Traditional Linear Elastic Fracture Mechanics Research Articles

Investigation of fracture performance of asphalt mixtures considering size effect law and equivalent crack propagation law

The integration of the Size Effect Law (SEL) and the equivalent Linear Elastic Fracture Mechanics (LEFM) in characterizing the fracture behavior of asphalt mixtures has received limited attention. This study presents a preliminary exploration into the application of equivalent LEFM on the fracture characteristics of two asphalt mixtures, AC10 and AC16, accounting for variations in specimen size. Semi-circular Bending (SCB) tests were conducted on specimens with four different diameters (D = 76 mm, 100 mm, 125 mm, and 150 mm) and three notch-to-radius ratios (α = 0.2, 0.4, and 0.6) at a temperature of −10 °C. The equivalent crack propagation (ECP) length, crack growth resistance, and the size of the Fracture Process Zone (FPZ) were determined and subjected to analysis. The findings revealed a size effect on the ECP length, crack growth resistance, and FPZ size, with an increase in specimen size leading to a corresponding increase in these parameters. Conversely, an increase in α resulted in a decrease in all three types of data. A power law relationship was established between the ECP length and crack growth resistance. It was observed that AC16 demonstrated superior fracture resistance compared to AC10, particularly in terms of crack growth resistance. The initial notch length, ECP length, and FPZ size were found to be of the same order of magnitude, suggesting that the equivalent LEFM can produce more accurate fracture results under low temperatures than the traditional LEFM.

A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis

This study investigated the relationship between fracture toughness (Kc) and energy release rate (Gc) through fracture morphology analysis, emphasizing the critical role of fractal dimensions in accurately characterizing fracture surfaces. Traditional linear elastic fracture mechanics (LEFM) models relate Gc to Kc by combining energy principles with the nominal area of the fracture surface. However, real materials often exhibit plasticity, and their fracture surfaces are not regular planes. To address these issues, this research applied fractal theory and introduced the concept of ubiquitiform surface area to refine the calculation of fracture surfaces, leading to more accurate estimates of Gc and Kc. The method was validated through standard compact tensile specimen tests on a nickel-based superalloy at 550 °C. Additionally, the analysis of fractal dimension differences and dispersion in various fracture regions provides a novel perspective for evaluating the fracture toughness of materials.

A digital twin feasibility study (Part I): Non-deterministic predictions of fatigue life in aluminum alloy 7075-T651 using a microstructure-based multi-scale model

The Digital Twin (DT) concept has the potential to revolutionize the way systems and their components are designed, managed, maintained, and operated across a vast number of fields from engineering to healthcare. The focus of this work is the implementation of DT for the health management of fatigue critical structures. This paper is the first part of a two-part series. The second part focuses on the use of in-situ diagnostics to reduce uncertainty in fatigue life predictions once a life-limiting fatigue crack has reached the point where it is observable. In contrast, the focus of this work is to form a non-deterministic prediction of fatigue life prior to the accumulation of observable damage, a condition that often dominates the majority of a component or system’s lifetime. This predictive capability is enabled by a DT framework that simulates crack growth from initiation to failure using microstructure-based, multi-scale modeling. Two models are used in this work, one that incorporates microstructure explicitly and one that uses more traditional linear elastic fracture mechanics. The models are joined by a transition crack length between the micro- and macroscales, which facilitates both the coupling of fatigue life predictions and the transference of uncertainty across scales. The ability to predict fatigue life under uncertainty and across scales is demonstrated in the context of a geometrically complex, metallic test specimen subjected to uniaxial fatigue loading. Conclusions are drawn regarding the feasibility of the approach as a DT-based health management method.

Fretting fatigue lifetime estimation using a cyclic cohesive zone model

Abstract Over the past decades, many numerical procedures aiming to predict the life of components subjected to fretting fatigue have been developed. Most procedures combine estimates of crack initiation and propagation lives in order to obtain total lifetime. Nevertheless, crack initiation life estimates are generally not easy to define. An alternative is to consider the failure in a cycle-by-cycle analysis using cyclic cohesive zone model (CCZM), accounting for loading and unloading damage accumulation at crack front. However, a cycle-by-cycle analysis is extremely computational demanding. To overcome this issue, we propose an extrapolation procedure in junction with CCZM for the crack propagation modelling, which is substantially faster than a complete cycle-by-cycle analysis. This approach is compared, in terms of accuracy of life estimates, to traditional linear elastic fracture mechanics and experimental data.

Fracture Parameters of Cement Mortar with Different Structural Dimensions Under the Direct Tension Test.

In this paper, we measured the fracture properties of cement mortar—which is composed of sand and has a nearly constant diameter—using a direct tension test. Four double-notched mortar bar specimens with different structural dimensions were assessed. The failure load, load-crack mouth opening displacement, and elongation of the gauge length were measured under direct displacement control. The fractured surfaces were scanned and measured so that we could calculate the tensile strength accurately and determine the fracture energy and characteristic length. The average ratio of total fracture energy (GF) to specific fracture energy (Gf) was 1.94; this was lower than the typical value for concrete, of 2.5. The direct tension test showed that the double-notched mortar specimens had a smaller fracture processing zone after the initiation of tensile cracks, so the tail portion of the softening branch was small. This decreased the GF/Gf ratio. We verified this result based on a nonlinear fracture mechanics simulation and found that it agreed well with our experimental results. We also investigated the size effects of four different scaled specimens while holding the ratio of structural dimension, d, and notch length, a is constant, so that there was no shape effect. The traditional linear elastic fracture mechanics (LEFM) prediction and Bažant’s size effect law yield a gradient closer to 1/2 in the case of relatively large specimens. In the case of our cement mortar specimens, this prediction was not supported, where the value of the slope was 1/0.727. This was unexpected because LEFM predicts strong size effects. One possible explanation for this result is that the size effects of concrete are most often evaluated using a bending test; also, concrete has a larger maximum aggregate size than mortar. Due to the random heterogeneities in aggregate distribution, higher tail energies may be seen for concrete, leading to differences in the GF/Gf ratio. At the same time, the peak tensile stress could be affected by the relationship between structural dimensions and aggregate size.

Viscoplastic crack initiation and propagation in crosslinked UHMWPE from clinically relevant notches up to 0.5mm radius.

Highly crosslinked UHMWPE is now the material of choice for hard-on-soft bearing couples in total joint replacements. However, the fracture resistance of the polymer remains a design concern for increased longevity of the components in vivo. Fracture research utilizing the traditional linear elastic fracture mechanics (LEFM) or elastic plastic fracture mechanics (EPFM) approach has not yielded a definite failure criterion for UHMWPE. Therefore, an advanced viscous fracture model has been applied to various notched compact tension specimen geometries to estimate the fracture resistance of the polymer. Two generic crosslinked UHMWPE formulations (remelted 65kGy and remelted 100kGy) were analyzed in this study using notched test specimens with three different notch radii under static loading conditions. The results suggest that the viscous fracture model can be applied to crosslinked UHMWPE and a single value of critical energy governs crack initiation and propagation in the material. To our knowledge, this is one of the first studies to implement a mechanistic approach to study crack initiation and propagation in UHMWPE for a range of clinically relevant stress-concentration geometries. It is believed that a combination of structural analysis of components and material parameter quantification is a path to effective failure prediction in UHMWPE total joint replacement components, though additional testing is needed to verify the rigor of this approach.

On the toughness measurement for ductile polymers by orthogonal cutting

The fracture toughness, Gc, of three commercial polymers (HDPE, PP and PEEK) has been determined using a cutting test method. The traditional linear elastic fracture mechanics tests were conducted for comparison. The results showed that the cutting analysis is capable of giving valid fracture data for ductile polymers. However, when the cut depth is small, e.g. less than 100μm, an inverse size effect on Gc was observed in cutting, i.e. the measured toughness of the polymers tends to decrease with the decrease of the cutting depth. Possible mechanisms for such a scale effect on fracture energy are discussed.

Numerical analysis of surface crack propagation in flexible pavements using XFEM and cohesive zone model

Surface initiated (top-down) cracking in the longitudinal direction of pavements has become a predominant mode of failure in thick asphalt pavements. Most previous researchers studied crack propagation using the traditional Linear Elastic Fracture Mechanics (LEFM) method by calculating the stress intensity factor around the crack tip. In this paper, Extended Finite Element Method (XFEM) was used to study the key factors causing surface initiated crack propagation under surface tension and/or shear. A two-dimensional (2-D) finite element (FE) model for a two-lane flexible pavement was built to predict pavement responses and crack propagation potential under various scenarios. It was found that surface tension is the major driving force for crack propagation when the crack is at some distance away from tire loading. The results show that the distance from the location of crack to tire loading, the depth and direction of the crack, and the modulus ratio between the hot-mix asphalt (HMA) layer and the base layer have significant influences on crack propagation under surface tension. On the other hand, this study shows that shear stress can induce surface initiated crack propagation near the loading area as the shear resistance of material becomes low at the high temperature.

Quantitative Acoustic Emission Fatigue Crack Characterization in Structural Steel and Weld

The fatigue crack growth characteristics of structural steel and weld connections are analyzed using quantitative acoustic emission (AE) technique. This was experimentally investigated by three-point bending testing of specimens under low cycle constant amplitude loading using the wavelet packet analysis. The crack growth sequence, that is, initiation, crack propagation, and fracture, is extracted from their corresponding frequency feature bands, respectively. The results obtained proved to be superior to qualitative AE analysis and the traditional linear elastic fracture mechanics for fatigue crack characterization in structural steel and welds.

Simulation-based strategies for microstructure-sensitive fatigue modeling

Further efforts to provide more direct dependence of fatigue life estimation methods on microstructure of alloy systems must consider various factors that are not explicitly addressed by conventional fatigue design tools such as the strain-life curve, the stress-life curve, the modified Goodman diagram, or fatigue limit concepts, or by traditional linear elastic fracture mechanics approaches. In this work, we offer insight from micromechanical perspectives on tradeoffs of fatigue crack formation and growth regimes in low cycle and high cycle fatigue, including considerations of effects of notches of various scales. Relations between remote loading conditions and microstructure-scale cyclic plasticity/crack behavior are considered as a function of stress amplitude and microstructure to support assessment of intrinsic microstructure fatigue resistance (percolation limits for connected microplasticity) as well as effects of extrinsic features such as non-metallic inclusions. Algorithms are summarized for computing nonlocal cyclic plastic shear strain and inferring fatigue resistance, both in terms of mean behavior and variability with microstructure. Several applications are presented, including intrinsic and extrinsic fatigue resistance of Ni-base superalloys, fatigue of polycrystals, cast A356-T6 Al alloy, and fretting fatigue of Ti–6Al–4V.

Macroscopic measure of the cohesive length scale: Fracture of notched single-crystal silicon

We study atomistically the fracture of single-crystal silicon at atomically sharp notches with opening angles of $0\ifmmode^\circ\else\textdegree\fi{}$ (a crack), $70.53\ifmmode^\circ\else\textdegree\fi{},$ $90\ifmmode^\circ\else\textdegree\fi{}$ and $125.3\ifmmode^\circ\else\textdegree\fi{}.$ Such notches occur in silicon that has been formed by etching into microelectromechanical structures and tend to be the initiation sites for failure by fracture of these structures. Analogous to the stress intensity factor of traditional linear elastic fracture mechanics which characterizes the stress state in the limiting case of a crack, there exists a similar parameter K for the case of the notch. In the case of silicon, a brittle material, this characterization appears to be particularly valid. We use three interatomic potentials; that which gives critical K values closest to experiment is the modified embedded atom method (MEAM). Because the units of K depend on the notch angle, the shape of the K versus angle plot depends on the units used. In particular when an atomic length unit is used the plot is almost flat, showing---in principle, from macroscopic observations alone---the association of an atomic length scale to the fracture process. Moreover the normal stress on the actual fracture plane at this distance from the notch tip turns out to be even flatter and emerges as a possible fracture criterion, namely 33 MPa at a distance of one \AA{} (for MEAM silicon).

On the Growth of Small Fatigue Cracks in Two Squeeze-Cast Aluminum Alloys

It is now recognized that the fatigue lifetime of many structural components is determined by the rate of growth of small fatigue cracks. However it is not a straightforward matter to analyze the growth of these small cracks through the use of a traditional linear-elastic fracture mechanics approach for the following reasons: (1) on going from the micro-crack growth range to the macro-crack growth range, fatigue crack growth behavior undergoes a transition from stress control to stress intensity factor control; (2) because of the large plastic zone size to crack length ratio in the small crack growth regime, crack growth is elastic-plastic in nature rather than linear-elastic, and (3) the crack closure level increases from zero up to the level associated with a macroscopic fatigue crack as the fatigue crack increases in length in the small crack regime. The present paper presents an analysis of short crack growth data in two squeeze-cast aluminum alloys, and also discusses the Nisitani-Goto elastic-plastic relationship for fatigue crack growth.

On the fatigue behavior of γ-based titanium aluminides: role of small cracks

Gamma-TiAl based alloys have recently received attention for potential elevated temperature applications in gas-turbine engines. However, although expected critical crack sizes for some targeted applications (e.g. gas-turbine engine blades) may be less than ∼500 μm, most fatigue-crack growth studies to date have focused on the behavior of large (on the order of a few millimeters) through-thickness cracks. Since successful implementation of damage-tolerant life-prediction methodologies requires that the fatigue properties be understood for crack sizes representative of those seen in service conditions, the present work is focused on characterizing the initiation and growth behavior of small ( a∼25–300 μm) fatigue cracks in a γ-TiAl based alloy, of composition Ti–47Al–2Nb–2Cr–0.2B (at.%), with both duplex (average grain size of ∼17 μm) and refined lamellar (average colony size of ∼145 μm) microstructures. Results are compared to the behavior of large ( a>5 mm), through-thickness cracks from a previous study. Superior crack initiation resistance is observed in the duplex microstructure, with no cracks nucleating after up to 500 000 cycles at maximum stress levels ( R=0.1) in excess of the monotonic yield stress, σ y. Comparatively, in the lamellar microstructure cracks nucleated readily at applied maximum stresses below the yield stress (85% σ y) after as few as 500 cycles. In terms of crack growth, measurements for small fatigue cracks in the duplex and lamellar microstructures showed that both microstructures have comparable intrinsic fatigue-crack growth resistance in the presence of small flaws. This observation contrasts previous comparisons of large-crack data, where the lamellar structure showed far superior fatigue-crack growth resistance than the duplex structure. Such “small-crack effects” are examined both in terms of similitude (i.e. crack tip shielding) and continuum (i.e. biased microstructural sampling) limitations of traditional linear elastic fracture mechanics.

Reliability of Electroless Processed Thin Layered Solder Joints

AbstractThere has recently been an increasing interest in using electroless processes to produce the metal thin film stacks that make up the bond pads in solder ball grid array (BGA) packages. Electroless processes produce a more uniform and better controlled film thickness, but the resulting metal stacks have exhibited less mechanical reliability than that of traditional electrolytic stacks. This paper addresses a layered system consisting of a eutectic Sn-Pb solder sandwiched between stacks of Cu, Ni, and Au thin films. The samples were tested to determine cyclic fatigue behavior and fracture toughness values using traditional linear elastic fracture mechanics techniques. Surprisingly, fatigue crack propagation occurred in the middle of the solder layer even though the electroless interface was expected to be very weak. In contrast, fracture tests did appear to cause failure near an interface, but not necessarily at the electroless interface. Fracture toughness values measured for these samples were much lower than those reported for bulk metals. These results are discussed in terms of the microstructures present in order to determine possible relationships between the microstructure of the solder joint and its fracture behavior.

Basic issues in the mechanics of high cycle metal fatigue

Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach. Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.

On the variation of the stress intensity factor along the front of a surface flaw

Stress intensity factors along the front of semicircular and part-circular surface flaws in bodies under uniform tension and under pure bending have been determined by photoelastic stress freezing and compared to other solutions. The variation of K1 reflects the change in the stress singularity λ, from 0.5 at the deepest point to 0.3 at the surface. The importance of the results on the evaluation of crack growth using traditional linear elastic fracture mechanics is discussed.