International Journal of Fracture最新文献

Ni₂MnGa magnetic shape memory alloys (MSMAs) experience the shape memory effect due to magnetic field-induced or mechanical stress-induced microstructure reorientation. However, crack initiation and propagation, influenced by the evolving twin microstructure under coupled magneto-mechanical loading, can significantly hamper its function in applications. This study presents a semi-empirical approach to evaluate fracture toughness and fracture energy in Ni₂MnGa using Vickers microindentation. An improved analytical expression is proposed, extending the classical indentation-based fracture model to incorporate magneto-mechanical effects and microstructural evolution through a stress and field dependent exponential term. Experimental results confirm that the transverse magnetic field facilitates crack growth, decreasing the fracture energy, while axial compressive stress impedes crack growth, increasing the fracture energy of the alloy. The proposed empirical relationship provides configuration-specific fracture energy values for the alloy and contributes to identifying loading conditions least conducive to fracture initiation and growth in MSMAs.

A novel computational analysis is developed to model mode II fracture of a bimaterial specimen in an End Notched Flexure test considering frictional sliding contact between the crack faces. In the Comninou contact model of interface cracks, the frictional contact zone at the tip of an interface crack between dissimilar linear elastic materials entails a stress singularity, which is weaker than the square root singularity. This weak singularity results in a zero Energy Release Rate (ERR) (G_{II}=0) in such cracks. Therefore, the classical Griffith criterion cannot be used to predict crack growth in this case. To address this challenging issue, a new approach based on the Coupled Criterion (CC) introduced by Leguillon (Eur. J. Mech. A/Solids 21, 61-72, 2002), which adopts the Finite Fracture Mechanics (FFM) hypothesis proposed by Hashin (J. Mech. Phys. Solids, 44, 1129-1145, 1996), is developed. The CC is satisfied when both the stress and incremental energy criteria are satisfied simultaneously. A novel CC implementation is required to address the nonlinearity caused by the frictional contact between the interface crack faces, particularly the frictional dissipation of energy during the growth of such interface cracks. The methodology developed involves Finite Element Analysis (FEA) to compute shear stress and relative displacements along the crack path, the change of the potential energy and the energy dissipated by friction. Finally, the implemented CC provides the critical load and finite crack advance at the initiation of crack propagation. The numerical study presented considers various combinations of isotropic materials and friction coefficients.

Accurately analyzing local failure areas, such as penetration or perforation in concrete structures under extreme conditions, such as those caused by shaped charge jet penetration, is of paramount importance for ensuring structural integrity and safety. This study addresses these challenging problems by developing a GPU-parallelized smoothed particle hydrodynamics solver, which incorporates advanced multiphase SPH models, complex constitutive models, and equations of state (EOS) for metal and concrete materials. Enhanced with variable smoothing lengths, this solver improves the accuracy of simulations. Numerical simulations of high-velocity impacts (HVI) on metal and concrete materials were conducted to validate the solver’s capability and precision. The simulations confirmed that shock waves propagate according to material properties, with stable pressure fields and logically coherent crack formations. Comparative analysis with experimental observations demonstrated improved accuracy, with relative errors for depth of penetration (DOP) and average borehole diameter under 5%. Furthermore, parametric tests examining variations in shaped charge geometry and concrete compressive strength showed reasonable variations in crater morphology. These results indicate that the developed SPH solver effectively addresses a wide range of shaped charge jet collision problems and presents a promising alternative to experimental methods for extreme conditions.

The Mode I problem for a semi-infinite crack in an infinite clamped strip, introduced by James R. Rice, is ideal for demonstrating the power of energy methods. This configuration is also appealing to experimentalists, as it is characterized by the energy release rate that does not change as the crack grows. However, under plane strain conditions, the problem leads to an anomalous solution for the energy release rate for incompressible materials. This anomaly is explained and resolved by considering the problem for a long crack in a long strip. The new solution is valid for compressible, nearly incompressible, and incompressible materials.

At present, there is an abundance of results showing that the phase-field approach to fracture in elastic brittle materials — when properly accounting for material strength — describes the nucleation of fracture from large pre-existing cracks in a manner that is consistent with the Griffith competition between bulk deformation energy and surface fracture energy. By contrast, results that demonstrate the ability of this approach to describe Griffith fracture propagation are scarce and primarily restricted to Mode I in the setting of infinitesimally small deformations. Aimed at addressing this lacuna, the main objective of this paper is to show that the phase-field approach to fracture describes Mode III fracture propagation in a manner that is indeed consistent with the Griffith energy competition. This is accomplished via direct comparisons between phase-field predictions for fracture propagation in the so–called trousers test and the corresponding results that emerge from the Griffith energy competition. The latter are generated from full-field finite-element solutions that — as a second main contribution of this paper — also serve to bring to light the hitherto unexplored limitations of the classical Rivlin-Thomas-Greensmith formulas that are routinely used to analyze the trousers test.

The intrinsic strength of rubber, T₀ is one of the key parameters when describing fracture behaviour of elastomer because it is at this specific value of energy that crack growth initiates within loaded rubber material. The Coesfeld Intrinsic Strength Analyzer (ISA) has been established as the most efficient equipment to directly analyse T₀ for various rubber materials. However, to obtain the most reliable and reproducible results it is crucial to understand the influence of boundary conditions of the ISA measuring methodology. Therefore, in this study sets of boundary conditions were chosen to be analysed through mechanical response of reference EPDM material with known T₀ value. For the purposes of this study the effects of individual boundary conditions were compared through directly measured value of intrinsic cutting energy, S₀ which is proportional to T₀. Blade sharpness and geometry showed the greatest impact followed by repetition of blade and specimen milling direction whereas the relaxation time and number of measuring strains showed no significant influence. The results of this study show that the knowledge of blade micro-geometry is at its most importance during the T₀ analyses. Moreover, the data clearly indicates possible future modification of boundary conditions to achieve a very efficient testing procedure with significantly reduced time required for the analyses.

This study investigates the enhancement of fracture toughness in Ti-6Al-4V ELI, fabricated via laser powder bed fusion (LPBF), through a tailored cyclic heat treatment applied below the β-transus temperature to transform the martensitic microstructure into a bimodal configuration. Fracture toughness experiments were conducted using fatigue pre-cracked four-point bend specimens at room temperature, evaluating two orientations in additively manufactured (AM), heat-treated (HT) and wrought (WR) conditions. The findings reveal that stress-relieved AM samples demonstrated good ductility without compromising strength in uniaxial tension tests. However, they exhibited poor fracture toughness and pronounced anisotropy in crack initiation along directions parallel and perpendicular to the build orientation. This behavior is attributed to the (text{Widmanst}ddot{text{a}}text{tten}) microstructure and residual prior (upbeta ) grain boundaries. The cyclic heat treatment significantly enhanced fracture toughness in both orientations. This improvement is attributed to the larger colony size and higher initial strain hardening rate observed in the HT condition, achieving fracture toughness values comparable to wrought Ti-6Al-4V ELI. Fractographic analysis identified void-sheeting as the primary deformation mechanism governing crack propagation across all conditions. EBSD analysis further revealed that hard crystallographic orientations hindered crack initiation and propagation in HT samples. Additionally, ET1 twinning activity near the crack tip played a critical role in improving fracture toughness by blunting the crack tip and limiting its progression. This study offers valuable insights into the microstructural determinants of fracture toughness in additively manufactured Ti-6Al-4V ELI and underscores the potential of strategic heat treatments to achieve mechanical properties comparable to those of wrought materials.

Polymethyl methacrylate (PMMA) is a benchmark brittle material for dynamic crack propagation studies. Despite extensive research, significant inconsistencies persist in reported fracture parameter values, complicating the establishment of a consensus on their sensitivity to the cracking regime. This study aims to rigorously determine these properties while identifying the origins of these discrepancies. To minimize microbranching effects that can strongly influence fracture surface roughness, crack propagation was restricted to subcritical velocities using a strip-band-specimen (SBS) geometry and a dedicated experimental setup. This approach ensured a quasi-steady propagation regime with minimal inertial effects. Dynamic toughness was evaluated using resistance curves constructed from Williams series expansion and displacement fields obtained via digital image correlation (DIC). Fracture energy was assessed through two complementary methods: a global energy balance and an indirect analytical approach based on Irwin’s generalized relation. Two distinct propagation regimes were identified: a stable regime (90 – 180 (hbox {m}.hbox {s}^{-1})) with smooth fracture surfaces and an unstable regime (180 – 320 (hbox {m}.hbox {s}^{-1})) characterized by the emergence of conical microstructures, followed by a transition to fully disrupted propagation beyond 320 (hbox {m}.hbox {s}^{-1}), marking the onset of microbranches. A key outcome of this study is the validation of global fracture energy estimation through the local approach, and vice versa, allowing the derivation of one fracture property from the other – an unprecedented achievement for PMMA in dynamic crack propagation. This was made possible by the experimental setup and specimen geometry, which effectively minimized parasitic effects such as inertia and microbranching. Additionally, the findings confirm a strong correlation between surface roughness and the evolution of fracture energy from the earliest stages of dynamic propagation.

This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. Traditional phase-field models often implement degradation and dissipation functions in terms of the phase-field variable that, despite offering satisfactory results, their physical interpretation and their extension to anisotropic fracture behavior is not always clear. To address this challenge, we develop a framework inspired by the nucleation, growth, and coalescence of microstructural voids to model macroscopic fracture. The proposed approach employs homogenization techniques to calculate the effective material properties when introducing voids of varying sizes and shapes. By solving the homogenization problem for different void geometries, we obtain degradation functions that relate the size of microstructural voids to the homogenized constitutive tensor. These degradation functions provide a direct link between microscale damage mechanisms and macroscale fracture behavior. Comparative analyses with conventional AT1 and AT2 models reveal strong correlations between their response and those obtained via homogenization techniques. This relationship highlights the ability of homogenized models to not only replicate established results but also provide a new understanding of the phase-field variable.

Wedge splitting tests were conducted on a granite and a gneiss with similar mineralogy but different microstructure. The basic properties of the two rock types were characterized by petrographic analyses and mechanical tests. The granite specimens were split in one material direction, perpendicular to the rift plane, and the gneiss specimens were split in three different material directions, parallel and perpendicular to the foliation (and along and across a lineation). The effect of having a large blunt versus a sharp notch on the crack initiation was studied in the granite. The wedge splitting tests are unconventional for testing rocks and allowed to study the crack initiation and propagation under mode I loading condition in the quasi-brittle granite and brittle gneiss. The fracture energy and strain energy release rate were calculated. The strain energy release rate for gneiss, when splitting along and across the foliation, was around 45% and 60% of the values for the structurally isotropic granite. The fracture toughness was calculated from the strain energy release rate and was larger than corresponding values obtained from linear elastic fracture mechanics (LEFM). There was an effect on the early cracking stages by using a sharp notch compared with using a large blunt notch on the granite specimens, but the required largest force to split the specimens remained the same for the two notch types. The crack initiation started at a splitting force corresponding to 78% and 90% of the maximum splitting force on the specimens with a sharp notch and a large blunt notch, respectively. The results with a full force-displacement response during the crack propagation obtained for the brittle gneiss are unique. Most fracture mechanics results on rock materials are obtained from standard tests and LEFM and not via the measured strain energy release rate.