A method for evaluating residual stress in copper strip based on nanoindentation technology

Abstract

A method for evaluating the residual stress of copper strip based on nanoindentation technology belongs to the technical field of residual stress detection, and includes the following steps: S1. Obtain the P-h unloading function of the sample to be measured through nanoindentation test P ( h ) : S2. Establish an elastic work model of residual stress W e : S3. Calculate the residual stress of the specimen through the elastic work model. Based on the elastic work model during the unloading process, on the one hand, the residual stress state (compressive stress or tensile stress) of the specimen is directly obtained through the P-h curve. On the other hand, it is effectively combined with the David model, and the residual stress inside the specimen is obtained by comparing the elastic work of the stress-free and stressed specimens, which perfects the idea of evaluating residual stress based on work. Using the elastic work model in the present invention to evaluate the residual stress of materials has the advantages of simple method and strong practicability.

Description

Technical Field

[0001] The invention belongs to the technical field of residual stress detection, and in particular relates to a method for evaluating the residual stress of a copper strip based on nanoindentation technology. Background Art

[0002] During the metal material processing and forming process (such as drawing, rolling, welding and heat treatment, etc.), it will be affected by various process factors, resulting in different degrees of residual stress inside the material. The residual stress state varies due to different generating conditions. Generally speaking, there will be a large residual compressive stress inside the material after rolling. The existence of residual stress will have a great impact on the strength, dimensional accuracy, corrosion performance, etc. of the material. At present, the production of lead frame copper alloy strips at home and abroad is mainly achieved by rolling combined with multi-stage aging treatment. However, due to the residual stress inside the copper strip, the strip warps during the subsequent etching process, which seriously affects the utilization rate of the product. Therefore, it is urgent to find a way to eliminate residual stress to solve the problem of strip warping after etching.

[0003] In order to eliminate residual stress, we must first understand the residual stress state inside the material. At present, the methods for detecting residual stress are mainly divided into two types: destructive testing and non-destructive testing. Destructive testing mainly includes drilling, ring core and grooving methods, but destructive testing methods will cause certain damage or destruction to the material; non-destructive testing mainly includes X-ray diffraction, neutron diffraction, nanoindentation technology, etc. Among the above methods, nanoindentation technology has gradually attracted widespread research interest due to its simple material testing method and its ability to characterize materials at a very small scale.

[0004] In many models for evaluating residual stress based on nanoindentation technology, the residual stress inside the material is generally regarded as an equibiaxial state, which provides certain convenience for subsequent analysis. At present, few people have studied residual stress based on indentation work. David et al. proposed an energy-based method to evaluate residual stress in 2019, but the power law exponent of the loading curve was used in the study. Summary of the invention

[0005] The main purpose of the present invention is to overcome the deficiencies in the prior art. The present invention provides a method for evaluating residual stress of a copper strip based on nanoindentation technology.

[0006] The design concept of the present invention is to use elastic work to evaluate residual stress, that is, to further deduce it through the power law exponent of the unloading curve. Through a large number of finite element simulations, it is found that residual stress will affect the elastic recovery ratio, which means that the existence of residual stress will affect the elastic recovery during the unloading process, which will further affect the elastic work.

[0007] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0008] A method for evaluating residual stress of copper strip based on nanoindentation technology, using the power law index m of the indentation unloading curve to calculate the elastic work of indentation, and by comparing the elastic work of stressed and unstressed samples, the residual stress value on the sample surface is obtained, including the following steps:

[0009] S1. Obtain the Ph unloading function P(h) of the sample to be tested through nanoindentation test:

[0010] P = a(hh f ) m ;

[0011] Where a is the fitting parameter obtained experimentally, m is the power law index, h is the indentation depth, and h max is the maximum indentation depth, h f is the final depth of the indentation;

[0012] S2. Establishing the elastic work model W of residual stress e :

[0013]

[0014] Where P(h) is the Ph unloading function, a is the fitting parameter obtained experimentally, m is the power law index, and P max is the maximum residual stress, h is the indentation depth, h max is the maximum indentation depth, h f is the final depth of the indentation;

[0015] (1) In compressive stress state:

[0016] The elastic work of residual stress in compressive stress state is:

[0017] (2) In tensile stress state:

[0018] The elastic work of residual stress in tensile stress state is:

[0019] In the formula, is the stress in compressive stress state, is the elastic work in compressive stress state; is the stress in the stress-free state, is the elastic work in the stress-free state; is the stress in the tensile stress state, is the elastic work in tensile stress state; σ res is the residual stress, Ac is the real contact area, α is 24.7°;

[0020] S3. Different from the David model, the present invention only focuses on the elastic work during the indentation elastic unloading process and calculates the residual stress of the sample through the elastic work model:

[0021] The residual stress in compressive stress state is:

[0022]

[0023] The residual stress in the tensile stress state is:

[0024]

[0025] Furthermore, in the step S1, the sample is electropolished before the nanoindentation test, and then the sample is cleaned with acetone.

[0026] Furthermore, in step S1, the nanoindentation test adopts a fixed load mode with a maximum load of 10 mN.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The present invention is based on the elastic work model in the unloading process. On the one hand, the residual stress state (compressive stress or tensile stress) of the sample is directly obtained through the Ph curve. On the other hand, it is effectively combined with the David model to obtain the residual stress inside the sample by comparing the elastic work of the stress-free and stressed samples, thereby improving the idea of ​​residual stress evaluation based on work. The use of the elastic work model in the present invention to evaluate the residual stress of the material has the advantages of simple method, strong practicality, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is the Ph curve of the sample to be tested (thickness is 0.3 mm) under fixed load mode in a specific implementation manner. DETAILED DESCRIPTION

[0030] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0031] Example 1

[0032] The initial thickness of the copper alloy strip is 0.9 mm. In this embodiment 1, the strip is cold rolled to a thickness of 0.3 mm as the test sample. The residual stress on the surface of the test sample is all compressive stress. The test sample after homogenization is a stress-free state sample.

[0033] A method for evaluating residual stress of a copper strip based on nanoindentation technology comprises the following steps:

[0034] S1. Before the nanoindentation test, the sample was electropolished and then cleaned with acetone. The nanoindentation test adopted a fixed load mode with a maximum load of 10 mN. The Ph unloading function P(h) of the sample to be tested was obtained by the nanoindentation test:

[0035] P = a(hh f ) m ;

[0036] The Ph unloading function curve in this embodiment 1 is as follows Figure 1 As shown, the maximum indentation depth h max The final depth of the indentation h f As shown in Table 1; through a set of (cold-rolled 0.3 mm sample) unloading curves fitted by function, the fitting parameters a and power law index m obtained experimentally are shown in Table 1;

[0037] S2. Establishing the elastic work model W of residual stress e :

[0038]

[0039] Where, the maximum load P max 10mN;

[0040] In compressive stress state:

[0041] The elastic work of residual stress in compressive stress state is:

[0042] In the formula, is the stress in compressive stress state, is the elastic work in compressive stress state; is the stress in the stress-free state, A is the elastic work in the stress-free state; c is the actual contact area. According to Hertz’s elastic contact theory, A c The value of α is 24.7° (Bosch pressure head);

[0043] S3. The residual stress of the compressive stress state of the sample to be tested is calculated by the elastic work model:

[0044]

[0045] In this embodiment 1, the residual stress σ res As shown in Table 1.

[0046] Table 1

[0047]

[0048] Example 2

[0049] The initial thickness of the copper alloy strip is 0.9 mm. In this embodiment 2, a sample with a thickness of 0.3 mm after tensioning and straightening is selected as the sample to be tested. The residual stress on the surface of the sample to be tested is tensile stress, and the homogenized sample is selected as a stress-free sample.

[0050] A method for evaluating residual stress of a copper strip based on nanoindentation technology comprises the following steps:

[0051] S1. Before the nanoindentation test, the sample was electropolished and then cleaned with acetone. The nanoindentation test adopted a fixed load mode with a maximum load of 10 mN. The Ph unloading function P(h) of the sample to be tested was obtained by the nanoindentation test:

[0052] P = a(hh f ) m ;

[0053] The maximum indentation depth h in this embodiment 2 max The final depth of the indentation h f As shown in Table 2; through a set of unloading curves (0.3mm tension straightening specimens) fitted by function, the fitting parameters a and power law index m obtained experimentally are shown in Table 2;

[0054] S2. Establishing the elastic work model W of residual stress e :

[0055]

[0056] Where, the maximum load P max 10mN;

[0057] In tensile stress state:

[0058] The elastic work of residual stress in tensile stress state is:

[0059] In the formula, is the stress in the stress-free state, is the elastic work in the stress-free state; is the stress in the tensile stress state, A is the elastic work in the tensile stress state; c is the actual contact area. According to Hertz’s elastic contact theory, A c The value of α is 24.7° (Bosch pressure head);

[0060] S3. Calculate the residual stress of the sample using the elastic work model:

[0061]

[0062] In this embodiment 2, the residual stress σ of the sample to be tested res As shown in Table 2.

[0063] Table 2

[0064]

[0065] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for evaluating residual stress of copper strip based on nanoindentation technology, characterized in that: The following steps are involved: S1. Obtain the Ph unloading function P(h) of the sample to be tested through nanoindentation test: P=a(h-h f ) m ; Where a is the fitting parameter obtained experimentally, m is the power law index, h is the indentation depth, and h max is the maximum indentation depth, h f is the final depth of the indentation; S2. Establishing the elastic work model W of residual stress e : Where P(h) is the Ph unloading function, a is the fitting parameter obtained experimentally, m is the power law index, and P max is the maximum residual stress, h is the indentation depth, h max is the maximum indentation depth, h f is the final depth of the indentation; (1) In compressive stress state: The elastic work of residual stress in compressive stress state is: (2) In tensile stress state: The elastic work of residual stress in tensile stress state is: In the formula, is the stress in compressive stress state, is the elastic work in compressive stress state; is the stress in the stress-free state, is the elastic work in the stress-free state; is the stress in the tensile stress state, is the elastic work in tensile stress state; σ res is the residual stress, A c is the real contact area, α is 24.7°; S3. Calculate the residual stress of the sample using the elastic work model: The residual stress in compressive stress state is: The residual stress in the tensile stress state is:

2. The method for evaluating residual stress of a copper strip based on nanoindentation technology according to claim 1, characterized in that: In the step S1, the sample is electropolished before the nanoindentation test, and then the sample is cleaned with acetone.

3. The method for evaluating residual stress of a copper strip based on nanoindentation technology according to claim 1, characterized in that: In step S1, the nanoindentation test adopts a fixed load mode with a maximum load of 10 mN.

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