CN112903163A - Material residual stress determination method based on partial stress equivalence - Google Patents

Abstract

The invention discloses a material residual stress determination method based on partial stress equivalence, which comprises the steps of S1, obtaining the loading curvature C of a material to be determined in a residual stress-free area₀(ii) a S2, carrying out cone pressing on the region containing the residual stress to obtain the corresponding loading curvature C_R(ii) a S3 curvature C based on loading₀And C_RAnd calculating the dimensionless residual stress of the material to be measured, and realizing the measurement of the residual stress of the material. The method can conveniently measure the residual stress of the structure or the single shaft in a micro-damage way, and is a measuring method with strong universality, convenient operation and high precision.

Description

Material residual stress determination method based on partial stress equivalence

Technical Field

The invention belongs to the technical field of material residual stress (or working stress) determination, and particularly relates to a material residual stress determination method based on partial stress equivalence.

Background

The traditional residual stress measuring method comprises a destructive detection method and a nondestructive detection method, wherein the destructive detection method is to release part or all of residual stress through local machining, then measure displacement or strain generated by stress release at a specific position, and further calculate the magnitude and direction of the residual stress through an elastic theory, such as a drilling method, a slot cutting method, a ring core method, a layer-by-layer milling method and the like; the nondestructive detection method is a method of measuring the amount of change in some physical quantities due to residual stress by a specific means and then reversely finding the amount of change in some physical quantities due to residual stress from the amounts of change, for example, X-ray diffraction, neutron diffraction, ultrasonic wave, magnetic measurement, and raman spectroscopy. The destructive detection method has higher precision and mature technology, but the detection process can cause damage to components which are possibly not allowed; the nondestructive testing requires expensive equipment and is complex to test.

The press-in method is a micro-damage method that can be used to detect residual stress, and is not mature so far. In 1998, Suresh and Giannakopoulos decomposed the equibiaxial residual stress tensor into a tensor composed of the residual stress σ_RThe sum of the constituent hydrostatic stress tensor and the bias stress tensor, and assuming the bias stress sigma_RAnd cone penetration mean stress (F)_R-F₀)/A_cIs equivalent to the formula (I) in which F_RAnd F₀Indentation loads corresponding to the presence and absence of residual stress at the same indentation displacement, A_cFor the contact area, the equation seems simple, but the relationship between the indentation displacement and the contact area is related to a plurality of factors such as material constitutive relation parameters, and is difficult to be represented by an explicit equation. The method needs to perform cone press-in tests on materials with residual stress and materials without residual stress respectively, and when the press-in depth of the materials cannot be obtained through zero residual stress press-in, the residual stress cannot be obtained, which is the greatest limitation of the application of the method. In 2003, Lee and Kwon adopt a stress equivalent mode different from that of the Suresh method, the contact area is expressed as a function of load, and a residual stress model only related to the load is established by combining a load difference value with and without residual stress at the maximum indentation displacement.

Disclosure of Invention

Aiming at the defects in the prior art, the method for measuring the residual stress of the material based on the partial stress equivalence solves the problem that when the existing residual stress is measured, when a cone indentation formula based on the energy density equivalence is used for obtaining C₀And the limitation of using a non-residual stress state as a reference.

In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a method for measuring residual stress of a material based on bias stress equivalence comprises the following steps:

s1, obtainingLoading curvature C of material to be tested in stress-free state₀；

S2, carrying out cone pressing on the region containing the residual stress to obtain the corresponding loading curvature C_R；

S3 curvature C based on loading₀And C_RAnd calculating the dimensionless residual stress of the material to be measured, and realizing the measurement of the residual stress of the material.

Further, in the step S1, the loaded curvature C in the unstressed state is obtained₀The method comprises the steps of obtaining a load-displacement curve through pressing in a region without residual stress, and then obtaining the load-displacement curve through fitting according to a Kick law, or obtaining the load-displacement curve through a known H law parameter by using a cone pressing semi-analytic formula based on energy density median equivalence.

Further, the dimensionless residual stress R of the material to be tested in step S3 is:

in the formula, σ_RAs residual stress, σ_yNominal yield strengths alpha and eta are intermediate parameters;

wherein α ═ e₀n+e₁N is a strain hardening index,

lambda is an intermediate variable, theta is a half cone angle of the pressure head, and phi is a residual stress type parameter;

k is the strain hardening coefficient, E is the modulus of elasticity, K₀＝c₀，k₁＝c₁+c₂n，k₂＝c₃，k₃＝c₄+c₅n，k₄＝c₆+c₇n，k₀～k₄Is an intermediate variable, e₀～e₁And c₀～c₇Are all dimensionless principlesAnd (4) counting.

Further, in the step S3, when the residual stress is equibiaxial residual stress,

when the residual stress is uniaxial residual stress,

the invention has the beneficial effects that:

(1) in actual operation test, the prior related art generally needs to perform press-in test under two states of no residual stress and residual stress, and the invention can or can not need the state of no residual stress as reference, so the test is more convenient and quicker;

(2) the method can conveniently measure the biaxial or uniaxial residual stress of the component and the like in a micro-damage manner, and is a measuring method with strong universality, convenient operation and high precision.

Drawings

Fig. 1 is a flow chart of a method for determining residual stress of a material based on a bias stress effect according to the present invention.

FIG. 2 is a diagram illustrating the results of finite element analysis verification of equibiaxial residual stress in the present invention.

FIG. 3 is a schematic diagram of a finite element analysis verification result of uniaxial residual stress provided by the present invention.

FIG. 4 is a schematic diagram showing a 45# steel equi-biaxial residual stress indentation load-displacement curve and a comparison of the prediction result of the method.

FIG. 5 is a schematic diagram showing a 45# steel uniaxial residual stress indentation load-displacement curve and a comparison of the prediction result of the method.

Detailed Description

The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.

Example 1:

as shown in fig. 1, a method for determining residual stress of a material based on partial stress equivalence comprises the following steps:

s1, acquiring the loading curvature C of the material to be measured in the residual stress-free area₀；

S2, carrying out cone pressing on the region containing the residual stress to obtain the corresponding loading curvature C_R；

S3 curvature C based on loading₀And C_RAnd calculating the dimensionless residual stress of the material to be measured, and realizing the measurement of the residual stress of the material.

In step S1, the region without residual stress is pressed in to obtain a load-displacement curve, and then fitting is performed according to the kirk law, or the load-displacement curve is obtained by a cone pressure semi-analytic expression based on the energy density median equivalent through known H-law parameters.

Wherein the loading curvature C is obtained by pressing in a non-residual stress sample₀During the process, a conical pressure head with a half cone angle of 70.3 degrees is used for carrying out conical pressing in a residual stress-free area to obtain a load-displacement curve, and the load curvature C is obtained according to the regression of the following formula (1)₀；

The conical indentation load-displacement curve conforms to the Kick rule:

F＝Ch² (1)

in the formula, F is press-in load, h is press-in displacement, and C is a loading coefficient;

acquiring loading curvature C by cone pressing semi-analytic expression based on energy density median equivalence₀The stress-strain relationship of the material conforms to the Hollomon power law (H-law):

wherein E is the modulus of elasticity, and K ═ E_nσ_y ^1-nIs the strain hardening coefficient, σ isTrue stress, ε is true strain, σ_yIn order to be the initial yield stress, the stress,ⁿis the strain hardening index;

for solving for C₀The cone press-in semi-analytic formula of (a) is:

in the formula, epsilon_y＝σ_yE is the initial yield strain, d₁Is equal to epsilon_yRelated parameter, d₂Is constant, n is the strain hardening index, θ is the indenter half-cone angle, in this example 70.3 °.

It should be noted that the residual stress in the present embodiment also refers to the working stress below the yield strength.

The dimensionless residual stress R of the material to be tested in the embodiment is provided based on the principle of bias stress equivalence; the principle of equivalent offset stress residue is as follows: offset stress phi sigma of residual stress in press-in direction_RAnd (F)_R-F₀)/A_cEquivalence, where φ is a residual stress type parameter, σ_RAs residual stress, F_RAnd F₀The load at which the maximum pressure displacement exists or not, A_cIs a projected contact surface; based on this, the residual stress R of the material to be tested in step S3 of the present embodiment is:

in the formula, σ_RAs residual stress, σ_yFor nominal yield strength, α and η are intermediate parameters;

wherein α ═ e₀n+e₁N is a strain hardening index,

lambda is an intermediate variable, theta is a half cone angle of the pressure head, and phi is a residual stress type parameter;

k is the strain hardening coefficient, E is the modulus of elasticity, K₀＝c₀，k₁＝c₁+c₂n，k₂＝c₃，k₃＝c₄+c₅n，k₄＝c₆+c₇n，k₀～k₄Is an intermediate variable, e₀～e₁And c₀～c₇Are all dimensionless constants.

Wherein, when the residual stress is equibiaxial residual stress,

when the residual stress is uniaxial residual stress,

for equibiaxial residual stress, e₀～e₁And c₀～c₇Values of (d) are given in Table 1, for uniaxial residual stress, e₀～e₁And c₀～c₇The values of (A) are as listed in Table 2, and for the parameter values in tables 1 and 2, the residual stress measurement of most common materials can be covered;

represents 1: e corresponding to equibiaxial residual stress₀～e₁And c₀～c₇Value of (2)

Table 2: uniaxial residual stress corresponding to₀～e₁And c₀～c₇Value of (2)

Example 2:

in the present embodiment, each is obtained by finite element analysisThe indentation load displacement curve under the working condition is adopted, and then the method of the invention is adopted to obtain the dimensionless residual stress

And pre-applied dimensionless residual stress

As shown in fig. 2 and 3, it can be seen that the present invention achieves better results over a wide range of equiaxed and uniaxial residual stresses.

Example 3:

as for the 45# steel, a predetermined stress was first applied thereto by a stress applying device, and then the steel was cone-pressed, and the magnitude of the applied stress was predicted by the method of the present invention, and as a result, as shown in fig. 4 and 5, it can be seen that the residual stress predicted by the method and the residual stress previously applied were well matched with each other.

Claims (4)

1. A method for measuring residual stress of a material based on bias stress equivalence is characterized by comprising the following steps:

s1, acquiring the loading curvature C of the material to be measured in the stress-free state₀；

S2, carrying out cone pressing on the region containing the residual stress to obtain the corresponding loading curvature C_R；

S3 curvature C based on loading₀And C_RAnd calculating the dimensionless residual stress of the material to be measured, and realizing the measurement of the residual stress of the material.

2. The method for determining residual stress of material based on partial stress equivalence according to claim 1, wherein in step S1, the loaded curvature C in the stress-free state is obtained₀The method comprises the steps of obtaining a load-displacement curve through pressing in of a region without residual stress, and then obtaining the load-displacement curve through fitting according to a Kick law, or obtaining the load-displacement curve through a known Hollomon law parameter by using a cone pressing-in semi-analytic expression based on energy density median equivalence.

3. The method for determining residual stress of material based on partial stress equivalence according to claim 1, wherein the dimensionless residual stress R of the material to be tested in step S3 is:

in the formula, σ_RAs residual stress, σ_yFor nominal yield strength, α and η are intermediate parameters;

wherein α ═ e₀n+e₁N is a strain hardening index,

lambda is an intermediate variable, theta is a half cone angle of the pressure head, and phi is a residual stress type parameter;

k is the strain hardening coefficient, E is the modulus of elasticity, K₀＝c₀，k₁＝c₁+c₂n，k₂＝c₃，k₃＝c₄+c₅n，k₄＝c₆+c₇n，k₀～k₄Is an intermediate variable, e₀～e₁And c₀～c₇Are all dimensionless constants.

4. The method for determining residual stress of material based on partial stress equivalence according to claim 3, wherein in step S3, when the residual stress is equibiaxial residual stress,

when the residual stress is uniaxial residual stress,

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