Mechanical characterization of polytetrafluoroethylene polymer using full-field displacement method

The aim of this work is to estimate two important material properties of the polytetrafluoroethylene (PTFE) polymer by means of a single experimental test. The displacement fields around a crack tip are used for estimating the modulus of elasticity (or, Young's modulus) and Poisson's ratio. These parameters are evaluated by fitting linear fracture mechanic expression of displacement fields in the vicinity of the crack, for mode I, to the experimental data. Measurements of these displacements are carried out using digital image correlation (DIC) method. In this way, the experimental procedure is conducted by loading a double-edge-cracked plate specimen. In order to validate the results, two available experimental tests have been performed. The modulus of elasticity is determined by means of the tensile test, using a standard test machine. Moreover, the Poisson's ratio is obtained by measuring lateral compressive and longitudinal extensional strain using DIC method.     

Elastic analysis of a mode II crack in a decagonal quasi—crystal

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.     

Numerical Evaluation of <Emphasis Type="Italic">T</Emphasis>-stress under Mixed Mode Loading Through the Use of Coarse Meshes

The present paper investigates the employment of coarse meshes in evaluating the T-stress with the displacement method. Several finite element analyses have been carried out with different mesh refinements and accuracies. Mode I and mixed mode I/II loadings have been considered in finite element analyses. Under mode I loading, single and double edge notched geometries have been considered, while plate with central crack has been considerd for mixed mode loading condition. The analyses are compared with the results by the well-nown stress based approach, and showed that the displacement method permits the evaluation of the T-stress with the employment of coarse meshes. By the way, several precautions must be taken when dealing with coarse and very coarse meshes.     

Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.     

On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

Elastic–plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs’ parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.     

Detection of fatigue-induced micro-cracks in a pipe by using time-reversed nonlinear guided waves: a three-dimensional model study

Localization of fatigue-related micro-cracks in pipelines is of increasing importance in industrial applications. A three-dimensional (3D) fatigue-crack imaging technique combining nonlinear guided waves with time reversal is proposed in this paper for potential applications in pipeline inspections. By using this method, the non-classical nonlinear guided waves generated from micro-cracks with hysteretic behavior are recorded, and the third harmonic waves are used to reconstruct the fatigue-crack images in a pipe by using a time reversal (TR) process. The feasibility of this method is examined by the imaging simulations for a steel pipe with varied defect areas. A finite-difference time-domain (FDTD) code is programmed to solve the wave equations under cylindrical coordinates, and simulate the experimental process of wave propagation. The results show that: (1) the proposed technique has excellent spatial retrofocusing capability; (2) the accuracy of defect localization and sizing depends on the crack orientation and the adopted guided wave mode; and (3) different displacement/stress components have varied sensitivities to the crack orientation.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

Reference-free impedance-based crack detection in plates

Impedance-based damage detection techniques gained popularity among structural health monitoring (SHM) and nondestructive testing (NDT) communities due to their sensitivity to local damage and applicability to complex structures. In general, conventional impedance-based techniques identify damage by comparing “current” impedance signals with “baseline” ones obtained from the pristine condition of a structure. However, in-situ structures are often subject to changing temperature and loading conditions that can adversely affect measured impedance signals and cause false-alarms. In this paper, a “reference-free” impedance method, which does not require direct comparison of the current impedance signals with the previously obtained baseline impedance signals, is developed for crack detection in a plate-like structure. The proposed technique utilizes a single pair of PZTs collocated on the opposite surfaces of a structure to extract mode conversion produced by crack formation. Then, a reference-free damage classifier is developed and performed on the extracted mode conversion for instantaneous damage diagnosis. Numerical simulations and experimental tests have been conducted explicitly considering varying temperature and loading conditions to demonstrate the robustness of the proposed damage detection technique under varying operational and environmental conditions.     

The interaction of the S0 Lamb mode with vertical cracks in an aluminium plate

This article presents the interaction of the first symmetric Lamb mode S0 with vertical cracks in an aluminium plate placed in vacuum. The cracks are symmetrical regarding to the median plane of the plate and their heights are increasing from 0% to 100% of the plate thickness, by steps of 25%. The frequency-thickness product is chosen to be lower than the S1 frequency cut-off. A modal decomposition method is used to solve the diffraction problem. The variation with the height of the crack of the reflection and transmission coefficients of modes propagating in the far field is predicted. The displacement fields at both sides of the cracks are also calculated, so that it is possible to quantify the crack-opening displacement. These results are compared to numerical predictions obtained using a finite element software. Measurements are also conducted and compared to the predictions.     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.     

Measurement of Stress Intensity Factors of a Mixed-Mode Interface Crack by a Speckle Photography

The image-processing system based on a two-dimensional Fourier transform is presented for the analysis of Young’s fringes pattern created from a double-exposure speckle photograph. The fringe spacing and orientation are determined using only one Young’s fringes pattern without any other diffraction halo patterns. The stress-intensity factors of a mixed-mode interface crack were measured by speckle photography. A compact normal and shear specimen with an interface crack was employed. This specimen enables us to carry out the experiment under various kinds of mixed-mode loading. A steel and an epoxy resin were used as dissimilar materials. The displacement along the crack lines at the free surface was measured by speckle photography. The K₁ and K₁₁ values were determined by a least squares method using displacement data along the crack lines. Three-dimensional finite element analysis was carried out on the same specimen. An accuracy of stress intensity factors obtained by the speckle photography was discussed by comparison of results obtained by the finite element analysis.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.     

Effects of surface treatment and weave structure on interlaminar fracture behaviour of plain glass woven fabric composites: Part II. Report of the 2nd round robin test results

This paper reports the second part of the results from the round robin test program proposed by the Society of Interfacial Materials Science (SIMS) to characterise the interlaminar fracture behaviour of E-glass woven fabric reinforced vinylester composites. Special emphasis was placed on the study of loading direction (i.e. weft and warp directions) effect on interlaminar shear strength and fracture toughness. Ten laboratories worldwide participated in this test (Table 1). Each laboratory was supplied with composite laminates and conducted the tests according to its own procedure. The results showed that although there were large variations in absolute magnitude between laboratories, a general trend was established with higher interlaminar fracture resistance in the weft direction than in the warp direction for a given silane agent. The larger number of strands running in the warp direction with rougher, more undulating areas perpendicular to the direction of crack propagation was mainly responsible for this result. The results also confirmed the previous finding that the mode I interlaminar fracture toughness increased with increasing silane agent concentration.     

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion

In this work, some recent mixed mode I/II fracture toughness results obtained from Perspex (or polymethylmethacrylate (PMMA)) with four simple cracked specimens subjected to the conventional three-point bend loading are reanalysed based on local energy concept. Although all the mentioned samples have been tested under the same and similar mode mixities, different fracture toughness envelopes were obtained for mixed mode I/II fracture of PMMA. The averaged strain energy density (SED) criterion has been applied in the past for different types of notched specimens (including U, V, O and keyhole notches). It is shown that the mixed mode tensile-in plane shear fracture toughness data obtained from the semicircular and triangular crack type specimens are successfully predicted for sharp cracked PMMA samples using the SED criterion.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

Indentation fracture and indentation delamination in ZnO film/Si substrate systems

ZnO films with thicknesses ranging from 0.202 to 1.535?µm were deposited by using the magnetron sputtering technique on Si (100) substrates 525?µm thick. Then, Vickers indentation tests were carried out on the ZnO/Si systems at room temperature, in which the applied load varied from 10?mN to 2.0?N. The experimental results show that only indentation-induced radial cracking occurred in the systems with film thicknesses equal to and thinner than 0.554?µm, from which the residual stress in the films was extracted to be 387?MPa in compression. For the systems with film thicknesses equal to and thicker than 0.832?µm, only indentation-induced delamination occurred when indentation loads were low. Under high indentation loads, radial cracking concurrently occurred with delamination. The radial cracks were invisible at the film surfaces because the crack length was smaller than the delamination size. The critical film thickness for indentation-induced delamination was found to be around 0.7?µm for the ZnO/Si systems. Combining the composite hardness models with the indentation-induced delamination model, we developed a method to determine the interfacial fracture energy between a film and its substrate. The novel method is particularly useful for indentation equipment without any displacement measurement devices. Using the new method, we extracted the interfacial fracture energy to be about 12.2?J?m^?2 and from 9.2 to 11.7?J?m^?2 for the cases without and with buckling respectively of delaminated films. Consequently, the pure mode I interfacial fracture energy was calculated to be 10.4?J?m^?2 for the ZnO/Si systems.     

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.     

Basic solution of four parallel non-symmetric permeable Mode-III cracks in a piezoelectric/piezomagnetic composite plane

The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites.