Theoretical And Experimental Study On Measuring Elastic Constants Of Engineering Materials By Resonant Ultrasound Spectroscopy

High-temperature alloy,composite material,wood,ceramic and other engineering materials are widely used in aerospace,automobile,construction,medical equipment and other engineering fields.Elastic modulus is an important performance parameter of materials,which plays an important role in structural design and optimization.Under uniaxial tension of isotropic materials,the relationship between stress and strain can be expressed by elastic modulus.The elastic modulus of anisotropic materials is different in all directions,and its stress-strain relationship is more complicated.In order to comprehensively describe the elastic properties of various symmetrical materials in different directions,the materials are regarded as small units.Three normal stresses and three shear stresses along the three-dimensional coordinate system are set respectively,and the strains correspond to them.At this time,the relationship between stress and strain in each direction can be expressed by a 6×6 elastic constant matrix.The number of independent constants in the elastic constant matrix is related to the symmetry of materials.The higher the symmetry of materials,the smaller the number of independent elastic constants.Triclinic symmetric materials have 21 independent elastic constants,while isotropic materials have only 2 independent elastic constants.When traditional testing methods(such as tensile test)measure the elastic constants of anisotropic materials,it is necessary to prepare samples along the anisotropic direction and carry out the test,which has low measurement accuracy,high testing cost and low efficiency.It is difficult to meet the rapid measurement requirements in the engineering field.Resonant ultrasound spectroscopy is a nondestructive testing method for the elastic constants of solid materials,which is different from the tensile test that depends on stress-strain relationship.Based on the resonance excited by ultrasonic signal,this method can complete the measurement of all anisotropic elastic constants only once.It has high repeatability and measurement accuracy,and is convenient for testing under service conditions.Aiming at titanium alloy and needle-punched carbon/carbon composites,which are typical materials in aerospace field,the theoretical and experimental research of resonant ultrasound spectroscopy is carried out in this paper.The main research contents are as follows.Firstly,based on the measurement principle of resonant ultrasound spectroscopy,this paper divides the research content into three parts: forward model framework,inverse model framework and experimental test system,which are discussed in depth in turn.In the forward model,Rayleigh-Ritz method and finite element method are used to approximate the free resonance frequency.By analyzing the calculation principle,results and time of the forward algorithm,the applicable occasions of each forward algorithm are determined,paving the way for the subsequent analysis.In the inverse algorithm,the resonance frequency calculated by the forward algorithm is matched with the resonance frequency measured by the experiment.The error between the two groups of frequencies is minimized by constantly changing the elastic constant in the forward model,which is the measured value of the material.The calculation principles of Levenberg-Marquardt algorithm,particle swarm optimization algorithm,fuzzy inference algorithm and Bayesian algorithm are analyzed.The unified data are used to verify the algorithm,and their global convergence,convergence speed and calculation fitting degree are compared.Accordingly,the application scenarios of four algorithms are proposed to realize efficient and accurate global convergence calculation.After analyzing the application of forward and inverse algorithm,this paper further studies the experimental test scheme,and builds the resonant ultrasound spectroscopy test system at room temperature and high temperature.The test sample is in an approximate free vibration state.The frequency sweep signal output by the transmitting transducer excites resonance,and the vibration signal collected by the receiving transducer is processed by the lock-in amplifier to obtain the frequency spectrum and phase diagram.In order to analyze the measurement error caused by experimental factors in practical application,the boundary conditions of the sample in diagonal clamping and three-point support schemes are numerically simulated by finite element software.By changing the magnitude and direction of clamping force and exciting force,the influence of clamping force and exciting force on resonance peak can be judged,which provides the basis for the implementation of the test scheme.The high temperature atmosphere is realized by custom coil induction heating.The hightemperature transducer is improved on the basis of the room-temperature transducer,and the test temperature is greatly increased by using a heat-resistant alumina buffer rod.The measurement results of room temperature and high temperature transducers are compared,and the signal changes caused by the buffer rod are analyzed.Based on the above research,the elastic constants of TC4 titanium alloy parallelepiped samples were measured.By judging the changing trend of frequency with elastic constant,a stable interval between adjacent modes is selected as the basis for identifying measurement modes.Levenberg-Marquardt algorithm,fuzzy inference algorithm and particle swarm optimization algorithm are used to invert the elastic constants,and the characteristics of the above-mentioned inversion algorithms are verified.After that,TC4 sample was tested at 100?500? at high temperature,and the variation tendency of elastic constant with temperature was analyzed.Fuzzy inference algorithm is used to calculate the elastic constant at high temperature,and the initial elastic constant values in the algorithm refer to the calculation results at the previous temperature.Finally,the anisotropic elastic constants of the needle-punched carbon/carbon composite parallelepiped samples were measured,and the reliability of the resonant ultrasound spectroscopy testing system was verified.