Low-cycle fatigue-crack indications by strain gages operating in elastic strain fields

This paper describes the response of bonded electrical-resistance strain gages to low-cycle fatigue cracking of four, cyclically pressurized, boxlike structures. The strain-pressure “signatures” of gages installed on flexural parts of the structures were recorded semicontinuously. By observing the changes in signatures of certain gages, it was possible to follow indirectly the initiation and propagation of internal low-cycle fatigue cracks. The described technique appears feasible as a crack-detection system, or as an adjunct to some other type of damage-warning system. It is suggested that the sensitivity and accuracy of this technique make it possible to substitute “crack initiation” for “through cracking” as a criterion for fatigue failure in design.     

A delamination gage for carbon fiber composites

A graphite crack gage familiar to fracture testing of nonconductive polymeric materials has been adapted to measure delamination growth in carbon fiber composites. The gage consists of a continuous graphite film whose conductance changes linearly with respect to crack length. The development of an insulation technique so that the electrical film may be applied to carbon fiber composites is described. Further constraints on the gage design occur due to the narrow profiles of conventional delamination specimens. These limitations are reviewed in detail along with appropriate methods for manufacturing and calibration of the gage for delamination experiments. A simple shunt voltage measurement circuit is described along with a derivation of the relationship of crack length to voltage. Two example applications are provided: stable delamination growth in a conventional double cantilever beam (DCB) specimen and dynamic delamination growth in a single-edge-notched (SEN) strip. The electrical delamination length measurements from the DCB tests were found to compare well with the location of the delamination front determined by microscopy and radiography. These results give confidence in dynamic delamination results where growth rates exceeding 1000 m/s were measured. Sample evaluations of delamination toughness are made using the experimental data; compliance methods are used in the case of the DCB analysis, and dynamic finite element methods are used in the case of the SEN strip analysis.     

Small attachable interferometric strain gages

Laser-based interferometry from two tiny reflective indentations can be used to measure in-plane strain/displacement over a very short gage length (on the order of 100 μm). If the specimen material is not reflective, then some other means of generating the interference patterns must be found. This paper describes two kinds of attachable gages: plated acetate replicas of indentations and reflective foils that are indented after application. In either case, the gage is applied with the techniques used for foil-resistance gages and the gage itself is very small. The manufacturing procedures are described. The results of experiments comparing the strain to that measured with foil-resistance gages are presented. Finally, the small interferometric gage is used to measure strain on one of the metal strips in a foil-resistance gage.     

A stress criterion for crack growth

A stress criterion for crack growth was developed from test results with 7075-T6 aluminum-sheet specimens containing transverse machined cracks. Stress distributions near the crack tip were obtained using strain gages and by reducing the strain data to stresses with the aid of Reuss plasticity theory. These distributions indicated the biaxial nature of stress at the crack tip, the high stress gradients a short distance from the tip, and the variation in stress-concentration factor with crack length. Crack growth was found to occur when the effective stress at the crack root reached the engineering ultimate strength.     

Application of carbon-powder-polymer composite as a continuous crack-length sensor

This paper explores the application of carbon-powder-impregnated polymeric composites for measuring crack extensions. The strain sensitivity of the gage material is shown to be very small. In the first series of tests, the gage material is characterized by measuring the change in electrical resistance due to machined slits for various gage lengths. The measured response is compared with the response predicted from a very simple electrical model. On the basis of good correlation and repeatability, the usefulness of such gages to measure crack extensions is assessed by a second series of tests. Further work to improve the gage response by optimizing the shape of the gage and making the gage and the adhesive layer thinner is proposed. The presented concept, with improvements, can result in a reliable, inexpensive crack gage requiring inexpensive instrumentation. Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

基于局域分析的疲劳短裂纹群体演化随机模型

采用局域裂纹数密度描述金属材料中不同局部区域的疲劳短裂纹群体损伤的发展情况通过考虑在不同局域存在的材料性质的随机涨落及局部损伤对损伤总量发展的影响，建立了局域裂纹数密度演化随机方程对方程数值求解从而模拟了材料的疲劳短裂纹损伤过程结果显示出主裂纹出现的随机性，并讨论了裂纹总数与最大裂纹尺度在统计意义上的演化特征     

An experimental method for determining dynamic fracture toughness

The boundary and loading conditions in many dynamic fracture test methods are frequently not well defined and, therefore, introduce a degree of uncertainty in the modeling of the experiment to extract the dynamic fracture resistance for a rapidly propagating crack. A new dynamic fracture test method is presented that overcomes many of these difficulties. In this test, a precracked, three-point bend specimen is loaded by a transmitter bar that is impacted by a striker bar fired from a gas gun. Different levels of energy can be imparted to the specimen by varying the speed and length of the striker to induce different crack growth rates in the material. The specimen is instrumented with a crack ladder gage, crack-opening displacement gage and strain gages to develop requisite data to determine toughness. Typical data for AISI 4340 steel specimen are presented. A simple quasi-dynamic analysis model for deducing the fracture toughness for a running crack from these data is presented, and the results are compared with independent measurements.     

Effects of pressure on small foil strain gages

This paper describes the behavior of small foil strain gages under high pressure. Effects of pressure were determined and calibration curves were established in prelininary experiments. The calibrations were then used for correcting measured strains in pressure vessels. Preliminary experiments at room temperature were conducted on small foil strain gages for pressures up to 35,000 psi. The effects of pressure on the gages bonded with a cynoacrylate contact cement, a room-temperature epoxy cement, a high-temperature epoxy cement and a filled epoxy resin were evaluated. Because the contact cement was least affected by pressure and was easiest to apply, it was chosen for use in successive experiments with different gage installations. Calibration curves were determined for strain gages of 0.031-, 0.062- and 0.125-in. gage lengths. The compensating gages were under atmospheric pressure. The calibrations included the pressure effects of gages bonded on both concave and convex surfaces, and the effect of tensile prestrains. Data could be duplicated for successive pressure tests and for several gage installations. The calibration curves proved to be an effective way for obtaining accurate readings from the foil strain gages bonded internally to a pressure vessel.     

Monitoring Fatigue Crack Growth in Compact Tension Specimens Using Piezoelectric Sensors

This paper aims to report the results of an experimental study on the application of piezoelectric dynamic strain sensors for crack length measurement in fracture mechanics specimens. The performance of the piezoelectric sensors was assessed through fatigue crack propagation tests in compact tension (CT) specimens. Sensors of polarized polyvinilidene fluoride polymer (PVDF) were bonded to the back face of CT specimens, in the same manner as the electrical resistance strain gages installed for crack length measurement in the back face strain technique. The results showed that, mainly due to its high sensitivity to strain, the use of piezoelectric materials as dynamic strain sensors can contribute to the experimental investigation in the field of fracture mechanics.     

Gage-length errors in the resolution of dispersive stress waves

The effect of measuring the time history of a passing dispersive wave with a finite-length gage is to introduce time and amplitude errors between the actual values and the measured values of the wave function. In this paper, mathematical expressions relating the size of these errors to the gage length, properties of the material, and spectral content of the incident wave are derived. These expressions are used to predict the response of a long, resistance strain gage, attached in the longitudinal direction on the lateral surface of a long slender rod of a linear viscoelastic material (Lexan), to a short pulse. The shape of the pulse just before and just after the region of the long gage was measured by means of very short gages. The dispersion and attenuation properties of the material were obtained from the short-gage data. This information and the previously derived mathematical-correction equations were used to predict the response of the long gage. Good agreement was obtained between the predicted and measured values of the response of the long gage. In addition, the correction equations and the response of the long gage were used to predict the incident pulse. Good agreement with the known experimental values was obtained.     

Measurement of static strain at 2,000° F

This paper describes the work being done at Hughes Aircraft Company using capacitance strain gages to measure static strains at temperatures up to and including 2,000° F. A new configuration of the capacitance gage is described with a gage length of 0.50 in. Methods of attaching the gage have been developed for welding, bonding and flame-spray installations. Instrumentation procedures and methods are defined. Statistical accuracy and test results are discussed on the results obtained from a lot of 60 gages. Results discussed were obtained on Rene 41, titanium and L605 stainless steel. Data analysis on the gage includes gage factor, gage factor vs. temperature, apparent strain, linearity, hysteresis, temperature effects, drift, and zero shift.     

An investigation of the use of strain gages to measure welding-induced residual stresses

The measurement of weld-induced residual stress is important in structures that are subjected to cyclic loading during their service life. Depending on their magnitude, stresses can influence the rate of crack growth under cyclic loading and hence affect the life of the structure. Because the level of residual stress may change during service, measurement of these changes is necessary for accurate life prediction of the structures. The measurement of welding-induced residual stress using strain gages poses significant problems, the most important being the potential damage to the gages by high temperatures generated in the welding process. This laboratory study was undertaken to assess the suitability and signal stability of commercially available resistive strain gages for the measurement of postweld residual stresses in a submarine hull structure. Adhesively bonded and weldable-type strain gages were attached to the surface of a 35 mm thick steel plate, which was then subjected to thermal cycles similar to those encountered during welding construction of a submarine pressure hull. This paper describes the strain gage application procedure, changes in the strain gage output at end of each experimental stage and the history of changes in the residual stress.     

Dynamic plastic response of foil gages

Little research has been devoted to the accuracy of the response of resistance strain gages to dynamic plastic strain because of the lack of an easy-to-use comparative strain-measuring technique. The dynamic interferometric strain gage provides a suitable standard of comparison. Foil-gage response is compared directly with interferometric strain-gage response in a longitudinal-impact experiment. The accuracy of the foil gage does not decrease with increasing maximum strain (up to 8 percent). The error in shape of the strain wave does not vary drastically with distance from the point of impact. In contrast to previous work, foil gages are found to be reasonably accurate strain transducers for dynamic plastic strain.     

The effects of high pressure on foil strain gages on convex and concave surfaces

The present investigation was undertaken to determine whether a linear pressure-strain response could be obtained for gages mounted on convex and concave specimens subjected to hydrostatic pressures to 140 ksi. This is an extension of a previously reported work where flat surfaces only were considered. Linear pressure-strain curves were obtained for five different types of foil strain gage having gage lengths varying from 1/16 to 1/4 in. These were mounted on steel, aluminum and magnesium specimens having diameters ranging from 1/4 in. convex to 3/8 in. concave. The inverse slope of the pressure-strain curves was compared with the compressibility constant 1–2v)/E to determine a percent deviation. In this constant,v andE are Poisson's ratio and the modulus of elasticity respectively. Experimental results show the percent deviation to be a function of the compressibility constant of the material and the radius of curvature and that these two parameters are inter-related. The percent deviation was found to be essentially independent of gage length for the range of specimen configurations investigated except where the radius of curvature of the specimen induces problems in mounting the gages. Since a linear pressure-strain response was obtained, it is possible to correct the strain readings for gages mounted on specimens of varied hydrostatic compressibility and geometrical configuration.     

Experimental and theoretical study on numerical density evolution of short fatigue cracks

Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements. The project supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.     

The use of a high-modulus-inclusion gage in nonlinear viscoelastic materials

The behavior of an inclusion in a host material subjected to a stress system depends primarily on the ratio of the tangent moduli,E inclusion/E host. An inclusion of suitable material used in the form of a gage will give an identifiable photoelastic-fringe pattern. This pattern is related to the applied biaxial stresses in the diametral plane of the gage, and is independent of the actual modulus and strains in the host material provided that the moduli ratio is more than 300. A program of work has been carried out to verify the use of such an inclusion gage in low-modulus nonlinear viscoelastic materials. The gage geometry used in this work consisted of a hollow cylinder of birefringent material with a ratio of outside diameter to inside diameter of 5 to 1. The host materials were either unfilled or highly filled carboxyl-terminated polybutadiene rubbers. The moduli ratios for both host materials were such that the gages act as rigid inclusions. A theoretical study has also been conducted to find the optimum measuring points within the gage and the fringe patterns created by selected biaxial-stress ratios. The study also showed that the gage sensitivity is virtually independent of Poisson's ratio but depends on the biaxial ratio of the stresses. The values of the sensitivity factor obtained experimentally were close to those derived theoretically. The stressfringe order at the optimum measuring points was obtained by Tardy compensation, and the biaxial-stress ratio determined either from fringe-pattern recognition or by measuring points. Future applications and uses of such a stress-measuring technique will be described.     

Small-crack closure measurements in titanium alloys

An automated interferometric displacement gage was used to monitor crack-mouth-opening behavior of naturally initiated small surface cracks in a series of titanium alloys having a range of microstructures and deformation characteristics. Findings indicate that the transient development of crack closure plays a significant role in the early propagation of small fatigue cracks.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 6–10.     

Initiation and propagation of fatigue crack in pure aluminium single crystals

The fatigue crack initiation and propagation in the pure aluminum single crystals with different orientations are investigated. Acoustic Emission (AE) technique is used to monitor the fatigue crack initiation and propagation data. The results show that the acoustic emission technique could be used for detecting fatigue crack initiation and propagation. The total counts of AE are plotted as a function of the number of fatigue cycles, and change in slope of the curve corresponded to the initiation of the fatigue crack. The fatigue crack initiation and propagation are related to the specimen crystalline orientation. Specifically, they depend on the ratio K of the Schmid factor of the secondary slip system, to that of the primary one. The greater the ratio K, the easier the fatigue crack initiates and the faster the fatigue crack propagates. When the ratio K is equal or close to one, the fatigue crack grows either along a cleavage plane which intersects both the primary plane and the secondary one or along the primary slip plane and the secondary one. Growth along alternating planes can also occur giving rise to a zigzag path. When the ratio K is much less than one, the fatigue crack grows along the primary slip plane only. The results are explained with a model for the faceted mode of fatigue crack growth.     

Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material

Based on the complex variable method and the technique of conformal mapping, the anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material is studied. The exact solutions of field intensity factors and energy release rate are presented in closed-form with the assumption that the surfaces of the cracks and the elliptical hole are electrically impermeable. With the variation of the hole-size and the crack length, the present results can be reduced to the cases of two symmetrical edge cracks and a single edge crack emanating from a circular hole given by Wang and Gao [Wang, Y.J., Gao, C.F., 2008. The mode III cracks originating from the edge of a circular hole in a piezoelectric solid. International Journal of Solids and Structures 45, 4590–4599]. Moreover, new models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and a single edge crack emanating from an elliptical hole, two asymmetrical edge cracks emanating from a circular hole, T-shaped crack, cross-shaped crack and semi-infinite plane with an edge crack. Numerical examples are then conducted to reveal the effects of the hole-size and the crack length on the field intensity factors and the energy release rate.     

THERMAL FRACTURE OF FUNCTIONALLY GRADED PLATE WITH PARALLEL SURFACE CRACKS

This work examines the fracture behavior of a functionally graded material （FGM） plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors （TSIFs） at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.