Transient analysis in a fracturing magnesium plate

Transient displacement and strain distributions in the vicinity of running-crack tips were determined experimentally in centrally notched magnesium plates. The moiré-fringe technique was used together with a Q-spoiled laser which was the light source for single-flash photography. The specimen was designed such that net-section yield occurred prior to fracture and, thus, the crack propagated through the yielded region. Displacement distributions in the vicinity of such running-crack tips were found to vary as\(\sqrt r \) for radial distances as close asr=0.08 in. Transient moiré-fringe patterns were then differentiated graphically to obtain longitudinal strain distributions in the vicinities of running-crack tips. These transient-displacement and transient-strain distributions were compared with equivalent static results. For this ductile material, both the transient and static results showed qualitative agreement with the displacement and strain distributions in an infinitely elastic plate in the region ahead of the crack tip. For the region above the crack tip, the transient and static results differed appreciably.     

The ductile fracture of anisotropic materials

A theoretical solution is obtained which adapts the Dugdale model to anisotropic materials. The effect of anisotropy is shown to modify each isotropic field equation by amultiplicative constant which is a function of the anisotropic-material constants. A limit on the validity of a Dugdale-type solution is found using a von Mises' yield criterion which implies that the crack and plastic zone will extend along a direction other than the crack line. As long as the material is within pirescribed limits, the Dugdale finiteness condition is shown to be affected by material anisotropy only in the calculation of a yield stress. Experimental results on crack-opening displacements are presented which indicate that a large degree of anisotropy is necessary to cause significant deviations from isotropic theory. Results are presented which indicate that anisotropy does affect the direction of crack propagation.     

On wave and fracture propagation in Rock Media

Experimental-stress-analysis techniques were used to study wave and fracture propagation in rock media. Marble and granite plates were loaded explosively. Wave propagation was observed through isochromatic-fringe patterns on bonded photoelastic coatings and moiré-fringe patterns. These patterns were recorded with a Beckman and Whitley camera operating at rates from 250,000 to 1,000,000 frames per second. Dilatational, shear and Rayleigh wave velocities were determined. The leading part of the pulse is compressive and shows appreciable attenuation. The trailing part goes into tension, causing widespread tensile fracture. The velocity of propagation of this fracture zone in marble was nearly equal to the theoretical terminal velocity. In the case of induced cracks in marble and granite, the velocities of crack propagation were appreciably lower than the theoretical terminal values. Experimental results obtained were discussed and interpreted for their relevance to the rapid-excavation process in rock.     

Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

Strain analysis of composites by moiré methods

Moiré techniques were developed, adapted and applied to the determination of strain fields in filamentary composite laminates. Conventional techniques, using 1000 line-per-inch (Ipi) arrays bonded or photoprinted onto the specimen, were applied to glass-epoxy and boron-epoxy specimens with holes and cracks. Techniques for tenfold fringe multiplication were also applied to glass-epoxy and boron-epoxy laminates with holes. A reflective surface of glass-like smoothness was produced on the specimen and a 500 dot-per-inch grid photoprinted on it. A rigid distortion-free camera was used for recording replicas of the specimen grid by projection photography. These replicas were analyzed with a 200 line-per-millimeter (5080 Ipi) grating for reconstruction of moiré-fringe patterns. These patterns were analyzed by graphical and mechanical differentiation using second-order moiré. Strain distributions and strain-concentration factors were in very good agreement with theoretical and other experimental results.     

The influence of grating characteristics on moiré fringe multiplication

Coherent optical techniques of fringe multiplication can be used to enhance the sensitivity of moiré measurements. However, for some coherent optical-processing systems, the significance of the resulting interference pattern is influenced by the characteristics of the gratings being processed. Analysis of one commonly used system for fringe multiplication involving two bar and space amplitude gratings reveals that accuracy of displacements and strains calculated from a fringe pattern is very sensitive to the transmission ratios of the gratings being processed. For variations of the transmission ratio of only 10 percent from the ideal case of 50 percent, the interference patterns produced by optical processing no longer correspond to multiplied moiré-fringe patterns.     

Three-dimensional effects in interfacial crack propagation

The paper describes the use of crack-opening interferometry for examining the variation in normal crack-opening displacements (NCOD) along the front of an interfacial crack in an edge-cracked bimaterial strip under biaxial loading. For the glass/epoxy combination considered here, the crack front was concave in the direction of crack growth, in contrast to previous observations with a glass/polyurethane/glass sandwich specimen and cracks in homogeneous materials. The NCOD were greatest in the interior of the specimen for all mode-mixes considered and the exponents in a power-law fit of NCOD versus distance from the crack front decreased towards the free surface. The exponents varied with mode-mix, suggesting that interfacial crack-front geometries could be similarly affected.     

Stable crack growth in aluminum tensile specimens

Post's white-light moiré interferometry was used to obtain sequential records of the transientU _y -displacement fields associated with stable crack growth in 7075-T6 and 2024-0, single-edge-notched (SEN) specimens with fatigued cracks. TheU _y -displacement fields are used to evaluate the crack-tip opening displacement (CTOD), far- and near-fieldJ-integral values, Dugdale-strip-yield model, William's polynomial function and the HRR field. Paper was presented at 1985 SEM Spring Converence on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

聚碳酸酯板裂纹顶端的弹塑性研究

本文研究了聚碳酸酯板的延性断裂特征;提出了修正的强化Dugdale条带屈服模型,并用实验-数值计算混合法确定了强化弹塑性材料裂纹顶端附近的应力场参数.实验测定结果与理论等色线,计算的裂纹前沿塑性区长度相符合.由此,验证了所提出的修正强化Dugdale条带屈服模型的合理性.     

Techniques of fringe interpolation in moiré patterns

The objective of this paper is to report further developments on the application of the displacement-light-intensity law to fractional-fringe-order determination. The structure of moiré-fringe patterns is analyzed when the moiré fringes are recorded together with the lines producing them. A device used to record the information stored in the film is described. The influence of the combined effect of the film and the reading device is discussed. Departures from the ideal behavior of the whole process are analyzed together with the introduced errors. The mechanics of processing continuous moiré-fringe information is outlined together with the means utilized to reduce the influence of errors. Data are provided to show the degree of effectiveness achieved with the described process.     

Curved thermal crack growth in nonhomogeneous materials with different shaped external boundaries II. Experimental results

Curved thermal cracks are considered running along special principal stress trajectories in self-stressed two-phase solids with different cross sections. The resulting mixed boundary-value problems of the stationary plane thermoelasticity are solved by applying the finite element method. Moreover, using appropriate directional criteria established for crack path prediction, the further extension of thermal cracks starting at the external surfaces of different shaped two-phase solids has been determined. Furthermore, the corresponding fracture mechanical data like crack edge displacements, strain energy release rates and stress intensity factors, respectively, have been calculated. Finally, the theoretical investigations given in part I of the paper are compared with experiments using differing optical methods of the experimental stress analysis. The experimental results reported in part II of the paper and the theoretical calculations show a reasonable agreement.     

Moiré-fringe measurement

A simple technique and an apparatus layout, for measuring moiré-fringe spacings, used in conjunction with the moiré replica technique, are introduced. Results of measurements, using this new technique for evaluation grid spacings show an agreement of more than 99.9 percent between the actual grid spacing and those evaluated using the proposed apparatus.     

Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.     

Moiré fringes as parametric curves

Advantage is taken in this paper of the parametric properties of families of curves to express in a simple manner several fundamental properties of moiré fringes. Attention is called, in particular, to the necessary limitations on the angle of rotation of two gratings, and on the magnitude of their difference in pitch, to obtain an easily interpretable moiré-fringe pattern.     

A Self-Similar Crack Expansion method for three-dimensional cracks in an infinite or semi-infinite medium

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks are in good agreement with other analytical solutions.     

The moiré-grid analyzer method for the analysis of finite strain

Elements of Lagrangian finite-strain tensor are derived in terms of moiré-fringe intercepts with grid analyzer axes (Ξ,η); they are shown to be independent of the relative angle between the analyzer and the undeformed specimen grids. The role of the initial mismatch λ and initial rotation θ ₀ on initial patterns and patterns under finite strains are discussed. Aluminum tensile-test pieces photoengraved with 133 lines per inch (lpi) grid are tested; analyzer grid of 142 lpi is used. The axial strains calculated from moiré-fringe intercepts with (ξ,η), are in good agreement with average strain obtained from 3-in. gage length.     

Wave propagation in layered model due to point-source loading in low-impedance medium

Dynamic photoelastic and moiré techniques were used to study the incident, reflected and refracted waves in a layered model. The model, consisting of two birefringent layers with an impedance ratio of approximately 2∶1, was subjected to point-source explosive loading in the low-impedance medium. The isochromatic and moiré-fringe patterns were photographed with a Cranz-Schardin multiplespark camera operating at a rate of 200,000 frames per second. Propagation and attenuation characteristics of waves in both layers were studied. The formation of head-waves at the interface was clearly evident. Stress determinations were made in some instances using photoelastic and moiré data.     

The principle and application of sticking film moiré internnferometry

This paper presents a new method for obtaining a high-resolution one-dimensional or two-dimensional moiré pattern on a specimen. The technique uses a holographic film that adheres to the specimen. The film is twice exposed by a virtual holographic grating, then it is removed from the specimen, devellped, fixed, bleached, and illuminated. This process produces clearly visible moiré patterns. The method is used to measure elastic modulus values of some materials, deflection and longitudinal displacement of a beam, stress-intensity factors (SIF), crack-opening displacement (COD,J integral, and a dynamic deformation. This paper explains the principles of the method, derives two displacement equations of two-dimensional moiré interferometry, and discusses the reliability, range of application, and measuring precission of the new method.     

Characterization of short duration stress pulses generated by impacting laminated carbon-fiber/epoxy composites with magnetic flyer plates

Short duration stress pulses are of particular interest in determining the interfacial crack tip instability criteria for the dynamic fracture behavior of laminated carbon-fiber/epoxy composites. However, the heterogeneous architectures of laminated composites can alter the characteristics of a stress pulse as it propagates toward a crack tip. This makes it difficult to use standard dynamic testing techniques for characterizing these materials, since these techniques assume the characteristics of the stress pulse do not change as a result of propagation and can therefore be unambiguously determined from impact conditions. This paper presents a novel experimental technique that has been developed for characterizing short duration stress pulse propagation in laminated composite materials. In this technique, a dynamic moiré interferometer is used to capture fringe patterns corresponding to displacement fields associated with short duration stress pulses that were generated by impacting 0° and 90°/0°/90° carbon-fiber/epoxy composites with a magnetic flyer plate. Appropriate dynamic testing conditions for capturing high fidelity fringe patterns were determined using the recently developed dynamic moiré fringe contrast factor. The effects of the composite architecture on the propagation of short duration stress pulses observed with the dynamic moiré interferometer were confirmed by transient dynamic finite element analysis. From comparisons of experimental and numerical data, it was determined that the impact conditions for the magnetic flyer plate and laminated composite will not necessarily be planar, which has a significant effect on the intensity and duration of the propagating stress pulse.     

J resistance curves in aluminum SEN specimens using Moiré interferometry

TheU _y -displacement field obtained by white-light moiré interferometry were used to estimate the approximate far- and near-fieldJ-integral values associated with the subcritical crack growths in fatigue precracked 7075-T6 and blunt notched and fatigue precracked 2024-0 and 5052-H32 aluminum, single-edged notch (SEN) specimens. The initial phases of theJ-resistance curves for the somewhat brittle 7075-T6 and the two ductile 2024-0 and 5052-H32 aluminum SEN specimens are presented. Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.