Monitoring short fatigue cracks with miniature strain gages

An experimental technique to monitor the length and the opening level of a short fatigue crack is presented. It is based on the progressive decrease with crack length of the response of miniature strain gages installed on the surface near the crack plane. A first gage installed close to the crack plane can monitor cracks from 10 μm in depth to half a millimeter where the response saturates. Other gages at larger distances from the crack plane are less sensitive but can monitor longer cracks. The response is measured so that it is independent of strain-gage calibration, Young's modulus and Poisson's ratio. The paper first presents the basic principles and possibilities of the technique as well as a finite-element analysis performed on automatic welded joints with straight-fronted cracks for which the technique has been developed. The results give a correlation between gage response, crack length and gage location and the conditions of replacement of a gage reaching saturation. The practical exploitation of the technique has required further work to derive a continuous calibration of the gage response that includes corrections to account for the gage finite dimensions and the crack-plane inclination. This calibration is shown to give crack lengths that compare well with fractographic marks and typical results that have been obtained on short crack growth at the weld toe are presented. In particular, the resolution of the technique is put into evidence with results on the initial growth of a 0.1 mm nonpropagating crack. The paper finally points out the distinctive features that appear in current works to adapt the technique to the growth of semi-elliptical cracks of low and high aspect ratio.     

Dynamic strain measurement with the interferometric strain gage

The interferometric strain gage has a short gage length, high-frequency response and the capability of measuring large plastic strains. Furthermore, the gage is easily ruled directly onto the specimen, and no mechanical or electrical contact needs to be made during the measurement. These features make the interferometric strain gage particularly suitable for dynamic plastic-strain measurement. In this paper, the details of an experimental setup for generating and measuring dynamic plastic strain are given. The photometric techniques of measuring the fringe motion of the interference patterns are describle as well as the data-reduction procedure. A typical result is presented, and the validity of the method is established.     

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.     

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.     

Interaction of a diaphragm pressure gage with a viscoelastic halfspace

The results of an analysis to determine the interaction between a diaphragm pressure transducer and a solid propellant grain are presented. The solutions to a clamped circular plate and a halfspace are superposed to yield the desired solution. The boundary conditions on the halfspace are shown to be such that the solution to an internally pressurized Sneddon “penny-shaped” crack is applicable for an incompressible material. The problem is first solved elastically, in terms of a material-stiffness parameter which relates the diaphragm stiffness to the propellant stiffness. The solution is then extended to viscoelastic behavior through parameterization of the stiffness parameter. The electrical output of the diaphragm gage is determined and compared with the output from hydrostatic calibration, in order to determine the error or loss in gage sensitivity based on hydrostatic calibration, due to the interaction between the gage and the propellant.     

The diffractographic strain gage

A method for measuring strain using diffraction of light from a single aperture is described, and results of a comparison tensile test with an electrical-resistance strain gage are presented. The “diffractographic strain gage” is shown to have high sensitivity, linearity, accuracy and temperature compensation and the ability to operate in a variety of hostile environments. It is furthermore simple, inexpensive, and the data can be collected by eye without assistance from further instrumentation.     

Dynamic measurements of initiation toughness at high loading rates

An experimental method is described for measuring the dynamic initiation toughness of a sharp stationary crack. A plane specimen is utilized which consists of a central region 50-mm wide and 200-mm long with integral dog-bone ends. The loading is accomplished by the detonation of four small explosive charges which produce two tensile stress waves upon reflection from the dog-bone ends. The stress waves meet at the midpoint of the specimen and reinforce to produce a relatively large, uniformly stressed region with a very high loading rate. The crack is positioned at the midpoint of the specimen at the location where the reinforcing tensile stress waves meet. A series of photoelastic experiments were conducted using Homalite 100 as the model material to observe, in a full-field view, the arrival of the dilatational waves, the subsequent development of the stress field at the tip of the stationary crack and the initiation of the crack. The isochromatic fringe pattern was also used to determine the instantaneous value of the stress-intensity factorK(t) after the characteristic fringe loops developed in the region near the crack tip. Finally,K(t) was measured using a single strain gage positioned and oriented so that its signal output was proportional toK(t) and independent of the next two higher order terms in the series representation of the strain field. A method was developed to determine the instant of initiation from the strain-time trace. Results obtained from the photoelastic and strain measurements of the dynamic-initiation toughnessK _ID were consistently higher than the static value ofK _IC . Paper was presented at the 1987 SEM Fall Conference on Experimental Mechanics held in Savannah, GA on October 25–28.     

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.     

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 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.     

Measuring dynamic-strain profile and history with a drum camera

A low-speed drum camera has been used to continuously record the strain profile in several different types of impact tests. The drum camera was selected because it is inexpensive and simple to use, and it overcomes many of the inherent disadvantages of other dynamic-recording techniques. The use of the drum camera in recording the strain profile in tensile and torsional impact is illustrated, as well as the determination of impact velocity in collinear plastic impact of two bars. A detailed discussion of determination of the strain profile from the tensile-test film record is presented, including an analysis of the accuracy achieved. It was found that the drum camera is capable of measuring strains to an accuracy of approximately 1 percent for a gage length of 0.05 in. Strains varying from 1 to 100 percent were measured in the tensile test, with a nominal strain rate of 20 sec^?1. Strain rates of up to 2000 sec^?1 were successfully recorded in the torsional impact tests.     

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

Summary  The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems. Received 4 September 2001; accepted for publication 23 July 2002 The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation of Tsinghua University, and the Education Ministry of China.     

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.     

Dynamic behavior of concrete

Concrete and cement-paste specimens, representing a model of the actual structural material and of its adhesive component, respectively, were subjected to static and dynamic tests. Static tests on virgin specimens were carried out in order to evaluate the strength, elasticity and Poisson's ratio of the materials. The dynamic experiments were conducted in order to ascertain the response of the specimens to the propagation of one-dimensional pulses. Transient loading was accomplished by the central longitudinal impact of a 1/2-in.-diam steel sphere on a ballistically suspended 3/4-in.-diam Hopkinson bar of the material at an initial velocity of about 3260 or 1650 ips. The shocked specimens were also subsequently examined to determine whether changes in static material properties had occurred as a result of passage of the waves. Both static and dynamic tests yielded consistent results for a number of specimens cast and cured in identical fashion. Comparison of the properties of the virgin and the shocked specimens indicated little, if any, shock damage. While some minor grain damage was observed in microscopic examination of thin sections taken from some of the shocked specimens, other sections did not indicate any visible cracking of the grains. The wave-propagation process appeared to occur without dispersion and relatively little attenuation, indicating that the material could be represented on a macroscopic scale as an “elastic” substance with a small structural-damping coefficient. The obvious inhomogeneities of the concrete affected the gage response whenever a gage was mounted directly over a piece of aggregate. The dynamic response of the materials has been compared with the response of several types of rocks.     

A CW ultrasonic bolt-strain monitor

There exists a need for a relatively inexpensive system for measuring strain in bolts. The torque wrench is one technique for straining bolts which has been widely applied. Unfortunately, friction in the bolt threads and between the nut and the work tend to make such a simple system inaccurate. In practice, a torque wrench is unacceptable for many situations where strain is critical. In this article, an ultrasonic technique is described which can indicate changes in bolt strain to better than one part in 10⁴. The technique is based on the one-dimensional propagating-ultrasonic-wave model and uses a new ultrasonic instrument called a Reflection Oscillator Ultrasonic Spectrometer which is a closed-loop feedback marginal-oscillator system that frequency locks the device to the peak of a mechanical resonance in the bolt. The instrument indicates a shift in the bolt resonance frequency due to elongation and changes in velocity of sound due to strain. Data are presented comparing a standard torque wrench to the ultrasonic monitor for different measured stresses on the bolt as well as for different bolt conditions. The strain instrument can be used to monitor changing stresses, to measure material properties and may be applied as a strain gage or load cell.     

Determination of thermal-expansion characteristics of metals using strain gages

A method has been developed to measure thermal-expansion characteristics of metals using bonded resistance strain gages. The method allows rapid and accurate determination of expansion properties at similar or lower cost (depending on the particular application) than conventional dilatometric techniques. Other advantages include elimination of a need for perfectly flat sample material, elimination of specimen machining, and applicability to structures and components. To utilize this technique, the ‘apparent strain’ of the gage is determined by attaching it to a ‘standard’ material for which the thermal-expansion characteristics are accurately known and subtracting the known thermal response of the material from the total gage output. ‘Apparent strain’ is therefore the temperature-induced output of the gage when bonded to a material having a thermal-expansion coefficient of zero. When the gage is then attached to a test material and cycled through the same temperature range, this ‘apparent strain’ is subtracted from the total gage output to obtain the actual unit-length change of the test material. Using this technique, mean-expansion coefficients of experimental alloys were determined over the temperature range ?320°F (?196°C) to room temperature.     

Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric bimaterial

A plane strain problem for two piezoelectric half-spaces adhered by a very thin isotropic interlayer with a crack under the action of remote mixed mode mechanical loading and electrical flux is considered. The crack is situated either at an interface or in the interlayer. It is assumed that the substrates are much stiffer than the intermediate layer. Therefore, pre-fracture zones (plastic or damage) arise at the crack continuations. Normal and shear stresses are assumed to be constant in this zones and to satisfy some material equation, which can be taken from theory or derived experimentally. Modeling the pre-fracture zones by the crack continuations with unknown cohesive stresses on their faces reduces the problem to elastic interface crack analysis leading to a Hilbert problem. This problem is solved exactly. The pre-fracture zone lengths and stresses in these zones are found from algebraical and transcendental equations. The latter are derived from the conditions of stress finiteness at the ends of pre-fracture zones and the material equations. The electrical displacement at any point of the pre-fracture zones is found in closed form as well. Particular cases of symmetrical loading and of equivalent properties of the upper and lower bimaterial components are considered. Numerical results corresponding to certain material combinations and interlayer material equations are presented and analysed. In the suggested model, any singularities connected with the crack are eliminated, i.e., all mechanical and electrical characteristics are limited in the near-crack tip region.     

On the variation of fatigue-crack-opening load with measurement location

The work presented here evaluates the vlidity of using the load at the point of linearity on the displacement-load curve, as suggested by Elber, as an experimental measure of the crack-tip-opening load. Displacement-load behavior was investigated for a fatigue-cracked modified compact specimen of a nickel-base superally. Displacements were determined at the notch mouth using a standard clip-on gage, along the crack surface using a laser-interferometric displacement gage and, in the plastic zone ahead of the crack, using an optical-interferometry technique. Acoustic-emission monitoring was employed as a means to detect potential crack extension during measurement-load cycles and to detect physical-crack closure. The magnitude of the crack-tip-opening load, as determined from these measurmeents, is dependent on the distance from the crack tip at which the measurmenet is made. As an additional means of evaluating the crack-tip-opening load, crack-surface profiles are constructed from the displacement-load measurmeents made behind the crack tip. A discussion is given concerning the significance o these results in evaluating the validity of using the load at the point of linearity as a parameter to quantify crack closure.     

Transient response of a piezoelectric ceramic strip with an eccentric crack under electromechanical impacts

The transient response of a piezoelectric strip with an eccentric crack normal to the strip boundaries under applied electromechanical impacts is considered. By using the Laplace transform, the mixed initial-boundary-value problem is reduced to triple series equations, then to a singular integral equation of the first kind by introducing an auxiliary function. The Lobatto–Chebyshev collocation technique is adopted to solve numerically the resulting singular integral equation. Dynamic field intensity factors and energy release rate are obtained for both a permeable crack and an impermeable crack. The effects of the crack position and the material properties on the dynamic stress intensity factor are examined and numerical results are presented graphically.     

Attainable accuracy of strain measurements with thum-sevenson-weiss mechanical-inductive strain gages

This paper determines the accuracy that can be attained with the Thum-Svenson-Weiss mechanical-inductive strain-measuring method. After stating advantages and disadvantages of this measuring method, the strain gage, the electrical parts and the calibration equipment are described. The determination of accuracy is based on the laws of statistics considering all the errors as distributed completely at random. The behavior of the electrical parts, of the mechanical parts, of the strain gage and of the calibration equipment are separately investigated. It is evident from these investigations that the strain measurement with the Thum-Svenson-Weiss mechanical-inductive strain gages is one of the most accurate strain-measuring methods to date.