R Horstman

Multiaxial Fatigue: A Survey of the State of the Art

This paper surveys the current state of knowledge concerning multiaxial fatigue. Developments are presented in chronological order and are discussed so as to supplement existing reviews in this field. Emphasis is placed primarily on the criteria or methods of evaluation of fatigue strength under general multiaxial loading at room temperature. The survey indicates that the early development of the criteria was based on extensions of static yield theories to fatigue under combined stresses. These are stress-based criteria limited primarily to high-cycle fatigue. Most of the later criteria are strain-based. These criteria fall into two broad groups: the equivalent stress or strain type and the critical plane type. Most of these criteria commonly lack considerations of the cyclic stress-strain response. Their application to nonproportional loading suffers from difficulties in implementation or from inconsistencies with results of experiments. Recent approaches fall in the category of continuous damage evaluation methods. At present, these appear to be abstract or difficult to implement. All the above criteria are critically examined and compared. With this background, a new plastic work approach, proposed by the author, is discussed briefly.

Application of the Electrical Potential Method to Crack Length Measurements Using Johnson's Formula

The applicability of Johnsons equation for the potential drop to three specimen geometries is demonstrated. In addition, some remarks are made concerning the influence of crack length and specimen width on the resolution of the potential method.

On the Relationship Between Stretch Zone Formation and the J Integral for High Strain-Hardening Materials

The relationship between stretch zone formation, associated with crack tip blunting, and the J integral was evaluated for materials with high strain-hardening capabilities: Incoloy® 800, Inconel® 600, SA-387 Grade C steel, Type 304 stainless steel, and Alloy A-286. A conventional blunting line commonly used in the construction of a J integral crack growth resistance curve accurately describes stretch zone formation in intermediate and high strength alloys. For low-strength, high strain-hardening materials, however, this conventional blunting line overestimates apparent crack extension associated with stretch zone formation, and it results in an overestimation of ductile fracture toughness values. An alternative blunting line that better describes stretch zone formation in this class of materials is proposed.

Tentative Test Procedure For Determining the Plane Strain JI-R Curve

A tentative test procedure for the determination of the plane strain-crack growth resistance JI-R curve for metallic materials is presented. This procedure was prepared by a Working Group of ASTM Committee E24.08.03. It was evaluated with a round robin test program on HY130 steel, conducted in 1980 to 1981. The results of the testing program were reported in a companion paper, and the experiences were incorporated in this procedure. The procedure is written for the elastic compliance method of developing the plane strain JI-R curve. Recommended specimens are the pin-loaded compact and the three-point bend specimens. Details regarding apparatus, specimen preparation, test system calibration, testing, calculation of J and crack extension, and data qualification are specified.

Some Aspects of Fatigue Crack Closure in Two Contrasting Titanium Alloys

Fatigue crack growth at intermediate rates was measured in compact tension specimens of the microstructurally contrasting alloys Ti-6Al-4V (Imperial Metal Industries, Ltd. [IMI] titanium 318) and Ti-6Al-5Zr-0.5Mo-0.25Si (IMI titanium 685). Sinusoidal loading was used with a ratio of minimum load to maximum load R of 0.1. The incidence of crack closure was examined during fatigue with both direct current potential drop and crack-opening-displacement (COD) methods; COD was found to be more reliable for closure measurement than potential drop. In contract to the fine-grained IMI 318, the coarse-structured IMI 685 showed substantial load transfer across the crack faces during fatigue and this was attributed to mismatch of the fracture faces. It was shown that the large differences in crack growth rate between the two alloys could be substantially accounted for by an effective stress intensity factor range concept. Marked reductions in growth rate produced by variable amplitude loading of the IMI 318 could not be explained in terms of crack closure.

Stress Intensity Factors for Single-Edge-Crack Solid and Hollow Round Bars Loaded in Tension

Dimensionless stress intensity factors were determined for single-edge-crack solid and hollow round bars loaded in tension. These factors were calculated from experimental compliance (inverse slope of load-displacement curve) measurements made over a range of dimensionless crack depths (lengths) from 0.05 to 0.65. The tests were made with 76-mm (3-in.) diameter solid and hollow round bars notched on one side and loaded in axial tension. The hollow bar had an inner to outer diameter ratio of 0.33. A comparison was made with data in the literature for rectangular bars; for a crack depth to diameter ratio of 0.0001 the dimensionless stress intensity factor for a solid round bar is 0.55 compared with 2.0 for a rectangular bar.

A Summary of Fracture Mechanics Concepts

The basic concepts of fracture mechanics are presented in a logical sequence. Each concept is given in a concise definition-like paragraph. The concepts of toughness, process zone, crack, and linear-elastic fracture mechanics are first introduced. The crack-tip characterizations, that is, stress-intensity factor, crack extension force, J integral, and crack-tip opening displacement are then discussed. The constraints in plane stress, plane strain, and three dimensions are pointed out. Various methods of evaluating the crack-tip characterizations are explained. The concept of fracture toughness is presented in relation to resistance curves, dynamics, constraints, and fast-stable crack growth. Some practical empirical fracture toughness relations are given. Then slow-stable crack growth is discussed, that is, stress corrosion cracking, fatigue cracking, corrosion fatigue, and viscous (creep) cracking. The summary concludes with the concept of fracture control plans.

Absolute Measurements of Ultrasonic Attenuation Using Damped Nondestructive Testing Transducers

This paper reviews the method for making absolute ultrasonic attenuation measurements by means of nondestructive testing transducers and liquid buffer columns or solid buffer rods. The principle is that the transducer must be separated from the specimen so that the transducer cannot influence the echoes in the specimen. Then the attenuation coefficient in the specimen and the reflection coefficient at the buffer/specimen interface can be calculated from the amplitudes of the first three echoes in the buffer/specimen system. For absolute measurements, the amplitudes must be corrected for ultrasonic beam spreading (diffraction). The theory of the measurements and the corrections is recapitulated, and experimental examples are given showing the utility of the method. Experimental techniques are also recapitulated.

Chevron V-Notched Bend Specimen for KIc Measurement of Brittle Materials

A chevron V-notched bend specimen is proposed for plane-strain fracture toughness KIc testing of brittle materials. This specimen has the following distinctive advantages over more conventional toughness specimens: (1) the simple geometry can easily be machined, (2) no fatigue precracking is required, (3) no crack length measurements are required (KIc can be calculated from knowledge of the peak load alone), and (4) the test can easily be conducted at elevated temperatures. The proposed specimen was calibrated with a 7079-T6 aluminum alloy of known fracture toughness. Subsequently, the fracture toughness of the ceramic material Pyroceram® 9606 was determined with the same specimen design. The reproducibility of KIc values was found to be excellent: 2.64 MPa·m1/2 ± 3% (2.39 ksi·in.1/2 ± 3%). The proposed specimen design is also recommended as an inexpensive toughness screening test for other structural materials. The chevron V-notch crack starter used in the bend bar specimen is also recommended for use in other specimen designs to improve the capability for both fatigue and stress corrosion threshold testing. In view of the tremendous cost- and time-saving potential associated with the chevron V-notch design, it is recommended that a detailed finite element analysis be performed on this configuration to further substantiate the applied stress and stress intensity conditions.

Determination of Fracture Toughness JIc Under Quasi-Static and Dynamic Loading Conditions Using Wedge Loaded Specimens

A study of the variation of fracture toughness of American Iron and Steel Institute (AISI) 1045 (Unified Numbering System [UNS] G10450) steel in the annealed condition, which exhibits elastic-plastic behavior at the crack tip, with loading rates ranging from quasi-static to dynamic conditions was undertaken. A wedge loaded compact tension (WLCT) specimen geometry was used in both testing conditions. The onset of crack propagation was detected using a strain gage mounted near the crack tip. The fracture parameter JIc decreases by about 50% when the loading rate ˙KI increases from 0.5 to about 106 MPa · m½ s−1. The measured values of JIc using WLCT specimens were confirmed from previous data on this material using standardized three-point bending specimens as well as from evaluation of JIc from stretch zone width measurements using scanning electron microscopy of the fracture surface of the WLCT specimens.