mode-I Fractures Research Articles

Fracture toughness of alkali-activated concrete subjected to aggressive environment

This study investigates the fracture toughness of alkali-activated granulated blast-furnace slag (GBFS)-based geopolymer concrete (GPC), non-activated slag cement concrete, and ordinary Portland cement (OPC) concrete in acidic, alkaline, and chloride solutions over six months. A total of 580 centrally straight-notched Brazilian disc (CSNBD) specimens were cast to assess pure mode-I (0°), pure mode-II (28.7°), and mixed-mode (15° and 45°) fractures under these conditions. Microstructural analyses (SEM) were performed to evaluate microstructural changes after six months of exposure. Results showed that GPC exhibited the lowest initial fracture toughness but the smallest reduction (7 %-11 % depending on the mode) across all environments, with slag cement concrete and OPC experiencing reductions of 11 %-14 % and 14 %-21 %, respectively, in acidic conditions. In alkaline environments, GPC showed a 3 %-6 % decrease in fracture toughness, while OPC and slag cement concrete showed reductions of 6 %-13 %. The gradient boosting regressor accurately predicted the failure load of CSNBD specimens, achieving an R² score of 0.948. Finally, SHAP sensitivity analysis identified concrete type, exposure time, and environment as critical input features, consistent with experimental results.

Mixed-mode thermo-mechanical fracture: An adaptive multi-patch isogeometric phase-field cohesive zone model

This work presents an adaptive phase-field cohesive zone model (PF-CZM) for simulating mixed-mode crack nucleation and growth in isotropic rock-like materials subjected to thermo-mechanical interactions. The proposed approach combines an adaptive multi-patch isogeometric analysis (MP-IGA) and length-scale insensitive PF-CZM. The formulation captures the distinct critical energy release rates for Mode-I and Mode-II fractures, which is crucial for predicting mixed-mode thermo-mechanical fracture behavior in isotropic rock-like materials. The PF-CZM governing equations are solved with isogeometric analysis based on locally refined non-uniform rational B-splines (LR NURBS), and the complex structural geometry is exactly described with multiple LR NURBS patches. The field variables, such as displacement, phase-field, and temperature at the interface of adjacent patches, are coupled using Nitsche’s method. To enhance the computational efficiency while maintaining accuracy, a refinement-correction adaptive scheme combined with the structured mesh refinement strategy is developed. The proposed framework is validated against recent numerical and experimental results in the literature, particularly in the context of capturing complex behavior of mixed-mode crack propagation in isotropic rock-like materials subjected to thermo-mechanical loading.

Ice Adhesion Characterization Using Mode-I and Mode-II Fracture Configurations

Abstract The ice buildup on airborne structures operating in cold weather conditions has detrimental impacts on their safety and performance. Due to practical applications, there has been a significant interest in ice removal strategies. However, the current body of literature lacks comprehensive insights into the mechanistic aspects of the ice adhesion/breakage process, resulting in a wide range of reported adhesion strengths that differ by two orders of magnitude. To address this gap, we employed a fracture mechanics-based approach to investigate the fracture behavior of a typical ice/aluminum interface in terms of mode-I and mode-II fractures. We examine a range of surface roughness values spanning from 0.05 to 5 micrometers. An experimental framework employing a single cantilever beam and direct shear tests were developed. The near mode-I and mode-II interfacial fracture toughness and strength values were extracted from the experimentally measured force and displacement by both analytical and numerical models employing cohesive surfaces. The combined experimental and numerical results show that ice adhesion is primarily driven by cohesive interfacial failure, which exhibits almost mode-independent fracture behavior. Mode-I fracture shows directional instability of crack propagation, which is attributed to thermally induced residual tensile stress at the ice layer-substrate interface. The fractographic inspection reveals similar ice-grain size over the examined range of substrate roughness values. For the examined range of surface roughness and temperature, which induces the Wenzel state with full surface wetting at the interface, the ice adhesion is insensitive to the interfacial roughness in both mode-I and mode-II fracture.

Lithological controls on fault damage zone development by coseismic tensile loading

During subshear earthquake rupture opposing sides of the fault experience transient impulses of tensile and compressive peak mean normal stresses exceeding the strength of the rock resulting in off-fault damage. This damage is expected to be influenced by lithology and occur preferably on the nominally tensile side of ruptures because rocks are weaker in tension than compression. Whereas the static tensile strength of many rocks is known, our capacity to relate parameters used to quantify brittle deformation in fault damage zones commonly measured in the field, including fracture density and fragment size, to earthquake rupture conditions is poor. This is due to a lack of experimental data relating tensile strength, fracture density, and fragment size to lithology under transient loading conditions. To relate brittle damage to coseismic tensile loading conditions, we use a modified sample configuration for a Split Hopkinson Pressure Bar (SHPB) designed to induce tensile rock fragmentation. Experiments cover a range of rock types including granite, diabase, welded tuff, and sandstone. All crystalline rocks fail predominantly via mode-I fracture, while sandstone fails through localized dilation bands, distributed pore space expansion, and less common mode-I fractures. Measurements of fracture density, fragment size, and porosity change are compared to tensile strength and strain rate at failure. We derive empirical relationships for (1) the transition from fracture to dilation banding as a function of initial porosity and (2) the strain rate dependence of tensile strength. These empirical relationships are used to estimate the rock strength during earthquake rupture on the side of the fault loaded under tension for comparison to predicted stress decay with distance from a fault to estimate the lithology dependent extent and nature of coseismic fault damage. Our experiments offer new insights into the lithological controls on the formation of asymmetric fault damage zones by dynamic rupture.

Atomistic simulation of the effect of the dissolution and adsorption of hydrogen atoms on the fracture of α-Fe single crystal under tensile load

The local hydrogen distribution has significant influences on hydrogen embrittlement. In this work, mode-I fractures of (010)[100] pre-cracked α-Fe single crystal containing dissolved and absorbed hydrogen atoms are simulated by molecular dynamics and the time-stamped force-bias Monte Carlo methods. Statistics show that when located near the {112} plane, hydrogen atoms accelerate cleavage fracture and suppress the slip of {112}<111>; when located on the {110} plane, they promote martensite transformation and increase {110}<111> slip. Most adsorbed hydrogen atoms are concentrated near the inside of the crack surface and suppress fracture early by stress relaxation; therein concentrates stresses inside the matrix, and causes microvoid-coalescence fracture.

Fracture toughness analysis of HCCD specimens of Longmaxi shale subjected to mixed mode I-II loading

Longmaxi shale exhibits strong anisotropy due to its bedding planes induced by diagenesis. The anisotropic properties of shale have a significant effect on the stability control of geotechnical engineering. To investigate the influence of anisotropy of shale on its mixed mode fracture toughness, we performed Brazilian disc splitting tests on hollow center cracked disc shale specimens with different bedding and crack inclination angles (α and β, respectively). In this study, the fracture toughness of Longmaxi shale was calculated by the finite element method combined with either the J-integral or crack tip-opening displacement method. The results show that the dimensionless stress intensity factors and β values for pure mode-I and mode-II fractures both show anisotropic behavior by varying α. For all combinations of mode-I and mode-II loading, the fracture toughness also exhibits anisotropy by varying α; the mode-I fracture toughness decreases with increasing α when β > 30°, and the anisotropy is negligible for β = 0°. The anisotropy for mode-II fracture toughness is weak when β is small or large, whereas the anisotropy is significant when β = 45° and 60°. The effect of α on mode-I fracture toughness is greater than that on mode-II fracture toughness when β is small or large. Further, a comparison of four mixed-mode fracture criteria with the experimental results shows that the maximum tangential stress criterion for a transversely isotropic body can predict the mixed-mode fracture behavior of Longmaxi shale well. At the same time, it is suggested that the role of the T-stress should be considered to obtain more accurate prediction results.

The effects of a tectonic stress regime change on crustal-scale fluid flow at the Heyuan geothermal fault system, South China

The South China, Heyuan Fault Zone provides unique crustal exposure to study the meso- macroscale architecture of evolving fracture networks in response to a change in tectonic stress regime and associated changing fluid flow pathways. Multiple generations of fracturing across the fault zone reveal its structural evolution related to the change in stress regime from extensional (since the Mesozoic) to transpressive (in the Cenozoic), which coincides with generations of growth and fracturing on the microscale. Low angle, mode-I fractures, quartz veining, and a giant quartz reef (>75 m wide and 40 km long) were formed due to a combination of chemo-mechanical mechanisms, including a crucial phyllonite ‘cap rock’, during the extensional phase. This evolved through to a predominately sub-vertically aligned, shear fracture network, exhibiting only minor quartz precipitation. These open fractures are attributed to the transpressive regime experienced since the Cenozoic, in which strike-slip faults cross-cut the Heyuan Fault. We propose that this sub-vertical fracture network provides the fluid flow pathway supplying the present-day hot springs by penetrating through the phyllonite seal, which previously enabled SiO2 accumulation. Additionally, further quartz-reef building would likely be reduced due to (i) lack of seal integrity, and (ii) an unfavourable tectonic setting to channel the flow and provide accommodation space.

Healable, memorizable, and transformable lattice structures made of stiff polymers

Emerging transformable lattice structures provide promising paradigms to reversibly switch lattice configurations, thereby enabling their properties to be tuned on demand. The existing transformation mechanisms are limited to nonfracture deformation, such as origami, instability, shape memory, and liquid crystallinity. In this study, we present a class of transformable lattice structures enabled by fracture and shape-memory-assisted healing. The lattice structures are additively manufactured with a molecularly designed photopolymer capable of both fracture healing and shape memory. We show that 3D-architected lattice structures with various volume fractions can heal fractures and fully restore stiffness and strength over two to ten healing cycles. In addition, coupled with the shape-memory effect, the lattice structures can recover fracture-associated distortion and then heal fracture interfaces, thereby enabling healing of lattice wing damages, mode-I fractures, dent-induced crashes, and foreign-object impacts. Moreover, by harnessing the coupling of fracture and shape-memory-assisted healing, we demonstrate reversible configuration transformations of lattice structures to enable switching among property states of different stiffnesses, vibration transmittances, and acoustic absorptions. These healable, memorizable, and transformable lattice structures may find broad applications in next-generation aircraft panels, automobile frames, body armor, impact mitigators, vibration dampers, and acoustic modulators.

Karstification and fluid flow in carbonate units controlled by propagation and linkage of mesoscale fractures, Jandaíra Formation, Brazil

This study examines how centimeter- to meter-long fracture sets propagate, link and form m-long structures, which are then karstified in the vadose (aerated) zone in the upper parts of exposed layered carbonate units. We characterize the fracture patterns, including both mesoscale extensional joints, veins, stylolites and macroscale faults, within the Rosario pavement, which is a 1100-m-long, 340-m-wide outcrop in the Jandaíra Formation, Potiguar Basin in semiarid Brazil. The work compares the directions of the mesoscale structures with the strikes of surface collapse dolines and cave conduits at depths of 10–20 m. The main results indicate that the background (diffuse) deformation consists mostly of bed-perpendicular, stratabound N-S-striking veins and extensional (opening mode-I) fractures and E-W- to ENE-WSW-striking stylolites, which are consistent with the same stress field. Both sets of structures are laterally continuous and are commonly traceable across the pavement. Linkage of stylolites and stratabound fractures formed via throughgoing fractures that affected several layers, as deep as 15 m. The throughgoing fractures were favorable structures for fluid pathway formation and karstification in the epigenetic environment. We conclude that sets of mesoscale structures fit with the orientations of the collapse dolines and subhorizontal cave passages, and induced hydraulic anisotropy within the vadose level. These findings indicate that the fractures, veins and stylolites grow, link and form localized vertical conduits for water percolation and karst development. These findings can constrain future models and numerical simulations of karst conduits in investigations of groundwater and oil reservoirs.

A new bond model in peridynamics theory for progressive failure in cohesive brittle materials

In this study, a new bond damage model is proposed in the framework of the bond-based peridynamics theory to better describe the progressive failure process in cohesive brittle materials. The new bond model is able to account for the progressive failure and residual strength of bonds. The peridynamics theory is further coupled with the classical finite element method in order to efficiently describe failure processes at a large scale of structures. Several benchmark tests concerning mode-I and mixed-mode fractures in concrete structures are studied to verify the efficiency of the coupled peridynamics-finite element method. The obtained numerical results are in good agreement with the experimental data for both overall force–displacement responses and crack propagation patterns. It is found that the new bond damage model significantly improves the prediction of progressive failure process in cohesion brittle materials with respect to the classical elastic-brittle bond model.

Stress enhanced tensile fractures in elliptical clast in conglomerate

Mode-I fractures within the elliptical clasts from Archaean age Chitradurga Schist Belt (Dharwar craton, south India) are analyzed to decipher the paleostress condition. These fractures are characterized as systematic, steeply dipping and parallel to each other. The analysis is performed in three steps – (1) fixing and transforming of the coordinate systems to describe the elliptic domain under far-field stress, (2) proposing suitable complex potentials for inclusion and matrix followed by the plane strain solution for elliptical domain to fractured clasts, (3) obtaining the state of stresses readily inside the inclusion. We conclude that the mode-I fractures in elliptical clasts are developed due to far-field stress enhancement inside the rigid clasts at shallow depth. The deduced paleostress conditions also fit very well with the orientation and sense of previously revealed regional tectonics. We infer that the amplification of stresses in the rigid inclusions is function of elastic moduli of the clast and matrix, ellipticity of the clasts and remote stresses. We interpret that the enhanced intra-clast differential stresses are more for the clast with higher aspect ratio; thus is more susceptible for tensile fracturing, than the lower one for a constant applied far-field stresses. We also estimate the minimum breakage loads as well as minimum depths, required for the clasts of different aspect ratio to develop tensile fractures in them. We imply that fractured elliptical clasts can be regarded as an important paleostress indicator.

An improved ordinary state-based peridynamic model for cohesive crack growth in quasi-brittle materials

Ordinary state-based peridynamics (OSBPD) is a well-established peridynamic (PD) model, but its applications are restricted in brittle fracture because the failure models proposed in OSBPD are mainly to describe brittle fracture rather than quasi-brittle fracture. This work attempts to propose a damage model to overcome this limitation for the investigation of damage and crack propagation in quasi-brittle materials. To this aim, a PD version of the cohesive zone model (CZM) is established in OSBPD for the fracture analysis of quasi-brittle materials. A degradation curve is proposed in the damage model to represent the cohesive effect in fracture process zone (FPZ), which is similar to the tension softening curve in CZM. The damage model can be uniquely determined once the tensile strength, the elastic modulus, the specific fracture energy, and tension softening constitutive law are given. Moreover, several representative examples of mode-I and mixed mode concrete fractures are simulated using OSBPD to validate the proposed damage model. The predicted load-displacement curves and crack paths in all the cases are in good agreement with the experimental results or other numerical results. In addition, a re-loading approach is proposed to obtain the descending part of load-displacement curve when the load-controlled loading procedure is adopted.

Role of heterogeneities in jointing (fracturing) of geological media: Numerical analysis of fracture mechanisms

Fracture process is investigated using finite-difference simulations with a new constitutive model. It is shown that both geometry and fracture mechanism itself depend on the preexisting heterogeneities that are stress concentrators. In the brittle regime (low pressure, P), Mode-I fractures propagate normal to the least stress σ3 from the imposed weak zones. At high P, shear deformation bands are formed oblique to σ3. At intermediate values of P, the fracture process involves both shear banding and tensile cracking and results in the initiation and propagation of pure dilation bands. The propagating band tip undulates, reacting on the failure mechanism changes, but its global orientation is normal to σ3. The σ3-normal fractures are joints. There are thus two types of joints resulting from Mode-I cracking and dilation banding, respectively. The obtained numerical results are in good agreement with and explain the results from previous similar experimental study.

Deformation behavior of migmatites: insights from microstructural analysis of a garnet–sillimanite–mullite–quartz–feldspar-bearing anatectic migmatite at Rampura–Agucha, Aravalli–Delhi Fold Belt, NW India

In the present study we investigate the microstructural development in mullite, quartz and garnet in an anatectic migmatite hosted within a Grenvillian-age shear zone in the Aravalli–Delhi Fold Belt. The migmatite exhibits three main deformation structures and fabrics (S1, S2, S3). Elongated garnet porphyroblasts are aligned parallel to the metatexite S2 layers and contain crenulation hinges defined by biotite–sillimanite–mullite–quartz (with S1 axial planar foliation). Microstructural evidence and phase equilibrium relations establish the garnet as a peritectic phase of incongruent melting by breakdown of biotite, sillimanite ± mullite and quartz at peak P–T of ~ 8 kbar, 730 °C along a tight-loop, clockwise P–T path. Monazite dating establishes that the partial melting occurred between ~ 1000 and 870 Ma. The absence of subgrains and systematic crystal lattice distortions in these garnets despite their elongation suggests growth pseudomorphing pre-existing 3-D networks of S1 biotite aggregates rather than high-temperature crystal plastic deformation which is noted in the S1 quartz grains that exhibit strong crystallographic preferred orientation (CPO), undulatory extinction and subgrains. Mode-I fractures in these garnet porphyroblasts induced by high melt pressure during late stage of partial melt crystallization are filled by retrograde biotite–sillimanite. Weak CPO and non-systematic crystal lattice distortions in the coarse quartz grains within the S2 leucosome domains indicate these crystallized during melt solidification without later crystal plastic deformation overprint. In the later stages of deformation (D3), strain was mostly accommodated in the mullite–biotite–sillimanite-rich restite domains forming S3 which warps around garnet and leucosome domains; consequently, fine-grained S3 quartz does not exhibit strong CPOs.

Study The Mixed-Mode Delamination of The Epoxy/Cu Interface

The high density packaging, e.g. stacked die packages et al., includes interfaces between different materials. The device reliability is heavily related to the behavior of the interfaces. For instance, the delamination may propagate along dissimilar material interfaces and lead to electrical failure during the package manufacturing, testing processes and even in working state under severe environmental conditions. The interfaces between the epoxy-based composites and copper may be critical due to the large CTE mismatch of the materials. The interface fracture exhibits mixed-mode that combined with mode-I and model-II fractures. In this work, we designed the sandwich samples and a new apparatus to characterize the interface fracture of the epoxy/Cu interface. The sample can be loaded in different angles. The energy release rate and mode mixity were obtained upon the experimental results by the mixed-mode elastic fracture analysis. The method can be applied for other interface characterization in the packaging.

Determination of dynamic fracture parameters using a semi-circular bend technique in split Hopkinson pressure bar testing

Fracture initiation toughness, fracture energy, fracture propagation toughness, and fracture velocity are key dynamic fracture parameters. We propose a method to simultaneously measure these parameters for mode-I fractures in split Hopkinson pressure bar (SHPB) testing with a notched semi-circular bend (SCB) specimen. The initiation toughness is obtained from the peak load given dynamic force equilibrium. A laser gap gauge (LGG) is developed to monitor the crack surface opening displacement (CSOD) of the specimen, from which the fracture velocity and the fracture energy can be calculated. The feasibility of this methodology for coarse-grained solids is demonstrated with the SHPB-SCB experiments on Laurentian granite.

Evolution of boudins under progressively decreasing pore pressure A case study of pegmatites enclosed in marble deforming at high grade metamorphic conditions, Naxos, Greece

During ductile deformation of marbles under high grade metamorphic conditions on Naxos, Greece, pegmatites enclosed in the marbles were deformed in a brittle fashion forming blocky boudins with quartz crystallized in the interboudin zones. We studied the three-dimensional geometry of the boudins in the field and in two large samples. The first sample was serially sectioned to observe the structural and microstructural evolution; in the second sample we mapped the surface morphology of the deformed pegmatite. In profile, the boudins can be classified as symmetric torn type boudins, evolving towards asymmetric boudins with a later domino boudin component. In three dimensions, however, the morphology of the boudinaged pegma- tite is a simple set of normal faults with mode-I fractures in the fault tips and rotation of the fault blocks to accommodate the extension in the marble. Deformation history was constrained by petrology and microstructures in combi- nation with simple order of magnitude calculations of both the cooling and pore fluid pressure evolution. The dynamically recrystallized, coarse-grained calcite of the marble provides clear evidence that after the pegmatite intruded the marble and solidified, it was deformed at peak conditions of M2b metamorphism (� 670 °C and � 0.6 GPa). Such pegmatitic melts contain � 10 percent H2O which is released during crystalliza- tion. We infer that after crystallization of the pegmatite the pore fluid pressure in the pegmatite remained close to lithostatic due to the very low permeability of the surrounding marble, and the pegmatite was deformed at very low effective stress which led to brittle deformation of feldspar and mode-I fracturing of the pegmatite, forming torn type boudins. With time the pore fluid pressure slowly decreased, increasing the effective stress. Ongoing N-S extension thus resulted in slip along the quartz-filled interboudin zones and in block rotation, producing domino boudins.

負荷中に発生する弾性波の定量解析による気相蒸着Ｔｉ（Ｃ，Ｎ）膜の力学特性と内部応力

The objective of this study is to examine the mechanical strength of ARE-deposited Ti (C, N) film by using acoustic emission (AE) source characterization under tensile and compressive loading. Threshold stress in the substrate steel causes Mode-I fractures in the film as determined by quantitative source inversion of AE signals emitted from the limited Ti (C, N) area with a uniform stress distribution. Film fractures were invariably associated with the emergence of slip steps in the substrate steel. The threshold stress for film fractures under tensile loading was almost 9times greater than the stress under compressive loading.A simple method for estimating internal stresses in film from threshold stresses under different loading was also proposed. The internal stress in the film, estimated from the maximum strain criterion, was -3.8GPa which coincided with the reported internal stress measured using X rays.