Ceramic fracture resistance evaluation method based on free surface effect and fracture energy objective function

Abstract

The application discloses a ceramic anti-fracture performance evaluation method based on a free surface effect and a fracture energy target function, and comprises the following steps: S1, setting a cutting distance sequence h of an edge collapse test i and satisfying a free surface dominant boundary condition; S2, performing the edge collapse test, acquiring three-dimensional topography data of a fracture surface and calculating a real three-dimensional fracture surface area A fi ; S3, performing linear regression fitting with h i 2 as independent variables and A fi as dependent variables, verifying geometric similarity, and extracting a fracture area sensitivity parameter m; S4, combining a critical strain energy release rate G IC to construct a unified energy target function, calculating fracture energy and comprehensively evaluating ceramic anti-fracture performance. The application is based on the Griffith-Irwin theory and the free surface effect, constructs a general fracture energy target function containing energy, material properties and geometric constraints, verifies geometric similarity, extracts core parameters, establishes a general benchmark for advanced ceramic evaluation, and realizes a standardized method for quickly predicting ceramic fracture energy and anti-fracture performance only by using geometric variables.

Description

Technical Field

[0001] This invention belongs to the field of advanced ceramic material mechanical property testing and evaluation technology, specifically involving a method for evaluating the fracture resistance of ceramics based on free surface effect and fracture energy objective function. Background Technology

[0002] Advanced ceramics (such as zirconium oxide, silicon nitride, and aluminum nitride) are widely used in aerospace and precision manufacturing due to their excellent high-temperature mechanical properties. However, the inherent brittleness of ceramics makes their edge areas highly susceptible to chipping failure, severely impacting reliability. Therefore, accurately assessing the fracture resistance (i.e., the ease of fracture) of ceramic materials is crucial for material design and quality control. Especially for assessing the thermal brittleness of ceramics under high-temperature service environments, the accumulation of thermal stress and micro-damage leads to a significant deterioration in fracture energy, necessitating the development of a mechanical model that can quantitatively describe energy dissipation. While various testing methods exist, current technologies still have significant shortcomings in the completeness of theoretical models and the definition of physical boundaries.

[0003] 1. Lack of a thermal brittleness assessment system Advanced ceramics experience microscopic damage accumulation under thermal shock, which leads to a significant deterioration of the material's inherent fracture energy. Recent studies have shown that existing methods largely rely on residual strength measurements and lack quantitative models that link thermally induced energy degradation to macroscopic geometric fragmentation characteristics.

[0004] 2. Theoretical Failure and Measurement Dilemmas of Traditional Indentation Fracture Method (IF) The traditional Vickers indentation fracture method (IF) has long been used to evaluate the fracture toughness (K) of ceramics. IC This is a common method. This method is mainly based on the semi-empirical formula of Anstis et al., assuming K... IC ∝ c -1.5 Where c is the crack length at the indentation corner (Quinn, GD, & Bradt, RC (2007). On the Vickers indentation fracturetoughness test. Journal of the American Ceramic Society, 90(3), 673-680.). However, Quinn and Bradt (2007) pointed out that this physical model has serious inherent defects. The tips of ceramic microcracks are not only difficult to clearly identify due to the limitations of microscope resolution, but the crack morphology often fluctuates between half-penny and Palmqvist shapes, and is greatly affected by the residual stress field on the surface. This leads to extremely high artificial uncertainty in the measurement of c value, and the calculated KIC The resulting dispersion often exceeds 30%, failing to accurately and stably reflect the material's energy properties in resisting fracture.

[0005] 3. Edge fragmentation experiments lack a universal energy objective function. Edge fragmentation testing (ECT) has gained attention because it can simulate edge damage in actual service. However, existing research is mostly limited to measuring the two-dimensional projected dimensions of the fragmented material (such as the fragmentation width W or projected area), severing the essential connection between experimental data and fracture energy dissipation. According to the classical Griffith-Irwin fracture theory, fracture is essentially an energy dissipation process, and the total fracture energy E f Compared with the newly generated true three-dimensional fracture surface area A f Proportional. The existing assessment system fails to establish a system that includes an energy term (E). f ), material property item (G IC The general functional relationship between the ) and the geometric constraint term (h) makes it impossible to use experimental data to make regular predictions of fracture behavior based on energy conservation.

[0006] 4. Lack of boundary conditions for free surface effects In the mechanical analysis of edge fracture, the relative relationship between the cutting distance h and the sample width W is crucial in determining the crack propagation path, yet it is often overlooked in existing research. The study by Thouless et al. (Thouless, MD, Evans, AG, Ashby, MF, & Hutchinson, JW (1987). The edge cracking and spalling of brittle plates. Acta Metallurgica, 35(6), 1333-1341.) shows that the stress field distribution near the edge has a decisive influence on the crack trajectory. In fact, only when h « W can the zero-stress state of the free surface dominate the asymmetric release of strain energy, forcing the crack to deflect outwards and form a crack conforming to geometric similarity (A f ∝h 2(Wang, Y. & Chen, X. (2025). "Scaling Laws and Geometric Similarity in EdgeChipping of Brittle Solids." International Journal of Fracture, 241(2), 45-59.); Conversely, when h is large, the crack tends to propagate vertically downwards or even penetrate the sample, leading to the failure of geometric similarity. The lack of a clear definition of this key physical boundary (the free surface dominance region) makes many ECT-based evaluation results fail in large-scale engineering applications that are beyond their applicability. Summary of the Invention

[0007] The purpose of this invention is to provide a method for evaluating the fracture resistance of ceramics based on the free surface effect and the fracture energy objective function, so as to overcome the shortcomings of traditional methods such as discrete physical models and complex operation.

[0008] Based on the above objectives, the present invention adopts the following technical solution: A method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function includes the following steps: S1: Select W as the width of the ceramic sample to be tested or the characteristic dimension of the edge of the component to be tested, and set the cutting distance sequence of the edge fragmentation test as h. i The dominant boundary condition for the free surface is set to h. i « W and 0.3 mm ≤ h i ≤ 1.0 mm; S2: Perform an edge fragmentation test on the ceramic sample or component to be tested, obtain the three-dimensional morphology data of the fracture surface of the fragmented slices, and calculate each cutting distance h. i The corresponding true three-dimensional fracture surface area A fi ; S3: with h i 2 As the independent variable, the actual fracture surface area A fi Using [variable name] as the dependent variable, perform zero-intercept linear regression to fit the data and verify whether the data conforms to the geometric similarity law of edge collapse; if the verification is successful, establish the geometric similarity constitutive equation A for edge collapse. fi = m·h i 2 Extract and calculate the fracture area sensitivity parameter m; if the verification fails, the test boundary condition is deemed to have failed, and the evaluation ends. S4: Obtain the critical strain energy release rate G of the ceramic sample under test. ICCombining the fracture area sensitivity parameter m extracted in step S3, a unified energy objective function E for the edge fragmentation process is constructed. f (h i ) = G IC · m · h i 2 Calculate the fracture energy E f (h i The fracture resistance of ceramics is comprehensively evaluated by combining the fracture area sensitivity parameter m.

[0009] In step S1, the component to be tested is a ceramic structural part; the material of the ceramic sample to be tested is selected from one or more of alumina, silicon nitride, zirconium oxide, and aluminum nitride; the dominant boundary condition of the free surface is set to h. i / W ≤ 0.15.

[0010] In step S1, the ceramic structural component is an armor plate or a semiconductor wafer chuck.

[0011] In step S2, the three-dimensional morphology data is acquired by scanning the fracture surface of the fragmented slice layer by layer along the Z-axis using a laser confocal microscope. The three-dimensional morphology data is then processed using image processing software to denoise and perform threshold segmentation, reconstructing the three-dimensional solid surface and calculating each cutting distance h. i The corresponding true three-dimensional fracture surface area A fi .

[0012] In step S2, the denoising and thresholding processes were performed using Zeiss Arivis Pro software, with a denoising diameter of 8.29 μm and a threshold of 5.

[0013] In step S4, when evaluating the geometric resistance to fracture based on the fracture area sensitivity parameter m, the engineering general benchmark value m ≈ 17.10 for various types of hard and brittle advanced ceramics is used as the judgment criterion: when the m value of the ceramic material to be tested is lower than the benchmark value, the material is judged to have excellent fracture resistance; when the m value is higher than the benchmark value, the material is judged to have poor fracture resistance.

[0014] To achieve the above evaluation method, the core theory and physical mechanism of this invention are as follows: 1. A scale-independent model based on "local stress dominance" (addressing the applicability issue of large structural members) This invention, based on Saint-Venant's Principle, proposes a "localization hypothesis" for edge fracture. Research shows that when the cutting distance h is at a microscale (h ≤ 1.0 mm) and satisfies h / W ≤ 0.15, the stress intensity factor K at the crack tip is controlled only by the geometric constraints of the local free surface (sidewall), and is decoupled from the overall specimen width W or the macroscopic dimensions of the component. This means that whether it is a small laboratory specimen with W = 10 mm, or a large-scale ceramic armor or turbine blade, as long as the cutting distance h is the same, its edge fracture behavior follows completely consistent physical laws. Based on this, this invention establishes a universal evaluation method across scales.

[0015] 2. Decoupling energy terms from geometric terms (solving the problem of material property differences) Based on Griffith-Irwin fracture mechanics, the total energy E consumed during material fracture is... f Equal to the critical strain energy release rate G IC Compared with the actual fracture surface area A f The product of: E f = G IC · A f (1) This invention introduces a geometric similarity constitutive equation for edge fragmentation, namely, under the dominance of free surface effects, the fracture surface area A f It is proportional to the square of the cutting distance h: A f = m · h 2 (2) Where m is the fracture area sensitivity benchmark parameter.

[0016] By combining equations (1) and (2), a unified energy objective function describing the edge collapse process is constructed: E f (h) = G IC · m · h 2 = G IC · [ψ(υ)·ξ] · h 2 (3) Among them, G IC For including elastic modulus E and fracture toughness K IC The intrinsic material properties are defined as follows: the terms within the square brackets are the parameters m extracted in this invention, where υ is Poisson's ratio, ξ is the geometric correction factor, and ψ(υ) is the crack propagation trajectory shape factor.

[0017] For hard and brittle materials like advanced ceramics, the Poisson's ratio υ varies within a very narrow range (typically between 0.20 and 0.30). The crack propagation trajectory shape factor ψ(υ) is insensitive to material properties and is mainly controlled by the geometric correction factor ξ. Therefore, m can be defined as a "quasi-universal geometric correction factor." Through extensive experimental data correction, this invention extracts an engineering benchmark value of m ≈ 17.10. The physical significance of this parameter lies in: removing the interference of material microscopic mechanical constants (such as modulus), and purely characterizing the geometric tendency of brittle solids to form crack surfaces under free surface induction.

[0018] 3. Define the physical boundaries of the "free surface dominant region". This invention deeply reveals the physical nature of parameter m and its applicable boundaries. m characterizes the geometric tendency of a material's microstructure to seek the path of minimum energy dissipation under an asymmetric stress field (one side is the loading point, and the other side is the free surface). This method is effective only when h « W (sample width) (specifically, h ≤ 0.15 W). When h « W (the applicable area of ​​this invention), the free surface, as a zero-stress boundary, greatly induces the release of strain energy to that side, forcing the crack to deflect and peel off a surface conforming to geometric similarity (A). f ∝ h 2 The slices are then taken. At this point, m is a stability constant that can accurately characterize the fragmentation resistance. When h approaches W / 2, the stress fields on both sides of the indenter tend to be symmetrical, the free surface induced effect disappears, and the crack tends to propagate vertically downwards or even penetrate the sample, leading to the failure of geometric similarity.

[0019] 4. Realistic 3D capture and multi-material statistical regression of dynamic crack propagation Traditional methods only measure two-dimensional projections, neglecting the newly formed surface area due to microscopic deflection during crack propagation. This method utilizes laser confocal microscopy to precisely capture the complex curved surface (A) formed by the crack's outward deflection from the pre-fabricated notch (h) under the induction of the free surface. f To ensure the rigor and universality of the general benchmark parameters, this invention introduces multi-material joint statistical logic when fitting the constitutive equation: first, it implements zero-intercept linear regression fitting to ensure that the surface area is zero when the physical cutting distance is zero; second, it introduces mean standard error (SEM) to plot error bars, reflecting the fluctuations in the fracture behavior of different ceramic materials under the same prefabricated geometric constraints. By performing overall regression on the test data of various typical advanced ceramics, a general fracture area sensitivity benchmark parameter m ≈ 17.10, which is robust to the material's microelastic constants, is extracted, effectively eliminating the evaluation bias caused by the inherent properties of a single material.

[0020] Compared with the prior art, the present invention has the following beneficial effects: 1. Based on the Griffith-Irwin theory and the free surface effect, this invention constructs a general fracture energy objective function that includes energy, material properties and geometric constraints. By extracting core parameters, it realizes a method to quickly predict the fracture energy and fracture resistance of ceramics based solely on geometric variables. This solves the problems of neglecting the edge effect of large-sized components and the poor model universality caused by not considering the differences in material elastic constants in the prior art. 2. This invention, by aggregating experimental data from various advanced ceramics (alumina, silicon nitride, zirconium oxide, and aluminum nitride), and after eliminating random biases, performs statistical regression with mean error bars (SEM Error Bars) to extract a universally applicable fracture area sensitivity benchmark parameter. Even when the precise properties of the material are unknown, the fracture energy threshold E can be determined using the benchmark m value simply by measuring the cutting distance h. f Quantitative prediction can quickly determine the quality of a material's fracture resistance. 3. This invention utilizes this physical mechanism to capture the most sensitive "free surface fracture characteristics" of materials by locking a small scale range h, simplifying the complex fracture energy assessment into a regularized prediction model that is only related to the geometric variable h, thus realizing a rapid, quantitative and physically meaningful evaluation of the fracture resistance of ceramic materials. Attached Figure Description

[0021] Figure 1 This is a model construction and flowchart of the present invention; Figure 2 The actual three-dimensional fracture surface area A of four ceramics at different cutting distances. f Measurement data; Figure 3 This is a fitting diagram of the overall fracture surface area of ​​advanced ceramics obtained by the method of this invention. Detailed Implementation

[0022] The present invention will be further described below with reference to specific embodiments and accompanying drawings. Example

[0023] A method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function includes the following steps: S1: Experimental Setup and Boundary Delineation: Four typical advanced ceramic samples were selected: zirconium oxide (ZrO2), silicon nitride (Si3N4), aluminum nitride (AlN), and alumina (Al2O3). The sample width W = 10 mm. To capture the fracture characteristics of the free surface, a set cutting distance sequence h was set for the edge fragmentation test. i = 0.3, 0.5, 0.8, 1.0 mm (i.e., h) 2 =0.09, 0.25, 0.64, 1.00mm2 ), maximum cutting distance h max (1.0 mm) / W = 0.1, satisfying h ≤0.15W, ensuring that all experiments are strictly within the physical boundary dominated by the release of free surface strain energy.

[0024] S2: Acquisition of 3D Morphology and True Area: Edge fragmentation tests were conducted using a diamond indenter. Z-stack scanning was performed layer-by-layer along the Z-axis on the fracture surfaces of each fragmented section using a laser confocal microscope to acquire the 3D morphology data. Reconstruction was performed using Zeiss Arivis Pro software (denoising diameter set to 8.29 μm, threshold set to 5), and the distance h at each cut was measured. i The corresponding true three-dimensional fracture surface area A fi The result is as follows Figure 2 The data points are shown.

[0025] S3: Geometric similarity verification and constitutive equation establishment: using h i 2 As the independent variable, the actual fracture surface area A of each ceramic material is used. fi Using [variable name] as the dependent variable, a zero-intercept linear regression was performed to first verify geometric similarity. The fitting results showed that the data points for each material were highly linearly distributed, proving that under the boundary condition h ≤ 0.15W, the crack stably deflects towards the free surface, which conforms to the geometric similarity law. Subsequently, the constitutive equation A was established. fi = m·h i 2 Extract the fracture area sensitivity benchmark parameter m; The specific fitting parameters are as follows: The fitting equation for zirconium oxide (E ≈ 210 GPa) is A f = 16.8 · h 2 The fitting equation for silicon nitride (E ≈ 300 GPa) is A. f = 17.4 · h 2 The fitting slopes for alumina and aluminum nitride stabilize at 17.0 and 17.2, respectively. If the scatter plot shows non-linear divergence, it indicates that the free surface effect is lost, and the m value cannot be extracted at this time, so the process should end.

[0026] Data distribution and fitting results (see) Figure 2 The graph shows that the horizontal axis represents the square of the cutting distance, h. 2 (mm) 2 The vertical axis represents the actual fracture surface area A. f (mm) 2In the figure, black data points represent the overall average fracture surface area of ​​the four ceramic materials at corresponding cutting distances, and red error bars represent the standard error of the mean (SEM) in Table 1, reflecting the statistical confidence level of the data. The blue solid line is the overall zero-intercept linear fit line based on all data (A...). f = 17.10≈ h 2 This verifies the universality of constitutive models in macroscopic statistics.

[0027] S4: Construction and Comprehensive Evaluation of the Fracture Energy Objective Function: Obtaining the Critical Strain Energy Release Rate G of the Ceramic Material Under Test IC Construct a unified energy objective function E for the edge collapse process. f（hi） = G IC · m · h i 2 Based on this, a two-dimensional evaluation is conducted: 1. Relative geometric resistance assessment based on parameter m: The general benchmark value m ≈ 17.10 for various types of hard and brittle advanced ceramics extracted in this invention is introduced. When the m value of the ceramic material under test is lower than 17.10 (e.g., zirconia m = 16.8 in this example), it indicates that under the same geometric constraints, the energy dissipation path (surface area) required for material fracture is shorter, crack propagation is strongly suppressed, and it exhibits excellent fracture resistance. When the m value is higher than 17.10 (e.g., silicon nitride m = 17.4), it indicates that the material tends to form larger area fragmentation, and the damage tolerance is relatively low.

[0028] 2. Absolute energy assessment based on a unified objective function: Substitute the extracted m value into E f (h i Within the function, the component's machining allowance h can be calculated. i The total real fracture energy E required for macroscopic fragmentation to occur f This value intuitively reflects the energy threshold at which a material resists external forces.

[0029] Universality Demonstration: To establish an industry-standard evaluation benchmark, zirconia (E ≈ 210 GPa) and silicon nitride (E ≈ 300 GPa), which have significantly different elastic moduli, were compared. The results show that despite differences in inherent material properties and absolute fracture energy, the slope *m* of their area growth exhibits a high degree of consistency. The overall regression slope is *m*. total = 17.10, the overall regression equation is A f = 17.1 · h 2 (See Figure 3 The maximum deviation is only ±2%. This proves that the parameter m is a geometric constant that is robust to the elastic constant of the material.

[0030] like Figure 3 As shown in the figure, this figure presents the fitting results of the overall fracture surface area of ​​various advanced ceramics as a function of the square of the cutting distance. The horizontal axis in the figure represents the square of the cutting distance, h. 2 (Unit: mm) 2 The vertical axis represents the actual fracture surface area A. f (Unit: mm) 2 ).

[0031] Data Points and Error Bands: The black dots in the figure represent the overall average fracture surface area of ​​four typical advanced ceramics (zirconia, silicon nitride, aluminum nitride, and alumina) at the corresponding four cutting distances; the red error bar running through the black dots represents the mean standard error (Mean ± SEM). The small span of this error bar reflects the condition that h ≤ 0.15W and 0.3 mm ≤ h. i Under the free surface dominant boundary condition of ≤ 1.0 mm, the fracture behavior of ceramic materials with different elastic constants exhibits extremely low volatility, and the data have extremely high statistical confidence.

[0032] Overall Fit Line: The solid blue line in the figure is the curve obtained by performing an overall zero-intercept linear fit based on all ceramic test data. This fitted curve passes strictly through the origin, confirming the objective fact that "the surface area is zero when the cutting distance is zero" in a physical sense.

[0033] Core parameter extraction: The fitting equation for the blue solid line is A. f = 17.1 · h 2 This figure visually confirms that, despite the differences in the internal micromechanical properties of different ceramics, their macroscopic fracture surface areas, dominated by local free surface effects, all highly conform to the geometric similarity law. The overall fracture area sensitivity benchmark parameter m ≈ 17.10 (i.e., the slope of the straight line) extracted from this can serve as a general engineering benchmark for evaluating the fracture resistance of large-size ceramic components.

[0034] Quantitative prediction method: In engineering, small differences in Poisson's ratio can be ignored, and m=17.10 can be directly used as a general benchmark for evaluating the fracture resistance of large-size ceramic components. For a known critical strain energy release rate G... IC Approximately 40 J / m 2 For the novel ceramic, if the processing allowance (cutting distance) h = 0.5 mm is set, quantitative prediction can be directly performed using the general objective function of this invention: E f = G IC · m · h 2 = 40 · 17.10 · 0.5 2 = 171 mJ This embodiment verifies that once the general reference parameter m is determined by this method, the complex assessment of fracture energy dissipation can be simplified into a regularized model that relies solely on the geometric variable h, achieving the technical effect of determining fracture risk without repeated testing.

Claims

1. A method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function, characterized in that, Includes the following steps: S1: Select W as the width of the ceramic sample to be tested or the characteristic dimension of the edge of the component to be tested, and set the cutting distance sequence of the edge fragmentation test as h. i The dominant boundary condition for the free surface is set to h. i « W and 0.3 mm ≤ h i ≤ 1.0 mm; S2: Perform an edge fragmentation test on the ceramic sample or component to be tested, obtain the three-dimensional morphology data of the fracture surface of the fragmented slices, and calculate each cutting distance h. i The corresponding true three-dimensional fracture surface area A fi ; S3: with h i 2 As the independent variable, the actual fracture surface area A fi Using the variable as the dependent variable, perform zero-intercept linear regression to verify whether the data conforms to the geometric similarity law of edge collapse; If the verification passes, then the geometric similarity constitutive equation A for edge fragmentation is established. fi = m·h i 2 Extract and calculate the fracture area sensitivity parameter m; If the verification fails, the test boundary conditions are deemed invalid, and the evaluation ends. S4: Obtain the critical strain energy release rate G of the ceramic sample under test. IC Combining the fracture area sensitivity parameter m extracted in step S3, a unified energy objective function E for the edge fragmentation process is constructed. f (h i ) = G IC ·m · h i 2 Calculate the fracture energy E f (h i The fracture resistance of ceramics is comprehensively evaluated by combining the fracture area sensitivity parameter m.

2. The method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function as described in claim 1, characterized in that, In step S1, the component to be tested is a ceramic structural part; the material of the ceramic sample to be tested is selected from one or more of alumina, silicon nitride, zirconium oxide, and aluminum nitride; the dominant boundary condition of the free surface is set to h. i / W ≤ 0.

15.

3. The method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function as described in claim 2, characterized in that, In step S1, the ceramic structural component is an armor plate or a semiconductor wafer chuck.

4. The method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function as described in claim 1, characterized in that, In step S2, the three-dimensional morphology data is acquired by scanning the fracture surface of the fragmented slice layer by layer along the Z-axis using a laser confocal microscope. The three-dimensional morphology data is then processed using image processing software to denoise and perform threshold segmentation, reconstructing the three-dimensional solid surface and calculating each cutting distance h. i The corresponding true three-dimensional fracture surface area A fi .

5. The method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function as described in claim 4, characterized in that, In step S2, the denoising and thresholding processes were performed using Zeiss Arivis Pro software, with a denoising diameter of 8.29 μm and a threshold of 5.

6. The method for evaluating the fracture resistance of ceramics based on the free surface effect and fracture energy objective function as described in claim 1, characterized in that, In step S4, when evaluating the geometric resistance to fracture based on the fracture area sensitivity parameter m, the engineering general benchmark value m ≈ 17.10 for various types of hard and brittle advanced ceramics is used as the judgment criterion: when the m value of the ceramic material to be tested is lower than the benchmark value, the material is judged to have excellent fracture resistance; when the m value is higher than the benchmark value, the material is judged to have poor fracture resistance.

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