Method for obtaining material fracture toughness based on fatigue failure specimen
By testing materials with unstable crack propagation based on fatigue failure specimens, the problem of specimen size not meeting the plastic zone conditions was solved. This simplifies and improves the accuracy of plane stress fracture toughness testing for brittle materials, obtains fracture toughness curves, and improves the accuracy of plane strain fracture toughness prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI ELECTRIC POWER GENERATION EQUIPMENT CO LTD
- Filing Date
- 2022-07-12
- Publication Date
- 2026-04-17
AI Technical Summary
In the existing technology, for materials whose sample size does not meet the plastic zone size condition, it is difficult to effectively obtain the plane strain fracture toughness KIC and the plane stress fracture toughness KC, and the accuracy of the existing conversion model is not ideal.
Planar stress fracture toughness testing of crack-progressing materials based on fatigue failure specimens was conducted. By measuring the crack depth and load-deformation curves generated by the fatigue test, the stress intensity factor was calculated using calibration coefficients, and the relationship between ligament width and fracture toughness was fitted to predict plane strain fracture toughness.
This method simplifies and improves the accuracy of plane stress fracture toughness testing for brittle materials, reduces experimental costs, obtains fracture toughness curves with different ligament widths, and improves the accuracy of plane strain fracture toughness prediction.
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Figure CN117433888B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of metal material performance testing technology, specifically to a method for obtaining the fracture toughness of materials based on fatigue failure samples. Background Technology
[0002] Fracture toughness is an important parameter for damage tolerance assessment and service life evaluation of defective structural components. Based on the stress state at the defect tip, it can be divided into plane strain fracture toughness K. IC plane stress fracture toughness K C For materials with medium to low toughness and large workpieces, plane strain fracture toughness K is typically used. IC For design evaluation, plane stress fracture toughness K is suitable for small-sized workpieces, thin plates, and other components. C .
[0003] plane strain fracture toughness K IC The validity criteria for the test are quite stringent, requiring a sufficiently large specimen size to adequately constrain the plastic deformation at the crack tip. Increased triaxial stress corresponds to a decrease in fracture toughness, leading to brittle fracture, thus obtaining a relatively conservative fracture toughness. For highly tough metallic materials, specimens meeting the plane strain condition require a considerably large plastic zone size. This is supported by standards such as GB / T 21143-2014 "Unified Test Method for Quasi-Static Fracture Toughness of Metallic Materials" and ASTM E 399 "Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K". IC Standards such as "of Metallic Materials" set the size of the plastic zone as... For example, the fracture toughness K of a certain alloy material IC =150MPa.m 0.5 Yield strength R p0.2 =500MPa, calculate The prerequisite for conducting plane strain fracture toughness tests on this alloy is that the specimen thickness B, crack depth a, and ligament width Wa must all be greater than 225 mm. Such dimensional requirements are impractical for specimen preparation and testing machine operation. However, according to standard requirements, plane strain fracture toughness test results that do not meet the dimensional conditions of the plastic zone are invalid. Therefore, for materials whose specimen dimensions cannot meet the plane strain conditions, plane stress fracture toughness tests need to be conducted in conjunction with the actual dimensions of the component and the laboratory equipment conditions, followed by numerical conversion of plane strain fracture toughness. However, the accuracy of existing conversion models is not ideal.
[0004] Plane stress fracture toughness K CThere are few reference specifications for testing; currently, the only testing standards are ASTM E561 Standard Test Method for KR Curve Determination and HB 5261-1983 Metal Sheet K. R Curve Test Method, K R The curve represents the change in material toughness as crack propagation is expressed using the stress intensity factor. The K value corresponding to the point of tangency between the resistance curve and the crack propagation force curve is the plane stress fracture toughness K. C This method depends on the specimen thickness and is independent of the initial crack depth and specimen shape, making it easy to implement in engineering. However, this standard only applies to materials where cracks propagate slowly and steadily under plane stress conditions, and the required specimen width is still much larger than the plastic zone size, as in the alloys mentioned above, where the required CT specimen width to meet plane stress conditions is... MT sample width Therefore, the problem of not being able to meet the sample size requirements still exists.
[0005] In summary, for crack-propagated materials where the specimen size does not meet the dimensional requirements of the plastic zone, there is still no reasonable way to obtain the plane strain fracture toughness K. IC plane stress fracture toughness K C The experimental method. Summary of the Invention
[0006] To address the aforementioned shortcomings, this invention provides a method for obtaining the fracture toughness of materials based on fatigue failure specimens. This method utilizes fatigue failure specimens whose dimensions do not meet the existing plastic zone size conditions to perform plane stress fracture toughness tests on materials with unstable crack propagation, obtaining fracture toughness curves corresponding to different ligament widths, and then predicting the plane strain fracture toughness, thereby solving the problems existing in the prior art.
[0007] This invention provides a method for obtaining the fracture toughness of a material based on a fatigue failure specimen, comprising the following steps:
[0008] To determine whether the material under test is brittle, in a tensile test, the load-deformation curve of a brittle material can be divided into three stages: elastic deformation, plastic deformation and fracture stage. Generally, there is no obvious yield deformation stage and uniform plastic deformation stage.
[0009] Multiple circular cross-section specimens of the brittle material to be tested were made, the center diameter of the specimens was recorded, and then fatigue tests were carried out until the specimens failed due to fatigue.
[0010] Multiple failed specimens with visible cracks on the surface were selected. An extensometer was clamped on each failed specimen, and a tensile load was applied by a tensile testing machine until the failed specimen broke. The load-deformation curve was recorded.
[0011] Measure the maximum crack depth on the crack surface of the fracture surface of the specimen and calculate the ligament width;
[0012] Determine the slope b1 of the straight line L1 in the elastic deformation stage of the load-deformation curve, and draw a straight line L2 with a slope of b2 from the origin O, where b2 = 0.95b1; denote the load corresponding to the intersection of the straight line L2 and the load-deformation curve as the critical load F5.
[0013] Substituting the critical load F5, the center diameter of the specimen, and the maximum crack depth into equation (1), the calculated stress intensity factor K is denoted as the conditional fracture toughness K. Q :
[0014]
[0015] Where F is the load borne by the specimen; D is the center diameter of the specimen; a is the maximum crack depth; S0 is the original cross-sectional area at the center of the specimen, obtained from the formula... Determine; k0, k1, k2, k3...k n These are calibration coefficients; n≥4;
[0016] The conditional fracture toughness and ligament width obtained from multiple failed specimens are fitted according to Equation (2) to obtain the specific relationship between ligament width and conditional fracture toughness:
[0017] K Q =W+Ue -γ(D-a) Equation (2)
[0018] In the formula: W is the first fitting parameter, U is the second fitting parameter, γ is the first fitting exponent, e is the base of the natural logarithm, and Da is the ligament width;
[0019] Extending the ligament width-conditional fracture toughness fitting curve positively, the conditional fracture toughness K increases with the increase of ligament width. Q The fracture toughness continues to decrease until a plateau is reached; the fracture toughness value corresponding to this plateau is the plane strain fracture toughness K. IC .
[0020] Preferably, the strength and plasticity parameters and tensile curve characteristics of the reference material are used to determine whether the material to be tested is brittle.
[0021] Preferably, the circular cross-section specimen is a funnel-shaped specimen.
[0022] Preferably, the number of failed samples selected is no less than 5.
[0023] Preferably, the maximum crack depth in the crack surface on the fracture surface of the specimen is measured using an optical measuring device.
[0024] Preferably, in equation (1), k0, k1, k2, k3...kn Determined through calibration tests.
[0025] The advantages of this invention lie in its use of fatigue-failed specimens for plane stress fracture toughness testing of materials with unstable crack propagation. The cracks generated during fatigue testing serve as pre-cracks for the fracture toughness specimens, enabling the reuse of discarded specimens. The operation is simple and easy, simplifying the testing process and reducing experimental costs. It is suitable for plane stress fracture toughness testing of brittle materials that cannot meet the plane strain size determination criteria. This invention also obtains fracture toughness curves corresponding to different ligament widths, thereby predicting plane strain fracture toughness with high accuracy and strong practicality. Attached Figure Description
[0026] Figure 1 The load-deformation curve of the sample in Example 1;
[0027] Figure 2 This is a schematic diagram of the fracture surface of the circular cross-section specimen used in Example 1;
[0028] Figure 3 The conditional fracture toughness K of the sample in Example 1 Q A diagram showing the relationship between the ligament width Da;
[0029] Figure 4 This is a diagram showing the extended relationship between fracture toughness K and ligament width in Example 1. Detailed Implementation
[0030] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. These embodiments are only for illustrating the present invention and are not intended to limit the present invention. Unless otherwise specified, some steps or methods involved in the following embodiments are conventional methods in the art, and the materials and instruments involved are conventional materials and instruments unless otherwise specified.
[0031] The following will illustrate the method for obtaining material fracture toughness based on fatigue failure specimens provided by the present invention with reference to Example 1.
[0032] Example 1
[0033] Example 1 includes the following steps:
[0034] 1) The material to be tested is 15Cr. The yield strength R of 15Cr at room temperature is... p0.2 =1180 MPa, elongation after fracture A = 16.5%. In the tensile test, the load-deformation curve of 15Cr material can be divided into three stages: elastic deformation, plastic deformation, and fracture stage. Based on the comprehensive judgment, 15Cr is a brittle material, and step 2 can be continued.
[0035] 2) Prepare multiple hourglass-shaped specimens with a center diameter D = 6 mm from the material to be tested, and then conduct high-cycle fatigue tests on the multiple hourglass-shaped specimens until the specimens fail due to fatigue. Those skilled in the art can also prepare other circular cross-section specimens such as cylindrical or conical specimens as needed. In this invention, "center diameter" refers to the minimum diameter at the center of the circular cross-section specimen.
[0036] 3) Select multiple failed specimens with visible surface cracks. Clamp an extensometer onto each failed specimen and mount it on a tensile testing machine. Apply a tensile load to the specimen until it fractures. The extensometer measures the axial deformation of the specimen during the test. The testing software automatically records the load-deformation curve for each failed specimen, such as... Figure 1 As shown.
[0037] Since the crack shapes and depths in the selected failed specimens are not entirely consistent, the fracture test results obtained in step 3) will have a certain degree of dispersion. Therefore, the number of failed specimens with visible cracks on the surface selected in step 3) should be no less than 5. In this embodiment, 6 failed specimens are used.
[0038] 4) such as Figure 2 As shown, in a tensile test, the crack in the specimen gradually propagates from the crack initiation point to the fracture zone, forming a crack surface at the fracture. The maximum crack depth 'a' on the crack surface at the fracture is measured using optical measuring equipment (such as SEM), and the ligament width of the specimen, Da, is calculated.
[0039] 5) such as Figure 1 As shown, the load-deformation curve of any failed specimen includes the elastic deformation stage (the specimen deforms elastically, and the deformation is proportional to the load), the plastic deformation stage (to continue deforming the specimen, the load must be increased to overcome the increasing resistance to deformation inside the specimen), and the fracture stage (cracks in the specimen propagate rapidly, the load decreases rapidly, until the specimen breaks). The load corresponding to the starting point of the fracture stage is the maximum load F that the specimen can withstand during the tensile process. max .
[0040] When calculating fracture toughness based on this load-deformation curve, the maximum load F cannot be used. max Because the applied load is lower than the maximum load F max At this point, the crack has already begun to propagate gradually in the specimen. However, because the initial crack propagation is very small, it is not easily detected. Therefore, certain engineering assumptions are required to determine the critical load for crack instability propagation from the load-deformation curve. The determination method is as follows: determine the slope b1 of the straight line L1 in the elastic deformation stage of the load-deformation curve, and draw a straight line L2 with a slope of b2 from the origin O, where b2 = 0.95b1; the load corresponding to the intersection of the straight line L2 and the load-deformation curve is denoted as the critical load F5.
[0041] 6) Substitute the critical load F5, the center diameter D of the specimen, and the maximum crack depth a into equation (1), and denote the calculated stress intensity factor K as the conditional fracture toughness K. Q :
[0042]
[0043] Where F is the load borne by the specimen; D is the center diameter of the specimen; a is the maximum crack depth; S0 is the original cross-sectional area at the center of the specimen, obtained from the formula... Determine; k0, k1, k2, k3...k n is the calibration coefficient; n is a natural number greater than or equal to 4.
[0044] k0, k1, k2, k3...k n The calibration test was conducted to determine the calibration coefficient. Specifically, the calibration test included the following steps: N samples of the same size as those in step 2) were prepared from the material to be tested in step 1). These N samples underwent fatigue tests with different cycle numbers, fixed stress ratios, and fixed load ranges. The fatigue load and maximum crack depth of each sample were recorded. Then, the stress intensity factor K of the crack obtained for the corresponding cycle number was obtained using the finite element method. Finally, the fatigue load, maximum crack depth, center diameter, stress intensity factor K, and the selected value of n for these N samples were substituted into equation (1) to calculate the calibration coefficient. The larger the number of samples N, the more accurate the test results. To meet the calculation requirements of equation (1), N ≥ n + 1.
[0045] In this embodiment, the number of samples N used in the calibration test is 5, and n is 4. Equation (1) is as follows:
[0046]
[0047] Among them, k0 = 0.0461, k1 = -0.2416, k2 = 1.5233, k3 = -3.386, and k4 = 3.1884.
[0048] 7) The test results obtained from 6 failed samples in this embodiment are shown in Table 1:
[0049] Table 1. Experimental Results
[0050]
[0051] The conditional fracture toughness K in Table 1 Q The ligament width Da is fitted according to equation (2) to obtain the relationship between the ligament width Da and the conditional fracture toughness K. Q The specific relational formula, and such as Figure 3 The ligament width Da and conditional fracture toughness K are shown.Q Fitted curve.
[0052] K Q =W+Ue -γ(D-a) Equation (2)
[0053] In the formula: W is the first fitting parameter, U is the second fitting parameter, γ is the first fitting exponent, e is the base of the natural logarithm, and Da is the ligament width.
[0054] In this embodiment, the ligament width Da and the conditional fracture toughness K Q In the specific relationship, the first fitting parameter W = 149.6, the second fitting parameter U = 10725.7, and the first fitting index γ = 1.836.
[0055] 8) Determine the ligament width Da as the conditional fracture toughness K. Q The fitted curve extends positively, such as Figure 4 As shown, with the increase of the toughness band Da, the plane stress state gradually changes to the plane strain state, and the conditional fracture toughness K Q The fracture toughness continues to decrease until a plateau is reached; the fracture toughness value K corresponding to this plateau is the plane strain fracture toughness K. IC .
[0056] Since the trend of fracture toughness change when the ligament width approaches 0 is not clear, in step 8), the curves with ligament widths between 0 and the minimum ligament width obtained in the experiment (i.e., the minimum ligament width in Table 1) are not extended. Only the curves with ligament widths greater than the maximum ligament width obtained in the experiment (i.e., the maximum ligament width in Table 1) are extended, i.e., the aforementioned positive extension, to obtain the predicted plane strain fracture toughness K. IC .
[0057] To verify the effectiveness of the method of the present invention, a compact tensile specimen was also processed using 15Cr steel. The plane strain fracture toughness of the specimen was tested according to the standard GB / T 21143-2014, "Unified Test Method for Quasi-Static Fracture Toughness of Metallic Materials". The specimen thickness was 25 mm, the specimen width was 50 mm, the crack length was 31 mm, and the ligament width was 19 mm. The plane strain fracture toughness of the two specimens obtained from the test was 148.3 MPa / m. 0.5 and 141.02 MPa.m 0.5 The plane strain fracture toughness obtained by fitting the curve according to formula (2) of the present invention is 149.6 MPa.m for the same ligament width. 0.5 .like Figure 4 As shown, the deviations between the plane strain fracture toughness obtained according to the present invention and the plane strain fracture toughness obtained by standard test are 0.88% and 6.08%, respectively, which meet the deviation requirements and can verify the effectiveness of the method of the present invention.
[0058] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention.
Claims
1. A method for obtaining the fracture toughness of a material based on a fatigue failure specimen, characterized in that, Includes the following steps: Multiple circular cross-section specimens of the brittle material to be tested were made, the center diameter of the specimens was recorded, and then fatigue tests were carried out until the specimens failed due to fatigue. Multiple failed specimens with visible cracks on the surface were selected. An extensometer was clamped on each failed specimen, and a tensile load was applied by a tensile testing machine until the failed specimen broke. The load-deformation curve was recorded. Measure the maximum crack depth on the crack surface of the fracture surface of the failed specimen and calculate the ligament width; Determine the slope b1 of the straight line L1 in the elastic deformation stage of the load-deformation curve, and draw a straight line L2 with a slope of b2 from the origin O, where b2 = 0.95b1; denote the load corresponding to the intersection of the straight line L2 and the load-deformation curve as the critical load F5. The critical load F5, the center diameter of the sample, and the maximum crack depth are substituted into Equation (1), and the calculated stress intensity factor K is denoted as the conditional fracture toughness K Q : Equation (1) Where F is the critical load F5 borne by the failed specimen; D is the center diameter of the specimen; a is the maximum crack depth; S0 is the original cross-sectional area at the center of the specimen, obtained from the formula... Determine; k0, k1, k2, k3...k n These are calibration coefficients; n≥4; The conditional fracture toughness and ligament width obtained from multiple failed specimens are fitted according to equation (2) to obtain the specific relationship between ligament width and conditional fracture toughness: Equation (2) In the formula: W is the first fitting parameter, U is the second fitting parameter, γ is the first fitting exponent, e is the base of the natural logarithm, and Da is the ligament width; The width-condition fracture toughness fitting curve of ligament is extended forwardly, with the increase of ligament width, the condition fracture toughness K Q continuously decreases until a platform appears, the fracture toughness value corresponding to the platform is the plane strain fracture toughness K IC .
2. The method according to claim 1, characterized in that, By referencing the strength, plasticity parameters, and tensile curve characteristics of the reference material, it can be determined whether the material under test is brittle.
3. The method according to claim 1, characterized in that, The circular cross-section specimen is a funnel-shaped specimen.
4. The method according to claim 1, characterized in that, The number of failed samples selected should be no less than 5.
5. The method according to claim 1, characterized in that, The maximum crack depth in the cracked surface of the fracture surface of the failed specimen was measured using optical measuring equipment.
6. The method according to claim 1, characterized in that, In equation (1), k0, k1, k2, k3...k n Determined through calibration tests.
Citation Information
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