Dislocation Annihilation Research Articles

Break through the strength-ductility trade-off dilemma in aluminum matrix composites via precipitation-assisted interface tailoring

Strength-ductility trade-off is usually an inevitable scenario in most engineering materials, including metal matrix composites (MMCs) where reinforcement particles significantly degrade ductility. The decrease of ductility is mainly attributed to dislocation pile-ups at the high mismatch interface between reinforcement particles and matrix, which can not lead to effective dislocation multiplication and annihilation, finally leading to a low work hardening rate. To address this challenge, herein we propose a precipitation-assisted interface tailoring (PAIT) mechanism to improve the coherency of interface between reinforcement particles and matrix by introducing an interphase (IP). To achieve this PAIT mechanism, we design a manufacturing process combining the conventional casting, friction stir processing (FSP), hot extrusion with heat treatment. A TiB2/Al-Zn-Mg-Cu composite fabricated with this process shows higher strength and ductility, which stand out from most available Al-based materials. In this composite, a Mg(Zn1.5Cu0.5) IP is introduced to improve the coherency and strength of the TiB2/Al interface by transforming the high mismatch TiB2/Al interface into the low mismatch TiB2/IP/Al multi-interfaces (i.e. sandwich structure). This effectively promotes dislocation multiplication and subsequent dislocation annihilation to increase the work hardening rate by restricting the dislocation pile-ups surrounding the interface, thus leading to a higher ductility. Our study aims to overcome the strength-ductility trade-off of MMCs by tailoring interface structure, which can provide insight into the production of high-performance MMCs.

A peridynamic approach to solving general discrete dislocation dynamics problems in plasticity and fracture: Part II. Applications

In Part II of this work we extend the method introduced in Part I to consider dislocation dynamic evolution through dislocations nucleation, glide, pile-up, and annihilation. The SP DDD-PD scheme is employed to investigate uniaxial tension in a single crystal and a polycrystal and verify its accuracy. The model is then used to simulate elastoplastic fracture by considering interactions between dislocations and crack growth. For Mode I elastoplastic fracture in a single crystal, we observe that the crack path is “attracted” towards regions of high density of gliding dislocations, leading to an undulating crack paths, as observed in experiments but never replicated by continuum-level computational models before. Tests on different sample sizes show how the proximity of constraints to the crack tip can lead to plastic hardening. Ductile-to-brittle transition happens naturally in this model when the crack, under Mode I displacement-controlled loading, approaches a free edge. A new way to calibrate the critical bond strain based on the material toughness or fracture energy is proposed. The present SP DDD-PD scheme can be used to investigate complicated elastoplastic fracture problems in which the interaction between dislocation motion and damage is critical.

Adding Cr and Mo simultaneously enhances the strength and impact toughness of TiC microparticle-reinforced steel matrix composites at high temperatures

The excellent mechanical properties of titanium carbide (TiC) microparticle-reinforced steel matrix composites make them particularly applicable in engineering. In this study, the influence of adding Cr and Mo on the strength and impact toughness of TiC microparticle-reinforced steel matrix composites at 25–600 °C was systematically analysed and the strengthening and toughness mechanisms were elucidated. The results showed that the strength and impact toughness of the TiC microparticle-reinforced steel matrix composites at high temperatures were simultaneously enhanced by adding 3 wt% Cr and 0.5 wt% Mo. Cr and Mo mainly increased the contributions of dislocation, precipitation and solution strengthening by reducing the dislocation annihilation and the coarsening rate of carbides. Moreover, improving the tempering stability of the matrix increased the failure temperature of the TiC microparticles from 500°C to 600°C by adding Cr and Mo. The volume fraction of V1/V2 variant pairs with a 60° misorientation angle was increased by increasing the driving force of the phase transformation. Combined with the recovery of martensite at high temperatures, the density of the high-angle grain boundaries was increased, resulting in greater impact toughness at high temperatures.

Edge-crack free and high mechanical properties of AA7075 sheets by using cryorolling and subsequent aging

In this study, AA7075 sheets were processed by cryorolling and room-temperature rolling respectively, and subsequent aging. The microstructure evolution and mechanical properties of AA7075 sheets were investigated by hardness measurements, tensile tests, X-ray diffraction, scanning electron microscopy and transmission electron microscopy. Results show that with the rolling reduction ratio of 80%, the room-temperature rolled samples had massive edge cracks, while the cryorolled samples were in good shape and without any cracks. The improved ductility of materials in cryogenic environments, the reduced precipitation and the absence of shear bands in sheets during cryorolling contributed to the reduced edge cracks. Compared to solution treated samples, the yield strength and ultimate tensile strength of cryorolled samples were increased by 155% and 44%, respectively, and the elongation decreased as a loss, which is obviously better than that of room-temperature rolled samples. After the subsequent aging treatment, the strength and ductility of the rolled samples were simultaneously improved, the yield strength of cryorolled + peak-aged sample was increased by 44 MPa and the elongation was increased by 68% compared with those of the cryorolled samples. Compared with room-temperature rolled + peak-aged samples, the strength of cryorolled + peak-aged sample was higher, and the elongation to failure and uniform elongation were increased by 58% and 72%, respectively. Numerous nanosized GP zones and η' phases were precipitated after aging, and the precipitation strengthening is the main contributor to the strength enhancement of the samples after aging. The improved ductility of cryorolled + peak-aged samples is mainly due to the combined effect of dislocation annihilation, uniform deformation and fine precipitates in them.

Shear-compression flow behavior and thermoforming properties of GH4169 superalloy

Shear-compression deformation (SCD) is more proper than uniaxial compression to simulate the actual thermoforming with non-single strain modes. The flow behavior and thermoforming properties of GH4169 superalloy were studied by SCD at 1000–1200 ℃, 0.01–1 s−1. The flow curves showed significant fluctuation characteristics caused by the alternating dislocation proliferation and the dislocation annihilation. The slot region of shear-compression specimens (SCS) was most deformed, thus stress and strain drastically concentrated. The thermal activation energy of SCD was determined to be 556.5 KJ/mol, which was higher than that under uniaxial compression (411.0 KJ/mol). It’s indicated that the existence of shear strain increased the difficulty of thermoforming. Besides, the stress accumulation near the niobium-rich carbon-borides caused the severe instability cracking at 1200 ℃. In addition, virtually no change in size of the second phases during SCD except for 1100 ℃− 0.01 s−1. The fraction of deformation textures along the {110}, {111}, and {001} orientations decreased successively, indicating {110} was the prior orientation for grain rotating in SCD. Moreover, based on the processing map, the optimal SCD window was determined as 1135–1150 ℃ and 0.1–0.32 s−1 to guide the actual thermoforming of GH4169 superalloy.

Evolution of grain size and texture of Zn-0.5Cu ECAP alloy during annealing at 200 ℃ and its impact on mechanical properties

Due to the low recrystallization temperature, the microstructure of wrought Zn alloys is naturally unstable, which affects their mechanical properties and limits their application. Therefore, it is crucial to elucidate the effect of microstructural evolution on mechanical properties of wrought Zn alloys. In this work, annealing treatment was performed on a Zn-0.5Cu (wt%) equal channel angular pressure (ECAP) alloy at 200 °C for different durations to investigate the microstructure evolution and its effect on the mechanical properties. An abnormal phenomenon that strength and ductility of the ECAP alloy decrease monotonically with increasing annealing time was observed, which is remarkably different from most other metallic alloys (Mg, Al, Cu, etc.). Detailed microstructure observations were conducted to unveil the mechanisms behind this abnormal phenomenon. Annealing for 1440 min induced not only an abnormal increase in texture intensity from 17.06 to 30.53 (which can be ascribed to preferential growth of high-texture grains with the<−12 to 10 >and<01–10 >components) but also a significant grain growth from 3.3 µm to 32.7 µm. Grain growth and dislocation annihilation resulted in the loss of strength, while the abnormal decrease in ductility during annealing was primarily due to texture enhancement and grain coarsening. The present work could provide guidance for the production and application of wrought Zn alloys in biomedical fields.

Size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy ultrathin sheet

• Cyclic deformation behavior of superalloy foil is represented by cyclic shear test. • Nonlinear unloading behavior at microscale becomes evident. • Bauschinger effect are affected by both geometric and grain size effect. • Size effect on instantaneous and permanent softening is revealed. • Work hardening stagnation is related to dislocation evolution and size effect. Superalloy ultrathin sheet is widely utilized in thin-walled components of aero-engine because of its excellent comprehensive performance. Nevertheless, it is hard to precisely predict the springback phenomenon during the plastic deformation of superalloy ultrathin sheet due to the size effect. To explore size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy sheets, the uniaxial tensile, cyclic loading and unloading, and cyclic shearing tests were conducted on superalloy ultrathin sheets with diverse grain sizes and thicknesses of 0.2 and 0.25 mm. The experimental results demonstrated that the increasing grain size is accompanied with the decrease of flow stress of superalloy ultrathin sheet and the change of density of forest dislocation and moving dislocation. The dislocation annihilation rate of superalloy ultrathin sheet increases with decreasing t / d ratio, and the nonlinear unloading behavior becomes more obvious. Meanwhile, the degradation of elastic modulus becomes more evident with the increasing grain size. Driven by back stress, Bauschinger effect of superalloy ultrathin sheet becomes more apparent with larger t / d ratio. In addition, the fine-grained superalloy ultrathin sheet shows obvious earlier re-yielding and large instantaneous softening rates and the variation of t / d ratio also affect the permanent softening and work-hardening stagnation of superalloy ultrathin sheet.

Study on the deformation mechanism of the Al0.1CrFeCoNi high entropy alloy at different deformation degrees under electric pulse treatment

In this study, electrical pulses were used as a treatment to investigate the role played by dislocations in the deformation mechanism of the Al0.1CrFeCoNi high-entropy alloy (HEA) at different stages of deformation. The results demonstrated that the HEA was completely deformed through dislocation slip during compression, and no twins were evident. Under the action of Electric pulse treatment (EPT), the specimen expanded thermally owing to Joule heating. Additionally, the pulse current accelerated the movement of the dislocations and led to dislocation annihilation, softening the material without changing the grain shape. However, further application of EPT with the same parameters failed to produce significant changes in the dislocation density, a phenomenon that has rarely been reported before. Our results provide strong theoretical and technical support for the rapid annealing of metallic materials during processing and the use of HEA in electrical structural components, such as wear-resistant coatings or parts resistant to galvanic corrosion.

Deformation Behaviour of Cold-Rolled Ni/CNT Nanocomposites

Metal matrix nanocomposites (MMNCs) reinforced by carbon nanotubes (CNTs) are good candidates to produce structural components in the mobility industry, given their unique properties. The manufacture of these components can involve plastic deformation. Therefore, it is crucial to understand whether reinforcement can influence the deformation behaviour of these nanocomposites. Thus, this work aims to study the deformation behaviour of MMNCs, given their importance and the lack of studies on this topic. Although nickel is not the most widely used metal as a matrix of nanocomposites, it presents mechanical properties superior to other matrices, such as aluminium. In addition, this metal has proven to establish a strong interface and integration of carbon nanotubes, making it an exciting material for the production and study of these nanocomposites. In that sense, nickel matrix nanocomposites are reinforced by 1.00 %vol. CNTs were produced by powder metallurgy using ultrasonication as a dispersion/mixture method. For comparison purposes, a nickel matrix was produced under the same conditions. Samples with and without CNTs were cold-rolled with thickness reductions between 10 and 60% (logarithmic strains between 0.11 and 0.92) to investigate the deformation behaviour. Microstructural characterization was performed using scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD). Microhardness tests were applied to evaluate their mechanical properties. The results revealed that the nanocomposites exhibited a softening for small strains (0.11 and 0.22). This decrease in hardness was attributed to the decline in dislocation density observed by EBSD, due to the rearrangement and annihilation of pre-existing dislocations that originated during production. A possible inversion can explain the decrease in dislocation density when minor strains are applied in the dislocation or deformation trajectory, known as the Bauschinger effect. The difference in the texture evolution of the nanocomposites can be explained by the initial crystallographic orientations, which are influenced by the presence of CNTs.

The coupling influences and corresponding mechanisms of high efficiency thermal-magnetic treatments on the dimensional stability of Al-Cu-Mg alloy

Al-Cu-Mg alloys are widely utilized as a key component of gyroscope navigation systems, since their dimensional stability under different service environments (e.g., thermal or magnetic fields) is the determinant factor for reliable navigation. In this work, a preliminary treatment under the coupling of thermal-magnetic fields was applied to optimize the dimensional stability of the alloy by tailoring the microstructural defects and second phases. A lower thermal strain value of ∼1.58 × 10–3 was rapidly achieved after 6 h by high-efficiency thermal-magnetic treatments (523 K and B = 0.3 T), in comparison with ∼1.67 × 10–3 by thermal treatment. The dimensional variation was mainly attributed to the dislocation density, volume fraction and shape of the Al2CuMg phase. Furthermore, the nucleation rate of Al2CuMg phases and the annihilation of dislocations were promoted under the coupling effect of the thermal-magnetic treatments. These microstructural evolutions accelerated the reduction of the stored energy and lattice distortion, therefore rapidly decreasing the thermal strain. As a result, a thermal-magnetic field treatment may serve as an effective method to improve the dimensional stability of Al-Cu-Mg alloys for further application in the field of space exploration.

Dislocation kinetics explains energy partitioning during strain hardening: Model and experimental validation by infrared thermography and acoustic emission

The energy dissipation and storage during strain hardening of metals have been investigated by means of complementary in situ techniques - infrared thermography (IRT), digital image correlation (DIC) and acoustic emission (AE). Inspired by experimental results obtained in the present work and data available in literature, we proposed the analytically tractable thermodynamic modelling approach, which is conceptually based on a single-variable dislocation evolution approach with a total dislocation density serving as a principal variable governing the strain hardening process. Unified by the kinetic approach involving generation, annihilation and motion of dislocations, the models accounting for the acoustic emission behaviour and heat dissipation under load have been proposed and verified experimentally. For the first time, we were able to demonstrate that the key parameters governing the dislocation storage and annihilation rates can be, in principle, recovered from independent AE and IRT measurements. These results agree favourably with the predictions of the dislocation-based constitutive strain hardening models of the Kocks-Mecking type. The self-consistency, versatility and predictive capacity of the proposed modelling approach are demonstrated in the examples of Cu–Zn alloys with different concentrations of Zn varied from 0 to 30% and correspondingly different stacking fault energies.

Effects of Cu-rich phases on microstructure evolution and creep deformation behavior of a novel martensitic heat-resistant steel G115

In this work, effects of Cu-rich phases on the microstructure evolution and creep deformation behavior of G115 steels with 1 (1Cu steel) and 2 wt% Cu (2Cu steel) were systematically investigated under 160–220 MPa at 650 °C. The results showed that dispersedly distributed Cu-rich phases played a vital role in retarding the microstructural degeneration and improving the creep strength. The Cu-rich phases inside grains could induce dislocation tangle and prohibit dislocation annihilation during creep, but they could be dissolved into the matrix due to the cutting effect of mobile dislocation lines. The Cu-rich phases at grain boundaries could hinder the migration of martensitic lath boundaries and thus delayed the creep failure behavior. Moreover, the independent Cu-rich phases at grain boundaries could provide heterogeneous nucleation sites for Laves phases, which strengthening pinning effect. As a result, compared with the 1Cu steel, the creep threshold stress of the 2Cu steel was enhanced from 103.36 to 117.93 MPa, and the creep lifetime was also prolonged markedly.

Effect of V–III Ratio‐Based Growth Mode on the Surface Morphology, Strain Relaxation, and Dislocation Density of AlN Films Grown by Metal‐Organic Chemical Vapor Deposition

Herein, regulation of the growth mode through manipulating the V–III ratio during metal‐organic chemical vapor deposition (MOCVD) growth of AlN films on c‐plane sapphire substrates and optimization of the crystalline quality and surface morphology of AlN films are demonstrated. Based on detailed analyses of the evolution process of surface morphology, dislocation annihilation, and stress state of the AlN film during MOCVD growth, it is found that 2D rather than 3D growth mode introduces tensile stress as well as promotes edge‐type threading dislocation (ETD) propagation and crack generation, while 3D growth mode produces rough surface. These results would help to further understand the AlN growth mechanism and provide important guidance on the preparation of AlN‐related epitaxial structure.

Molecular dynamics study of acoustic softening effect in ultrasonic vibration assisted tension of monocrystalline/polycrystalline coppers

Ultrasonic vibration assisted metal forming is a promising technology, but the microscopic mechanism of the ultrasonic effect on metal deformation has not been fully understood yet. In this paper, by molecular dynamics simulation, the microscopic mechanism behind the acoustic softening effect of ultrasonic vibration was studied. The stress superposition and acoustic softening can be simulated simultaneously by molecular dynamics method, and the stress–strain response of the polycrystalline copper simulations agrees well with the experimental results. Based on the analysis of atomic kinetic energy and dislocation density, it is found that ultrasonic vibration increases the atomic kinetic energy and promotes the generation, multiplication, motion, and annihilation of dislocations in the plastic deformation process, resulting in a reduction of dislocation tangles and pile-ups. Therefore, the hindrance to crystal sliding is significantly decreased, which promotes the plastic deformation accompanied by a macroscopic reduction in flow stress of copper. As for different ultrasonic parameters, the influence laws of ultrasonic amplitude and frequency on the deformation behaviors of coppers are different. These findings play an essential role in revealing the mechanism of ultrasonic vibration assisted plastic forming.

Strain hardening in twinning-induced plasticity stainless steel produced by laser powder bed fusion

A modelling approach is presented to identify the deformation mechanisms of 316L stainless steel produced by laser powder bed fusion (LPBF). The approach incorporates the evolution of dislocations, forming a forest, and of twins, which develop a back-stress. The overall plasticity behaviour is described in terms of dislocation multiplication and annihilation progress with strain. The modelling is matched up with detailed electron microscopy observations; the combination of both demonstrates the deformation behaviour of LPBF builds is intrinsically different to that of wrought alloys. LPBFed samples undergo three stages of deformation, with the first developing twins, which formation quickly saturates; the second sees a dramatic increase in dislocation forest hardening, combined with dislocation recovery; and the third undergoes dynamic recrystallisation taking place around heavily twinned sections. Opposite to wrought alloys, LPBFed specimens decrease their density of statistically stored dislocations throughout deformation, and it is shown that this behaviour is replicated by other LPBFed metals, including high-entropy alloys. The intrinsic behavioural differences in LPBF plasticity is thought to be due to the presence of a residual stress; this promotes dislocation recovery from the onset of deformation.

Combination of severe plastic deformation and heat treatment for enhancing the corrosion resistance of a new Magnesium alloy

In the present study, various processes have been carried out on the extruded Mg-4Zn-4Al-0.6Ca-0.5Mn (wt%) alloy to achieve a low corrosion rate Magnesium (Mg) alloy. Microstructure studies revealed that the extruded alloy contained the needle-like Al-Mn second phases and the globular and elongated (Mg,Al)2Ca + ϕ(AlMgZn) phases. After solution treatment, the area fraction of the second phase decreased drastically from 5.1 % to 2.4 %. The later multi-directional forging (MDF) formed a modified ultrafine grain structure with an average grain size of 0.9 µm. The post-annealing process reduced the dislocation density of the heavily-deformed grains of the MDFed alloy, resulting in a grain size of 5.89 µm and an area fraction of 2.8 %. The annihilation of dislocations and homogeneous distribution of broken second phase particles after MDF and post-annealing processes improved the ultimate compressive strength and compressive strain from 352 MPa and 4.2 % for the extruded to 376 MPa and 5.1 % for the post-annealed alloy. Moreover, by applying solution treatment, MDF, and post-annealing, the corrosion rate of the extruded alloy drastically decreased from 2.13 mm/y to 0.76 mm/y due to grain refinement and reduced area fraction of phases and their random distribution. According to the corrosion results, the area fraction of second phase particles and the grain size obtained after different processes significantly influenced the corrosion properties, which was discussed in detail in the present study. On the one hand, the post-annealed alloy contained a significantly lower area fraction of particles than the extruded alloy, reducing micro-galvanic corrosion. On the other hand, significant grain refinement after the MDF process lowered the corrosion rate compared to the extruded alloy. However, the short-time annealing process annihilated the dislocations and high-energy sites while not significantly increasing the grain size and deteriorating the mechanical properties. Therefore, the combination of MDF and short-time annealing could be a remarkable route to obtaining the low corrosion rate and high strength Mg alloy.

Influence of Mg on tensile deformation behavior of high Mg-content Al-Mg alloys

Al-Mg based alloys are known to experience dynamic strain aging (DSA) at room temperature, which is often associated with the diffusion of mobile Mg atoms to dislocation segments temporarily arrested at obstacles (e.g., forest dislocations) upon deformation in the DSA regime. With the emergence of new promising high Mg-content (> 6 wt.%) Al-Mg alloys, the combined effects of Mg content and DSA on their tensile flow behavior need to be better understood. In the present work, the tensile deformation behavior of Al and Al-(5.3, 6.4, 7.6 and 8.7) wt.% Mg samples tested at room temperature and at strain rates ranging from 0.0001 to 0.1 s−1 was investigated, based on the Kocks-Mecking-Estrin model combined with a DSA model, the Haasen plot as well as transmission electron microscopy. Particular focuses are placed on the influence of Mg solutes on DSA and associated strain hardening effects, on dislocation accumulation and annihilation as well as on apparent activation volume. We show that the synergistic effect of the Mg-dislocation interactions and DSA effectively reduces the rate of dynamic recovery via suppressing dislocation cross-slip, leading to an enhanced strain hardening capacity for the Al-Mg alloys with a higher Mg content. The influences of DSA on the yield strength, flow stress and apparent activation volume of thermally-assisted deformation of the Al-Mg alloys are also discussed to elucidate fundamental insights into the development of new high Mg-content Al-Mg alloys with superior mechanical performance.

Tuning the mechanical properties of copper by changing deformation temperature and recrystallization fraction

In order to reveal the effects of cryogenic temperature on the relationship between mechanical properties and recrystallization percentage, the tensile mechanical behaviors of partial recrystallized copper have been investigated by tensile test at 293 K and 77 K, respectively. It is found the yield strength of copper maintains approximate linearity with recrystallization percentage at 77 K and 293 K. Microscopic observations manifested that the deformation twinning was not activated and dislocations slip still dominated plastic deformation at 77 K. Based on the proliferation and annihilation of dislocations, an exponent hardening model was employed to explain the simultaneous improvement of strength and ductility caused by cryogenic temperature.

Coupled diffusion-mechanics framework for simulating hydrogen assisted deformation and failure behavior of metals

Understanding of years-old multifaceted hydrogen-assisted damage evolution necessitates efforts to model the coupled diffusion-mechanics response in metallic materials. Informed by the dislocation-hydrogen interactions, understood earlier via experiments and/or multi-scale modeling techniques, this work presents a dislocation density-based crystal plasticity model coupled with a hydrogen diffusion/trapping model to simulate the hydrogen-assisted deformation and failure under the HELP mechanism of hydrogen embrittlement. The important role of hydrogen on dislocation multiplication, annihilation and dislocation interaction weakening are included in the presented framework. Two possible scenarios under HELP mechanism, leading to H-induced macroscopic softening or hardening as a result of trade-off between the hydrogen-induced weakening of dislocation interactions and hydrogen-induced increased dislocation density emerges from the simulation studies. These finding points towards the inevitable role of HELP mechanism to cause early failure in metals either working independently or in support with additional mechanisms.

Constitutive equation and dynamic recovery mechanism of high strength cast Al-Cu-Mn alloy during hot deformation

The hot deformation behavior and precipitates of cast AlCu4.4Mn0.6 alloy has been investigated by compression tests in a Gleeble-3500 thermodynamic simulator at the temperature range of 200−290 °C and strain-rate range of 0.01−10 s−1. The dynamic recovery (DRV) of AlCu4.4Mn0.6 alloy in hot deformation was sensitive to temperature and strain-rate, and was accelerated by increasing the deformation temperature and strain-rate. The heat-treated AlCu4.4Mn0.6 specimen exhibited high strength as the compressive flow stress was about 310 MPa at 290 °C and the strain-rate of 10−1. A accurate constitutive equation was established with the correlation coefficient (R) of 96.2 % and the average absolute relative error (AARE) of 4.65 %. The predicted flow stress was in good agreement with the experimental results. Nanoscale Ω, θ′ and T phases were uniformly distributed in the matrix of AlCu4.4Mn0.6 alloy and hindered dislocation movement in hot deformation process, leading work hard (WH) of the alloy. Meanwhile the DRV promoted the dislocation annihilation and polygonization, resulting in the formation of sub-boundaries and the softening of the alloy. The flow stress was almost stable or gradually decreased with the increase of strain.