A method for measuring the stress-strain relationship in the depth direction of gradient nanomaterial cylindrical specimens based on the peeling method
By abstracting the cylindrical specimen of gradient nanomaterials into a concentric cylindrical laminate using the delamination method, electrolytic delamination and tensile testing were performed. This solved the problem of measuring the stress-strain relationship in the depth direction of gradient nanomaterials, and enabled accurate measurement of the stress-strain response of each depth unit and optimization of material properties.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-06
- Publication Date
- 2026-04-03
AI Technical Summary
Existing technologies struggle to accurately measure the stress-strain relationship of gradient nanomaterials in the depth direction, especially the stress-strain response of each depth unit during tensile testing, and existing methods cannot fully reflect the plasticity of the material.
The gradient nanomaterial rod sample was abstracted into a concentric cylindrical laminate by the peeling method. Samples with different numbers of layers were obtained by electrolytic peeling. Tensile tests were performed and the stress-strain relationship was solved. The stress-strain response of each depth element was obtained by combining interpolation and smoothing.
It enables accurate measurement of the stress-strain response of gradient nanomaterials at various depths during tensile testing, fully reflecting the plasticity of the material, providing guidance for optimizing process parameters, and improving material performance.
Smart Images
Figure CN116858636B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of materials mechanics behavior, and in particular relates to a method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method. Background Technology
[0002] Gradient nanomaterials refer to materials whose structural unit dimensions vary spatially in a gradient manner. Their unique architecture exhibits superior mechanical properties, significantly improving material strength while retaining good plasticity. This technology has already been implemented in various pure metals (such as Cu, Fe, Ni, Ti) and alloys (such as stainless steel, titanium alloys, and nickel-based alloys). In engineering applications, the Shanghai Baosteel Research Institute utilizes ultrasonic mechanical grinding surface nano-sizing technology to treat the surface of cold-rolled straightening rolls. This significantly improves the wear resistance of the rolls without altering the material composition, increasing their service life from 2-3 days to 6-9 days. This technology is already in mass production at Baosteel. Furthermore, in the aerospace and nuclear power fields, where material performance requirements are high, gradient nanomaterials have broad application prospects. Taking 316L material as an example, 316L austenitic stainless steel, as a structural material in nuclear engineering, is widely used in key components of nuclear power equipment such as pressurized water reactor main loop piping, in-core support plates, and pressure vessel weld overlays. However, 316L austenitic stainless steel has relatively low strength and hardness, and poor fatigue and wear resistance. Due to factors such as equipment start-up / shutdown, flow-induced vibration, and cyclic thermal stress, these critical components are subjected to alternating loads for extended periods, posing a risk of fatigue failure. Fatigue cracks typically initiate on the component surface, thus surface strengthening can enhance fatigue resistance. Surface mechanical treatment can process surface materials into gradient nanostructures and introduce residual compressive stress, thereby significantly improving the high-cycle and low-cycle fatigue performance of the raw materials. However, while improving the mechanical properties of the material, its unique architecture makes the study of stress-strain relationships along the depth direction extremely complex. The gradient layer of the gradient nanostructure contains various characteristic structural units with different mechanical properties, which are non-uniformly distributed along the depth direction. In other words, the characteristic structural units do not satisfy statistical uniformity; therefore, the gradient layer material should be considered a heterogeneous material with non-uniform mechanical properties. To fully realize the potential of gradient nanomaterials, understanding the distribution of stress-strain relationships along the depth direction is indispensable. Currently, there are two types of measurement methods. One is to measure the material's strength through instrumented micro / nano indentation experiments, measure the hardness along the depth direction, and then use empirical formulas to establish the relationship between hardness and flow stress. This method cannot obtain detailed and accurate stress-strain curves, nor can it measure the material's plasticity. Another method involves using focused ion beam (FIB) to prepare micron-scale indented specimens. This method can obtain materials at different depths individually, and tensile tests can be performed on these materials to obtain stress-strain relationships at different depths. However, due to the size effect, the stress-strain curves obtained from micro-indented specimens are usually higher than those from macroscopic specimens. Furthermore, during the tensile testing of nanocrystalline / ultrafine-grained small specimens prepared by machining, necking occurs due to strain localization at very small strains (~5%), making it impossible to obtain the intrinsic plasticity of the material.Based on the above, this paper proposes a method for measuring the stress-strain relationship in the depth direction of gradient nanomaterial cylindrical specimens based on the peeling method. This method can almost completely (except for all stretching stages after necking) and accurately present the stress-strain response of each depth unit during the stretching process of gradient nanomaterials. Summary of the Invention
[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for measuring the stress-strain relationship in the depth direction of a circular rod sample of gradient nanomaterials based on the peeling method. This method aims to obtain the stress-strain response of each depth unit of the gradient nanomaterial during the tensile process, providing a theoretical basis for studying the strong synergistic effect of gradient nanomaterials and providing theoretical guidance for the preparation of excellent gradient nanomaterials.
[0004] The objective of this invention is achieved through the following technical solution: a method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method, comprising the following steps:
[0005] S1: Abstract the gradient nanostructured round rod sample into a concentric cylindrical laminate, divide the gradient part into N layers, process N+1 gradient nanostructured samples with the same thickness under the same working conditions, and number them in order from small to large diameter.
[0006] S2: Electrolytic stripping of gradient nanostructured round rod samples was performed to different degrees according to the numbering order. The larger the sample number, the more layers were stripped. The number of layers ranged from 0 to N layers, and the stripped samples were obtained.
[0007] S3: Perform tensile tests on the delaminated specimens to obtain strain-tensile force data for specimens with different numbers of delaminated layers;
[0008] S4: Smooth and interpolate the strain-tensile force data of specimens with different numbers of layers to obtain the tensile force corresponding to specimens with different numbers of layers at the same strain.
[0009] S5: Using the tensile force corresponding to different number of layers of specimens with the same strain obtained in step S4, the tensile force data of specimens with a difference of 1 layer are subtracted to obtain the strain-tensile force data of the different layer. Then, by dividing by the area of the different layer, the stress-strain relationship of the different layer is obtained, and the stress-strain relationship of the coarse grain layer and the N-layer gradient layer is solved.
[0010] S6: Based on the calculated stress-strain response of each gradient layer in the depth direction during the stretching process, we can understand the composition of the gradient nanostructure prepared by the current process. By comparing multiple sets of different process parameters, we can analyze the influence of each process parameter on the composition of the gradient structure, provide theoretical guidance for optimizing the process parameters for preparing gradient nanostructures, and further provide theoretical support for accurately controlling the performance of gradient nanostructures to prepare gradient nanomaterials that meet application scenarios.
[0011] In step S1, the concentric cylindrical laminate includes concentric pillars and a gradient portion surrounding the concentric pillars, wherein the gradient portion includes N sequentially stacked annular plates.
[0012] In step S2, the larger the sample number, the more layers are peeled off, ranging from 0 to N layers. The resulting peeled samples include: sample number 1 is the unpeeled sample; sample number 2 is the sample with 1 peeled gradient layer; sample number i is the sample with i-1 peeled gradient layer; and sample number N+1 is the sample with N peeled gradient layer. The N-layer peeled gradient layer sample is a coarse-grained sample.
[0013] In step S5, the tensile force data of samples with a difference of 1 in the number of delaminated layers are subtracted to obtain the strain-tensile force data of the delaminated layer, specifically including:
[0014] F N-i (ε)=F i (ε)-F i+1 (ε)
[0015] Among them, F i F represents the tensile force borne by the i-th layer of material during the stretching process. i-1 and F i These represent the tensile forces borne by the gradient nanostructure during stretching after the removal of layers i-1 and i, respectively, and ε represents the strain. In step S5, dividing by the area of the phase difference layer yields the stress-strain relationship of the phase difference layer, specifically including:
[0016] σ i (ε)=F i (ε) / S i
[0017] Where, σ i S represents the stress value during the tensile process of the i-th layer of material. i This represents the cross-sectional area of the i-th layer of material.
[0018] A further preferred embodiment of the method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method includes the following steps:
[0019] S1: The gradient nanostructured round rod sample is abstracted as a concentric cylindrical laminated plate. The gradient part is divided into N layers. Each layer has the same and uniformly distributed macroscopic mechanical properties. N+1 gradient nanostructured samples are processed under the same working conditions and numbered in order from small to large diameter.
[0020] S2: Electrolytic stripping of the samples is performed to different degrees according to the numbering order. The larger the sample number, the more layers are stripped. The number of layers ranges from 0 to N.
[0021] S3: Perform tensile tests on the delaminated specimens to obtain strain-tensile force data for specimens with different numbers of delaminated layers;
[0022] S4: Smooth and interpolate the strain-tensile force data of specimens with different numbers of layers to obtain the tensile force corresponding to specimens with different numbers of layers at the same strain.
[0023] S5: Subtract the tensile force data (under the same strain) from the samples with a difference of 1 in the number of delaminated layers to obtain the strain-tensile force data of the different layers. Divide this data by the area of the different layers to obtain the stress-strain relationship of the different layers. Solve the stress-strain relationship of the coarse-grained layer and the N-layer gradient layer using the load data of N+1 samples with different numbers of delaminated layers.
[0024] The gradient portion of a gradient nanostructure contains various structural units with different mechanical properties, distributed non-uniformly along the thickness direction. Therefore, the gradient portion should be considered a heterogeneous material with non-uniform mechanical properties. However, it is difficult to obtain the stress-strain response of a material whose mechanical properties change continuously along the thickness direction across all depth directions. In step S1 of this invention, a laminated plate model is used to represent each unit along the thickness direction of the gradient nanostructure in a discrete form. By selecting an appropriate number of layers and the layer interval, the computational difficulty can be greatly reduced while ensuring the accuracy of the stress-strain relationship of each unit.
[0025] To obtain the stress-strain response of each subdivided gradient layer from the entire gradient section, step S2 involves electrolysis to peel off the gradient nanostructure sample. By controlling the number of peeled layers, a batch of samples containing different numbers of gradient layers is obtained. The N gradient layers and the 1 coarse-grained layer are considered as N+1 unknowns. The N+1 combinations of samples with different numbers of peeled layers after electrolysis are considered as N+1 equations, providing a theoretical basis for calculating the stress-strain relationship of the N gradient layers and the 1 coarse-grained layer.
[0026] In step S5, tensile data from specimens containing different numbers of gradient layers are studied using the laminate model assumed in step S1. By pairwise subtraction of tensile force data between specimens with adjacent delamination numbers, the tensile forces borne by each gradient layer and coarse-grained layer during the tensile process are successfully extracted from the specimen tensile data. Combining this with knowledge of materials mechanics, the tensile forces are converted into stress values, thus solving for the stress-strain relationship of each gradient layer and coarse-grained layer. This step obtains the tensile force data of the coarse-grained layer and each gradient layer through a reverse method, rather than directly obtaining the individual gradient layer material and tensile force data through methods such as focused ion beams. Since individually obtained gradient layer materials lack the constraint of other layers (especially coarse-grained layers) during the tensile process, they experience necking due to strain localization at relatively small strains (~5%), making it impossible to obtain the intrinsic plasticity of the material. This method, through a reverse approach, reconstructs the stress-strain response of each gradient layer during the tensile process relatively completely (strain range exceeding 40%), thus providing a more realistic understanding of the stress-strain response of each gradient layer and coarse-grained layer during the tensile process of gradient nanostructures.
[0027] Compared with the prior art, the advantages of the present invention are as follows:
[0028] This method directly measures the macroscopic stress-strain response of the specimen and calculates the quasi-static stress-strain curve of the corresponding thin-layer material based on the test results of adjacent specimens in the radial dimension. A significant feature of this method is its ability to effectively suppress strain localization and fully exhibit the intrinsic plasticity of the thin-layer material, allowing the thin-layer material to exhibit its inherent properties perfectly integrated with the internal material. Furthermore, this method can be applied to functionally graded materials whose constitutive relations are not uniformly varied along the depth direction, providing a new research strategy for the study of the constitutive relations of functionally graded materials. Attached Figure Description
[0029] Figure 1 Schematic diagram of the layered structure of gradient nanomaterials
[0030] Figure 2 Actual picture of surface mechanical rolling treatment equipment
[0031] Figure 3 Gradient nanostructure 316L physical image
[0032] Figure 4 Diameter distribution of 316L sample with gradient nanostructure
[0033] Figure 5 Image of a sample diameter measured with a laser diameter gauge
[0034] Figure 6 Schematic diagram of electrolytic stripping layer
[0035] Figure 7 Photograph of actual equipment used in electrolysis experiments
[0036] Figure 8 Scatter plot of the difference between the diameter of samples with different numbers of layers after electrolysis and the target diameter.
[0037] Figure 9 Strain-tensile force curves of 316L specimens with gradient nanostructures at different thicknesses were obtained.
[0038] Figure 10 A comparison chart of the smoothed and interpolated data curves and the original experimental data curves.
[0039] Figure 11 A schematic diagram illustrating the tensile force during the stretching process of the Ni-th layer.
[0040] Figure 12 The actual stress-strain curves of the 316L sample with a gradient nanostructure and a depth axis spacing of 150 μm are shown.
[0041] Figure 13 The curve showing the hardness of the 316L sample with gradient nanostructure as a function of depth. Detailed Implementation
[0042] The present invention will be further described in detail below with reference to the accompanying drawings.
[0043] A method for calculating the constitutive relation of gradient directions in gradient nanomaterials based on the delamination method includes the following steps:
[0044] Step 1: Abstract the gradient nanostructured round rod sample into a concentric cylindrical laminated plate. The gradient part is divided into N layers. Each layer has the same and uniformly distributed macroscopic mechanical properties. Process N+1 gradient nanostructured samples under the same working conditions and number them in order from smallest to largest diameter.
[0045] The gradient nanostructure is abstracted as a concentric cylindrical laminate, and the gradient part is divided into N layers (see schematic diagram). Figure 1 N is a user-defined parameter. This parameter should be selected to ensure that the macroscopic mechanical properties of each thin layer differ little within its defined range, approximately satisfying a uniform distribution (the gradient portion prepared by the authors was approximately 1 mm thick, and the overall radius of the sample was 4.113 mm. The gradient portion was divided at 50 μm depth intervals, hence N was set to 20). Following the selected parameter N, N+1 gradient nanomaterials were prepared under the same processing conditions (the authors prepared the gradient nanostructure samples through surface mechanical rolling treatment; the processing equipment is described in [link to relevant documentation]). Figure 2 Images of the 316L gradient nanostructure samples prepared using this device are shown below. Figure 3 These samples are considered to have a consistent gradient nanostructure. The fabricated samples were numbered from smallest to largest diameter (see below for the corresponding diameters of the 316L gradient nanostructure samples fabricated by the authors using SMRT). Figure 4The reason for numbering the specimens by diameter is to minimize the dimensional difference between adjacent specimens, thereby reducing the error in the subsequent tensile force calculation (Formula 2 in step 5). Figure 3 The diameter difference between adjacent numbered samples is less than 3 μm, and the difference in cross-sectional area is less than 0.1%. The sample diameter is obtained by selecting three different cross-sections of the sample gauge length, aligning the laser diameter gauge with the cross-section in sequence, rotating the sample and measuring the diameter data corresponding to 10 different angles at each cross-section, and averaging the total of 30 data points. The diameter of the sample after peeling is also obtained by the same measurement method. Figure 5 Image showing the diameter of a sample measured using a laser diameter gauge.
[0046] Step 2: Electrolytically peel off the samples to different degrees according to their numbering order. The larger the sample number, the more layers are peeled off. The number of peeled layers ranges from 0 to N.
[0047] According to the numbering sequence, N+1 gradient nanomaterial samples were subjected to electrolytic exfoliation of different degrees. The electrolysis schematic diagram is shown below. Figure 6 The components include: 1-lead cylinder, 2-beaker, 3-stainless steel electrolyte, 4-gradient nanostructure sample, 5-wire, and 6-DC power supply. See the attached image for an actual electrolysis experiment. Figure 7 The sample was connected to the positive terminal of a DC power supply via a wire, and the lead cylinder was connected to the negative terminal. Stainless steel electrolyte was used as the electrolytic medium. The electrolysis rate was affected by current, temperature, and sample diameter. During long-term continuous electrolysis, the temperature could be considered constant in the steady state, and the sample diameter also changed relatively little, thus it could also be considered constant. Based on these factors, the electrolysis rate was mainly controlled by adjusting the circuit current during electrolysis. The authors controlled the steady-state current within the range of 6-8 A, corresponding to an electrolysis rate of 3-5 μm / min. The larger the sample number, the more layers were peeled off, ranging from 0 to N layers. For example, sample #1 was an unpeeled sample, sample #2 was a sample with one gradient layer peeled off, sample #i was a sample with i-1 gradient layers peeled off, and sample #N+1 was a sample with N gradient layers peeled off (only the coarse-grained layer was retained). Figure 8 To compare the actual diameter and target diameter of samples after electrolysis with different numbers of layers, the diameter error caused by electrolysis was controlled within ±2µm. The number of layers removed from samples with different numbers was different, and samples with different numbers of layers were finally obtained, including one sample without layers and one sample with x gradient layers removed (where x traverses all integers from 1 to N).
[0048] Step 3: Perform tensile tests on the delaminated specimens to obtain strain-tensile force data for specimens with different numbers of delaminated layers;
[0049] Tensile tests were performed on the delaminated specimens from step 2 using a tensile testing machine, and the strain-load data were recorded. Figure 9The figures show strain-tensile force curves of 316L stainless steel specimens with different numbers of layers peeled off, obtained by the author using a tensile testing machine (model INSTRON3369). Due to experimental error, data for specimens with two layers peeled off are missing.
[0050] Step 4: Smooth and interpolate the strain-tensile force data of specimens with different numbers of peeled layers to obtain the tensile force corresponding to specimens with different numbers of peeled layers under the same strain.
[0051] The data exported from the tensile testing machine exhibits fluctuations, affecting subsequent tensile force differential calculations. Therefore, the `smooth` function in MATLAB is used for data smoothing. Furthermore, the strain data exported by the testing machine for specimens with different delamination numbers do not correspond one-to-one, making subsequent tensile force differential calculations impossible. Therefore, an interpolation algorithm (the author uses the built-in interpolation algorithm in Oringin, taking 2400 strain-tensile force data pairs at equal strain intervals within the strain range of 0-0.527) is used to obtain the tensile force data at a specified strain for specimens with different delamination numbers (corresponding to F in subsequent step 5). j (ε)), after smoothing and interpolation, the data is compared with the original experimental data. Figure 10 After smoothing and interpolation, the data curve falls within the fluctuation range of the experimental data curve (see...). Figure 9 (Enlarged image), therefore the data was not distorted after processing.
[0052] Step 5: Subtract the tensile force data (under the same strain) from the samples with a difference of 1 in the number of delaminated layers (adjacent numbers) to obtain the strain-tensile force data of the different layers. Divide this data by the area of the different layers to obtain the stress-strain relationship of the different layers. By using the tensile force data of N+1 samples with different numbers of delaminated layers, the stress-strain relationship of the coarse-grained layer and the N gradient layers can be solved.
[0053] In gradient nanomaterials, the tensile force during stretching is jointly borne by the coarse-grained layer and the gradient layer, as expressed by:
[0054]
[0055] Where F is the total tensile force borne by the tensile layer, σ is the stress value, S is the area of the corresponding layer, ε is the strain, subscript k is the gradient layer number, subscript c is the coarse-grained layer, and subscript j represents the removal of the j-th gradient layer (e.g., F2 is the total tensile force borne by the material after removing two layers). Based on the above formula, the tensile force data (under the same strain) of samples with a difference of 1 in the number of layers removed are subtracted, as shown in the schematic diagram. Figure 11 As shown, the phase difference layer is obtained ( Figure 6 The i-th layer bears the tensile force during the stretching process. The expression is:
[0056] F i (ε)=F i-1 (ε)-Fi (ε) (2)
[0057] Among them, F i This represents the tensile force borne by the i-th layer during the stretching process. Combining equations 1 and 2, we obtain equation 3:
[0058] F i (ε)=σ i (ε)*S i (3)
[0059] Divide both sides by the area S corresponding to the i-th layer. i (This can be obtained based on the sample size, layer depth, and thickness), thus yielding the stress-strain expression for the i-th layer:
[0060] σ i (ε)=F i (ε) / S i (4)
[0061] Thus, the stress-strain relationship of the i-th layer is obtained. By iterating through all integers in [0, N] with i, the stress-strain relationship of the coarse-grained layer and all gradient layers can be obtained. Figure 12 The actual stress-strain curves of the 316L sample with a gradient nanostructure are shown at a depth interval of 150 μm. The initial yield strength of the material within a 150 μm thickness range from the surface exceeds 1200 MPa, and the stress level generally decreases with increasing depth, which is consistent with the hardness distribution pattern. The hardness versus depth curve is shown below. Figure 13 .
Claims
1. A method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method, characterized in that, Includes the following steps: S1: Abstract the gradient nanostructured round rod sample into a concentric cylindrical laminate, divide the gradient part into N layers, process N+1 gradient nanostructured samples with the same thickness under the same working conditions, and number them in order from small to large diameter. S2: Electrolytic stripping of gradient nanostructured round rod samples was performed to different degrees according to the numbering order. The larger the sample number, the more layers were stripped. The number of layers ranged from 0 to N, and the stripped samples were obtained. S3: Perform tensile tests on the delaminated specimens to obtain strain-tensile force data for specimens with different numbers of delaminated layers; S4: Smooth and interpolate the strain-tensile force data of specimens with different numbers of layers to obtain the tensile force corresponding to specimens with different numbers of layers at the same strain. S5: Using the tensile force corresponding to different number of layers of specimens with the same strain obtained in step S4, the tensile force data of specimens with a difference of 1 layer are subtracted to obtain the strain-tensile force data of the different layer. Then, by dividing by the area of the different layer, the stress-strain relationship of the different layer is obtained, and the stress-strain relationship of the coarse grain layer and the N-layer gradient layer is solved. In step S5, the tensile force data of samples with a difference of 1 in the number of delaminated layers are subtracted to obtain the strain-tensile force data of the delaminated layer, specifically including: ； Among them, F i F represents the tensile force borne by the i-th layer of material during the stretching process. i-1 and F i ε represents the tensile force borne by the gradient nanostructure during the stretching process after the i-1 and i layers of material are removed, respectively, and ε represents the strain. In step S5, the stress-strain relationship of the phase difference layer is obtained by dividing by the area of the phase difference layer, specifically including: ； Where, σ i S represents the stress value during the tensile process of the i-th layer of material. i This represents the cross-sectional area of the i-th layer of material; S6: Adjust the preparation parameters of the gradient nanostructured rod according to the stress-strain relationship of the coarse-grained layer and the N-layer gradient layer in step S5.
2. The method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method according to claim 1, characterized in that, In step S1, the concentric cylindrical laminate includes concentric pillars and a gradient portion surrounding the concentric pillars, wherein the gradient portion includes N sequentially stacked annular plates.
3. The method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method according to claim 1, characterized in that, In step S2, the larger the sample number, the more layers are peeled off, with the number of layers ranging from 0 to N. The resulting peeled sample includes: Sample number 1 is an unpeeled sample, sample number 2 is a sample with 1 peeled gradient layer, sample number i is a sample with i-1 peeled gradient layer, and sample number N+1 is a sample with N peeled gradient layer.
4. The method for measuring the stress-strain relationship in the depth direction of a gradient nanomaterial cylindrical rod sample based on the peeling method according to claim 3, characterized in that, The N-layer gradient layer sample is a coarse-grained sample.