G. T. Hahn

Local yielding attending fatigue crack growth

Fatigue crack growth rate measurements were performed at 100°C on an Fe-3Si steel in three thickness conditions and at different ΔK-levels. The test pieces were subsequently sectioned and etched to reveal the plastic deformation attending crack growth both on the surface and in the interior. Unlike preceding studies, the Fe-3Si steel displayed classical cyclic crack growth: well-defined fatigue striations with a spacing close to the per-cycle growth rate, and essentially the same growth rates that have been reported for low and medium strength steels. A highly strained region, approximately one-fifth the size of the monotonie plastic zone, is identified as the cyclic plastic zone. On this basis three regions with distinct cyclic strain histories that precede the crack are identified: a microstrain region wherein the material receives ∼103 to 104 strain cycles in the range 0 < ΔεP ≲ 10-3; a cyclic plastic zone corresponding to ∼200 cycles in the range 10-3 < Δ∈P ≲ 10-1, and a COD-affected zone that receives ∼10 strain cycles in the range 10-1 ≲ Δ∈P ≲ 1. It is suggested that the damage associated with the instabilities in the fatigue substructure to overstrain contribute to the growth mechanism.

Mechanisms of fast fracture and arrest in steels

Studies of the unstable propagation and arrest of brittle fractures were conducted on four steels: plain carbon steel, 3 pct Si steel, A-517, and 4340. Unstable fractures were initiated in double-cantilever-beam test specimens by forcing a wedge between the two beams under compression. These fractures propagate at essentially constant wedge opening displacement and can be made to arrest within the confines of the specimen. The strain energy stored in the specimen at the onset of propagation was varied systematically by changing the root radius of the starting slot. The experiments show that Ka, the stress intensity at arrest, is not a materials constant but depends on the strain energy stored in the specimen. Values of άrcR, the average energy dissipation rate during propagation, calculated for the four steels, are in the range23- GIc ≲ άcrR ≲ G{Ic}. Detailed metallographic examinations show that brittle fractures appear highly segmented on interior sections, but that the individual segments are interconnected. This morphology is attributed to isolated, difficult-to-cleave regions, comparable in size to the grains, which are bypassed and remain unbroken at relatively large distances behind the crack front. Etching studies conducted on a silicon steel reveal that the plastic deformation attending crack propagation is largely confined to the plastic stretching of the ligaments behind the crack front. Increases in the size, number, and toughness of the ligaments with temperature coincide with the brittle-to-ductile transition. An analytical model consisting of an elastic crack with a regular array of tractions representing the ligaments supports the view that the ligaments are the principal source of brittle crack propagation resistance in the steels.

Fracture of steels containing pearlite

The relative effects of pearlite and spherodite on ductile, cleavage, and fatigue failure are summarized. Neither the cleavage strength nor the fatigue endurance limit appear to depend directly on cementite contentper se. Spherodized steels cleave less readily than ferrite/pearlite steels. Ductile fracture resistance is lowered considerably by both types of cementite, pearlite being more deleterious. Ferrite/pearlite steels appear to exhibit slower fatigue crack growth rates at low stress intensity levels than high strength steels. At high stress intensity levels the behavior is reversed. Slip-incuded cracking of carbide lamellae appears easier than that of spherodized carbides. In ductile fracture situations the crack spreads progressively through a pearlite colony via preferential cracking of carbides and rupture of the intervening ferrite accompanied by large local shear strains. Fatigue fracture proceeds with formation of frequent branches, preferentially along the pearlite colony interface.

The variation of KIc with temperature and loading rate

The relation, KIcY2 = (Σ*/2.35)3, where KIc is plane strain fracture toughness, Y is the local value of yield stress in the crack-tip plastic zone, and Σ* is the cleavage stress of an unnotched bulk specimen, is shown to be a reasonable approximation to the data from a large number of investigations. The relation is shown to be consistent with the results of metallographic studies of subcritical crack formation. Methods of extrapolating KIc to high strain rates and low temperatures are suggested.

A Crack Arrest Measuring Procedure for K Im , K ID , and K Ia Properties

New developments are described which offer a flexible procedure for measuring the fracture resistance values, K I m , K I D , and K I a which characterize the crack arrest behavior of materials. The procedure relies on a dynamically stiff, wedge-loading which limits dynamic energy exchanges between the test specimen and the testing machine. This makes it possible to interpret both small and large crack jumps without recourse to crack velocity measurements. The procedure is general and can be applied to ordinary and duplex rectangular and contoured double-cantilever-beam (DCB) specimens, and to compact and single-edge-notched (SEN) specimens when dynamic analyses for these shapes become available. The paper examines the virtues of the different specimen configurations, size and thickness requirements, possible upper and lower bounds on the size of the crack jump, and the problem of branching and side grooves. Measurements of specimen machine interactions are described. Results obtained for A533B steel with a series of rectangular DCB specimens illustrate the dependence of K I a on the size of the crack jump as well as the previously proposed relations between K I a and K I m or K I D . The results confirm that the K I m (or K I D ) values obtained with the new procedure from static measurements of load point displacement and the crack length at arrest agree with values derived from crack velocity measurements. The experiments also illustrate that duplex DCB specimens with modest dimensions (400 by 140 by 50 mm) have the capacity for measuring K I m and K I D values in excess of 150 MPa.m 1 /2.

Crack arrest in steels

Abstract This paper examines 3 theories that have been used to characterize the arrest capabilities of steels and structures: (1) The static analysis, arrest toughness ( K Ia ) theory; (2) The dynamically loaded/stationary crack toughness ( K Id ) theory, and (3) The dynamic analysis, propagating crack energy or toughness ( R ID or K ID ) theory. These three concepts are examined in the light of measurements of unstable fracture and crack arrest in wedge-loaded DCB test pieces together with a fully dynamic analysis of the experiments.

A preliminary study of fast fracture and arrest in the DCB test specimen

This paper describes measurements of unstable fracture and arrest in a 4340 steel, wedge-loaded DCB (double cantilever beam) test specimen with a blunted starting notch but which is well below the limiting speeds predicted by Broberg and Yoffe, specimen which accounts for transverse inertia forces. Preliminary results of crack speed and arrest measurements are described and compared with results of the dynamic analysis. These results reveal that: (a) the inclusion of inertia forces in the equation of motion leads to substantial improvement in the prediction of crack speeds over previous quasi-static analyses, (b) a crack in a wedge-loaded DCB specimen tends to propagate at a constant velocity which depends upon the bluntness of the starting notch but which is well below the limiting speed predicted by Broberg and Yoffe, and (c) the kinetic energy in the system tends to be recovered. It is concluded that the wedge-loaded DCB test specimen shows promise as a vehicle for characterizing the dynamic fracture toughness and crack arrest capabilities of structural materials.

Rapid crack propagation in a high strength steel

The relation between fracture velocity and the energy dissipated by unstable fractures in high strength 12.7 mm-thick plates of SAE 4340 steel has been measured using the wedgeloaded double-cantilever-beam (DCB) specimen. The experiments are analyzed using the dynamic beam-on-elastic-foundation model. In agreement with the model, steady-state crack velocities are attained. In addition, the theoretical velocity-arrest length relation is closely obeyed. Statically calculated values of the stress intensity at arrest,Ka, are relatively invariant, but in view of the kinetic energy contribution, are not regarded as a materials property. Increases in crack velocity up to ∼860 ms-1 are accompanied by a 2-fold increase in dynamic toughness (a 4-fold increase in the dynamic fracture energy) and by corresponding increases in the size of the shear lips. Measurements of the plastic work associated with the shear lips show that the per-unit-volume shear lip fracture energy, φSL = 0.21 J/mm3, is essentially constant over this range of velocity. These agreements imply that kinetic energy imparted to the test piece during propagation is substantially recovered and makes a significant contribution to the crack driving force.

The Speed of Ductile-Crack Propagation and the Dynamics of Flow in Metals

In this paper the connection between the speed of ductile-crack propagation and the dynamic-flow properties of metals is examined. A theoretical analysis based on a dynamic solution for the Dugdale crack model and employing descriptions of 1) the strains within the plastic zone, 2) the rate dependence of the flow stress, and 3) a simple criterion for ductile fracture is developed. The calculations are found to compare favorably with observed crack speeds of 1.6 to 410 ft/sec in 0.00175-in.-thick steel foil. It is concluded that ductile-crack speed is limited by the increased resistance to plastic flow at high strain rates. The key factors determined in the analysis are used to show that flow stress data for strain rates exceeding 104 sec−1 can be extracted from ductile-crackpropagation experiments.

An elastic-plastic analysis of a crack in a plate of finite size

Two great complexities are involved in determining the stress and strain fields in a body containing a crack. These arise in treating the plastically deformed regions at the ends of the crack and in accounting for the boundary conditions on the periphery of the body. Progress has been made in treating these complexities individually. A large number of completely elastic solutions for finite and semi-finite cracked plates (see, for example, the compilation by Feddersen [1]) and of elastic-plastic solutions for infinite cracked plates are available. Few elastic-plastic solutions for finite regions have been reported, however. Of these the anti-planestrain solutions of Bilby et al [2] and Koskinen [3] are particularly noteworthy.