Mechanical Twinning Research Articles

The determining role of carbon addition on mechanical performance of a non-equiatomic high-entropy alloy

• The role of C on the microstructure and mechanical properties are discussed. • The microstructure of the tensile specimen interrupted at different tensile strains are examined by EBSD and TEM. The deformation mechanism of a C-doped iHEA with excellent mechanical properties is discussed. • The contributions of different strengthening mechanism to yield strength are calculated and the comprehensive strengthening mechanism is discussed. The mechanical properties and deformation mechanism of a C-doped interstitial high-entropy alloy (iHEA) with a nominal composition of Fe 49.5 Mn 29.7 Co 9.9 Cr 9.9 C 1 (at.%) were investigated. An excellent combination of strength and ductility was obtained by cold rolling and annealing. The structure of the alloy is consisted of FCC matrix and randomly distributed Cr 23 C 6 . For gaining a better understanding of deformation mechanism, EBSD and TEM were conducted to characterize the microstructure of tensile specimens interrupted at different strains. At low strain (2%), deformation is dominated by dislocations and their partial slip. With the strain increase to 20%, deformation-driven athermal phase transformation and dislocations slip are the main deformation mechanism. While at high strain of 35% before necking, deformation twins have been observed besides the HCP phase. The simultaneous effect of phase transformation (TRIP effect) and mechanical twins (TWIP effect) delay the shrinkage, and improve the tensile strength and plasticity. What's more, compared with the HEA without C addition, the yield strength of the C-doped iHEA has been improved, which can be attributed to the grain refinement strengthening and precipitation hardening. Together with the lattice friction and solid solution strengthening, the theoretical calculated values of yield strength match well with the experimental results.

Mechanical property comparisons between CrCoNi medium-entropy alloy and 316 stainless steels

• The CrCoNi medium-entropy alloy shows a superior strength and ductility synergy, Charpy impact energy ( A K ), and fracture toughness at cryogenic temperatures as compared to both 316L and 316LN stainless steels. • These three alloys all rely heavily on shear transformations upon plastic straining, with deformation twinning dominating in CrCoNi while martensitic transformation involved in stainless steels. We systematically compared the mechanical properties of CrCoNi, a recently emerged prototypical medium-entropy alloy (MEA) with face-centered-cubic (FCC) structure, with hallmark FCC alloys, in particular, the well-known austenitic 316L and 316LN stainless steels, which are also concentrated single-phase FCC solid solutions and arguably next-of-kin to the MEAs. The tensile and impact properties, across the temperatures range from 373 K to 4.2 K, as well as fracture toughness at 298 K and 77 K, were documented. From room temperature to cryogenic temperature, all three alloys exhibited similarly good mechanical properties; CrCoNi increased its tensile uniform elongation and fracture toughness, which was different from the decreasing trend of the 316L and 316LN. On the other hand, the stainless steels showed higher fracture toughness than CrCoNi at all temperatures. To explain the differences in macroscopic mechanical properties of the three alloys, microstructural hardening mechanisms were surveyed. CrCoNi MEA relied on abundant mechanical twinning on the nanoscale, while martensitic transformation was dominant in 316L at low temperatures. The deformation mechanisms in the plastic zone ahead of the propagating crack in impact and fracture toughness tests were also analyzed and compared for the three alloys.

N-Iodosaccharin-pyridine co-crystal system under pressure: experimental evidence of reversible twinning.

This work presents a single-crystal X-ray diffraction study of an organic co-crystal composed of N-iodosaccharin and pyridine (NISac·py) under hydrostatic pressure ranging from 0.00 (5) GPa to 4.5 (2) GPa. NISac·py crystallizes in the monoclinic system (space group B21/e). The unconventional setting of the space group is adopted (the conventional setting is P21/c, No. 14) to emphasise the strongly pseudo-orthorhombic symmetry of the lattice, with a β angle very close to 90°. The crystal structure contains one molecule each of N-iodosaccharin (NISac) and pyridine (py) in the asymmetric unit (Z' = 1), linked via an Nsac...I...N'py halogen-bonding motif. A gradual modification of this motif is observed under pressure as a result of changes in the crystalline environment. Mechanical twinning is observed under compression and the sample splits into two domains, spanning an unequal volume that is mapped by a twofold rotation about the [100] direction of the B21/e unit cell. The twinning is particularly significant at high pressure, being reversible when the pressure is released. The structure of the twinned sample reveals the continuity of a substantial substructure across the composition plane. The presence of this common substructure in the two orientations of the twinned individuals can be interpreted as a structural reason for the formation of the twin and is the first observed example in a molecular crystal. These results indicate that the anisotropy of intermolecular interactions in the crystal structure results in an anisotropic strain generated upon the action of hydrostatic compression. Periodic density functional theory calculations were carried out by considering an isotropic external pressure, the results showing good agreement with the experimental findings. The bulk modulus of the crystal was obtained from the equations of state, being 7 (1) GPa for experimental data and 6.8 (5) GPa for theoretical data.

The effects of post weld heat treatment for welded high-Mn austenitic steels using the submerged arc welding method

The high-Mn austenitic steels exhibit fully austenitic structure at room temperatures while showing twinning mechanisms during deformations. In the SAW welding process, the microstructure and mechanical properties of heat affected zone (HAZ) and weld metal (WM) are affected by the welding heat causing potential degradation of mechanical properties due to the segregation and depletion of Mn in HAZ and WM regions. In this study, post weld heat treatment (PWHT) was performed at 800 °C, 900 °C and 1000 °C to improve the mechanical properties of welded high-Mn austenitic steels. We examined electron backscattered diffraction (EBSD) and energy dispersive X-ray spectroscopy (EDS) analysis to investigate the relationship between microstructure and mechanical properties after heat treatment. In particular, mechanisms of impact toughness improvement was identified by analyzing the microstructure and deformation behavior such as mechanical twin and grain size through the instrumented Charpy impact test and EBSD analysis.

Failure analysis of cartridge brass shell

Cartridge brass, because of its high ductility and formability, is used for the development of different ammunition components, plumbing accessories, fasteners, radiator cones etc. A series of cupping, annealing, deep-drawing, tapering and washing operations on the as-received brass disc are generally required for fabrication of different ammunition components. A 130 mm shell made up of cartridge brass was reported to crack during firing. These cracks led to shell expansion, which was stuck in the cannon and caused clogging. Failure analysis of brass shell was carried out. Overall composition of the brass shell was in accordance with 70/30 brass. Microstructural and mechanical characterization of the failed brass shell revealed presence of elongated grains, mechanical twins, relatively higher strength and lower ductility, which pointed out towards the possibility of insufficient annealing times. On the other hand, discoloration of the crack surface, porous and zinc depleted microstructure near cracks and transgranular mode of failure without multiple branching revealed that the brass shell suffered from plug type dezincification. Reduced strength of the studied brass shell due to dezincification helped in crack initiation whereas reduced ductility due to insufficient annealing time facilitated crack propagation. Use of alloys which are more resistant to dezincification as a starting material and optimization of annealing times to obtain desired levels of ductility, were recommended as corrective measures.

Evolution of deformation twinning mechanisms in magnesium from low to high strain rates

We present a systematic investigation of {101¯2} extension twinning mechanism in single crystal magnesium micropillars deformed over seven orders of magnitude of strain rate, from 10–4 to 500 s−1, revealing how the accommodation of newly formed twins evolves with and depends on the kinetic compatibility of interfacial processes when high deformation rates are imposed. By combination of post-mortem 3D Electron Backscattered Diffraction, Transmission Kikuchi Diffraction and Transmission Electron Microscopy techniques, this work unveils the progressive evolution of the accommodating twin mechanisms from low to high strain rate, correlating differences in mechanical behavior with differences in twin crystallography. Away from quasi–static conditions, simple considerations of twinning shear do not suffice to describe unconventional twin morphologies, requiring the competition between newly activated dislocations and lattice distortions for allowing the evolution of the twin boundary along non–invariant twin planes. Under shock compressions, the basal/prismatic transformation establishing a lattice misorientation of 90° entirely governs the parent → twin conversion. The results illustrated here confirm that some of the recent interpretations deduced by particular twin morphologies are not universally valid and that deformation twinning is not only stress- but also strongly time–controlled.

Cyclic hardening/softening and deformation mechanisms of a twip steel under reversed loading

Push-pull tests at fixed plastic strain amplitude or fixed stress amplitude were run on a TWIP steel, and followed by TEM observations, to analyze its cyclic behavior in relation with the deformation mechanisms. The kinematic and isotropic components of the flow stress were measured throughout the whole cyclic hardening/softening stages, and their evolution with the cumulated plastic strain was compared to those measured in tension. The rise of the internal stress was found responsible for the initial cyclic hardening, but this stress reached at most 50% of the flow stress, as compared to nearly 70% in tension. Special constitutive equations were identified to capture these evolutions, as well as the transition from hardening to softening. Both components of the flow stress slightly decrease during the softening stage, whose origin is discussed, based on TEM observations at peak stress amplitude, or after softening. The present measurements and TEM observations, combined with those from a previous study of twinning/detwinning kinetics in push-pull on the same steel [29], suggest that under cyclic loading, mechanical twinning cannot be responsible for significant kinematic hardening of intragranular nature (or “dynamic Hall-Petch effect”), but rather contributes to a back stress of intergranular origin.

The influence of temperature on the strain-hardening behavior of Fe-22/25/28Mn-3Al-3Si TRIP/TWIP steels

The influence of temperature and stacking fault energy (SFE) on the strain-hardening behavior and critical resolved shear stress for twinning was investigated for three Fe–22/25/28Mn–3Al–3Si wt.% transformation- and twinning-induced plasticity (TRIP/TWIP) steels. The SFEs were calculated by two different methods, density functional theory and statistical thermodynamic modeling. The dislocation structure, observed at low levels of plastic deformation, transitions from “planar” to “wavy” dislocation glide with an increase in temperature, Mn content, and/or SFE. The change in dislocation glide mechanisms from planar to wavy reduces the strain hardening rate, in part due to fewer planar obstacles and greater cross slip activity. In addition, the alloys exhibit a large decrease in strength and ductility with increasing temperature from 25 to 200 °C, attributed to a substantial reduction in the thermally activated component of the flow stress, predominate suppression of TRIP and TWIP, and a significant increase in the critical resolved shear stress for mechanical twinning. Interestingly, the increase in SFE with temperature had a rather minor influence on the critical resolved shear stress for mechanical twinning, and other temperature dependent factors which likely play a more dominant role are discussed.

Study on the construction theory of digital twin mechanism model for mechatronics equipment

Study on the construction theory of digital twin mechanism model for mechatronics equipment

Effects of increasing the strain rate on mechanical twinning and dynamic strain aging in Fe-12.5Mn-1.1C and Fe–24Mn-0.45C–2Al austenitic steels

Understanding the relationship between mechanical twinning and dynamic strain aging (DSA) in austenitic steels is necessary for steel development. DSA can be manipulated by changing the strain rate during tension tests, or by alloying austenitic steels with aluminum. In the current study, 12.5%Mn-1.1%C austenitic steel and 24%Mn-0.45%C–2%Al austenitic steel were investigated under different strain rates. Increases in the strain rate resulted in an enhanced resistance of the steels to the plastic deformation only during early stages of strain (at 3% strain) because of mechanical twinning promotion. On one hand, at 25% strain under low strain rate deformation, the Al-alloyed steel showed a tendency to form more twin plates than the Al-free steel as indicated by the transmission electron microscopy. On the other hand, at 25% strain under a high strain rate deformation, the Al-free steel showed an enhanced twin plates propagation due to a stronger self-segregation/depletion of the interstitial atoms (the carbon concentration ranged between 0 and 11 at.%) as revealed by the 3D atom probe tomography. Furthermore, the Al-alloyed steel showed a reduced twin volume fraction with a strain rate increase due to shifting of the stacking fault energy to higher values.

Hierarchical structure and deformation behavior of a novel multicomponent β titanium alloy with ultrahigh strength

Based on the general [Mo] equivalent criterion and d-electron orbital theory, a new ultrahigh-strength β titanium alloy with eight major elements (Ti-4.5Al-6.5Mo-2Cr-2.6Nb-2Zr-2Sn-1V, TB17) for industrial applications was developed. An ingot of five tons was successfully melted by thrice vacuum consumable arc melting. The microstructure and elements partitioning of different conditions were investigated systematically. The results suggest that the hierarchical structures of micro-scale first α phase (α f ), nano-scale secondary α phase (α s ), and ultrafine FCC substructures can be tailored by solution plus aging (STA) heat treatment. The lateral and epitaxial growth of α f phase promotes the HCP-α to FCC substructure transformation with the help of elements partitioning during the aging process. Moreover, the element V, generally regarded as β stabilizer, is found to mainly concentrate in the Al-rich α f phase in this study probably due to its relatively lower content and the strong bonding energy of Al-V. The hierarchical structure has a strong interaction with dislocations, which contributes to achieve a superhigh strength of 1376 MPa. In addition, the plastic strain is partitioned in the multi-scale precipitates (such as the α and FCC substructures) and β matrix, resulting in a considerable plasticity. TEM observation demonstrates that high density entangled dislocations at interfaces and mechanical twins exist in the STA sample after tensile test. It can be deduced that both dislocation slipping and twinning mechanisms are present in this alloy. Therefore, TB17 alloy can serve as an excellent candidate for structural materials on aircrafts that require high strength and lightweight. • A novel β titanium alloy with ultrahigh strength of 1376 MPa was developed. • The multi-scale hierarchical structures were tailored by heat treatment. • The transformation from HCP-α to FCC-substructure was observed. • The V element mainly concentrated in the micro-scale α lath.

Improved Fracture Toughness of Polycrystalline γ‐TiAl‐Based Intermetallic Alloys with a Favorable Deformation Mechanism of Twinning

High‐density deformation nanotwins markedly strengthen TiAl‐based alloys; however, the improvement in strength generally leads to a reduction in fracture toughness for most structural materials. It is, therefore, necessary to investigate the benefits of high‐density deformation nanotwins for the improvement in fracture toughness of TiAl‐based alloys. Herein, the fracture toughness of two Ti‐45.5Al‐4Cr‐2.5Nb alloys with a favorable deformation mechanism of twinning (prepared by annealing the continuous casting (C. C.) alloy at 1250 °C and 1270 °C for different durations, respectively) is investigated and compared with that of the unannealed continuous casting (C. C.) alloy, in terms of room‐temperature (RT) tensile properties and microstructures. It is found that the two heat‐treated Ti‐45.5Al‐4Cr‐2.5Nb alloys exhibits a higher fracture toughness than the C. C. alloy. Shear ligaments and slip bands are the main toughening mechanisms for the two heat‐treated alloys; their generation is closely related to the enhancement in the plastic deformability of lamellar structures. In addition, the increase in (B2 + γ)‐coupled structures is found to impose a negative effect on the toughening of the investigated alloys. High‐density deformation nanotwins favor the improvement in fracture toughness of TiAl‐based alloys by improving their fracture strength and plastic deformability, while decreasing their work‐hardening exponent.

Digital Twin-Based Risk Control during Prefabricated Building Hoisting Operations.

Prefabricated buildings have advantages when it comes to environmental protection. However, the dynamics and complexity of building hoisting operations bring significant safety risks. Existing research on hoisting safety risk lacks a real-time information interaction mechanism and lacks scientific control decision-making tools based on considering the correlation between safety risks. Digital twin (DT) has the advantage of real-time interaction. This paper presents a safety risk control framework for controlling prefabricated building hoisting operations based on DT. In the case of considering the correlation of the safety risk index of hoisting, the safety risk hierarchy model of hoisting is defined in the process of building the DT model. The authors have established a Bayesian network model into the process of the integrated analysis of the digital twin mechanism model and monitoring data to realize the visualization of the decision analysis process of hoisting safety risk control. The key degree of the indirect inducement variable to direct inducement variable was calculated according to probability. The key factor leading to the occurrence of risk was found. The effectiveness of the hoisting safety risk control method is verified by a large, prefabricated building project. This method provides decision tools for hoisting safety risk control, assists in formulating effective control schemes, and improves the efficiency of information integration and sharing.

Strengthening CrFeCoNiMn0.75Cu0.25 high entropy alloy via laser shock peening

For most metallic materials, surface hardening via modifying the near-surface microstructure is an effective method for improving mechanical properties. Among these processes, laser shock peening (LSP), which is versatile and nondestructive to the fabricated product shape, has received much attention. The present work has shown that the mechanical properties of CrFeCoNiMn0.75Cu0.25 high entropy alloy (HEA) have a significant improvement after LSP treatment. Yield strength more than two times of as-cast alloys is achieved in HEA samples treated by LSP for 4 cycles, due to the introduction of a gradient microstructure comprising subgrains, dense dislocations and nano-twins near the treated surface. The combination of dislocation hardening and mechanical twinning improves the strain hardening ability for the LSP-treated HEA, leading to excellent plasticity during tensile loading. Grain refinement also takes place via a faulting process of dislocation dissociation on nearly every {111} plane. Then, TEM observations and finite simulation of the LSP processed HEA samples after different levels of accumulated strain demonstrate that further tensile deformation is mainly accommodated by dislocations in the core region of the sample unaffected by the LSP, while the top LSP-affected layer accommodates little further plasticity as it is sufficiently hardened by the LSP. The present results indicate the possibility to develop gradient-structured HEAs with excellent mechanical properties using laser shock peening.

Effect of cryo-rolling on mechanical properties and microstructure of pure copper

It is a challenging task to achieve high strength without any loss in its electrical conductivity in pure copper because commonly used strengthening mechanisms such as alloying, grain boundary strengthening, and dislocation, result in an increase in strength but simultaneously reduce its electrical conductivity. However, if strengthening is achieved by introducing twin boundaries, then the reduction in electrical conductivity is minimal. These twin boundaries can be introduced in pure copper by low-temperature plastic deformation. Thus, the main objectives of the present research work are to understand the evolution of the microstructure and the resulting mechanical property correlation during liquid nitrogen temperature (LNT) deformation and to compare it with room temperature (RT) deformation. For profile rolling analysis, copper is subjected to profile rolling at both RT and LNT rolling processes to a true strain of 1.77 with a step size of 0.11% strain. High-resolution electron backscatter diffraction coupled with orientation image mapping technique and transmission electron microscopy are used for microstructural characterization of the profile-rolled copper samples. The microstructural characterization reveals mechanical twins of 10–100 nm thickness in samples subjected to LNT, whereas there are no traces of mechanical twins in RT samples. The mechanical characterization by tensile test and hardness test shows that the samples deformed at LNT conditions have superior properties compared to RT.

Influence of precipitate evolution on the impact fracture behavior in Nb-containing 16Cr–25Ni superaustenitic stainless steel weld metal

In this work, the precipitate evolution and its influence on the impact fracture behavior of Nb-containing 16Cr–25Ni superaustenitic stainless steel weld metal were systematically studied via scanning electron microscopy (SEM), X-ray diffraction (XRD), transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD). Results show completely transgranular ductile fracture mode of as-welded condition, of which the M6C carbides and Nb(C, N) carbonitrides contributed to the crack initiation, but the interface between M6C carbide and matrix was more prone to crack under impact load. In contrast, due to the semi-continuous distributed M23C6 carbides on the grain boundary, an intergranular/transgranular mixed mode was observed in the post-weld heat treatment (PWHT) sample. Additionally, the crack sources in grain interior were not limited to primary precipitation phases, whereas secondary M2(C, N) carbonitrides and M23C6 carbides also acted as preferential sites for crack initiation. The massive M2(C, N)/matrix and M23C6/matrix interfaces led to easier crack propagation path simultaneously. Moreover, the deformation mechanism were governed by dislocation slip and twinning in the impact fracture of as-welded sample, but the mechanical twins disappeared in the fractured sample at PWHT condition, which was attributed to the local stress concentration in the matrix could not exceed the critical twinning stress. Therefore, the combination of secondary precipitates induced embrittlement and weakened plastic deformation capacity of matrix, leading to the impact toughness declined from 91.0 ± 3.6 J to 34.3 ± 4.6 J after PWHT.

Microstructure-mechanical properties evaluation of AISI 304 steel during back-annealing

ABSTRACT In this research, the effect of back-annealing on the microstructure and mechanical properties of deformed austenitic stainless steel was studied. After the annealing treatment, the density of defects including mechanical twins and strain-induced martensite (SIM) were reduced in the microstructure. At 700°C both diffusional and shear reversion mechanisms (DRM and SRM) were active, while at higher temperatures (800 and 900°C) the SRM was dominant. After the annealing at 700°C for 60 min, the microstructure changed significantly and new grains were widely observed which resulted from the reversion of γ through the DRM and SRM. The results showed a decrease in yield (940 MPa) and ultimate tensile (978 MPa) strengths in annealed sample at 700°C for 10 min with respect to the deformed steel, while the total elongation has not changed significantly and remains around 20%. By increasing the annealing time to 60 min, the yield and ultimate tensile strengths of steel decreased to 640 and 830.4 MPa, respectively, and the total elongation increased significantly to 40.5%. The fracture surface of annealed sample at 700°C for 10 min was heterogeneous. After 60 min, the fracture surface became homogeneous and fine dimples were uniformly observed throughout the surface.

Circumventing the strength–ductility trade-off of β-type titanium alloys by defect engineering during laser powder bed fusion

In this study, we propose a novel defect engineering strategy for circumventing the strength–ductility trade-off of a β-type Ti–35Nb–7Zr–5Ta alloy and discuss its underlying mechanism. This strategy is based on the simultaneous introduction of dislocations and twins into the alloy structure through the thermal stress generated during additive manufacturing via laser powder bed fusion (LPBF). As a result, the LPBF-fabricated alloy contains high-density dislocations and two different types of nanosized {112}〈111〉 mechanical twins: unique zigzag-shaped and conventional lamellar ones. Interestingly, the produced alloy exhibits a high tensile yield strength of 816 MPa and large elongation of 16.5%, which significantly exceed the published values for other representative β-type titanium alloys fabricated by various material processing methods. Such a high yield strength is predominantly attributed to the introduced defects, and the relative contributions of dislocation strengthening and twin strengthening are equal to 58.0% and 26.1%, respectively. Meanwhile, the large elongation results from the inhibition effect of the produced twins on the dislocation motion as well as from their dislocation pass-through and growth. The obtained results can provide guidelines for the microstructural design and fabrication of novel β-type titanium alloys with excellent mechanical properties by defect engineering during additive manufacturing.

Multiple minor elements improve strength-ductility synergy of a high-entropy alloy

The developments of multicomponent high-entropy alloys usually put emphasis upon the roles of multiple principal elements in optimizing the various properties. Instead of tuning the principal elements, here we propose to use multiple minor alloying elements to improve performance of HEAs. To this end, the microstructure and mechanical behavior of a newly developed alloy, i.e., Fe35Ni20Co20Cr20Al2.5Ti1.0Cu1.0Si0.5 (at. %), have been investigated. The alloy decorated by the multiple minor alloying elements (i.e., Al, Ti, Cu and Si) exhibits a single face-centered cubic (FCC) γ phase in fully recrystallized state. Compared with the undecorated Fe40Ni20Co20Cr20 (at. %) counterpart with similar grain size, the yield strength of the decorated alloy sample with multiple minor elements is enhanced by ∼19% at a high elongation of ∼74%. Microstructural characterizations indicate that dislocation slip prevails at the early stages of plastic deformation while mechanical twins are observed to occur at the late deformation stage. The local stress field caused by the atomic size mismatch and elastic mismatch originated from the multiple minor elements significantly impedes the movement of dislocations thus improves the strength. Such retarding effect of the multiple minor elements on mobile dislocation further hinders the generation of stacking faults on adjacent atomic planes and thereby increases the FCC-γ phase stability, which also postpones the deformation twinning upon tension. This work demonstrates the practical significance of introducing multiple minor alloying elements with their synergistic effect into HEAs, and the design strategy enlarges the space for compositional design of advanced alloys.

Superlative room temperature and cryogenic tensile properties of nanostructured CoCrFeNi medium-entropy alloy fabricated by powder high-pressure torsion

Attaining decent tensile properties in materials fabricated by conventional powder metallurgy (PM) techniques has perennially been a pivotal challenge due to structural defects— typically pores. This work fabricates a nanostructured CoCrFeNi medium-entropy alloy with an uttermost relative density of 99.63% through PM, i.e., cold powder consolidation using high-pressure torsion followed by annealing. The cold-consolidated sample showed outstanding tensile strengths of 2.06 GPa and 2.81 GPa at room and cryogenic temperatures, respectively, which was never achieved in PM-processed materials. The enhanced cryogenic tensile properties can be associated with intensive mechanical twin activities. Additionally, engineering the microstructure through subsequent annealing leads to a desirable synergy of tensile strength and ductility, which are highly sought after in structural applications. The present findings pave the way to fabricate the parts with superior tensile properties for cryogenic applications through a PM-based approach.