Kc Lieb

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.

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.

Review of New Developments in Crack Propagation Studies

The application of fracture mechanics concepts to characterize crack growth at low and high temperatures under cyclic, creep, and creep-fatigue conditions is reviewed. The applicability and limitations of various fracture mechanics techniques in predicting cycle- and time-dependent crack growth are discussed. Also, applications of fracture mechanics to predict the fatigue life of various components and the behavior of cracks at near-threshold conditions are discussed with an emphasis given to the growth of small cracks.

A Simple Test Method for the Evaluation of Tearing Modulus

Material characterization studies using the multi-specimen J resistance curve procedure have been carried out for a variety of alloy steels. These results along with the data from the literature have been used to demonstrate that the J resistance curves can be normalized to a single R curve. It is shown that J-controlled crack growth is reasonably unvarying with the size of the specimen provided the minimum size requirements to insure a J-based dominance of the crack tip region are satisfied. A relatively simple procedure is proposed to permit an assessment of a critical value of the J integral, the slope of the J integral resistance curve, and the tearing modulus from a single specimen.

Void Content Prediction in Two-Size Aggregate Mixes

The purpose of this research was to develop a method to predict the interparticle voids in combinations of two sizes of aggregates. Theoretical concepts and predictions preceded the experimental work. Statistical techniques and computers were used in the design of the experiment and in the analysis of the data. Graphical presentations and illustrations were also used. The experimental work involved three types of rocks having different geometrical properties. Eight differently sized fractions of each of the three types of aggregates were tested. On the basis of the data collected and analyzed, it was concluded that two-size aggregate mixes that have the same size ratio and equal total packing volumes and that were compacted under identical conditions should have the same interparticle packing void contents. The data collected from the experiments were used to introduce a new method (graphical and analytical) to predict the packing void content in two-size aggregate mixes blended at any ratio. The developed blending design curves covered size ratios ranging between 0.20 and about 0.40. Only the percentage of the two constituents in the mix and the size ratio are needed to predict the packing void content by this new method.

Simplified Equations for Peak Position and for Its Standard Deviation in X-Ray Stress Measurement

Simplified equations for peak position and for its standard deviation resulting from counting statistics are derived in the n points parabola method. These equations are applicable to an even as well as an odd n and can be rapidly calculated even with an inexpensive on-line computer such as a microcomputer. Thus a rapid and precise peak determination can be made by use of these equations with an inexpensive X-ray stress measurement system. Various peak positions calculated by the n points and the three points parabola methods were compared. Two heat-treated steels were used. The n points method, using all the data points that fall above approximately 85% of the maximum intensity, gave the most satisfactory result. On the other hand, the three points method produced a large standard deviation of the peak position unless the three points were taken symmetrically about the diffraction peak.

Statistical Fatigue Failure Analysis

A statistical fatigue failure analysis based on the Weibull weakest link concept is described and applied to notched and smooth specimen data to provide an interpretation of the size effect in fatigue results for SAE 4340 steel. The technique of predicting component lifetimes and of calculating effective area and volume is presented.

Effect of Understressing and Coaxing on the Fatigue Limit of a Transverse Butt-Welded Joint

A test program was developed to compare both the effects of thermal stress relief and “understressing” and “coaxing” techniques on the predetermined fatigue limits of selected weldments. Approximately 100 specimens were cut from 1025 welded plate and reduced to a finished size of 6.35 mm (0.25 in.) thick by 31.75 mm (1.25 in.) wide by 279.4 mm (11 in.) long. A 6.35-mm (0.25-in.) diameter hole was drilled in the weld to control the failure location. The specimens were subjected to fully reversed bending at selected stress increments until failure occurred. The results indicated that understressing and coaxing produced a marked increase in the effective fatigue limit for all specimens with the most significant increase observed in the specimens that had no thermal stress relief of the weldments. One of the practical applications might be in a case in which a controlled break-in period for welded components is feasible and thermal stress relieving is not.