Notched sample fatigue life prediction method based on equivalent strain energy density

Abstract

The invention relates to a notched sample fatigue life prediction method based on equivalent strain energy density, and the method comprises the steps: obtaining a to-be-measured notched sample, setting any fatigue life of the to-be-measured notched sample, and calculating a critical distance based on the characteristic relation between the fatigue life and the critical distance; and obtaining the equivalent strain energy density of the critical distance, and inputting the equivalent strain energy density into the characteristic curve based on the strain energy density and the fatigue life to obtain the predicted life. According to the method, test data, finite element simulation and critical distance theories are fused, and a traditional stress control fatigue life prediction model is successfully expanded to the field of strain control low-cycle fatigue and creep-fatigue. According to the method, the test period and cost are remarkably reduced while the prediction precision is ensured, and the method has outstanding engineering practical value and technical popularization potential.

Description

Technical Field

[0001] The invention relates to the technical field of fatigue life reliability analysis of high-temperature reactors, in particular to a notched specimen fatigue life prediction method based on equivalent strain energy density. Background Art

[0002] Core petrochemical equipment (coke towers, catalytic reactors, etc.) faces extremely harsh working conditions during their service. Due to the long-term operation of the equipment under high temperature and high pressure conditions, creep damage is inevitable. In addition, due to the particularity of the process flow, the equipment needs to be frequently started and stopped, resulting in fatigue damage to the reactor. In addition to single damage, the superposition of this cyclic load and the high temperature and high pressure environment makes high-temperature equipment extremely susceptible to fatigue crack initiation and propagation. In addition, the discontinuous structural features formed during the manufacturing process of high-temperature reactors to achieve multifunctional integration will cause uneven stress / strain distribution, posing a threat to the safe operation of high-temperature reactors and greatly affecting the efficiency of chemical production. Therefore, studying the creep-fatigue life prediction method of high-temperature reactors with notches has important research value and engineering significance for ensuring the high-quality and healthy development of the petrochemical industry.

[0003] In the fatigue life prediction of notched specimens, the strain energy life prediction model has become one of the important tools in the engineering field due to its unique advantages in multi-axial stress field analysis. When a specimen is subjected to external load, the energy stored due to deformation is called strain energy. The strain energy stored per unit volume is called strain energy density, such as Figure 1 As shown in the figure, strain energy is divided into elastic strain energy and plastic strain energy. Plastic strain energy is only generated when plastic deformation occurs:

[0004] Elastic strain energy density (ESED) and plastic strain energy density (PSED) can be calculated using equations (1) and (2):

[0005]

[0006] Among them, Δε p and Δε e are plastic strain and elastic strain respectively, n ' is the cyclic strain hardening exponent. The total strain energy density can be obtained by adding the elastic strain energy density and the plastic strain energy density:

[0007]

[0008] Critical distance theory was developed to account for the impact of the stress state in the high-stress region near the notch root on fatigue damage. However, most existing critical distance theories are based on low-cycle fatigue testing under stress control. Few studies have investigated the effectiveness of critical distance theory in predicting low-cycle fatigue and creep-fatigue life under strain control. Because traditional methods require extensive experimental data for life prediction, increasing both financial and time costs, a life prediction model suitable for notched specimens under strain control is urgently needed. Summary of the Invention

[0009] To address the aforementioned challenges of the existing technology, the present invention aims to provide a fatigue life prediction method for notched specimens based on equivalent strain energy density. By incorporating strain energy density as a core damage parameter, this method effectively integrates the dual damage effects of stress and strain to achieve accurate predictions over a wider range. While maintaining prediction accuracy, this method significantly reduces the time and financial investment required by traditional testing methods, providing a highly efficient solution for reliability assessment of engineering components.

[0010] To achieve the above object, the present invention provides the following solutions:

[0011] The fatigue life prediction method of notched specimen based on equivalent strain energy density includes:

[0012] Obtaining a notched specimen to be tested, giving an arbitrary fatigue life of the notched specimen to be tested, and calculating the critical distance based on a characteristic relationship between fatigue life and critical distance;

[0013] The equivalent strain energy density of the critical distance is obtained, and the equivalent strain energy density is input into a characteristic curve based on strain energy density and fatigue life to obtain a predicted life.

[0014] Optionally, obtaining the characteristic relationship includes:

[0015] Obtaining the fatigue life of the notched specimen, inputting the fatigue life of the notched specimen into the characteristic curve to obtain the strain energy density;

[0016] Finite element simulation is performed on the notched specimen under strain-controlled low-cycle fatigue and creep-fatigue loads to extract the equivalent strain energy density of the notch root cross section;

[0017] The strain energy density attenuation path from the maximum point along the notch root to the center of the notch specimen is obtained. When a node appears where the strain energy density is equal to the equivalent strain energy density of the cross section at the notch root, the distance from the node to the notch root is a critical distance that is a multiple of the target, and a characteristic relationship between fatigue life and critical distance is established.

[0018] Optionally, establishing the characteristic relationship based on fatigue life and critical distance includes:

[0019] l0=A×N f B

[0020] Where l0 is the critical distance, A and B are material constants, and N f is the fatigue life.

[0021] Optionally, obtaining the equivalent strain energy density of the critical distance includes: taking the strain energy density at the node corresponding to the notched specimen to be tested as the equivalent strain energy density of the critical distance.

[0022] Optionally, obtaining the characteristic curve includes:

[0023] obtaining a smooth specimen, performing finite element simulation on the smooth specimen under strain-controlled low-cycle fatigue and creep-fatigue loads, and obtaining creep-fatigue test data;

[0024] The characteristic curve based on strain energy density and fatigue life is drawn according to the creep-fatigue test data.

[0025] Optionally, drawing the characteristic curve based on strain energy density and fatigue life includes:

[0026] ΔW t ×N f β =C

[0027] Where ΔW t is the strain energy density, N f is the fatigue life, β and C are material constants.

[0028] Optionally, the finite element simulation includes: a pre-processing stage and a post-processing stage;

[0029] The pre-processing stage includes: defining material properties, meshing, applying cyclic displacement and boundary constraints;

[0030] The post-processing stage includes: solving statics and extracting equivalent strain energy density distribution data at the notch root.

[0031] Optionally, obtaining the predicted lifespan includes:

[0032] Inputting the equivalent strain energy density into a characteristic curve based on strain energy density and fatigue life to obtain the fatigue life of the notched specimen to be tested;

[0033] The fatigue life of the notched specimen to be tested is used as a new fatigue life to replace the arbitrary fatigue life, and recalculated until the fatigue life of the notched specimen to be tested is equal to the new fatigue life, thereby outputting the fatigue life as the predicted life.

[0034] The beneficial effects of the present invention are:

[0035] Due to the relationship between the critical distance l0 and fatigue life N of different notched specimens under strain control f The functional relationship shows significant differences. Therefore, the present invention obtains the corresponding parameterized expression through step-by-step operation, or introduces the stress concentration factor K t This method achieves adaptive correction for specimens with different notches. Furthermore, this invention overcomes the limitations of traditional critical distance theory in pure fatigue testing and, for the first time, extends it to the field of life prediction in creep-fatigue testing. By combining strain energy density with critical distance theory, it effectively integrates the dual damage effects of stress and strain, achieving accurate predictions over a wider range.

[0036] Compared with the traditional life prediction method that relies on massive test data and high capital investment, the present invention uses the smooth sample ΔW under strain control to t -N f The characteristic curve is combined with finite element simulation to construct the critical distance l0 and fatigue life N f The quantitative correlation model effectively avoids the need for large-scale test samples, significantly reducing the cost-effectiveness of the entire life cycle while ensuring prediction accuracy. At the same time, the present invention adopts a streamlined and standardized life prediction process, and reduces the difficulty of engineering application through clearly correlated functional expressions.

[0037] This method combines experimental data, finite element simulation, and critical distance theory to successfully extend the traditional stress-controlled fatigue life prediction model to the strain-controlled low-cycle fatigue and creep-fatigue fields. While ensuring prediction accuracy, this method significantly reduces testing cycles and costs, demonstrating outstanding engineering value and potential for technological dissemination. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 The strain energy stored in unit volume is the strain energy density diagram;

[0040] Figure 2 This is a flow chart of a method for predicting fatigue life of a notched specimen based on equivalent strain energy density according to an embodiment of the present invention;

[0041] Figure 3 The smooth member ΔW of the embodiment of the present inventiont -N f Schematic diagram of the curve;

[0042] Figure 4 Schematic diagram of a two-dimensional axisymmetric model of a notched specimen according to an embodiment of the present invention;

[0043] Figure 5 The critical distance l0 and fatigue life N in the embodiment of the present invention are f Function relationship diagram of ;

[0044] Figure 6 This is a diagram of the life prediction results of an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] This embodiment discloses a fatigue life prediction method for a notched specimen based on equivalent strain energy density, comprising: obtaining a notched specimen to be tested, giving an arbitrary fatigue life of the notched specimen to be tested, and calculating a critical distance based on a characteristic relationship between fatigue life and critical distance; obtaining an equivalent strain energy density at the critical distance, inputting the equivalent strain energy density into a characteristic curve based on strain energy density and fatigue life, and obtaining a predicted life.

[0048] like Figure 2 As shown, this embodiment proposes a fatigue life prediction method for notched specimens based on equivalent strain energy density, which includes the following implementation steps: first, a smooth specimen is used to obtain low-cycle fatigue and creep-fatigue test data under strain control conditions, and the total strain energy density ΔW of the smooth specimen is plotted. t and fatigue life N f Characteristic curve between; Test fatigue life N for notched specimen f , from ΔW t -N f Find the corresponding strain energy density in the characteristic curve The stress-strain field of the notched specimen under the same loading conditions was analyzed by finite element simulation method to obtain the equivalent strain energy density on the cross section of the notch root. Distribution data; Apply the point method in critical distance theory to determine the critical distance l0 of notched specimen under given life; Establish the relationship between critical distance l0 of notched specimen and fatigue life N f Function expression between; given any fatigue life N of the sample to be predicted f1 , through the critical distance l0 and fatigue life N f Solve the function expression between the corresponding critical distance l0; perform finite element simulation analysis on the predicted sample, and determine its equivalent strain energy density based on the calculated critical distance l0 Equivalent strain energy density Substitute the smooth sample ΔW t -N f The characteristic curve is used to reverse the life span and obtain the predicted life span N f2 ; Establish iterative convergence criterion, when N f2 =N f1 The calculation is terminated when the predicted life span N is output. f2 , if N f2 ≠N f1 , then N f2 Give N f1 Recalculate and execute the above iterative process repeatedly until N f2 =N f1 .

[0049] Furthermore, obtaining the characteristic relationship includes: obtaining the fatigue life of the notch specimen, inputting the fatigue life of the notch specimen into the characteristic curve, and obtaining the strain energy density; performing finite element simulation on the notch specimen under strain-controlled low-cycle fatigue and creep-fatigue loads, and extracting the equivalent strain energy density of the notch root cross section; obtaining the strain energy density attenuation path from the maximum value point along the notch root to the center of the notch specimen, when a node with a strain energy density equal to the equivalent strain energy density of the notch root cross section appears, the distance from the node to the notch root is a critical distance that is a target multiple, and a characteristic relationship based on fatigue life and critical distance is established.

[0050] Specifically, for the notched specimen test fatigue life N f , through ΔW t -N f Characteristic curve determines its corresponding strain energy density

[0051] Conduct finite element simulations of notched specimens under strain-controlled low-cycle fatigue and creep-fatigue loads to extract the equivalent strain energy density on the notch root cross section Distribution data;

[0052] Specifically, a notched specimen finite element model is constructed based on a two-dimensional axisymmetric modeling method, and the simulation process is completed through finite element software, which includes two stages: pre-processing and post-processing. The pre-processing stage requires defining material properties, completing mesh division, and applying cyclic displacement and boundary constraints; the post-processing stage includes statics solution and extracting the equivalent strain energy density distribution data of the notch root cross section. Figure 4 shown.

[0053] The strain energy density attenuation path along the maximum point of the notch root to the center of the specimen is positioned to meet The node of the condition, the distance from the node to the root of the notch is half of the critical distance l0, and the strain energy density at the node is the equivalent strain energy density required by the critical distance theoretical model.

[0054] According to the above steps, several groups of notched specimens are selected again to test fatigue life N f , combined with the critical distance theoretical point method, the critical distance value l0 and equivalent strain energy density corresponding to different fatigue lives are obtained respectively According to the formula:

[0055] l0=A×N f B

[0056] The fitting results are A and B, where A and B are material constants. Figure 5 After all the fitting is completed, a complete creep-fatigue life prediction model of notched specimen based on the strain-controlled critical distance theory of equivalent strain energy density can be obtained.

[0057] Furthermore, obtaining the equivalent strain energy density of the critical distance includes: taking the strain energy density at the node corresponding to the notched specimen to be tested as the equivalent strain energy density of the critical distance.

[0058] Furthermore, obtaining the characteristic curve includes: obtaining a smooth specimen, performing finite element simulation on the smooth specimen under strain-controlled low-cycle fatigue and creep-fatigue loads, and obtaining creep-fatigue test data; and drawing a characteristic curve based on strain energy density and fatigue life according to the creep-fatigue test data.

[0059] Specifically, the function is used based on the low-cycle fatigue and creep-fatigue test data of smooth specimens under strain control:

[0060] ΔW t ×N f β =C

[0061] ΔW of the fitted smooth sample t -N f Characteristic curves, such as Figure 3 As shown, where Nf is the fatigue life of the test, ΔW t is the strain energy density.

[0062] Furthermore, the finite element simulation includes: a pre-processing stage and a post-processing stage; the pre-processing stage includes: defining material properties, meshing, applying cyclic displacement and boundary constraints; the post-processing stage includes: static solution and extracting the equivalent strain energy density distribution data at the notch root.

[0063] Specifically, the specific implementation method of finite element simulation of notched specimens is: constructing a finite element model of the notched specimen based on the two-dimensional axisymmetric modeling method, and completing the simulation process through finite element software, which includes two stages: pre-processing and post-processing; the pre-processing stage requires defining material properties, completing mesh division, and applying cyclic displacement and boundary constraints; the post-processing stage includes static solution and extracting the equivalent strain energy density distribution data at the notch root.

[0064] Furthermore, obtaining the predicted life includes: inputting the equivalent strain energy density into a characteristic curve based on strain energy density and fatigue life to obtain the fatigue life of the notched specimen to be tested; replacing any fatigue life with the fatigue life of the notched specimen to be tested as a new fatigue life, and recalculating until the fatigue life of the notched specimen to be tested is equal to the new fatigue life, thereby outputting the fatigue life as the predicted life.

[0065] Specifically, if Figure 6 As shown, the life prediction process is as follows: first, the fatigue life N of the sample to be predicted is given f1 , substitute it into the formula:

[0066] l0=A×N f B

[0067] The critical distance l0 is obtained. The equivalent strain energy density of the sample to be predicted is determined based on the critical distance l0 obtained above by performing finite element simulation on the sample to be predicted. The equivalent strain energy density obtained above is Substitute ΔW t -N f The characteristic curve is used to reverse the life span and obtain the predicted life span N f2 If N f2 =N f1 , then terminate the iteration and output the predicted life span N f2 Otherwise, N f2 Reassign to N f1 Repeat the above steps until N f2 =N f1 .

[0068] This example combines experimental data, finite element simulation, and critical distance theory to successfully extend the traditional stress-controlled fatigue life prediction model to the strain-controlled low-cycle fatigue and creep-fatigue domains. This method significantly reduces test cycles and costs while ensuring prediction accuracy, demonstrating outstanding engineering practicality and potential for technological dissemination.

[0069] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A fatigue life prediction method for notched specimens based on equivalent strain energy density, characterized in that: include: Obtaining a notched specimen to be tested, giving an arbitrary fatigue life of the notched specimen to be tested, and calculating the critical distance based on a characteristic relationship between fatigue life and critical distance; The equivalent strain energy density of the critical distance is obtained, and the equivalent strain energy density is input into a characteristic curve based on strain energy density and fatigue life to obtain a predicted life.

2. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 1, characterized in that: Acquiring the feature relationship includes: Obtaining the fatigue life of the notched specimen, inputting the fatigue life of the notched specimen into the characteristic curve to obtain the strain energy density; Performing finite element simulation on the notched specimen under strain-controlled low-cycle fatigue and creep-fatigue loads to extract the equivalent strain energy density of the notch root cross section; The strain energy density attenuation path from the maximum point along the notch root to the center of the notch specimen is obtained. When a node appears where the strain energy density is equal to the equivalent strain energy density of the cross section at the notch root, the distance from the node to the notch root is a critical distance that is a multiple of the target, and a characteristic relationship between fatigue life and critical distance is established.

3. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 2, characterized in that: Establishing the characteristic relationship based on fatigue life and critical distance includes: l0=A×N f B Where l0 is the critical distance, A and B are material constants, and N f is the fatigue life.

4. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 2, characterized in that: Obtaining the equivalent strain energy density of the critical distance includes: taking the strain energy density at the node corresponding to the notched specimen to be tested as the equivalent strain energy density of the critical distance.

5. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 1, characterized in that: Obtaining the characteristic curve includes: Obtaining a smooth specimen, performing finite element simulation on the smooth specimen under strain-controlled low-cycle fatigue and creep-fatigue loads, and obtaining creep-fatigue test data; The characteristic curve based on strain energy density and fatigue life is drawn according to the creep-fatigue test data.

6. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 5, characterized in that: Drawing the characteristic curve based on strain energy density and fatigue life includes: ΔW t ×N f β =C Where ΔW t is the strain energy density, N f is the fatigue life, β and C are material constants.

7. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 5, characterized in that: The finite element simulation includes: a pre-processing stage and a post-processing stage; The pre-processing stage includes: defining material properties, meshing, applying cyclic displacement and boundary constraints; The post-processing stage includes: solving statics and extracting equivalent strain energy density distribution data at the notch root.

8. The fatigue life prediction method of notched specimen based on equivalent strain energy density according to claim 1, characterized in that: Obtaining the predicted lifespan includes: Inputting the equivalent strain energy density into a characteristic curve based on strain energy density and fatigue life to obtain the fatigue life of the notched specimen to be tested; The fatigue life of the notched specimen to be tested is used as a new fatigue life to replace the arbitrary fatigue life, and recalculated until the fatigue life of the notched specimen to be tested is equal to the new fatigue life, thereby outputting the fatigue life as the predicted life.

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