Net-section Strain Energy Research Articles

Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture

A large structural size effect on brittle fracture energy was observed in studies of impact fracture of steels by Stanton, Batson and Docherty, nearly 100 years ago. The size effect was seen in macroscopically brittle fractures of geometrically similar specimens tested over a large size range. These historical findings have great significance in designing large-scale steel structures such as ships and bridges. However, there has been no physical principle or theory yet to explain the size effects observed by Stanton, Batson and Docherty. In the present work, a new approach based on net-section mechanics is used to explain the size effect. It is shown that the change in net-section strain energy predicts well the size effect on fracture energy , under the constant condition of cleavage crack initiation stress at the notch root. The spectacular decrease in specific fracture energy with increased specimen size is explained by noting the three-dimensional nature of stored strain energy and the two-dimensional nature of fracture energy dissipated in the crack layer. By scaling both energies to a reference cubic specimen volume and equating, an expression that describes the inverse size dependence of specific fracture energy has been formulated. The mechanics of the size effect is illustrated by assessing the theory with extensive experimental data. Further, scaling laws for fracture energy have been developed. This work honours the pioneering studies of Stanton, Batson and Docherty, which have been instrumental for the development of the present theory and analysis.

A fatigue crack growth prediction model for cracked specimen under variable amplitude loading

The objective of this study was to propose a crack growth prediction model for cracked specimens under large and variable amplitude loading conditions. In this study, the concept of change in net-section strain energy was applied to simulate elastic–plastic fracture behavior, and three-dimensional fitting of the results with respect to changes in the net-section strain energy, load ratio, and crack growth rate was performed to create the crack growth prediction model. The validity of the generated model was examined using comparisons with experimental data as well as simulation results from existing crack growth models under several variable loading conditions.

Application of strain energy based approach for evaluation of fatigue crack growth retardation effect under random overload

Fatigue crack growth in structural components subjected to random amplitude loading is a significantly complex problem. Many models have been proposed to estimate the retardation effect due to a single overload, though for the random overload sequence, there is still a lack of effective quantitative description methods. In this research, a new time to crack initiation (TTCI) type for the calculation of equivalent initial flaw size (EIFS) is proposed based on the change in net-section strain energy density. For a certain number of fatigue cycles and current crack lengths, the value of EIFS can be obtained by solving the corresponding integral equation. The proposed EIFS calculation method was applied for the prediction of fatigue crack growth under single overload and random overload sequences. The prediction results agree well with the experimental data for different conditions. For a certain single overload or overload spectrum, the retardation effect is reflected in the decrease in EIFS, which appears to propagate from a smaller initial crack length. The proposed method shows that the new TTCI type of EIFS can be used as the quantitative characterization of the retardation effect due to the random overload sequence.

The nature of specimen-size-effect on fatigue crack growth and net-section fracture mechanics approach to extract the size-independent behavior

A specimen-size-effect is found in the experimental fatigue crack growth behavior of single-edge-cracked fracture specimens, where the specimen length-to-width ratio was varied by about a factor of four. This effect appears from certain geometric correction factors (GCFS) used for the calcuation of the stress intensity range in fracture mechanics. It is shown that the net-section-based fracture mechanics approach provides a unique correlation of the fatigue crack growth data, for all specimen sizes, when the change in the net-section strain energy is used as the crack driving force parameter. The fatigue crack growth data could be correlated extremely well, when an effective specimen length, including the elastic strain energy of the specimen portion within the grips, is included in the driving force calculations. This effective length is determined by shear-lag analysis. It is also demonstrated that a true size-independent fatigue crack growth behavior can be obtained through the net-section based approach, using the concept of the change in net-section strain energy.

Fracture mechanics analysis of generalized compact tension specimen geometry using the mechanics of net-section

Fracture mechanics analysis of a generalized compact tension specimen, on the basis of the mechanics of deformation of the net-section, is shown to provide a simple and a broadly useful expression for stress intensity factor calculations. A single analytical expression is found to be sufficient for the characterization of crack behavior in compact tension, extended compact tension and wedge splitting test specimens without any restriction on the specimen length (or height) and width. The analysis is enabled by the concept of the change in net-section energy, which is determined by summing the changes in strain energies of the net-section of the generalized specimen for tension and bending deformation modes, which result from the introduction of the crack. This is equivalent in concept to the increase in strain energy upon the introduction of the crack, as in the Griffith’s fracture theory. The square-root of the change in net-section strain energy parameter multiplied by the elastic modulus provides an expression that is equivalent to the conventional stress intensity factor expression. The application of the net-section based expression to the standard compact tension, the extended compact tension and the wedge-splitting test specimens shows very good agreements with the crack behaviors as expressed by the stress intensity factor expressions for the respective geometries. The proposed method enables easy analytical determination of stress intensity factors for any asymmetrically-loaded mode-I crack problem.

Net-section based approach for fatigue crack growth characterization using compact tension specimen: Physical correlation of mean stress or stress ratio effects

A new approach is demonstrated here for the correlation of fatigue crack growth (FCG) data, generated using compact tension (CT) specimens, for various mean stress levels or stress ratios (R) of testing. The approach uses the change in the cyclic strain energy of the net-section as a parameter to correlate fatigue crack growth rates. The derivation of the change in net-section strain energy, for the CT specimen, is demonstrated here on the basis of energy principles of solid mechanics. The total change in net-section strain energy is determined as the sum of the changes in the tension and the bending strain energy components, arising from the tensile stress and the bending moment acting on the net-section of the CT specimen. This leads to a compact physical equation for the change in cyclic strain energy, which is expressed as a direct function of applied cyclic load level, crack length, stress ratio, and specimen dimensions. Extensive experimental evaluations, using the data for steels, copper and titanium alloys, were conducted and are presented here to show that the change in net-section strain energy can successfully correlate the fatigue crack growth for various stress ratios or mean stress levels. The present work provides a new direction for physically-based characterizations of fatigue crack growth data generated using CT specimens.

Mechanics of fatigue crack growth under large-scale plasticity: A direct physical approach for single-valued correlation of fatigue crack growth data

The major challenge in the mechanics of elastic-plastic fatigue crack growth is to find a physically based driving force parameter to correlate the crack growth rates under different loading conditions. Specifically, a parameter that can provide single-valued correlation of crack growth rates, in stress-controlled and strain-controlled fatigue, is needed. Approaches of the past used either cyclic strain (strain intensity factor) or nonlinear-fracture-mechanics based (cyclic J-integral, ΔJ) parameter, to correlate fatigue crack growth. The validity of these approaches, however, has not been established. Further, the J-integral based approach requires experimental load-deflection curves, recorded after every crack length increment, and geometry-correction factors, which are numerically determined and complicated. In the present work, a physically based approach, based on thecumulative change in the cyclic strain energy of the net-section, is used to develop new parameters that can successfully correlate fatigue crack growth behavior in a variety of loading situations. The driving force parameter, capturing the change in the net-section cyclic strain energy, is determined analytically from elastic-plastic behavior of material and from the relative sizes of cracked and uncracked sections in the crack plane. Load-deflection measurements, geometric correction factors, or numerical methods are not needed in the present approach. Remarkably, excellent correlations of fatigue crack growth, in a variety of specimen geometries and for various stress/strain levels, have been found in both stress- or strain-controlled fatigue conditions. This work, extending the author’s earlier works for elastic fatigue crack growth, validates that the change in net-section strain energy is a fundamental quantity in the mechanics of fatigue crack growth.

A new approach to the mechanics of fatigue crack growth in metals: Correlation of mean stress (stress ratio) effects using the change in net-section strain energy

An unsolved problem in the mechanics of fatigue crack growth is why mean stress or stress ratio in a fatigue cycle has a profound effect on growth rate when compared in terms of stress intensity factor range (ΔK). Specifically, there has not been any fracture-mechanically-consistent theory to explain the effects of mean stress on fatigue crack growth. In this work, a new and generalized driving force parameter for fatigue crack growth, which effectively incorporates the mean stress or stress ratio effect, is developed from energy principles of solid mechanics. A successful explanation of the effect of mean stress on the growth rate is provided. The driving force is the accumulated change in net-section strain energy, which develops as a function of increasing crack length and decreasing net-section size in fatigue. A generalized mechanics analysis, showing how to account for the stress amplitude and the maximum stress of a fatigue cycle in the change in net-section strain energy, is presented. Equivalently, the new crack growth parameter can also be interpreted as the cumulative work done by cyclic loading at the crack length at which the crack growth data is determined. Several experimental data, including some historically significant fatigue crack growth data, generated on aluminum, steel and titanium alloys, are used to demonstrate the success of the correlation. As a further validation of the proposed concept, it is shown that the empirical Walker parameter (ΔK0.5Kmax0.5), which had some success in correlating stress ratio effect, is in fact related to the change in net-section strain energy.

New approach for the correlation of fatigue crack growth in metals on the basis of the change in net-section strain energy

A new approach to correlate fatigue crack growth data of metals on the basis of the change in net-section strain energy is presented. Extensive experimental data, including some historically significant fatigue crack growth data, generated using center-cracked (CCT) and single-edge notched (SENT) tension specimens, are used to demonstrate this correlation. It is shown that this correlation, quite remarkably, is as strong as that based on the stress intensity factor range (ΔK) in fracture mechanics. The reason for this surprising similarity is explored using the analysis of the net-section stress increase in fracture mechanics specimens. It is found that the actual role of the finite-width-correction factor in fracture mechanics is to create the stress amplification effect on the finite specimen, having a given crack length, to produce the same K as that of an infinite specimen. The present work demonstrates that the phenomenon of fatigue crack growth can be easily understood on the basis of the accumulated change in net-section strain energy which directly relates to the accumulated work done at the loading ends, which determines the rate of fatigue crack growth. It is a simpler and a physical approach for the accurate description of fatigue crack growth behavior of metals. The approach simultaneously validates the use of fracture mechanics parameters (∆K) for fatigue crack growth, by providing the insight that the physical meaning of stress intensity factor is embedded in the change in the net-section strain energy.

Fatigue crack growth in miniature specimens: The equivalence of ∆K-correlation and that based on the change in net-section strain energy density

In fatigue crack growth experiments of miniature specimens of Ti-6Al-4V alloy, it is shown that the stress intensity factor range (∆K) cannot uniquely correlate the crack growth rates based on the standard stress intensity factor solution, but can only on the basis of the solution for uniformly displaced ends. It also is shown that, remarkably, a similar and strong correlation exists between the change in the net section strain energy amplitude and the rate of fatigue crack growth. The proposed approach is direct and simpler and it throws a new light on the nature of driving force for fatigue crack growth in structural materials.