International Journal of Fracture最新文献

The compliance method is widely used to measure crack length during testing of fracture mechanical properties such as fracture toughness and fatigue crack growth rate. Traditionally, the compliance is obtained from the load/deflection records. We present a time domain based differential compliance method, in which the compliance is obtained directly from the vibration waveform of a simple resonance assembly. The compliance computation from time domain signal offers high resolution and low noise providing unprecedented possibilities such as so called “rate-control” testing with fatigue frack growth rate directly controlled by a closed loop system. The differential approach enables to significantly reduce the effect of specimen clamping and material property changes during the test. The method has been utilized in many research project and its gradual development was described in several papers. This, paper, however, for the first time, summarizes and updates all important details of the technique necessary for its implementation as well as the derivation of the used vibrational model. It also describes the advantages and disadvantages of the method and its application potential in testing materials resistance to fatigue crack growth.

The fracture toughness of soft polymeric materials can be enhanced by inducing energy dissipation. While dissipation may be introduced through various chemical or physical mechanisms, at the continuum scale it is manifested in the hysteresis under a loading-unloading cycle. Such inelastic behavior, resembling the Mullins effect in filled rubber, may lead to ambiguities in the interpretation of fracture toughness measurements. Here we use finite element simulations to elucidate the mechanics of crack growth in soft inelastic solids. Specifically, we consider the pure shear configuration and adopt a phenomenological model to capture the Mullins effect. It is found that the apparent energy release rate continues to increase after the crack growth is initiated, resulting in a crack growth resistance curve. The physical origin of the resistance curve is attributed to the formation and expansion of a damage zone surrounding the crack tip. We use the simulation results to illustrate how the resistance curve is related to the force-stretch curve as well as their dependence on sample dimensions. Moreover, we discuss the interpretation of fracture toughness based on the resistance curve and the force-stretch curve. Our results can provide guidance to experimental characterization of fracture toughness in soft inelastic solids.

Under high-temperature adverse environments, the premature failure of air plasma spray thermal barrier coatings (APS-TBCs) is a preliminary phenomenon that can significantly limit the application of TBCs in gas turbine engines. The delamination failure of TBCs typically occurs at the interfaces between the topcoat and bond coat due to thermal mismatch stress and thermal gradient, resulting in crack propagation and final spallation failure of the coating. This paper undertakes a study of the delamination of TBCs using multi-physics methodologies. Heat transfer was cyclically implemented into the TBC model, resulting in a thermal gradient, to simulate the in-service operation of the TBC system. A variational-based sintering model for a topcoat of TBCs is incorporated into the simulation. The high-temperature creep model of the topcoat, thermal growth oxide (TGO) and bond coat is included. The stress field across the TBCs was calculated during the thermal cycles, with the location of high-stress concentration selected as the potential crack initiation site. Phase field damage modelling was conducted to study crack propagation, initially located at the high-tensile stress off-peak interface. Results indicate that at the off-peak interface, the crack propagates rapidly in the top right direction during the first few cycles, then stops propagating as the TGO thickens, because the location of the maximum principal stress is moved away from the interface. Since the accumulated stress at the crack tip at the end of cycles, cracks have the potential to propagate with a prolonged thermal cycle service.

Architected lattice materials (ALM) have gained significant attention due to their superior mechanical properties compared to conventional bulk metals. However, limited studies in the literature focus on modeling the fracture behavior of ALM structural elements, particularly using beam kinematics coupled with phase-field (PF) damage models to reduce computational costs than analyzing an equivalent 2D model. The present study develops a beam-based PF model using Timoshenko beam theory to simulate localized damage evolution in brittle ALM grids. The proposed model employs a homogenized damage function to capture the overall damage state across the beam cross-section, bypassing the need to resolve damage variations within the section. Two damage approximation functions, constant and parabolic, are explored to describe damage across the cross-section. Damage evolution is attributed to a combination of tensile axial energy, shear energy, and a fraction of flexural strain energy. A series of numerical simulations, from isolated beam tests to full-scale ALM grid analyses, demonstrate the efficacy of the proposed model. Results indicate that the fraction of flexural strain energy((alpha )) influencing damage evolution varies with the beam’s depth-to-length ratio, while boundary conditions show negligible impact on (alpha ) for a fixed ratio. Model validation through comparisons with 2D simulations and experimental data highlights accurate predictions of load-displacement responses and crack patterns. Moreover, the proposed approach achieves significant computational efficiency, reducing the degrees of freedom for the lattice system from 3.2 million in a 2D model to just 58,000. Correspondingly, computational time decreases from 14 hours and 43 minutes to only 7 minutes and 20 seconds. These results underscore the potential of the proposed beam-based PF model as a computationally efficient and accurate tool for analyzing damage behavior in ALM.

This paper investigates the stress singularity at the crack tip in a two-dimensional Neo-Hookean hyperelastic material, with a focus on how far-field strain influences the crack tip field distribution. The study demonstrates that, under small far-field strains, the crack tip field can be generally divided into three regions: Region I—the asymptotic neo-Hookean crack tip field as (rrightarrow 0); Region II—a finite-radius nonlinear neo-Hookean zone; and Region III—an outer linear elastic region. Within Region III, a subregion may still obey the asymptotic linear elastic solution when the radial distance is sufficiently small. As the far-field strain increases, both the asymptotic linear subregion and the broader linear region shrink and eventually vanish, leaving only the nonlinear zones. This multiscale structure reflects the principle of small-scale nonlinearity, wherein nonlinear effects are confined to an inner core. The inner core consists of Region I, where asymptotic neo-Hookean fields dominate, and Region II, where general nonlinear effects prevail. Initially, this inner core is nested inside Region III. At sufficiently small far-field strains, Region III itself contains an inner core that follows asymptotic linear elastic crack tip fields. As loading intensifies, Regions I and II expand, and Region III—first its asymptotic core, then the broader linear zone – .- progressively diminishes, culminating in a large-scale nonlinearity regime. We also identify and quantify the characteristic length scales over which each region exists and dominates—nonlinear fields in Regions I and II and linear elastic behavior in Region III. An important point is that at the crack tip, Region I always governs the local field, although its extent may be small under small far-field strains, making it difficult to capture in computational simulations. To address this, we introduce a rescaling method to better resolve this near-tip behavior.

This paper presents a novel failure evaluation method for fracture instability analysis of ring-stiffened titanium alloy cylinders under hydrostatic pressure. The quantification of fracture instability behavior for a titanium alloy cylinder remains unclear. In this work, we propose a post-buckling mode analysis for fracture instability, considering the relationship between plastic strain and structural deformation. Further, a novel fracture failure criterion involving material properties and structural parameters is established, bringing the proposal of a structural failure range evaluation method for titanium alloy cylinders. By incorporating the strain rate effect into the constitutive model of the two-phase (alpha +beta ) titanium alloy Ti-6Al-4 V, we developed a dynamic finite element model for studying the fracture instability of the titanium alloy cylinder. The theoretical results and finite element simulation results are finally verified by the collapse experiment of a titanium alloy cylinder. The findings can provide a fundamental basis for designing and service safety evaluation of titanium alloy cylinders.

The tensile strength and fracture properties of concrete play a vital role in the design of large concrete structures. These properties are evaluated from indirect tests on small-sized specimens. As concrete is known to exhibit a strong size effect, it is important to evaluate these properties from large-sized specimens through a direct tension test. In this research, we perform direct tension tests on large-sized concrete specimens under displacement control. The conditions under which the specimens have to be prepared and tested, and the challenges faced are highlighted. It is seen that the tensile strength is almost half the values that are suggested in major codes of practice. Important elastic and fracture properties under direct tension, including tensile strength, fracture toughness, fracture energy, critical crack mouth opening displacement, critical crack length, and softening law parameters, which find application in non-linear finite element models, are evaluated.

In the first part of the companion paper, experimental procedures for conducting direct tension tests on large concrete specimens were discussed, together with the fracture properties and size effects. In this paper, we delve into the details of micromechanisms of fracture and failure in concrete under direct tension using digital imaging and acoustic emission (AE) techniques. The surface cracking characteristics are obtained from imaging, while the evolution of microcracks in the fracture process zone (FPZ) are predicted through AE events and energy. The differences in microcrack initiation, and their coalescence to form macrocracks for different sizes of specimens are explained, and the size of the FPZ is estimated. It is concluded that in large-size specimens, the size of FPZ is relatively smaller with the formation of microcracks, their coalescence to form macrocracks, and the propagation of the final crack taking place almost simultaneously, leading to a brittle failure.

In practical projects, concrete members are often subjected to multiple axial stress states, and the actual fracture process is more complex. This study utilizes a novel gap tensile test method and two-dimensional random circular aggregate mesoscopic numerical simulation to investigate notched concrete fracture characteristics. On the basis of Bažant's Type II size effect law (SEL) and linear elastic fracture mechanics (LEFM), fracture parameters such as fracture energy, notch tensile strength, and fracture toughness of concrete under biaxial tensile stress were obtained. The results indicate, compared with uniaxial loading, that crack–parallel tensile stress significantly affects the key fracture parameters of concrete. As the crack–parallel tensile stress increases, the peak fracture load of all the concrete samples tend to monotonically decrease. Compared with that when the normalized crack–parallel tensile stress η = 0, the peak load decreases by approximately 5, 20, and 40% when η is 0.19, 0.38, and 0.57, respectively, for different specimen dimensions. When the normalized crack–parallel stress increases to 0.57, the fracture energy, fracture toughness, and notch tensile strength decrease by approximately 30–80%. The crack–parallel tensile stress induces predamage in the weak interfacial transition zone (ITZ) of the concrete, leading to a reduction in the load-bearing capacity. Likewise, it can be expected that this degradation effect will be even more severe in low-strength concrete.

We propose a method for quantifying the competition between tunnel and delamination cracking in laminates. Based on the analytical relation between the compliance derivative and the energy release rate, which we refer to as the compliance method, the competition between the two damage mechanisms is investigated based on compliance maps that may be precomputed, thus providing an efficient tool for predicting damage development in laminates without ad hoc fracture simulations. Tunnel and delamination cracking in an off-axis layer, much thinner than the load-carrying layers of a laminate, are used as an example to illustrate the proposed methodology. However, the compliance method is generalizable to any parameterizable cracking mechanism. The cracks are simulated in a specialized two-dimensional off-axis finite element framework, which fully captures the three-dimensional solution. The method is validated against the energy balance method for tunneling cracks and the virtual crack closure technique for delamination cracks. The method has great potential in the context of nondestructive testing, where future damage states can be predicted from precomputed or experimentally determined compliance maps, thus reducing computational and experimental costs.