Estimation of dynamic elastic constants from the amplitude and velocity of Rayleigh waves

In this paper a method is proposed to characterize the elasticity of isotropic linear materials from the generation and detection of an acoustic surface wave. For the calculation of the elastic constants, it is sufficient that only one of the faces of the sample be accessible. The methodology is based on both the measurement of the Rayleigh wave velocity and on the determination of the normal to longitudinal amplitude ratio calculated from the normal and longitudinal components of the displacement of a point. The detection of two consecutive surface wave pulses using a single experimental setup permits the determination of the elastic constants. The method is applied to calculate Young's modulus and Poisson's ratio of an aluminum sample as well as their systematic uncertainties. The results obtained give a relative uncertainty for Young's modulus on the order of the sixth part of that calculated for Poisson's ratio.     

A linear least squares approach for evaluation of crack tip stress field parameters using DIC

In the present work, an experimental study is carried out to estimate the mixed-mode stress intensity factors (SIF) for different cracked specimen configurations using digital image correlation (DIC) technique. For the estimation of mixed-mode SIF׳s using DIC, a new algorithm is proposed for the extraction of crack tip location and coefficients in the multi-parameter displacement field equations. From those estimated coefficients, SIF could be extracted. The required displacement data surrounding the crack tip has been obtained using 2D-DIC technique. An open source 2D DIC software Ncorr is used for the displacement field extraction. The presented methodology has been used to extract mixed-mode SIF׳s for specimen configurations like single edge notch (SEN) specimen and centre slant crack (CSC) specimens made out of Al 2014-T6 alloy. The experimental results have been compared with the analytical values and they are found to be in good agreement, thereby confirming the accuracy of the algorithm being proposed.     

A comparison of DIC and grid measurements for processing spalling tests with the VFM and an 80-kpixel ultra-high speed camera

During the last decades, the spalling technique has been more and more used to characterize the tensile strength of geomaterials at high-strain-rates. In 2012, a new processing technique was proposed by Pierron and Forquin [1] to measure the stress level and apparent Young’s modulus in a concrete sample by means of an ultra-high speed camera, a grid bonded onto the sample and the Virtual Fields Method. However the possible benefit to use the DIC (Digital Image Correlation) technique instead of the grid method has not been investigated. In the present work, spalling experiments were performed on two aluminum alloy samples with HPV1 (Shimadzu) ultra-high speed camera providing 1?Mfps maximum recording frequency and about 80?kpixel spatial resolution. A grid with 1?mm pitch was bonded onto the first sample whereas a speckle pattern was covering the second sample for DIC measurements. Both methods were evaluated in terms of displacement and acceleration measurements by comparing the experimental data to laser interferometer measurements. In addition, the stress and strain levels in a given cross-section were compared to the experimental data provided by a strain gage glued on each sample. The measurements allow discussing the benefit of each (grid and DIC) technique to obtain the stress-strain relationship in the case of using an 80-kpixel ultra-high speed camera.     

Local zone wise elastic and plastic properties of electron beam welded Ti–6Al–4V alloy using digital image correlation technique: A comparative study between uniform stress and virtual fields method

Joining of materials using welding results in the formation of material zones with varying microstructure across the weld. Extraction of the mechanical properties of those individual heterogeneous zones are important in designing components and structures comprised of welds. In this study, the zone wise local extraction of the elastic and plastic properties of an electron beam welded Ti–6Al–4V titanium alloy has been carried out using both the uniform stress method (USM) and the virtual fields method (VFM) involving digital image correlation (DIC) technique. The surface strain field obtained using DIC technique from a transverse weld specimen tensile testing is used for extracting the zone wise strain evolution. Initially, using uniform stress assumption, zone wise full range stress–strain curves are extracted. In USM methodology, the elastic and plastic material models are fitted to the zone wise stress–strain curves and required parameters are extracted from it. But inherent disadvantage is lot of images need to be processed for the parameter extraction. Recently, VFM is gaining lot of popularity in characterization domain as it is robust, accurate and faster. VFM is based on the principle of virtual work where, the weak form of local equilibrium equations and kinematically admissible virtual displacement fields are utilized for parameter extraction. Hollomon׳s power law is used here as the hardening rule. Young׳s modulus, Poisson׳s ratio, yield stress, strength coefficient and strain hardening exponent are the parameters extracted zone wise using both USM and VFM. A Vicker׳s microhardness measurement is also conducted across the weld zone towards mapping the strength behavior. Fusion zone has reported higher yield strength, strength coefficient and Poisson׳s ratio. Young׳s modulus value is found decreasing from base metal towards the fusion zone. The trend observed in parameter variation across the weld zone obtained by both USM and VFM compares very well. Due to various advantages associated with VFM technique it is generally recommended for parameter extraction.     

Crack Tip Opening Angle as a Fracture Resistance Parameter to Describe Ductile Crack Extension and Arrest in Steel Pipes under Service Pressure

The angle between two element sides representing the crack tip is defined as the crack tip opening angle (CTOA). Its critical value is used as a criterion of fracture resistance for characterizing stable tearing in thin metallic materials. Various methods are used for determination of the CTOA. Optical microscopy is one of the most common methods as well as fitting of experimental load-displacement diagrams by the finite element method (DIC). Additionally, analytical analysis using the experimental load-displacement curve method (SSM) derived from the plastic hinge model of deflection in three-point bending of a ductile specimen is applied. This approach assumes a constant rotation centre distance. Values of CTOA for API 5L X65 pipe steel found by three methods—DIC, CNM, and SSM—are given. Values of CTOA given by these three methods are similar and close to 20°. A discussion on the different parameters used to characterize the fracture resistance of running cracks in a pipe under service pressure is presented. The energy of fracture at impact determined by Charpy or drop-weight tear test (DWTT) tests and the critical J energy parameter are considered as well as the yield locus after damage, cohesive zone energy, and CTOA is another approach. One notes that CTOA is assumed to be constant during stable crack extension and decreases linearly with crack length during the instable and primary phase. A numerical technique to describe a ductile running crack using the node release technique and using CTOA as the fracture resistance criterion is presented. This method is compared with three different two-curve methods (TCMs): the Battelle, high strength line pipe (HLP), and HLP-Sumitomo methods. The Batelle TCM, as the oldest method, based on Charpy energy, gives a strongly conservative prediction. Predictions by the CTOA method are close to those obtained by the HLP-Sumitomo one.     

结构和变形对单壁碳纳米管力学性能的影响

使用分子动力学方法模拟了单壁碳纳米管的拉伸变形行为和泊松比,并从单壁碳纳米管晶胞单元的结构特征角度,系统分析了管径、螺旋性和应变对力学性能的影响．模拟结果显示,单臂性碳纳米管(8,8)-(22,22)和锯齿性碳纳米管(9,0)-(29,0)的拉伸弹性变形可以分别达到35％-38％和20％-27％,拉伸条件下这些碳纳米管的弹性模量随管径的增大从960 GPa下降到750 GPa,并且锯齿性碳纳米管的弹性模量比单臂性碳纳米管的弹性模量要高．通过对三根具有相同直径和不同螺旋性的碳纳米管(9,9),(12,6)和(16,0)分别在拉伸和压缩条件下的模拟发现,随着变形的增大,碳纳米管的泊松比将减小;在相同的拉伸应变下,碳纳米管的泊松比随其螺旋角的减小而减小,而在相同的压缩应变下,碳纳米管的泊松比随其螺旋角的减小而增大．     

A digital image correlation method for fatigue test experiments

In this paper, a method based on the digital image correlation (DIC) technique is proposed to monitor the crack growth process during a cyclic fatigue test. Stroboscopic illumination is used to acquire DIC speckle pattern images while the test sample is dynamically loaded. The proposed DIC algorithm uses the fact that the load is periodic to increase the accuracy of the displacement field estimates (a sinusoidal fitting method is introduced for this purpose). Using the appropriate post-processing both the crack lengths and the stress intensity factors can be estimated in function of the number of fatigue cycles. A validation test case on an aluminum U-profile will be presented in the paper.     

A fast digital image correlation method for deformation measurement

Fast and high-accuracy deformation analysis using digital image correlation (DIC) has been increasingly important and highly demanded in recent years. In literature, the DIC method using the Newton-Rapshon (NR) algorithm has been considered as a gold standard for accurate sub-pixel displacement tracking, as it is insensitive to the relative deformation and rotation of the target subset and thus provides highest sub-pixel registration accuracy and widest applicability. A significant drawback of conventional NR-algorithm-based DIC method, however, is its extremely huge computational expense. In this paper, a fast DIC method is proposed deformation measurement by effectively eliminating the repeating redundant calculations involved in the conventional NR-algorithm-based DIC method. Specifically, a reliability-guided displacement scanning strategy is employed to avoid time-consuming integer-pixel displacement searching for each calculation point, and a pre-computed global interpolation coefficient look-up table is utilized to entirely eliminate repetitive interpolation calculation at sub-pixel locations. With these two approaches, the proposed fast DIC method substantially increases the calculation efficiency of the traditional NR-algorithm-based DIC method. The performance of proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. Results reveal that the computational speed of the present fast DIC is about 120-200 times faster than that of the traditional method, without any loss of its measurement accuracy     

Theoretics-directed effect of copper or aluminum content on the ductility characteristics of Al-based(Al_3Ti,AlTi,AlCu,AlTiCu_2)intermetallic compounds

First-principle simulations have been applied to investigate the effect of copper(Cu) or aluminum(Al) content on the ductility of Al_3Ti,AlTi,AlCu,and AlTiCu_2 alloys.The mechanical stable and elastic properties of Al-based intermetallic compounds are researched by density functional theory with the generalized gradient approximation(DFT-GGA).The calculated lattice constants are in conformity with the previous experimental and theoretical data.The deduced elastic constants show that the investigated Al_3Ti,AlTi,AlCu,and AlTiCu_2 structures are mechanically stable.Shear modulus,Young's modulus,Poisson's ratio,and the ratio B/G have also been figured out by using reckoned elastic constants.A further analysis of Young's modulus and Poisson's ratio reveals that the third added element copper content has significant effects on the Al-Ti-based ICs ductile character.     

Experimental study on the micromechanical behavior of a PBX simulant using SEM and digital image correlation method

The micro-scale mechanical behavior of a polymer-bonded explosive (PBX) simulant was experimentally studied using a scanning electron microscope (SEM) imaging system and digital image correlation (DIC) method. The semi-circular bend (SCB) test was chosen for the study. During the testing, a series of SEM images of the specimen was acquired in situ. The natural micro-structural features of the specimen were used as random speckle pattern for DIC analysis. The displacement and strain fields at the area of interest were obtained by DIC. The deformation and damage of PBX were analyzed. Heterogeneous strain fields demonstrated the damage evolution underneath the specimen surface and predicted possible micro-crack growth. Based on the contour plots of the correlation coefficient, the formation and extension of microscopic cracks were quantitatively analyzed.     

Elastic constants determination by direct measurement of the beat wavelength between A0 and S0 Lamb modes with pulsed TV holography

A whole-field optical technique of high sensitivity, namely pulsed TV holography with phase evaluation by the Spatial Fourier Transform Method, is applied to the acquisition of instantaneous displacement fields of ultrasonic Lamb waves in aluminium plates a few millimetres thick. Two Lamb modes, the A0 and S0 ones, are simultaneously generated in the plate, producing a clear beating. Several values of the beat wavelength, corresponding to different excitation frequencies, are obtained by direct measurement of the distance between nodes in the wave field. The obtained values are fitted to the theoretical Rayleigh–Lamb frequency spectrum in order to determine the elastic constants of the plate material. We conclude that it is necessary to know the value of another parameter to univocally solve the problem, and so the bulk longitudinal wave velocity is measured by the pulse-echo method. Then the Poisson's ratio is obtained and, from these two parameters, the Young's modulus can also be determined.     

Processing discontinuous displacement fields by a spatio-temporal derivative technique

In this paper, a digital image correlation (DIC) method coupling cross-correlation with spatio-temporal differential techniques was proposed for assessing discontinuous displacement fields. The accuracy and robustness of the algorithm was assessed on a set of numerical tests by processing computer generated speckled-pattern images. Fracture mechanical tests in mode I were considered, in which both in-plane and out-of-plane rigid-body movements were taken into account. The ability for recovering the analytical asymptotic displacement field in mode I was analysed, and stress intensity factor, crack opening displacement and crack tip location were used as quantitative parameters for validation purposes. Throughout these tests, the results obtained with the proposed method were systematically compared to the ones from Aramis DIC-2D commercial code. Globally, the results computed from both methods are in good agreement with reference values. However, due to the high spatial resolution (point-wise characteristic), a better matching of the displacements in the neighbour of discontinuities could be obtained by the proposed method.     

3-D computer vision in experimental mechanics

Optical methods that give displacement or strain fields are now widely used in experimental mechanics. Some of the methods can only measure in-plane displacements/strains on planar specimens and some of them can give both in-plane and out-of-plane displacement/strain fields on any kind of specimen (planar or not). In the present paper, the stereovision technique that uses two cameras to measure 3-D displacement/strain fields on any 3-D object is presented. Additionally, a quite inclusive list of references on applications of stereovision (and 3-D DIC) to experimental mechanics is given at the end of the paper.     

Complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and Young's moduli as a function of temperature and hydrostatic pressure

Two independent systems to measure the dynamic complex Young's and bulk moduli of viscoelastic materials as a function of temperature and hydrostatic pressure are described. In the Young's modulus system, a bar-shaped sample is adhered to a piezoelectric shaker and mounted vertically inside an air-filled pressure vessel. Data are obtained using both the traditional resonant approach and a wave-speed technique. In the bulk modulus system, the compressibility of a sample of arbitrary shape immersed in Castor oil and placed inside a pressure chamber is measured. Data can be obtained at frequencies typically ranging from 50 Hz to 5 kHz, at temperatures comprised between −2 and 50 °C and under hydrostatic pressures ranging from 0 to 2 MPa (Young's), or 6.5 MPa (bulk). Typical data obtained with both systems are presented, and it is shown how these data can be combined to completely characterize the elasticity of the material under investigation. In particular, they can be used to obtain experimental values of the complex Poisson's ratio, whose accurate measurement is otherwise quite challenging to perform directly. As an example, the magnitude and loss tangent of Poisson's ratio are presented for a nearly incompressible rubber.     

PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM

The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase.     

Uncertainty quantification in DIC with Kriging regression

A Kriging regression model is developed as a post-processing technique for the treatment of measurement uncertainty in classical subset-based Digital Image Correlation (DIC). Regression is achieved by regularising the sample-point correlation matrix using a local, subset-based, assessment of the measurement error with assumed statistical normality and based on the Sum of Squared Differences (SSD) criterion. This leads to a Kriging-regression model in the form of a Gaussian process representing uncertainty on the Kriging estimate of the measured displacement field. The method is demonstrated using numerical and experimental examples. Kriging estimates of displacement fields are shown to be in excellent agreement with ‘true’ values for the numerical cases and in the experimental example uncertainty quantification is carried out using the Gaussian random process that forms part of the Kriging model. The root mean square error (RMSE) on the estimated displacements is produced and standard deviations on local strain estimates are determined.     

On a simple impact test method for accurate measurement of material properties

A simple impact test method is presented to accurately measure the elastic and shear moduli and Poisson's ratio of a uniform Aluminum 6061-T651 cylindrical specimen with free boundary conditions. The elastic modulus is determined from the longitudinal vibration of the specimen and the shear modulus is determined from its torsional vibration. A new technique is developed to mount an accelerometer on the specimen to measure its torsional vibration. The Poisson's ratio determined for the specimen matches exactly with its known value.     

Gel phase vesicles buckle into specific shapes

Osmotic deflation of giant vesicles in the rippled gel phase P(β') gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of 1 μm, and must be described with a large Poisson's ratio.     

Determination of displacement distributions in bolted steel tension elements using digital image techniques

Digital imaging methods have found a great interest in various engineering fields to study stress-deformation characteristics of materials. Recent enhancements in visual instrumentation with the availability of cost-effective hardware and software products make the digital imaging techniques a viable tool to replace direct strain or displacement measurement methods in engineering applications. In this study, deformation characteristics of bolted steel connections are investigated by calculating in-plane displacement distributions using digital image correlation method (DIC). Validation of the method is presented by comparing the strains measured in standard tension specimens using electrical resistance strain gages and the DIC method. Finite element analysis of the connection specimen is also performed to compare the in-plane displacement distributions calculated from both methods. Results from the validation process indicate that the strains obtained from the DIC method compare well with the results of strain gages. The findings also indicate that the displacement distributions calculated from the finite element method may differ from those of the DIC method in terms of distribution pattern, and the location and magnitude of the extreme values of displacements. It is suggested that the proposed method can be used to determine the in-plane displacement distributions for the bolted connections, hence to evaluate their deformation characteristics under loading.     

Single-step scanner-based digital image correlation (SB-DIC) method for large deformation mapping in rubber

The incremental digital image correlation (DIC) method has been applied in the past to determine strain in large deformation materials like rubber. This method is, however, prone to cumulative errors since the total displacement is determined by combining the displacements in numerous stages of the deformation. In this work, a method of mapping large strains in rubber using DIC in a single-step without the need for a series of deformation images is proposed. The reference subsets were deformed using deformation factors obtained from the fitted mean stress-axial stretch ratio curve obtained experimentally and the theoretical Poisson function. The deformed reference subsets were then correlated with the deformed image after loading. The recently developed scanner-based digital image correlation (SB-DIC) method was applied on dumbbell rubber specimens to obtain the in-plane displacement fields up to 350% axial strain. Comparison of the mean axial strains determined from the single-step SB-DIC method with those from the incremental SB-DIC method showed an average difference of 4.7%. Two rectangular rubber specimens containing circular and square holes were deformed and analysed using the proposed method. The resultant strain maps from the single-step SB-DIC method were compared with the results of finite element modeling (FEM). The comparison shows that the proposed single-step SB-DIC method can be used to map the strain distribution accurately in large deformation materials like rubber at much shorter time compared to the incremental DIC method.