CN111024486B - Creep behavior prediction method for unidirectional ceramic matrix composite - Google Patents
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Abstract
The invention discloses a creep behavior prediction method of a unidirectional ceramic matrix composite, which is based on the fact that the fiber and matrix strain in a bonding region are the same, obtains the fiber and matrix stress in the bonding region under different creep stress and time, and further obtains the change of the crack density of the matrix. And combining a shear model to obtain the fiber stress change in the creep process, considering the fiber failure and the load born by the failed fiber, and finally calculating the creep curve of the unidirectional ceramic matrix composite. The method can accurately predict the creep curve of the unidirectional ceramic matrix composite material at different temperatures and creep stress levels, and discloses the mesoscopic failure mechanism of the internal components of the material. On the other hand, the whole calculation process is simple and efficient, and the defects of high cost and long time consumption of the experimental method are overcome.
Description
Technical Field
The invention relates to the technical field of composite material creep behavior prediction, in particular to a method for predicting the creep behavior of a unidirectional ceramic matrix composite material.
Background
With the development of the aircraft engine technology and the improvement of the performance thereof, in addition to the improvement and optimization of the design scheme, higher requirements are also put forward on the materials for the aircraft engine. Ceramic Matrix Composites (CMCs) have been gradually and widely used in aircraft engine hot end components, such as tailpipe, governor, combustor liner, etc., due to their characteristics of high specific strength, high specific modulus, and excellent high temperature resistance.
Under the actual service environment of the aircraft engine, the ceramic matrix composite structural member bears the combined action of high temperature and load, and the material can generate creep behavior, so that the performance of the material is degraded, even creep fracture occurs, and the safe use of the aircraft engine is seriously threatened. Therefore, it is necessary to study the creep mechanism and behavior of the ceramic matrix composite material in a high temperature environment. The fiber arrangement of the unidirectional ceramic matrix composite material is along the same direction, the structural form of the unidirectional ceramic matrix composite material is simpler, and the unidirectional ceramic matrix composite material is a preferred material for researching the failure mechanism and the mechanical behavior of the material. The creep mechanism and behavior of the unidirectional ceramic matrix composite material in a high-temperature environment are researched, and a solid foundation can be laid for researching the creep behavior and failure mechanism of the woven ceramic matrix composite material.
The current research on the creep behavior of materials mainly comprises two aspects of experimental test and theoretical simulation. The test mainly comprises the steps of testing the deformation of the material under constant load, obtaining a creep curve of the material under the constant load, and analyzing the creep curve. Because the ceramic matrix composite material has high preparation cost and long preparation period, and the creep test time is often long, if the creep behavior of the material is tested by adopting the test, a large amount of manpower and material resources are often consumed, and because the internal structure of the ceramic matrix composite material is relatively complex, the failure mechanism inside the material is difficult to describe in the test process, so the mesoscopic failure mechanism inside the material needs to be explained by means of theoretical simulation. In the prior art, a method for predicting the creep behavior of a material by adopting theoretical simulation is mainly used for simulating the creep behavior of the material on the basis of parameters of a model obtained by fitting a creep curve obtained by experimental test. For example, patent CN108256179A, "a method for predicting a material creep curve", provides a method for predicting a creep curve, but the method mainly fits a test creep curve to obtain parameters in a creep model, and predicts the creep curve of a material under a certain stress and temperature based on the parameters obtained by fitting, but the method cannot effectively reflect the mesoscopic failure mechanism of the material, and at the same time, the method is only applicable to metals and metal-based composite materials, and is not applicable to unidirectional ceramic-based composite materials. The patent CN103323343A "determination method and prediction method of creep failure life of polymer material" provides a determination and prediction method of creep failure life, which is mainly based on creep test curves under different stresses, and performs straight line fitting on the curve at the steady state stage to obtain the critical point of creep failure of the material, and based on this, determines the failure strain and creep life of the material. However, the method can not simulate the microscopic failure mechanism of the material, and is only suitable for polymer materials and is not suitable for unidirectional ceramic matrix composite materials. The literature, "CMCs creep mechanical behavior and mesomechanics simulation" ([ D ]. Nanjing university of aerospace, 2017) develops the creep test research of the unidirectional ceramic matrix composite, but a prediction method of a creep curve of the unidirectional ceramic matrix composite is not given, and the mesoscopic failure mechanism of the unidirectional ceramic matrix composite is not disclosed.
Therefore, the method for predicting the creep behavior of the unidirectional ceramic matrix composite material is an important and difficult technical problem in the technical field.
Disclosure of Invention
The invention aims to provide a creep behavior prediction method of a unidirectional ceramic matrix composite, which is based on the fact that the fibers in a bonding region and the matrix have the same strain, so that the fibers in the bonding region and the matrix stress under different creep stresses and different time are obtained, and the change of the crack density of the matrix is further obtained. And combining a shear model to obtain the fiber stress change in the creep process, considering the fiber failure and the load born by the failed fiber, and finally calculating the creep curve of the unidirectional ceramic matrix composite. The method not only can accurately predict the creep curve of the unidirectional ceramic matrix composite material under different temperatures and creep stress levels, but also reveals the mesoscopic failure mechanism of the internal components of the material. On the other hand, the whole calculation process is simple and efficient, and the defects of high cost and long time consumption of the experimental method are overcome.
In order to achieve the above object, with reference to fig. 1, the present invention provides a method for predicting creep behavior of a unidirectional ceramic matrix composite, where the method includes:
s1: setting creep stress and creep time;
s2: under the conditions of current creep stress and creep time, calculating the fiber and matrix stress in the bonding area of the unidirectional ceramic matrix composite, judging whether matrix cracks are generated, if not, switching to the step S5, otherwise, executing the step S3;
s3: determining an average matrix crack spacing based on the critical matrix strain energy;
s4: determining the fiber stress distribution between two adjacent cracks based on the fiber stress distribution of the bonding area;
s5: determining the failure number of the fibers based on the stress distribution and the strength distribution of the fibers, judging whether the fibers are completely failed, if so, ending the process, otherwise, calculating the stress distribution of the broken fibers and the residual intact fibers, and entering the step S6;
s6: calculating the strain of the material, outputting, repeating the steps S2-S5 until the material fails or the creep reaches a specified time, and ending the process.
In a further embodiment, the step S2 of calculating the fiber and matrix stresses in the bond area of the unidirectional ceramic matrix composite under the current creep stress and creep time conditions includes the steps of:
s21: in the creep process of the unidirectional ceramic matrix composite, if the strain of the bonding region fiber and the matrix is the same, the stress of the bonding region fiber and the matrix can satisfy the following equation set:
wherein σf0,σm0Respectively bonding zone fiber and matrix stress, Ef,EmIs the modulus of elasticity, v, of the fibres and the matrixf.vmVolume fractions of the fiber and the matrix respectively, sigma is creep stress of the unidirectional ceramic matrix composite, t is creep time, Af,AmIs a constant number, Pf1,Pm1Denotes a constant, P, related to the creep stress of the fiber and the matrixf2,Pm2Is a constant related to the fiber and matrix creep time;
s22: and solving the equation system to obtain the stress magnitude of the bonding area fiber and the matrix.
In a further embodiment, in step S2, the basis for determining whether the crack is generated is:
if the matrix stress of the bonding area is smaller than the matrix cracking stress, judging that no matrix crack is generated, and the fiber stress of the whole material is the fiber stress of the bonding area; otherwise, it is judged that the matrix crack is generated.
In a further embodiment, in step S3, the process of determining the average matrix crack spacing based on the critical matrix strain energy includes the steps of:
s31: determining the critical matrix strain energy criterion as follows:
Um＝Ucrm
in the formula of Um,UcrmRespectively, matrix strain energy and critical matrix strain energy, wherein UmCan be expressed as:
wherein σmIs the matrix stress distribution in the mean matrix crack spacing, SmArea of matrix, L mean matrix crack spacing;
s32: cracking stress sigma of critical matrixmcrSubstituting the matrix strain energy formula to obtain Ucrm；
And substituting the matrix stress of the bonding area into the matrix strain energy formula, and combining a critical matrix strain energy criterion to obtain the average matrix crack spacing under the current creep load and creep time, wherein the calculation formula is as follows:
in the formula, LdThe expression for the interfacial debonding length is shown below:
wherein, tauiIs the interfacial friction between the fibres/matrix, rfIs the fiber radius.
In a further embodiment, in step S4, the process of determining the fiber stress distribution between two adjacent cracks based on the fiber stress distribution of the bonding region includes the steps of:
s41: under the current load, when the debonding length of the interface is larger than half of the crack spacing of the matrix, judging that the interface is completely debonded, otherwise, judging that the interface is partially debonded;
s42: based on the shear-lag model, the fiber stress distribution when the interface part is debonded is as follows:
when the interface is completely debonded, the fiber stress distribution is as follows:
in a further embodiment, in step S5, the process of determining the number of fiber failures based on the fiber stress distribution and the fiber strength distribution includes the following steps:
s51: testing to obtain the strength data of the fiber monofilaments at high temperature;
s52: obtaining the fiber defect intensity distribution at high temperature;
s53: comparing the fiber stress with the fiber strength to determine the number of fiber failures
In a further embodiment, in step S5, the calculating of the stress distribution of the broken fibers and the remaining intact fibers means,
calculating the load borne by the failed fiber according to the following formula:
wherein, LbiIndicating the distance of the ith failure fiber fracture position from the crack plane;
based on the equilibrium equation of forces at the crack plane, the load stress σ' actually sustained by the unbroken fibers under an external load σ is calculated:
wherein N represents the total number of fibers.
In a further embodiment, in step S6, the material strain is calculated and output, and the above steps S2-S5 are repeated until the material fails or the creep reaches a prescribed time,
substituting the load stress sigma' actually born by the unbroken fibers under the external load sigma as the current creep stress into the step S2, and repeatedly executing the steps S2-S5 until no fibers continue to fail or all fibers fail under the current load and creep time.
In a further embodiment, the prediction method further comprises:
s7: the fiber stress distribution formula is substituted into the formula shown below to calculate the intact fiber strain:
wherein, αf,αcThe thermal expansion coefficients of the fiber and the composite material are respectively, and delta T is the difference value between the preparation temperature and the creep deformation temperature of the material;
the composite strain is obtained from the intact fiber strain.
Compared with the prior art, the technical scheme of the invention has the following remarkable beneficial effects:
(1) the creep curve of the unidirectional ceramic matrix composite material under different temperatures and creep stress levels can be accurately predicted, and the mesoscopic failure mechanism of the internal components of the material is disclosed.
(2) The whole calculation process is simple and efficient, and the defects of high cost and long time consumption of an experimental method are overcome.
It should be understood that all combinations of the foregoing concepts and additional concepts described in greater detail below can be considered as part of the inventive subject matter of this disclosure unless such concepts are mutually inconsistent. In addition, all combinations of claimed subject matter are considered a part of the presently disclosed subject matter.
The foregoing and other aspects, embodiments and features of the present teachings can be more fully understood from the following description taken in conjunction with the accompanying drawings. Additional aspects of the present invention, such as features and/or advantages of exemplary embodiments, will be apparent from the description which follows, or may be learned by practice of specific embodiments in accordance with the teachings of the present invention.
Drawings
The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of the method for predicting creep behavior of a unidirectional ceramic matrix composite of the present invention.
FIG. 2 is a representative voxel map of the material after matrix cracking has occurred.
FIG. 3 is a schematic of a fiber/matrix stress distribution, wherein 3(a) the fiber/matrix stress distribution is partially debonded and 3(b) the fiber/matrix stress distribution is fully debonded.
FIG. 4 is a graph of average matrix crack spacing as a function of creep time.
FIG. 5 is a graph illustrating creep of a unidirectional ceramic matrix composite.
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
With reference to fig. 1, the invention provides a method for predicting creep behavior of a unidirectional ceramic matrix composite, comprising the following steps:
(1) and obtaining the fiber and matrix stress in the bonding area of the unidirectional ceramic matrix composite material under a certain creep stress and creep time. During creep of the unidirectional ceramic matrix composite, assuming the bond site fiber and matrix strains are the same, the bond site fiber and matrix stresses satisfy the equation set shown below:
wherein σf0,σm0Respectively bonding zone fiber and matrix stress, Ef,EmIs the modulus of elasticity, v, of the fibres and the matrixf.vmVolume fractions of the fiber and the matrix respectively, sigma is creep stress of the unidirectional ceramic matrix composite, t is creep time, Af,AmIs a constant number, Pf1,Pm1Denotes a constant, P, related to the creep stress of the fiber and the matrixf2,Pm2Is a constant related to the fiber and matrix creep time. Solving equation (1) yields the stress levels of the bonding region fibers and the matrix. And (4) if the matrix stress of the bonding area is smaller than the matrix cracking stress, no matrix crack is generated, the fiber stress of the whole material is the fiber stress of the bonding area, and the step (4) is executed, otherwise, the step (2) is executed.
In this example, the creep related parameters of the unidirectional ceramic matrix composite are shown in Table 1.
TABLE 1 unidirectional ceramic matrix composites high temperature creep related parameters
(2) The average matrix crack spacing is determined based on the critical matrix strain energy. The critical matrix strain energy criterion is:
Um＝Ucrm(2)
Um,Ucrmrespectively, matrix strain energy and critical matrix strain energy, wherein UmCan be expressed as:
wherein σmIs the matrix stress distribution in the mean matrix crack spacing, SmArea of matrix, L mean matrix crack spacingmcrSubstituting equation (3) can obtain Ucrm. The average matrix crack spacing under the current creep load and creep time can be obtained by substituting the matrix stress of the bonding area into the formula (3) and combining the formula (2), and the calculation formula is as follows:
wherein, LdThe expression for the interfacial debonding length is shown below:
wherein, tauiIs the interfacial friction between the fibres/matrix, rfIs the fiber radius.
In this example, the voxel is analyzed as represented by a material with an average matrix crack spacing, as shown in FIG. 2. The change in average matrix crack spacing with creep time is shown in fig. 4. It can be seen from the figure that the average matrix crack spacing decreases faster at the beginning of creep, i.e. the material develops many matrix cracks faster. As creep time increases, the matrix cracks gradually tend to saturate.
(3) Determining the fiber stress distribution between two adjacent cracks based on the fiber stress distribution of the bonding area. Under the current load, when the debonding length of the interface is larger than half of the crack spacing of the matrix, the interface is completely debonded, otherwise, the interface is partially debonded. Based on the shear-lag model, the fiber stress distribution when the interface part is debonded is as follows:
when the interface is completely debonded, the fiber stress distribution is as follows:
the fiber and matrix stress distribution at the interface with partial and complete debonding is shown in fig. 3(a) and 3 (b). In this example, the interface gradually changed from partial debonding to full debonding with increasing creep time and the transition occurred at minute 34.
(4) And determining the failure number of the fibers based on the fiber stress distribution and the fiber strength distribution, and judging whether the fibers completely fail. The fiber monofilament strength data at high temperature is obtained through tests, and the fiber defect strength distribution at high temperature is obtained, wherein the method for obtaining the fiber defect strength distribution at high temperature can adopt the prior art, for example, the patent with the publication number of CN106777562B, namely 'a method for determining the strength of a ceramic matrix composite'. Comparing the fiber stress with the fiber strength to determine the number of fiber failures Nf. If all the fibers fail, the calculation is finished, otherwise, the load borne by the failed fibers is calculated as follows:
wherein, LbiIndicating the distance of the ith failure fiber fracture site from the crack plane. Based on the equilibrium equation of forces at the crack plane, the load stress σ' actually sustained by the unbroken fibers under an external load σ is calculated:
wherein N represents the total number of fibers. And (3) bringing the formula (8) into the step (1), and repeatedly executing the steps (1) to (4) until no fiber continues to fail or all the fibers fail under the current load and creep time.
(5) And calculating the strain of the material, outputting, and repeating the steps until the material fails or creep reaches a specified time. And the intact fiber strain is the strain of the composite material. The intact fiber strain is calculated by substituting equation (5) or (6) into the equation shown below:
wherein, αf,αcThe thermal expansion coefficients of the fiber and the composite material are respectively, and the delta T is the difference value between the preparation temperature and the creep deformation temperature of the material.
In this example, the creep curve of the unidirectional ceramic matrix composite at 100 minutes was calculated as shown in FIG. 5. It is found from the graph that the rate of increase in creep deformation gradually decreases as the creep time increases.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily defined to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, as the disclosed concepts and embodiments are not limited to any one implementation. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.
Claims (9)
1. A method for predicting creep behavior of a unidirectional ceramic matrix composite, the method comprising:
s1: setting creep stress and creep time;
s2: under the conditions of current creep stress and creep time, calculating the fiber and matrix stress in the bonding area of the unidirectional ceramic matrix composite, judging whether matrix cracks are generated, if not, switching to the step S5, otherwise, executing the step S3;
s3: determining an average matrix crack spacing based on the critical matrix strain energy;
s4: determining the fiber stress distribution between two adjacent cracks based on the fiber stress distribution of the bonding area;
s5: determining the failure number of the fibers based on the stress distribution and the strength distribution of the fibers, judging whether the fibers are completely failed, if so, ending the process, otherwise, calculating the stress distribution of the broken fibers and the residual intact fibers, and entering the step S6;
s6: calculating the strain of the material, outputting, repeating the steps S2-S5 until the material fails or the creep reaches a specified time, and ending the process.
2. The method of claim 1, wherein the step S2 of calculating the fiber and matrix stresses in the bond regions of the unidirectional ceramic matrix composite under the current creep stress and creep time conditions includes the steps of:
s21: in the creep process of the unidirectional ceramic matrix composite, if the strain of the bonding region fiber and the matrix is the same, the stress of the bonding region fiber and the matrix can satisfy the following equation set:
wherein σf0,σm0Respectively bonding zone fiber and matrix stress, Ef,EmIs the modulus of elasticity, v, of the fibres and the matrixf,vmVolume fractions of the fiber and the matrix respectively, sigma is creep stress of the unidirectional ceramic matrix composite, t is creep time, Af,AmIs a constant number, Pf1,Pm1Denotes a constant, P, related to the creep stress of the fiber and the matrixf2,Pm2Is a constant related to the fiber and matrix creep time;
s22: and solving the equation system to obtain the stress magnitude of the bonding area fiber and the matrix.
3. The method of predicting creep behavior of a unidirectional ceramic matrix composite according to claim 1, wherein in step S2, the criterion for determining whether a matrix crack is generated is:
if the matrix stress of the bonding area is smaller than the matrix cracking stress, judging that no matrix crack is generated, and the fiber stress of the whole material is the fiber stress of the bonding area; otherwise, it is judged that the matrix crack is generated.
4. The method of claim 2, wherein the step S3 of determining the mean matrix crack spacing based on the critical matrix strain energy comprises the steps of:
s31: determining the critical matrix strain energy criterion as follows:
Um＝Ucrm
in the formula of Um,UcrmRespectively, matrix strain energy and critical matrix strain energy, wherein UmCan be expressed as:
wherein σmIs the matrix stress distribution in the mean matrix crack spacing, SmArea of matrix, L mean matrix crack spacing;
s32: cracking stress sigma of critical matrixmcrSubstituting the matrix strain energy formula to obtain Ucrm；
Substituting the matrix stress of the bonding area into the matrix strain energy formula, and combining a critical matrix strain energy criterion to obtain the average matrix crack distance under the current creep load and creep time, wherein the calculation formula is as follows:
in the formula, LdThe expression for the interfacial debonding length is shown below:
wherein, tauiIs the interfacial friction between the fibres/matrix, rfIs the fiber radius.
5. The method of predicting creep behavior of a unidirectional ceramic matrix composite according to claim 4, wherein said step S4 of determining the fiber stress distribution between two adjacent cracks based on the fiber stress distribution of the bond region comprises the steps of:
s41: under the current load, when the debonding length of the interface is larger than half of the crack spacing of the matrix, judging that the interface is completely debonded, otherwise, judging that the interface is partially debonded;
s42: based on the shear-lag model, the fiber stress distribution when the interface part is debonded is as follows:
when the interface is completely debonded, the fiber stress distribution is as follows:
6. the method of claim 1, wherein the step S5 of determining the number of fiber failures based on the fiber stress distribution and the fiber strength distribution comprises the steps of:
s51: testing to obtain the strength data of the fiber monofilaments at high temperature;
s52: obtaining the fiber defect intensity distribution at high temperature;
s53: and comparing the fiber stress with the fiber strength to determine the fiber failure number.
7. The method of claim 5 wherein said calculating stress distribution of broken fibers and residual intact fibers in step S5 is performed by,
calculating the load borne by the failed fiber according to the following formula:
wherein, LbiIndicating the distance of the ith failure fiber fracture position from the crack plane;
based on the equilibrium equation of forces at the crack plane, the load stress σ' actually sustained by the unbroken fibers under an external load σ is calculated:
wherein N represents the total number of fibers, NfThe total number of broken fibers.
8. The method of claim 1, wherein in step S6, calculating the material strain and outputting it, repeating the above steps S2-S5 until the material fails or the creep reaches a predetermined time,
substituting the load stress sigma' actually born by the unbroken fibers under the external load sigma as the current creep stress into the step S2, and repeatedly executing the steps S2-S5 until no fibers continue to fail or all fibers fail under the current load and creep time.
9. The method of predicting creep behavior of a unidirectional ceramic matrix composite of claim 5, further comprising:
s7: substituting the fiber stress distribution formula into the following formula to calculate the intact fiber strain:
wherein, αf,αcThe thermal expansion coefficients of the fiber and the composite material are respectively, and delta T is the difference value between the preparation temperature and the creep deformation temperature of the material;
the composite strain is obtained from the intact fiber strain.
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