THE NONDESTRUCTIVE EVALUATION OF AXIAL STRESS OF A BOLT IN SITU BY COMBINATION OF SHEAR AND LONGITUDINAL WAVE

Transcription

1 he 1 th International Conference of the lovenian ociety for Non-Destructive esting»application of Contemporary Non-Destructive esting in Engineering«eptember 4-6, 13, Portorož, lovenia More info about this article: HE NONDERUCIVE EVAUAION OF AXIA RE OF A BO IN IU BY COMBINAION OF HEAR AND ONGIUDINA WAVE Xiao i 1, Qinxue Pan 1, Chunguang Xu 1,, *, Wentao ong 1 1 chool of Mechanical Engineering, Beijing Institute of echnology No.5, Zhongguancun outh treet, 181, Beijing, China, bt @gmail.com Department of Mechanical Engineering, Northwestern University 181 Hinman Avenue, Evanston, 68, Illinois, UA, xucg@bit.edu.cn * Corresponding author: Chunguang Xu (Visiting Professor of Northwestern University) ABRAC his paper provides a non-destructive way to evaluate axial stress in a tightened bolt which are made of austenitic stainless steel (A-7), low-carbon steel(4.8) and carbon steel(8.8) by the combination of shear wave and longitudinal wave. By using finite element analysis, a more precise model to deduce axial stress in a tightened bolt based on the contributions of former researchers has been established. his model has also been verified by strain gauge testing. According to the Acoustoelasticity theory, ultrasonic wave propagation in the metal transit time associated with the stress state. Whether shear wave or longitudinal wave cannot detect axial stress of bolt which is tightened or fixed in the structure separately. Only through the division of transit time of shear wave and longitudinal wave, the influence of the length of bolt could be eliminated. Meanwhile, formulas also been provided. An ultrasonic transducer (.5MHz) has been used to stimulating the two different waveforms. Besides the formulas which have been issued, a comparison with field measurement to tensile testing also has been given and a more convincing result has been provided. eywords: Bolt axial stress, Finite element analysis, hear wave and longitudinal wave, Ultrasonic stress measurement, Acoustoelasticity 161

2 1. Introduction As commonly used industrial connections, bolts have a very broad application prospects. Meanwhile, the bolt axial stress which is the most influential factor that can influence the performance, life time and many other important features of bolt often cannot be measured accurately. When the bolt axial stress is not sufficient, it will cause unreliable connection, the work relaxation, vibration and even slippage. At the time that bolt axial stress is too large, it will increase the bolt size, leading to fatigue and even rupture, causing a serious accident. Currently, the torque wrench which is commonly used in the industrial field cannot provide accurately axial stress of a bolt because the cap bolts, nuts and surface friction contact surface, bolt thread friction caused by the payment of its own moment are all related to the axial stress of a bolt. Ultrasonic method as an effective bolt axial stress ND method has been widely used recently, but it is limited to the axial stress measurement during the installation process and for tightened bolt axial stress measurements are powerless. herefore, it is necessary to propose an efficient, non-destructive way to testing the axial stress of the tightened bolt. [1-4]. heoretical background.1 Acoustoelasticity theory According to the Acoustoelasticity theory [5], transverse and longitudinal ultrasonic wave propagation direction and the polarization direction have relationship with stress status as follows: 1. he propagation of longitudinal wave along the direction of stress: σ l + m ρ V111 = l + m + (4l + 1m + 4m) + l + l 3 (1) m. tress direction along the propagation direction, the polarization direction perpendicular to the shear stress: σ ln ρ V = m + + 4l + 4m + m () m Where, i in thev ijk is the load direction; is the direction of wave propagation; j is the wave polarization direction; k = l + m (3) 3 16

3 Where ρ is density, l, m are the econd-order elastic constants of the material; l, m, n are the hird-order elastic constants of the material. For the purposes of semi-infinite plate: l = ρ V m (4) 111 m = ρ V 131 (5) According to the basic assumptions of elasticity: Corresponding to a certain temperature, if there is a correspondence relationship between stress and strain, and this relationship are time-independent, and also independent of deformation history can be known as perfectly elastic material. Perfectly elastic assumption makes the study of elasticity of the material elastic constants does not change with stress or strain changes. In the axial stress is less than the bolt material yield limit, before the bolt can be considered as a perfectly elastic body, as the temperature is stable(room temperature), the econd elastic constant and the hird elastic constant of the bolt material does not vary with changes in axial stress increases.. Bolt axial stress measurement ince bolt length l cannot be measured after installation (Fig. 1), the thickness of the cap and the length of the exposed portion of the tail of the fixed bolt can only be measured. herefore, it is necessary to establish a new way to measure the axial stress of a bolt indirectly in order to avoid measuring bolt length. Fig. 1 chematic of a fastening bolt According to the finite element simulation technology, when bolt nut is fixed and axial load is applied to the bolt cap, axial stress distribution of the bolt can be simulated accurately. Bolt axial stress areas (Fig.) are mainly concentrated on the cylindrical area which between the top surface of the nut to the bottom surface of the nut. [6-8] 163

4 Fig. he simulation of a bolt axial stress herefore, the following model (Fig.3) can be established: A single bolt is taken for the model that is the length of the bolt and ' is the length of the stress region. Fig.3 chematic of a bolt model aking into account the overall temperature measurement for linear expansion of the bolt and the elastic deformation of the bolt stress region [9], as shown in Esq. (6) and (7): = ( 1 + t β ) l (6) σ ' = (1 + ) l' E t (7) t = t (8) Where t,t are current temperature and standard temperature( C). β, E are linear thermal expansion coefficient and Young's modulus. According to Esq. (1) and (), the OF (time of flight) of longitudinal wave and shear wave ultrasonic can be expressed as equation (9) and (1): σ '(1 + t β )(1 + ) + E σ l m ρ = l + m + (4l + 1m + 4m) + l + l ( ')(1 + t β ) 3 m V (9) σ ' (1 + t β )(1 + ) E σ ln ρ = m + + 4l + 4m + m ( ' )(1 + t β ) 3 4m V (1) 164

5 Where, are the OF of longitudinal waves and shear wave. V V, are the velocities of longitudinal waves and shear wave under no axial stress. V, V are the velocities of longitudinal waves and shear wave under stressσ. o simplify, σ σ A = ( ' ) (11) l + m = ( 4l + 1m + 4m) + l + l m ln = + 4l + 4m + m 4m aking the actual measurement into account, the measurement time is very short,where t =.Dividing the two equations (7) and (8), the original equation can be simplified as: A ( ) l + m + σ V 3 = A ( ) m + σ V 3 (1) (13) (14) o simplify, Final expression for the stress is: ( M = ( A ) V A ) V 3 (15) ( M ) m l σ = (16) M 3 ince, are unknown, according to equation (15),the two coefficient can be obtained via a tensile test on a tensile machine: 3. Experimental procedures ( M ) m l = M + 3 (17) σ 3.1 ample description 165

6 Fig.4 est bolts he test samples are measured in three different materials (Fig.4), strength, specifications of bolts. hown in able 1: able1: Bolt type and properties 1# A-7:C:.1 i:1 Mn: P:.5 :.3 Cr:15~ Mo:.7 Ni:1.75~.5 Cu:4 Ingredient # 4.8:C:.55 P:.5 :.6 B:.3 3# 8.8:C:.5~.55 P:.35 :.35 B:.3 Number Name Material σ. σ B D 1# A-7 Austenitic stainless steel # 4.8 ow-carbon steel # 8.8 Carbon steel Explanation: σ. [MPa] yield stress σ B [MPa] tensile strength D [mm] diameter [mm] bolt length In order to better achieve a stable coupling effect, the screw cap and tail of these 3 bolts were carried out by milling planarized, laboratory temperature controlled at 6 C. 3. Measurement device he measurement system (Fig.5) includes an Olympus 573PR pulse transceiver device, a ektronix DPO414B oscilloscope and the Ultrasonic transducer (/ mode). his ultrasonic transducer can generate and receive longitudinal wave and transverse wave signal(.5mhz) simultaneously by the stimulation of 573PR.Finally,the OF of transverse and longitudinal 166

7 waves can be measured accurately by the DPO414B oscilloscope. he experimental tensile machine can provide a maximum N pulling force and the bolt which is clamped with a special chucking device. 4. Result and discussion Fig. 5 ensile test system components In order to facilitate the measurement and calculation, so the formula (17): ( M ) m l b = 3 (18) σ inseling these 3 kinds of different materials of bolts, set axial stress are: MPa.he results are shown in table, 3 and4: able : Austenitic stainless steel bolt axial tensile stress measurement result tress M b E E E E E E E E E E E E+13 Explanation: A=43.3mm = m/s = l =9.816E+1 m =7.571E+1 ρ =785kg/ m 3 167

8 tress [MPa] bolt axial stress [] OF of longitudinal wave [] OF shear wave able 3: ow carbon steel bolt axial tensile stress measurement results tress M b E E E E E E E E E E E E+13 A=4.mm = m/s = m/s l =1.87E+1 m =7.891E+1 ρ =785kg/ m 3 able 4: Carbon steel bolt axial tensile stress measurement results tress M b E E E E E E E E E E E E+13 A=43.56mm = m/s = m/s l =11.31E+1 m =8.59E+1 ρ =785kg/ m 3 According to Equation (17), under the different stress conditions, the, the same. Based on table 3 and 4,, of the bolts are not need to be fitted. Making M value as the abscissa, 168

9 respectively, b value as ordinate. rend curves of three different materials can be calculated as: Fig.6 A-7 Austenitic stainless steel bolt M-b graph Fig ow carbon steel bolt M-b graph Fig Carbon steel bolt M-b graph From the distribution curves shown in Fig.6,Fig.7 and Fig.8,exclude 4.8 carbon steel bolts at 1MPa and 75MPa distortion of the data points (due to measurement error causes),these three steel bolts are expressed as: ~ 1MPa as a linear distribution, 1 ~ 3MPa to another linear 169

10 distribution. According to ~ 1MPa, 1 ~ 3MPa stress distribution of these two intervals, which need to be linear, fitted, to calculate the value of,.calculation results are shown in table 5. able 5: Matlab least squares fit of the stress measurement coefficient Material Coefficient ~1MPa 1~3MPa A-7.96E E E E E E E E E E E E Conclusion As it is shown in the result, the OF measurement error<8ns,bolt axial stress measurement error<±1mpa hus, the measurement of axial stress in a tightened bolt by the combination of shear wave and longitudinal wave can be used to measure the axial stress accurately and also Can be widely used in aircraft manufacturing, bridges, nuclear power plants and other areas of critical equipment fastening bolt axial stress measurement. 6.Reference [1] azuo MARUYAMA,tress analysis of a bolt-nut joint by the finite element method and the copper-electroplating method Bulletin of the JME,Vol.17,No.16,April,1974 [] Johnsan G C. Journal of esting and Evaluation, sep 1986,14. [3] Deputat J. Ultrasonic technique for Measuring stress in screw. Ninth conference on non-destructive testing. [4] E.anala Determination of near surface residual stresses on welded joints using ultrasonic methods ND&E International,Vol.8,No.,pp.83-88,1995 [5] Rose, Joseph.Ultrasonic Waves in olid Media.Cambridge University.4-9. [6] YANG Guoqing, WANG Fei, HONG Jun, et al. heoretical analysis method for bolted member stiffness[j]. Journal of Xi'an Jiaotong University, 1, 46(7): [7] NAAR A, ABBOUD A. An improved stiffness model for bolted joints[j]. AME J Mech Des, 9, 131(1): 1-1. [8] MUO J C, ONE N R. Computation of member stiffness in the design of bolted joints[j]. J Mech Design, 6, 18(6): [9] Chandrasekaran N, alamu.relationship between stress and temperature dependence of ultrasonic shear velocity. Nondestructive Methods for Material Property Determination,