Ding Xia shaw * teclab.cn Ruitaike (China) Co., Ltd

Summary:This article introduces a non-contact detection method based on laser ultrasound for the detection and evaluation of residual stresses in materials. Laser ultrasound has the characteristics of numerical accuracy and deeper detection depth in residual stress detection. In addition, due to the advantages of non-contact, non-destructive, broadband, and high precision of laser ultrasound, it is easy to apply in harsh environments such as high temperature and high pressure, and can achieve rapid and real-time detection. It has a wide range of application scenarios in the field of non-destructive evaluation and testing.

keyword:Laser ultrasonic residual stress detection

Background:Residual stress refers to the internal stress that remains in equilibrium within an object without considering external forces or uneven temperature fields. The fundamental reason for its occurrence is the uneven plastic deformation inside the object; The main reasons for uneven plastic deformation include uneven mechanical deformation, uneven stress field, and temperature field. The non-destructive testing of residual stress distribution in materials is particularly important and necessary before and after processing. Based on the detection results, the processing technology and post processing aging treatment can be optimized to minimize the deformation of materials caused by residual stress. At present, there are destructive blind hole methods for detecting residual stress, as well as non-destructive methods such as XRD (X-ray scattering), neutron scattering, micro magnetic multi parameter detection, and ultrasonic testing. According to the detection principle, ultrasonic methods can be divided into PZT piezoelectric ultrasonic transducer contact detection method, EMAT electromagnetic ultrasonic detection method, and LUS laser ultrasonic non-contact detection method. Laser ultrasound has unique advantages in non-contact detection of residual stresses in materials under complex working conditions due to its ability to achieve large lift off and high spatial and temporal resolution.

Theoretical basis of ultrasonic measurement of surface average stress:

Based on classical acoustic elasticity theory, for plane stress, the velocity of small amplitude Rayleigh waves propagating in a uniformly deformed solid medium surface will vary. In an initially isotropic homogeneous elastic body, establish a spatial coordinate system as shown in Figure 1, where "1" and "2" correspond to the directions of the material's plane principal stresses σ 1 and σ 2, respectively, and "3" is the thickness direction of the material. When the material is subjected to plane biaxial stress, the relationship between the surface wave velocity and stress propagating along the "1" and "2" directions, i.e., the acoustic elastic equation, can be expressed as:

Figure 1. Coordinate system of the tested material

(1 and 2)

In the equation, v1 and v2 are the surface wave velocities along the "1" and "2" directions in the presence of (σ 1, σ 2), v0 is the surface wave velocity in the absence of stress in the material, and K1 and K2 are the acoustic elastic coefficients of the surface wave. Assuming that the material is isotropic and the temperature change is small, the acoustic elastic coefficients depend on the propagation direction and stress direction of the surface wave. The acoustic elastic coefficients K1 and K2 are respectively related to the second-order and third-order elastic constants of the material. Therefore, with knowledge of the second-order and third-order elastic constants of the material, the values of K1 and K2 can be directly calculated. For most metal materials, K1 ≫ K2, equations (1)~(2) can be simplified into equation (3):

(3)

In the equation, v is the surface wave velocity along the stress direction, K is the acoustic elastic coefficient along the propagation direction of the surface wave, and:

K=(n+4υ )/8υ

(4)

σ is the stress along the direction of surface wave propagation, υ is the second-order elastic constant of the material, and n is the third-order elastic constant of the material. That is, the approximate value of stress can be obtained by the relative velocity change and acoustic elastic coefficient along the stress direction. Compared with measurement errors caused by temperature changes and texture, the error caused by ignoring K2 is extremely small.

Theoretical basis of ultrasonic measurement of average stress in the thickness direction:

The principle of acoustic elasticity holds that when elastic waves propagate in stressed solid materials, their velocity is related to the material's density, second-order elastic constant, higher-order elastic constant, and stress. The changes in longitudinal wave velocity and stress in isotropic materials can be simplified as follows:

(5)

By differentiating the two sides of equation (5) and considering that the change in sound velocity caused by stress is very small, the formula can be simplified as follows:

(6)

D σ represents the change in stress, dV_LRepresenting the change in longitudinal wave propagation velocity, VL₀Representing the longitudinal wave velocity of ultrasound in solid materials under zero stress state, kL represents the longitudinal wave acoustic elasticity coefficient.

In actual measurement, we often measure the propagation time rather than the speed of sound directly. Therefore, by transforming and simplifying formula (6), we can obtain:

(7)

σ 0 is the initial stress; TL0 and TL are the propagation times required for longitudinal waves to propagate at a fixed distance under stresses of σ 0 and σ, respectively.

Due to the fact that the longitudinal wave acoustic elasticity coefficient is only related to material properties, it can be seen that the stress difference and acoustic time difference are linearly related. At this point, it is only necessary to make zero stress specimens to obtain TL0 and σ 0, and then conduct tensile tests using a tensile testing machine to obtain the longitudinal wave acoustic elastic coefficient. Then the residual stress value can be measured by detecting the sound time TL of the tested workpiece part.

However, this theory and method, when used for single-sided tensile testing calibration of the tested sample, may affect the sound T due to the deformation of the sample generated by the tensile testing machine during the stretching process_L0The impact is greater than the influence of stress on sound, making it impossible to accurately measure stress values. In addition, even if accurate T values are obtained in zero stress calibration specimens_L0In the testing of the tested sample, if there is a slight deviation between the thickness of the calibration site and the thickness of the tested site, it can also lead to inaccurate measurement results.

Therefore, a measurement method and theory are needed to eliminate the influence of deformation and thickness, in order to measure the average residual stress in the thickness direction. To achieve this demand, it is possible to consider using a combination of longitudinal and transverse waves. Based on the thermoelastic effect of laser ultrasound, the excitation laser can generate longitudinal waves, transverse waves, and surface waves on the surface of the measured object. Based on the theory of acoustic elasticity, the relationship between the sound velocity and stress of shear transverse waves in materials is expressed as follows:

(8) And (9)

By comparing formula (5) and formula (9), we can obtain:

(10)

Vs0 is the shear transverse wave velocity at zero stress state, Ks is the transverse wave acoustic elastic coefficient, which is also only related to material properties. At this point, the residual stress values in the thickness direction are no longer related to thickness.

Experiment and Data:

Using a standard FSW stir friction welding process with a welding speed of 6 mm/s and a rotation speed of 1000 RPM, a 2.3mm AA2024-T3 aviation grade aluminum alloy sheet is used. During the welding process and subsequent residual stress measurement, the test plate is tightly clamped onto the thick steel plate to avoid deformation caused by welding or subsequent actions. The FSW friction stir welding process combines 3D finite element simulation technology. Simply put, during the simulation process, the welding head acts as a heat source moving along the weld seam without considering the agitation of the material itself, as the heat input at the agitation head is the main source of residual stress. Based on this simulation model, the distribution of temperature and stress during the welding process can be obtained. As shown in Figure 2: a) Temperature variation curve across the weld seam; b) Stress variation curve, where Z represents along the weld seam and X represents across the weld seam.

Figure 2. Finite Element Simulation Results of Temperature and Stress in Weld Seam Accessories

The laser ultrasonic detection system uses a filtered signal of around 10 MHz for sound velocity measurement. And the stress position curve is obtained by scanning through the movement of the workpiece and lens. From the analysis of measurement results, the stress variation curve is highly consistent with the simulation results. However, in the simulation results of the Z-curve, the transition point from tensile stress to compressive stress is located at 8 mm, while in the laser ultrasonic measurement results, this transition point is located at 11 mm.

Figure 3. LUS Laser Ultrasonic Testing System and Its Working Principle Diagram

Drawing (Top) Original Drawing (Bottom)

Figure 4. Residual stress measurement results of LUS laser ultrasound

Conclusion:

The residual stress position change curve of aluminum alloy thin plate stir friction welding measured by laser ultrasound is highly consistent with the curve change trend of finite element simulation results. However, there is a slight error in the transition point between tensile and compressive stress. In addition, the measurement of average stress in the thickness direction has not yet been carried out. But this also indicates the feasibility of using laser ultrasound for high-temperature online detection of residual stress.

reference:

Defect Detection and Residual Stress Measurement in Friction Stir Welds using Laser Ultrasonics

Ultrasonic shear and longitudinal wave testing method of residual stress