Fracture Test Data Research Articles

A new approach to fracturing test interpretation using the PKN model

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG 0 −2/3 , CG 0 1/3 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G 0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G 0 are found somehow, the fracture length and the fracture volume at the end of pumping can be calculated.

Effects of the geological parameters on rock blasting using the Hopkinson split bar

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG−2/30, CG1/30 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G0 are found somehow, the fracture length and the fracture volume at the end of pumping can be caluclated.

A new approach to fracturing test interpretation using the PKN model

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG −2/3 0 , CG 1/3 0 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G 0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G 0 are found somehow, the fracture length and the fracture volume at the end of pumping can be caluclated.

An evaluation of mechanical strength test specimens for brittle materials

Several alternative test specimens for the determination of the fracture strength of a brittle material have been studied. These include a ring-supported ball-loaded thin circular disc, a disc symmetrically supported on three equispaced balls and loaded at the centre through a fourth ball, a cylinder under axial compressive point-loading, and a ‘pure shear’ beam specimen. The stress distributions in these specimens have been determined photoelastically and the stress data used to interpret fracture test data for batches of each specimen made from reactor-grade graphite. The stochastic nature of the fracture data has also been considered.

セラミックスの破壊強度データベースと信頼性設計システム

For application of ceramics to mechanical and structural components, a data base system for fracture strength of ceramics was developed. In this data base system, various fracture strength test data of ceramics are compiled with the data of their manufacturing process and the test environment, which are used to retrieve various fracture test data. The fracture strength of ceramics obtained by each test varies usually in spite of being same in material and test environment. For estimating the strength as a material constant independent of each testing method, this system performs a unified analysis for all the fracture strength test data retrieved. This unified analysis method can estimate the material constant expressed by the delayed fracture strength normalized in terms of cummulative effective hold time Nfteff=1sec and effective volume Veff=1mm3.Furthermore, a reliability design system was developed for analyzing the strength reliability of the structural components of ceramics against the actual service loads. It is possible by this system to determine the allowable design stress by applying the normalized strength properties to the probabilistic analysis.This system has a wide applicability in performing the reliability-based design of ceramic structural components as well as in developing ceramic materials.

A 3-D finite element analysis of a chevron-notched, three-point bend fracture specimen for ceramic materials

A 3-D finite element analysis of a chevron-notched, three-point bend specimen was used to determine the load point displacement (LPD) and the crack mouth opening displacement (CMOD) for four initial crack-depth-to-width ratios of the chevron notch. Relations between the LPD and CMOD specimen compliances, as functions of crack length, were developed and the LPD compliance versus crack length relations were compared with previous analyses. In addition, the LPD compliance versus crack length relations are used to modify previously developed geometry correction factors for the stress intensity factor. The LPD/CMOD relations are then applied to calculate the LPD from the CMOD measured during the fracture testing of silicon nitride and silicon carbide chevron-notched, three-point bend specimens. The work-of-fracture values for the two ceramic materials are compared using the calculated and the measured LPD. The fracture toughness values are compared as calculated from the modified and the unmodified geometry correction factors for the stress intensity factor. Finally, the crack growth resistance curves are determined from the fracture test data.

BS5500 appendix D: An assessment based on wide plate brittle fracture test data

This paper summarises an internationally funded assessment of the low temperature fracture toughness requirements of the British Standards Institution Document BS5500:1976, ‘Specification for unfired fusion welded pressure vessels’. The assessment was based on an analysis of wide plate brittle fracture tests, supporting chemical compositions and small-scale mechanical test data from worldwide sources, all these data having been collated in a programme of work involving The Welding Institute (UK), Gent University Research Centre of Welding (Belgium) and Delft University of Technology Metallurgical Department (Netherlands). The assessment showed that the BS5500 requirements are generally safe. However, attention is drawn to the relatively few wide plate test data that are available for section thicknesses less than 25 mm.

Comparison of fracture test data for some high strength steels stressed in a saline medium and in gaseous hydrogen

In this study, a comparison is made of the results of fracture tests conducted on four steels of high yield strength ( YS ≥ 1200 N/mm 2) stressed either in gaseous hydrogen at a pressure of 1 atmosphere or in a saline solution of 0.6 M NaCl. The steels involved were NiCrMo (35 NCD 16), Si (61S7), CrMo (45 CD4) and SiCrMo (45 SCD 6) grades. The tests were conducted with C.T. type fracture mechanics notched specimens. It is shown that: 1. (1) the non-propagation thresholds of the cracks are substantially higher in gaseous hydrogen (1 atm) than in the saline solution, 2. (2) if one considers that this threshold may be used as a criterion of the ultimate strength of steels in the presence of hydrogen, the rating obtained for the four steels investigated is the same whether the tests be carried out in the aqueous or gaseous media, 3. (3) the life of the specimen, other conditions being equal, is about 10 times shorter in H 2 than in the 0.6 M NaCl solution, 4. (4) the fracture appearances are not esactly the same in the two media: in addition to grain boundary decohesion zones, many quasi-cleavage zones and characteristic asperities on the exposed grain boundaries are found in hydrogen.

FRACTURE DESIGN CRITERIA FOR STRUCTURAL ADHESIVE BONDING‐PROMISE AND PROBLEMS

ABSTRACTThe joining of load bearing structures using organic resin adhesives is an established technology in aircraft, spacecraft, and automobile construction and is being considered in ship construction; especially for hydrofoil and other advanced craft. The failure analysis of structural adhesive joints must be based on fracture criteria since these joints fail by linear elastic brittle fracture. Accordingly, the Navy has supported work over the past decade on developing an adhesive fracture test methodology and data base.Recent work at the Naval Research Laboratory (NRL) had demonstrated that fracture testing of structural adhesive joints is fundamentally more complex than the fracture testing of monolithic structures. Specifically, there is a very strong bond thickness effect; and more importantly, testing must be done under combined stress conditions. Opening‐mode (cleavage) tests alone are not sufficient. A study of the adhesive fracture behavior of structural adhesives has established why this additional testing is necessary. Work remains to be done on developing analytical relationships for the effect of joint geometry on adhesive fracture behavior.

The Unit Strength Concept in the Interpretation of Beam Test Results for Brittle Materials

SYNOPSISBrittle materials are usually characterised in terms of the “modulus of rupture” obtained from the results of fracture tests on beam specimens. This is not a fundamental quantity. Alternative quantities (the mean strength of unit volume and of unit area) are introduced which are independent of the size of the specimen and the form of test, which allow the correlation of results from different tests, and which may be validly used in design calculations. After an outline of the necessary theory, the derivation of the two “unit strengths” and their use in correlating test results are illustrated using fracture data from a series of reaction-bonded silicon nitride beams. Minimum values obtained are:- mean uniaxial fracture stress of unit volume, 140 N/mm2per cm3; mean uniaxial fracture stress of unit surface area, 180 N/mm2per cm2.A means of allowing for the effects of contact friction in the analysis of beam fracture test data is presented. The ignoring of these effects may result in a significant over-estimate of strength. The measured coefficient of friction decreased with increased load intensity.