Specimen Compliance Research Articles

The Influence of Specimen Size on the Fracture Behavior of a Structural Steel at Different Temperatures

Abstract A broad experimental study was carried out in order to analyze the influence of different geometrical parameters (thickness, width, and crack length) and temperature on the fracture behavior of a structural steel. The J-integral versus crack growth resistance curves (J-R curves) were determined using indirect measurements of the crack size based on the variation of the specimen compliance, together with the physical determination of crack lengths obtained during testing using a color marking procedure. This last technique allows the reliability and accuracy of the data to be improved and provides additional information that can be used to reduce the typical scatter of the results. Only the initial crack size of the specimen has an influence on the J-R behavior of the steel due to the triaxiality modification of the crack tip stress state developed in the specimen. On the other hand, the J-R curve of the steel is also independent of temperature. Temperature affects only the J values at which cleavage or unstable fracture takes place.

Numerical Modelling of Roughness and Plasticity Induced Crack Closure Effects in Fatigue

The incidence of roughness induced fatigue crack closure has been studied by finite element modelling. Closure analyses in the literature have been reviewed and been shown to lack a reasonable treatment of: (a) propagating elastic-plastic cracks, and (b) the influence of the characteristically inhomogeneous plastic deformation associated with near-threshold crack growth in many materials. Based on an analysis of both overall specimen compliance and node behaviour along the crack path, the present modelling shows: (a) an increasing effect of crack path angle on roughness induced closure levels in keeping with the simple analytical model of Suresh and Ritchie; (b) the mechanism by which closure occurs is more strongly dependent on residual plastic strains in the wake than global shear displacements of the fracture surfaces due to mixed-mode behaviour at the crack tip; and (c) the closure levels are relatively low compared to experimental data, consistent with the absence of environmental irreversibility in the finite element models and the idealised crack path morphologies that were studied. Slip band simulations show a significant increasing effect of inhomogeneous deformation on closure levels, improving the apparent accuracy of the modelling results.

Characterization of Mode II Delamination Growth in Glass/Epoxy Composite Cylinders

Delamination growth in filament wound composite cylinders has been characterized for shear (mode II) loading. Beam specimens were machined from cylinders with embedded aluminum films to define an initial delamination. The specimens were machined so that the delamination was at one end, and the beam axis parallel to the cylinder axis. Analysis of compliance and energy release rate of beam specimens configured in ENF mode II loading was performed based on a formulation for cylindrical shear-deformable shells. The contribution from residual thermal stress to the energy release rate was examined, but found negligible for the [±θ]n (n = 6 and 12) glass/epoxy specimens under consideration (θ = 30°, 55° and 85°). Contoured loading bars and supports were prepared for experimental ENF testing of beams with curved cross-section machined from composite cylinders. The experimental compliance data were in close agreement with predictions over the ranges of crack lengths, beam thicknesses, and ply angles examined. The mode II fracture toughness increased with increased angle θ at the ±θ interface.

A Study on the Compliance of a Compact Tension Test Specimen

For integrity evaluation of cracked or damaged structures, fracture toughness test results in ASTM are widely used. The fracture toughness values of the structures are used as an effective design criterion in nuclear plants and aircraft structures. Sometimes the difference of P- curve trend during the unloading /reloading cycle in the fracture toughness test using partial unloading compliance was observed. The phenomenon as a possible source of error in determining fracture toughness may be caused by the residual stress during unloading work-hardening and bucking of a specimen. Therefore, we evaluate the effect of bucking and compressive residual stress during the K-R and J-R testing using a finite element method.

Elastic Foundation Analysis of Tilted Sandwich Debond (TSD) Specimen

The tilted sandwich debond (TSD) specimen for characterizing debonding of a sandwich structure is analyzed using elastic foundation theory. The face sheet is considered as a cantilever beam in the debonded region of the specimen and as a beam of finite length supported by an elastic foundation in the bonded region. An analytical model for the beam deflection is developed that may be utilized for design of the specimen, fracture analysis, and data reduction of face/core debond toughness. A parametric investigation was conducted to examine how material and geometrical parameters of the constituents of the sandwich and test configuration influence the compliance of the TSD specimen. Testing was performed on a sandwich consisting of glass/vinylester face sheets over a H200 PVC foam core. The compliance predictions for this and a previously examined sandwich agreed favorably with experimental data over a large range of crack lengths and tilt angles. The debond toughness reduced from experimentally calibrated compliance and from the foundation model was consistent.

Elastic Foundation Analysis of Tilted Sandwich Debond (TSD) Specimen

The tilted sandwich debond (TSD) specimen for characterizing debonding of a sandwich structure is analyzed using elastic foundation theory. The face sheet is considered as a cantilever beam in the debonded region of the specimen and as a beam of finite length supported by an elastic foundation in the bonded region. An analytical model for the beam deflection is developed that may be utilized for design of the specimen, fracture analysis, and data reduction of face/core debond toughness. A parametric investigation was conducted to examine how material and geometrical parameters of the constituents of the sandwich and test configuration influence the compliance of the TSD specimen. Testing was performed on a sandwich consisting of glass/vinylester face sheets over a H200 PVC foam core. The compliance predictions for this and a previously examined sandwich agreed favorably with experimental data over a large range of crack lengths and tilt angles. The debond toughness reduced from experimentally calibrated compliance and from the foundation model was consistent.

The Variation of G1c and δ1c with Crack Growth Rate in Polyethylene

The crack growth rate in HMN 5202 polyethylene has been studied as a function of stress intensity using deeply notched three-point bend specimens. The load-line displacement in response to a static applied load has been measured, with the material compliance as a function of time determined from the specimen compliance prior to the initiation of crack growth. Measured specimen compliance as a function of time after crack growth begins is used to determine crack growth rate as a function of stress intensity. The experimentally determined crack growth rate as a function of stress intensity has been compared to theoretical predictions by Williams and Schapery. This comparison implies that both critical crack tip opening displacement, 61c, and critical energy release rate, GIn, increase with increasing crack growth rate. The results also show that the crack growth rate is significantly reduced by plane stress conditions at the surface of the specimen.

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0] 6, [±30] 5 and [±45] 5 laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.

CHARACTERIZATION OF DELAMINATION GROWTH BEHAVIOUR OF HYBRID BONDED LAMINATES

Abstract— The objective of this work is to study the delamination growth behaviour of hybrid composite‐aluminium bonded laminates. A modified Double Crack Lap Shear (DCLS) specimen was chosen for this study. An expression relating the delamination size and the compliance of a DCLS specimen was derived, and a test method for the delamination growth rate in DCLS specimens developed. The delamination sizes and the delamination growth rates of DCLS specimens were determined by monitoring the compliances of specimens during fatigue. Delamination growth rates at different stress ratios (R= 0.1, 0.3,0.5) were measured. A Walker‐type equation for the delamination growth rate was obtained by a multiple linear regression analysis.It was shown that the compliance method for determining the delamination growth rate of DCLS specimens is not only convenient and practical, but also accurate. The delamination size in DCLS specimens increases linearly with cycles during fatigue, i.e. delamination growth rate is constant, independent of delamination size. The energy release rate was adopted to characterize delamination growth behaviour. Good agreement between the Walker equation and test results of the delamination growth rate was found.

Stress‐Rupture of Nicalon/SiC Continuous Fiber Ceramic Composites in Air at 950°C

The stress‐rupture behavior of plain‐weave CG‐Nicalon/enhanced SiC was studied in air at 950°C. It was found that this material exhibits delayed failure and that the lives of specimens subjected to constant stress levels of 80, 100, and 120 MPa were 21.6, 9.6, and 2.7 h, respectively. The strain histories of these tests revealed a continuous increase of the specimen compliance and accelerated deformation prior to failure. It is shown that both the shape of the strain vs time curves and the time dependence of the loss of strength can be explained using a simple model based on the oxidation‐induced stress‐rupture of the reinforcing fiber bundles.

Dislocation-defect analysis during micro-indentation using displacement rate changes

Micro-indentation with step-ramp displacement rate changes has been developed to nullify the machine and specimen compliance and to directly measure the apparent activation work, Δw′, of the deforming material. The Cottrell-Stokes relation is obeyed for an eutectic solder, but in contrast, nominally pure Al in the annealed and pre-rolled states indicate that the type of obstacle barrier continuously changes as a function of strain rate. Thus it is deduced that for high homologous temperature testing, either dislocation-dislocation interactions or jog dragging are detected, whereas at lower temperatures other defects are generated especially when the total plastic volume under the indenter is minute. These results can be correlated to the evolution of debris at high strains detected by tensile tests.

Influence of bridging stresses on specimen compliances

Bridging effects in ceramic materials influence the compliance of cracked bodies. This effect has to be taken into consideration for crack length measurements based on the compliance method. As examples, the loading-point and crack-mouth compliances are computed for two bridging relations. It can be seen that the crack length obtained from the compliance is shorter than the real one.

COD compliance of edge-cracked three-point bend round bars calculated with slice synthesis method

the slice synthesis method has been proved to be a simple and efficient analytical approach for calculating compliance of various fracture toughness specimens which have relatively complex crack configurations.The specimen to be studied is an edge-cracked three-point-bend round bar

Fracture mechanism of cross-ply carbon/carbon composites

Mode I fracture toughness tests were carried out on (0/90) cross-ply carbon/carbon composite laminates in order to investigate the applicability of the concept of the fracture toughness based on linear elastic fracture mechanics. Tests were carried out by using both compact tension (CT) and single edge notched beam (SENB) specimens. Effect of the root radius of the starter notch was also investigated in order to find out its sensitivity on the fracture behavior. Although the load-displacement relation showed nonlinear behavior, the relation between the specimen compliance calculated by the straight line from the origin of the load-displacement axis and the measured crack length followed the polynomial equations based on the linear elastic fracture mechanics. Fracture toughness values were calculated by using the stress intensity factor. The relation between the fracture toughness and the increment of crack length (R-curve) was independent of the specimen shapes, the starter notch lengths, and the root radius of the starter notch. The fracture toughness values first increased rapidly until the increment of the crack length equaled 1 mm, and then leveled off. For the case of SENB specimens, tests without starter cracks were also carried out. These tests indicated that both the crack propagation behavior and the resultant R-curve were similar to those of normal SENB specimens. Comparison between the fracture toughness value and the bending strength yielded that the length of the latent crack is about 1 mm. X-ray observation showed that plenty of microcracks had already existed before the fracture load was applied. Microscopic observation showed that the crack growth process was characterized as pull-out of fibers. The length of fiber pull-out with the increment of crack growth was discussed in conjunction with the R-curve behavior.

On use of double cantilever beam for coatings and adhesion tests

The compliance model of Double Cantilever Beam (DCB) for testing coatings and adhesion has been proposed and verified experimentally. The model is based on the assumption that the coating modifies the stiffness of a foundation of DCB onto which the beam is fixed, according to a simple series-spring law. The model includes multi-coated specimens, in particular the specimen with thermal sprayed ceramic coating, with an additional layer of epoxy adhesive for attachment of a symmetrical DCB arm. It was found, that the compliance of DCB specimens with a coating is significantly increased for a coating thickness larger than ∼1% of the arm thickness, and a coating Young's modulus smaller than ∼50% of the arm modulus. The model results, verified by experiment, have profound consequences on calculations of the strain energy release rate in fracture tests for coatings, brazed joints etc. The total compliance of the arm and coating assembly scales with the coating stiffness, and thus the model can be utilised for rigidity evaluation of a variety of coatings on standard substrates, e.g. paints or polymer coatings on metals.

Subcritical fatigue crack growth in alumina—I. Effects of grain size, specimen size and loading mode

The effect of both grain size and specimen size upon the slow fatigue crack growth characteristics in alumina is investigated using notched double cantilever beam type specimens. The fatigue crack growth rate can be described by the usual power law, d a/d N = A ( K max) n , with a value of n between 13 and 20. Both threshold stress intensity factor and crack growth rate, for a given value of the maximum applied stress intensity factor, are influenced by the load ratio R. An anomalous “short crack behaviour” was observed and is discussed. From the recorded load-notch opening displacement curves, it is shown that the fatigue cracks are bridged by both frictional ligaments, which give rise to a hysteresis loop, and elastic ligaments which decrease the specimen compliance. The equivalent bridging load (the load measured at loading pins) which is required to overcome the bridging resistance is measured as a function of crack length. It is shown that the elastic ligaments make the largest contribution to the bridging forces, which are much larger for the large grain size alumina. An effect of specimen size upon the crack growth resistance was also observed.

Elastic Compliance of Four-Point Bend Specimens Comprising Two Linear-Elastic Materials Bonded with a Thin Layer

Abstract The four-point bend “sandwich” specimen, comprising two identical linear-elastic substrates joined by a thin elastic layer, is widely used in the study of strength and toughness of bimaterial joints loaded under nominal mode I loading. As an aid to crack monitoring in such specimen geometries, the linear-elastic compliance based on load-line displacement, back-face strain, and crack-opening displacement has been determined for a wide range of substrate/layer material combinations using finite-element analyses. Calculations for bimaterial systems, with elastic moduli ratios varying from 0.2 to 5 and with joining layer thicknesses between 100 and 500 μm, show that for crack sizes between 0.1 to 0.7 of the specimen width, the compliance is significantly different from that of the bulk substrates, even when the layer is very thin. It is concluded that crack-opening displacements are preferable for the monitoring and detection of interfacial and near-interfacial cracks in this specimen geometry, as the compliance based on these displacements is the least sensitive to errors from either measurement site or crack location.

Tactual discrimination of softness.

1. We investigated the ability of humans to tactually discriminate the softness of objects, using novel elastic objects with deformable and rigid surfaces. For objects with deformable surfaces, we cast transparent rubber specimens with variable compliances. For objects with rigid surfaces ("spring cells") we fabricated telescoping hollow cylinders with the inner cylinder supported by several springs. To measure the human discriminability and to isolate the associated information-processing mechanisms, we performed psychophysical experiments under three conditions: 1) active touch with the normal finger, where both tactile and kinesthetic information was available to the subject: 2) active touch with local cutaneous anesthesia, so that only kinesthetic information was available; and 3) passive touch, where a computer-controlled mechanical stimulator brought down the compliant specimens onto the passive fingerpad of the subject, who therefore had only tactile information. 2. We first characterized the mechanical behavior of the human fingerpad and the test objects by determining the relationship between the depth and force of indentation during constant-velocity indentations by a rigid probe. The fingerpad exhibited a pronounced nonlinear behavior in the indentation depth versus force trace such that compliance, as indicated by the local slope of the trace, decreased with increases in indentation depth. The traces for all the rubber specimens were approximately linear, indicating a constant but distinct value of compliance for each specimen. The fingerpad was more compliant than each of the rubber specimens. 3. All the human subjects showed excellent softness discriminability in ranking the rubber specimens by active touch, and the subjective perception of softness correlated one-to-one with the objectively measured compliance. The ability of subjects to discriminate the compliance of spring cells was consistently poorer compared with that of the rubber specimens. 4. For pairwise discrimination of a selected set of rubber specimens, kinesthetic information alone was insufficient. However, tactile information alone was sufficient, even when the velocities and forces of specimen application were randomized. In contrast, for discriminating pairs of spring cells, tactile information alone was insufficient, and both tactile and kinesthetic information were found to be necessary. 5. The differences in the sufficiency of tactile information for the discrimination of the two types of objects can be explained by the mechanics of contact of the fingerpad and its effect on tactile information. For objects with deformable surfaces, the spatial pressure distribution within the contact region depends on both the force applied and the specimen compliance.(ABSTRACT TRUNCATED AT 250 WORDS)

Measurement and Evaluation of Interface Fracture Processes in Ceramic-Metal Joint by Ultrasonic Method.

Fracture processes in the bending of Si3N4-steel joints were investigated. The initiation stresses of interface fracture and cracked areas were measured by the ultrasonic method. The results obtained are as follows. (1) The increase of the ultrasonic echo height corresponds to the increase of the specimen compliance. Using the ultrasonic method, the interface fracture process can be detected. (2) The interface crack grew on the interface in a stable manner with increasing stress intensity factor, K1. (3) At the maximum stress, the interface crack deflected to the ceramic side in an unstable manner. The criterion for the deflection is that the stress intensity factor K1 for the interface crack taking into consideration the joining residual stress component must reach the KIC for Si3N4.

Autoclave for investigating the influence of high-temperature aqueous media on the resistance of structural materials to crack initiation

In contemporary standards of strength and durability analysis of components of nuclear equipment, their predicted service life is estimated only on the basis of data on crack growth from a certain fixed size to the critical size. Investigations of the influence of high-temperature reactor water on the precracking time under conditions of cyclic loading originated relatively recently. This is explained by difficulties connected with recording the time of crack initiation (CI) in an autoclave with a high-temperature aqueous medium under pressure. As a result of the tests, it was shown that media of this sort decrease significantly the number of cycles prior to CI, and cracks begin to nucleate after 10-100 cycles of low-cycle loading. It is necessary to study the influence of high-temperature aqueous media on the precracking time in structural steels. Determination of the precracking time in structural materials placed in a high-temperature aqueous medium involves the problem of recording the time of CI. Hence, the design features of a testing installation are determined by the method of detecting nucleating cracks. Since the time of CI cannot be recorded visually at a temperature of the aqueous medium of 573 K under equilibrium pressure, it is necessary to usemore » indirect methods. Measurements of specimen resistance based on the use of high-frequency currents and the polarization method distort the testing conditions because any external potential applied to a specimen affects the characteristics of electrochemical reactions proceeding on the metal surface in the course of destruction. The method used to measure specimen compliance in the process of crack growth is not sensitive enough to detect the time of CI. An analysis of these and other indirect methods shows that the time of crack initiation in specimens loaded in a high-temperature aqueous medium can be recorded most efficiently by the resonance method.« less