A Weakest-Link Model for the Prediction of Fatigue Crack Growth Rate

1978 ◽  
Vol 100 (2) ◽  
pp. 170-174 ◽  
Author(s):  
Kong Ping Oh
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Average Rate ◽  
Joint Probability ◽  
Random Variable ◽  
Weakest Link ◽  
Link Theory ◽  
Link Model ◽  
Joint Probability Density

A weakest-link theory is proposed for analyzing the rate of fatigue crack growth. The joint probability density of a fatigue crack growing an amount X between x and x+dx, and in time η between N and N+dN cycles is derived from an initial probability function. The rate of crack growth is then obtained as the expectation of the random variable (X/η). It is shown that the average rate of crack growth obeys the power law for small ΔK, and that the power is a function of the shape parameter in the Weibull distribution.

The effect of crystal orientations on fatigue crack growth

1968 ◽  
Vol 46 (19) ◽  
pp. 2225-2226 ◽  
Author(s):  
R. W. Lardner
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Plastic Zone ◽  
Crack Growth ◽  
Average Rate ◽  
Previous Theory ◽  
Line Material ◽  
Dislocation Arrays ◽  
Mode 2 ◽  
Slip Planes

A previous theory of fatigue crack growth in metals was based on an analysis of the plastic zone at the tip of a crack in terms of coplanar dislocation arrays. This analysis has been extended to the case of oblique slip planes. It is shown that, for the case of a crack growing in mode 2 through a polycrystal-line material, the average rate of growth through the differing orientations of many grains is almost identical with that obtained by the coplanar analysis.

The Effect of Material Heterogeneity and Random Loading on the Mechanics of Fatigue Crack Growth

1986 ◽  
Vol 108 (3) ◽  
pp. 268-275
Author(s):  
T. S. Srivatsan ◽  
M. Sambandham ◽  
A. T. Bharucha-Reid
Keyword(s):  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Material Constant ◽  
Random Variable ◽  
Present Theory ◽  
Nickel Steel ◽  
Random Loading

This paper reviews the experimental work on the influence of variable amplitude or random loads on the mechanics and micromechanisms of fatigue crack growth. Implications are discussed in terms of the crack driving force, local plasticity, crack closure, crack blunting, and microstructure. Due to heterogeneity in the material’s microstructure, the crack growth rate varies with crack tip position. Using the weakest link theory, an expression for crack growth rate is obtained as the expectation of a random variable. This expression is used to predict the crack growth rates for aluminum alloys, a titanium alloy, and a nickel steel in the midrange region. It is observed using the present theory that the crack growth rate obeys the power law for small ΔK and that the power is a function of a material constant.

Scaling of Static Fracture of Quasi-Brittle Structures: Strength, Lifetime, and Fracture Kinetics

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Jia-Liang Le ◽  
Zdeněk P. Bažant
Keyword(s):  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Size Effect ◽  
Crack Growth ◽  
Failure Probability ◽  
Structural Strength ◽  
Chain Model ◽  
Weakest Link

The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime, and size effect of quasi-brittle structures, which are the structures in which the fracture process zone size is not negligible compared to the cross section size. The theory is based on the recognition that the failure probability is simple and clear only on the nanoscale since the probability and frequency of interatomic bond failures must be equal. The paper outlines how a small set of relatively plausible hypotheses about the failure probability tail at nanoscale and its transition from nano- to macroscale makes it possible to derive the distribution of structural strength, the static crack growth rate, and the lifetime distribution, including the size and geometry effects [while an extension to fatigue crack growth rate and lifetime, published elsewhere (Le and Bažant, 2011, “Unified Nano-Mechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: II. Fatigue Crack Growth, Lifetime and Scaling,” J. Mech. Phys. Solids, 1322–1337), is left aside]. A salient practical aspect of the theory is that for quasi-brittle structures the chain model underlying the weakest-link statistics must be considered to have a finite number of links, which implies a major deviation from the Weibull distribution. Several new extensions of the theory are presented: (1) A derivation of the dependence of static crack growth rate on the structure size and geometry, (2) an approximate closed-form solution of the structural strength distribution, and (3) an effective method to determine the cumulative distribution functions (cdf’s) of structural strength and lifetime based on the mean size effect curve. Finally, as an example, a probabilistic reassessment of the 1959 Malpasset Dam failure is demonstrated.

A discrete dislocation analysis of fatigue crack growth

2001 ◽  
Vol 11 (PR5) ◽  
pp. Pr5-69-Pr5-75
Author(s):  
V. S. Deshpande ◽  
H. H.M. Cleveringa ◽  
E. Van der Giessen ◽  
A. Needleman
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Discrete Dislocation

Fatigue Investigation of Elastomeric Structures

2010 ◽  
Vol 38 (3) ◽  
pp. 194-212 ◽  
Author(s):  
Bastian Näser ◽  
Michael Kaliske ◽  
Will V. Mars
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Material Behavior ◽  
Period Effect ◽  
Numerical Representation ◽  
Material Force ◽  
Strain Behavior ◽  
Dissipative Effects ◽  
Elastomeric Materials

Abstract Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.

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