engines. In the research and application of CMCs, the existing mature aero-engines are fully utilized for assessment and verification from low temperature to high temperature, stator components to rotor components [1–6]. Firstly, the stator parts with medium temperature (700°C–1000°C) and medium load (less than 120 MPa) were developed, i.e., exhaust nozzle flaps and sealings; then the medium stator parts with high temperature (1000°C∼1300°C) were developed, such as combustion chamber flame tube, flame stabilizer, turbine guide vane, and turbine outer ring; and the stator or rotor parts with higher load (more than 120 MPa), such as high-pressure turbine rotor and stator, have been developed [7–9]. The commercial aero-engines require low fuel consumption, low noise, and low NOx emissions, so new requirements are put forward for pressure ratio and turbine front temperature. CMC has the characteristics of light weight, high-temperature resistance, corrosion resistance, and impact resistance, so it is expected to be used in combustion chambers, turbines, exhaust nozzles, and other components of the next generation of commercial aero-engines [10–12].For fiber-reinforced CMCs, the mechanical properties depend tremendously on the load transfer at the fiber/matrix interface [13, 14]. The interface properties of the fiber/matrix interface shear stress and the interface debonding energy affect the tensile and fatigue behavior of fiber-reinforced CMCs [15–20]. Vagaggini et al. [21] developed an approach to establish the relationship between the interface properties and the hysteresis loops of fiber-reinforced CMCs and divided the interface debonding energy into small and large, which affects the shape of the hysteresis loops upon unloading and reloading. Domergue et al. [22] measured the interface properties of unidirectional SiC/CAS and SiC/SiC composites using the hysteresis loops, and the interface shear stress of SiC/SiC composite is much higher than that of SiC/CAS composite, leading to unsaturation of matrix cracking of SiC/SiC composite till tensile fracture. Curtin et al. [23] predicted the tensile stress-strain behavior of mini-SiC/SiC composite considering matrix cracking evolution, fiber damage, and ultimate failure. It was found that the matrix cracking stress affects the brittle and tough behavior of fiber-reinforced CMCs. Carrere et al. [24] investigated the influence of the interphase on the matrix cracking deflection in mini-SiC/C/SiC composite with a pyrocarbon interphase. The deflection of the matrix cracking depends on the interface bond strength between the fiber and the matrix. Xia and Curtin [25] investigated the high interface shear stress on the tensile strength of fiber-reinforced CMCs considering the stress concentration at the interface debonding tip. When the bond strength is high and the fiber/matrix interface frictional shear stress in the debonding region is low, the stress concentration occurs near the interface debonding tip. Sauder et al. [26] investigated the influence of the interface characteristics on the tensile and loading/unloading behavior of two different mini-SiC/SiC composites. The interphase thickness and the fiber surface roughness affect the fiber/matrix interface shear stress at the debonding region, and then the tensile behavior of fiber-reinforced CMCs. Under cyclic loading, the fiber/matrix interface shear stress decreases with applied cycles, which depends on the peak stress, stress ratio, loading frequency, temperature, and environment [27–35].In this paper, the effect of the fiber/matrix interface properties on the tensile and fatigue behavior of 2D woven SiC/SiC composites is investigated. The relationships between the interface properties and the composite tensile and fatigue damage parameters are established. The effects of the interface properties on the first matrix cracking stress, matrix cracking evolution, first and complete interface debonding stress, fatigue hysteresis dissipated energy, fatigue hysteresis modulus, and fatigue hysteresis width are analyzed. The experimental tensile and fatigue behavior of SiC/SiC composites is predicted for different interface properties.


## 2. Theoretical Analysis

In the present analysis, the fiber failure is considered in the analysis of the first matrix cracking stress, matrix cracking density, interface debonding stress, and the fatigue hysteresis-based damage parameters.


### 2.1. First Matrix Cracking Stress

For the first matrix cracking of fiber-reinforced CMCs, the energy balance relationship can be determined as(1)ασ2+βσ+γ=0,where(2)α=ldEc,β=−2VfldTEc,γ=43τirf2VfEcVmEmEfld3+VfldT2Ef−2Vfτild2rfEfT−Vmζm−4Vfldrfζd,where ld denotes the fiber/matrix interface debonding length; Ef, Em, and Ec denote the fiber, matrix, and composite elastic modulus, respectively; Vf and Vm denote the fiber and the matrix volume, respectively; rf denotes the fiber radius; ζm and ζd denote the matrix fracture energy and the interface debonding energy, respectively; τi denotes the fiber/matrix interface shear stress in the debonding region; and T denotes the fiber intact stress:(3)σVf=TσcTm+11−exp−Tσcm+1,where σc denotes the fiber characteristic strength and m denotes the fiber Weibull modulus.


### 2.2. Matrix Cracking Density

The energy balance relationship to evaluate the matrix cracking evolution is given by(4)Umσ>σmc,lc,ld=Ucrmσmc,l0,where(5)Um=AmEm43VfτiVmrfld2ld+σmo2lc2−ld−2σmoVfVmT−σfo−2VfτirfVmld−rfρexp−ρlc/2−ldrf−1+VfVmT−σfo−2VfτirfVmld2−rf2ρexp−2ρlc/2−ldrf−1,ld<lc2,Amlc36EmτiVfrfVm2,ld=lc2,Ucrm=12kAml0σmocr2Em,where Am is the cross-sectional area of matrix in the unit cell; k denotes the critical matrix strain energy parameter; l0 is the initial matrix crack spacing; and σmocr denotes the matrix axial stress in the interface bonded region at the first matrix cracking stress.


### 2.3. Fatigue Hysteresis-Based Damage Parameters

The initial fiber/matrix interface debonding stressσd and the interface complete debonding stress σb can be obtained as(6)σd=VfEcτiρVmEm1+1+4VmEmEfrfEcρ2τi2ζd,σb=VfEcτiρVmEm1+ρlcrf+1+4VmEmEfrfEcρ2τi2ζd.The fatigue hysteresis dissipated energyUe can be given by(7)Ue=∫σminσmaxεunloadingσ−εreloadingσdσ,where(8)εunloading=TUEf+4τiEfy2rflc−τiEf2y−ld2y+ld−lcrflc−αc−αfΔΤ,ld<lc2,TUEf+4τiEfy2rflc−2τiEf2y−lc/22rflc−αc−αfΔΤ,ld=lc2,εreloading=TREf−4τiEfz2rflc+4τiEfy−2z2rflc+2τiEfld−2y+2zld+2y−2z−lcrflc−αc−αfΔΤ,ld<lc2,TREf−4τiEfz2rflc+4τiEfy−2z2rflc−2τiEflc/2−2y+2z2rflc−αc−αfΔΤ,ld=lc2,where TU and TR denote the intact fiber stress upon unloading and reloading, respectively.The fatigue hysteresis width ∆ɛ can be given by(9)Δε=εunloadingσmin+σmax2−εreloadingσmin+σmax2.The fatigue hysteresis modulusE can be obtained as(10)E=σmax−σminεmaxσmax−εminσmin.


## 2.1. First Matrix Cracking Stress

For the first matrix cracking of fiber-reinforced CMCs, the energy balance relationship can be determined as(1)ασ2+βσ+γ=0,where(2)α=ldEc,β=−2VfldTEc,γ=43τirf2VfEcVmEmEfld3+VfldT2Ef−2Vfτild2rfEfT−Vmζm−4Vfldrfζd,where ld denotes the fiber/matrix interface debonding length; Ef, Em, and Ec denote the fiber, matrix, and composite elastic modulus, respectively; Vf and Vm denote the fiber and the matrix volume, respectively; rf denotes the fiber radius; ζm and ζd denote the matrix fracture energy and the interface debonding energy, respectively; τi denotes the fiber/matrix interface shear stress in the debonding region; and T denotes the fiber intact stress:(3)σVf=TσcTm+11−exp−Tσcm+1,where σc denotes the fiber characteristic strength and m denotes the fiber Weibull modulus.


## 2.2. Matrix Cracking Density

The energy balance relationship to evaluate the matrix cracking evolution is given by(4)Umσ>σmc,lc,ld=Ucrmσmc,l0,where(5)Um=AmEm43VfτiVmrfld2ld+σmo2lc2−ld−2σmoVfVmT−σfo−2VfτirfVmld−rfρexp−ρlc/2−ldrf−1+VfVmT−σfo−2VfτirfVmld2−rf2ρexp−2ρlc/2−ldrf−1,ld<lc2,Amlc36EmτiVfrfVm2,ld=lc2,Ucrm=12kAml0σmocr2Em,where Am is the cross-sectional area of matrix in the unit cell; k denotes the critical matrix strain energy parameter; l0 is the initial matrix crack spacing; and σmocr denotes the matrix axial stress in the interface bonded region at the first matrix cracking stress.


## 2.3. Fatigue Hysteresis-Based Damage Parameters

The initial fiber/matrix interface debonding stressσd and the interface complete debonding stress σb can be obtained as(6)σd=VfEcτiρVmEm1+1+4VmEmEfrfEcρ2τi2ζd,σb=VfEcτiρVmEm1+ρlcrf+1+4VmEmEfrfEcρ2τi2ζd.The fatigue hysteresis dissipated energyUe can be given by(7)Ue=∫σminσmaxεunloadingσ−εreloadingσdσ,where(8)εunloading=TUEf+4τiEfy2rflc−τiEf2y−ld2y+ld−lcrflc−αc−αfΔΤ,ld<lc2,TUEf+4τiEfy2rflc−2τiEf2y−lc/22rflc−αc−αfΔΤ,ld=lc2,εreloading=TREf−4τiEfz2rflc+4τiEfy−2z2rflc+2τiEfld−2y+2zld+2y−2z−lcrflc−αc−αfΔΤ,ld<lc2,TREf−4τiEfz2rflc+4τiEfy−2z2rflc−2τiEflc/2−2y+2z2rflc−αc−αfΔΤ,ld=lc2,where TU and TR denote the intact fiber stress upon unloading and reloading, respectively.The fatigue hysteresis width ∆ɛ can be given by(9)Δε=εunloadingσmin+σmax2−εreloadingσmin+σmax2.The fatigue hysteresis modulusE can be obtained as(10)E=σmax−σminεmaxσmax−εminσmin.


## 3. Results and Discussion

The effects of fiber/matrix interface properties on the tensile and fatigue damage are analyzed. The SiC/SiC composite is used to the case analysis, and the material properties are given byVf = 15%, Ef = 400 GPa, Em = 350 GPa, rf = 6 μm, αf = 4.5 × 10−6/°C, αm = 4.6 × 10−6/°C, ∆T = −1000°C, ζm = 6 J/m2, ζd = 1.2 J/m2, τi = 30 MPa, σc = 3.0 GPa, and m = 5.


### 3.1. Effect of the Interface Properties on the First Matrix Cracking Stress

The first matrix cracking stress, the fiber/matrix interface debonding length, and broken fibers fraction versus the fiber/matrix interface shear stress and interface debonding energy curves for different fiber volume are shown in Figures1 and 2. When the fiber/matrix interface shear stress and interface debonding energy increase, the first matrix cracking stress increases, the fiber/matrix interface debonding length decreases, and the broken fibers fraction increases.Figure 1
(a) The first matrix cracking stress versus the interface shear stress curves; (b) the interface debonding length versus the interface shear stress curves; (c) the broken fibers fraction versus the interface shear stress curves for different fiber volume.
(a)
(b)
(c)Figure 2
(a) The first matrix cracking stress versus the interface debonding energy curves; (b) the interface debonding length versus the interface debonding energy curves; (c) the broken fibers fraction versus the interface debonding energy curves for different fiber volume.
(a)
(b)
(c)When the fiber volume isVf = 15%, the first matrix cracking stress increases from σmc = 132 MPa at τi = 10 MPa to σmc = 180 MPa at τi = 50 MPa and from σmc = 143 MPa at ζd/ζm = 0.1 to σmc = 242 MPa at ζd/ζm = 0.9; the fiber/matrix interface debonding length decreases from ld/rf = 10.8 at τi = 10 MPa to ld/rf = 4.9 at τi = 50 MPa and from ld/rf = 7.2 at ζd/ζm = 0.1 to ld/rf = 4.7 at ζd/ζm = 0.9; and the broken fibers fraction increases from q = 0.06% at τi = 10 MPa to q = 0.42% at τi = 50 MPa and from q = 0.1% at ζd/ζm = 0.1 to q = 2.6% at ζd/ζm = 0.9.When the fiber volume isVf = 25%, the first matrix cracking stress increases from σmc = 217 MPa at τi = 10 MPa to σmc = 286 MPa at τi = 50 MPa and from σmc = 224 MPa at ζd/ζm = 0.1 to σmc = 410 MPa at ζd/ζm = 0.9; the fiber/matrix interface debonding length decreases from ld/rf = 7.5 at τi = 10 MPa to ld/rf = 3.5 at τi = 50 MPa and from ld/rf = 5.1 at ζd/ζm = 0.1 to ld/rf = 3.2 at ζd/ζm = 0.9; and the broken fibers fraction increases from q = 0.06% at τi = 10 MPa to q = 0.31% at τi = 50 MPa and from q = 0.07% at ζd/ζm = 0.1 to q = 2.9% at ζd/ζm = 0.9.


### 3.2. Effect of the Interface Properties on the Matrix Cracking Density

The matrix cracking density, fiber/matrix interface debonding length, and broken fibers fraction versus the applied stress curves for different fiber/matrix interface shear stress and interface debonding energy are shown in Figures3 and 4. When the fiber/matrix interface shear stress increases, the matrix cracking density, saturation matrix cracking stress, and the interface debonding length increase; and when the interface debonding energy increases, the matrix cracking density decreases, and the saturation matrix cracking stress increases.Figure 3
(a) The matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves for different interface shear stress.
(a)
(b)
(c)Figure 4
(a) The matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves for different interface deboned energy.
(a)
(b)
(c)When the fiber/matrix interface shear stress isτi = 20 MPa, the matrix cracking density increases from λ = 0.09/mm at σmc = 155 MPa to λ = 2.5/mm at σsat = 230 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.9% at σmc = 155 MPa to 2ld/lc = 60.8% at σsat = 230 MPa; and the broken fibers fraction increases from q = 0.169% at σmc = 155 MPa to q = 2% at σsat = 230 MPa. When the fiber/matrix interface shear stress is τi = 40 MPa, the matrix cracking density increases from λ = 0.13/mm at σmc = 178 MPa to λ = 3.9/mm at σsat = 267 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.96% at σmc = 178 MPa to 2ld/lc = 63.4% at σsat = 267 MPa; and the broken fibers fraction increases from q = 0.38% at σmc = 178 MPa to q = 4.9% at σsat = 267 MPa.When the fiber/matrix interface debonding energy isζd/ζm = 0.1, the matrix cracking density increases from λ = 0.1/mm at σmc = 149 MPa to λ = 3.5/mm at σsat = 240 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 1% at σmc = 149 MPa to 2ld/lc = 72% at σsat = 240 MPa; and the broken fibers fraction increases from q = 0.1% at σmc = 149 MPa to q = 2.4% at σsat = 240 MPa. When the fiber/matrix interface debonding energy is ζd/ζm = 0.5, the matrix cracking density increases from λ = 0.13/mm at σmc = 208 MPa to λ = 2.7/mm at σsat = 280 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.8% at σmc = 208 MPa to 2ld/lc = 47% at σsat = 280 MPa; and the broken fibers fraction increases from q = 1% at σmc = 208 MPa to q = 7% at σsat = 280 MPa.


### 3.3. Effect of the Interface Properties on the Fatigue Hysteresis-Based Damage Parameters

The initial fiber/matrix interface debonding stress and the complete interface debonding stress, fatigue hysteresis dissipated energy, fatigue hysteresis modulus, and fatigue hysteresis width versus the fiber/matrix interface shear stress and interface debonding energy curves for different fiber volume are shown in Figures5 and 6. When the fiber/matrix interface shear stress and the interface debonding energy increase, the initial interface debonding stress and the complete interface debonding stress increase, the fatigue hysteresis dissipated energy decreases, the fatigue hysteresis modulus increases, and the fatigue hysteresis width decreases.Figure 5
(a) The initial interface debonding stress and complete interface debonding stress versus the interface shear stress curves; (b) the fatigue hysteresis dissipated energy versus the interface shear stress curves; (c) the fatigue hysteresis modulus versus the interface shear stress curves; (d) the fatigue hysteresis width versus the interface shear stress curves for different fiber volume.
(a)
(b)
(c)
(d)Figure 6
(a) The initial interface debonding stress and complete interface debonding stress versus the interface debonding energy curves; (b) the fatigue hysteresis dissipated energy versus the interface debonding energy curves; (c) the fatigue hysteresis modulus versus the interface debonding energy curves; (d) the fatigue hysteresis width versus the interface debonding energy curves for different fiber volume.
(a)
(b)
(c)
(d)When the fiber volume isVf = 15%, the initial fiber/matrix interface debonding stress increases from σd = 95 MPa at τi = 20 MPa to σd = 98 MPa at τi = 40 MPa and from σd = 69 MPa at ζd/ζm = 0.1 to σd = 201 MPa at ζd/ζm = 0.9; the complete fiber/matrix interface debonding stress increases from σb = 215 MPa at τi = 20 MPa to σb = 338 MPa at τi = 40 MPa and from σb = 250 MPa at ζd/ζm = 0.1 to σb = 381 MPa at ζd/ζm = 0.9; when the fatigue peak stress is σmax = 150 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 29.1 kJ/m3 at τi = 20 MPa to Ue = 15.4 kJ/m3 at τi = 40 MPa; the fatigue hysteresis modulus increases from E = 143 GPa at τi = 20 MPa to E = 202 GPa at τi = 40 MPa; and the fatigue hysteresis width decreases from Δε = 0.03% at τi = 20 MPa to Δε = 0.015% at τi = 40 MPa; when the fatigue peak stress is σmax = 250 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 103.8 kJ/m3 at ζd/ζm = 0.3 to Ue = 49.3 kJ/m3 at ζd/ζm = 0.9; the fatigue hysteresis modulus increases from E = 130 GPa at ζd/ζm = 0.3 to E = 155 GPa at ζd/ζm = 0.9; and the fatigue hysteresis width decreases from Δε = 0.06% at ζd/ζm = 0.3 to Δε = 0.028% at ζd/ζm = 0.9.When the fiber volume isVf = 20%, the initial fiber/matrix interface debonding stress increases from σd = 131 MPa at τi = 20 MPa to σd = 135 MPa at τi = 40 MPa and from σd = 95 MPa at ζd/ζm = 0.1 to σd = 277 MPa at ζd/ζm = 0.9; the complete fiber/matrix interface debonding stress increases from σb = 303 MPa at τi = 20 MPa to σb = 477 MPa at τi = 40 MPa and from σb = 352 MPa at ζd/ζm = 0.1 to σb = 534 MPa at ζd/ζm = 0.9; when the fatigue peak stress is σmax = 150 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 3.9 kJ/m3 at τi = 20 MPa to Ue = 2.1 kJ/m3 at τi = 40 MPa; the fatigue hysteresis modulus increases from E = 251 GPa at τi = 20 MPa to E = 289 GPa at τi = 40 MPa; and the fatigue hysteresis width decreases from Δε = 0.003% at τi = 20 MPa to Δε = 0.0017% at τi = 40 MPa; when the fatigue peak stress is σmax = 300 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 86.7 kJ/m3 at ζd/ζm = 0.3 to Ue = 11.5 kJ/m3 at ζd/ζm = 0.9; the fatigue hysteresis modulus increases from E = 177 GPa at ζd/ζm = 0.3 to E = 251 GPa at ζd/ζm = 0.9; and the fatigue hysteresis width decreases from Δε = 0.043% at ζd/ζm = 0.3 to Δε = 0.004% at ζd/ζm = 0.9.


## 3.1. Effect of the Interface Properties on the First Matrix Cracking Stress

The first matrix cracking stress, the fiber/matrix interface debonding length, and broken fibers fraction versus the fiber/matrix interface shear stress and interface debonding energy curves for different fiber volume are shown in Figures1 and 2. When the fiber/matrix interface shear stress and interface debonding energy increase, the first matrix cracking stress increases, the fiber/matrix interface debonding length decreases, and the broken fibers fraction increases.Figure 1
(a) The first matrix cracking stress versus the interface shear stress curves; (b) the interface debonding length versus the interface shear stress curves; (c) the broken fibers fraction versus the interface shear stress curves for different fiber volume.
(a)
(b)
(c)Figure 2
(a) The first matrix cracking stress versus the interface debonding energy curves; (b) the interface debonding length versus the interface debonding energy curves; (c) the broken fibers fraction versus the interface debonding energy curves for different fiber volume.
(a)
(b)
(c)When the fiber volume isVf = 15%, the first matrix cracking stress increases from σmc = 132 MPa at τi = 10 MPa to σmc = 180 MPa at τi = 50 MPa and from σmc = 143 MPa at ζd/ζm = 0.1 to σmc = 242 MPa at ζd/ζm = 0.9; the fiber/matrix interface debonding length decreases from ld/rf = 10.8 at τi = 10 MPa to ld/rf = 4.9 at τi = 50 MPa and from ld/rf = 7.2 at ζd/ζm = 0.1 to ld/rf = 4.7 at ζd/ζm = 0.9; and the broken fibers fraction increases from q = 0.06% at τi = 10 MPa to q = 0.42% at τi = 50 MPa and from q = 0.1% at ζd/ζm = 0.1 to q = 2.6% at ζd/ζm = 0.9.When the fiber volume isVf = 25%, the first matrix cracking stress increases from σmc = 217 MPa at τi = 10 MPa to σmc = 286 MPa at τi = 50 MPa and from σmc = 224 MPa at ζd/ζm = 0.1 to σmc = 410 MPa at ζd/ζm = 0.9; the fiber/matrix interface debonding length decreases from ld/rf = 7.5 at τi = 10 MPa to ld/rf = 3.5 at τi = 50 MPa and from ld/rf = 5.1 at ζd/ζm = 0.1 to ld/rf = 3.2 at ζd/ζm = 0.9; and the broken fibers fraction increases from q = 0.06% at τi = 10 MPa to q = 0.31% at τi = 50 MPa and from q = 0.07% at ζd/ζm = 0.1 to q = 2.9% at ζd/ζm = 0.9.


## 3.2. Effect of the Interface Properties on the Matrix Cracking Density

The matrix cracking density, fiber/matrix interface debonding length, and broken fibers fraction versus the applied stress curves for different fiber/matrix interface shear stress and interface debonding energy are shown in Figures3 and 4. When the fiber/matrix interface shear stress increases, the matrix cracking density, saturation matrix cracking stress, and the interface debonding length increase; and when the interface debonding energy increases, the matrix cracking density decreases, and the saturation matrix cracking stress increases.Figure 3
(a) The matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves for different interface shear stress.
(a)
(b)
(c)Figure 4
(a) The matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves for different interface deboned energy.
(a)
(b)
(c)When the fiber/matrix interface shear stress isτi = 20 MPa, the matrix cracking density increases from λ = 0.09/mm at σmc = 155 MPa to λ = 2.5/mm at σsat = 230 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.9% at σmc = 155 MPa to 2ld/lc = 60.8% at σsat = 230 MPa; and the broken fibers fraction increases from q = 0.169% at σmc = 155 MPa to q = 2% at σsat = 230 MPa. When the fiber/matrix interface shear stress is τi = 40 MPa, the matrix cracking density increases from λ = 0.13/mm at σmc = 178 MPa to λ = 3.9/mm at σsat = 267 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.96% at σmc = 178 MPa to 2ld/lc = 63.4% at σsat = 267 MPa; and the broken fibers fraction increases from q = 0.38% at σmc = 178 MPa to q = 4.9% at σsat = 267 MPa.When the fiber/matrix interface debonding energy isζd/ζm = 0.1, the matrix cracking density increases from λ = 0.1/mm at σmc = 149 MPa to λ = 3.5/mm at σsat = 240 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 1% at σmc = 149 MPa to 2ld/lc = 72% at σsat = 240 MPa; and the broken fibers fraction increases from q = 0.1% at σmc = 149 MPa to q = 2.4% at σsat = 240 MPa. When the fiber/matrix interface debonding energy is ζd/ζm = 0.5, the matrix cracking density increases from λ = 0.13/mm at σmc = 208 MPa to λ = 2.7/mm at σsat = 280 MPa; the fiber/matrix interface debonding length increases from 2ld/lc = 0.8% at σmc = 208 MPa to 2ld/lc = 47% at σsat = 280 MPa; and the broken fibers fraction increases from q = 1% at σmc = 208 MPa to q = 7% at σsat = 280 MPa.


## 3.3. Effect of the Interface Properties on the Fatigue Hysteresis-Based Damage Parameters

The initial fiber/matrix interface debonding stress and the complete interface debonding stress, fatigue hysteresis dissipated energy, fatigue hysteresis modulus, and fatigue hysteresis width versus the fiber/matrix interface shear stress and interface debonding energy curves for different fiber volume are shown in Figures5 and 6. When the fiber/matrix interface shear stress and the interface debonding energy increase, the initial interface debonding stress and the complete interface debonding stress increase, the fatigue hysteresis dissipated energy decreases, the fatigue hysteresis modulus increases, and the fatigue hysteresis width decreases.Figure 5
(a) The initial interface debonding stress and complete interface debonding stress versus the interface shear stress curves; (b) the fatigue hysteresis dissipated energy versus the interface shear stress curves; (c) the fatigue hysteresis modulus versus the interface shear stress curves; (d) the fatigue hysteresis width versus the interface shear stress curves for different fiber volume.
(a)
(b)
(c)
(d)Figure 6
(a) The initial interface debonding stress and complete interface debonding stress versus the interface debonding energy curves; (b) the fatigue hysteresis dissipated energy versus the interface debonding energy curves; (c) the fatigue hysteresis modulus versus the interface debonding energy curves; (d) the fatigue hysteresis width versus the interface debonding energy curves for different fiber volume.
(a)
(b)
(c)
(d)When the fiber volume isVf = 15%, the initial fiber/matrix interface debonding stress increases from σd = 95 MPa at τi = 20 MPa to σd = 98 MPa at τi = 40 MPa and from σd = 69 MPa at ζd/ζm = 0.1 to σd = 201 MPa at ζd/ζm = 0.9; the complete fiber/matrix interface debonding stress increases from σb = 215 MPa at τi = 20 MPa to σb = 338 MPa at τi = 40 MPa and from σb = 250 MPa at ζd/ζm = 0.1 to σb = 381 MPa at ζd/ζm = 0.9; when the fatigue peak stress is σmax = 150 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 29.1 kJ/m3 at τi = 20 MPa to Ue = 15.4 kJ/m3 at τi = 40 MPa; the fatigue hysteresis modulus increases from E = 143 GPa at τi = 20 MPa to E = 202 GPa at τi = 40 MPa; and the fatigue hysteresis width decreases from Δε = 0.03% at τi = 20 MPa to Δε = 0.015% at τi = 40 MPa; when the fatigue peak stress is σmax = 250 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 103.8 kJ/m3 at ζd/ζm = 0.3 to Ue = 49.3 kJ/m3 at ζd/ζm = 0.9; the fatigue hysteresis modulus increases from E = 130 GPa at ζd/ζm = 0.3 to E = 155 GPa at ζd/ζm = 0.9; and the fatigue hysteresis width decreases from Δε = 0.06% at ζd/ζm = 0.3 to Δε = 0.028% at ζd/ζm = 0.9.When the fiber volume isVf = 20%, the initial fiber/matrix interface debonding stress increases from σd = 131 MPa at τi = 20 MPa to σd = 135 MPa at τi = 40 MPa and from σd = 95 MPa at ζd/ζm = 0.1 to σd = 277 MPa at ζd/ζm = 0.9; the complete fiber/matrix interface debonding stress increases from σb = 303 MPa at τi = 20 MPa to σb = 477 MPa at τi = 40 MPa and from σb = 352 MPa at ζd/ζm = 0.1 to σb = 534 MPa at ζd/ζm = 0.9; when the fatigue peak stress is σmax = 150 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 3.9 kJ/m3 at τi = 20 MPa to Ue = 2.1 kJ/m3 at τi = 40 MPa; the fatigue hysteresis modulus increases from E = 251 GPa at τi = 20 MPa to E = 289 GPa at τi = 40 MPa; and the fatigue hysteresis width decreases from Δε = 0.003% at τi = 20 MPa to Δε = 0.0017% at τi = 40 MPa; when the fatigue peak stress is σmax = 300 MPa, the fatigue hysteresis dissipated energy decreases from Ue = 86.7 kJ/m3 at ζd/ζm = 0.3 to Ue = 11.5 kJ/m3 at ζd/ζm = 0.9; the fatigue hysteresis modulus increases from E = 177 GPa at ζd/ζm = 0.3 to E = 251 GPa at ζd/ζm = 0.9; and the fatigue hysteresis width decreases from Δε = 0.043% at ζd/ζm = 0.3 to Δε = 0.004% at ζd/ζm = 0.9.


## 4. Experimental Comparisons

Morscher et al. [36–38] performed the experimental investigations on the first matrix cracking stress, matrix cracking evolution, and fatigue hysteresis loops of 2D SiC/SiC composites. The first matrix cracking stress, matrix cracking density, and the fatigue hysteresis loops of 2D Hi-Nicalon™, Sylramic™, and Tyranno™ SiC/SiC composites are predicted. The material properties of SiC/SiC composites are listed in Table 1.Table 1
Material properties of 2D SiC/SiC composites.
Items
Hi-Nicalon™ SiC/SiC
Sylramic™ SiC/SiC
Tyranno™ SiC/SiC
r
f (μm)
7
5
5.5
V
f (%)
14–18
12–21
29
E
f (GPa)
270
310
170
E
m (GPa)
350
350
350
α
f (10−6/°C)
3.5
5.4
4
α
m (10−6/°C)
4.6
4.6
4.6
σ
c (GPa)
3
2.6
1.9
m
5
5
5


### 4.1. First Matrix Cracking Stress

The experimental and predicted first matrix cracking stress versus the fiber volume curves of 2D Hi-Nicalon™ SiC/SiC composite for different fiber/matrix interface shear stress curves is shown in Figure7. The fiber/matrix interface shear stress is in the range of τi = 10–40 MPa at the interface debonding energy of ζd/ζm = 0.2. The first matrix cracking stress increases with the fiber volume and the interface shear stress; the interface debonding length decreases with the fiber volume and increases with the interface shear stress; and the broken fibers fraction decreases with the fiber volume and increases the interface shear stress.Figure 7
(a) The experimental and predicted first matrix cracking stress versus the fiber volume curves; (b) the interface debonding length versus the fiber volume curves; (c) the broken fibers fraction versus the fiber volume curves of 2D Hi-Nicalon™ SiC/SiC composite.
(a)
(b)
(c)The experimental and predicted first matrix cracking stress versus the fiber volume curves of 2D Sylramic™ SiC/SiC composite for different interface shear stress curves is shown in Figure8. The interface shear stress is in the range of τi = 5–25 MPa at the interface debonding energy of ζd/ζm = 0.1. The first matrix cracking stress increases with the fiber volume and the interface shear stress; the interface debonding length decreases with the fiber volume and the interface shear stress; and the broken fibers fraction decreases the fiber volume and increases with the interface shear stress.Figure 8
(a) The experimental and predicted first matrix cracking stress versus the fiber volume curves; (b) the interface debonding length versus the fiber volume curves; (c) the broken fibers fraction versus the fiber volume curves of 2D Sylramic™ SiC/SiC composite.
(a)
(b)
(c)


### 4.2. Matrix Cracking Density

The experimental and predicted matrix cracking density versus the applied stress curves for different interface shear stress of 2D Hi-Nicalon™ SiC/SiC composite is shown in Figure9. When the interface shear stress is low, the first matrix cracking stress, matrix cracking saturation stress, and saturation matrix cracking density are low. For the initial stage of matrix cracking evolution, the predicted result using low interface shear stress of τi = 20 MPa agreed with experimental data; however, for the stage of matrix cracking evolution at high stress, the predicted results using high interface shear stress of τi = 50 MPa agreed with experimental data. During matrix cracking evolution, the fiber/matrix interface debonding length and broken fibers fraction increase.Figure 9
(a) The experimental and predicted matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves of 2D Hi-Nicalon™ SiC/SiC composite.
(a)
(b)
(c)The experimental and predicted matrix cracking density versus the applied stress curves for different interface shear stress of 2D Sylramic™ SiC/SiC composite is shown in Figure10. For the initial stage of matrix cracking evolution, the predicted result using the low interface shear stress of τi = 10 and 20 MPa agreed with experimental data; however, for the stage of matrix cracking evolution at high stress, the predicted results using the high interface shear stress of τi = 50 MPa agreed with experimental data. Under tensile loading, the interface debonding length increases after saturation of matrix cracking, and the fiber failure occurs at first matrix cracking stress.Figure 10
(a) The experimental and predicted matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves of 2D Sylramic™ SiC/SiC composite.
(a)
(b)
(c)


### 4.3. Fatigue Hysteresis-Based Damage Parameters

The experimental and predicted hysteresis loops of 2D Sylramic™ SiC/SiC composite under the fatigue peak stresses ofσmax = 200, 240, and 275 MPa for different interface properties are shown in Figure 11. When the fatigue peak stress is σmax = 200, 240, and 275 MPa, the predicted fatigue hysteresis loops for the interface shear stress of τi = 30, 40, and 50 MPa and the interface debonding energy of ζd/ζm = 0.1, 0.2, and 0.3 are shown in Figure 11. The predicted results using the interface shear stress of τi = 50 MPa and ζd/ζm = 0.3 agreed with the experimental hysteresis loops.Figure 11
The experimental and predicted hysteresis loops of 2D Sylramic™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 200 MPa for different interface shear stress; (b) the fatigue peak stress of σmax = 200 MPa for different interface debonding energy; (c) the fatigue peak stress of σmax = 240 MPa for different interface shear stress; (d) the fatigue peak stress of σmax = 240 MPa for different interface debonding energy; (e) the fatigue peak stress of σmax = 275 MPa for different interface shear stress; (f) the fatigue peak stress of σmax = 275 MPa for different interface debonding energy.
(a)
(b)
(c)
(d)
(e)
(f)The experimental and predicted hysteresis loops of 2D Tyranno™ SiC/SiC composite under the fatigue peak stress ofσmax = 120 and 145 MPa for different interface properties are shown in Figure 12. When the fatigue peak stress is σmax = 120 and 145 MPa, the predicted fatigue hysteresis loops for the interface shear stress of τi = 20, 30, and 40 MPa and the interface debonding energy of ζd/ζm = 0.1, 0.2, and 0.3 is shown in Figure 12. The predicted results using the interface shear stress of τi = 30 MPa and ζd/ζm = 0.1 agreed with the experimental hysteresis loops.Figure 12
The experimental and predicted fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 120 MPa for different interface shear stress; (b) the fatigue peak stress of σmax = 120 MPa for different interface debonding energy; (c) the fatigue peak stress of σmax = 145 MPa for different interface shear stress; (d) the fatigue peak stress of σmax = 145 MPa for different interface debonding energy.
(a)
(b)
(c)
(d)The fatigue hysteresis loops of 2D Hi-Nicalon™ SiC/SiC composite under the fatigue peak stress ofσmax = 140 and 150 MPa are shown in Figure 13. When the fatigue peak stress is σmax = 140 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 50, 60, 70, and 80 MPa are shown in Figure 13(a), in which the predicted fatigue hysteresis loops with τi = 50 MPa agreed with experimental data; when the fatigue peak stress is σmax = 150 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 30, 40, and 50 MPa are shown in Figure 13(b), in which the predicted fatigue hysteresis loops with τi = 40 MPa agreed with experimental data. Under cyclic fatigue loading, the interface wear leads to the degradation of the interface shear stress.Figure 13
The experimental and predicted fatigue hysteresis loops of 2D Hi-Nicalon™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 140 MPa for N = 13000 cycles and (b) the fatigue peak stress of σmax = 150 MPa for N = 27000 cycles.
(a)
(b)The fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under the fatigue peak stress ofσmax = 230 and 240 MPa are shown in Figure 14. When the fatigue peak stress is σmax = 230 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 40, 50, and 60 MPa are shown in Figure 14(a), in which the predicted fatigue hysteresis loops with τi = 50 MPa agreed with experimental data; when the fatigue peak stress is σmax = 240 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 20, 30, and 40 MPa are shown in Figure 14(b), in which the predicted hysteresis loops with τi = 30 MPa agreed with experimental data. Under repeated loading/unloading, the interface shear stress decreases due to the interface wear.Figure 14
The experimental and predicted fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 230 MPa for N = 16000 cycles and (b) the fatigue peak stress of σmax = 240 MPa for N = 85 cycles.
(a)
(b)


## 4.1. First Matrix Cracking Stress

The experimental and predicted first matrix cracking stress versus the fiber volume curves of 2D Hi-Nicalon™ SiC/SiC composite for different fiber/matrix interface shear stress curves is shown in Figure7. The fiber/matrix interface shear stress is in the range of τi = 10–40 MPa at the interface debonding energy of ζd/ζm = 0.2. The first matrix cracking stress increases with the fiber volume and the interface shear stress; the interface debonding length decreases with the fiber volume and increases with the interface shear stress; and the broken fibers fraction decreases with the fiber volume and increases the interface shear stress.Figure 7
(a) The experimental and predicted first matrix cracking stress versus the fiber volume curves; (b) the interface debonding length versus the fiber volume curves; (c) the broken fibers fraction versus the fiber volume curves of 2D Hi-Nicalon™ SiC/SiC composite.
(a)
(b)
(c)The experimental and predicted first matrix cracking stress versus the fiber volume curves of 2D Sylramic™ SiC/SiC composite for different interface shear stress curves is shown in Figure8. The interface shear stress is in the range of τi = 5–25 MPa at the interface debonding energy of ζd/ζm = 0.1. The first matrix cracking stress increases with the fiber volume and the interface shear stress; the interface debonding length decreases with the fiber volume and the interface shear stress; and the broken fibers fraction decreases the fiber volume and increases with the interface shear stress.Figure 8
(a) The experimental and predicted first matrix cracking stress versus the fiber volume curves; (b) the interface debonding length versus the fiber volume curves; (c) the broken fibers fraction versus the fiber volume curves of 2D Sylramic™ SiC/SiC composite.
(a)
(b)
(c)


## 4.2. Matrix Cracking Density

The experimental and predicted matrix cracking density versus the applied stress curves for different interface shear stress of 2D Hi-Nicalon™ SiC/SiC composite is shown in Figure9. When the interface shear stress is low, the first matrix cracking stress, matrix cracking saturation stress, and saturation matrix cracking density are low. For the initial stage of matrix cracking evolution, the predicted result using low interface shear stress of τi = 20 MPa agreed with experimental data; however, for the stage of matrix cracking evolution at high stress, the predicted results using high interface shear stress of τi = 50 MPa agreed with experimental data. During matrix cracking evolution, the fiber/matrix interface debonding length and broken fibers fraction increase.Figure 9
(a) The experimental and predicted matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves of 2D Hi-Nicalon™ SiC/SiC composite.
(a)
(b)
(c)The experimental and predicted matrix cracking density versus the applied stress curves for different interface shear stress of 2D Sylramic™ SiC/SiC composite is shown in Figure10. For the initial stage of matrix cracking evolution, the predicted result using the low interface shear stress of τi = 10 and 20 MPa agreed with experimental data; however, for the stage of matrix cracking evolution at high stress, the predicted results using the high interface shear stress of τi = 50 MPa agreed with experimental data. Under tensile loading, the interface debonding length increases after saturation of matrix cracking, and the fiber failure occurs at first matrix cracking stress.Figure 10
(a) The experimental and predicted matrix cracking density versus the applied stress curves; (b) the interface debonding length versus the applied stress curves; (c) the broken fibers fraction versus the applied stress curves of 2D Sylramic™ SiC/SiC composite.
(a)
(b)
(c)


## 4.3. Fatigue Hysteresis-Based Damage Parameters

The experimental and predicted hysteresis loops of 2D Sylramic™ SiC/SiC composite under the fatigue peak stresses ofσmax = 200, 240, and 275 MPa for different interface properties are shown in Figure 11. When the fatigue peak stress is σmax = 200, 240, and 275 MPa, the predicted fatigue hysteresis loops for the interface shear stress of τi = 30, 40, and 50 MPa and the interface debonding energy of ζd/ζm = 0.1, 0.2, and 0.3 are shown in Figure 11. The predicted results using the interface shear stress of τi = 50 MPa and ζd/ζm = 0.3 agreed with the experimental hysteresis loops.Figure 11
The experimental and predicted hysteresis loops of 2D Sylramic™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 200 MPa for different interface shear stress; (b) the fatigue peak stress of σmax = 200 MPa for different interface debonding energy; (c) the fatigue peak stress of σmax = 240 MPa for different interface shear stress; (d) the fatigue peak stress of σmax = 240 MPa for different interface debonding energy; (e) the fatigue peak stress of σmax = 275 MPa for different interface shear stress; (f) the fatigue peak stress of σmax = 275 MPa for different interface debonding energy.
(a)
(b)
(c)
(d)
(e)
(f)The experimental and predicted hysteresis loops of 2D Tyranno™ SiC/SiC composite under the fatigue peak stress ofσmax = 120 and 145 MPa for different interface properties are shown in Figure 12. When the fatigue peak stress is σmax = 120 and 145 MPa, the predicted fatigue hysteresis loops for the interface shear stress of τi = 20, 30, and 40 MPa and the interface debonding energy of ζd/ζm = 0.1, 0.2, and 0.3 is shown in Figure 12. The predicted results using the interface shear stress of τi = 30 MPa and ζd/ζm = 0.1 agreed with the experimental hysteresis loops.Figure 12
The experimental and predicted fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 120 MPa for different interface shear stress; (b) the fatigue peak stress of σmax = 120 MPa for different interface debonding energy; (c) the fatigue peak stress of σmax = 145 MPa for different interface shear stress; (d) the fatigue peak stress of σmax = 145 MPa for different interface debonding energy.
(a)
(b)
(c)
(d)The fatigue hysteresis loops of 2D Hi-Nicalon™ SiC/SiC composite under the fatigue peak stress ofσmax = 140 and 150 MPa are shown in Figure 13. When the fatigue peak stress is σmax = 140 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 50, 60, 70, and 80 MPa are shown in Figure 13(a), in which the predicted fatigue hysteresis loops with τi = 50 MPa agreed with experimental data; when the fatigue peak stress is σmax = 150 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 30, 40, and 50 MPa are shown in Figure 13(b), in which the predicted fatigue hysteresis loops with τi = 40 MPa agreed with experimental data. Under cyclic fatigue loading, the interface wear leads to the degradation of the interface shear stress.Figure 13
The experimental and predicted fatigue hysteresis loops of 2D Hi-Nicalon™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 140 MPa for N = 13000 cycles and (b) the fatigue peak stress of σmax = 150 MPa for N = 27000 cycles.
(a)
(b)The fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under the fatigue peak stress ofσmax = 230 and 240 MPa are shown in Figure 14. When the fatigue peak stress is σmax = 230 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 40, 50, and 60 MPa are shown in Figure 14(a), in which the predicted fatigue hysteresis loops with τi = 50 MPa agreed with experimental data; when the fatigue peak stress is σmax = 240 MPa, the experimental and predicted fatigue hysteresis loops using the interface shear stress of τi = 20, 30, and 40 MPa are shown in Figure 14(b), in which the predicted hysteresis loops with τi = 30 MPa agreed with experimental data. Under repeated loading/unloading, the interface shear stress decreases due to the interface wear.Figure 14
The experimental and predicted fatigue hysteresis loops of 2D Tyranno™ SiC/SiC composite under (a) the fatigue peak stress ofσmax = 230 MPa for N = 16000 cycles and (b) the fatigue peak stress of σmax = 240 MPa for N = 85 cycles.
(a)
(b)


## 5. Conclusions

In this paper, the effect of the fiber/matrix interface properties on the tensile and fatigue behavior of 2D SiC/SiC composites was investigated. The relationships between the interface properties and the composite tensile and fatigue damage were established. The effects of the fiber/matrix interface properties on the first matrix cracking stress, matrix cracking evolution, first and complete interface debonding stress, fatigue hysteresis dissipated energy, fatigue hysteresis modulus, and fatigue hysteresis width were analyzed. The experimental first matrix cracking stress, matrix cracking evolution, and fatigue hysteresis loops of 2D SiC/SiC composites were predicted using different interface properties:(1)
When the interface shear stress increases, the first matrix cracking stress increases and the broken fibers fraction increases; the matrix cracking density, the saturation matrix cracking stress, and the interface debonding length increase; the initial interface debonding stress and the complete interface debonding stress increase, the hysteresis dissipated energy decreases, the hysteresis modulus increases, and the hysteresis width decreases.(2)
When the interface debonding energy increases, the first matrix cracking stress increases and the broken fibers fraction increases; the matrix cracking density decreases and the saturation matrix cracking stress increases; and the initial interface debonding stress and the complete interface debonding stress increase, the hysteresis dissipated energy decreases, the hysteresis modulus increases, and the hysteresis width decreases.



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*Source: 3618984-2020-01-08.xml*