K. Sadananda

Analysis of overload effects and related phenomena

Overloads and underloads perturb steady state fatigue crack growth conditions and affect the growth rates by retarding or accelerating the growth. Clear understanding of these transient effects is important for the reliable life prediction of a component subjected to random loads. The overload effects have predominately been attributed to either plasticity induced crack closure behind the crack tip, residual stresses ahead of the crack tip, or a combination of both. These effects are critically examined in the context of the Unified Approach proposed by the authors. Recent experimental and analytical evaluation of crack closure has confirmed its negligible contribution to crack growth and has demonstrated that changes in the stresses ahead of the crack tip are more important than closure behind the crack tip. It is shown that the overload effects and other transient effects arise due to perturbation of the stresses ahead of the crack tip, and these can be accounted for by the two parametric approach emphasized in the unified theory. It is shown that related phenomena including the role of Kmax, the existence of propagation threshold Kpr, and effects of overloads on Kpr and Kmax etc, are all accounted for by the Unified Approach.

Critical parameters for fatigue damage

Abstract The fatigue damage analysis is examined from a historical perspective. The analysis indicates that some of the issues concerning the basic disparities between the experiment and model/interpretations. To help understand these issues, we have developed an approach with two driving force parameters to analyze the fatigue behavior. Such an approach helps in viewing the damage in terms of an intrinsic problem rather than an extrinsic one. In the final analysis one needs to unify the overall damage processes such that the description is complete from the crack initiation stage to short crack to long crack to final failure. In order to unify the damage process, three basic parameters are introduced for describing the overall fatigue process. These are Δ K , K max and internal stress contribution to K max . In addition, there are other effects from environment and temperature that can contribute to these parameters. In particular K max seems to play an important role in the overall damage process. We find that the internal stress is the missing link that can bridge the gap between the four main stages of damage that lies between the crack nucleation stage to final failure. Examples are sited in support of this view of explanation. Finally, it is suggested that systematic experimental data and analytical modeling to describe the internal stress gradients is required to help in forming a reliable life prediction methodology.

Crack tip driving forces and crack growth representation under fatigue

Abstract Fatigue is considered as a two load parameter problem involving two crack tip driving forces. Conventional representation of crack growth rates, d a /d N , as a function of a single driving force, Δ K , is considered as inadequate. Mean stress effects are treated normally as R -ratio effects. These effects are due to a second crack tip driving force, K max . The role of K max has been generally ignored, even though it has more dominating influence than Δ K . A unified Approach developed by the authors considers interplay of these two governing forces, Δ K and K max , as fundamental to fatigue. Superimposed environmental effects and static load effects naturally follow in this Unified Approach, since K max is the governing parameter for these.

Fatigue crack growth mechanisms in steels

Abstract Fatigue crack growth behavior of structural steels is examined by using the Unified Approach developed by the authors. In this approach, fatigue requires two-load parameters involving maximum stress intensity, Kmax, and stress intensity amplitude, △K. For a fatigue crack to grow, both Kmax and △K must exceed their respective threshold values. Similarly, for any other crack growth rate, two limiting values, Kmax∗ and △K∗ are required to enforce the growth rate. The variation of these two critical values forms the crack growth trajectory map, which is defined by plotting △K∗ vs. Kmax∗ as a function of crack growth rate. In this trajectory map, the line defined by △ K ∗= K max ∗ represents pure fatigue crack growth behavior induced by cyclic strains. It is shown that this line provides a reference norm for defining deviations in the trajectory resulting from environmental and/or monotonic fracture modes superimposed on fatigue. Using this approach, we have examined the crack growth behavior of many structural steels. The trajectory maps of these steels show deviations due to superimposed environmental effects. These effects vary with grain size, yield strength, microstructure, and chemistry. In addition, for a given material, changes in the trajectory paths occur because of changing crack growth mechanisms. Analysis of material behavior using trajectory maps provides a clear understanding of the relative magnitude of cyclic and environmental damage and how the microstructure, chemistry, and crack tip plasticity affect fatigue crack growth behavior of steels.

Short crack growth and internal stresses

Abstract Short crack growth behavior has been examined using the two parametric approach developed earlier by the authors. It is commonly accepted that there is a lack of similitude in the description of the short crack growth behavior. Contrary to this understanding, it is shown that there is no anomaly in the short crack growth behavior. The apparent anomaly arises because of ignoring: (1) the second parameter associated with the threshold K ∗ max ; and (2) the existence of internal stresses in the crack tip field where the short cracks nucleate and grow. In the case of short cracks nucleating from notches the internal stresses can be pre-existing or can be generated in situ if they form at a free surface. In the latter case, formation of intrusions and extrusions at the persistent slip bands are the precursors for the crack nucleation providing the necessary internal stresses. Thus short cracks grow under a total force, consisting of both internal and applied stresses, satisfying the same two thresholds for long cracks. Examples are provided from the literature to illustrate the concepts. It is shown that the internal stresses decrease as a short crack grows out of the existing stress field. These internal stresses can be predicted using elastic or elastic-plastic continuum approximations. Application of this concept is extended to understand the role of: (1) residual stresses; and (2) the transformation induced internal stresses on the crack growth. Based on the analysis, we restate the similitude concept as: equal crack tip forces result in equal crack growth rates for the same crack growth mechanism, provided all the contributing forces are taken into consideration.

A theoretical evaluation of crack closure

Premature crack closure has been considered an important factor affecting the applied driving force under cyclic load. Among several factors that induce crack closure, plasticity and oxidation or corrosion have been recognized as the most significant. An analytical estimation of both is made using dislocation theory. The analysis indicates that (a) plasticity originating from crack tip does not induce crack closure and (b) closure arising from asperity ridges due to oxides, corrosion products or surface roughness is small and insignificant unless crack is completely packed with asperities.

Fatigue thresholds of Ni-Ti alloy near the shape memory transition temperature

The fatigue thresholds of nickel-titanium alloy with martensite start temperature of 80°C were measured in air from room temperature to 150°C and load ratios of 0.1 to 0.9. The ΔK versus K max fundamental threshold curves are characteristic of ductile metals at all temperatures tested and are consistent with the existence of two threshold parameters, ΔK th * and K max,th * , for cyclic and maximum stress intensity, respectively. ΔK th * increases linearly with temperature, while K max,th * , exhibits a transition between 80 and 100°C, decreasing by half as a function of temperature. Compliance curves suggest the existence of crack closure in the stable martensite regime below 100°C, but little or no crack closure in the stress-induced martensite regime above 100°C up to 150°C. The results suggest that both crack closure and the existence of an intrinsic fundamental threshold curve with both ΔK and K max thresholds as a function of load ratio are necessary to fully account for R dependence of ΔK th .

Role of microstructures on the growth of long fatigue cracks

Abstract An analysis is presented to understand the role of microstructures on the two crack growth driving force parameters, K ∗ max and Δ K ∗ th , without invoking the extrinsic crack closure concepts. Microstructural variables considered are: grain size, precipitates and stacking fault energy. It is shown that K ∗ max is strongly affected by the scale of the microstructure, such as grain size or precipitate spacing. For each case, the mode of slip deformation and environment affects the fatigue resistance as represented by K ∗ max . However, the microstructures seem to have a smaller effect on Δ K ∗ th . Also, the enhanced planarity of slip from the reduction in stacking fault energy has a pronounced effect on K ∗ max when compared with the materials deforming under homogeneous slip.

Extension of the Unified Approach to fatigue crack growth to environmental interactions

Abstract Environmental effects on fatigue crack growth were examined using the Unified Approach developed by the authors. According to this approach, K max and Δ K are two intrinsic parameters simultaneously required for quantifying fatigue crack growth data. The two parameters led to two intrinsic thresholds that must be simultaneously exceeded for a fatigue crack to grow. Environmental interactions being time and stress-dependent processes affect fatigue crack growth through K max parameter. Based on an extensive analysis of literature data, we have classified environmental effects into four basic types. In addition, we have defined a true reference state for an inert fatigue behavior. Classification procedures and methods of estimating the magnitude of environmental effects using the Unified Approach for fatigue crack growth were discussed taking examples from the literature.

Analysis of Fatigue Crack Closure and Thresholds

A critical examination of fatigue crack closure concepts indicates that (a) procedures commonly followed in estimating crack closure are in error, (b) complete premature crack closure occurs only when cracks are completely filled with oxides or corrosion products, (d) such closure manifests as an infinite slope in the load-displacement (crack mouth opening) curves; rarely observed in experiments, (e) asperities cause only local closure, (f) their contribution is less significant than is assumed and (g) plasticity does not contribute to closure. New concepts are developed to explain fatigue phenomena hitherto attributed to crack closure. Implications of these concepts to understand fatigue crack growth are discussed.