Mixed-mode Fracture Research Articles

Effect of grain morphology and interface on the toughness of nacre-like aluminas

Ceramic composites that are both tough and strong are needed for extreme environments, ranging from aerospace and nuclear, to medical applications. Bioinspired ceramic composites tackle this challenge by mimicking tough natural structures. Nacre-like aluminas (NLAs) are ceramics processed using advanced colloidal techniques to obtain a microstructure resembling the brick-and-mortar structure of nacre. NLAs can achieve flexural strengths up to 600 MPa and fracture toughnesses ranging from 5 MPa.m1/2 up to 16 MPa.m1/2 after crack propagation. These high values mainly rely on deflection mechanisms; these can operate at temperatures up to 1200°C and under impact testing. The fracture properties have been found to be highly dependent on the mortar composition and processing technique used. However, we still don't know how far we can extend the structural properties of NLAs by changing their mortar strength and brick morphology. In this study, we combine mode I wedge splitting testing and in situ synchrotron X-ray microtomography of mixed-mode SENB fracture testing along with a kinked crack analytical formulation to study the microstructure-properties relationship in NLAs having two mortar compositions/morphologies. We compare the toughness values obtained in mode I and II with deflection models and study the effect of mode-mixity on the NLA toughness. Our findings show the grain morphology strongly influences the fracture behaviour, with the longer grain material showing longer stable crack deflection which could be further optimised going forwards. By contrast the mortar properties which provide deflection and local toughening mechanisms may be nearing their optimal strength.

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.

Theoretical analysis of mode I fracture of adhesively bonded bi-material DCB joints

There has been a disputation about how to achieve a pure mode I fracture and thus measure its toughness for an adhesively bonded bi-material double cantilever beam (DCB) specimen. This paper therefore develops a theoretical methodology to calculate the normal and shear stress distributions in the adhesive layer and to perform data reduction and mode partitioning for generic bi-material DCB specimens. The theoretical model is validated using experimental data. The adhesive layer in a generic bi-material DCB joint is loaded both in normal and shear based on the predicted stress distributions in the adhesive layer, resulting in a mixed mode fracture behavior. The prediction results substantiate that a strain-based design principle eliminates the shear stresses and thus leads to pure mode I fracture in bi-material DCB specimens. This paper justifies that the established data reduction method is applicable for measuring mode I fracture toughness when a bi-material DCB is designed according to the strain-based design criterion.

Laser lap joining of R60702 zirconium alloy and 304 stainless steel utilizing CoNiTiV high entropy alloy

In this study, the laser lap welding of R60702 zirconium alloy and 304 stainless steel was successfully achieved by incorporating CoNiTiV high entropy alloy (HEA) interlayer. The addition of HEA interlayer altered elemental diffusion and prevented the formation of Zr-Fe intermetallic compounds. The maximum tensile and shear strength of the joint (998.4 N) is 2.5 times that of the sandwich joint without the HEA layer (392.1 N), with the displacement also increasing by 85 %. The inclusion of the intermediate HEA layer transforms the original brittle fracture mode into a tough-brittle mixed fracture mode. The elimination of Zr-Fe intermetallic compounds is the primary factor contributing to the enhancement of mechanical properties. The main phase composition includes α-Zr, Cr2Zr, CoTi2, Ni7Zr2 and Zr3Co phase.

Improving Mixed-Mode Fracture Properties of Concrete Reinforced with Macrosynthetic Plastic Fibers: An Experimental and Numerical Investigation

Improving Mixed-Mode Fracture Properties of Concrete Reinforced with Macrosynthetic Plastic Fibers: An Experimental and Numerical Investigation

A phase-field length scale insensitive mode-dependent fracture model for brittle failure

This article presents a consistent phase-field length scale insensitive mode-dependent fracture model for brittle failure by proposing mode-factor dependent degradation functions that incorporate the effect of two additional fracture parameters, namely the mode-II critical energy release rate and mode-II fracture strength, on the overall mechanical response. Using the proposed mode-factor dependent degradation functions and employing a recently proposed modified strain decomposition scheme, we provide analytical expressions for the mode-I and mode-II fracture strengths corresponding to the mode-dependent parts of the elastic energy. Adopting a modified Benzeggagh–Kenane (B–K) criteria, we propose mode-dependent driving forces by deriving expressions for the critical energy release rate corresponding to individual fracture modes. The proposed model provides a consistent coupling between the different fracture modes and can thus predict fracture for all possible mode-mixity ratios. A parametric study is carried out to unravel the effect of mixed-mode fracture parameters on the mechanical response of isotropic materials by considering a few representative numerical examples. The numerical results from the proposed model show an excellent agreement with experimental results reported in the literature.

Grain-refined metastable β titanium alloy with suppressed ω-assisted nucleation and enhanced mechanical properties

The mechanical characteristics of metastable β titanium alloys are related to the α precipitates that form during aging. Although precipitation behavior can be modulated by ω-assisted nucleation, the influence of grain size (GS) on this process has not been fully considered. In this study, the effects of grain refinement on mechanical properties and ω-assisted nucleation were investigated by aging the Ti-5.3Cr-4.9Mo-4.9 V-4.3Al-0.9 Nb-0.3Fe (TB18) alloy with coarse grains (87 μm) or fine grains (25 μm) at different heating rates (RH). It was found that ω-assisted nucleation depends on the RH, with a lower RH promoting the processes of ω-assisted nucleation and the precipitation of finer secondary α (αs) plates. The vacancy concentration after annealing reduced with decreasing GS, indicating that ω-assisted nucleation is suppressed by grain refinement. Additionally, grain refinement significantly improved the ductility of the TB18 alloy. This effect was attributed to enhanced homogeneous plastic deformation and an increase in slip systems, such as pyramidal <c+a> slip on αs plates. At ultimate tensile strengths of 1300–1550 MPa, the elongation of the fine-grained specimens was typically 2–3 times greater than that of the coarse-grained specimens. Furthermore, the corresponding mixed fracture mode involved a greater extent of ductile fracture. Therefore, the mechanical properties of metastable β titanium alloys are primarily limited by coarse β grains.

A Comparative Study on the Performance and Microstructure of 304NG Stainless Steel in Underwater and Air Laser Welding.

In order to facilitate the application of underwater laser welding technology in in situ repairs of nuclear power plants, this study conducted comparative experiments between local dry underwater laser welding and laser welding in air on 304NG nitrogen-controlled stainless steel. The aim was to explore its microstructural evolution and mechanical properties in underwater environments. It was found that, near the fusion line of laser welding in air, columnar dendrites gradually evolved into cellular dendrites toward the weld center, eventually disappearing, resulting in a skeletal ferrite and serrated austenite structure. The underwater laser welding joints exhibited similar characteristics yet with more pronounced alternation between columnar and cellular dendrites. Additionally, the size of cellular dendrites decreased significantly, and needle-like ferrite was observed at the weld center. The hardness of underwater laser welded joints was slightly higher than that of in-air laser welded joints. Compared to laser welding in air, the strength of underwater laser welding joints increased from 443 MPa to 471 MPa, and the displacement increased from 2.95 mm to 3.45 mm, both types of welded joints exhibited a mixed mode fracture characterized by plasticity and brittleness.

Assessment of fracture toughness in fibrous concrete via Brazilian test: Experimental study with low-clinker cementitious binder

As the predominant and cost-effective material in the construction industry, concrete is susceptible to tension weaknesses, leading to significant flaws such as cracking and brittle fracturing. Recent advancements in fibrous concrete have emerged as a solution to mitigate these issues. Incorporating steel fibers in concrete has emerged as a promising solution to improve crack resistance and structural integrity. This study focuses on developing eco-friendly concrete using a low-clinker cementitious binder and short steel fibers to enhance fracture toughness and mitigate the environmental impact by effectively utilizing lime sludge. Concrete specimens were prepared with three binder types: treated lime sludge (TLS) at 15 % and 30 % and calcined clay (CC) at 15 % and 30 %, replacing conventional clinker. Short steel fibers were added at 1.5 % by volume to enhance mechanical properties. Fracture toughness was evaluated using notched Brazilian disc specimens, assessing mode I, II, and mixed-mode (I/II) fracture at multiple notch orientations (β = 0°, 15°, 28.83°, 45°, 60°, 75°, and 90°). Microstructural analysis during strength development was performed using scanning electron microscopy and X-ray diffraction. The findings revealed that specimens containing 15 % TLS, 30 % CC, and 1.5 % steel fibers exhibited the highest fracture toughness. Mode II fracture toughness exceeded mode I, indicating improved resistance to crack propagation. The addition of fibers to the specimens under mode II demonstrated improved fracture toughness, ranging from 0.44 to 0.53 MPa·m^1/2 compared to the corresponding non-fibrous specimens. The fibrous specimens showed significantly higher ultimate loads at β = 90° compared to β = 0°, indicating superior crack resistance and structural integrity under perpendicular loading conditions. The Brazilian disc specimens demonstrated variability in fracture toughness across different loading orientations, highlighting their suitability for mixed-mode fracture assessment.

Effect of lubricants during the rolling process on the mixed mode fracture behavior of the as-rolled material

Friction is one of the major factors in energy consumption and metal depreciation during various mechanical processes. Lubrication is often used during the process of forming metals to cope with friction and its consequences. Mineral lubricants are employed in the rolling process to decrease the rolling force and enhance the quality of the sheets. This research aims to compare the performance of mineral lubricants such as crude oil, gas oil, and CM405A to enhance the production efficiency of the aluminum forming process, especially in the rolling process. The ring compression test was utilized to evaluate the influence of lubrication on the friction coefficient which was extracted through calibration curves. Then, the effect of friction coefficient was experimentally examined during the forming process through rolling. Al 1050 was rolled by the mentioned lubricants. The pre-cracked rolled samples were then tested by fracture test at different loading angles of 0 (pure mode-I), 45(mixed-mode of I and II), and 90(pure mode-II). J-R curves were extracted using elastic–plastic fracture theory based on material characteristics. The fracture tests indicated maximum resistance to crack growth occurred in the sample prepared with CM405A lubricant. In contrast, the lowest crack growth resistance was recorded in the case where crude oil was employed as a lubricant. In the end, the SEM images of the fractured surfaces were explored for a deeper understanding of the fracture behavior. Although a combination of brittle and ductile fracture mechanisms can be observed on the fractured surfaces, cleavage was the dominant phenomenon and fracture mechanisms.

Interlaminar fracture behaviour of emerging laminated-pultruded CFRP plates for wind turbine blades

Laminated pultruded composite plates are gaining interest for use in wind turbine blades due to their excellent structural performance with affordable cost. However, there is limited understanding of their fracture properties. The present work explores the interlaminar fracture behaviour of pultruded composite plates, bonded through resin infusion, to form thick CFRP structures. Mode-I, −II, and mixed-mode (I/II) tests were performed to obtain fracture properties at different mixed-mode ratios. Mode I crack propagation exhibits stick–slip behaviour, resulting in brittle failure in a few steps, while mode II provides more stable crack propagation along with cohesive failure. The mixed-mode fracture patterns follow the trend of the mode-mix ratios, in which higher mode-mix ratios (more mode II) induce more stable crack propagation. Benzeggagh-Kenane and power law criteria were compared regarding their prediction of crack initiation toughness given a mode mix ratio, and a linear relation between the mixed-mode I/II fracture toughness components could exist at interfaces of laminated pultruded plates. Meanwhile, applicability of testing standards and the effect of manufacturing-induced defects on fracture properties are thoroughly discussed. The results show that existing standards provide sufficient support for characterising fracture properties of bonded pultruded plates; and that manufacturing-induced defects can be detrimental to crack propagation and cause more brittle behaviour in mode I dominant cases, while beneficial effect of defects by toughening the interface was exhibited in mode II dominant cases.

Fracture behavior of a Ni-20 wt.%Cr binary alloy processed by Laser Powder Bed Fusion: Influence of the specimen building orientation and rotation angle between layers

This work provides a comparative study on the influence of the manufacturing process on the tensile and fracture properties of a Ni-20 wt.%Cr binary alloy produced by Laser Powder Bed Fusion (L-PBF). Two main processing parameters were investigated: the orientation of the samples with respect to the building direction (horizontal and vertical) and the rotation angle between layers (67° and 90°). Tensile and three-point bending tests were conducted to study the mechanical behavior. Monotonic tensile results suggest that the choice of the printing parameters affected the yield and ultimate tensile strength values, but was not influential to elongation. An increase in yield and ultimate tensile strengths of up to 15 % was noted for horizontal specimens compared to the vertical ones, and an increase of 10 % for an angle of 67° rather than 90°. Fracture toughness values remained in a range of 200 to 450 kJ/m2 regardless of the set of parameters considered. For a rotation angle of 67°, the fracture toughness was similar for both building orientations, but vertical specimens exhibited better resistance to crack propagation after initiation, with a tearing modulus increased by 50 % compared to horizontal ones. In contrast, building orientation was detrimental to specimens built with a rotation angle of 90°, as both fracture toughness and tearing modulus decreased drastically (up to 70 %) for a horizontal orientation rather than a vertical one. Microstructural observations highlighted mixed fracture modes for all L-PBF configurations, though crack propagation seemed mainly intergranular for horizontal specimens, and transgranular for vertical specimens. Fracture mechanisms were mostly governed by the grain orientation, size and morphology, while the crystallographic texture and the nano-oxides located in the dendrite arm spacing had a second-order influence. The pores and meltpool boundaries did not appear to play a significant role in crack propagation.

In vitro corrosion-fatigue behaviour of rare-earth containing magnesium WE43 in sterile complex cell culture medium

Rare-earth containing magnesium alloys are promising biomedical materials for a new generation of biodegradable orthopaedic implant systems due to their excellent biocompatibility, mechanical and biodegradation properties. However, chemo-mechanical interactions in aggressive physiological corrosion environments result in rapid degradation and early loss of mechanical integrity, limiting its broader application for orthopaedic implants. To date, only few studies have assessed the corrosion-fatigue behaviour of medical-grade magnesium alloys in an organic physiological corrosion environment, especially under sterile test conditions. In the present work, the corrosion-fatigue behaviour of fine-grained medical-grade magnesium alloy WE43MEO was systematically analysed under in vitro conditions using an organic physiological fluid DMEM. The experimental results showed that the fatigue strength of the alloy is nearly unaffected by a 1-day precorrosion, while a 7-day precorrosion resulted in a significant deterioration of mechanical integrity. In corrosion-fatigue experiments, the fatigue life was considerably reduced by interactions between corrosion and fatigue damages. The SEM analysis revealed that the mixed mode of intergranular and transgranular fracture in the crack propagation zone transits to intergranular cracking dominant mode under the corrosion-fatigue conditions due to hydrogen embrittlement.

A comparative study on microstructures of a high-Zn AlZnMgCuZr alloy fabricated by casting and melt spinning

A high-Zn Al–27Zn-1.5Mg-1.2Cu-0.08Zr alloy was prepared by traditional casting and melt spinning. The as-casted alloy consists of well-developed α-Al dendrites with many coarse η-phase and low solute concentration, coarse network precipitates at grain boundaries and the α-Al/η-phase eutectic structures at triple junctions. Due to these featured structures, the as-cast alloy exhibits a low tensile strength of 101 MPa with room temperature and high temperature (300 °C) damping capacity of 0.0058 and 0.027 respectively. Comparatively, the as-spun alloy reveals gradient cross-sectional microstructures after solidification: an ultrafine grained region near the wheel surface, a transition region and an equiaxed-grained region near the ribbon free surface, with changes of precipitate morphologies from granular shape to network shape via vermicular. High-density nano-sized η′-phase/GP-zones within α-Al grains result in a higher tensile strength (121 MPa) of as-spun alloy with room temperature and high temperature (300 °C) damping capacity of 0.0049 and 0.048 respectively. Fracture analysis shows that the as-casted alloy fails in a mixed-mode fracture, comprised predominantly of transgranular fracture, quasi-cleavage fracture, cleavage fracture and dimple fracture, whereas the as-spun alloy failed in cleavage fracture and dimple fracture.

Microstructure and properties of SLMed Ta-10W and rolled Ta-10W fiber laser welded joint

This study focused on the mechanical properties and microstructure of fiber laser-welded joints of Ta-10W alloy manufactured by selective laser melting (SLM) and rolled. In the SLMed base material side of the weld, columnar grains were formed along the weld, extending up to half of the weld width. The base material’s anisotropy influenced the subgrain morphology, and grain orientation changed after welding. When the building direction of the SLMed Ta-10W was perpendicular to the welding direction, slender columnar subgrains were prone to forming in the SLM side weld. In contrast, when the building direction was parallel to the welding direction, equiaxed subgrains tended to form in the weld. In the rolling base material side weld, mainly equiaxed grains were formed, with subgrain morphology and orientation randomly distributed. In the weld center, fine-grain zones of 10–20 μm, comprising fine grains of 2–5 μm diameter, were observed in all welds under study. Room-temperature tensile strengths of both welds were approximately 620 MPa, falling between the strengths of the two base materials. Their fracture surfaces displayed a mixed mode of cleavage and intergranular fracture. High-temperature strengths of rolled-SLMed joints varied with SLM directions X and Z, reaching 124.94 and 107.87 MPa, respectively, and exhibiting similar fracture characteristics dominated by intergranular fracture.

Experimental study of the fatigue failure behavior of aluminum alloy 2024-T351 under multiaxial loading

Multiaxial fatigue has been drawing much attention because it is more applicable to engineering practice. In this paper, an experimental study of aluminum alloy (AA) 2024-T351 was carried out under multiaxial loading with an aim to assess the damage evolution process and failure mechanism under in-phase and out-of-phase loadings. Firstly, fatigue life and stress response under multiaxial cyclic loads were obtained, and it found that although there is non-proportional hardening, the fatigue life subjected to proportional loading is significantly shorter than that of under a nonproportional loading, which was tried to be explained by the ductility of the material. Secondly, a detailed analysis of the damage evolution process based on the degradation of the elastic modulus and the fatigue failure process based on the digital image correlation (DIC) method was provided. Next, a micro-analysis of the specimens’ fracture appearance was conducted to obtain the fracture characteristics and found that AA2024-T351 presents a dominant shear fracture mode under proportional loading and a mixed mode of tensile and shear fracture under non-proportional loading. Last but not least, The Fatemi-Socie criterion was modified by considering the material’s ductility and the interaction between normal stress and shear stress acting on the critical plane. The multiaxial life prediction results of the modified FS model for AA2024-T351 in this paper were all within the scatter bands of 3 on life.

Fracture and multiple-cracking modelling of strain-hardening cementitious composites

Strain-hardening cementitious composites (SHCC), composed of short fibres embedded within brittle matrix, exhibit distinctive pre-peak strain-hardening characteristics and remarkable tensile ductility. The fracture and failure process of SHCC, involving both hardening and softening stages as a result of matrix multiple micro-cracking and strain localization, is highly complex and poses a significant challenge for numerical modelling. In the present paper, a novel numerical framework, characterized by the bi-layer superposed cohesive zone strategy, is developed for the numerical modelling of fracture and multiple cracking of SHCC, at both the material scale and structural scale. The developed model is based on diffused cohesive interface model, but with adaptions to consider fibre bridging mechanism. The crack interface is simulated by two cohesive elements sharing the same nodes: one for the matrix-cohesion effect and the other for the fibre-bridging effect. Cohesive constitutive relations of matrix cohesion and fibre bridging are carefully assigned. The proposed model is first validated on the material scale through a uniaxial tension test. With the aid of a random material field, multiple-cracking phenomenon and stress fluctuation are successfully predicted by the model. The model is then applied to the structural fracture modelling, where four case studies, including both pure mode I and mixed mode fracture, are performed. The size effect and boundary effect on the fracture behaviour are well captured by the numerical modelling. The model proposed in the current work has the potential to be extended to the multiple cracking modelling of other materials.

Development of large-size dissimilar stainless steel/α-Ti alloy joints by diffusion bonding using vacuum hot press: Interface microstructure and tensile response in the temperature range of 77–773 K

In the present study, dissimilar metal joints of SS321 and Ti–5Al-2.5Sn (α-Ti alloy) are produced by diffusion bonding at temperatures of 850, 900, and 950 °C under 10 MPa pressure for 30 min duration using a vacuum hot press (VHP). The interface of the joints was characterized through scanning electron microscopy coupled with energy dispersive spectroscopy and electron backscattered diffraction analysis for examining microstructure, morphology, and microchemistry across the interface. The effect of change in the heating process during diffusion bonding on the growth kinetics of interface layers was investigated. The interface of the joints comprised of intermetallic phases of σ phase, χ phase, (Fe,Cr)2Ti, FeTi and β-Ti. The joint produced at 900 °C has exhibited a maximum tensile strength of 315 MPa, 253 MPa, and 208 MPa at the test temperatures of −196 °C (77 K), room temperature (300 K), and 500 °C (773 K), respectively. Reduction in joint strength was noticed at test temperatures of RT and −196 °C for the samples bonded at a higher temperature of 950 °C due to the increased widths of the intermetallic phases at the interface. The effect of the bonding temperature on the tensile strength of the joints at an elevated test temperature of 500 °C was found to be negligible; however, the joints displayed good retention of strength along with substantial strain hardening followed by ductility at 500 °C. Fracture surfaces of RT and −196 °C tested samples showed the mixed mode of featureless smooth and cleavage fracture, whereas the 500 °C tested sample displayed planar interface failure. The zone of failure of the joints was noted to be around the interphase layer made of (Fe,Cr)2Ti + FeTi intermetallics.

Experimental and virtual testing of mode II and mixed mode crack propagation under dynamic loading

Under static loading, measuring experimentally the mode II and mixed mode fracture toughness of composite materials and adhesive joints is well standardised. However, under dynamic loading, no standard procedure has been defined yet. Therefore, this paper proposes an experimental methodology to measure the mode II and mixed mode interlaminar fracture toughness of composite materials and adhesive joints. The methodology is based on a modified split Hopkinson compression bar. Two different data reduction schemes are explored and compared, one based on measuring the crack length, and another based on measuring the force from the strains in the transmitted bar. The two data reduction methods provided considerably different results. By using the method based on measuring the force, the mode II and mixed mode fracture toughness for both interlaminar and adhesive joints decreased for higher strain rates, while the opposite was found with the other approach. The method based on the crack length measurement was deemed to be unreliable due to the difficulties in measuring it.

Mixed-mode fracture analysis of CORC cables with double-edge cracks under tension and torsion

The Conductor on round core (CORC) refers to a circular cable that is helically wound with rare-earth-barium-copper-oxide ((RE)BCO) high-temperature superconducting (HTS) tapes. This type of cable finds extensive applications in large superconducting magnets. However, the mechanical–electrical performance of CORC cables is hindered by microscopic edge cracks that occur during the mechanical slitting process of HTS tapes. In this paper, the mixed-mode stress intensity factor (SIF) of cracks in CORC cables under different loading conditions is investigated using the extended finite element method (XFEM). The design variables of CORC cables are optimized by considering the effect of various factors such as the crack parameter, the winding angle, the core radius, and the Poisson’s ratio of the winding core on the SIF. The results indicate that the impact of each factor on the mixed-mode SIF varies depending on the loading mode. Notably, the influence of the winding angle on the SIF is particularly significant and intricate. In the case of tensile loading, a smaller winding angle proves advantageous in impeding crack propagation. Conversely, the most dangerous winding angle for torsional loads is 45°. The divergence of these effects can be indirectly indicated by theoretical solutions regarding the tape strain along the helix direction. For the cases examined, the results have shown that the crack propagation path is independent of these factors, and the direction of propagation is perpendicular to the edge of the tape.