T. H. Topper

Some Studies of the Influence of Localized and Gross Plasticity on the Monotonic and Cyclic Concentration Factors

The variation in monotonic and cyclic concentration factors (namely, Kt, Ke, Kσ) due to localized and gross plasticity is presented and discussed for two alloys of contrasting stress-strain behavior, an aluminum alloy 2024 T351 and a mild steel SAE 1015. Thin plates with circular and elliptical holes made of these alloys were subjected to monotonic and cyclic straining in a servo controlled testing machine. Predominant in the monotonic behavior of the concentration factors is the rapid increase in strain concentration factor in notched mild steel plates, attributed to the unrestrained plastic flow (Luders deformation) characteristic of this material. Such behavior is compared to the response of the continuously strain hardening aluminum alloy when subjected to a similar nominal strain history. The dominant feature of the cyclic behavior is the variation in the notch strains as influenced by the overall hardening or softening phenomenon which accompanies cyclic plastic deformation. With the aid of these results, the accuracy of the Neuber rule is checked and restrictions to its application in fatigue life predictions of notched members using smooth specimen data are presented.

THE EFFECT OF LARGE PRESTRAINS ON FATIGUE

Evaluation of the fatigue behavior of stamped parts requires a knowledge of the effects of large prestrains on fatigue. This paper reports the results of a test program carried out to investigate the effect of tensile and rolling prestrains on the fatigue strength of SAE 1010 and Maxiform 50 steels. Large rolling-induced prestrains were shown to cause a significant increase, while large tensile prestrains (up to 0.9 times the true fracture strain of the steel) caused a moderate increase in the long-life fatigue properties of these steels. Still larger tensile prestrains (0.95 times the true fracture strain) caused the fatigue strength to reduce to its initial value.

Fatigue-damage evaluation for mild steel incorporating mean stress and overload effects

Successful estimation of the service life of a structure or component which is subjected to a complex history of loading, depends on a suitable cumulative-damage summation technique. A general technique must be capable of predicting the effects on fatigue life of geometry, mean stress or strain, occasional overloads or overstrains, frequency of cycling and environment. As a contribution towards the general solution, this paper describes the utilization of a fatigue-damage summation method which incorporates two of these variables, mean stress and overloads. The method is tested for complex load histories in mild-steel specimens in the intermediate to long-life range.A four-part constant-stress-amplitude testing program was carried out consisting of: (a) tests with a constant mean stress, (b) tests on prestrained specimens, (c) tests with a mean stress applied in one block of cycles, and (d) tests with a mean stress applied in frequent regularly spaced short blocks.The constant-mean-stress results, which include several values of mean stress both tensile and compressive, are reduced to a single curve on a stress-life plot with either of two simple parameters (from Morrow and Smith, et al.) as ordinate. The prestrained specimen tests result in another curve lower than the first, showing the reduction in life due to the few initial cycles of high strain.These two effects are then incorporated into a cumulative-damage summation technique which is based on the well-known Miners rule. The two curves on the stress-life plot are the foundation for the subsequent summations. The technique assumes that the first application of an overload causing appreciable plastic straining reduces the remaining fatigue life. A significant point is that this assumption apparently holds for both tensile and compressive overloads. The accuracy of this technique is demonstrated for a wide range of stress conditions and loading histories.

On the Relation Between Stress and Strain-Concentration Factors in Notched Members in Plane Stress

The validity of the relationship between stress and strain-concentration factors proposed by Neuber, i.e., the geometric mean of the stress and strain-concentration factors is equal to the linear elastic-stress-concentration factor, is investigated for plane-stress problems. The physically nonlinear plane-stress problem of an infinite plate with a circular hole is solved by a perturbation method. Applicability of the solution and the restrictions on the relationship are discussed with reference to theoretical and experimental results.

A Model for Fatigue Crack Growth Delay Under Two-Level Block Loads

After reviewing previous attempts to quantify delay, a composite stress intensity parameter, (Kl m a x /K h m a x ) ΔKl, is proposed to correlate the number of delay cycles in simple two-level variable-load amplitude tests for various combinations of stress levels. Its application is restricted in the present investigation to room temperature tests in an air environment. Delay (cycles) is defined herein as the period of apparent zero crack growth after the overload, and the stress intensity factors, Kl m a x and K h m a x refer to the stress intensities accompanying the lower and higher load levels, respectively. It is hypothesized on the basis of experimental observations that material under different two-level block loading sequences, but having equal values of the parameter, will experience the same delay. Good correlations for data on aluminum alloys, titanium alloys, and carbon steel taken from the work of several investigators are obtained using the parameter. An empirical model relating the delay to a power function of the parameter is suggested. Limitations of the model are pointed out and discussed. The engineering significances of the parameter with respect to the determination of crack propagation life and crack arrest conditions are discussed.

Cyclic-deformation behavior of notched mild-steel plates in plane stress

Notched rectangular SAE 1015 mild-steel plates were subjected to controlled cyclic nominal stresses or strains in a closed-loop servo-controlled fatigue-testing machine. Resistance strain gages were used to measure strains at the notch roots. These strains showed that large mean strains and strain ranges prevailed at these notches, though nominal strains were fully reversed and small. Inelastic stress- and strain-concentration factors calculated at various cycles were used to check the accuracy of the Neuber relation between these concentration factors and elastic stress-concentration factor. Limitations of this relation and characteristic notch-strain behavior mentioned above are discussed with reference to the peculiarities of the stress-strain relationships of this material.

Performance of miniature resistance strain gages in low-cycle fatigue

Experimental results describing the behavior of five types of miniature resistance strain gages subjected to cyclic strains of high amplitude are presented. Test procedure and instrumentation are described. Changes in zero drift and changes in gage sensitivity are discussed with respect to various strain gage and test variables. Mechanisms of gage failure, effect of variation of imposed strain and hysteresis in gage response are discussed.

A generalized model of structural reversed plasticity

This paper describes and experimentally verifies a simplified generalized force-local deformation model capable of simulating the stable fluctuating elastoplastic response displayed by structural systems subjected to proportional cyclic loads. The principal generalized force-deformation characteristics of these systems under cyclic proportional loads are outlined. Essential stable force-deformation features related to the model are memory of prior deformation and the Masing kinematic hardening rule which states that the force-deformation hysteresis-loop shape is obtained by magnifying the cyclic force-deformation curve by a factor of two.Five types of structural specimens made from three metals were cyclically stabilized using an incremental step-loading sequence after which their stable cyclic deformation responses were generated. The proposed modeling process was then used to simulate each of these fifteen stable responses with generally good accuracy. The maximum hysteresis loop tip prediction error did not exceed 7.7 percent of the corres-ponding range of force.The model is readily adaptable to digital computation and it should be useful for fatigue-analysis procedures or earth-quake-response studies.

New equipment for cyclic biaxial testing

Methods of achieving biaxial-stress states in fatigue tests are reviewed. A new design of equipment that produces five distinct biaxial-stress states by simultaneous direct pressurization and axial loading of thinwalled cylindrical specimens is described. Four variations of stress state are obtained by the use of two sizes of specimen and by reversal of the pressurizing connections. The fifth state is obtained by direct pressurization without axial load. The actual magnitudes of stress in the specimen are computed from the output of the load cell in the reaction frame in which the biaxial-testing device is mounted. Additional stress ratios are obtained using standard uniaxial and torsional cyclic-testing arrangements.The initial program using this equipment was to investigate the effects of biaxiality on the cyclic properties and low-cycle fatigue behavior of normalized 1018 mild steel, under fully reversed constant-amplitude strain control. Control was achieved using a servo-controlled, electrohydraulic testing system with one of the two clipon strain transducers, that were mounted on the specimen, providing the controlling electrical signal. The system allowed direct recording of the stress-strain hysteresis loops in both principal directions. The behavior of the equipment and the modes of failure of the specimens are described and some test data are presented. The range of application and limitations of the equipment for further cyclic biaxial testing are discussed.

Crack Propagation in Notched Mild Steel Plates Subjected to Cyclic Inelastic Strains

MILD STEEL (SAE 1015) PLATE SPECIMENS WITH CENTRAL CIRCULAR HOLES WERE USED TO STUDY CRACK PROPAGATION IN THE INELASTIC STRAIN REGION. THESE THIN PLATES WERE SUBJECTED TO COMPLETELY REVERSED CONSTANT AMPLITUDE CYCLIC STRAINS IN A SERVOCONTROLLED TESTING MACHINE. FATIGUE CRACK PROPAGATION RESULTS IN THE INELASTIC STRAIN REGION SHOWED THAT THE RATE OF CRACK GROWTH IS A POLYNOMIAL FUNCTION OF THE EQUIVALENT STRESS INTENSITY FACTOR DEVELOPED IN THIS WORK. THE RELATION IS SIMILAR TO THE EQUATION PROPOSED BY PARIS AND ERDOGAN FOR AN ELASTIC CASE AND DESCRIBES CRACK PROPAGATION RATES FOR BOTH ELASTIC AND INELASTIC STRAIN LEVELS. THE EQUIVALENT (OR MODIFIED) STRESS INTENSITY FACTOR INDIRECTLY REPRESENTS ACTUAL CRACK TIP STRESSES AND STRAINS AND REDUCES TO THE ELASTIC STRESS INTENSITY FACTOR. WITH THE AID OF THE RESULTS OF THE PRESENT STUDY, OTHER METHODS PROPOSED BY VARIOUS INVESTIGATORS FOR PREDICTING CRACK PROPAGATION RATES ARE ALSO DISCUSSED. /ASTM/