Intrinsic Toughening Mechanisms Research Articles

Optimizing heterostructure parameters towards enhanced toughening in micro/nano-reinforced bimodal-grained Al alloy composites

We manipulated soft coarse-grained (CG) domains to design optimized and toughened B4Cp/6061Al composites, featuring bimodal domains with in-situ MgO nanoparticles (n-MgO) and ex-situ carbon nanotubes (CNTs). Manipulating CG fractions influenced heterostructure parameters such as CG band width and domain distribution. A systematic optimization strategy integrating intrinsic/extrinsic toughening and strengthening mechanisms identified optimal conditions for maximizing strength-ductility-toughness. The optimal 20:80 CG-to-ultrafine-grain (UFG) weight ratio offered an ultimate strength of 550 MPa and ∼7 % elongation. Intrinsic toughening mechanisms enhanced UFG domain dislocation storage capacity. Multiscale analysis of crack behavior revealed pronounced crack-blunting in well-dispersed CG domains. Extrinsic toughening mechanisms included nanobridge formation, crack-deflection, micro-crack proliferation, and crack-branching. Micromechanical behavior was examined using the strain gradient model. Designing strong and ductile micro/nano-reinforced bimodal grained composites requires selecting a smaller amount of CG domains, a CG band width larger than double the interface affected zone (IAZ), and larger grain sizes in the CG domains.

Superior fracture resistance and topology-induced intrinsic toughening mechanism in 3D shell-based lattice metamaterials.

Lattice metamaterials have demonstrated remarkable mechanical properties at low densities. As these architected materials advance toward real-world applications, their tolerance for damage and defects becomes a limiting factor. However, a thorough understanding of the fracture resistance and fracture mechanisms in lattice metamaterials, particularly for the emerging shell-based lattices, has remained elusive. Here, using a combination of in situ fracture experiments and finite element simulations, we show that shell-based lattice metamaterials with Schwarz P minimal surface topology exhibit superior fracture resistance compared to conventional octet truss lattices, with average improvements in initiation toughness up to 150%. This superiority is attributed to the unique shell-based architecture that enables more efficient load transfer and higher energy dissipation through material damage, structural plasticity, and material plasticity. Our study reveals a topology-induced intrinsic toughening mechanism in shell-based lattices and highlights these architectures as a superior design route for creating lightweight and high-performance mechanical metamaterials.

Enhanced strength–ductility synergy of SiC particles reinforced aluminum matrix composite via dual configuration design of reinforcement and matrix

To overcome the strength-ductility conflict in particle reinforced aluminum matrix composites (PRAMCs), a novel dual configuration strategy of microstructure was proposed in this work. The dual configuration including both heterogeneous grain structure and hybrid reinforcements was obtained by powder metallurgy, which was designed as submicron-sized SiC particles (SiCsm)/Al and micron-sized SiC particles (SiCm)/2024Al components. Representative alternating coarse grain (CG) bands containing SiCm and ultra fine grain (UFG) bands with dispersed SiCsm were revealed in microstructural characterizations. Compared to corresponding homogeneous composites with the same fraction particles, the dual configuration composite achieved simultaneous enhancement in strength and ductility and remained a comparable Young’s modulus of 98GPa, which represented 442 MPa in yield strength, 590 MPa in ultimate strength and 8.7 % in fracture elongation. The extra strength provided by hetero-deformation induced (HDI) strengthening is a potential dominant strengthening mechanism. The intrinsic toughening mechanisms primarily contribute to HDI strain hardening and enhanced dislocation accumulation capacity, while the extrinsic toughening mechanisms presumably attribute to more uniform microcrack distribution and blunting effect of CG zones on cracks. Our work provides a feasible route including ball milling and powder assembly to preparate high-modulus aluminum matrix composites for strength-ductility balance design.

High fracture toughness of an ultra-strong medium Mn steel with fibrous ferrite in a martensitic matrix

Developing ultrahigh strength steels that are fracture resistant and economical would be appealing for structural applications. In this work, an ultra strong-and-tough steel was fabricated by introducing fibrous ferrite into martensite matrix. This steel exhibited an ultrahigh yield strength and tensile strength, 1560 and 2103 MPa respectively, along with a 7.3 % uniform elongation. The fracture toughness and smoothly rising R-curve were measured through the elastic-plastic unloading compliance method using miniaturized side-grooved compact tension (CT) specimens. A high fracture toughness (KIC≈105 MPa m1/2) that is superior to many steels at the same strength level was achieved. The heterogeneous microstructure of fibrous ferrite embedded in a martensitic matrix allows for high strain hardening rate and adequate micro-void formation, consequently leading to higher fracture strain and the occurrence of localized necking. The toughening mechanisms of CT samples are discussed according to the energy criterion for fracture. The expanded plastic deformation area (intrinsic toughening mechanism), deflecting and bridging the primary crack propagation as well as interface delamination between fibrous ferrite and martensite (extrinsic toughening mechanisms) significantly improve the overall fracture resistance. The current findings promote the development of high-strength and high-toughness medium-Mn steels for structural applications.

Toughening mechanism in superstructure Hf6Ta2O17 thin film

Fracture toughness is a key indicator to estimate the anti-peeling performance of thermal barrier coatings (TBCs). A unique superstructure endows Hf6Ta2O17 with an outstanding phase stability and mechanical property, which also poses great challenges for studying its intrinsic toughening mechanism. Here, the superstructure Hf6Ta2O17 single crystal film was epitaxially grown on YSZ(011) substrate by pulsed laser deposition. An uncommon ripple pattern near the Vickers indentation crack tips was first reported. The pop-in signals in the load-displacement curve indicated it may be relevant to ferroelastic domain transformation, which was further confirmed by spontaneous strain distribution in HRTEM. The transformation path, predicted by DFT, was conducted in b→c ferroelastic domain through in-plane rotation of Hf–O/Ta–O polyhedrons. The corresponding critical stress for domain transformation was up to 5.83 GPa. In addition, an intrinsic ductility was confirmed with a high Pugh ratio B/G of 2.49, much larger than the critical value (1.75) for brittle-ductile transition. These two mechanisms make contribution to the superior fracture toughness of Hf6Ta2O17. This work provides a deep insight into the toughening mechanism of ceramics and paves the way to design of next-generation TBCs.

Tuning chemical short-range order for simultaneous strength and toughness enhancement in NiCoCr medium-entropy alloys

The pursuit of enhancing strength and toughness remains a critical endeavor in the field of structural materials. This study explores two distinct strategies to overcome the traditional strength-toughness trade-off. Specifically, we manipulate the chemical composition and short-range order (SRO) of the NiCoCr medium-entropy alloy, which has shown remarkable fracture toughness in recent experiments. Utilizing molecular dynamics simulations, we uncover nano-scale deformation mechanisms during crack propagation. Our findings highlight that optimizing the SRO degree leads to improvements in both atomic scale strength and toughness defined as the area underneath stress-strain curves from MD simulations. In contrast, a trade-off between strength and toughness persists when only manipulating the Ni content in the NiCoCr alloy. Based on the simulation results, we establish a strong correlation between toughness, strength, surface energies, and unstable stacking fault energies. These factors are influenced by the chemical composition and SROs in NiCoCr, with SROs acting as strong obstacles to dislocations, thereby contributing to additional strength. The exceptional toughness of NiCoCr with SRO arises from a synergy of intrinsic and extrinsic mechanisms, including dislocation glide, nanobridging during nanovoid coalescence and zigzag crack path. It is found that, in the presence of SRO, intrinsic toughening mechanisms usually associated with crack tip blunting and dissipation can also facilitate the onset of extrinsic toughening mechanisms of nanobridging and zig-zag crack path associated with nanovoid formation and coalescence. This study emphasizes the importance of tailoring SRO in designing materials with enhanced strength and toughness.

Microstructure and mechanical properties of SiCp/CF/Al hybrid composites with heterostructure constructed by macroscopic “core-shell” structure

Designing heterostructure is an effective way to comprehensively improve the strength-ductility of composites. However, the current methods of heterostructure integration consumes a large amount of energy. In this study, a macroscopic “core-shell” structure is designed with low cost and low energy consumption. The SiC particles (SiCp) and carbon fiber (CF) reinforced aluminum-based hybrid composite (SiCp/CF/Al) with heterostructure was fabricated utilizing the spark plasma sintering (SPS) method. The microstructure, interfacial structure, and mechanical properties of the SiCp/CF/Al before and after hot rolling were comprehensively investigated. The results revealed that the Vickers hardness values of the rich particle zone with high SiCp content were 54.32% and 48.10% higher than those of the poor particle zone before and after hot rolling, respectively. The synergistic strengthening effect of SiCp and CF significantly enhanced the yield strength and plasticity of the SiCp/CF/Al. Before and after hot rolling, the yield strength of SiCp/CF/Al was 242.68% and 173.16% of single CF-reinforced Al matrix composites, respectively. The extrinsic toughening was achieved through crack passivation and deflection at the interface of the rich particle zone and poor particle zone. Furthermore, the hindering and storing effects of the SiCp and CF on dislocations represented the primary intrinsic toughening mechanisms.

Additive manufacturing of ULTEM 9085: Weak interface-enriched multi-toughening mechanisms and fracture resistance optimization

Modulating the fracture toughness can be used to tailor or enhance the mechanical performances in the design of specific additively-manufactured engineering structures. In this research, we explored the fracture behavior of ULTEM 9085 materials fabricated by material extrusion (MEX) 3D printing technique, with a particular emphasis on the effect of weak interfaces between deposited beads. Under quasi-static bending condition, the MEX-fabricated ULTEM 9085 exhibits brittle and quasi-brittle fracture behaviors by adjusting the print orientations and raster angles. Several intrinsic toughening mechanisms are identified, including crack deflection and twisting, fibril bridging, constrained microcracking and delamination of the weak interface. Notably, the samples that experienced delamination along the weak interface displayed the highest performance in terms of the fracture toughness. To achieve high fracture toughness, we employed an analytical model based on linear elastic multilayers fracture mechanics to understand the crack onset and predict the crack propagate orientation. Based on the insight gained from this model, we proposed an intuitive optimal strategy to enhance the fracture resistance by fine turning the bonding strength and layer height to trigger the crack deflecting towards and propagating at the weak interface consistently. By implanting this approach, we achieved an increase of over 35% in fracture resistance while effectively preventing the catastrophic failure, demonstrating exceptional fracture-resistant performance. Overall, our study elucidates the impact of layer-by-layer MEX-induced weak interfaces on the fracture resistance of MEX-fabricated high temperature engineering materials. The findings of this research hold potential for engineering applications, particularly in optimizing the design of additive manufactured products aiming at high fracture resistant.

Role of extrinsic and intrinsic toughening mechanisms in graphene nanosheets reinforced magnesium matrix layered composites

Constructing a layered structure is an effective approach to achieve a balance between strength and toughness. The toughening mechanisms of layered composites are generally considered to include reinforcement bridging, pullout, and crack deflection. However, the above toughening mechanisms are more applicable to ceramic matrix composites with predominantly cleavage fracture. For metal matrix composites with a larger fracture process zone, the energy consumption in crack propagation may be dominated by the plastic deformation at the crack tip. Therefore, elucidating the dislocation emission behavior and the interaction between graphene nanosheets (GNSs) and crack is the key to revealing the toughening mechanisms. In this work, the extrinsic and intrinsic toughening mechanisms for the layered GNS/Mg composites were investigated systematically. The three-dimensional reconstruction of the fracture morphology, combined with statistical analysis and molecular dynamic (MD) simulations, elucidates that macroscopic crack deflection in layered composites does not always result in a microscopically longer crack propagation path. The mitigation and redistribution of stress concentration and the promotion of dislocation emission at the crack tip induced by the GNS layers are proposed to be critical toughening mechanisms in the GNS/Mg layered composites.

Hierarchical toughening mechanisms in face centered cubic CoCrFeMnNi high-entropy alloy at room temperature and cryogenic temperatures

As a class of promising structural material, recently synthesized face centered cubic phased high-entropy alloys (HEAs) exhibit excellent room-temperature (RT) fracture toughness as well as an abnormally increasing one at cryogenic temperatures (CTs). The intrinsic toughening mechanisms are not yet well understood. Attention here is focused on the atomistic crack initiation and propagation in a model HEA CoCrFeMnNi under RT and CTs, by means of atomistic simulations integrated with theoretical analysis. Hierarchical deformation mechanisms of the incipient plasticity; the local amorphization; and the formation, growth, and coalescence of voids are found, based on which the strain energy stored in the material is continually dissipated, resulting in the outstanding fracture toughness of the HEA at both RT and CTs. The origin for low-temperature toughening may be attributed to fewer immobile dislocations at CTs, delaying the occurrence of amorphization and microvoids. The differences in mechanisms for low-temperature toughening of the HEA and low-temperature embrittlement of traditional metals are further comparatively revealed. This study provides mechanistic insights into the fundamental understanding of intrinsic toughening mechanisms in the HEA.

Improved interlaminar fracture toughness of carbon fiber/epoxy composites by a combination of extrinsic and intrinsic multiscale toughening mechanisms

Carbon fiber reinforced polymer (CFRP) composites with hierarchical structure interleave composed of nanoscale core-shell rubber (CSR) and microscale short carbon fiber (SCF) were fabricated. The hierarchical structure interleave exhibits superior interlaminar toughening efficiency than either CSR or SCF alone. Triggering intrinsic and extrinsic toughening mechanisms at different scales by CSR and SCF, respectively, the mode-I critical energy release rate (GIC) and mode-II critical energy release rate (GIIC) of multi-phase interleaved CFRP composite are 127% and 154% higher than those of unmodified sample. While the tensile properties and glass transition temperature (Tg) are not compromised. The fracture toughness of epoxy/CSR system was also investigated to better understand the effect of matrix toughness on interlayer toughness of CFRP. Numerical analysis and fracture surface observations revealed the synergistic toughening mechanisms in SCF/CSR interleaved CFRP composites. The synergy between nanoscale intrinsic toughening mechanism and microscale extrinsic toughening mechanism, evolving with crack propagation, contributes to a greater energy absorption. The usefulness of the present study for preparation of high-performance CFRP is discussed.

On mode-I and mode-II interlaminar crack migration and R-curves in carbon/epoxy laminates with hybrid toughening via core-shell rubber particles and thermoplastic micro-fibre veils

This study investigates the influence of hybrid toughening—via core-shell rubber (CSR) particles and non-woven thermoplastic veils—on the delamination resistance, crack migration and R-curve behaviour in carbon fibre/epoxy laminates under mode-I and mode-II conditions. Core-shell rubber particles, varying in size from 100 nm to 3 μm, with 0–10 wt% content, are dispersed within the epoxy resin, and thermoplastic micro-fibre veils with polyphenylene sulfide (PPS) fibres, with 5–20 g/m 2 areal weight, are introduced at the interlaminar region to achieve hybrid toughening. Carbon fibre/epoxy laminates are manufactured with a two-part resin using vacuum infusion and out-of-autoclave curing. Double cantilever beam (DCB) and four-point end-notch-flexure (4ENF) specimens are used to obtain mode-I and mode-II fracture energies and R-curves. Damage mechanisms and crack paths are characterised using fractography that provide understanding of energy dissipation. The results show that the hybrid toughening significantly improves fracture initiation and propagation energies ( i.e . mode I initiation by ∼245% and propagation by ∼275%, and mode-II initiation by ∼64% and propagation ∼215%) by extrinsic and intrinsic toughening mechanisms. Moreover, it is shown that rising R-curves can be achieved with hybrid toughening when compared with falling R-curves obtained with just thermoplastic veil toughening. Fractography revealed that the hybrid toughening constrained the crack predominantly within the veil region, making it harder to grow and absorb more energy.

Micro/nano-reinforcements in bimodal-grained matrix: A heterostructure strategy for toughening particulate reinforced metal matrix composites

To overcome strength-ductility trade-off in particulate metal matrix composites (PRMMCs), we developed a novel and controllable strategy, for the first time, via a combination of micro/nano-reinforcements and ultrafine/coarse-grained (UFG/CG) matrices. A powder assembly was developed to fabricate micro B4Cp/6061Al composites, which features UFG/CG matrices containing ex/in-situ nano dispersoids and exhibits superior combination of strength and ductility. It was found that such a novel architecture possesses both intrinsic and extrinsic toughening. As the intrinsic toughening mechanisms, enhanced dislocation storage capability of UFG regions, twinning, and hetero-deformation induced toughening were detected. Moreover, crack-deflection induced by nano dispersoids as well as crack-blunting at UFG/CG regions were considered as the main extrinsic toughening mechanisms. The proposed strategy can be applied to design the architecture of other PRMMCs with both high strength and high ductility. Aluminum alloys; Powder processing; Heterostructures; Particulate reinforced composites; Microstructural toughening

The importance of rate-dependent effects in modelling the micro-damage process zone in cortical bone fracture

A greater mechanistic understanding of bone’s fracture process is important to the development of better diagnostic and therapeutics for bone fragility and fracture. To aid in better understanding the fracture process of bone, in earlier work, a continuum damage mechanics (CDM)-based computational model was developed and experimentally validated for modelling the micro-damage process zone (MDPZ). The MDPZ is an important intrinsic toughening mechanism that forms during cortical bone fracture. Interestingly, to accurately model the MDPZ in the CDM-based model, rate-dependent effects were required. This was achieved by using a viscosity regularization scheme available in ABAQUS, the commercial FE software used to develop the model. In this study, a review of the CDM-based model is given, after which it is used to explore the significance of rate-dependent effects on the formation of the MDPZ. Specifically, we show how variations in the rate-dependent effect drastically affects the formation of the MDPZ. Furthermore, using data from previous work carried out by Willett and co-workers, irradiated bovine cortical bone was used as a case study to demonstrate the need for accounting for rate dependent effects in modelling the MPDZ. In this paper, it is shown that even if other degraded mechanical properties are accounted for, there is still a need to account for the reduction in rate-dependent effects, because of the irradiation, to accurately model the MDPZ and match experimental load deflection curves and J-integral fracture toughness values.The importance of rate dependency in MPDZ formation alludes to a strain rate hardening mechanism at play in its formation which has been previously explored in other biological nanocomposites such as nacre. In addition, it adds credence to the importance of the organic phase and probably the importance of intra- and interfibrillar interfaces found in the mineralised collagen fibril to bone’s intrinsic fracture resistance.

Bond Switching in Densified Oxide Glass Enables Record-High Fracture Toughness.

Humans primarily interact with information technology through glass touch screens, and the world would indeed be unrecognizable without glass. However, the low toughness of oxide glasses continues to be their Achilles heel, limiting both future applications and the possibility to make thinner, more environmentally friendly glasses. Here, we show that with proper control of plasticity mechanisms, record-high values of fracture toughness for transparent bulk oxide glasses can be achieved. Through proper combination of gas-mediated permanent densification and rational composition design, we increase the glasses' propensity for plastic deformation. Specifically, we demonstrate a fracture toughness of an aluminoborate glass (1.4 MPa m0.5) that is twice as high as that of commercial glasses for mobile devices. Atomistic simulations reveal that the densification of the adaptive aluminoborate network increases coordination number changes and bond swapping, ultimately enhancing plasticity and toughness upon fracture. Our findings thus provide general insights into the intrinsic toughening mechanisms of oxide glasses.

Improved impact property of long glass fiber‐reinforced polypropylene random copolymer composites toughened with beta‐nucleating agent via tunning the crystallization and phase

AbstractCrystallization and phase engineering offer a promising route to significantly improve the impact property of long glass fiber‐reinforced polypropylene random copolymer (LGF/PPR) composites. However, the nucleation and crystallization mechanism in the crystallization process, and the resulting phase change mechanism are still unclear, which severely limits the remarkable improvement of the toughness of LGF/PPR composites. Herein, we successfully fabricate toughened LGF/PPR composites with excellent heat deflection temperature and impact toughness via tuning the crystallization behavior and phase structure generated by introducing β‐nucleating agent (β‐NA). Through differential scanning calorimeter and wide‐angle X‐ray diffraction analysis, the influence of LGF and β‐NA on the nucleation and crystallization mechanism of the PPR matrix was revealed. Therefore, the critical crystallization parameters were calculated, and then the correlation was established with tensile and impact properties through regression analysis. The results show that the impact strength of β‐PPR and β‐LGF/PPR/MPPR are remarkably increased by 50.1% and 26.3% at the critical β‐NA content of 0.2 and 0.1 wt%, respectively, due to the intrinsic toughening mechanism. This work may pave the way for preparing a class of LGF/PPR composites with high‐impact toughness.

Engineering toughening mechanisms in architectured ceramic-based bioinspired materials

Ceramics offer many attractive properties including low-density, high compressive strength, remarkable thermal stability, and high oxidation/corrosion resistance. However, these materials suffer from brittleness, which substantially limits the range of their applications, where high toughness is required. This investigation draws inspiration from a concept of architectures with three-dimensional (3D) networks of weak interfaces targeting high toughness ceramics. In this study, a comprehensive method combining an advanced computational model with 3D digital image correlation (DIC) was developed to engineer bioinspired multilayered architectured ceramics and assesses their toughening and deformation mechanisms when subjected to a low-velocity impact load regime. A complete finite element (FE) analysis was conducted to precisely evaluate the crack growth and displacement field of the architectured ceramics and is compared to those of plain ceramics. The damage and displacement evolution results from FE analysis and experimental testing revealed that the primary source of toughening of the architectured ceramic systems is extrinsic, resulting from extensive crack deflection and delamination. Crack propagation along an irregular long path at the weak interfaces of architectured layers increased the toughness of the plain ceramics by two orders of magnitude. Based on the DIC data, both extrinsic and intrinsic toughening mechanisms were captured: sliding of the tiles in the architectured ceramics and channel plastic deformation in adhesive interlayers, respectively.

Controlling microstructure of FeCrMoBC amorphous metal matrix composites via laser directed energy deposition

Fe-based amorphous coatings are typically known for their high hardness and wear resistance and are often applied using thermal spraying techniques. When cladding these materials, using laser directed energy deposition (DED), it becomes possible to vary the cooling rate to create unique microstructures. Herein, it is demonstrated that a common FeCrMoBC coating alloy, typically known for its high hardness, can be fabricated into a variety of microstructures using DED, including an amorphous metal matrix composite with a soft dendritic phase and intrinsic toughening mechanism. The work offers the promise of using DED to fabricate custom claddings with high toughness as well as providing a potential route for creating ductile-phase-reinforced metallic glass composites using additive manufacturing.

Mechanical properties of extruded glass fiber reinforced thermoplastic polyolefin composites

AbstractEngineered structural materials are required to feature a combination of deformability (ductility) and strength to be considered damage‐tolerant for safety‐critical applications. These two mechanical properties, however, tend to be mutually exclusive, encouraging optimization of the trade‐off between strength and toughness. In this report, an elastomer and a glass fiber were incorporated into a blend of two grades of polypropylene (PP) to improve matrix toughness through both intrinsic and extrinsic toughening mechanisms. This study investigates the impact resistance (at 23°C and −30°C), and strength, stiffness, deformability, and processability of extruded compatibilized glass fiber reinforced thermoplastic polyolefin (TPO) composites at 23°C. For the hybrid composites contribution of different toughening mechanisms in attainment of the final impact strength is governed by the testing temperature and processing (extruder screw) speed. The intrinsic toughening mechanism induced by the presence of the ethylene α‐olefin copolymer is suppressed by the introduction of glass fiber at 23°C, irrespective of screw speed and screw configuration design. The heat distortion temperature (HDT), flexural modulus, and tensile strength exhibit a marked improvement by glass fiber inclusion at 23°C. By evaluating the performance of the composites at −30°C, it was observed that the impact energy of the elastomer modified hybrid composites may be enhanced in the same manner as the glass fibers toughen the brittle unmodified PP matrix. It was noted that contrary to the tensile properties at break, the yield behavior of the composites containing fibers, severely shortened, is independent of the presence of the fibers at 23°C.

Strength and toughness trade-off optimization of nacre-like ceramic composites

Bio-inspired by abalone nacre, all ceramic brick-and-mortar composites with impressive mechanical properties have been recently manufactured. Albeit comprising only brittle constituents, extrinsic reinforcement mechanisms impart to these nacre-like ceramics high toughness and non-catastrophic crack propagation properties. While several models have been developed to understand the mechanical properties of natural and synthetic brick-and-mortar materials, they have always considered a ductile interface and focused mostly on intrinsic toughening mechanisms. Modeling so far has not captured the extrinsic toughening mechanisms responsible for the properties of nacre-like ceramics. Here we show that the Discrete Element Method (DEM) can account for reinforcement mechanisms such as microcracking and crack deflection, and quantitatively assess strength, initiation toughness and crack growth toughness. Two approaches are studied to enhance strength and toughness of nacre-like ceramics, either by reinforcing the interface globally (an increase of the interface strength) or locally (addition of nano-bridges). We combine the results to provide design guidelines for synthetic brick-and-mortar composites comprising only brittle constituents.