Coherent Gradient Sensing Method Research Articles

In-situ residual deformation field analysis of laser repaired metal components by coherent gradient sensing method

Directed Energy Deposition (DED) technology plays an important role in metal additive manufacturing and remanufacturing. However, the quality and repeatability of DED products are still regarded as a challenge that hinders their widespread applications, especially in cutting-edge sectors. As a promising approach to meet that challenge, the in-situ monitoring of mechanical quantities during DED process, such as deformation and stress, has attracted extensive attention in both academic and engineering fields. In this study, a coherent gradient sensing (CGS) system that matches DED equipment is developed and used for in-situ monitoring the residual deformation of DED repaired metal components. The accuracy of the CGS system has been verified by measuring the curvature of a spherical mirror, and the relative error of the curvature is within 2.5% as a whole. Then, through single-layer/double-layers repair experiments, the influence of dwell time between adjacent tracks, cooling process between adjacent layers, and scanning path of the second layer on the residual deformation are analyzed. In single-layer repair experiment, the value of residual deformation increases with the dwell time, while its distribution characteristic almost keeps the same. In double-layers repair experiment, the anisotropy of residual deformation field is mainly influenced by the deposition direction of the second layer. Compared with parallel deposition path in double-layer repair experiment, the orthogonal deposition path results in a reduction of both the anisotropy and the maximum value of residual deformation field. Moreover, in the cooling process of orthogonal deposition, the residual deformation increases while the distribution characteristic remains unchanged. In conclusion, the feasibility of residual deformation measurement by CGS method in DED repairing process is verified, which provides both data support and tool for the future industrial application.

Fracture assessments of blunt V-notches using the coherent gradient sensing (CGS) method

In this paper, the coherent gradient sensing (CGS) method is extended to study the local stress fields and fracture behavior of a blunt V-notch tip. First, the optical governing equations of the CGS method are derived based on Filippi’s stress equation for blunt V-notches and the concept of the notch stress intensity factor (NSIF). Moreover, the CGS fringe patterns in the vicinity of the blunt V-notch tip with different opening angles and notch radii are theoretically synthesized. Next, the fracture property of a blunt V-notch is experimentally studied using a series of three-point-bending polymethyl methacrylate (PMMA) specimens with different geometrical configurations. Finally, the generalized NSIFs up to the initiation of a fracture are evaluated using the proposed CGS method. The CGS fringe patterns in the experimental results exhibit a reasonable agreement with the theoretical fitted fringes, and the NSIFs and notch fracture toughness at the blunt V-notch tip are consistent with those obtained in previous theoretical studies and finite element simulations.

In-situ monitoring of the deformation during Fused Deposition Modeling process using CGS method

Additive manufacturing has been widely applied in various industrial sectors due to its numerous advantages. From available reports, in-situ real-time monitoring is still a challenge during additive manufacturing process. In this study, the Coherent Gradient Sensing (CGS) method is applied to in-situ monitoring during Fused Deposition Modeling (FDM) process for the first time. And a CGS system is designed to realize deformation monitoring during FDM process. By using the system, the full-field deformation evolution of Polylactic Acid (PLA) is studied at different stages of FDM process. Besides, it was found that the evolution process of the deformation can be divided into three stages during cooling process: fast cooling stage, transitional cooling stage and slow cooling stage. The results demonstrate that the CGS method has the advantages of real-time, full-field, intuitive, vibration resistant, and possess a good potential to be applied in stress analysis of other 3D printing techniques.

Special considerations in reflective coherent gradient sensing method for measuring large deformations

In this study, reflective coherent gradient sensing (CGS) method is introduced to measure large deformations of Ni–Cr alloy in instrumented indentation. The effects of grating distance, collimation property of incident beam, camera lens focal length, screen and specimen location are analyzed. The presence or absence of screen and the camera lens focal length are found out to be the most important factors when measuring large deformations with CGS method. Moreover, we develop a method to obtain the ‘true’ interferograms by Fourier and inverse Fourier transformation algorithms. The measuring scale of reflective CGS method for large deformation is obtained. A criterion is developed to distinguish the boundaries between small and large deformations in measuring inhomogeneous deformations with reflective CGS method.

A Novel Phase Shifting Technique of Coherent Gradient Sensing Method for Measuring Crack-tip K-Dominance

A novel phase shifting method for coherent gradient sensing (CGS) is proposed to automate fringe processing. The phase shifting of CGS interferograms can be simply realized by placing three plane-parallel plates sequentially between the two gratings in the traditional CGS method. The phase shifting method is deduced theoretically and the full-field wrapped phase value can be calculated accurately from four or more interferograms. A calibration test that determines the elasto-optic constant for a polymethyl methacrylate (PMMA) sheet is implemented as a verification experiment. Results show the proposed phase shifting method is valid for transmission CGS measurement. As an application, the proposed phase-shifted CGS method is applied to measure the crack tip K-dominance in a PMMA sheet. In addition, the phase shifting method is shown to be valid for reflective CGS measurement.

Mixed-mode fracture investigation of PMMA with initial single/double crack(s) interference using phase-shifted coherent gradient sensing method

Phase-shifted coherent gradient sensing (CGS) was used to investigate the mixed-mode fracture of brittle polymer material. A previously developed phase shifting method for reflective CGS proved effective for transmitted CGS measurement. Using this method, fracture experiments on PMMA specimens with an offset single crack under three-point bending were performed. Also, mixed-mode fracture experiments with initial double crack interference were performed. A series of CGS interferograms were used to describe the fracture characteristics around the crack tip, such as the stress intensity factor, fracture toughness, fracture mixity, crack initiation and propagation. The effects of offset distance on fracture characterization are discussed and the interference effects of double cracks were investigated through varied crack lengths and distances. The comparison between the numerical and experimental K-dominance results shows good agreement. Moreover, the crack growth directions and fracture toughness are estimated using three fracture criteria and compared to the experiment results. It is found that the maximum tangential stress (MTS) and the strain energy density (SED) criterion tally with the experiment results well when KI/KII>5. These results are useful for evaluating the strength and lifespan of PMMA materials and structures.

Load Detection of Functionally Graded Material Based on Coherent Gradient Sensing Method

AbstractFunctionally graded material (FGM) has some particular characteristics due to the gradual variation of physical properties. The study on mechanical behavior of FGM is of great research value. In this work, a large scale FGM which filled with small glass spheres has been prepared by gravity assisted casting technique. The elastic material constants in static condition are measured. One optical experimental method, coherent gradient sensing (CGS), is introduced to study the mechanical behavior of FGM which has variation of material property in power-law. The governing equations of CGS which is used to represent the optics-mechanics relation of the singular field near the point of the outside force are derived based on the power-law asymptotic expansion. The experimental result shows this CGS method as a nondestructive methodology can be used to detect the damage in FGM with high accuracy.

Phase-shifted reflective coherent gradient sensor for measuring Young’s modulus and Poisson’s ratio of polished alloys

In this study, the Young’s modulus and Poisson’s ratio of Ni-Cr Alloy are measured using phase-shifted reflective coherent gradient sensing (CGS) method. Three-point bending experiment is applied to obtain the Young’s modulus by measuring the specimen out-of-plane displacement slopes. Bending experiment of a circular plate with fixed edges loaded by a centric concentrated force is applied to obtain the specimen bending stiffness. The Poisson’s ratio is then solved by substituting the bending stiffness into Young’s modulus. The results show that the phase-shifted reflective CGS method is valid for measuring Young’s modulus and Poisson’s ratio of metals and alloys. In addition, the reflective specimen surfaces are obtained with precision finishing operations and the polishing parameters are optimized for CGS measurement. This method is more effective than the reflecting film transfer method, which is widely used in previous studies.

Analysis and improvement of accuracy, sensitivity, and resolution of the coherent gradient sensing method.

The coherent gradient sensing (CGS) method, one kind of shear interferometry sensitive to surface slope, has been applied to full-field curvature measuring for decades. However, its accuracy, sensitivity, and resolution have not been studied clearly. In this paper, we analyze the accuracy, sensitivity, and resolution for the CGS method based on the derivation of its working principle. The results show that the sensitivity is related to the grating pitch and distance, and the accuracy and resolution are determined by the wavelength of the laser beam and the diameter of the reflected beam. The sensitivity is proportional to the ratio of grating distance to its pitch, while the accuracy will decline as this ratio increases. In addition, we demonstrate that using phase gratings as the shearing element can improve the interferogram and enhance accuracy, sensitivity, and resolution. The curvature of a spherical reflector is measured by CGS with Ronchi gratings and phase gratings under different experimental parameters to illustrate this analysis. All of the results are quite helpful for CGS applications.

Full-field Measurement of Topography and Curvature by Coherent Gradient Sensing Method at High Temperature

Coherent gradient sensing (CGS) method, a real time, full-field optical technique, is insensitive to vibrations and able to provide slope and curvature maps and surface topographies, to investigate non-uniform deformations. In this paper, we analyze the thermal effects on the optical path in CGS due to air convection, and the influence of grating thickness and refractive index on the measurement accuracy. A modified governing equation is derived considering the grating thickness, which is demonstrated by testing a standard sample. Finally, we apply CGS method to measure the full-field deformation of a specimen at high temperature.

Improvement for optical mechanics method of coherent gradient sensing

Coherent gradient sensing (CGS) is double grating lateral-shearing interferometric technique with the simplicity of the optical set-up, non-contact, real-time, full-field optical information and variable resolution, which has shown many applications in the study of quasi-static as well as dynamic crack-tip field in both homogeneous and composite materials. It can be used both in a reflection mode (for opaque materials) and in a transmission mode (for transparent materials). The accuracy of the fringe order in the CGS interference image will deeply influence the precision of experimental study. Because of the difference in the optical principle from other optical methods, the fringe order of CGS cannot be obtained through the phase-shift technology. In this paper, a kind of modified CGS method is introduced and analyzed, which can accurately obtain the fringe order of random position in the CGS interference image. This method does not need additional optical set-up and complicated image processing techniques, but only needs several (greater than two) CGS interference images under different loadings. Static fracture experiments show that this method can evidently improve the precision of the CGS method.

Phase Shifting Full-Field Interferometric Methods for Determination of In-Plane Tensorial Stress

A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.

Modification of Coherent Gradient Sensing (CGS) to Accurately Get the Fringe Order

In this paper, a novel optical method, namely, Coherent Gradient Sensing (CGS) is used to study the fracture properties of IR window materials in the guidance missile. CGS can produce high contrast fringes and provide some degree of control on the sensitivity of measurement during experiment. It is highly attractive for solid mechanics applications, especially to new materials, such as IR window materials. But the accuracy of the fringe order in the CGS interference image will deeply influence the precision of experiment. Because of the different optical principle from other method, the fringe order of CGS can’t be obtained through the phase-shift technology. To satisfy the precision request of IR window materials, a kind of modified CGS method, loading CGS method is introduced and analyzed, which can accurately obtain the fringe order of random position in the CGS interference image. This method doesn’t need additional optical set-up and complicated image processing techniques, but only need two CGS interference images under different loading. Static fracture experiments of ZnS show that this method can evidently improve the precision of the CGS method.

Improvement of measurement error for modified coherent gradient sensing

Recently, a novel optical method, coherent gradient sensing (CGS), has been widely used in the study of deformation near crack tips under quasi-static and dynamic conditions, which can produce high contrast fringes and provide some degree of control on the sensitivity of measurement during experiment. It involves a simple optical set-up and is relatively insensitive to vibrations and rigid body motions. Like other interferometries, such as electronic speckle pattern interferometry, moiré method, etc, the accuracy of the fringe order in the CGS interference image will deeply influence the precision of experimental study. But because of the different optical principle, the fringe order of CGS cannot be obtained through the phase-shift technology. In this paper, a modified CGS method is introduced and analysed, which can accurately obtain the fringe order of a random position in the CGS interference image. The modified CGS method needs two original CGS optical set-ups, and can be used in static and dynamic conditions, which requires no complicated image processing techniques. Static fracture experiments on mode-I crack in homogeneous materials show that this modified method can evidently improve the measurement precision of the CGS method.

Mixed-Mode Dynamic Crack Growth in Functionally Graded Glass-Filled Epoxy

Compositionally graded glass-filled epoxy sheets with edge cracks initially along the gradient are studied under dynamic loading conditions. Specimens with monotonically varying volume fraction of reinforcement are subjected to mixed-mode loading by eccentric impact relative to the crack plane. The optical method of Coherent Gradient Sensing and high-speed photography are used to map transient crack tip deformations before and after crack initiation. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are examined experimentally. To elucidate the differences in fracture behavior due to functional grading, a homogeneous sample is also tested. The differences in both pre- and post-crack initiation behaviors are observed interms of crack initiation time, crack path, crack speed and stress intensity factor histories. When a crack is situated on the compliant side of the sample, it kinks significantly less compared to when it is on the stiffer side. Crack tip mode mixity histories show small but positive values during crack growth from the stiffer side of the sample towards the compliant side whereas a small but negative mode mixity prevails for the opposite configuration.

Fracture investigation at V-notch tip using coherent gradient sensing (CGS)

Local deformation field and fracture characterization of mode I V-notch tip are studied using coherent gradient sensing (CGS). First, the governing equations that relate to the CGS measurements and the elastic solution at mode I V-notch tip are derived in terms of the stress intensity factor, material constant, notch angle and fringe order. Then, a series of CGS fringe patterns of mode I V-notch are simulated, and the effects of the notch angle on the shape and size of CGS fringe pattern are analyzed. Finally, the local deformation field and fracture characterization of mode I V-notch tip with different V-notch angles are experimentally investigated using three-point-bending specimen via CGS method. The CGS interference fringe patterns obtained from experiments and simulations show a good agreement. The stress intensity factor obtained from CGS measurements shows a good agreement with finite element results under K-dominant assumption.

Effect of mode mixity on K-dominance and three dimensionality in cracked plates

The method of Coherent Gradient Sensing (CGS) in transmission, in conjunction with two and three dimensional finite element methods, is used to study the effect of mode mixity on crack tip stress fields. Using a two dimensional finite element analysis the outer bounds of the region of K-dominance were determined. A three dimensional finite analysis was utilized to study the effect of mode mixity on the three dimensional nature of the stress field in the immediate vicinity of the crack tip and to obtain an inner bound of the region of K-dominance. It was noted that increasing mode mixity leads to an increased rotation of the three dimensional zone, keeping its shape and size unchanged. In contrast, the region of K-dominance is seen to dramatically depend on mode mixity, both in shape and size. In addition, an analysis of the CGS interferograms was conducted to obtain an estimate of the regions of K-dominance experimentally. A least squares fit data analysis technique was used to extract fracture parameters, namely the stress intensity factors KI, KII and subsequently the crack tip phase angle, φ. The data points used for the least square fitting were obtained from the determined regions of K-dominance. The same fracture parameters were also evaluated from the finite element analysis, and good agreement was found between experimental measurements and finite element predictions.

A Study of the Fracture Behavior of Unindirectional Fiber- Reinforced Composite Using Coherent Gradient Sensing (CGS) Interferometry

The feasibility of using Coherent Gradient Sensing (CGS) interferometry for studying the fracture behavior of unidirectional fiber-reinforced composites is investigated in this paper. First, the solution for the deformation field surrounding the tip of a crack in an orthotropic material is summarized. Specifically, the most singular term in the asymptotic expansion is explicitly presented. Then, the quantities that relate to the CGS measurements are derived in terms of the spatial position, stress intensity factors, and material constants. Based on these results, synthetic CGS fringe patterns are plotted numerically, and the effects of material anisotropy and crack-tip mixity on the shape of CGS fringe pattern are investigated. In addition, a finite difference interpretation of CGS fringes caused by the finite spacing of the CGS diffraction gratings is taken into account in the simulation. Finally, the initiation fracture toughness and the subsequent resistance curve behavior of a particular unidirectional graphite/epoxy composite are measured using the CGS method. The optically measured stress intensity factors compare successfully to values obtained from the load measurements and the available analytical solutions.

Analysis of coherent gradient sensing (CGS) by fourier optics

A coherent laser beam reflected or transmitted from a deforming plate specimen acquires an optical path difference (phase change) which is related to the deformation and stress field. The optical method of Coherent Gradient Sensing (CGS) uses two parallel grating plates to displace (shear) and recombine the distorted light beam emerging from the specimen. Fringes are produced on the image plane by the interference of the shifted and unshifted beams. The fringe pattern is related to the spatial difference of the phase in the shearing direction. If the shearing distance is small enough, the spatial difference of the phase approximates to its gradient. Each fringe in the image represents a locus of equal gradient component of the phase in the shearing direction. The technique is interpreted by means of wave optics, using the Fraunhofer approximation and the paraxial theory of lenses. The assumptions made in earlier analyses have been removed here. A more precise analysis based on Fourier optics is presented. The simplicity of the optical setup and variable resolution of the technique have led to its frequent use in the area of solid mechanics, including fracture mechanics. Some examples are discussed in the second half of this paper.

Shear dominated transonic interfacial crack growth in a bimaterial-I. Experimental observations

In this work we describe a series of impact experiments performed on PMMA/4340 steel edge cracked bimaterial plates. Specimens were impacted at 20 m s −1 in a one point bend configuration using a high speed gas gun. Dynamic interfacial crack propagation was observed using the optical method of Coherent Gradient Sensing and high speed photography. Very high crack tip accelerations (10 8 m s −2) and very high crack tip speeds (up to 1.5 c R PMMA) were measured and are reported. Quantitative measurements show that in experiments in which the crack tip speed entered the intersonic range for PMMA, the stress field surrounding the crack tip was shear dominated. The observation of high shear around the crack tip can also be explained using wave propagation arguments. It is found that the reason for attainment of intersonic (with respect to PMMA) crack tip speeds is directly related to the large amounts of energy necessary to initiate the crack tip under shear dominated conditions. A comparison with the theoretical results of Part II in this study is also made. There seems to be an unfavorable region of stable crack propagation velocities in the intersonic regime. This region is c s pmma < v < √2 c s PMMA. In all experiments performed, the propagating crack accelerated quickly out of this region. In the few interferograms that do actually correspond to crack propagation in this unfavorable velocity range, crack face contact was observed. This observation is also in agreement with the findings of Part II of this investigation.