A method for predicting thermal residual stress and thermal residual strain of fiber reinforced ceramic matrix composites by hysteresis loop

Abstract

The present application belongs to the technical field of mechanical property testing of fiber reinforced ceramic matrix composites, and particularly relates to a method for predicting thermal residual stress and thermal residual strain of fiber reinforced ceramic matrix composites through hysteresis loop. Firstly, the fiber reinforced ceramic matrix composite is cyclically loaded and unloaded in tension to obtain a cyclic loading and unloading stress-strain curve with different peak stresses; through analysis of the stress-strain curve within 0.005%, the elastic modulus of the elastic section of the composite material is obtained; through analysis of the stress-strain curve of the loading section hysteresis loop, the tangent modulus at the peak stress is obtained; the thermal residual strain at the peak stress is calculated according to the peak strain and the tangent modulus of the hysteresis loop; and the thermal residual stress and thermal residual strain of the composite material are obtained through the elastic modulus of the composite material, the tangent modulus at the peak stress and the thermal residual strain.

Description

Technical Field

[0001] This invention belongs to the field of mechanical property testing technology for fiber-reinforced ceramic matrix composites, specifically relating to a method for predicting thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites using hysteresis loops. Background Technology

[0002] Fiber-reinforced ceramic matrix composites possess advantages such as high temperature resistance, corrosion resistance, low density, high specific strength, and high specific modulus. Compared to high-temperature alloys, they can withstand higher temperatures and exhibit superior mechanical properties. Currently, fiber-reinforced ceramic matrix composites are used in the fabrication of aero-engine combustion chambers, turbine guide vanes, turbine housing rings, and exhaust nozzles.

[0003] Residual thermal stress and strain are key parameters affecting the mechanical properties of fiber-reinforced ceramic matrix composites (FRCs). Due to the mismatch in thermal expansion coefficients between the fiber and the matrix, FRCs exhibit significant residual thermal stress, causing the matrix to bear substantial residual tensile or compressive stress, thus impacting the mechanical properties of the composites. Existing methods for measuring residual thermal stress in FRCs (such as X-ray diffraction and ultrasonic methods) have low predictive accuracy and cannot accurately assess the residual thermal stress and strain, thereby hindering the accurate evaluation of the mechanical properties of FRCs. Summary of the Invention

[0004] In view of this, the present invention provides a method for predicting the thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites by means of hysteresis loops. The prediction method provided by the present invention can accurately assess the thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites, thereby accurately assessing the mechanical properties of fiber-reinforced ceramic matrix composites.

[0005] To address the aforementioned technical problems, this invention provides a method for predicting the thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites using hysteresis loops, comprising the following steps:

[0006] (1) The fiber-reinforced ceramic matrix composite material is subjected to cyclic loading and unloading tension to obtain cyclic loading and unloading stress-strain hysteresis loops with different peak stresses; the peak loading stress increases in each cycle during the cyclic loading and unloading tension process, and the state of the fiber-reinforced ceramic matrix composite material during loading includes elastic segment and nonlinear segment;

[0007] (2) The elastic modulus of the fiber-reinforced ceramic matrix composite material is obtained by calculating the stress-strain hysteresis loop of the elastic segment during cyclic loading and unloading.

[0008] (3) The tangent modulus at the peak stress is calculated based on the stress-strain hysteresis loop of the cyclic loading and unloading process.

[0009] (4) The thermal residual strain at the corresponding peak stress is calculated based on the peak strain in the cyclic loading and unloading stress-strain hysteresis loop and the tangent modulus at the peak stress obtained in step (3); there is no temporal order between steps (2) and (4);

[0010] (5) Based on the elastic modulus of the elastic segment of the fiber-reinforced ceramic matrix composite material obtained in step (2), the tangential modulus at the peak stress obtained in step (3), and the thermal residual strain at the peak stress obtained in step (4), the thermal residual stress and thermal residual strain of the fiber-reinforced ceramic matrix composite material are calculated.

[0011] Preferably, in step (2), the elastic modulus of the elastic segment is obtained from the relationship shown in Equation 1:

[0012]

[0013] Among them, E c Let σ be the elastic modulus of the elastic segment. 0.005％ The stress corresponding to 0.005% of the cyclic loading and unloading stress-strain hysteresis loop.

[0014] Preferably, the tangent modulus at the peak stress in step (3) is obtained from the relationship shown in Equation 2:

[0015]

[0016] Among them, E p σ is the tangent modulus at the peak stress. p For peak stress, σ rl To reload stress, ε p ε is the strain at the peak stress. rl The strain corresponding to the reloaded stress.

[0017] Preferably, the thermal residual strain at the peak stress in step (4) is obtained from the relationship shown in Equation 3:

[0018]

[0019] Where, ε t E represents the thermal residual strain at the peak stress. p ε is the tangent modulus at the peak stress. p denoted as the strain at the peak stress.

[0020] Preferably, the thermal residual stress of the fiber-reinforced ceramic matrix composite material in step (5) is obtained from the relationship shown in Equation 4:

[0021]

[0022] Where, σ r E represents the thermal residual stress in fiber-reinforced ceramic matrix composites. c E represents the elastic modulus of the elastic segment. p ε is the tangent modulus at the peak stress. t This represents the thermal residual strain at the peak stress.

[0023] Preferably, the thermal residual strain of the fiber-reinforced ceramic matrix composite material in step (5) is obtained from the relationship shown in Equation 5:

[0024]

[0025] Where, ε r E represents the thermal residual strain of fiber-reinforced ceramic matrix composites. c E represents the elastic modulus of the elastic segment. p ε is the tangent modulus at the peak stress. t This represents the thermal residual strain at the peak stress.

[0026] Preferably, the peak stress during the initial unloading in the cyclic loading and unloading tension is the initial matrix cracking stress σ. mc .

[0027] Preferably, the loading process is a process in which stress gradually increases, and the rate of stress increase is 0.008 to 0.012 MPa / s.

[0028] Preferably, the unloading process is a process of gradually reducing stress, and the stress reduction rate is 0.008 to 0.012 MPa / s.

[0029] Preferably, the increase in peak load stress during each cycle of the cyclic loading and unloading stretching process is 20–50 MPa.

[0030] This invention provides a method for predicting the thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites using hysteresis loops, comprising the following steps: (1) subjecting the fiber-reinforced ceramic matrix composite to cyclic loading and unloading tension to obtain cyclic loading and unloading stress-strain hysteresis loops with different peak stresses; wherein the peak stress of loading increases in each cycle during the cyclic loading and unloading tension, and the state of the fiber-reinforced ceramic matrix composite during loading includes an elastic segment and a nonlinear segment; (2) calculating the elastic modulus of the fiber-reinforced ceramic matrix composite based on the cyclic loading and unloading stress-strain hysteresis loop of the elastic segment; (3) calculating the elastic modulus of the fiber-reinforced ceramic matrix composite based on the cyclic loading and unloading stress-strain hysteresis loop of the elastic segment; (3) The tangential modulus at the peak stress is obtained by calculating the cyclic loading and unloading stress-strain hysteresis loop during the process; (4) The thermal residual strain at the corresponding peak stress is calculated based on the peak strain in the cyclic loading and unloading stress-strain hysteresis loop and the tangential modulus at the peak stress; there is no time sequence between steps (2) and (4); (5) The thermal residual stress and thermal residual strain of the fiber-reinforced ceramic matrix composite are calculated based on the elastic modulus of the elastic segment of the fiber-reinforced ceramic matrix composite obtained in step (2), the tangential modulus at the peak stress obtained in step (3), and the thermal residual strain at the peak stress obtained in step (4). This invention first applies cyclic loading and unloading tension to fiber-reinforced ceramic matrix composites to obtain cyclic loading and unloading stress-strain curves at different peak stresses. By analyzing the stress-strain curves within 0.005%, the elastic modulus of the composite material in the elastic segment is obtained. By analyzing the stress-strain curve of the hysteresis loop in the loading segment, the tangential modulus at the peak stress is obtained. The thermal residual strain at that peak stress is calculated based on the peak strain and tangential modulus of the hysteresis loop. Using the elastic modulus of the composite material, the tangential modulus at the peak stress, and the thermal residual strain, the thermal residual stress and residual strain of the composite material are obtained, thereby accurately predicting the mechanical properties of the composite material. Attached Figure Description

[0031] Figure 1 The graph shows the predicted thermal residual stress results of the three-dimensional needle-punched C / C-SiC ceramic matrix composite material in Example 1. Detailed Implementation

[0032] The method for predicting thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites by means of hysteresis loops described in this invention includes multiple parameters. To clearly understand this invention, the parameters, parameter symbols, and parameter meanings involved in the prediction method of this invention are explained first, as shown in Table 1.

[0033] Table 1. Parameter description of the method for predicting thermal residual stress in fiber-reinforced ceramic matrix composites using hysteresis loops.

[0034]

[0035]

[0036] Note: Composite material refers to fiber-reinforced ceramic matrix composite material, fiber refers to the fiber in fiber-reinforced ceramic matrix composite material, and ceramic matrix refers to the ceramic matrix in fiber-reinforced ceramic matrix composite material.

[0037] This invention provides a method for predicting thermal residual stress and thermal residual strain in fiber-reinforced ceramic matrix composites using hysteresis loops, comprising the following steps:

[0038] (1) The fiber-reinforced ceramic matrix composite material is subjected to cyclic loading and unloading tension to obtain cyclic loading and unloading stress-strain hysteresis loops with different peak stresses; the peak loading stress increases in each cycle during the cyclic loading and unloading tension process, and the state of the fiber-reinforced ceramic matrix composite material during loading includes elastic segment and nonlinear segment;

[0039] (2) The elastic modulus of the fiber-reinforced ceramic matrix composite material elastic segment is obtained by calculating based on the cyclic loading and unloading stress-strain hysteresis loop of the elastic segment.

[0040] (3) The tangent modulus at the peak stress is calculated based on the stress-strain hysteresis loop of the cyclic loading and unloading process.

[0041] (4) The thermal residual strain at the corresponding peak stress is calculated based on the peak strain in the cyclic loading and unloading stress-strain hysteresis loop and the tangent modulus at the peak stress obtained in step (3); there is no temporal order between steps (2) and (4);

[0042] (5) Based on the elastic modulus of the elastic segment of the fiber-reinforced ceramic matrix composite material obtained in step (2), the tangential modulus at the peak stress obtained in step (3), and the thermal residual strain at the peak stress obtained in step (4), the thermal residual stress and thermal residual strain of the fiber-reinforced ceramic matrix composite material are calculated.

[0043] This invention applies cyclic loading and unloading tensile testing to fiber-reinforced ceramic matrix composites, obtaining cyclic loading and unloading stress-strain hysteresis loops with different peak stresses. During the cyclic loading and unloading tensile testing, the peak loading stress increases with each cycle, and the state of the fiber-reinforced ceramic matrix composite during loading includes elastic and nonlinear segments. In this invention, the fiber-reinforced ceramic matrix composite preferably includes C / C-SiC fiber-reinforced ceramic matrix composites, C / SiC fiber-reinforced ceramic matrix composites, or SiC fiber-reinforced ceramic matrix composites, more preferably C / C-SiC fiber-reinforced ceramic matrix composites. In this invention, the C / C-SiC fiber-reinforced ceramic matrix composite is preferably a three-dimensional needle-punched C / C-SiC fiber-reinforced ceramic matrix composite.

[0044] In this invention, one cycle of the cyclic loading and unloading includes a loading process and an unloading process. In this invention, the loading process is a process of gradually increasing stress; the unloading process is a process of gradually decreasing stress. In this invention, during the loading and unloading process, the rate of stress increase is preferably 0.008–0.012 MPa / s, more preferably 0.01 MPa / s; the rate of stress decrease is preferably 0.008–0.012 MPa / s, more preferably 0.01 MPa / s. In this invention, the peak stress of the initial unloading in the cyclic loading and unloading tension is the initial matrix cracking stress σ. mc The initial matrix cracking stress is obtained through experimental testing. In this invention, the peak loading stress increases with each cycle during the cyclic loading and unloading tensile process, and the increase is preferably Δσ. The loading and unloading are repeated until the composite material fractures. In this invention, Δσ is preferably 20–50 MPa, more preferably 25–45 MPa.

[0045] In this invention, the stress-strain hysteresis loops of cyclic loading and unloading with different peak stresses are complete stress-strain hysteresis loops during the cyclic loading and unloading process.

[0046] After obtaining the cyclic loading and unloading stress-strain hysteresis loops for different peak stresses, this invention calculates the elastic modulus of the elastic segment of the fiber-reinforced ceramic matrix composite material based on the cyclic loading and unloading stress-strain hysteresis loops of the elastic segment in step (2). In this invention, the elastic modulus of the elastic segment is preferably obtained from the relationship shown in Equation 1:

[0047]

[0048] Among them, E c Let σ be the elastic modulus of the elastic segment. 0.005％ The stress corresponding to 0.005% of the cyclic loading and unloading stress-strain hysteresis loop.

[0049] In this invention, the composite material is in the elastic segment when the applied stress is within 0.005% of the peak stress. When the applied stress exceeds 0.005% of the peak stress, it enters the nonlinear segment.

[0050] After obtaining the cyclic loading and unloading stress-strain hysteresis loops for different peak stresses, this invention calculates the tangent modulus at the peak stress based on the cyclic loading and unloading stress-strain hysteresis loops during loading. In this invention, the tangent modulus at the peak stress in step (3) is preferably obtained from the relationship shown in Equation 2:

[0051]

[0052] Among them, E p σ is the tangent modulus at the peak stress. pFor peak stress, σ rl To reload stress, ε p ε is the strain at the peak stress. rl The strain corresponding to the reloaded stress.

[0053] After obtaining the tangent modulus at the peak stress, the present invention calculates the corresponding thermal residual strain at the peak stress based on the peak strain in the cyclic loading and unloading stress-strain hysteresis loop and the tangent modulus at the peak stress obtained in step (3). In the present invention, the thermal residual strain at the peak stress in step (4) is preferably obtained by the relationship shown in Equation 3:

[0054]

[0055] Where, ε t E represents the thermal residual strain at the peak stress. p ε is the tangent modulus at the peak stress. p denoted as the strain at the peak stress.

[0056] After obtaining the thermal residual strain at the corresponding peak stress, the present invention calculates the thermal residual stress and thermal residual strain of the fiber-reinforced ceramic matrix composite material based on the elastic modulus of the elastic segment, the tangential modulus at the peak stress, and the thermal residual strain at the peak stress. In the present invention, the thermal residual stress of the fiber-reinforced ceramic matrix composite material in step (5) is preferably obtained by the relationship shown in Equation 4:

[0057]

[0058] In this invention, the thermal residual strain of the fiber-reinforced ceramic matrix composite material in step (5) is preferably obtained from the relationship shown in Equation 5:

[0059]

[0060] Where, σ r For the thermal residual stress of fiber-reinforced ceramic matrix composites, ε r E represents the thermal residual strain of fiber-reinforced ceramic matrix composites. c E represents the elastic modulus of the elastic segment. p ε is the tangent modulus at the peak stress. t This represents the thermal residual strain at the peak stress.

[0061] This invention first applies cyclic loading and unloading tension to fiber-reinforced ceramic matrix composites to obtain cyclic loading and unloading stress-strain curves at different peak stresses; by analyzing the stress-strain curves within 0.005% of the peak stress, the elastic modulus of the composite material in the elastic segment is obtained; by analyzing the stress-strain curve of the hysteresis loop in the loading segment, the tangential modulus at the peak stress is obtained; the thermal residual strain at the peak stress is calculated based on the peak strain and tangential modulus of the hysteresis loop; and the thermal residual stress and residual strain of the composite material are obtained using the elastic modulus of the composite material, the tangential modulus at the peak stress, and the thermal residual strain.

[0062] This invention preferably employs a micromechanical method to predict the mechanical properties of composite materials; the micromechanical method preferably includes a tensile stress-strain curve or a stress-strain hysteresis loop. By comparing the results of predicting the mechanical properties of composite materials using the micromechanical method with those predicted using the method provided by this invention, it can be seen that the prediction method provided by this invention can accurately predict the mechanical properties of composite materials.

[0063] To further illustrate the present invention, the technical solutions provided by the present invention will be described in detail below with reference to the embodiments, but they should not be construed as limiting the scope of protection of the present invention.

[0064] Example 1

[0065] Three-dimensional needle-punched C / C-SiC fiber-reinforced ceramic matrix composites were used as test samples, and the test environment temperature was 25℃. The thermal residual stress and participating strain of the three-dimensional needle-punched C / C-SiC fiber-reinforced ceramic matrix composites were predicted according to the prediction method provided in this invention, thereby accurately evaluating the mechanical properties of the test samples.

[0066] The basic parameters involved in the test sample are as follows:

[0067] σ mc =10MPa, σ 0.005％ =7.5MPa, σ p =20MPa, σ rl =19MPa, ε p =0.0158%, ε rl =0.0152%, Δσ = 20MPa, the rate of stress increase during loading is 0.01MPa / s; the rate of stress decrease during loading is 0.01MPa / s.

[0068] The predicted thermal residual stress σ of the three-dimensional needled C / C-SiC ceramic matrix composite material r =1.06±2.63MPa and residual strain ε r =-0.003±0.0025% Result as follows Figure 1 As shown.

[0069] Depend on Figure 1 It can be seen that the prediction method provided by the present invention can predict the thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites.

[0070] The prediction method provided by this invention can accurately predict the overall thermal residual stress and thermal residual strain of composite materials, as well as the thermal residual stress and thermal residual strain values ​​of the fibers and matrix inside the composite material. However, traditional X-ray or ultrasonic methods cannot obtain specific values ​​of thermal residual stress and thermal residual strain, and cannot comprehensively reflect the thermal residual stress and thermal residual strain inside the composite material.

[0071] Although the above embodiments have provided a detailed description of the present invention, they are only some embodiments of the present invention, and not all embodiments. People can obtain other embodiments based on these embodiments without creative effort, and these embodiments all fall within the protection scope of the present invention.

Claims

1. A method for predicting thermal residual stress and thermal residual strain of fiber-reinforced ceramic matrix composites using hysteresis loops, comprising the following steps: (1) The fiber-reinforced ceramic matrix composite was subjected to cyclic loading and unloading tension to obtain cyclic loading and unloading stress-strain hysteresis loops with different peak stresses. During the cyclic loading and unloading tensile process, the peak loading stress increases with each cycle, and the state of the fiber-reinforced ceramic matrix composite material during loading includes an elastic segment and a nonlinear segment. (2) The elastic modulus of the fiber-reinforced ceramic matrix composite material is obtained by calculating the stress-strain hysteresis loop of the elastic segment during cyclic loading and unloading. (3) The tangent modulus at the peak stress is calculated based on the stress-strain hysteresis loop of the cyclic loading and unloading process. (4) The thermal residual strain at the corresponding peak stress is calculated based on the peak strain in the cyclic loading and unloading stress-strain hysteresis loop and the tangent modulus at the peak stress obtained in step (3); there is no temporal order between steps (2) and (4); (5) Based on the elastic modulus of the elastic segment of the fiber-reinforced ceramic matrix composite material obtained in step (2), the tangential modulus at the peak stress obtained in step (3), and the thermal residual strain at the peak stress obtained in step (4), the thermal residual stress and thermal residual strain of the fiber-reinforced ceramic matrix composite material are calculated.

2. The prediction method according to claim 1, characterized in that, In step (2), the elastic modulus of the elastic segment is obtained from the relationship shown in Equation 1: Among them, E c Let σ be the elastic modulus of the elastic segment. 0.005％ The stress corresponding to 0.005% of the cyclic loading and unloading stress-strain hysteresis loop.

3. The prediction method according to claim 1, characterized in that, The tangent modulus at the peak stress in step (3) is obtained from the relationship shown in Equation 2: Among them, E p σ is the tangent modulus at the peak stress. p For peak stress, σ rl To reload stress, ε p ε is the strain at the peak stress. rl The strain corresponding to the reloaded stress.

4. The prediction method according to claim 1, characterized in that, The thermal residual strain at the peak stress in step (4) is obtained from the relationship shown in Equation 3: Where, ε t E represents the thermal residual strain at the peak stress. p ε is the tangent modulus at the peak stress. p denoted as the strain at the peak stress.

5. The prediction method according to any one of claims 1 to 4, characterized in that, The thermal residual stress of the fiber-reinforced ceramic matrix composite material in step (5) is obtained from the relationship shown in Equation 4: Where, σ r E represents the thermal residual stress in fiber-reinforced ceramic matrix composites. c E represents the elastic modulus of the elastic segment. p ε is the tangent modulus at the peak stress. t This represents the thermal residual strain at the peak stress.

6. The prediction method according to any one of claims 1 to 4, characterized in that, The thermal residual strain of the fiber-reinforced ceramic matrix composite material in step (5) is obtained from the relationship shown in Equation 5: Where, ε r E represents the thermal residual strain of fiber-reinforced ceramic matrix composites. c E represents the elastic modulus of the elastic segment. p ε is the tangent modulus at the peak stress. t This represents the thermal residual strain at the peak stress.

7. The prediction method according to claim 1, characterized in that, The peak stress during the initial unloading in the cyclic loading and unloading tension is the initial matrix cracking stress σ. mc .

8. The prediction method according to claim 1 or 7, characterized in that, The loading process is a process in which stress gradually increases, and the rate of stress increase is 0.008 to 0.012 MPa / s.

9. The prediction method according to claim 1 or 7, characterized in that, The unloading process is a process of gradually reducing stress, with a stress reduction rate of 0.008 to 0.012 MPa / s.

10. The prediction method according to claim 1, characterized in that, The increase in peak stress during each cycle of the cyclic loading and unloading tensioning process is 20–50 MPa.

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