Compliance Calibration Technique Research Articles

Application of digital image correlation to derive Paris' law constants in granite specimens

This study investigates the effectiveness of Digital Image Correlation (DIC) as a powerful tool for deriving Paris' law constants in black granite specimens subjected to cyclic loading. A series of monotonic and cyclic loading tests on rectangular granite specimens yields valuable insights into geological material fatigue behavior, establishing monotonic tests as foundational references for subsequent cyclic loading experiments. Innovative DIC software application enables precise tracking and analysis of Crack Mouth Opening Displacement (CMOD) values, revealing distinct, observable patterns in crack growth during cyclic loading. A notable contribution lies in the implementation of a compliance calibration technique integrating Finite Element Method (FEM), facilitating the direct linkage between CMOD values and effective crack lengths, resulting in highly accurate Paris' law constants. With an average of 1.04 E −7 for C and 8.95 for m, these constants are essential for predicting fatigue crack propagation in granite specimens. This research underscores DIC's efficacy as a pivotal fatigue analysis tool, enhancing predictive capabilities for structural safety and durability assessments in geological materials, while emphasizing the crucial role of advanced imaging and numerical techniques in material science and structural engineering. It lays a robust foundation for future geological material studies and comprehensive structural integrity assessments.

Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests

Nonlinear finite element analyses are used to examine the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests. Energy release rates are first determined by a recently developed direct energy balance approach. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause both tests to be inherently nonlinear. The effect of these nonlinearities on the energy release rate is shown to be larger in the four point than the three point test and to increase with increasing roller diameter, increasing coefficient of friction along the crack plane, and decreasing supporting span length. For the four point test, the effect of these nonlinearities is also shown to increase with increasing ratio of inner to outer span length. Next, energy release rates at the onset of crack advance are determined by a simulated compliance calibration technique. This “perceived toughness” is compared with predictions of the “true toughness” given by the direct energy balance approach at the same load. It is shown that perceived toughnesses from this simulated compliance calibration procedure are larger than previously reported results that were obtained in a similar fashion using linear theory. In addition, the perceived toughness is shown to strongly depend upon the range used for fitting the load versus deflection data to obtain compliance. These findings are used to make some general recommendations regarding use of the two test methods and their associated data reduction techniques.

Effects of Friction, Geometry, and Fixture Compliance on the Perceived Toughness from Three-and Four-Point Bend End-Notched Flexure Tests

Linear and nonlinear finite element analyses are used to examine the effects of friction, test geometry, and fixture compliance on the perceived toughness as obtained from threeand four-point bend end-notched flexure tests. To this end, a newly developed ‘direct energy balance approach’ is used to obtain the ‘true’ energy release rate for any given specimen, test geometry, and coefficient of friction. Finite element analyses are also used in a simulated compliance calibration technique, which is combined with experimental results from fixture compliance tests to obtain a perceived toughness, i.e., the value that would be obtained by experiment. By varying the different parameters, the individual and combined effects of friction, test geometry, and fixture compliance on the ratio of the perceived to true toughness is obtained. The approach is applied to two graphite/epoxy materials for which toughnesses by the three(3ENF) and four-point bend end-notched flexure (4ENF) tests are obtained experimentally for a range of geometries. These experiments produced larger perceived mode II toughnesses, GIIc, by the 4ENF than the 3ENF test, and GIIc values from the 4ENF test were observed to decrease with increasing outer span length. The finite element simulations were shown to accurately recreate the perceived values of GIIc obtained from these tests. Moreover, the finite element simulations indicate that the true toughness values are essentially constant for a given material. These findings are used to make some general recommendations for choosing 3ENF and 4ENF specimen and test geometries, as well as to discuss the relative advantages and disadvantages of the 3ENF and 4ENF test methods.

Fatigue crack growth of high-strength concrete in wedge-splitting test

In this study, a wedge-splitting testing was carried out for the investigation of fatigue crack growth behavior of high strength concrete. Selected test variables were concrete compressive strength (28, 60, and 118 MPa) and stress ratio (6, 13%). In order to apply the target stress ratio, the maximum and the minimum fatigue loadings were 75–85 and 5–10% of ultimate static load, respectively. Fatigue testing was preceded by crack mouth opening displacement (CMOD) compliance calibration, and then the fatigue crack growth was computed by crack length vs. the CMOD compliance relations acquired by the CMOD compliance calibration technique. In the fatigue test, the frequency of loading cycle was 1 Hz, and the initial notch length a 0 was 30% of specimen height. To verify the applicability of the CMOD compliance calibration technique to wedge-splitting testing, the crack lengths measured by this method were compared with those predicted by linear elastic fracture mechanics (LEFM) and dye penetration testing. On the basis of the experimental results, an LEFM-based empirical model for fatigue crack growth rate ( da/dn − Δ K I relationship) that takes strength into account was suggested. The fatigue crack growth rate increased with the strength of concrete. It appeared that the da/dN − Δ K I relationship depended on stress ratio, and the effect was evaluated by the proposed equation. In addition, the comparisons between the CMOD compliance calibration technique and the other methods supported the validity of this technique in the wedge splitting test.

Fracture energy measurements of 2-D carbon/carbon composites

Fracture toughness of ceramic-matrix composites cannot be provided by an intrinsic fracture parameter. The presence of a fracture process zone induces stress redistribution mechanisms that partially shield the crack tip area from the applied stress field. The shape and size of the process zone depends upon extrinsic factors such as specimen shape and thickness, load distribution on the propagation zone, etc. The present work deals with the determination of the crack growth resistance curve ( R-curve) of carbon/ carbon ( C C ) composites using the standard compact tension geometry. Two different material thicknesses were used and both monotonie and loading/unloading test patterns were applied. The determination of the R-curve in all cases was based on a compliance calibration technique. The results show that the monotonic loading leads to higher plateau values for the R-curve of the C C material compared to that calculated from cyclic loading and referred to the same material thickness. Furthermore, the thicker specimens appear to have slightly higher plateau values. A precise examination of damage initiation and propagation was attempted to explain the monitored differences.

Prediction of changes in elastic moduli due to water-rock interaction during operation of granitic hdr geothermal system

Young's modulus of granitic rock samples under the simulated conditions of a geothermal reservoir, such as a pressurized high temperature water environment up to 350°C, was measured by means of the compliance calibration technique. The results obtained indicate a significant change in modulus with increasing test temperature and exposure time in a hydrothermal environment, which can be considered as a consequence of an increase in microcrack aperture due to chemical dissolution. The applicability of the laboratory results to hot dry rock geothermal field data is also demonstrated.

Effect of interaction of macrocracks on the stress intensity factor in a beam

Beams with a central edge crack, as well as other noncentral vertical and inclined edge cracks distributed symmetrically, subjected to three-point as well as four-point bending, are analysed using the finite element technique. Values of stress intensity factor K 1 at the central crack tip for a crack-to-beam depth ratio a w equal to 0.5, are calculated for various cracked-beam configurations, using the compliance calibration technique as well as method of strain energy release rate. These are compared with the value of K 1 for the case of a beam with central edge crack alone. Results of the present parametric study are used to specify the range of values pertaining to basic parameters such as crack-to-beam depth ratios, geometry and position with respect to central edge crack, of other macrocracks for which interaction exists. Accordingly, the macrocracks are classified as either interacting or noninteracting types. Hence for noninteracting types of cracks, analytical expressions available for the determination of K 1 in the case of beam with a central edge crack alone, are applicable.

STUDY ON A CRACK PROPAGATION AND FRACTURE TOUGHNESS OF ROCKS

Fracture toughness tests of rocks were performed to investigate a crack propagation behavior and fracture toughness (K1C) of rocks under a confining pressure or a low temperature. Fracture process markedly indicated nonlinearity. So, in this paper a crack length is evaluated by compliance calibration technique using results of fracture toughness test and then K1C is calculated with a maximum load and a crack length. As for a shape and scale effect of K1C, experiments showed that beam specimens was adequate for rocks. K1C of rocks linearly increases in the pressure range to 15 MPa and a temperature dependence of K1C is caused for water saturated rocks. A cyclic strain incremental tests indicates that J-integral is a effective parameter as the crack growth criteria.

Fracture toughness evaluation of granite in a high temperature pressurized water environment.

Fracture toughness tests based on the R-curve method using the unloading compliance calibration technique were conducted under the condition of a simulated crustal environment of a geothermal reservoir (confining pressure 18 MPa, maximum temperature350°C). The results obtained indicate that a significant reduction of both the elastic modulus and fracture toughness was observed with increasing temperature, and a single linear relationship was obtained between the fracture toughness KIC(J) and the elastic modulus E. In order to interpret the KIC(J)-E relationship, a model was proposed using stress-strain-opening displacement at a crack tip based on the fracture process zone.

Fracture Toughness and its Relation to Initial Tangent Modulus of Granitic Rock

This paper describes the relationship between fracture toughness and initial tangent modulus, i.e., Young's elastic modulus in tension, of granitic rock. ASTM standard specimens for notched three-point-bend and compact tension tests, which contained various levels of water or were subjected to thermal cycle, were used to correlate fracture toughness to Young's modulus. Furthermore, fracture toughness tests were carried out at high temperature and in pressurized water environment to evaluate the fracture and deformation behaviors under a simulated condition of geothermal reservoir.Based on the linear elastic fracture mechanics, elastic modulus was precisely measured for granitic rock samples by means of a compliance calibration technique prior to fracture toughness tests. Fracture toughness was determined by means of AE technique from an abrupt increasing point of AE activity.The results obtained in this study indicate that a significant increase in fracture toughness (KiAE) appears with increasing elastic modulus (E) and fracture toughness has a simple linear relationship with elastic modulus. Theoretical consideration based on the atomic scale fracture model by Gilman can give an adequate explanation to this relationship between KiAE and E.It is suggested that the effect of water content on the elastic modulus and fracture toughness can be interpreted as the result of internal friction on the micro-crack plane. An optical microscopic study led to a conclusion that the decrease in elastic modulus and fracture toughness with increasing temperatue is due to the increase in thermally-induced micro-crack in the rock sample. The result obtained at high temperature/pressurized water environment may be attributed to highly activated chemical reaction at the crack tip.

Fatigue crack growth measurement in a CSM composite using compliance and Moiré techniques

In the present work fatigue crack growth tests under constant load conditions were carried out on centre-notched biaxial specimens in order to measure the effects of load biaxiality in air and also in a dilute acidic environment. Initially a compliance calibration technique was used to determine the effective crack length so as to overcome difficulties connected with visual measurement and to present the fatigue results on a fracture mechanics basis when using conventional stress intensity factors. However, the compliance method becomes unreliable when the biaxiality factor is large or the crack length small, so the Moiré fringe technique was used to provide a method independent of biaxiality and probably of the usual environmental effects. Measurement of the fringe separation allowed the crack length to be determined, while dislocations in the fringe pattern showed the crack opening mode. The merits of the two techniques were compared and assessed using the Paris law relationship, based on conventional fracture mechanics.

Double torsion fracture toughness test for evaluating transverse cracking in composites

An important failure mode of composite laminates is transverse cracking in the plies as a result of an applied load perpendicular to the fibre direction. This is a matrix-dominated mode. Transverse cracking in a composite can take place at loads below the failure load of the fibres. The damage sometimes leads to catastrophic failure and to property degradation of the laminates. A better understanding of this failure mode is particularly desirable. There has been a fair amount of work [1-7] on the mechanical behaviour of transverse cracking. It has been shown that the transverse crack process is controlled by the fracture toughness, defined by the critical strain energy release rate Gc, associated with this type of failure. The measurement of G e provides basic information about the transverse crack resistance of the laminates. In addition, it provides the materials scientist with an index for selecting resin matrix materials for composites to better resist transverse cracking. There are numerous test methods for measuring the fracture toughness of composite laminates. Most of them are based on tests originally used for homogeneous materials. The application of these techniques to angle-ply and cross-ply composites has not been all that satisfactory because of the complex damage phenomena involved. These composites do not usually fail with a single crack as is usually the case with homogeneous materials. Different methods have been developed to test laminates for transverse cracking parallel to the fibres. For example, Sanford and Stonesifer [8] used double edge notched (DEN) and single edge notched (SEN) specimens for evaluating the fracture toughness of (0 °) fibreglass laminates. Parvizi et al. [5] also used DEN and notched three point bend specimens for fracture toughness measurement on (0 °) fibreglass laminates. Slepetz and Carlson [9] employed compact tension specimens to test (0 °) S-glass/epoxy and (0 °) graphite/epoxy composites. The compliance calibration technique has been most conveniently employed for measuring the Gc of composites. The specimen compliance, C, against crack length, a, relationship is first established. In order to obtain an accurate C-a curve, a large enough population of specimens must be tested. In this respect, a test method which yields a linear C-a relationship is certainly more convenient to use, for example, the double torsion (DT) test [10, 11 ]. In addition to the advantage of rapid calibration of the C-a relationship, the test requires very simple specimen geometries which greatly minimize the machining operation involved. In this study, the double torsion test was investigated for its applicability to characterize transverse cracking in unidirectional fibre composites. This method has been successful for measuring fracture toughness of brittle homogeneous materials such as glass [10], ceramics [11] and glassy polymers [12-14]. When the technique was applied here to laminates, the load-displacement curves of the specimens were found to be different from those of the homogeneous materials. A correct interpretation of the results, however, led to the determination of meaningful fracture toughness related to transverse cracking. The original double torsion test technique was suggested by Outwater and developed by Kies and Clark [10]. The specimen is a rectangular plate supported along its two longer edges. In our case, the fibre direction was along the longer axis of the specimen. The specimen can be supported by either two rollers (Fig. 1) [11-14] or four steel spheres [15, 16]. In this study, we have experimented with test fixtures built with both of these supporting conditions. The load was applied to the specimen through two steel spheres as shown in Fig. 1.

Fracture characterization of composites with chopped fiberglass reinforcement

The fracture toughness of Sheet Molding Compound, known as SMC in the plastics industry, was investigated. Two different analytical techniques were used to determine the fracture toughness based upon the tensile testing of prenotched compact tension specimens over a wide range of crack length to width ratios (a/w) and different fiber volume fractions. The first approach used was to develop a Solid Sap finite element computer program to evaluate the stress intensity factor near a crack-tip. The stress intensity factor corrresponding to the load which causes incipient crack growth of the specimen was then defined as the fracture toughness of the material. A second method, known as the compliance calibration technique, was also used. The principal concept of this method requires calculating a critical energy release rate, which can be determined experimentally using compact tension specimens. Fracture toughness was then evaluated on the basis of the calculated critical energy release rate.

Determination of effective elastic modulus by compliance calibration for measurement of fracture toughness of rock : Kim, K; Stout, M G Proc 19th US Symposium on Rock Mechanics, Stateline, Nevada, 1–3 May 1978, V1, P203–209. Publ Reno: University of Nevada, 1978

This work describes a method of determining the effective elastic modulus of a fracture toughness sample geometry based on a compliance calibration technique. The method consists of testing a series of rock samples with various crack lengths and comparing the compliance vs. crack length curve obtained thereby with that of a material of known elastic properties. The effective elastic properties of westerly granite were determined by this method using double cantilever beam and double torsion fracture toughness sample geometries. These results are compared with the elastic constants obtained from ultrasonic and uniaxial tension tests. 10 references.

Effect of crack tip damage on fracture of random fiber composites

Damage at the tip of a notch in a random glass fiber reinforced epoxy resin has been observed and appears to initiate at approximately 65% of the fracture load. The damage zone increases with increasing load. An effective crack length corresponding to the damage zone has been determined using a compliance calibration technique. Pre-notched specimens have been subjected to constant load and the effective crack length increase determined by measuring crack mouth displacements or compliance changes. It is shown that fracture occurs when a critical value of the stress intensity factor is reached.

Crack-growth relationships for glass-reinforced plastics and their application to design

Crack-growth tests under zero-tension fatigue loading were carried out on a chopped strand mat and a glass-fabric-reinforced polyester resin. A compliance calibration technique was used to measure crack growth so as to overcome difficulties with visual measurement. The Paris (1957) power relationship based on stress intensity factor range was applicable to the results, but the value of the exponent was much greater than reported values for metals and polymers.It is suggested that a crack-growth criterion could be used as the basis of a safe-life design method overcoming difficulties associated with conventional fatigue data in extrapolating to long lives and allowing for size effects and for incipient damage.