Continuous Softening Research Articles

Strain glass transition in Ti48Ni50Co2 alloy

Limited studies have been conducted on the impact of the Ni/Ti ratio on the strain glass (STG) transition behavior in TiNiCo alloys. For this work, Ti50-xNi48+xCo2 (x = 1, 2) alloys with varying Ni/Ti ratios are prepared to investigate the microstructural evolution, temperature-dependent electrical resistivity, and dynamic mechanical characteristics. It was found that no martensitic transformation occurs in Ti48Ni50Co2 owing to the increasing Ni/Ti ratio, but instead a STG transition was confirmed by the existence of nanodomains. Consequently, a continuous softening of storage moduli over a broad temperature range was observed.

Influence of Severe Plastic Deformation and Aging on Low Cycle Fatigue Behavior of Al-Mg-Si Alloys.

Strain-controlled low cycle fatigue (LCF) tests were conducted on conventionally grained (CG) and ultrafine-grained (UFG) Al-Mg-Si alloys treated under various aging conditions. In the cyclic stress response (CSR) curves, CG peak-aged (PA) alloys showed initial cyclic hardening and subsequent saturation, whereas CG over-aged (OA) alloys displayed cyclic softening behavior close to saturation. The UFG materials exhibited continuous cyclic softening except for UFG 3; it originates from the microstructural stability of the UFG materials processed by severe plastic deformation (SPD). Using a strain-based criterion, the LCF behavior and life of the CG and UFG materials were analyzed and evaluated; the results are discussed in terms of strengthening mechanisms and microstructural evolution. In the CG materials, the LCF life changed markedly owing to differences in deformation inhomogeneity depending on the precipitate state. However, the UFG materials displayed a decreasing LCF life as cyclic softening induced by dynamic recovery became more severe; additionally, a relationship between the microstructural stability of the UFG materials and the cyclic strain hardening exponent n' was suggested.

Investigation of ratcheting fatigue behavior and failure mechanism of 1Cr18Ni10Ti pressure pipe under different force amplitudes and internal fluid pressure

This work reports on the development of an improved testing system to examine the effects of force amplitude and internal fluid pressure on ratcheting behavior and failure mechanism of 1Cr18Ni10Ti aero-engine pipe. Experimental results indicate that the ratcheting displacement and its rate during steady stage increase with the increasing force amplitude or internal fluid pressure, exhibiting a reverse tendency to fatigue life. Continuous cyclic softening response until fatigue fracture was observed in all conditions. Furthermore, microstructural evolution was characterized by SEM, EDS, XRD, and EBSD. The critical force amplitude to trigger noticeable dislocation accumulation and transition from austenite to ferrite phase was evaluated to be around 1900 N. The results highlight the decreased high-angle grain boundary (HAGB) and increased dislocation density causing the sample with a higher force amplitude to be more inclined to fracture. The initiation of fatigue crack was accelerated by the accumulation of dislocation within ferrite phase grains. Similar fatigue fracture morphology with ovalization phenomenon was observed in all conditions. To predict the ratcheting fatigue life of aero-engine thin wall pipes, a validated fatigue life estimation model considering steady ratcheting displacement rate based on a finite element analysis (FEA) model was conducted, and all of the fatigue data are contained in a 1.1X scatter band.

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue.

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Hot deformation behavior and microstructure evolution of a novel Mn-containing HEA

The deformation behavior and microstructure evolution of a novel Mn-containing HEA were explored during the deformation temperature ranges of 800∼1100 °C, and strain rate ranges of 0.001∼1s−1. The study results indicate that the true stress-strain curves after work hardening exhibit continuous softening type at low strain rate ranges of 0.001–0.01 s−1, while softening then steady-state type at high strain rate ranges of 0.1∼1s−1, respectively. The activation energy (Q) and stress exponent (n) are calculated to as 404.6 kJ/mol and 4.9016, respectively. As the strain increases, the flow instability is prone to expand towards the regions of lower strain rate and higher deformation temperature, and the optical processing window is determined at 1050–1100 °C and 0.001–0.002 s−1. The strain and stress field distribution of the FEM simulations reveal the inhomogeneous deformation and the damage field distribution predict the crack region of deformation specimen. The critical (εc)/peak strain (εp) for DRX do not display a proportional relationship with strain rate and an inversely proportional relationship with deformation temperature, and the relationship between εc and εp can be expressed as: εc = (0.3–0.5) εp. Only the discontinuous dynamic recrystallization (DDRX) mechanism is activated in the whole range of deformation conditions, but it is not fully carried out. Because of the inhomogeneous stress distribution, the dynamic recrystallized grains show bimodal grain size. Furthermore, the recrystallized grains do not grow significantly due to the synergistic contribution of sluggish diffusion effect, high solution hardening effect and the trimodal B2 precipitate phase distribution.

Modelling the Deformation of Polydomain Liquid Crystal Elastomers as a State of Hyperelasticity

A hyperelasticity modelling approach is employed for capturing various and complex mechanical behaviours exhibited by macroscopically isotropic polydomain liquid crystal elastomers (LCEs). These include the highly non-linear behaviour of nematic-genesis polydomain LCEs, and the soft elasticity plateau in isotropic-genesis polydomain LCEs, under finite multimodal deformations (uniaxial and pure shear) using in-house synthesised acrylate-based LCE samples. Examples of application to capturing continuous softening (i.e., in the primary loading path), discontinuous softening (i.e., in the unloading path) and auxetic behaviours are also demonstrated on using extant datasets. It is shown that our comparatively simple model, which breaks away from the neo-classical theory of liquid crystal elastomers, captures the foregoing behaviours favourably, simply as states of hyperelasticity. Improved modelling results obtained by our approach compared with the existing models are also discussed. Given the success of the considered model in application to these datasets and deformations, the simplicity of its functional form (and thereby its implementation), and comparatively low(er) number of parameters, the presented isotropic hyperelastic strain energy function here is suggested for: (i) modelling the general mechanical behaviour of LCEs, (ii) the backbone in the neo-classical theory, and/or (iii) the basic hyperelastic model in other frameworks where the incorporation of the director, anisotropy, viscoelasticity, temperature, softening etc parameters may be required.

A unified pseudo-elastic model of continuous and discontinuous softening in the finite deformation of isotropic soft solids

Building on a recently devised approach of hyperelasticity with intrinsic softening, a new framework for capturing both continuous and discontinuous softening in the finite deformation of isotropic incompressible elastomers is considered here. The continuous and discontinuous softening effects of interest pertain to the loading and unloading paths, respectively, and the model is developed within the theory of pseudo-elasticity. The performance of the model in capturing these effects is then compared with the deformation behaviour of a variety of elastomers, including a range of hydrogels from truly independent double-network (t-DN) to tough and nanocomposite hydrogels, dielectric elastomers and carbon-black filled rubber specimens, under uniaxial and multiaxial deformations. The model is demonstrated to show a favourable simulation and prediction of the extant experimental data. The application of the model is then extended to capturing the softening behaviour under rate-dependent loading, based on a prior work by the authors incorporating the rate effects directly into the pseudo-hyperelastic model, by assuming that the model parameters evolve with the deformation rate. The capability of the model to capture the rate-dependent effects accurately will be shown by considering the rate-dependent behaviour of two hydrogel specimens. Given the simplicity of the functional form of the model, akin to a standard pseudo-elastic model, the low(er) number of model parameters, the ability to capturing the softening behaviour in the deformation of a wide range of elastomeric materials, and the easy extension for incorporating additional features such as the rate-effects, the proposed model provides another step towards the unification of various complex deformation features into a single modelling framework, for a more universal application to the finite deformation of soft solids.

The Microstructures, Mechanical Properties, and Deformation Mechanism of B2-Hardened NbTiAlZr-Based Refractory High-Entropy Alloys.

The NbTiAlZrHfTaMoW refractory high-entropy alloy (RHEA) system with the structure of the B2 matrix (antiphase domains) and antiphase domain boundaries was firstly developed. We conducted the mechanical properties of the RHEAs at 298 K, 1023 K, 1123 K, and 1223 K, as well as typical deformation characteristics. The RHEAs with low density (7.41~7.51 g/cm3) have excellent compressive-specific yield strength (σYS/ρ) at 1023 K (~131 MPa·cm3/g) and 1123 K (~104.2 MPa·cm3/g), respectively, which are far superior to most typical RHEAs. And, they still keep appropriate plastic deformability at room temperature (ε > 0.35). The superior specific yield strengths are mainly attributed to the solid solution strengthening induced by the Zr element. The formation of the dislocation slip bands with [111](101_) and [111](112_) directions and their interaction provide considerable plastic deformation capability. Meanwhile, dynamic recrystallization and dislocation annihilation accelerate the continuous softening after yielding at 1123 K.

The cyclic deformation behavior and microstructural evolution of 304L steel manufactured by selective laser melting under various temperatures

The low cycle fatigue (LCF) tests with strain-controlled are carried out to investigate the cyclic deformation behavior of 304L steel manufactured by selective laser melting (SLM 304L) at room temperature (RT), 300 °C, and 650 °C. According to the experimental results, the continuous cyclic softening behavior of SLM 304L is presented at different temperatures. Meanwhile, due to the external force during the fatigue test, the substructure morphology is changed from the elongated cellular substructure of the as-built SLM 304L to the cell substructure of the failure sample at different temperatures. Moreover, since the dislocation rearrangement process is a net decrease in dislocation density, the continuous cyclic softening behavior is presented. Besides, the dynamic recovery and recrystallization promote the cyclic softening behavior of SLM 304L at high temperatures. Additionally, when the multiplication and annihilation of dislocations research the equilibrium state, the dislocation density has no obvious change in the microstructure, leading to the steady state of the cyclic response curve. Finally, considering the influence of the crack closure effect, a new fatigue life prediction model is proposed and discussed.

A generalisation of the Pucci–Saccomandi model of rubber elasticity

The Pucci–Saccomandi model of rubber elasticity, also known as the Gent–Gent model, is generalised in this manuscript for a more enhanced applicability to a wider range of finite deformation behaviours, rubber-like material types, and an increased modelling accuracy. The generalising of interest is developed by devising a higher order rational approximant, i.e., of order [1/1], of the response functions. The proposed model is shown to be a parent to some of the celebrated limiting chain extensibility, classical WI1,I2 and generalised neo-Hookean models. The application of the proposed generalised model to the finite deformation of various isotropic incompressible rubber-like materials is demonstrated, including natural unfilled and filled rubbers, commercial polymers and biomaterials. The considered datasets exhibit various deformation behaviours from the classical large deformation of natural rubbers to the downward concavity of filled rubbers, strain/shear softening behaviours of polymers and the softening behaviour of biomaterials up to the onset of failure. The modelling results are directly compared with those of the Gent–Gent model, where the higher accuracy of the proposed model and its capability to favourably capture the aforementioned challenging and varied behaviours is established. In particular, the Gent–Gent model is shown unsuitable for capturing such downward concavity, shear/strain softening and continuous softening to failure behaviours. Given the improved modelling predictions, simplicity of the functional form of the devised model, and its relatively low number of model parameters, the proposed model is presented as a more general, comprehensive and versatile modelling tool for application to the finite deformation of various isotropic incompressible soft materials.

Mechanism of ratcheting deformation of HSLA steel: Effects of internal stresses and dislocation density

The objective of this study is to elucidate the mechanism of ratcheting deformation of HSLA steel in relation to the evolution of internal stresses i.e. effective stress (σef) and backstress (σb) associated with the generation of dislocations during asymmetric cyclic loading. Effective and back stresses are calculated from the stress-strain hysteresis loops and dislocation density is estimated from the X-ray diffraction technique. The results exhibit an increase in the accumulation of ratcheting strain associated with a sharp reduction in fatigue life by the increment in stresses. A continuous cyclic softening until the final failure is observed for all the ratcheting tests. It is noticed that the effect of stress amplitude is more prominent than the mean stress for controlling cyclic softening, which is evidenced by the evolution of effective stress and backstress in association with dislocation density. Additionally, transmission electron microscopic images are used to correlate strain conditions and substructural patterns.

Continuous softening up to the onset of failure: A hyperelastic modelling approach with intrinsic softening for isotropic incompressible soft solids

This paper seeks to put forward an alternative notion for modelling the continuous softening in the finite deformation of incompressible isotropic rubber-like materials, up to the onset of failure. Based on the proposition that ‘there is no fundamental reason as to why the basic constitutive parameters of the (hyper)elastic state of a material cannot determine the natural evolution of softening and failure in that material’, the concept of hyperelasticity with intrinsic softening is posited. In contrast to the currently available theories of continuum damage mechanics and energy limiters, which superpose external parameters onto the basic hyperelastic model, the alternative approach presented here postulates that if a hyperelastic strain energy function accommodates a comprehensive set of constitutive parameters and has an appropriate functional form, it will intrinsically capture the observed continuous softening in the stress–deformation curves of soft solids, up to the onset of failure. Examples of this notion are presented using a specific hyperelastic model previously proposed by the author, applied here to extant datasets of a wide variety of isotropic incompressible soft solids, ranging from soft tissues to protein gels and 3D printed biomaterials, that include the softening behaviour. The favourable modelling results obtained via this approach are demonstrated. It is conferred that these results portend a versatile modelling tool for application to the whole-range deformation of soft solids, up to the onset of failure, and make the case for devising a unified theory for modelling both continuous and discontinuous softening in the finite deformation of rubber-like materials.

Low-Cycle Fatigue Behavior and Fracture Characteristics of Low-Cost Ti-2Fe-0.1B Alloy

In recent decades, the effect of Fe element addition on titanium alloy has been investigated extensively due to the development of low-cost titanium alloys, as well as B microalloying, which could decrease the grain size of titanium alloys during the casting process. As a key structural material, the study of the fatigue behavior of titanium alloys is crucial and always attractive for scientists. Hence, in this paper, the low cycle fatigue (LCF) behavior and fracture characteristics of a low-cost Ti-2Fe-0.1B alloy with a lamellar structure were investigated systematically, five different strain amplitudes (Δεt/2) in the range from 0.6% to 1.4% were selected to control the LCF process. It was found that the Ti-2Fe-0.1B alloy exhibits continuous cyclic softening behavior in the cycle as a whole at Δεt/2 ≤ 1.2%, while at Δεt/2 = 1.4%, it exhibits slight cyclic hardening at the initial stage of the cycle, then shows cyclic softening. Compared with pure titanium and other typical titanium alloys, the Ti-2Fe-0.1B alloy indicated maximum fatigue life under the same strain amplitude, it can be attributed to the fine grain size result from the effect of Fe element and trace B, which could hinder the dislocation movement and crack propagation.

Systematic analysis of distinct flow characteristics and underlying microstructural evolution mechanisms of a novel fine-grained P/M nickel-based superalloy during isothermal compression

Isothermal forging (IF) is an effective method for forming difficult-to-deform materials like P/M superalloys. Understanding the isothermal compression microstructural evolution mechanism of a novel P/M superalloy provides the basis for its optimized IF planning. In this study, the isothermal compression tests of a novel fine-grained P/M nickel-based superalloy were carried out at 1000–1150 °C with strain rates of 0.001–0.01 s−1. The results indicated that the alloy exhibits three distinct flow characteristics: continuous softening after reaching the peak stress, near-steady superplastic flow, and discontinuous hardening, corresponding to different strain rate sensitivity exponent (m) values. Varied microstructural evolution mechanisms, including grain boundary sliding (GBS), dynamic recrystallization (DRX), and grain growth, are dominated in different m-value domains. Meanwhile, different roles of primary γ' play in microstructural evolution were clarified. A moderate fraction of primary γ' with 8.5%–14.2% can well coordinate the GBS and hinder excessive grain growth at a high m value domain (m > 0.4). When 0.2 < m < 0.4, the role of the primary γ' is changed to promote dislocation accumulation, accelerating the nucleation of DRXed grains. As the primary γ' is dissolved at 1150 °C, obvious grain growth was observed after compression. Work hardening effect by overgrown grains competed with DRX softening results in the discontinuous rising stress.

Special deformation mechanisms dominated by grain boundary sliding of extrusion–refined Ti–22Al–25Nb alloy during compression in single BCC phase field

The deformation behavior of Ti–22Al–25Nb alloys with refined initial grain size was investigated under isothermal uniaxial compression in the BCC (B2) single-phase field, where a high-temperature extrusion process was used to produce the test materials with finer initial grains. As compressed at low to moderate strain rates, the present material exhibits significant continuous flow softening. To study the deformation and softening mechanisms during the compression, the samples' microstructures were examined using EBSD. The analysis shows that this alloy has a considerable grain boundary sliding (GBS) mechanism in addition to the conventional mechanisms of dynamic recovery (DRV), dynamic recrystallization (DRX), and texture softening. For the first time, this study offers direct evidence of the presence of GBS in current alloys. And the dominant role of GBS in high-temperature deformation and softening of current alloys was identified by comparing the impacts of various mechanisms on the dislocation density distribution. Besides, the impact of GBS on texture evolution was also discussed.

Effect of Nb–V microalloying on low-cycle fatigue property of Fe–Mn–Al–C austenitic steel

The tensile and low-cycle fatigue properties of Fe–Mn–Al–C austenitic steels without and with Nb–V microalloying are analyzed comparatively. The Nb–V microalloyed Fe–Mn–Al–C steel shows higher strength and lower elongation. The cyclic deformation behavior is noted as continuous cyclic softening. The fatigue life of the Nb–V microalloyed steel is higher at total strain amplitudes of 0.4% and 0.6%, but lower at 0.8% than that of the non-microalloyed one. The microstructures of the steels after fatigue test show parallel deformation bands, which are composed of planar dislocations. The precipitation of (Nb,V)C has a positive influence on improving the fatigue life compared with the κ-carbides.

Creep-fatigue interaction behavior of simulated microstructures and the actual weldment of P91 steel

The paper presents first of its kind study on the creep-fatigue interaction (CFI) behavior of simulated coarse grain (CG), fine grain (FG) and inter-critical (IC) heat-affected zones (HAZs) of P91 steel weldment. Total axial strain-controlled fatigue tests were conducted at 550 °C using trapezoidal waveform and introducing 30-min hold at peak tensile strain of ±0.6%. Irrespective of the initial microstructure, the alloy exhibited continuous cyclic softening throughout the deformation under CFI condition. Strain localization together with interlinkage of subsurface creep cavities caused enhanced crack propagation that resulted in the lowest fatigue life in the case of ICHAZ. The actual weldment failed in the interface between FGHAZ and ICHAZ. The mode of failure was found to be largely governed by Type IV cracking.

Changes in the mechanical properties of human mesenchymal stem cells during differentiation.

A thorough understanding of the changes in mechanical property behind intracellular biophysical and biochemical processes during differentiation of human mesenchymal stem cells (hMSCs) is helpful to direct and enhance the commitment of cells to a particular lineage. In this study, displacement creep of the mesenchymal cell lineages (osteogenic, chondrogenic and adipogenic hMSCs) were determined by using atomic force microscopy, which was then used to determine their mechanical properties. We found that at any stages of differentiation, the mesenchymal cell lineages are linear viscoelastic materials and well matched with a simple power-law creep compliance. In addition, the viscoelasticity of mesenchymal cell lineages showed different trends during differentiation. The adipogenic hMSCs showed continuous softening at all stages. The osteogenic and chondrogenic hMSCs only continuously soften and become more fluid-like in the early stage of differentiation, and get stiffened and less fluid-like in the later stage. These findings will help more accurately imitate cellular biomechanics in the microenvironment, and provided an important reference in the biophysics biomimetic design of stem cell differentiation.

High-temperature deformation behavior and microstructural evolution of NbZrTiTa refractory high entropy alloy

The hot deformation behaviors and microstructural evolution of an equiatomic NbZrTiTa refractory high entropy alloy (RHEA) were studied by using isothermal compression tests in a range of temperatures (900 °C∼1200 °C) and strain rates (10−3 s−1∼1 s−1). A category of Arrhenius power law relationship was constructed and the activation energy was calculated to be 336–403 kJ mol−1 throughout the strain. The dislocation piling-up and kink bands found in local microstructural areas at low temperatures and high strain rates contributed to intense strain hardening and subsequent strain softening. As the temperature increased and the strain rate decreased, a sharp drop in flow stress was observed after the peak stress. This may be explained by dislocations pinned by short-range ordering (SRO) structures being unlocked. The higher dislocation density and newly emerging fine grains near deformed grain boundaries suggested that the dynamic recrystallization (DRX) was responsible for the continuous flow softening. Discontinuous DRX (DDRX) was the main DRX mechanism in this work, however, the isolated equiaxed grains in initial grains and large cumulative misorientation along the interior of the deformed grains were also found at the high temperatures and low strain rates, which demonstrated that the continuous DRX (CDRX) occurred.

Low cycle fatigue behavior of near-alpha titanium alloys used in deep-driving submersible: Ti-6Al-3 Nb-2Zr-1Mo vs. Ti-6Al-4 V ELI

The low cycle fatigue (LCF) of Ti-6Al-3 Nb-2Zr-1Mo and Ti-6Al-4 V ELI with a bimodal structure were compared at different total strain amplitudes (∆εt/2) from 0.5 % to 1.0 %. Because the Ti-6Al-3 Nb-2Zr-1Mo exhibited a higher tensile elongation, but a lower yield strength than Ti-6Al-4 V ELI, it displayed a slightly longer fatigue life than Ti-6Al-4 V ELI when ∆εt/2 was larger than 0.7 % (plastic deformation predominated), while its fatigue life became shorter when ∆εt/2 was less than 0.7 % (elastic deformation predominated). Both Ti-6Al-3 Nb-2Zr-1Mo and Ti-6Al-4 V ELI showed a continuous cyclic softening behavior due to the rearrangement or mutual annihilation of initial dislocations during cyclic deformation, and the variation of cyclic softening rate depended on ∆εt/2 was consistent with the variation of fatigue life depended on ∆εt/2. In cyclic deformation, the prismatic and basal slips were easier to activate, and the dislocation bands were denser and more homogeneous in the Ti-6Al-3 Nb-2Zr-1Mo than that in the Ti-6Al-4 V ELI due to the actual Al content in former was smaller than that in latter, which was beneficial to reduce local stress concentration and prolong fatigue life.